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10 Nov – A riot has erupted at a controversial offshore refugee-detention facility in Australia following the death of an asylum seeker.
Immigration officers and refugees confirmed on Monday a standoff between detainees and officers at the detention camp on Christmas Island, located more than 2,000km northwest of Perth in the Indian Ocean, after a Kurdish Iranian refugee died there.
Fazel Chegeni, in his 30s, was reportedly found at the bottom of a cliff.
“On Saturday morning [November 7] the department was advised of the escape of an illegal maritime arrival from Christmas Island Immigration Detention Centre [CI IDC] by service provider staff.
“The matter was referred to the Australian Federal Police who commenced a search and discovered a deceased person today [November 8],” the Australian government said in a news release.
The Department of Immigration said staff and security have been withdrawn for security purposes and denied a large scale riot was taking place.
“The protest action began when a small group of Iranian detainees took part in a peaceful protest following the escape from, and death outside the centre, of a detainee on Sunday,” its news release said.
Currently, there are about 285 asylum-seekers at the Christmas Island camp. Section 501 of Australia’s Migration Act permits the deportation of a non-Australian citizen who fails the “character test”, the portal for which includes any prison sentence longer than 12 months.
A member of RISE, a rights group campaigning for refugee rights in Melbourne, said refugees heard the Iranian man screaming for help, then later saw him in a body bag.
“The detention centre detains asylum-seekers under administrative detention methods, just like Guantanamo and just like Palestinian prisoners in Israel,” she told Al Jazeera over the phone.
“These cases cannot be taken to court and the refugee him or herself sometimes does not know what they are doing there.
“They could claim they are investigating the asylum seeker, but in the end it is punishment.
“Those who arrive by boat are not allowed to have mobile phones with them, but those who arrive by plane are.
“And if they manage to sneak in mobile phones, security does random checks where they take them away.
“Between 2010 and 2011, there were five deaths in eight months in a detention centre in the suburbs of Sydney.
“Two detention centres were destroyed following that.
“The government does not learn from its past experiences.”
Twenty-five-year-old detainee Matej Cuperka told the ABC that ex-convicts who had their Australian visas cancelled after serving time in jail started the riot.
“The death [of the Iranian man] is very, very suspicious,” he said.
“They [the inmates who are rioting] believe Serco officers did something to him.
“I clearly heard him in the morning screaming for help, and the next thing I see they be bringing him in a body bag, and after that the whole place went into lockdown.
“About 30 people started a fight with the emergency response team in front of the medical [clinic] where officers left their stations and put the place in lockdown.”
“They are setting fires everywhere,” Mr Cuperka added.
“They started [on Sunday night]. They have broken into the canteen, into the property area, they started fires over there and now they starting in the compound.
“There are cars full of officers driving around the complex. They are just having a look through the window,
Another detainee, who stressed that he had not been involved in the riots, said “most of the compounds have actually been broken into, including the medical [compound]”.
“The canteen, I can see from where I’m standing now, has been completely ransacked and is burning as I speak to you,” he said.
“It’s a complete disaster zone.
“The compound that I’m in … there’s a lot of spot fires in there, all the cameras have been smashed up, all the kitchen has been smashed up, the offices have been breached and all the computers and everything has been broken up.”
The Immigration Department said the camp’s perimeter had not been breached and “the department and its service providers [were] working together to resolve the situation”.
Mr Dutton said there had been an initial response by Serco officers and there would be “further responses from the appropriate authorities either negotiating or dealing with those people who have caused disturbances there”.
The Christmas Island camp also houses New Zealand citizens being deported from Australia, as well as asylum seekers.
New Zealand Labour MP Kelvin Davis said he had been told detainees had “taken over the detention centre”.
“I’m hearing that the guards have exited the detention centre, that fences have been torn down and that detainees in the segregated area are mixing with the mainstream detainees,” he told the ABC.
“Some of them have been on that island for four, five years and, quite frankly, everyone’s sick of being treated like animals and right now they’re turning around and biting.”
Mr Davis said he had been told at least one detainee had overdosed and the Emergency Response Team had taken 20 minutes to reach him.
“He told me about an asylum seeker who had taken an overdose of drugs. They were trying to get medical help for this guy, 20 minutes, and finally the Emergency Response Team managed to drag this guy out.
“I would like to think the authorities would take a step back and look to negotiate because I don’t think these guys really want to riot… they would like a peaceful resolution of the situation, they certainly don’t want to end up getting beaten up by the riot squad.
“A number of people have gone back to their individual cells and they are barricading themselves in.”
Mr Davis said detainees on the island had told him they were angry about what they believed was a “cover-up” of the truth about how the man died.
Last week, human teeth were found in a meal served to an asylum seeker in the Manus Island detention centre, just a few days after almost 100 asylum seekers reportedly suffered from food poisoning.
Speaking to Al Jazeera over phone on Saturday, Ian Rintoul, an Australian refugee advocate who is in touch with asylum-seekers on the island, said asylum seekers managed to call activists and inform them human teeth were found in a lunch meal served to a refugee.
The Australian government’s Department of Immigration announced on Twitter that it is investigating the reports.
“A few days ago over 100 asylum-seekers and staff members were poisoned from the food at the Manus detention centre,” Rintoul said.
“There has been constant problems with the food there. Refugees have complained about the quality of the food such as the smell from the meat provided.
“Refugees have also found flies and insects in their food several times.
“There are constant problems in these detention centres. Water is one of them. The sewage goes out to the bay and, if it rains, it washes up on the compound.
“The toilets are mostly non-functional too.”
Rintoul said asylum-seekers find ways to contact refugee advocates and inform them of these issues, but of late attacks and raids on the centres have been mounted to confiscate the refugees’ phones.
“Nothing will change. The problems are created by the detention centres themselves,” he told Al Jazeera.
“Tensions have not been resolved since Reza Barati was killed in 2014. The Australian government has embarked on a brutal system.”
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import $ from '../core/renderer';
import { noop, ensureDefined } from '../core/utils/common';
import { isDefined, isPromise } from '../core/utils/type';
import { extend } from '../core/utils/extend';
import { inArray } from '../core/utils/array';
import { each } from '../core/utils/iterator';
import { Deferred, fromPromise } from '../core/utils/deferred';
import { getPublicElement } from '../core/element';
import errors from '../core/errors';
import domAdapter from '../core/dom_adapter';
import { render } from './widget/utils.ink_ripple';
import messageLocalization from '../localization/message';
import registerComponent from '../core/component_registrator';
import DropDownList from './drop_down_editor/ui.drop_down_list';
// STYLE selectBox
const DISABLED_STATE_SELECTOR = '.dx-state-disabled';
const SELECTBOX_CLASS = 'dx-selectbox';
const SELECTBOX_POPUP_CLASS = 'dx-selectbox-popup';
const SELECTBOX_CONTAINER_CLASS = 'dx-selectbox-container';
const SELECTBOX_POPUP_WRAPPER_CLASS = 'dx-selectbox-popup-wrapper';
const SelectBox = DropDownList.inherit({
_supportedKeys: function() {
const that = this;
const parent = this.callBase();
const clearSelectBox = function(e) {
const isEditable = this._isEditable();
if(!isEditable) {
if(this.option('showClearButton')) {
e.preventDefault();
this.reset();
}
} else if(this._valueSubstituted()) {
this._preventFiltering = true;
}
this._preventSubstitution = true;
};
const searchIfNeeded = function() {
if(that.option('searchEnabled') && that._valueSubstituted()) {
that._searchHandler();
}
};
return extend({}, parent, {
tab: function() {
if(this.option('opened') && this.option('applyValueMode') === 'instantly') {
this._cleanInputSelection();
}
if(this._wasSearch()) {
this._clearFilter();
}
parent.tab && parent.tab.apply(this, arguments);
},
upArrow: function(e) {
if(parent.upArrow && parent.upArrow.apply(this, arguments)) {
if(!this.option('opened')) {
this._setNextValue(e);
}
return true;
}
},
downArrow: function(e) {
if(parent.downArrow && parent.downArrow.apply(this, arguments)) {
if(!this.option('opened')) {
this._setNextValue(e);
}
return true;
}
},
leftArrow: function() {
searchIfNeeded();
parent.leftArrow && parent.leftArrow.apply(this, arguments);
},
rightArrow: function() {
searchIfNeeded();
parent.rightArrow && parent.rightArrow.apply(this, arguments);
},
home: function() {
searchIfNeeded();
parent.home && parent.home.apply(this, arguments);
},
end: function() {
searchIfNeeded();
parent.end && parent.end.apply(this, arguments);
},
escape: function() {
const result = parent.escape && parent.escape.apply(this, arguments);
this._cancelEditing();
return isDefined(result) ? result : true;
},
enter: function(e) {
const isOpened = this.option('opened');
const inputText = this._input().val().trim();
const isCustomText = inputText && this._list && !this._list.option('focusedElement');
if(!inputText && this.option('value') && this.option('allowClearing')) {
this.option({
selectedItem: null,
value: null
});
this.close();
} else {
if(this.option('acceptCustomValue')) {
e.preventDefault();
if(isCustomText) {
this._valueChangeEventHandler(e);
if(isOpened) this._toggleOpenState();
}
return isOpened;
}
if(parent.enter && parent.enter.apply(this, arguments)) {
return isOpened;
}
}
},
space: function(e) {
const isOpened = this.option('opened');
const isSearchEnabled = this.option('searchEnabled');
const acceptCustomValue = this.option('acceptCustomValue');
if(!isOpened || isSearchEnabled || acceptCustomValue) {
return;
}
e.preventDefault();
this._valueChangeEventHandler(e);
return true;
},
backspace: clearSelectBox,
del: clearSelectBox
});
},
_getDefaultOptions: function() {
return extend(this.callBase(), {
placeholder: messageLocalization.format('Select'),
fieldTemplate: null,
valueChangeEvent: 'change',
acceptCustomValue: false,
onCustomItemCreating: function(e) {
if(!isDefined(e.customItem)) {
e.customItem = e.text;
}
},
showSelectionControls: false,
/**
* @name dxSelectBoxOptions.allowClearing
* @type boolean
* @default true
* @hidden
*/
allowClearing: true,
tooltipEnabled: false,
openOnFieldClick: true,
showDropDownButton: true,
displayCustomValue: false,
useInkRipple: false,
useHiddenSubmitElement: true
});
},
_init: function() {
this.callBase();
this._initCustomItemCreatingAction();
},
_initMarkup: function() {
this.$element().addClass(SELECTBOX_CLASS);
this._renderTooltip();
this.option('useInkRipple') && this._renderInkRipple();
this.callBase();
this._$container.addClass(SELECTBOX_CONTAINER_CLASS);
},
_renderInkRipple: function() {
this._inkRipple = render();
},
_toggleActiveState: function($element, value, e) {
this.callBase.apply(this, arguments);
if(!this._inkRipple || this._isEditable()) {
return;
}
const config = {
element: this._inputWrapper(),
event: e
};
if(value) {
this._inkRipple.showWave(config);
} else {
this._inkRipple.hideWave(config);
}
},
_createPopup: function() {
this.callBase();
this._popup.$element().addClass(SELECTBOX_POPUP_CLASS);
this._popup.overlayContent().attr('tabindex', -1);
},
_popupWrapperClass: function() {
return this.callBase() + ' ' + SELECTBOX_POPUP_WRAPPER_CLASS;
},
_cancelEditing: function() {
if(!this.option('searchEnabled') && this._list) {
this._focusListElement(null);
this._updateField(this.option('selectedItem'));
}
},
_renderOpenedState: function() {
this.callBase();
if(this.option('opened')) {
this._scrollToSelectedItem();
this._focusSelectedElement();
}
},
_focusSelectedElement: function() {
const searchValue = this._searchValue();
if(!searchValue) {
this._focusListElement(null);
return;
}
const $listItems = this._list._itemElements();
const index = inArray(this.option('selectedItem'), this.option('items'));
const focusedElement = index >= 0 && !this._isCustomItemSelected() ? $listItems.eq(index) : null;
this._focusListElement(focusedElement);
},
_renderFocusedElement: function() {
if(!this._list) {
return;
}
const searchValue = this._searchValue();
if(!searchValue || this.option('acceptCustomValue')) {
this._focusListElement(null);
return;
}
const $listItems = this._list._itemElements();
const focusedElement = $listItems.not(DISABLED_STATE_SELECTOR).eq(0);
this._focusListElement(focusedElement);
},
_focusListElement: function(element) {
this._preventInputValueRender = true;
this._list.option('focusedElement', getPublicElement(element));
delete this._preventInputValueRender;
},
_scrollToSelectedItem: function() {
this._list && this._list.scrollToItem(this._list.option('selectedItem'));
},
_listContentReadyHandler: function() {
this.callBase();
const isPaginate = this._dataSource && this._dataSource.paginate();
if(isPaginate && this._needPopupRepaint()) {
return;
}
this._scrollToSelectedItem();
},
_renderValue: function() {
this._renderInputValue();
this._setSubmitValue();
return new Deferred().resolve();
},
_renderInputValue: function() {
return this.callBase().always(function() {
this._renderInputValueAsync();
}.bind(this));
},
_renderInputValueAsync: function() {
this._renderTooltip();
this._renderInputValueImpl().always(function() {
this._refreshSelected();
}.bind(this));
},
_renderInputValueImpl: function() {
this._renderField();
return new Deferred().resolve();
},
_setNextItem: function(step) {
const item = this._calcNextItem(step);
const value = this._valueGetter(item);
this._setValue(value);
},
_setNextValue: function(e) {
const dataSourceIsLoaded = this._dataSource.isLoaded()
? new Deferred().resolve()
: this._dataSource.load();
dataSourceIsLoaded.done((function() {
const selectedIndex = this._getSelectedIndex();
const hasPages = this._dataSource.pageSize();
const isLastPage = this._dataSource.isLastPage();
const isLastItem = selectedIndex === this._items().length - 1;
this._saveValueChangeEvent(e);
const step = e.key === 'ArrowDown' ? 1 : -1;
if(hasPages && !isLastPage && isLastItem && step > 0) {
if(!this._popup) {
this._createPopup();
}
if(!this._dataSource.isLoading()) {
this._list._loadNextPage().done(this._setNextItem.bind(this, step));
}
} else {
this._setNextItem(step);
}
}).bind(this));
},
_setSelectedItem: function(item) {
const isUnknownItem = !this._isCustomValueAllowed() && (item === undefined);
this.callBase(isUnknownItem ? null : item);
if(!isUnknownItem && (!this._isEditable() || this._isCustomItemSelected())) {
this._setListOption('selectedItem', this.option('selectedItem'));
}
},
_isCustomValueAllowed: function() {
return this.option('acceptCustomValue') || this.callBase();
},
_displayValue: function(item) {
item = (!isDefined(item) && this._isCustomValueAllowed()) ? this.option('value') : item;
return this.callBase(item);
},
_listConfig: function() {
const result = extend(this.callBase(), {
pageLoadMode: 'scrollBottom',
onSelectionChanged: this._getSelectionChangeHandler(),
selectedItem: this.option('selectedItem'),
onFocusedItemChanged: this._listFocusedItemChangeHandler.bind(this)
});
if(this.option('showSelectionControls')) {
extend(result, {
showSelectionControls: true,
selectionByClick: true
});
}
return result;
},
_listFocusedItemChangeHandler: function(e) {
if(this._preventInputValueRender) {
return;
}
const list = e.component;
const focusedElement = $(list.option('focusedElement'));
const focusedItem = list._getItemData(focusedElement);
this._updateField(focusedItem);
},
_updateField: function(item) {
const fieldTemplate = this._getTemplateByOption('fieldTemplate');
if(!(fieldTemplate && this.option('fieldTemplate'))) {
const text = this._displayGetter(item);
this.option('text', text);
this._renderDisplayText(text);
return;
}
this._renderField();
},
_getSelectionChangeHandler: function() {
return this.option('showSelectionControls') ? this._selectionChangeHandler.bind(this) : noop;
},
_selectionChangeHandler: function(e) {
each(e.addedItems || [], (function(_, addedItem) {
this._setValue(this._valueGetter(addedItem));
}).bind(this));
},
_getActualSearchValue: function() {
return this._dataSource.searchValue();
},
_toggleOpenState: function(isVisible) {
if(this.option('disabled')) {
return;
}
isVisible = arguments.length ? isVisible : !this.option('opened');
if(!isVisible) {
this._restoreInputText(true);
}
if(this._wasSearch() && isVisible) {
this._wasSearch(false);
const showDataImmediately = this.option('showDataBeforeSearch') || this.option('minSearchLength') === 0;
if(showDataImmediately && this._dataSource) {
if(this._searchTimer) return;
const searchValue = this._getActualSearchValue();
searchValue && this._wasSearch(true);
this._filterDataSource(searchValue || null);
} else {
this._setListOption('items', []);
}
}
if(isVisible) {
this._scrollToSelectedItem();
}
this.callBase(isVisible);
},
_renderTooltip: function() {
if(this.option('tooltipEnabled')) {
this.$element().attr('title', this.option('displayValue'));
}
},
_renderDimensions: function() {
this.callBase();
this._dimensionChanged();
},
_isValueEqualInputText: function() {
const initialSelectedItem = this.option('selectedItem');
const value = this._displayGetter(initialSelectedItem);
const displayValue = value ? String(value) : '';
const inputText = this._searchValue();
return displayValue === inputText;
},
_popupHidingHandler: function() {
if(this._isValueEqualInputText()) {
this._cancelEditing();
}
this.callBase();
},
_restoreInputText: function(saveEditingValue) {
if(this.option('readOnly')) {
return;
}
this._loadItemDeferred && this._loadItemDeferred.always((function() {
const initialSelectedItem = this.option('selectedItem');
if(this.option('acceptCustomValue')) {
if(!saveEditingValue) {
this._updateField(initialSelectedItem);
this._clearFilter();
}
return;
}
if(this.option('searchEnabled')) {
if(!this._searchValue() && this.option('allowClearing')) {
this._clearTextValue();
return;
}
}
if(this._isValueEqualInputText()) {
return;
}
this._renderInputValue().always((function(selectedItem) {
const newSelectedItem = ensureDefined(selectedItem, initialSelectedItem);
this._setSelectedItem(newSelectedItem);
this._updateField(newSelectedItem);
this._clearFilter();
}).bind(this));
}).bind(this));
},
_focusOutHandler: function(e) {
if(!this._preventNestedFocusEvent(e)) {
const isOverlayTarget = this._isOverlayNestedTarget(e.relatedTarget);
if(!isOverlayTarget) {
this._restoreInputText();
this._clearSearchTimer();
}
const shouldCancelSearch = this._wasSearch() &&
!this.option('acceptCustomValue') &&
this.option('searchEnabled') &&
this.option('opened') &&
!isOverlayTarget;
if(shouldCancelSearch) {
this._searchCanceled();
}
}
this.callBase(e);
},
_isOverlayNestedTarget: function(target) {
return !!$(target).closest(`.${SELECTBOX_POPUP_WRAPPER_CLASS}`).length;
},
_clearTextValue: function() {
if(this.option('selectedItem')) {
this.option('value', null);
}
},
_shouldOpenPopup: function() {
return this._needPassDataSourceToList();
},
_isFocused: function() {
const activeElement = domAdapter.getActiveElement();
return this.callBase() && $(activeElement).closest(this._input()).length > 0;
},
_renderValueChangeEvent: function() {
if(this._isEditable()) {
this.callBase();
}
},
_isEditable: function() {
return this.option('acceptCustomValue') || this.option('searchEnabled');
},
_fieldRenderData: function() {
const $listFocused = this._list && this.option('opened') && $(this._list.option('focusedElement'));
if($listFocused && $listFocused.length) {
return this._list._getItemData($listFocused);
}
return this.option('selectedItem');
},
_readOnlyPropValue: function() {
return !this._isEditable() || this.option('readOnly');
},
_isSelectedValue: function(value) {
return this._isValueEquals(value, this.option('value'));
},
_shouldCloseOnItemClick: function() {
return !(this.option('showSelectionControls') && this.option('selectionMode') !== 'single');
},
_listItemClickHandler: function(e) {
const previousValue = this._getCurrentValue();
this._focusListElement($(e.itemElement));
this._saveValueChangeEvent(e.event);
if(this._shouldClearFilter()) {
this._clearFilter();
}
this._completeSelection(this._valueGetter(e.itemData));
if(this._shouldCloseOnItemClick()) {
this.option('opened', false);
}
if(this.option('searchEnabled') && previousValue === this._valueGetter(e.itemData)) {
this._updateField(e.itemData);
}
},
_shouldClearFilter: function() {
return this._wasSearch();
},
_completeSelection: function(value) {
this._setValue(value);
},
_loadItem: function(value, cache) {
const that = this;
const deferred = new Deferred();
this.callBase(value, cache)
.done((function(item) {
deferred.resolve(item);
}).bind(this))
.fail((function() {
const selectedItem = that.option('selectedItem');
if(that.option('acceptCustomValue') && value === that._valueGetter(selectedItem)) {
deferred.resolve(selectedItem);
} else {
deferred.reject();
}
}).bind(this));
return deferred.promise();
},
_loadInputValue: function(value, callback) {
this._loadItemDeferred = this._loadItem(value).always(callback);
return this._loadItemDeferred;
},
_isCustomItemSelected: function() {
const selectedItem = this.option('selectedItem');
const searchValue = this._searchValue();
const selectedItemText = this._displayGetter(selectedItem);
return !selectedItemText || searchValue !== selectedItemText.toString();
},
_valueChangeEventHandler: function(e) {
if(this.option('acceptCustomValue') && this._isCustomItemSelected() && !this._isValueChanging) {
this._isValueChanging = true;
this._customItemAddedHandler(e);
this._isValueChanging = false;
}
},
_initCustomItemCreatingAction: function() {
this._customItemCreatingAction = this._createActionByOption('onCustomItemCreating');
},
_createCustomItem: function(text) {
const params = {
text: text
};
const actionResult = this._customItemCreatingAction(params);
const item = ensureDefined(actionResult, params.customItem);
if(isDefined(actionResult)) {
errors.log('W0015', 'onCustomItemCreating', 'customItem');
}
return item;
},
_customItemAddedHandler: function(e) {
const searchValue = this._searchValue();
const item = this._createCustomItem(searchValue);
this._saveValueChangeEvent(e);
if(item === undefined) {
this._renderValue();
throw errors.Error('E0121');
}
if(isPromise(item)) {
fromPromise(item)
.done(this._setCustomItem.bind(this))
.fail(this._setCustomItem.bind(this, null));
} else {
this._setCustomItem(item);
}
},
_setCustomItem: function(item) {
if(this._disposed) {
return;
}
item = item || null;
this.option('selectedItem', item);
if(this._shouldClearFilter()) {
this._filterDataSource(null);
}
this._setValue(this._valueGetter(item));
this._renderDisplayText(this._displayGetter(item));
},
_clearValueHandler: function(e) {
this.callBase(e);
return false;
},
_wasSearch: function(value) {
if(!arguments.length) {
return this._wasSearchValue;
}
this._wasSearchValue = value;
},
_searchHandler: function(e) {
if(this._preventFiltering) {
delete this._preventFiltering;
return;
}
if(this._needPassDataSourceToList()) {
this._wasSearch(true);
}
this.callBase(e);
},
_dataSourceFiltered: function(searchValue) {
this.callBase();
if(searchValue !== null) {
this._renderInputSubstitution();
this._renderFocusedElement();
}
},
_valueSubstituted: function() {
const input = this._input().get(0);
const isAllSelected = input.selectionStart === 0 && input.selectionEnd === this._searchValue().length;
const inputHasSelection = input.selectionStart !== input.selectionEnd;
return this._wasSearch() && inputHasSelection && !isAllSelected;
},
_shouldSubstitutionBeRendered: function() {
return !this._preventSubstitution
&& this.option('searchEnabled')
&& !this.option('acceptCustomValue')
&& this.option('searchMode') === 'startswith';
},
_renderInputSubstitution: function() {
if(!this._shouldSubstitutionBeRendered()) {
delete this._preventSubstitution;
return;
}
const item = this._list && this._getPlainItems(this._list.option('items'))[0];
if(!item) {
return;
}
const $input = this._input();
const valueLength = $input.val().length;
if(valueLength === 0) {
return;
}
const inputElement = $input.get(0);
const displayValue = this._displayGetter(item).toString();
inputElement.value = displayValue;
this._caret({ start: valueLength, end: displayValue.length });
},
_cleanInputSelection: function() {
const inputElement = this._input().get(0);
const endPosition = inputElement.value.length;
inputElement.selectionStart = endPosition;
inputElement.selectionEnd = endPosition;
},
_dispose: function() {
this._renderInputValueAsync = noop;
delete this._loadItemDeferred;
this.callBase();
},
_optionChanged: function(args) {
switch(args.name) {
case 'onCustomItemCreating':
this._initCustomItemCreatingAction();
break;
case 'tooltipEnabled':
this._renderTooltip();
break;
case 'displayCustomValue':
case 'acceptCustomValue':
case 'showSelectionControls':
case 'useInkRipple':
this._invalidate();
break;
case 'allowClearing':
break;
default:
this.callBase(args);
}
},
_clean: function() {
delete this._inkRipple;
this.callBase();
}
});
registerComponent('dxSelectBox', SelectBox);
export default SelectBox;
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Influence of spaceflight, hindlimb suspension, and venous occlusion on alpha 1-adrenoceptors in rat vena cava.
Effects of hindlimb suspension, spaceflight, and venous occlusion were examined in isolated strips from rat vena cava by using both [3H]prazosin-binding and contraction responses evoked by norepinephrine. Sensitivity to norepinephrine was decreased without modification of the maximal contractile response. Furthermore, the high K(+)-induced contractions were not affected, suggesting that there was no interference with voltage-dependent Ca2+ channels. The sensitivity of the norepinephrine-induced contraction to prazosin was decreased, and Scatchard analysis of [3H]prazosin binding indicated an increase in the dissociation constant without variation in maximal binding capacity. A similar increase in the dissociation constant was obtained in control rats after pretreatment with 3 microM norepinephrine or 0.1 microM phorbol 12,13-dibutyrate to desensitize the protein kinase C. This effect was completely abolished in the presence of GF-109203X, a selective inhibitor of protein kinase C. Taken together, these data indicate that altered gravity conditions induce a desensitization of alpha 1B-adrenoceptors depending on increased protein kinase C activity. This effect can be mimicked by venous occlusion and may be responsible for reduced contractile responses to norepinephrine.
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// Andrés Mejía
using namespace std;
#include <algorithm>
#include <iostream>
#include <iterator>
#include <numeric>
#include <sstream>
#include <fstream>
#include <cassert>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <string>
#include <cstdio>
#include <vector>
#include <cmath>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>
////////////// Prewritten code follows. Look down for solution. ////////////////
#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x)
#define For(i, a, b) for (int i=(a); i<(b); ++i)
#define D(x) cout << #x " is " << (x) << endl
const double EPS = 1e-9;
int cmp(double x, double y = 0, double tol = EPS) {
return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1;
}
////////////////////////// Solution starts below. //////////////////////////////
int main(){
long long n;
while (cin >> n) {
if (n == 0) break;
long long root = sqrt(n);
cout << (root * root == n ? "yes" : "no") << endl;
}
return 0;
}
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Q:
Comparison of the effects of collisions from an NFL Nose Tackle and a Car with roughly the same momenta
If you get hit an NFL Defensive Tackle who runs at roughly 17mph (7.6m/s) it'd hurt a lot, but if you got hit by a normal car at 1.3mph (about 0.6m/s) it hardly hurts at all, and a collision from an extremely slow moving Oil Tanker with a huge mass would likely be almost unnoticeable, but they all have roughly the same momentum, when Force = dP/dt. Why?
A:
Due to the amount of momentum (and energy) transferred to you. Assuming a completely inelastic process (and an idealized one dimensional setup) you get from the conservation of momentum ($v$ is the initial velocty, $p$ the initial momentum, $v'$ is the final velocity, $M$ is the mass of the object hitting you, $m$ is your mass):
$$ p = M v = (M + m) v' $$
$$ v' = \frac{M}{M + m}v$$
If you keep the momentum constant, this means, that $v$ scales as $p/M$, so a tanker with the same momentum will be very slow.
The energy dissipated in the collision process will be:
$$ E = \frac 1 2 Mv^2 - \frac 1 2 (M + m) v'^2 = \frac 1 2 \left(M - \frac{M^2}{M + m}\right) v^2 = \frac 1 2 \frac{mM}{M + m} v^2.$$
Formulated in terms of the momentum we get:
$$ E = \frac 1 2 \frac{mM}{m + M} \frac{p^2}{M^2} = \frac 1 2 p^2 \frac{m}{M (m + M)}. $$
Calculating numbers for the specific cases ($m \approx 100\,\mathrm{kg}$, $M_\text{NFL} \approx 100\,\mathrm{kg}$, $M_\text{car} \approx 1000\,\mathrm{kg}$, $M_\text{tanker} \approx \infty$, $v_\text{NFL} \approx 10\,\mathrm{m/s}$, $p \approx 1000\,\mathrm{kg\cdot m/s}$):
$$E_\text{NFL} = 2500\,\mathrm{J}$$
$$E_\text{car} = 45\,\mathrm{J}$$
$$E_\text{tanker} \approx 0\,\mathrm{J}.$$
While pain and damage done by an object depends on many factors, the most important is probably energy dissipated in your body (more specifically weighted by the volume of tissue). The dissipation volume for the tanker or the car will be pretty large (perhaps half of your body).
The NFL tackle will be done with a rigid point of the tackler's body (something like the elbow?), so the energy will be dissipated in a quite small volume of your body, while the dissipated energy will be much larger than in the car or tanker case. This way you can also understand why being shot does so much damage (although it has even less mometum. Depending on the fire arm, it is on the order of the momentum of a pedestrian). To stop the bullet the amount of energy will be disspated in a very small volume of your body. (As you are much heavier than the bullet nearly all the bullets energy will be lost, and this energy scales like $\propto mv^2$).
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Car burglar breaks into and hides at "R" Rancho Market
LOS ANGELES, Calif. — A suspected car burglar who apparently broke into a Florence-area market through a skylight hid from sheriff’s deputies for several hours today until law enforcement officers went in to get him.
Deputies were sent to the "R" Ranch Market at 8601 Hooper Ave. about 5:20 a.m. on a report of someone breaking into cars, and the suspect apparently broke into the market.
The area was sealed off, and a Special Weapons Team surrounded the market, eventually arresting the man about noon.
The suspect was wheeled out of the building on a gurney and taken to a hospital for what broadcast outlets said were facial injuries. A sheriff’s spokesman said the injuries were “possibly sustained during the commission of a crime.”
Deputies withheld the suspect’s name pending booking.
According to broadcast reports, the man was trying to break into vehicles in the parking lot of the market and holed up in the building — possibly entering through a skylight — when law enforcement officers arrived.
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Inspirational
Greetings! Lee Tobin McClain here, urging you to give inspirational romance a try, even if it’s not your usual fare. Why? Here are six reasons.
Without the sex, there’s more room for other aspects of romance. “Hey, Christian romance, that’s like a contradiction in terms!” is a line that at least eight men have used on me, each thinking himself supremely clever. But actually, most women don’t think that romance happens only between the sheets. There can be lots of conversation and roses and, well, feelings in Christian romance, and that’s the part a lot of women crave more of.
Without the sex, there’s room for more story depth. One of the Love Inspired editors told me that, because the line doesn’t have love scenes, they need more backstory and conflict and angst. That can make for some compelling stories . . . about things like abuse and class conflict and serious illness, to name three difficult topics I’ve covered in recent books.
Sometimes, you want heartwarming. Especially around the holidays, most of us get nostalgic for a simpler time, for a sense of community, for small towns and big hearts and neighbors that care. Real life can fall pretty short, but an inspirational romance never does. These stories are sweet and will make you feel good on an otherwise stressful or dark day.
You’ll get a better feeling about Christians. There are extremists in every faith, and the rants of Christian extremists can be off-putting., focused more on what the extremists are against (gay marriage! evolution!) than on what Christianity is supposed to be for (loving God and loving your neighbor). But Christian fiction tends to be warm and loving. You’re not likely to find families with two mommies or lessons on evolutionary biology in a Christian romance novel, but you won’t find any bashing, either. I’d argue that Christian authors, as creatives, are some of the most open-minded Christians out there.
Anticipation can be very sexy. Did you ever notice how, when you’re reading a red-hot romance, the intensity can drop off after the first love scene? Despite the requisite fight that follows the consummation, the buildup to the second love scene isn’t usually as exciting as the buildup to the first. In Christian romance, the anticipation continues throughout the novel and the final consummation is left to your imagination—a pretty colorful place, if the cliché about the most important sex organ being between the ears holds true.
Sometimes, you need a little spirituality. Even if you’re not a churchgoer nor the type of person who’d hang a cross-stitched bible verse on the living room wall, most of us hunger for faith in something outside ourselves. When a parent dies or a job falls through or a teenager drives you crazy, it can help to watch characters with similar struggles find a solution in their faith. In Christian fiction, some kind of relationship with God—be it outspoken or bubbling gently under the surface—forms part of the answer to life’s problems. That can be a huge comfort.
Whether you read Christian romance frequently or never, I’d be honored if you’d try my Sacred Bond series of romance novels. No risk: Book one in the series, His Baby Bond, is free on all platforms!
Lee Tobin McClain read Gone With The Wind in the third grade and has been an incurable romantic ever since. When she not writing emotional, faith-infused love stories with happy endings, she’s probably driving around a carload of snarky teen girls, playing with her rescue dog and cat, or teaching aspiring writers in Seton Hill University’s MFA program. She is probably not cleaning her house.
War hero John Moretti sees the delinquent boys he mentors as the sons he never had, and he wants to give them every opportunity to reform. Crime victim Annie Bauer views them as dangerous threats to her elderly grandma, who lives next door to the boys’ residential school. When the Baby Jesus is stolen from Grandma’s yard nativity scene, the boys’ potential involvement may send them straight to hard-core juvie, and break the fragile connection that’s building between Annie and John. Until the so-called delinquents join together to make a sacred bond . . .
Poor-but-proud Kendra Forrester doesn’t need an arrogant millionaire to tell her how to raise her sister’s baby. But when handsome Zeke King arrives at her Colorado cabin demanding custody of his brother’s child, strategy dictates that she let him stick around. Battling mountain weather and the baby’s illness brings these two opposites together, but their own insecurities, their dead siblings’ secrets, and a jealous former boyfriend threaten their tentative bond. Only the Lord and the Sacred Bond Brotherhood can help Kendra and Zeke form a family for their baby.
As the wedding music starts playing, poor little rich girl Hope DeMille learns that her husband-to-be loves someone else, but her domineering, high-society father won’t let her back out of the expensive wedding he’s funded. Enter Rock Anderson, a former inner-city kid mentored by Hope’s parents, who’s always wanted Hope. After helping Hope escape, Rock gets her a job at his urban mission and helps her find meaning in her life. But when Hope’s powerful father seeks revenge and one of the inner-city kids goes missing, it’ll take the best efforts of the Sacred Bond brotherhood to help this opposite-sides-of-the-tracks couple overcome their differences and commit to love.
Synopsis: The angel in this story is Michael’s next door neighbour, LeeAnn Wagner. Since he was a child, he has been told that he is will never amount to anything in his life, and certainly not when he grows up, but how long can a man who was originally unwanted by his mother go on believing in what she said – surely it can’t control a man’s life. LeeAnn can understand what Michael is going through as she has had a similar childhood where she was at the mercy of parents who were always fighting around her. LeeAnn can soothe his worried heart and help heal his past, but only if he lets her inside.
Review: Michael has been pushed round almost every foster home in the land, and hates the feeling of being with a family, yet also being alone as they will never understand him or make him feel as though he belongs with them as part of a family. His life with his foster sister, Eliza has gone beyond what he thinks is tolerable, and feels it is time for him to move on with LeeAnn in order to make a life for himself, one he will be comfortable with. Though he is given the chance of living a good enough life with her, he does the one thing no one expects and leaves her for the armed forces, as he can’t control the love he feels for her, and finds it might consume her. Although he has found Christ, and felt better about his decision, he still feels like a coward for not giving himself the life he should have had with her.
Michael has been manipulated most of his life since he has been with Eliza, and now he has a life of his own, but he still feels incomplete without the woman he loves. In this novel he is constantly torn between his love for her, and his own need to be apart from her. This is enough to cause anyone to be unsure of their life, and as he has had the worst possible life as a young man, he believes he has done the right thing, even though his heart tells him otherwise. Readers will spend most of the novel wondering whether they will get back together at all, and if they do whether it will be a fairytale ending, or only an amicable one. Karen Wiesner is a true romantic whatever she writes, so I couldn’t imagine she would disappoint readers by giving it an okay ending.
Juicy bits:
Michael leaving his blackmailing foster sister.
The story is well paced.
Readers can get into the minds of the characters.
If you are a Christian and a romantic at heart – this is the book for you.
Readers will like the reference to why the Heirlooms series is called that.
Bad bits:
Michael leaving LeeAnn for a long time – it’s not good, dammit!
Why we liked it: Karen Wiesner always puts plenty of soul and heart into her novels and stories, and she has excelled with this one about two people who should be together – but aren’t.
When I was ready to publish my fifth novel, I knew I had to do it myself. There are a host of reasons why authors should self-publish, but many still believe it’s an impossible undertaking. Let me make a molehill out of that mountain.
As with just about anything, especially major decisions, you need to have a game plan; and self-publishing is a major decision. You’re offering your work to the praise and derision of the world. This shouldn’t be taken lightly.
But the weight of the decision can be lightened by knowing exactly what steps to take next. So, after writing that epic book, you need to do a few things before the world is ready for it’s awesomeness. Now, plans can vary, but this is essentially what I’ve learned (and followed) from indie author pioneers.
1. Hire and editor. ‘Nuff said.
2. Hire a formatter. Unless you want to do it yourself. I can tell you from experience (formatting for print using Createspace) the money I spent on both the ebook and print formats was well worth it. Plus, you’ll receive several formats to upload to a variety of places.
3. Hire a cover artist. Why, oh why do people create their own covers? Unless you do it for a living, spare us the cut and paste/drawings/sketches/whatever and let us want to buy your book because of the great cover you’ll be hiring someone to do.
4. Copyright. You don’t have to do this right away, but at least you’ll be covered if ever you need to prove you’re the original creator of that masterpiece.
5. Buy ISBNs. Again, this is optional as many distribution sites allow you to buy/use their free ISBNs (Smashwords, Amazon…)
6. Open Accounts with Distributors. Amazon, Barnes and Noble, Smashwords (which will populate a host of others), All Romance Ebooks, etc. Unless you’re participating in Amazon’s KDP Select program, where your book will be sold by Amazon exclusively, have your work sold everywhere so people don’t have to search for it.
Don’t forget to set a price for success=sales. Too high (regardless of what you believe it’s worth) won’t generate sales and too low won’t attract the readers who’ll remember you and buy your next book.
About the Author: From childhood, K. Victoria Chase enjoyed writing stories and plays and reading Christian romance. She received degrees in Criminal Justice and Diplomacy and worked as a federal law enforcement officer for several years before deciding to try her hand at writing a complete novel. Today, K. Victoria Chase is an Amazon bestselling author both in the US and the UK. She writes both clean and Christian interracial romance.
Noted for her Christian Romance titles, Karen tells the tale of Della Flynn who hates being in the same city, Chicago for so long and wants to get out. It doesn’t help that it’s a dangerous place to live, but when her husband dies, she is left to figure out her life on her own with her son, River, and discover what her husband left her behind.
He promised her they wouldn’t have to live there long, but she is annoyed that he seemed to have settled where they were and didn’t want to move on even though it was a dangerous place to bring up a child in. He thinks they have to stay put where they are for good reason; they don’t have enough money to leave. Her mother is in a nursing home, and that seems to take up most of the cash they have, and she needs to work until her husband gets a better job. They are both unhappy, but his death makes things worse in a way.
Her husband had always thought of home as being where the family is, but Della, annoyed at what he originally said, thinks of their home town as being further from the reality. She hates the place, and no one can change her mind. His death leaves her unhappy, but makes her realize that she doesn’t have to stay. Della has plenty of pent up emotions clouding her judgement, and most of them are about her husband. She hates that he left their marital bed over a triviality, and went off with another woman, lied cheated so many times and hurt her so badly.
Readers will get the impression he might have done it all on purpose to make her feel bad for asking to leave Chicago so many times before, but it depends on how you read into it. This novel, like most of her others starts out disastrous, but as the story moves on, the circumstances of the main female character get better, and usually with time.
Summary: Pacific Coast Justice Series-Book One As a law enforcement officer, C. Edwards, has always upheld the law and followed her agency’s protocols. And prior to becoming a divorcée, she was also the faithful wife. No one would categorize Carly’s life as perfect, but at least it has a semblance of stability. Now all that’s about to change!
As Carly searches for answers regarding who murdered Mayor Teresa Burke, she’ll uncover deeply protected secrets. Secrets those in power would kill to keep. With body counts rising, Carly will find herself in a race to stay alive! She never would’ve guessed it, but she’ll have to rely on the two people she’s been avoiding the most. Her ex-husband (Nick) and God.
Review: Janice Cantore is a new-to-me author. And the first thing that impressed me was the flow of the story. Everything flowed perfectly! There were no abrupt and jarring scene changes. It was one continuous smooth storytelling. Secondly, the suspense is top-notch. Furthermore, as a former police officer, Cantore’s uniform dispatch signals were accurate. As a civilian, I also found her descriptions of police procedures insightful.
Recommendations: Recommended for readers who enjoy police stories and inspirational tales of faith and hope.
What I Enjoyed:
Element: I liked the police officers’ sobriquets: Carly is Crash, Joe is Control, and Nick is Face.
Scene: There’s a scene where an officer risks his life for another. I wept copiously! I wouldn’t say I used an entire box of tissues, but it was close!
Extras: After the story there’s an author interview; that was a novel element.
Disclaimer: I requested this novel from NetGalley because of my interest in police stories.
No one likes to compete with anyone in their household, do they? Ashley has to, and she doesn’t like it one bit, as she has been doing it since she was a young girl. Her sister was always treated differently to her, and given everything she wanted in return for doing nothing. Ashley, on the other hand, is a born giver who receives nothing for what she does.
As an adult, Ashley is determined to make a go of her life despite her past woes, but is it as easy as that?
And, it wasn’t just her sister who hurt her all those years ago when she was a kid – her mother pretended to care for her, and be the perfect Christian when she wanted something from them or other people. And as usual, others think highly of her as a mother, when in actual fact only Ashley knows what she was really like. In order for her to have a decent future, she must leave the past behind her, and make a fresh start, find a man, and some friends who will compliment her.
There is one man who can help her see sense and break the hold the past has on her, and he is Jay Samuels. They had a deep and meaningful love before, but even when she meets him again, she can’t feel the same way about him as he does her – so there’s a problem of communication between them. The question is, will she string him along and use him to make her feel better about herself, or will she eventually tell him that she doesn’t feel the same about him.
Somewhere deep inside she wants to be happy, even though she puts up impenetrable defenses against other men. He can help her, but she has to be ready to be helped. Her troubled emotions in this novel only lead her to more heartache. It is a rather dark read as her emotions can rub off on the reader, as she continually makes the mistake of not letting Jay into her mind, and helping her with her troubles.
In the fourth of her Family Heirlooms Series, Karen has brought us Samantha Samuels under a difficult set of circumstances where she has had a bad run in with Ryder Feldmann, a young man troubled and cruel who had decided not to take her father’s counselling seriously enough to listen to him. Instead he has done the worst thing imaginable, he has offered physical violence in return, and more than that, mental hurt from him when she thought he was doing him some good.
Realizing that she could do some good to others instead of dwelling on the past hurts she had suffered, she decides to undergo training for counselling those who are victims of violence such as rapes, beatings and random violence in the home. Setting up at the Wisconsin counselling centre, but she doesn’t expect to find the man she had fallen for before her ordeal with the troubled teen many years ago. She doesn’t know how she will feel if she does meet him, and there will be a time when he does, as he shares the same building as the clinic, and he appears at services at their local church, so to be honest she can’t miss him.
Kyle is the brother of Ryder Feldmann, the one who had hurt her before, and ended their relationship. He has felt bad ever since, even though Ryder has been incarcerated for his sins. He can’t do anything to anyone, but it doesn’t stop the guilt Kyle feels after. He still loves Samantha deeply, but doesn’t want to be seen the same way as his brother – and so feels troubled when he first meets her. He wants more than anything else to get their relationship back to the way it was, but she is still so sad and unhappy, and who can blame her after what his brother put her through. He wants to love her and hold her, even marry her, but what happened to her has tarnished that part of her that had been open to his love.
How can he make her see him as different from his brother, and have her love him again? It’s a lot to ask a woman, especially after what she has been through, but if she has a little faith, she can see that he is a better man.
This book is all about forgiving, but it takes Samantha a lot to get over what she has endured for years, and after a brutal rape as she has suffered, no one could ask her to just get over it so easily. It takes time, and lots of it to forgive someone for doing so cruel a thing as that. Who can blame her for making Kyle wait for her answer as to whether she will be his and love him again just as she did before. She knows it isn’t his fault, or hers, and the man responsible is in jail, but if time heals all, what can she do with Kyle, but try and patch their relationship together so they can make a new start. He knows forgiving is hard, and it will even take a long time for him to forgive what his brother did to her. This isn’t all about forgiveness though, there is also the injustice aspect as her attacker is due to be out after three years in prison, while Samantha still bears the scars. The reader will wonder how bad Kyle will be feeling after he comes out – and the worry will be whether he will try to come back and see him even if he doesn’t want to know him.
There are lots of emotions in this novel, love, hate, but the forgiving, as I said takes time, and it does in this.
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Navarro Ridge
Navarro Ridge () is a rugged ridge, long, that extends from the Coombs Hills southeastward to the west side of Cambridge Glacier. The central peak of the ridge rises to . It was named by the Advisory Committee on Antarctic Names in 2008 after members of the Navarro family who carried on support activities for the US Antarctic Program at the McMurdo, South Pole and Palmer Stations in the period 1989 to 2008: Kenneth Navarro, Palmer Station logistics supervisor who worked for 18 summer and four winter seasons at the three stations; Kenneth's wife Carol Gould Navarro, engaged in logistics and administration at Palmer and McMurdo for five summers and four winters; his sister Suzanne McCullough Navarro, a cook at McMurdo for four summers and one winter; his brother Steven Navarro, carpenter at Palmer and McMurdo for three summers and one winter; Kenneth and Carol's sons, Eliot Gould and Tyler Gould, also worked a few seasons in Antarctica.
References
Category:Mountains of Victoria Land
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All wire-free communication applications require so-called low noise amplifiers (LNA) in order to amplify the input signal as far as possible without additional noise. Since ever higher frequencies are used in wire-free communication applications, it becomes necessary to adapt the low noise amplifiers in such a way that they are suitable for said higher frequencies. Furthermore, the power loss of the low noise amplifiers or of an entire receiver in which a low noise amplifier is incorporated should be kept as small as possible. Typical examples of low noise amplifiers are disclosed.
In order still to achieve a sufficient gain of the low noise amplifiers even at high frequencies, coils are usually used in the design of circuit layouts. Coils that are provided for such applications generally have high quality factors, as a result of which it becomes possible to use the relevantly equipped low noise amplifiers. One disadvantage of using coils, however, is that they usually lead to a low available bandwidth of the receiver, that is to say that, when using coils, increasing the quality factor of the low noise amplifier is accompanied by a reduction of the bandwidth available for the use of the low noise amplifier. It can happen in this case that the bandwidth of the low noise amplifier does not suffice to process the bandwidths required for present-day wire-free communication applications.
One possibility for compensating for this disadvantage is to provide a plurality of capacitances in the circuit layout which are connected in parallel with the coil and together with the latter form a resonant circuit. Said capacitances are typically embodied as so-called metal to metal capacitances (MIMCaps). By using such capacitances in low noise amplifiers, it is possible to increase the bandwidth of the signals which can be processed by the low noise amplifiers, but by the same token the quality factor of the low noise amplifiers is reduced in this case.
One possibility for shifting the center frequency, i.e., the resonant frequency, of such a resonant circuit is to use switches, e.g., transistors, which are connected in series with the MIMCaps. The transistors make it possible for individual ones of the capacitances incorporated to be connected and disconnected, as a result of which the resonant frequency, i.e., the center frequency, of the resonant circuit is varied, i.e., the resonant circuit is detuned. Such a detuneable low noise amplifier is disclosed, by way of example.
For these and other reasons, there is a need for the present invention, including providing an integrated amplifier, an electronic communication unit with integrated amplifier and a method for operating the electronic communication unit with integrated amplifier, the integrated amplifier having a smaller space requirement, compared with the low noise amplifiers known in the prior art.
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27 A.3d 1102 (2011)
131 Conn.App. 404
Sabele GRAY
v.
Richard E. GRAY.
Nos. 30512, 31700.
Appellate Court of Connecticut.
Argued May 25, 2011.
Decided September 13, 2011.
*1103 Richard E. Gray, Sr., pro se, the appellant (defendant).
Bourke G. Spellacy, with whom, on the brief, was David R. Makarewicz, Hartford, for the appellee (plaintiff).
BEACH, ESPINOSA and PELLEGRINO, Js.
ESPINOSA, J.
The self-represented defendant, Richard E. Gray, appeals from several judgments of the trial court rendered in favor of the plaintiff, Sabele Gray, following a judgment of dissolution. In AC 30512, the defendant claims that the court abused its discretion by: (1) finding him in contempt for not making support payments to the plaintiff; (2) modifying his support payments in the manner that it did; (3) denying his motion to compel the plaintiff to produce certain financial documents; (4) excluding certain evidence and failing to take into consideration other evidence; and (5) failing to sanction the plaintiff more harshly for her contemptuous conduct. In AC 31700, the defendant claims that the court abused its discretion by: (1) finding him in contempt for not paying an arrearage on support payments owed the plaintiff; (2) ordering him to return his children's passports to the plaintiff; and *1104 (3) failing to hold an evidentiary hearing related to the passport issue. We affirm the judgments of the trial court.
The following facts are relevant to our consideration of this appeal. The parties were divorced on August 12, 2003. In the dissolution judgment, the court ordered the defendant to pay the plaintiff $6000 in child support and $2750 per month in alimony. On September 11, 2005, the parties signed a postjudgment stipulation that provided for reduced monthly alimony and child support payments, totaling $4500, until June 6, 2008, when the payments were to return to their original levels.[1] The court entered an order incorporating this agreement on October 3, 2005. The defendant paid the reduced amount to the plaintiff between October 3, 2005, and June 6, 2008. The defendant then paid the reduced amount for June, 2008, and subsequently made no alimony or child support payments to the plaintiff in the months of July, August, September or October of that year. Instead, in each of these months, the defendant made payments equaling the reduced amount into separate bank accounts for the stated purpose of providing for the education of two of the parties' children.
On November 5, 2008, the court, Calmar, J., found the defendant to be in contempt for failing to make support payments directly to the plaintiff in the original amount, as required by the postjudgment stipulation of the parties. Nevertheless, the court found that the defendant had demonstrated a substantial change in circumstances and agreed with the defendant that a modification of his support payments was warranted. The court, therefore, modified the defendant's $6000 per month child support obligation but did not modify the alimony obligation of $2750 per month. On November 23, 2009, the court, Vitale, J., found the defendant to be in contempt of a court order requiring him to pay a pendente lite arrearage, in the amount of $201,500, to the plaintiff. The court recalculated the interest due on the arrearage but left undisturbed the initial method and monthly amount of payment set at the dissolution proceeding. The defendant appealed both rulings. Additional facts will be set forth as necessary.
I
AC 30512
A
The defendant first claims that the court abused its discretion by finding him in contempt for not making any support payments to the plaintiff between June, 2008, and October, 2008. The defendant alleges that by making payments to bank accounts for the benefit of the children, he was not violating any court order. Alternatively, the defendant asserts that the violation was not wilful. We disagree.
We review decisions of the trial court in family cases for an abuse of discretion. "The standard of review in family matters is that this court will not disturb the trial court's orders unless it has abused its legal *1105 discretion or its findings have no reasonable basis in fact. . . . It is within the province of the trial court to find facts and draw proper inferences from the evidence presented. . . . [E]very reasonable presumption will be given in favor of the trial court's ruling, and [n]othing short of a conviction that the action of the trial court is one which discloses a clear abuse of discretion can warrant our interference." (Internal quotation marks omitted.) Rosato v. Rosato, 77 Conn.App. 9, 13, 822 A.2d 974 (2003).
A court may only find a party in contempt when that party has wilfully failed to comply with a court order. "To constitute contempt, a party's conduct must be wilful. . . . Noncompliance alone will not support a judgment of contempt. . . . We review the court's factual findings in the context of a motion for contempt to determine whether they are clearly erroneous." (Internal quotation marks omitted.) Kravetz v. Kravetz, 126 Conn.App. 459, 466, 11 A.3d 1141 (2011).
In the dissolution proceeding in this case, the court ordered the defendant to make support payments to the plaintiff in the amount of $6000 in child support and $2750 per month in alimony. The postjudgment stipulation entered into by the parties on September 11, 2005, provided that support payments would be reduced to $4500 per month until June 6, 2008, when the payments would return to their original amount. In June, 2008, rather than making payments to the plaintiff as required by the court's original order, the defendant took it upon himself to deposit amounts equal to the payment agreed to in the stipulation agreement, in accounts for the parties' children. Contrary to the defendant's position, the court reasonably concluded that these actions were a knowing and wilful failure to comply with the court's order that, after June 6, 2008, payments be made directly to the plaintiff, in the original amount, as set forth in the parties' stipulation. Although the defendant may have decided to make payments in a way that better suited him, the court ordered him to make payments directly to the plaintiff, not to bank accounts for the benefit of the children. Accordingly, there was ample support for the court's finding that the defendant wilfully violated its order, and a finding of contempt was not improper.
B
The defendant next claims that, on November 5, 2008, the trial court, Calmar, J., abused its discretion in modifying his child support obligations. The record reflects that the court modified the support payments such that the defendant was required to pay the plaintiff $1868 in child support and $2750 in alimony. The court also required the defendant to pay $373 monthly toward the pendente lite arrearage. Specifically, the defendant claims that even though the court found a substantial change in his financial circumstances, in that he had assumed responsibility for the educational expenses of one of the parties' children, the court did not modify his obligations sufficiently. Neither the defendant's scant analysis of this claim nor our review of the record leads us to conclude that the trial court abused its discretion.
C
The defendant also contends that the court improperly denied his motion to compel the plaintiff to produce certain financial documents. Specifically, the defendant moved to compel the plaintiff to complete a financial affidavit that she had filed previously with the court and in which she listed the value of certain stocks *1106 as "unknown." The court noted that the plaintiff completed this affidavit by providing the value of the stocks, and the court had the completed affidavit when it received evidence regarding support payments. The court, therefore, denied the motion. Nevertheless, the defendant asserts that the court did not have all of the relevant information. "The well settled standard of review in domestic relations cases is that this court will not disturb trial court orders unless the trial court has abused its legal discretion or its findings have no reasonable basis in the facts. . . . In determining whether there has been an abuse of discretion, the ultimate issue is whether the court could reasonably conclude as it did." (Internal quotation marks omitted.) Hathaway v. Hathaway, 60 Conn.App. 818, 818-19, 760 A.2d 1280 (2000). After reviewing the record, we conclude the court did not abuse its discretion. The defendant requested that the plaintiff include the value of stocks listed on a financial affidavit, and she did so in time for the completed affidavit to be considered by the court.
D
The defendant also claims that the court abused its discretion by: (1) excluding evidence about his state of mind that is relevant to resolving the issue of contempt; and (2) not crediting alleged past payments to the plaintiff against his support obligations. The defendant does not, however, develop these arguments in his brief, making only bare assertions. Additionally, with regard to the claim concerning crediting past payments, the defendant does not set forth the claim in his statement of issues, as required by Practice Book § 63-4(a)(1). "Although we are solicitous of the rights of pro se litigants. . . [s]uch a litigant is bound by the same rules . . . and procedure as those qualified to practice law." (Internal quotation marks omitted.) Traylor v. State, 128 Conn.App. 182, 185 n. 2, 15 A.3d 1173 (2011). "We consistently have held that [a]nalysis, rather than mere abstract assertion, is required in order to avoid abandoning an issue by failure to brief the issue properly. . . . [A]ssignments of error which are merely mentioned but not briefed beyond a statement of the claim will be deemed abandoned and will not be reviewed by this court." (Internal quotation marks omitted.) Keating v. Ferrandino, 125 Conn.App. 601, 603-604, 10 A.3d 59 (2010). As the defendant has not briefed these issues beyond making statements of the claims, these issues are deemed abandoned on appeal, and we decline to review them.
E
Finally, the defendant claims that the court abused its discretion by granting his motion for contempt but not punishing the plaintiff harshly enough for violating visitation orders regarding the parties' children. Specifically, the defendant asserts that because the plaintiff failed to abide by fourteen court-ordered visitation days, the court's order of one additional weekend of visitation with each daughter in his favor amounts to an award for the plaintiff. We review the severity of the sanctions chosen by the court for an abuse of discretion. See Edmond v. Foisey, 111 Conn.App. 760, 774-75, 961 A.2d 441 (2008); see also Hathaway v. Hathaway, supra, 60 Conn.App. at 818-19, 760 A.2d 1280. The court here did not abuse its discretion. Awarding makeup visitation days is an appropriate remedy, and the court could reasonably conclude based on the facts that an award of additional weekend visitation to the defendant was a suitable sanction for the violation.
*1107 II
AC 31700
A
The defendant first contends that, on November 23, 2009, the court, Vitale, J., abused its discretion in finding him in contempt for not paying the pendente lite arrearage. The defendant again argues that he did not violate a court order and that, alternatively, any violation was not wilful. In accordance with the standard of review set forth earlier in this opinion, we review the ruling for an abuse of discretion.
In finding the defendant in contempt, the court concluded that the defendant's interpretation of the post-judgment stipulation, as barring the plaintiff from bringing a contempt action against the defendant for noncompliance and allowing the defendant to reduce the arrearage on the basis of certain unstated "`offsets'" and an "`accounting'," had no reasonable basis in the record. The defendant does not address this determination in his brief and has failed to demonstrate that an order requiring payment of the arrearage did not exist.
The defendant argues that any violation was not wilful for two reasons. First, the defendant contends that he was unaware that his nonpayment of the pendente lite arrearage was contemptuous conduct because, at the time of the dissolution proceeding, the court did not find him in contempt for his nonpayment of the arrearage. This argument is without merit. The court found, and the record reflects, that the defendant had notice of the court's order to pay the arrearage. His suggestion that a prior holding of contempt was necessary is disingenuous. Second, the defendant contends, as he did before the trial court, that the monthly arrearage payment exceeded his ability to pay. The court thoroughly addressed this issue and concluded that the defendant failed to present a clear and complete record of his financial status. Thus, the court reasonably concluded that the defendant failed to demonstrate an inability to pay the arrearage payment he was ordered to satisfy at the dissolution proceeding, an obligation that was suspended for only the period of time agreed to in the parties' postjudgment stipulation.
B
Next, the defendant asserts that the court abused its discretion in ordering that he return his children's passports to the plaintiff. The following additional facts are relevant to this claim. Over the summer of 2009, the defendant asked the plaintiff for the passports of their two youngest children so he could take the children on a European vacation. The plaintiff, who had physical custody of the children, gave the passports to the defendant and asked for their return following the vacation. Later, the defendant refused to return the passports. In response to a motion, the court ordered the defendant to return the passports within ten days. Eventually, the defendant returned the passports to the plaintiff and appealed from this order.
At the hearing at which the court ruled on the plaintiff's motion for the return of the passports, the court unambiguously rejected the defendant's contention that the plaintiff, who had physical custody of the children, should not also have custody of the passports because she might refuse to let the defendant use them in the future as a way of thwarting his travel plans with the children. The court rejected this purely speculative rationale, noting that it was not in the plaintiff's interest to interfere with the defendant's right to visitation and travel with the children. The court *1108 concluded that the plaintiff, in her role as the parent with physical custody of the children, should retain custody of the passports. The defendant has not demonstrated that the court's exercise of discretion in this family matter was unsound or based upon improper considerations, and we reject the claim.
C
The defendant also claims with respect to the order for the return of the passports that the court took no evidence and that if it had, the result of the proceeding would have been different. As with the evidentiary claims in AC 30512, however, the defendant merely makes an assertion without support in the record or in law. We decline to review this claim because the defendant has not briefed the claim beyond making a statement of the claim. It is, therefore, deemed abandoned. See section I D of this opinion; Keating v. Ferrandino, supra, 125 Conn.App. at 603-604, 10 A.3d 59.
The judgments are affirmed.
In this opinion the other judges concurred.
NOTES
[1] The agreement provides in relevant part:
"Plaintiff agrees she will continue to accept $4500 as the monthly payments to be made to her until 6/6/08, and no additional arrearages with respect to alimony, child support and/or any other payment requirements shall accrue during this time. Neither Plaintiff nor Defendant will seek any modifications of or findings of contempt with respect to monthly alimony, child support or other payments until 6/6/08, as long as Defendant continues to pay the agreed $4500 monthly amounts, plus medical expenses as required. . . . The original alimony and support orders as set forth in the Decision shall be in full force and effect to all monthly payments required by Defendant after the 6/6/08 date. . . ."
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Zebrafish as a model to study PTPs during development.
Protein-tyrosine phosphatases (PTPs) have important roles in signaling, but relatively little is known about their function in vivo. We are using the zebrafish as a model to study the function of PTPs at the organismal, cellular and molecular level. The zebrafish is an excellent experimental model for the analysis of gene function. We have developed methods to quantitatively study effects of PTP knockdown or expression of (mutant) PTPs, particularly with respect to gastrulation cell movements. Moreover, we have studied the phosphoproteome of zebrafish embryos. In this review, we will discuss methods to manipulate the zebrafish genome and techniques that we have developed to assess developmental defects during gastrulation and to assess differences in the phosphoproteome.
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BUG REPORT: scrolling makes the position: absolute; dropdown box move around the pageRESOLVED FIXED: changed position: absolute; to position: fixed;BUG REPORT: scrolling down before opening the dropdown box makes it appear further down the page based on how far the user has scrolled down.
Also, you are wrong. I fucking hate fixed-top titlebars. Because 99.999999% of them take up at least 25% of the screen, which cuts down on my already limited vertical real-estate. I don't need shit floating overtop of what I'm reading. Especially when I scroll down, and the line I last read goes behind the titlebar. Normally I'd just scan the top line at the top of the browser window to see where I am. Not anymore. Now I need to look at the top of the browser window, realize that isn't the top of the page, then look down to find where the top line is. It breaks muscle memory. Therefore it is bad.
Also it breaks in-page searching, since if the word you're looking for is behind the floating header, you will never see it highlight.
And if I want something in the header, I'll press HOME or CTRL-PGUP. I have never once needed something in the header when I was mid-page.
@ben_lubar This further cements my resolve that anyone using position:fixed for anything is doing it wrong and needs to stop doing whatever they are doing.
fixed is the correct position here, I think, they just need to set the menu's top correctly.
I believe that absolute would be preferable. The problem is that the autocomplete elements are essentially siblings of the composer control when they should be descendants of it. With the element hierarchy that is in place, there isn't really a "great" solution.
@abarkerabsolute only works when it's the child of descendent of relative, otherwise it'll be absolute relative to the body element. Either way, it's subject to moving when you scroll, which fixed isn't, as that is relative to the window, not the document.
Besides, the issue isn't fixed vs absolute: the issue is the auto-complete always appears below, even when there isn't room.
Either way, it's subject to moving when you scroll, which fixed isn't, as that is relative to the window, not the document.
That depends on what it is positioned relative to. If the auto-complete dropdown were absolute and a descendant of the composer area, it would not change position when the thread is scrolled. Depending on exactly how the structuring was done, it might change position based on the scrolling of the editor, but that might be considered desireable UI because it would keep the dropdown next to the point of insertion.
But because the auto-complete elements are not descendents of the composer, all that goes out the window. You can't easily keep the dropdown near the point of insertion (especially since every dropdown has a unique ID). Any changes in window size completely screw you over. And so on.
After a quick experiment with Chrome's dev tools, it looks like the dropdown can be moved into the composer element and set to absolute without breaking anything. That will fix the scrolling-with-body issue properly, and make solving the appear-out-of-frame issue easier to solve (I think).
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About Us
The Norsemen are a group of supporters from all walks of life including:
Past players
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Police
Fire Brigade
Local Business men
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We have been a support group to the Norwood Football Club since 1970 and currently we are the largest financial sponsor.
Our support has been wide and varied from:
Financial support for struggling families
Player support at all levels
Special project support around the Club
Financial support to the operations department
Business and planning support to the club
Organisation of bars, BBQs etc.
The Norsemen go about their business in a quiet manner and membership is open to all, value for membership is very little however the value of our membership is knowing that the club is always been supported and taken care of at all times. We ensure that every membership dollar returns to the club in every instance. We do not pay any players directly or indirectly.
The Norseman also attracts sponsorship from many outside companies not associated with the football club. These sponsors are traditionally companies connected to members via business networks away from Mullum Mullum Road.
We donate trophies to outside Auskick clinics in an effort to promote the NFC, Support the Wonga Park Coterie group for development of Junior cricketers who in turn play football in our Junior Club.
We also donate trophies to the Norwood Football Club and work hand in hand with the Norwood Cricket Club and the Norwood Golf Club during the summer promoting the Norwood Football Club.
If you would like to know anything more about the Norsemen please feel free to contact us.
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Tuesday, August 2, 2011
Life Lessons from Bike Rides
Me and my bike, we’re the best of friends. When I’m out riding my bike through the countryside in the summer, I have peace of mind. As long as I have this escape, this get-away, I know that I will be ok, that everything will be ok. Everything is what it is, and will be what it will be. When I was out riding today I realized something: stepping into the unknown is like stepping into a shadow. Before you enter it, the shadow just seems very dark and black and you feel blind. But as soon as you enter it, your eyes only take a second to adjust. So the unknown isn’t that scary, all we have to do is adjust. I learn a lot from my bike rides. I learned to keep my mouth shut or bugs will fly into it. I learned to be aware; the road is not always going to be smooth. I know that I have to keep my eyes in front of me to watch for bumps and potholes, but that I must also keep looking around me. There is so much beauty all around us- keep looking, you might see a butterfly. And there might be some trash along the road, pick it up. I learned about balance on my bike, and that sometimes you’ll fall but it’s not the end of the world. So maybe life is less like a flowing river and more like a bike ride down a long road.
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About Me
I am an illustrator and fine artist who grew up in the small town of Walkerton in northern Indiana. I recently graduated from the Savannah College of Art and Design. I am excited to see where life takes me and am ready to welcome all kinds of opportunities!
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Q:
Does $\chi(g^{-1})=\overline{\chi (g)}$ hold for infinite groups
Let $\chi$ be the character of some representation $\rho:G \to GL(M)$ over $\mathbb C$.
Suppose $G$ is a group, then $\forall g \in G$ of finite order $n$, $ \chi(g^{-1})=\overline{\chi (g)}$
Proof: $\rho(g)^n=\rho(g^n)=\rho(e)=\textrm{id}$. Hence the characteristic polynomial of $\rho(g)$ divides $x^n-1$ and so the characteristic polynomial of $\rho(g)$ has distinct roots. Thus there is a basis $\mathcal B$ of $M$ composed of eigenvectors of $\rho(g)$ and so $[\rho(g)]_\mathcal B$ is diagonal. Then $\chi(g)=\sum_i \lambda_i$ where the $\lambda_i$ are the eigenvalues of $\rho(g)$. Now $[\rho(g^{-1})]_\mathcal B=[\rho(g)]_\mathcal B ^{-1}$ which has the $\lambda_i ^{-1}$ on the diagonal. So $\chi(g^{-1})=\sum_i \lambda_i^{-1}.$ But since $\rho(g)^n=\textrm{id}, \, [\rho(g)]_\mathcal B^n=I $ so for any eigenvector $v_i$ with eigenvalue $\lambda_i$, $\rho(g)^n(v_i)=\lambda_i^n v=v_i$. Hence $\lambda_i$ is an $n$-th root of unity and has $\lambda_i^{-1}=\overline{\lambda_i}$. Therefore $\chi(g^{-1})=\sum_i \lambda_i^{-1}=\sum_i \overline{ \lambda_i}=\overline{\sum_i \lambda _i}=\overline{\chi(g)}.$
You can see that my proof of this relies heavily on the existence of this finite $n$. I am therefore wondering:
For an element $g\in G$ of infinite order, is it still true that $ \chi(g^{-1})=\overline{\chi (g)}$?
A:
As a rule of thumb, look at simple examples first. Consider any nonunitary one-dimensional complex representation of your favorite locally compact noncompact group, $\Bbb R$...
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Multilayer optical films are known. Such films typically incorporate a large number of very thin layers of different light transmissive materials, the layers being referred to as microlayers because they are thin enough so that the reflection and transmission characteristics of the optical film are determined in large part by constructive and destructive interference of light reflected from the layer interfaces. Depending on the amount of birefringence (if any) exhibited by the individual microlayers, and the relative refractive index differences for adjacent microlayers, and also on other design characteristics, the multilayer optical films can be made to have reflection and transmission properties that may be characterized as a reflective polarizer in some cases, and as a mirror in other cases, for example.
Reflective polarizers composed of a plurality of microlayers whose in-plane refractive indices are selected to provide a substantial refractive index mismatch between adjacent microlayers along an in-plane block axis and a substantial refractive index match between adjacent microlayers along an in-plane pass axis, with a sufficient number of layers to ensure high reflectivity for normally incident light polarized along one principal direction, referred to as the block axis, while maintaining low reflectivity and high transmission for normally incident light polarized along an orthogonal principal direction, referred to as the pass axis, have been known for some time. See, e.g., U.S. Pat. No. 3,610,729 (Rogers), U.S. Pat. No. 4,446,305 (Rogers et al.), and U.S. Pat. No. 5,486,949 (Schrenk et al.).
More recently, researchers from 3M Company have pointed out the significance of layer-to-layer refractive index characteristics of such films along the direction perpendicular to the film, i.e. the z-axis, and shown how these characteristics play an important role in the reflectivity and transmission of the films at oblique angles of incidence. See, e.g., U.S. Pat. No. 5,882,774 (Jonza et al.). Jonza et al. teach, among other things, how a z-axis mismatch in refractive index between adjacent microlayers, more briefly termed the z-index mismatch or Δnz, can be tailored to allow the construction of multilayer stacks for which the Brewster angle—the angle at which reflectance of p-polarized light at an interface goes to zero—is very large or is nonexistent. This in turn allows for the construction of multilayer mirrors and polarizers whose interfacial reflectivity for p-polarized light decreases slowly with increasing angle of incidence, or is independent of angle of incidence, or increases with angle of incidence away from the normal direction. As a result, multilayer films having high reflectivity for both s- and p-polarized light for any incident direction in the case of mirrors, and for the selected direction in the case of polarizers, over a wide bandwidth, can be achieved.
Some multilayer optical films are designed for narrow band operation, i.e., over a narrow range of wavelengths, while others are designed for use over a broad wavelength range such as substantially the entire visible or photopic spectrum, or the visible or photopic wavelength range together with near infrared wavelengths, for example.
Some reflective films are designed to reflect light specularly, such that a collimated incident beam is reflected as a collimated or substantially collimated (e.g., having a full-width-at-half-maximum power of no more than 1.0 degrees, or no more than 0.3 degrees) reflected beam. A conventional household or automotive mirror is an example of a specularly reflective film. Other reflective films are designed to reflect light diffusely, such that a collimated incident beam is reflected into a large cone, such as an entire hemisphere, of different scattering directions—for example, the reflected light may have a full-width-at-half-maximum power of at least 15 degrees, or at least 45 degrees). “Flat white” paint is an example of a diffusely reflective film.
In some cases, it is desirable for a reflective film to provide a mixture or suitable balance of specular reflection and diffuse reflection. We refer to such films as “semi-specular” reflective films. One application for such a film may be an edge-lit optical cavity that emits light over an extended area, which may be useable as a backlight, for example. Three such cavities are depicted in FIGS. 1a, 1b, and 1c. An edge-mounted light source may be mounted at the left end of each cavity, but is omitted from the drawings for generality.
A pure specular reflector performs according to the optical rule that “the angle of reflection equals the angle of incidence.” This is seen in the hollow cavity 116a of FIG. 1a. There, front and back reflectors, 112a, 114a are both purely specular. A small portion of an initially launched oblique light ray 150a is transmitted through the front reflector 112a, but the remainder is reflected at an equal angle to the back reflector 114a, and reflected again at an equal angle to the front reflector 112a, and so on as illustrated. This arrangement provides maximum lateral transport of the light across the cavity 116a, since the recycled ray is unimpeded in its lateral transit of the cavity 116a. However, no angular mixing occurs in the cavity, since there is no mechanism to convert light propagating at a given incidence angle to other incidence angles.
A purely Lambertian (diffuse) reflector, on the other hand, redirects light rays equally in all directions. This is seen in the hollow cavity 116b of FIG. 1b, where the front and back reflectors 112b, 114b are both purely Lambertian. The same initially launched oblique light ray 150b is immediately scattered in all directions by the front reflector 112b, most of the scattered light being reflected back into the cavity 116b but some being transmitted through the front reflector 112b. Some of the reflected light travels “forward” (generally to the right as seen in the figure), but an equal amount travels “backward” (generally to the left). By forward scattering, we refer to the lateral or in-plane (in a plane parallel to the scattering surface in question) propagation components of the reflected light. When repeated, this process greatly diminishes the forward-directed component of a light ray after several reflections. The beam is rapidly dispersed, producing minimal lateral transport.
A semi-specular reflector provides a balance of specular and diffusive properties. In the hollow cavity 116c of FIG. 1c, the front reflector 112c is purely specular but the back reflector 114c is semi-specular. The reflected portion of the same initially launched oblique light ray 150c strikes the back reflector 114c, and is substantially forward-scattered in a controlled amount. The reflected cone of light is then partially transmitted but mostly reflected (specularly) back to the back reflector 114c, all while still propagating to a great extent in the “forward” direction.
Semi-specular reflectors can thus be seen to promote the lateral spreading of light across the recycling cavity, while still providing adequate mixing of light ray directions and polarization. Reflectors that are partially diffuse but that have a substantially forward directed component may thus transport more light across a greater distance with fewer total reflections of the light rays. Reference is made to PCT publication WO 2008/144644 (Weber et al.).
Certain design challenges arise when combining a diffusing layer with an MOF. Reference in this regard is made to PCT publication WO 2007/115040 (Weber), “Wide Angle Mirror System”. The design challenges stem from the MOF effectively being optically immersed in a medium of refractive index greater than air, such that light scattered at highly oblique angles by the scattering layer can propagate through the microlayers of the MOF at angles (“supercritical” angles) that are more oblique than the critical angle for the MOF when immersed in air. This effect, combined with the fact that the reflection band of the MOF shifts to shorter wavelengths as the propagation angle increases, and the fact that the spectral width of the reflection band is limited by the number of optical repeat units (ORUs) of microlayers used in the MOF, can result in some of the scattered light, particularly at longer wavelengths, propagating all the way through the MOF to the back or rear major surface thereof. Any dirt or other disturbances such as absorbing materials that are present on such back major surface may cause that light to be absorbed or otherwise lost, detracting from the total reflectivity of the construction. Some solutions to these design challenges are discussed in the '040 PCT publication. However, additional solutions would be of benefit to optical system manufacturers and designers.
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t of 42/(q/854 + (-39)/91)?
7
Suppose -70*z + 68*z = -8. Suppose -z*w - 350 = -5*v - w, -w = -2*v + 140. What is the tens digit of v?
7
Let n(r) = 310*r**2 + 4*r + 6. Suppose 17*w + 65 - 48 = 0. What is the tens digit of n(w)?
1
Let m(c) = 2 - 8*c**2 - 3*c - 14*c**2 + 21*c**2. Let v be m(-2). Suppose 0*h = 3*x + 2*h - 269, v*x - 3*h = 336. What is the tens digit of x?
8
Suppose -52*l + 44*l + 1216 = 0. Suppose -272 = -5*j - t, 7*j - l = 4*j + 5*t. What is the units digit of j?
4
Let m(n) = 8*n**2 - 143*n - 51. What is the ten thousands digit of m(-68)?
4
Suppose -q + 8*m + 14 = 4*m, -4*q + 35 = -9*m. What is the units digit of (q*(-25712)/(-96))/((-2)/(-6))?
7
What is the hundreds digit of (-10)/(-60) - 6/(-36) - 409620/(-18)?
7
Let b = 726 + -500. Let m = b - 90. What is the hundreds digit of m?
1
Let w(j) = -4*j - 35. Let y be w(-5). Let i(v) = v**2 + 5*v - 15. What is the hundreds digit of i(y)?
1
Let t(g) be the second derivative of 413*g**3/6 - 81*g. What is the tens digit of t(1)?
1
Let z(m) = 180*m**3 - 12*m**2 + 33*m - 36. What is the ten thousands digit of z(4)?
1
Let t be (-2852592)/(-168) - ((-24)/(-14) - 2). What is the tens digit of (-2)/(-12) - t/(-72)?
3
Let l = 106 + -42. Suppose 4*n + x - 221 = 0, n + 64 = 2*n + 2*x. Let o = l + n. What is the tens digit of o?
1
Suppose 5*i = 5*k - 106290, k - 4*i - 27116 + 5879 = 0. What is the hundreds digit of k?
2
Suppose -23*w = -9*w + 5*w - 651510. What is the hundreds digit of w?
2
Suppose -19*u + 23*u + 2*x - 25102 = 0, 2*x - 18826 = -3*u. What is the thousands digit of u?
6
Let s be (0 - -1)*(-2 - -2). Let v(t) = -80*t - 8664. Let r be v(-114). Suppose s = -10*m + r + 1664. What is the tens digit of m?
1
Let u(q) = 9*q**2 + 6*q - 22. Suppose 0 = -6*p + 2*p - 24. What is the hundreds digit of u(p)?
2
Let i(q) = -402*q**3 - 16*q**2 + 13. What is the hundreds digit of i(-2)?
1
Suppose 8*u + 294 = 11*u. Suppose -2*s = -9*s - u. What is the units digit of 6/s + 18512/91?
3
Let i = -32 - -17. What is the units digit of 2/i + ((-20408)/(-60) - -3)?
3
Let c = -18238 + 33034. What is the tens digit of c?
9
Let z = 2140 - 2120. Let l(w) = 203*w**2 + 4*w + 4. Let s be l(4). What is the tens digit of s/z - (-2)/(-5)?
6
Let u(p) = -10*p**3 + 2*p**2 + 2*p + 1. Let r be u(-1). Suppose 4*i - 8055 = -r*i. What is the units digit of i?
7
Let x(n) be the first derivative of 17*n**2/2 + 23*n + 1409. Let z be -2 + 11/1 + -1. What is the hundreds digit of x(z)?
1
Let q(p) = 26*p + 0*p - 22*p + 9*p + 72*p + 89. What is the tens digit of q(8)?
6
Let y = -4716 - -9647. What is the tens digit of y?
3
Let t(z) = z**3 - 30*z**2 + 357*z + 35. What is the tens digit of t(29)?
4
Let l(s) = -s + 8. Let g be l(4). Suppose -3*z = g*v - 543, v - 42 - 90 = 3*z. Suppose 0 = 5*w - v - 75. What is the tens digit of w?
4
Let j(z) = -z**3 + 24*z**2 - 18*z + 5. Let y be j(23). What is the tens digit of (-19)/((-38)/y) + 5?
6
Suppose 4*s + 55502 = 3*z - 34238, 0 = 2*z + 5*s - 59888. What is the tens digit of z?
2
Let d be (176/(-24))/(4/(-198)). Let j = d + 189. What is the units digit of j?
2
Let a = 16 - 13. Suppose -103 = a*i + 29. Let x = 2 - i. What is the units digit of x?
6
What is the units digit of -11 - 5 - -12 - -30202?
8
Let d be 1/(-1*(-2)/10). Suppose 0 = -d*i + 9*i + 280. What is the tens digit of i/3*(2 - 5)?
7
Let k be 5*-3*4/(-12). Let w(x) = 13*x**2 - 16*x + 6. What is the hundreds digit of w(k)?
2
Suppose 15*j - 21*j = -210. Suppose -j*a = -37*a + 2688. Suppose -3*z = -10*z + a. What is the hundreds digit of z?
1
Suppose -4*x + 100039 = 3*l - 51154, 0 = -3*x + 2*l + 113365. What is the hundreds digit of x?
7
Let r = 21320 - 13418. What is the thousands digit of r?
7
Let v(j) = -20*j. Let h be v(-1). Let r(d) = 36179*d**3 - 31 - 26*d + 36178*d**3 - 72356*d**3 - 18*d**2. What is the units digit of r(h)?
9
Let m(o) = 21*o**2 + 175*o + 65. What is the thousands digit of m(-19)?
4
Let j = -197 + 210. Suppose 0*z + 5564 = j*z. What is the hundreds digit of z?
4
Let n(q) = 209*q**2 - 10*q + 98. What is the units digit of n(-9)?
7
Suppose 25 + 29 = -6*u. Let k(r) = r**2 + 9*r + 4. Let l be k(u). Suppose l*v - 20 = 0, 2*f + 19 = 4*f - v. What is the units digit of f?
2
Suppose 478*k = 320*k + 2696586. What is the ten thousands digit of k?
1
Let j(w) = -6*w - 25. Let q be j(-12). Let d(i) = -i**2 + i**2 - i**2 + 6*i + q - 8*i. What is the tens digit of d(0)?
4
Let m = -12330 + 31120. What is the ten thousands digit of m?
1
Suppose 2*c - 480 + 476 = 0. Suppose -s = 4*u - 5945, -5*u + 2*u - c*s = -4460. What is the tens digit of u?
8
Suppose 0 = 5*l + 2*k - 69, l - 5*l + 75 = -5*k. Suppose 0 = 5*m - y - l, 3*y - 10 = y. What is the tens digit of (4/(-7))/(m/(-434))?
6
Let r = 145 + -140. Suppose -4*a + 2*q = -8*a + 1472, -a + 390 = -r*q. What is the tens digit of a?
7
Let l = 82 - 84. Let q be (3/l)/(4/16*-2). Suppose 58 = 2*c + 2*p - 50, 4*p = q*c - 141. What is the tens digit of c?
5
Suppose -265*d - 59*d + 8691300 = 0. What is the hundreds digit of d?
8
Let s = 90199 - 61991. What is the hundreds digit of s?
2
Let y be ((-29)/(-3) - -2)*(-6)/(-5). Suppose 2187 - 9635 = -y*p. What is the tens digit of p?
3
Suppose -2*k = 8 - 38. Suppose -k*h + 23275 = 8440. What is the tens digit of h?
8
Let w(b) = 161*b - 16672. What is the tens digit of w(190)?
1
Let t(k) = 8*k**2 - 7*k + 22. Let h be t(-6). Let w = -287 - -47. Let f = w + h. What is the units digit of f?
2
Let f(d) = -d**3 - d**2 + 5*d + 124. Suppose -5*u - 3*c + 5 = 17, c + 4 = 0. What is the units digit of f(u)?
4
Let h = 5251 - 1260. What is the thousands digit of h?
3
Let g be (96 + -1)/(0 - -1). Let k(c) = -c**3 + c**2 + 29*c + 72. Let d be k(-5). Suppose 4*p - g - d = 0. What is the units digit of p?
3
Suppose -18*u - 11245 = 4829. Let c = -561 - u. What is the hundreds digit of c?
3
Suppose 3*d + o = 5*d - 3495, -2 = 2*o. Let k = d + -1142. What is the tens digit of k?
0
Suppose 4*z = 23 - 7. Suppose 15*k - 882 = 12*k - 3*t, -3*k + 879 = z*t. What is the hundreds digit of k?
2
Suppose 5*h - 10 = 0, -17*l = -22*l + 4*h + 52. What is the hundreds digit of (l/(-14) - 22/7) + 1129?
1
Let n(t) = 2*t**2 + t + 1. Let c(b) = -13*b**2 - 13*b + 4. Let i(p) = 3*c(p) + 21*n(p). What is the tens digit of i(12)?
4
Suppose r = 2*z - 33855, r - 67707 = -30*z + 26*z. What is the hundreds digit of z?
9
Let x(r) = 4*r + 54. Let p be x(-12). Suppose -2 = -2*a + p, -5*a = -2*c + 706. What is the units digit of c?
3
Let b = -19 - -24. Suppose -b*f = 3*r - 14, 0*f - 4 = -4*f. Suppose -r*n - 2*n = 25, -x + 148 = 4*n. What is the hundreds digit of x?
1
Let m(f) = -346*f**3 + 4*f**2 - 10*f + 16. Let h be m(-5). Suppose 41*x - h = 14*x. What is the units digit of x?
8
Let c(u) = 1252*u + 7. Let f be c(1). Let y = f - 667. What is the hundreds digit of y?
5
Suppose 4*s - 58 - 20 = -5*a, -4*s + a = -90. Let v be (1 + -2)/((-1)/s). Suppose -23*r + v*r + 40 = 0. What is the tens digit of r?
4
Let i(p) = p**3 + 16*p**2 - 13*p + 8. Let m be i(-16). Suppose 4*d - m = 1228. Suppose -4*c + b + 281 = 0, -4*c - c - 2*b = -d. What is the units digit of c?
1
Let y be (-4 - (-39)/6)*(-4)/(-5). Suppose 39 = -y*u - 11*u. What is the units digit of (78/(-12))/(u/18)?
9
Let i(f) = 87*f**2 - 205*f - 3593. What is the ten thousands digit of i(-22)?
4
Let g(s) = -s**3 - 400 - 427 - 15*s**2 + 843 - 8*s. Let r be -17 + 2/(1/1). What is the units digit of g(r)?
6
Let q(m) = -m**3 + 7*m**2 + 9*m - 4. Let i be q(8). Let u be (-3 + -6)/(i/(-132)). Suppose 7*n - 592 = u. What is the hundreds digit of n?
1
What is the tens digit of 185376/42 - 180/(-140)?
1
Suppose -3*a - 66 = -7*q + 4*q, 5*q + 2*a = 82. What is the tens digit of 2 + 1066/18 + (-4)/q?
6
Let r = -20 - -2. What is the units digit of (498/r)/((-7)/126)?
8
Let c(o) = -604*o - 6287. What is the thousands digit of c(-34)?
4
Suppose 1009*i + 36 = 1012*i. What is the units digit of 10*(-6)/i - (-1743)/3?
6
Suppose -2*l - 4*u + 33876 = -15520, 4*l = -5*u + 98774. What is the tens digit of l?
8
Let j(q) = 42 - 3*q**2 + 18*q + 20*q**2 - 16*q**2 - 6. What is the hundreds digit of j(7)?
2
Suppose 0 = -5*h + 2*p + 77962, -3*h - 144*p = -148*p - 46780. What is the thousands digit of h?
5
Suppose 7*i = 16*i + 4086. What is the tens digit of (i/(-28) - (-26
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Identifying sensitive sources and key control handles for the reduction of greenhouse gas emissions from wastewater treatment.
This research investigates the effects of adjusting control handle values on greenhouse gas emissions from wastewater treatment, and reveals critical control handles and sensitive emission sources for control through the combined use of local and global sensitivity analysis methods. The direction of change in emissions, effluent quality and operational cost resulting from variation of control handles individually is determined using one-factor-at-a-time sensitivity analysis, and corresponding trade-offs are identified. The contribution of each control handle to variance in model outputs, taking into account the effects of interactions, is then explored using a variance-based sensitivity analysis method, i.e., Sobol's method, and significant second order interactions are discovered. This knowledge will assist future control strategy development and aid an efficient design and optimisation process, as it provides a better understanding of the effects of control handles on key performance indicators and identifies those for which dynamic control has the greatest potential benefits. Sources with the greatest variance in emissions, and therefore the greatest need to monitor, are also identified. It is found that variance in total emissions is predominantly due to changes in direct N2O emissions and selection of suitable values for wastage flow rate and aeration intensity in the final activated sludge reactor is of key importance. To improve effluent quality, costs and/or emissions, it is necessary to consider the effects of adjusting multiple control handles simultaneously and determine the optimum trade-off.
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Effects of prenatal yoga on women's stress and immune function across pregnancy: A randomized controlled trial.
The effects of prenatal yoga on biological indicators have not been widely studied. Thus, we compared changes in stress and immunity salivary biomarkers from 16 to 36 weeks' gestation between women receiving prenatal yoga and those receiving routine prenatal care. For this longitudinal, prospective, randomized controlled trial, we recruited 94 healthy pregnant women at 16 weeks' gestation through convenience sampling from a prenatal clinic in Taipei. Participants were randomly assigned to intervention (n=48) or control (n=46) groups using Clinstat block randomization. The 20-week intervention comprised two weekly 70-min yoga sessions led by a midwife certified as a yoga instructor; the control group received only routine prenatal care. In both groups, participants' salivary cortisol and immunoglobulin A levels were collected before and after yoga every 4 weeks from 16 to 36 weeks' gestation. The intervention group had lower salivary cortisol (p<0.001) and higher immunoglobulin A (p<0.001) levels immediately after yoga than the control group. Specifically, the intervention group had significantly higher long-term salivary immunoglobulin A levels than the control group (p=0.018), and infants born to women in the intervention group weighed more than those born to the control group (p<0.001). Prenatal yoga significantly reduced pregnant women's stress and enhanced their immune function. Clinicians should learn the mechanisms of yoga and its effects on pregnant women. Our findings can guide clinicians to help pregnant women alleviate their stress and enhance their immune function.
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Ugc net environmental sciences syllabus 2018 there will be two question papers ugc net environmental science ugc net environmental science paper ii. Here are some reading material and previous year question papers of the aecc paper on environmental studies/ science at university of delhi.
Environmental science question paper
Isc specimen question paper -2017 environmental science (t hree hours) maximum marks: 70 (candidates are allowed additional 15 minutes for only reading the paper. Question description you will need to submit research paper topic for approval by no later than the end of third week you have considerable freedom in choosing a. Free online cbse ugc net, set, slet guide book in library and information science is prepared by badan barman it covers the syllabus, solved question papers of.
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Way back in October, we told you about Joel Embiid’s acting role in go90’s “The 5th Quarter,” a mockumentary web-series telling “greatest untold and untrue stories in sports history.” Joel’s episode, “The Processor” is the first episode of season three. Here it is below:
And because we couldn’t resist, here’s some gifs:
We also spoke to showrunner and producer Michael D. Ratner (below with Embiid), who previously worked on the Netflix documentary “One in a Billion” and is currently working on a project with Kevin Hart.
Here’s some of what Ratner told us:
They had talked to Joel about possible doing something last year, but it was important for JoJo that he focused on getting on the court.
“Some episodes are like ‘insert athlete here,’” Ratner said, but ‘The Processor’ was built around Joel.
The Nerlens Noel cameo came about during the summer (when Joel’s parts were also filmed). Nerlens was already playing for Dallas at that time, but he was spending his summer in LA, so he was around to act.
Joel memorized all of his lines in advance for his scripted debut, nailing everything in a couple of takes and even adding some improvisation. Ratner said they let Joel have fun with “the whole back and forth with the other woman in the office,” which is perhaps the funniest part of the whole show, and the crew was holding back laughter as Joel tried different things out.
Ratner told us that while there may be a documentary about Joel’s life in the future, we also shouldn’t rule out more scripted work.
He may not be at that kind of star level yet, but I never knew how badly I needed a Joel Embiid-hosted episode of SNL until right now.
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The bill, titled “The Cannabis Regulation and Taxation Act,” was drafted by Richard M. Evans, an attorney from Northampton. The bill would legalize the possession, consumption and sale of marijuana for people over 21 and establish a series of licenses requiring annual fees.
The bill contains a lot of rules concerning cannabis packaging and licensing fees, but that is a good thing. Marijuana laws need to be specific, lest they get lost in the mire of “what ifs.” People want to know exactly what they are voting for.
Besides, the more specific a bill is, the less it can be demonized by lies from its opponents.
Massachusetts is going to be another legalization battleground, and it is a place where we have a good chance of winning. But it is up to us – the marijuana activists – and to those in MA who want to see this bill passed. Share stories and speak out; if you live in MA, contact your representative and let them know you want this bill passed. And let them know that your vote depends on theirs.
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The Bury man who has been at the centre of an international storm after brokering a meeting between Donald Trump Jr and a Russian lawyer says there have been a “mountain of misconceptions” about the incident.
The US President’s son has released emails showing that in the run-up to American election he met the lawyer, who he thought was offering damaging material on Hillary Clinton.
Former Manchester journalist Rob Goldstone, who was raised in Whitefield , and worked for the Radcliffe Times, arranged the meeting.
Mr Goldstone has now told the M.E.N.: “I am waiting to release an official statement hopefully today which I believe will clear up the mountain of misconceptions and comments about these emails.”
After leaving Greater Manchester, Mr Goldstone worked for the Birmingham Evening Mail and in radio.
In this country he was known for his impressive ability as a reporter, off-the-wall sense of humour and obsession with tennis.
He later became a music publicist based in New York, and at one time was working for superstar Michael Jackson during his 1986 Australian tour.
He now runs a PR company, Oui 2 Entertainment.
(Image: Twitter)
Currently on holiday in Greece, he is at the centre of controversy after reports he had arranged a meeting between Donald Trump Jr and Natalia Veselnitskaya who apparently promised damaging material about Hillary Clinton during last year’s presidential campaign.
Mr Goldstone manages Russian pop star Emin Agalarov, whose father, Aras, is a Moscow-based real estate developer who was Mr Trump’s business partner in taking the Miss Universe competition to Moscow in 2013.
Last year he organised Emin’s European tour which included a performance at Manchester’s Band on The Wall.
In 2013, Mr Trump featured in a music video by Emin with that year’s Miss Universe contestants.
Mr Goldstone arranged the meeting between Trump Jr and Ms Veselnitskaya on June 9th 2016, two weeks after Mr Trump had secured the Republican nomination.
Ms Veselnitskaya had promised damaging information on his father’s Democratic rival. But that, according to Mr Trump Jr, did not materialise.
According to the New York Times, the offer by Ms Veselnitskaya was part of a Russian government effort to help his father’s election campaign, and that information was sent in an email by Mr Goldstone to Mr Trump Jr.
US officials are currently investigating alleged Russian meddling in the US election.
On Facebook last year Mr Goldstone posted that he checked in at Trump Tower on June 9th of last year with the caption “preparing for a meeting.”
The New York Times reported Sunday that the meeting, which also was attended by Trump’s then-campaign chair Paul Manafort and now-White House senior adviser Jared Kushner, was arranged on the premise that Veselnitskaya would provide damaging information on soon-to-be Democratic presidential nominee Hillary Clinton.
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the rule of thumb is: you dont understand a certain sport, you shut up about it.
i don't know anything about american football, it looks utterly ridiculous and boring to me, but based on my total lack of knowledge i shut up about it.
maybe you should consider a similar course of action, you are after all talking about the most popular sport in the entire world....
uhm, no. next to nothing really. you won't find any sport that has as large a fanbase as soccer almost anywhere in the world. in fact, in recent years the world cup and champions league finales were watched by more people around the globe than the super bowl.
yeah, true, but outside of the US no one gives a shit about NASCAR.
on an international level, formula 1 is really where it's at.
and now guess what nationality the greatest F1 driver of all times is....
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Gals!
is a shōjo manga written and illustrated by Mihona Fujii. The manga was published by Shueisha and serialized in Ribon from 1998 to 2002. The manga was also published in the U.S. by CMX. In 2019, Mihona Fujii announced that the series will continue from November 5 on Shueisha's Manga Mee app, taking off from the manga's ending.
An anime adaptation produced by Studio Pierrot entitled aired in Japan on TV Tokyo between April 1, 2001 and March 31, 2002, running a length of 52 episodes. The first 26 episodes had been licensed and dubbed for North American distribution by ADV Films under the name Super Gals! and was distributed on DVD from 2003 to 2004. The Right Stuf International announced at Anime Expo 2006 that they had licensed all the episodes, including 27-52 and released a subtitled boxset containing the remaining 26 episodes on January 16, 2007. A box set containing all 52 episodes was also released in 2010.
Plot
The series revolves around the kogal (generally known as gyaru, or "gal") subculture in Japan. The title character, Ran Kotobuki is the self-proclaimed "world's greatest gal." As a teenager in Shibuya, she is determined to live out the gal lifestyle for the rest of her life, and she has gained a reputation as the most respected gal in all of Shibuya. However, she comes from a family of police officers—her grandparents, her parents, and her older brother are all officers, and her younger sister is set on following in their footsteps. Ran has other dreams for her future, but as frequently shown, she has acquired the family's sense of justice and spirit. Her two friends, Miyu and Aya, also have their own problems and circumstances.
The sequel manga is following manga's ending storyline. While Ran, Miyu. Aya, and their friends still hangout in Shibuya after they graduate. Ran still deciding her carrer, Miyu is now part of Kotobuki family after she marry Yamato and she decided searching her missing mother alongside with Yamato and his family as well her friends so she can tell her that Miyu will always love her and showing her new life. Aya is now a university student alongside Rei as they attend the same campus.
Characters
The first nine volumes of the CMX translation have the family name first.
Main
Ran Kotobuki is the title character of the series and its main protagonist. She is a strong-willed, athletic, and attractive gal with orange hair with a red streak who rules the streets of Shibuya. Although she comes from a long line of police officers, she is ditzy and absent-minded when it comes to school and the only subject she gets good grades on is physical education and her poorest subjects are mathematics and literature. When she was in elementary school, she was enthusiastic about becoming a police officer, but quit the ambition after learning that she won't be able to dye her hair or wear her favorite accessories. She is usually obsessed with anything that is trendy or catches her eye, usually brown-nosing guys who find her cute to buy them, and is also quite gluttonous. But inside her heart, she has a strong sense of justice that runs in her blood and is extremely intimidating and tough when she's in combat mode. She is a role model to the junior students at Hounan High for her social status as a magnificent gal for justice and her very understanding nature for teens who are learning to cope, but some look upon her with jealousy and anger. Despite being an underachiever, Ran is smart and has a good memory on what she is interested in (such as shopping). There is a running gag in the manga that some of her friends say that if only she used that (memory, concentration, etc.) on studying, she'd get somewhere in life. She also has a foreign friend, Vivian Lin, a Taiwanese celebrity who looks amazingly like her, whom she met during a school trip to Taiwan (only shown in two stories of the manga). Ran wishes that she has soft hair, but according to Rui Otahata, Rei Otohata's cousin, her hair is damaged and dry due to the amount of bleach she pours on it. Her favorite color of her silhouette is red.
Miyu is an independent, headstrong, and kind-hearted classmate with blonde hair with an orange ombre of Ran and one of her closest friends. However, behind her romantic and cute cover lies a dark past. When she was in third grade, her parents divorced (her father is currently remarried) and she lived with her mother, who paid more attention to looking for a new man rather than to see Miyu grow up (she despised Miyu because she reminded her of her divorced husband). She once was the leader of a street gang called the "Resistance", often wreaking mayhem and irritation during middle school and had a rough-mannered and threatening personality that Ran despised. One day, Yamato (by then a rookie cop) saved her from a tough situation, and his dedication to helping with Miyu's problems made her fall in love with him. Because of that, she left the life of crime and became more polite after Yamato told her his wish for her to be good and eventually became great friends with Ran. However, she remains an incredible fighter and can get back to her previous violent self when someone completely upsets her and when she becomes uncharacteristically furious. In conversation, she has a habit of referring to herself in the third person, though occasionally uses first person in more serious situations. Ran often remarks how Miyu is "lovey-dovey" with Yamato and there is a running gag on both series when they are interrupted when they are trying to kiss, usually by Ran. When her mom eventually moved out, she moved into a new apartment and married Yamato in Hawaii in the manga. Her favorite color of her silhouette is yellow.
Aya is one of the top students with black hair in Ran's class, but she was secretly doing enjo kōsai to earn money according to the first chapter/episode, since her parents were very strict about her being in number one in academics and wouldn't let her do any part-time jobs or go out. Ran found out and confronted her about it, fortunately making her realize that she was doing the wrong thing before Aya could actually "do it" with somebody. Since then, Aya became good friends with Ran and Miyu. She is a shy but honest and studious individual who enjoys academics while also longing for excitement every now and then, which is thankfully provided by Ran. Aya strengthens and changes during course of the series. She's usually a crybaby when it comes to sad or happy moments, but she grows braver and learns to stand on her own. She has deep feelings for Rei Otohata but her shyness leads to complications in their relationship, especially as Otohata initially dates her due to pity rather than affection, but the two eventually manage to establish a genuine relationship by the end of the series. Her favorite color of her silhouette is blue.
Rei Otohata is a student at Meisho Daichi High School (Champion High School in ADV's dub). He is also known as "#1", because he was featured in a magazine as being the coolest and most handsome teenage guy in the area. He rides a motorcycle and is good friends with Yuya. He has a cold and detached demeanor, and is constantly annoyed by Ran. He has trouble expressing his feelings towards others. He initially likes Ran but tends to hide this well, but later reciprocate Aya's feelings for him by the end of the series.
Yuya is also a student at Meisho Daichi High School, and he is known as "#2" or "Second Place", as he was the runner-up to Rei in a popularity magazine poll. He and Rei are friends. Early in the series, he develops a crush on Ran, even role-playing how it would be nice to date her, but Ran is oblivious to the fact. The crush gets worse when Tatsuki joins in and confesses successfully to Ran. As time passes, he helps Mami Honda out to the point that Mami starts falling for him, even though he still has a crush on Ran. Near the end of the series, he gets over Ran, and ends up dating Mami.
Tatsuki Kuroi (also nicknamed Tatsukichi) is a wild and kind student at Machida West High School, and he calls himself "the parapara king of Machida" (also known as "Machida Black", since the "kuro" in his last name means "black"). In the manga he is also called Blackwell (the literal translation of his surname). He is often nicknamed "Monkey Boy" since his personality is very similar to that of a monkey. He becomes Ran's boyfriend, although she studiously avoids anything remotely approaching intimacy other than hugging or holding hands, thus calming him. He likes to use English words and phrases in his conversations. Sometimes he says a phrase in English then he will say then same phrase in Japanese, or he will say a phrase beginning in Japanese and ending in English, and then he will say the same phrase again, switching the Japanese and English parts (example: "Black nichiyōbi", "Black Sunday", and then "Kuroi Sunday"). He also likes to call Yuya "brother" in English.
Supporting
Ran's and Sayo's older brother. Unlike Ran, he has a sensitive and passionate personality that shows through his job as a cop, and is usually on duty at the Shibuya "koban". The only thing that annoys him is when Ran causes trouble in Shibuya and he has to bring her to the police station. His love interest is Ran's best friend, the much-younger Miyu Yamazaki, whom he first met when he was a rookie cop and when Miyu was a troublesome and violent gangster. It was he that helped her to be good, since he was the only one who believed in her. In the end, he helped Miyu move into her new apartment and married her after she finished high school.
Ran's and Yamato's younger sister. She dreams of being a detective like her father has. Sayo and her boyfriend, Masato Iwai, often roleplay as conspicuous detectives, drawing the attention of onlookers and inciting frustration from Ran who is bothered by their antics. She is very energetic and enthusiastic about everything she does - however, she is slightly accident prone and often falls face down when she tries to run away or exit in a dramatic fashion. She ends her sentences with the phrase . In the end of the series she is still with Masato and they both go the same high school that Ran goes to.
Ran's father is the local Chief of Detectives. He disapproves of his daughter's lifestyle. He tries his best to make Ran say that she wants to be a police officer, and often tries various tactics to get her to do various jobs helping the people (like refusing to giving her money). He is also famous for employing a technique called "Taizo's Giant Swing of Fury" on Ran when he loses patience with her and once on Sayo.
Ran's mother who is also a police officer. It is a running gag throughout the series about her mysterious age, as she appears to be much younger than her husband. She is much more patient with Ran and the entire family in general- she never seems upset by Ran's choice to be a Gal as is very supportive of her children. Towards the end of the manga, she tells Miyu that she considers Miyu her daughter, showing just how nurturing she can be.
Mami is a gal from the neighboring Ikebukuro district where she is known as the "Queen of Ikebukuro". She has a fierce rivalry with Ran and participates in several competitions with her. She develops feelings for Yuya after he comforts her during some of the matches. She later forms a truce with Ran. In the anime, she comes from a very rich family.
Harue is Mami's best friend. She was once a member of a gang called the "Eagles", which was broken up by Miyu's "Resistance" gang. She once sent in a nasty email to everyone in school about Miyu and her past.
Masato is Sayo's boyfriend since the beginning of junior high. He fell in love with her as "the cute girl who always wore a hat" (which she only wore because she cut her bangs too short). From then on, they were a steady couple. He's a bit fun-loving and kind of weird like Sayo and imitates as a junior cop with her, but very just and gallant, especially to Sayo. At the end of the series, he goes to the same high school as Sayo, and they are still a couple.
Naoki Kuroi is Tatsuki's little brother. He's a street-smart, outgoing, but good-hearted boy who, like his brother, thinks of himself as a ladies man, but ends up having crushes on every girl he meets, including Ran, Miyu, Aya, Sayo, and, at the end of the TV series, he has a crush on Kasumi. He enjoys riding a skateboard. He works at their father's ramen shop every now and then, and someday wants to run the business. At first Naoki is upset that Tatsuki does not want to take over the family business, but Tatsuki tells Naoki that he wants to do what he wants.
Ran's teacher. He is very annoyed whenever Ran arrives late or comes up with a pathetic excuse for not having her homework. He is called "Naka-Teach" by Ran. Nakanishi tries to help Ran to do better in school by making her go to his after school classes and always has to scold her.
and
Satsuki
Rie
Satsuki and Rie are Ran's schoolmates since elementary school. Satsuki has blonde hair in a short ponytail, and Rie has black hair.
Red
Yellow
Blue
The three ganguro girls who enjoy bugging Ran. They are identified by the colors red, yellow, blue. They spend much of their time in "sun-salos".
Kazuki is a boy who befriends Aya. He acts nice to Aya but disapproves Aya hanging around non-academic friends. He becomes angry at Rei for the way he treats Aya, and confesses to Aya.
Anime-only
A country girl who wants to be Ran's disciple.
Kasumi is a glasses girl whose dream is to be the number one gal in Shibuya and overthrow Ran. Her reasons for becoming a gal is because, when she was younger, she was picked on by some guys. A gal (who appears to have been Towa) saves her from being bullied. Her and Ran have a strong rivalry and she tries her hardest to do something that would cause Ran to lose her title as number 1. This usually involves using a disguise. However all of her plans against Ran usually fail, and either she says who she is, or Ran and her friends figure out her disguise. She also finds out Ran's secret from Towa, although it's never revealed what Ran's secret is. She also has a strong sense of right, when needed. When her and Ran where trying to save up enough money to buy a jacket that each of them want badly. Kasumi sells items at a flea market in order to raise money, but when a boy wants a refund for a toy that does not work, she gives back the money to the boy. In the end she goes to the same High School as Ran, and Naoki falls for her when she tells him not to cry.
Towa is a young woman who runs the Palm Tree Cafe. She is friends with Yamato and the actor who plays Detective Kudoh. She has known Ran since Ran was just a little girl, and they used to play together. Towa was one of the first gals in Shibuya, and was the number one gal back in the day, before Towa passed the title to Ran. She overreacts at times, and when Ran upsets her, she says that she will tell her friends her secret (which is never revealed). She also has a black belt in Karate, and is also kind hearted. When Miyu needs a place to stay, she lives in the empty room at the Palm Tree Cafe. At the end of the series she gives the manager job to the actor who plays "Detective Kudoh", as she quits her job.
and
Minigal Tan
Minigal White
These chibi gals introduce the various gal-terminology throughout the series.
Chapters
Original
Reprint
Staff
Original Story: Mihona Fujii / Serialized in "Ribbon" by Shueisha
Planning: Keisuke Iwata (TV Tokyo), Yuji Nunokawa
Producers: Tomoko Gushima (TV Tokyo), Ryunosuke Tsuno
Series Composition: Masashi Kubota (credited as Masashi Kubot)
Character Design: Yuko Kusumoto, Hiroto Tanaka
Art Director: Junichi Higashi
Color Design: Yuko Sato
Director of Photography: Naohisa Haijima
Editor: Masahiro Matsumura
Sound Director: Toshiki Kameyama
Music: Hikaru Nanase
Music Produced by: Lantis
Music Producer: Yoshiyuki Ito
Music in Cooperation with: TV Tokyo Music
Director: Tsuneo Kobayashi
Produced by: TV Tokyo, Studio Pierrot (Eps. 1-41) → Pierrot (Eps. 42-52)
Opening Animation
Storyboards & Direction: Pochi Shibuya
Key Animation: Masayuki, Atsuko Inoue, Kaori Higuchi, Junko Abe, Yukihiro Kitano
Ending Animation
Storyboards & Direction: Tsuneo Kobayashi
Key Animation: Hiroto Tanaka
English Version Staff
Season 1
English Language & Subtitled Versions Presented by ADV Films
Executive Producers: John Ledford, Mark Williams
Produced & Directed by: David Harrison (Eps. 1-18) → Jin Ho Chung (Eps. 19-26)
International Coordinator: Toru Iwakami
Project Translator: Shoko Oono
ADR Script: David Carren, David Harrison (Eps. 6-26)
Subtitle Script & Timing: Jonathan Lotman
English ADR Recorded at: Industrial Smoke & Mirrors
Sound Design & Mix: Brent Marshall
Recording Engineers: Bryan Leach (Eps. 1-10), Henry Rogers (Eps. 6-14), Richard Stanford (Eps. 6-18) → Jacob A. Gragard (Eps. 19-22), Jason Grundy (Eps. 11-14, 23-26), Matt Wittmeyer (Eps. 1-10, 19-26)
Post Production: Monkey Boy Post
Post Production Manager: Shelly Thomas
Editors: Christopher Nelson (Eps. 1-5) → Bill Newton (Eps. 6-26), Neil O'Sullivan
Production Assistants: Marta Bechtol, Miyuki Kamiya, Maki Nagano, Carole Pavlik
SUPERGALS © 2001 Minaho Fujii/Shueisha, TV Tokyo•Gals! Project
English Language & Subtitled Versions © 2003 (Eps. 1-14) → 2004 (Eps. 15-26) A.D. Vision, Inc.
DVD (Eps. 1-10) → DVD Layout, Design and Navigation (Eps. 11-26) © 2003 (Eps. 1-14) → 2004 (Eps. 15-26) A.D. Vision, Inc. All other elements are the property of their respective owners. All rights reserved. (Eps. 11-26)
Theme songs
Opening
Lyricist: Kana / Composer: Kana / Arranger: Akio Noyama / Singers: dicot
Ending
Lyricist: Ikuno Takagi / Composer: Isao Yoshida / Arranger: Isao Yoshida / Singers: Jungle Smile
Episode list
Episodes are numbered as streets, such as "1st street", "2nd street", and so forth. They are also stylized with heart symbols and right arrows. the English titles are generally from the RightStuf version.
Season 1
Season 2: The Heart of Shibuya
In North America, the episodes were not dubbed into English, but were presented as Japanese with English subtitles.
Video games
Three video games have been created by Konami. The first video game has the same title as the anime and was released on July 26, 2001. The second video game was entitled and was released on February 7, 2002. The third video game was entitled and was released on August 8, 2002.
Other appearances
Several Gals! character make their appearances outside their series in Kochira Katsushika-ku Kameari Kōen-mae Hashutsujo crossover manga named Shin Kochikame
Reception
T.H.E.M. Anime reviews gave the anime series five stars out of five, calling it one of the "most bright, well-animated titles to come out of fiscally-challenged Pierrot in quite some time". Chris Beveridge gave the complete DVD set an overall positive review, saying it is "ten discs of excellent anime at a fantastic price point that needs to be seen, enjoyed and treasured". Erin Finnegan of Anime News Network recommended the series to anyone who is a fan of hyperactivity or Shibuya street culture. Bamboo Dong of Anime News Network gave the anime the complete DVD set an A for the Japanese voice acting, a B+ for the English voice acting, a B+ for story, a C for Animation, an A− for art and a B for music.
See also
Para Para, a dance often seen in this series, is a type of dancing where the dancers perform preset movements, usually unique to the song.
References
Further reading
External links
Official Pierrot Webpage
Official TV Tokyo webpage
Official Konami website
Official Konami website 2
Official Konami website 3
Official Studio Pierrot website
Official Right Stuf webpage
Official Enoki Films webpage
Category:Japanese children's television series
Category:1998 manga
Category:2001 anime television series
Category:2001 Japanese television series debuts
Category:2001 video games
Category:2002 Japanese television series endings
Category:2002 video games
Category:Comedy anime and manga
Category:Shueisha franchises
Category:Shueisha manga
Category:Pierrot (company)
Category:TV Tokyo shows
Category:School life in anime and manga
Category:Shōjo manga
Category:Konami games
Category:Game Boy Color games
Category:PlayStation (console) games
Category:Falling block puzzle games
Category:CMX titles
Category:ADV Films
Category:Japanese high school television series
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Solid-state image sensors have found widespread use in camera systems. The solid-state imager sensors in some camera systems are composed of a matrix of photosensitive elements in series with switching and amplifying elements. The photosensitive sensitive elements may be, for example, photoreceptors, photo-diodes, phototransistors, charge-coupled device (CCD) gate, or alike. Each photosensitive element receives an image of a portion of a scene being imaged. A photosensitive element along with its accompanying electronics is called a picture element or pixel. The image obtaining photosensitive elements produce an electrical signal indicative of the light intensity of the image. The electrical signal of a photosensitive element is typically a current, which is proportional to the amount of electromagnetic radiation (light) falling onto that photosensitive element.
Of the image sensors implemented in a complementary metal-oxide-semiconductor (CMOS)- or MOS-technology, image sensors with passive pixels and image sensors with active pixels are distinguished. The difference between these two types of pixel structures is that an active pixel amplifies the charge that is collect on its photosensitive element. A passive pixel does not perform signal amplification and requires a charge sensitive amplifier that is not integrated in the pixel.
FIG. 1A illustrates one embodiment of a conventional pixel structure used within a synchronous shutter image sensor. A synchronous shutter image sensor is used to detect the signal of all the pixels within the array at (approximately) the same time. This is in contrast to an asynchronous shutter image sensor that may be implemented with a 3T (three transistor) or 4T (four transistor) pixel structure that does not include a sample and hold stage. Such an asynchronous shutter image sensor outputs the state of a pixel at the moment of read out. This gives movement artifacts because every pixel in the array is not sensing a scene at the same moment.
The pixel structure of FIG. 1A that is used in a synchronous shutter image sensor includes a light detecting stage and a sample and hold stage. The light detecting stage includes a photodiode, a reset transistor and a reset buffer (e.g., a unity gain amplifier). The sample and hold stage includes a sample transistor, one or more memory capacitors (represented by the capacitor C in FIG. 1A), a sample buffer and a multiplexer, i.e., switch or select transistor coupled to a column output of the pixel array.
FIG. 1B illustrates one conventional circuit configuration of the synchronous pixel of FIG. 1A. The reset transistor of the light detecting stage is used to reset the pixel to a high value, and then the voltage on the gate of the source follower transistor M1 starts dropping due to the photocurrent generated in the photodiode. The source follower transistor M1 operates as a unity gain amplifier to buffer the signal from the photodiode. The sample and hold (S&H) stage of FIG. 1B “sample” loads the voltage signal of source follower transistor M1, through the sample transistor, on the memory capacitor (Cmem). The voltage signal from the source follower transistor MI will remain on the memory capacitor when the sample transistor is turned off.
Before that, however, the switch, or pre-charge, transistor briefly unloads the Cmem capacitor. The voltage (Vmem) applied to the back plate of Cmem may be a fixed voltage, but in practice, a varying voltage for Vmem may help to shift the voltage on the memory node, so as to drive the source follower transistor M2 in a more suitable regime. A potential problem with the pixel structure illustrated in FIG. 1B is with respect to current leakage that may cause a loss of stored information. In particular, the sample capacitor Cmem charge may leak to ground (GND) through the pre-charge transistor. For the pixel shown in FIG. 1B, when the pre-charge transistor is off, this means that the gate of the pre-charge transistor is at logical “0” (e.g., GND) and the gate-source voltage (VGS) of the pre-charge transistor is zero. A CMOS process, utilizing metal-oxide-semiconductor field-effect-transistors (MOSFET), is typically used to implement pixel structures currently used in image sensors. With deep submicron CMOS technologies, the MOSFET drain current at VGS=0 is not really zero and, therefore, a significant current leakage (Ioff) can occur when the pre-charge transistor is off that results in the memorized voltage on the sample, or memory, capacitor Cmem leaking away. Such leakage current Ioff results in a loss of the stored information with even fA leakage potentially affecting the signal that is output to the column of the pixel array. As such, the pixel structure of FIG. 1B may not optimal for long (e.g., a fraction of a second or longer) memory times.
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Whole-body and local dosimetry in rats exposed to 2.45-GHz microwave radiation.
Rat cadavers oriented parallel to the electric field were exposed to 2.45-GHz microwave radiation. The weights of the cadavers ranged from approx. 5 to 320 g and their lengths ranged from approx. 5 to 21.5 cm. Whole-body specific absorption rates (SAR) were measured using calorimetric techniques, and local specific absorption rates were obtained from time-temperature profiles measured with a non-interacting thermistor probe (Vitek). The whole-body SARs decreased by a factor of 12 in rat pups weighing 5 g as compared to adult rats weighing 320 g. The local SARs in the colon were slightly higher than the whole-body SARs for animals in the weight range from 40 to 320 g and approx. 2.5 times higher in animals ranging from 10 to 30 g. The local SARs in the brain were two to three times higher than the whole-body SARs for animals ranging in weights from 20 to 320 g. The data show that it is important to measure both whole-body SARs and local SARs when conducting experiments to determine biological effects in order to adequately explain any biological changes and to extrapolate data from different sizes and species of animals.
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// Copyright (c) 2018-present, GM Cruise LLC
//
// This source code is licensed under the Apache License, Version 2.0,
// found in the LICENSE file in the root directory of this source tree.
// You may not use this file except in compliance with the License.
// #BEGIN EXAMPLE
import React from "react";
import Worldview, { Lines } from "regl-worldview";
// #BEGIN EDITABLE
function Example() {
const lines = [
{
pose: {
position: { x: 0, y: 0, z: 0 },
orientation: { x: 0, y: 0, z: 0, w: 0 },
},
scale: { x: 0.1, y: 0.1, z: 0.1 },
color: { r: 0, g: 1, b: 0, a: 1 },
points: [
{ x: 0, y: -3, z: 1 },
{ x: 1, y: -2, z: 1 },
{ x: 0, y: -3, z: 0 },
{ x: 1, y: -2, z: 0 },
{ x: 0, y: -3, z: 1 },
{ x: 1, y: -2, z: 1 },
{ x: 0, y: -3, z: 0 },
{ x: 1, y: -2, z: 0 },
],
// There are 8 points, so 4
poses: [
{
position: { x: 0, y: 0, z: 0 },
orientation: { x: 0, y: 0, z: 0, w: 0 },
},
{
position: { x: 0, y: 0, z: 0 },
orientation: { x: 0, y: 0, z: 0, w: 0 },
},
// shift the last two lines
{
position: { x: 2, y: 2, z: 0 },
orientation: { x: 0, y: 0, z: 0, w: 0 },
},
{
position: { x: 2, y: 2, z: 0 },
orientation: { x: 0, y: 0, z: 0, w: 0 },
},
],
colors: [],
},
];
return (
<Worldview defaultCameraState={{ distance: 10 }}>
<Lines>{lines}</Lines>
</Worldview>
);
}
// #END EXAMPLE
export default Example;
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Executive secretary of Venezuela's opposition Unified Democratic Panel (MUD) Ramón Guillermo Aveledo said early on Wednesday, one day ahead of the presidential swearing-in ceremony as provided for in the Constitution, that the opposition would resort to different domestic and foreign legal bodies to seek enforcement of the Constitution of Venezuela and the declaration of Hugo Chávez's temporary absence.
"The president is not here and the pertaining constitutional mechanism should be enforced. We will do anything, within the limits of freedom, civility, patriotism, and pacific and democratic struggle. We will do our best as citizens to defend the Constitution," Aveledo said when interviewed by private TV news channel Globovisión.
First, the opposition alliance plans to resort to the Venezuelan Supreme Tribunal of Justice (TSJ) to request annulment of the Congress' resolution approved on Tuesday, which authorizes Hugo Chávez to stay out of the Venezuela for an indefinite period while keeping his presidential powers.
"There is a regulation providing that temporary absences are valid for 180 days. This is a long term, yet they (pro-government deputies) have dismissed this regulation because of their interests and their internal rivalry, right inside the Government. This does not do any good to the country," the MUD's leader stressed.
Aveledo said that the opposition does not want to hold a vote tomorrow or that the president's powers are transferred to dissenters. Instead, the opposition seeks the declaration of Chávez's temporary absence. "Absence is a clear fact and while the president needs some time to recover and come back (to Venezuela), the Congress's speaker should take over."
The MUD's leader added that the opposition would also resort to international organizations such as the Organization of American States (OAS) and the Common Market of the South (Mercosur).
Twitter: @ocarinaespinoza
Translated by Jhean Cabrera
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share
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ADVERTISING SPACE
Dossier
Yamir Tovar (22) and Luis Fabián (21) were subjected by members of a ‘colectivo' (an armed pro-government gang) in the west Caracas neighborhood of Catia on February 20. Their bodies were found tied up and gagged; they were killed by headshots in execution style.
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The invention relates to methods and apparatus for inspecting in-service pipelines.
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Q:
How can i buid a query from a list using filters?
Let's say in some database i have People who has this attributes:
Name
Age
If i wanted to get all the people that are called Stuart or Steve i could use Q objects:
qs = People.objects.filter(Q(name='Stuart') | Q(name='Steve'))
But, what if i'm receiving a list of n names? Example:
['Bob, 'John','Rachel', 'Some other names that i don't know'...]
How could i build a query with those n unknown names on the list?
A:
the simple solution is to use standart filter __in=
name_list = ['Bob', 'John', 'Rachel']
qs = People.objects.filter(name__in=name_list)
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HOMESCHOOLERS: We have some very cool advertisers on this website, and as VegSource is supported by advertising, we're happy about that. If you can't see any ads, you might have an ad blocker, or a setting in your browser which blocks ads
from showing up. Consider turning on ads while on vegsource so that you can see what they have to offer, and so that this site can remain free.
Educational or Purely Entertaining VHS's and a few DVD's for Children & Family
Date:
April 12, 2014 at 12:00 am PST
I have lots of VHS videos and a DVD for children & family entertainment. All are in super condition. The cases may have some wear. All are very clean and smoke-free.
Everything I'm selling is clean, smoke free, and in great condition.
Each video is 50 cents. The DVD's are $1 to $4. I will weigh what you purchase to determine the shipping cost. I will accept a check, money order, or Paypal.
If you see anything you are interested in, please e-mail me directly at [email protected].
***I can send pictures.***
****ENTERTAINING****
1. 61* - DVD HBO Studios - Color - Dolby - Closed-captioned - 2001 - 108 minutes. This DVD is brand new, still factory wrapped, is clean, and odor free. Subtitles: English, Spanish, & French. "In the summer of 1961, Roger Maris and Mickey Mantle took on Babe Ruth's record - the 1927 single-season 60 home run slam. It would be a summer that no one would forget. Mickey Mantle is a Yankee favorite. The natural heir to his predecessors Joe DiMaggio, Lou Gehrig, and Babe Ruth. Also at bat is a young Midwesterner, Roger Maris. Maris is Mantle's opposite in almost every way. Quiet and soft-spoken, he doesn't add up to everything a sports legend should be. As the summer of 1961 unfolds, both Maris and Mantle find themselves approaching Babe Ruth's benchmark of 60 home runs. Facing mounting pressure from the media and the stands, they both know there's only room for one winner. The people make their choice known. But the people's favorite isn't the favorite to win." *****NOW $3.00*****________________________________________
2. CALL OF THE WILD - VHS Sterling Entertainment - Color - 1995 - 105 minutes. "Academy Award winner Charlton Heston heads north into the Klondike in Jack London's epic story of gold fever, romance, and adventure. Heston stars as Thorton, a US Mail carrier who must make an impossible 600 mile journey through the bitter Yukon wilderness to the Alaskan town of Dawson. After arriving in the town, Thorton gets caught up in Dawson's gold rush frenzy and sets out to find his fortune. Together with his sled dog Buck, Thorton begins an unrelenting search for riches in the icy rivers of Alaska. Follow Thorton and Buck in their perilous quest for gold as they hear the Call of the Wild!"
3. LITTLE WOMEN - DVD Columbia Pictures - closed-captioned - digitally mastered - widescreen - PG - 118 minutes. Subtitles: English, Spanish, Portuguese, Georgian, Chinese, & Thai. Dubbed: Spanish & Portuguese. This DVD is like new. It's clean and free of any odors. Winona Rider and Susan Sarandon star in this is family favorite movie. It's a stirring look at life in New England during the Civil War. With her husband off at war, Marmee (Sarandon) is left alone to raise their four daughters, her Little Women. There is the spirited Jo (Ryder); conservative Meg (Trini Alvarado); fragile Beth (Claire Danes); and romantic Amy (played at different ages by Kristen Dunst and Samantha Mathis). As the years pass, the sisters share some of the most cherished and painful memories of self-discovery, as Marmee and Aunt March (Mary Wickes) guide them through issues of independence, romance and virtue. Gabriel Byrne, Eric Stoltz, and Christian Bale co-star in this "handcrafted valentine." *****NOW $3.00*****
4. MARCH OF THE WOODEN SOLDIERS - VHS Goodtimes Home Video - Color - 78 minutes - 1991. "Few films in history achieve the rank of a beloved family classic, enjoyed anew by each succeeding generation. This video is based on Victor Herbert's famed 1903 operetta, Babes in Toyland. It is a timeless masterpiece. The greatest comedy team in films, Stan Laurel and Oliver Hardy, star in this elaborate musical fairy tale of innocence and optimism, now seen as never before in gorgeous, vibrant color. The boys are Stannie Dum and Ollie Dee, hapless employees of Toyland's toy factory who room in Old Mother Peep's shoe. Faced with eviction by the evil Silas Barnaby, Mother Peep needs to raise her mortgage, but the boys' plan to get the money from the toymaker goes awry. A spectacular entertainment with familiar music, high production values and charming performances by the much loved Laurel and Hardy. This is one of the truly great movies of all time."
5. THE PIED PIPER OF HAMLIN - DVD Digiview Productions - stereo Sound - Color - 2004 - 90 minutes. This DVD is in great shape. It has some mild scratches, but they don't affect the performance. The Pied Piper Of Hamelin' (1956) is a family treat for all ages and for all holidays. First filmed in color as a Hallmark TV special, it is a masterful, musical re-telling of the legendary fairy tale using the beautiful, mysterious music of Edward Grieg with new lyrics.
The cast is first-rate, with movie great Van Johnson brilliantly playing the strange and often frightening piper, as well as the kind school teacher Trueson, who is also the village conscience. Legendary movie villain Claude Rains is absolutely wonderful as the clever, sneering, and corrupt lord mayor of Hamelin. Jim Backus also appears as the King's messenger.
One highlight of the film is Van Johnson as the Pied Piper leading the rats out of Hamelin to their deaths in the river. He is playing on his pipe the haunting melody of 'In The Hall Of The Mountain King' from Mr. Grieg's 'Peter Guint Suite' as the cleverly animated rats march to oblivion!
Unlike the fairy tale, this 'Pied Piper Of Hamelin' has a happy ending with a lesson for everyone about greed, selfishness, and false pride. ******NOW $1.00*****
6. ROAD TO BALI - DVD Treasure Box Collection - Digitally Remastered - Color - 91 minutes. This CD is housed in a cardboard jacket that came with the CD. "In the only color "road" film Bob Hope and Bing Crosby ever made, the vaudeville duo this time find themselves in a tropical island adventure. While trying to avoid several unwanted marriage proposals in Melbourne, song-and-dance men Harold Bridley and George Cochran sign on as deep-sea divers headed for Bali. On the way, they are hired by the prince of the idyllic paradise to recover a sunken treasure. After the chest of priceless jewels is retrieved, Gridley and Cochran soon discover the prince is less than trustworthy and will stop at nothing to get his hands on the prize. Meanwhile, the two men meet the beautiful Princess Lala who has vowed to stop the Prince's evil plot. As they vie for the lovely Lala's affection, the slapstick team must rescue her from danger and steal back the treasure from the greedy Prince!" *****NOW $2.00*****
8. SHANE - VHS Paramount Pictures - 117 minutes - Color - Not rated - 1953. Starring Alan Ladd. “The story brings Alan Ladd, a drifter and retired gunfighter, to the assistance of a homestead family terrorized by a wealthy cattleman and his hired gun (Jack Palance). In fighting the last decisive battle, Shane sees the end of his own way of life. Mysterious, moody and atmospheric, the film is enhanced by the intense performances of its splendid cast.”
9. WHITE FANG TO THE RESCUE - VHS UAV Entertainment - Color - 98 minutes - doesn't indicate a rating. This video is new and still factory sealed. There is a split in the plastic along the bottom edge, but it's very apparent that the video could not have been removed through this small opening. This live-action movie is based on Jack London's Classic Tale. "When his master is killed in an ambush, White Fang hits the trail to revenge. The path leads him to a nearby city and a joyful reunion with his master's long lost son, Kim. Meanwhile, the murderers discover that Kim's father owned a prosperous gold mine and stake their claim in the fortune by kidnapping the young boy. Follow the action as White Fang comes to the rescue to free his new friend and avenge his master's death!
****EDUCATIONAL****
10. BIRD: SEE THE WORLD AS NEVER BEFORE - VHSby Eyewitness Video Series - narrated by Martin Sheen - 35 minutes - 1994 - Closed Caption, "Based on the revolutionary book series (21 million copies sold), Eyewitness video is the ultimate guide to natural history. Journey into a three-dimensional "virtual museum" where live-action photography creates the sensation of being inside the picture. State-of-the-art special effects and stunning graphics bring the natural world to life. Soar through the sky and around the world in this exciting journey from the bird's distant dinosaur past to its present astonishing variety. Look close-up at the staggering range of sizes, shapes, and habitats of these feathered creatures, and experience the miracle of flight."
12. THE FUNDAMENTALS OF IN-LINE SKATING - VHSby Variflex - 1999. Teaches you the use of proper equipment, basic skills, skater safety, rules of the road, and developing skills and building confidence. The video is still sealed in plastic.
13. MARTY STOUFFER'S WILD AMERICA: THE BEAUTY OF BUTTERFLIES - VHS by King World Direct - Color - 30 minutes - 1994. "Few of Nature's creations delight us more than the delicate, fluttering Butterfly. Come along as we explore their lives, meet the awesome variety of species and follow the Monarch Butterfly's thousand-mile trek to its wintering colonies. View the stages of the butterfly, especially the emerging butterfly. This exclusive home video presents a dazzling closeup look at The Beauty of Butterflies."
14. MARTY STOUFFER'S WILD AMERICA: PRECIOUS MOMENTS - VHSby King World Direct - Color - 58 minutes - 1995. "Ultimate joy is a wobbly young creature at play and definitive drama is a determined mother protecting it from danger. Share this magical time as we journey into the enchanting world of wild babies. Watch as Bear cubs roll and wrestle. Deer fawns dart and dodge, and fox kits flip and flop. Laugh at their playful antics and cheer at their narrow escapes! This exclusive home video represents the life work of America's premier naturalist Marty Stouffer. Marty Stouffer has spent over 25 years capturing America's rich natural heritage of wildlife and her magnificent wilderness on film."
****CHRISTIAN****
15. DAVID PENDLETON LIVE IN CONCERT: MAKING YOU BELIEVE ANYTHING CAN TALK - DVD a Revel Arts Production - Color - Dolby Digital - 2004 - 82 minutes. This DVD is like new. "David Pendleton is one of the nation's premiere ventriloquists. A 20-year veteran entertainer, David's humor and stellar technique keeps audiences laughing from start to finish. He brings to his show a wide range of comedic characters. Throughout all his high-energy entertainment, David mixes in humorous truths of God's plan for our lives. As comedy delights your heart, let the truths that are communicated change your life! Bonus comedy tracks by John Branyan & Rick Nielsen"
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Q:
Javascript library for BlackBerry
I'm currently starting in the web mobile development along with come trench brothers. I've done some things for iPhone and Android using jQuery and JQTouch. Recently we've been playing with the idea to also support BlackBerry devices to an application we are developing (which promises a lot of rework). Our initial tests with the BlackBerry simulators were a disaster... practically nothing works as expected (styles, jQuery ui components, etc..). So we believe jQtouch ended not being the silver bullet for this job (wierd huh? =P ).
We are now looking for a jQtouch-like library for BlackBerry's older models (Bold, Curve, Storm, Storm2... Torch has a Webkit implementation so it works like a charm).
Any ideas?
Update: ----
Im currently working with XUI which is the only option I have found for OS4.6 and 5. Its really light weight and wraps up some issues nicely. I'm only concerned on the poor documentation it has and the fact that there are almost no extensions/plugins so you basically need to create the UI components you require from scratch (which sucks big time).
A:
None exist for the older OS before 6.0.
Only basic Javascript and CSS work, like version 2.0.
The old browser was terrible, more like IE(I would even say worst) you see my point.
jQuery mobile will probably support it in a near future : http://jquerymobile.com/gbs/
So, stick to basic mobile web site for the BlackBerry older than 6.0.
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The columnar organization of the neocortex.
The modular organization of nervous systems is a widely documented principle of design for both vertebrate and invertebrate brains of which the columnar organization of the neocortex is an example. The classical cytoarchitectural areas of the neocortex are composed of smaller units, local neural circuits repeated iteratively within each area. Modules may vary in cell type and number, in internal and external connectivity, and in mode of neuronal processing between different large entities; within any single large entity they have a basic similarity of internal design and operation. Modules are most commonly grouped into entities by sets of dominating external connections. This unifying factor is most obvious for the heterotypical sensory and motor areas of the neocortex. Columnar defining factors in homotypical areas are generated, in part, within the cortex itself. The set of all modules composing such an entity may be fractionated into different modular subsets by different extrinsic connections. Linkages between them and subsets in other large entities form distributed systems. The neighborhood relations between connected subsets of modules in different entities result in nested distributed systems that serve distributed functions. A cortical area defined in classical cytoarchitectural terms may belong to more than one and sometimes to several distributed systems. Columns in cytoarchitectural areas located at some distance from one another, but with some common properties, may be linked by long-range, intracortical connections.
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Q:
Ubuntu 12.04 Freezes
Hello I recently moved from windows to ubuntu 12.04 64Bit
My system freezes up when I open up the file manager or Intellij IDEA, or randomly on all kind of "heavy" operations.
This did not occur on windows so I do not think it's a hardware problem.
I've read that this may be the cause of nvidia drivers, but I tried following several guides on how to update my nvidia drivers but to no avail (I have a nvidia 9600gt)
I have now tty mode while freezing, I saw a lot of Nouveau errors, so I'm pretty sure this is my problem, how can I fix this ?
A:
Problem: System will freeze and show graphical glitches ever so often.
Reason: My graphic card is not suitable for the open source Nouveau drivers.
Solution:
Download the correct driver for your card via Nvidia site (Mine was 340 for 9600GT)
sudo gedit /etc/modprobe.d/blacklist.conf and add the line blacklist nouveau to the end of the file.
Reboot your system.
Enter tty (Ctrl+Alt+F1)
Type sudo service lightdm stop (this will close your desktop)
Give permissions to the nvidia driver like so: sudo chmod +x NVIDIA-Linux-x86_64-340.58.run
Run the file like so : sudo ./NVIDIA-Linux-x86_64-340.58.run and follow instructions.
After all is done and well type sudo service lightdm start
Go back to desktop (ctrl+alt+F7)
|
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<p>The <tt class="xref docutils literal"><span class="pre">GeoExt.data</span></tt> module contains classes that extend map related
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The surgical treatment of anal incontinence.
This study is review of 31 patients undergoing surgery for anal incontinence. Three groups of patients are defined--those with incontinence due to trauma (nine patients), to a combination of trauma and degeneration (five patients), and to degeneration alone (17 patients). Two surgical techniques were used--either a direct repair of the anal sphincter or a postanal repair of the levator ani muscles and external sphincter (Parks operation). In the trauma group and the combined group the more common method used was a direct repair (ten patients)--five underwent a Parks operation. In the degeneration group all but one patient underwent a Parks operation. A defunctioning proximal colostomy was carried out in only four patients--all with incontinence due to trauma. Satisfactory continence was restored in 80% of these patients. Although this is a small series, the results are considered worthwhile and greater awareness and use of the above technique is recommended.
|
Q:
How to use Variables in Functions
How do I achieve getting userID in
obj.userID = mystring;
to be let userID = somerandomID?
I'm trying to add objects into JSON files using the fs module in nodejs. Here is the full code
'use strict';
var obj = require('./Referral/log.json');
const fs = require('fs');
let userID = `somerandomID`
fs.readFile('./Referral/log.json', (err, data) => {
if (err) throw err;
var mystring = `O54G9egD`;
obj.userID = mystring;
var config = JSON.parse(data);
fs.writeFile('./Referral/log.json', JSON.stringify(obj), function (err) {
console.log(`Added Referral code to log.`);
});
});
I'm probably using the worst way to make amendments to my JSON file, so any better solution would be greatly appreciated.
JSON file :
{"MrMinister":"bS1N793vTS","userID":"O54G9egD"}
A:
Try using obj[userID] instead of obj.userID
|
{
"parent": "item/generated",
"textures": {
"layer0": "thebetweenlands:items/ancient_leggings_green_gem"
}
}
|
)/(-2*sqrt(8)) + 5.
-5*sqrt(11)/2 + 6
Simplify (4 + 3*(4 + -4*(sqrt(128) + (sqrt(128) - (-1 + sqrt(128))))) + -5)**2.
192*sqrt(2) + 18433
Simplify (-5 + -2 + sqrt(539) + (sqrt(539)*1 - sqrt(539)) + -6*(0 + sqrt(539)) + sqrt(539) + 2)**2.
280*sqrt(11) + 8649
Simplify ((sqrt(2448) + (sqrt(2448) - (-1 + sqrt(2448))*3 - sqrt(2448)))*-6)**2 - (2 + (1*(sqrt(17) - -1*sqrt(612)))**2).
-5184*sqrt(17) + 352001
Simplify -2 + -4*sqrt(91)/sqrt(7)*1 + 3.
-4*sqrt(13) + 1
Simplify ((sqrt(132) + sqrt(132)*-1)*4*1)/((sqrt(588) + 2*sqrt(588))*3)*1.
0
Simplify 1*(5*(sqrt(539) + (-4*(sqrt(539) - (sqrt(539) + 0)) + sqrt(539) - sqrt(539)))*-4)**2.
215600
Simplify (sqrt(2205)*1)/(2*sqrt(441)).
sqrt(5)/2
Simplify 2*((sqrt(126) - sqrt(126)*-1)/sqrt(6))/(5*sqrt(7)*4).
sqrt(3)/5
Simplify (-5*sqrt(432) - sqrt(432) - sqrt(432))/((sqrt(224)/sqrt(8))/sqrt(7)).
-42*sqrt(3)
Simplify -2*(5 + (6*sqrt(7)*-2 - sqrt(7))) + ((-1*sqrt(126))/sqrt(2))/sqrt(9)*3.
-10 + 23*sqrt(7)
Simplify (-4*(sqrt(108) + -2*sqrt(108) - sqrt(108))*2 + -4)**2.
-768*sqrt(3) + 27664
Simplify ((sqrt(117) + (-1*sqrt(117) - sqrt(117))*-2 - (sqrt(117) + 2*sqrt(117)*6))/(sqrt(729) + 2*(sqrt(729) - -2*sqrt(729) - sqrt(729))))**2.
832/2025
Simplify sqrt(252)*2*5 - (sqrt(77) - sqrt(77)*2*-4)/sqrt(11).
51*sqrt(7)
Simplify ((3*(sqrt(28)*-4 + sqrt(28)))/(sqrt(4) - 3*sqrt(100)))**2.
81/28
Simplify (-1*(1*sqrt(231))/sqrt(7))/(sqrt(1584)*-2*1).
sqrt(3)/24
Simplify (-1*(0 + sqrt(1100) - sqrt(1100)) + sqrt(1100))**2 + 2*(sqrt(1100) + 2 + sqrt(1100) - sqrt(1100)).
20*sqrt(11) + 1104
Simplify ((1*sqrt(2299) + sqrt(2299))**2 + -4)*-1 + -3 + -1*sqrt(2299) + -2 + 4.
-9193 - 11*sqrt(19)
Simplify -5*(4 + -4 + -1*sqrt(448) + 5 + 1*sqrt(448))**2.
-125
Simplify (5 + (4*-5*sqrt(847) - (-5 + 0 + sqrt(847))))**2.
-4620*sqrt(7) + 373627
Simplify (4 + 4 + sqrt(72) + sqrt(72)*-2 + 4 + (2*sqrt(72)*4)**2)*-1.
-4620 + 6*sqrt(2)
Simplify (2*(sqrt(252) - 3*sqrt(252))/sqrt(7))/(sqrt(72)/(-3*sqrt(6)*3)).
36*sqrt(3)
Simplify (((sqrt(119) + sqrt(119)*-2)*2*2)/(((-1*sqrt(70))/sqrt(2))/sqrt(5)))**2.
272
Simplify (0 + -1 + 4 + (sqrt(275) - (-3 + sqrt(275) - sqrt(275))))**2.
60*sqrt(11) + 311
Simplify (sqrt(20) - 5*(sqrt(20) - (sqrt(20) - (sqrt(80)/sqrt(4) + sqrt(20)))))/(sqrt(324) + sqrt(324)*1)*6.
-3*sqrt(5)
Simplify -4 + (1*(sqrt(99) + sqrt(99) + 1*sqrt(99)))/(sqrt(324)*-3).
-4 - sqrt(11)/6
Simplify (sqrt(33)/((2*sqrt(3) - sqrt(3))*-2) + -3)*-3.
3*sqrt(11)/2 + 9
Simplify ((2*sqrt(187)*4 - sqrt(187) - sqrt(187))*2)/(2*sqrt(22)/(sqrt(4)/sqrt(2))).
6*sqrt(17)
Simplify (sqrt(65) + sqrt(65) + sqrt(65)*-2*6 + sqrt(65))/(2*sqrt(500)) + (2*sqrt(13)*4 - ((sqrt(26)/(sqrt(2)*1))**2 - sqrt(13)))*4.
-52 + 711*sqrt(13)/20
Simplify 3 + sqrt(11) + sqrt(77)/sqrt(7)*-3 + (-3*sqrt(11)*-3)**2.
-2*sqrt(11) + 894
Simplify 3*(-2 + sqrt(637)*-1)**2 + (1*sqrt(91)*-1)/(-1*sqrt(63)).
253*sqrt(13)/3 + 1923
Simplify (sqrt(308)/sqrt(7) + ((sqrt(11) + 0)*6 - sqrt(11)) + 0)*-3 + -3.
-21*sqrt(11) - 3
Simplify -3 + 5*(-3*(sqrt(208) + -3 + sqrt(208)))**2*-3.
-113538 + 6480*sqrt(13)
Simplify (sqrt(119) + -4*sqrt(119)*1)/(1*(sqrt(7) - sqrt(700))).
sqrt(17)/3
Simplify (-4 + sqrt(468) + -1 + (sqrt(468) + (2 + (2*sqrt(468) - sqrt(468)) + sqrt(468) + sqrt(468) - sqrt(468)) + sqrt(468))**2)*-4.
-29948 - 408*sqrt(13)
Simplify (sqrt(1088)*-2 + -3 - (0 + sqrt(1088) - sqrt(1088))*5 - -5*(sqrt(1088) + (sqrt(1088) - 4*(0 + sqrt(1088) + sqrt(1088)))))**2.
1536*sqrt(17) + 1114121
Simplify -1*(-4*4*(3*(sqrt(147) - (-3 + sqrt(147))) - sqrt(147)))**2.
-58368 + 32256*sqrt(3)
Simplify -6*((-2 + 1*sqrt(17) + 3 + 1 + sqrt(17))*2 + -5).
-24*sqrt(17) + 6
Simplify 2 + (sqrt(224)*2)/((sqrt(600) + sqrt(24))/sqrt(3)).
2*sqrt(7)/3 + 2
Simplify (sqrt(5) + 1 + 3 - (sqrt(405) + 2 + sqrt(5)) - ((sqrt(1470) + sqrt(30))/sqrt(6) - ((-1 + sqrt(5))*2 - sqrt(5))))**2.
1280
Simplify (-3*(sqrt(320)*-1 + sqrt(320)))**2 - (-1*-2*sqrt(720))**2.
-2880
Simplify -1 + (2*sqrt(76)/(3*sqrt(4)) - (3 + 2 + sqrt(19) - (0 + sqrt(171)))**2).
-102 + 62*sqrt(19)/3
Simplify (-4*(5 + sqrt(288) + -2 + sqrt(450)*-1))**2.
-288*sqrt(2) + 432
Simplify (-1 + sqrt(112) - (3 + sqrt(63)) - (1 + sqrt(21)/(sqrt(12)/sqrt(4)))) + -2.
-7
Simplify 2 + sqrt(8)/(4*sqrt(36)) + -5*(2*sqrt(8))/sqrt(4) + 3.
-119*sqrt(2)/12 + 5
Simplify (5*1*sqrt(98) + (0 + sqrt(98))*-5 - (-2 + -4*(1 + sqrt(98))))**2.
336*sqrt(2) + 1604
Simplify (2 + (1*sqrt(243) + sqrt(3))*-6)*4.
-240*sqrt(3) + 8
Simplify ((0 + sqrt(13))*3*5)**2 - (-6*(2 + sqrt(13))*-4)**2.
-2304*sqrt(13) - 6867
Simplify (sqrt(425) + 0 + 3)**2 + -5 + 4.
30*sqrt(17) + 433
Simplify (-2*sqrt(768)*4)/(-4*(sqrt(6) - sqrt(96)*-1)).
16*sqrt(2)/5
Simplify -5*(-4*(sqrt(20) + (sqrt(20) - (sqrt(20) + sqrt(2000)))))**2*2.
-259200
Simplify ((-5*(-2*sqrt(35) - sqrt(35))*-4)/((-2*sqrt(140)/sqrt(4))/sqrt(7)))**2.
6300
Simplify (-3*(-2 + 0 + -1*(0 + sqrt(612) + -2*sqrt(612))))**2.
-216*sqrt(17) + 5544
Simplify sqrt(22)/((sqrt(11) + (sqrt(11)*-3 - sqrt(11)))*5) - (-3 + 1*(sqrt(12)/sqrt(6) + sqrt(2))).
-31*sqrt(2)/15 + 3
Simplify ((-6*sqrt(832))/(sqrt(16)/sqrt(16)) + 5)**2.
-480*sqrt(13) + 29977
Simplify ((-1 + sqrt(1539) + sqrt(1539))*-3 + 2)*-1.
-5 + 54*sqrt(19)
Simplify 4 + ((sqrt(7056)*2 + sqrt(7056))*3 + sqrt(7056))/(-4*sqrt(567)*-1).
4 + 10*sqrt(7)/3
Simplify (-5*(-4*(sqrt(1029) + sqrt(1029)*-1))/(5*-4*2*sqrt(7)))**2.
0
Simplify 6*(sqrt(50))**2 + (sqrt(2) + -1 + -2 - sqrt(2))**2 - (4*(sqrt(162) + -1)**2 + sqrt(162)).
-343 + 63*sqrt(2)
Simplify 5 + (((-2*sqrt(330)*-1)/sqrt(11))/(sqrt(90)/((sqrt(144)/sqrt(4))/sqrt(4))))**2.
17
Simplify -5*(sqrt(175) + sqrt(175) + 5*2*sqrt(175))*-3*-5.
-4500*sqrt(7)
Simplify (sqrt(10) - sqrt(80)/sqrt(32) - sqrt(50)/(sqrt(20)/sqrt(4)))/(sqrt(242)*-2 - sqrt(8)/(sqrt(12)/sqrt(3))).
sqrt(5)/46
Simplify (-1 + 2*(2 + (sqrt(847)*-2 - sqrt(847)) + sqrt(847))*-1)**2.
-440*sqrt(7) + 13577
Simplify ((sqrt(245)*-1)**2 - (sqrt(360) + sqrt(40) - sqrt(40))/sqrt(8))*-3 - (1 + 3 + sqrt(20))*4.
-751 + sqrt(5)
Simplify (5*1*sqrt(70) - sqrt(70)*1*-6)/((sqrt(70)*2)/sqrt(7)*-3).
-11*sqrt(7)/6
Simplify ((sqrt(252)*2 + sqrt(252) + sqrt(252))*1)/((sqrt(108)/sqrt(4))/sqrt(3))*2.
16*sqrt(7)
Simplify -1 + sqrt(13) + -3*(sqrt(1573))**2 + (sqrt(13) + -4)**2 + 1.
-4690 - 7*sqrt(13)
Simplify ((4*-2*sqrt(209)*2)/(sqrt(121)/(sqrt(55)/sqrt(5)) + (sqrt(11) - sqrt(396)*-2)))**2.
1216/49
Simplify 5*(1 + sqrt(612) + -5 + -4)**2.
-480*sqrt(17) + 3380
Simplify -3 + -6*(2 + sqrt(52)*1)*-3 + 2.
35 + 36*sqrt(13)
Simplify -4 + -2 + (-5 + (sqrt(242) - (sqrt(242) + -5 + (sqrt(242) - (sqrt(242) + 1)))))**2 + -1.
-6
Simplify -5 + -2 + (sqrt(108) + 2 + 0)*-3 + 4.
-18*sqrt(3) - 9
Simplify 5 + (5*sqrt(360))/sqrt(8) - ((sqrt(8640) + sqrt(8640)*2 + sqrt(8640))/sqrt(12))**2*6.
-69115 + 15*sqrt(5)
Simplify 5 + (-5*sqrt(175)*1 + 5)**2 + -2.
-250*sqrt(7) + 4403
Simplify (sqrt(117) - (sqrt(117)*2 - sqrt(117)))/sqrt(9)*-5 - ((sqrt(117) + sqrt(13) + 2)**2 + sqrt(52) + -2).
-210 - 18*sqrt(13)
Simplify ((-6*(2*sqrt(270))/sqrt(6))/(-6*sqrt(72)/sqrt(2))*5)**2.
125
Simplify (3*sqrt(42)*-2 + 6*sqrt(672) + sqrt(42))/(-1*sqrt(96) + sqrt(96) + sqrt(726) + (sqrt(726)*-2 - sqrt(726) - sqrt(726))).
-19*sqrt(7)/33
Simplify 0 + 1 + sqrt(6)/sqrt(2) + (sqrt(108)/sqrt(6))/sqrt(6).
1 + 2*sqrt(3)
Simplify sqrt(136)/(-1*sqrt(8)) + sqrt(51)/sqrt(3) + 2 - sqrt(187)/(sqrt(396)*1).
-sqrt(17)/6 + 2
Simplify (4*(-2*sqrt(1573) - sqrt(1573)))**2 + (sqrt(78)*-2*1)/sqrt(6).
-2*sqrt(13) + 226512
Simplify -1 + (sqrt(57)/sqrt(3) - sqrt(19))*-5 + sqrt(190)/(sqrt(20)/sqrt(2)).
-1 + sqrt(19)
Simplify (6*(-5 + (sqrt(396) - (2 + sqrt(396) + -1) - sqrt(396))))**2.
2592*sqrt(11) + 15552
Simplify (-5*((sqrt(1100) - (2 + sqrt(1100) - sqrt(1100) - sqrt(1100))) + sqrt(1100))*5 - (5*(sqrt(1100) + -1) - (2*sqrt(1100) + -3 - sqrt(1100))))**2.
-82160*sqrt(11) + 6867804
Simplify ((sqrt(152) - sqrt(152)*-1 - sqrt(152)) + -1*sqrt(38)*2)/(-4*sqrt(2)*-1*1).
0
Simplify -3*((-4 + (sqrt(66) + (sqrt(66) - (sqrt(66)*2*5 - sqrt(66) - sqrt(66))))/sqrt(6) + -1)*-6)**2.
-45468 - 6480*sqrt(11)
Simplify ((3*(sqrt(1300) + -1*sqrt(1300) + sqrt(1300) + sqrt(1300)) - (sqrt(1300) + -1 + -1)) + 4 + 0)**2*6.
3600*sqrt(13) + 195216
Simplify ((sqrt(32)*1)/(sqrt(36)*-4))**2*-3.
-1/6
Simplify ((sqrt(320) - sqrt(320)*-2)*-4*4 + (sqrt(80) + 2 - ((sqrt(5) - sqrt(5)*-1) + -2)))**2.
-3056*sqrt(5) + 729636
Simplify (0 + 0 + sq
|
/*
* $Id$
*
* SARL is an general-purpose agent programming language.
* More details on http://www.sarl.io
*
* Copyright (C) 2014-2020 the original authors or authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package io.sarl.docs.doclet.proxy;
import java.lang.ref.WeakReference;
import java.lang.reflect.Array;
import java.lang.reflect.InvocationHandler;
import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;
import java.lang.reflect.Proxy;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import com.sun.javadoc.AnnotationTypeDoc;
import com.sun.javadoc.Doc;
import com.sun.javadoc.ProgramElementDoc;
import com.sun.javadoc.RootDoc;
import io.sarl.docs.doclet.SarlConfiguration;
import io.sarl.docs.doclet.exclude.ApidocExcluder;
/** Install the proxies for the {@code Doc}.
* This object is filtering the arrays that are replied functions in {@link RootDoc} or {@link ProgramElementDoc}.
*
* @author $Author: sgalland$
* @version $FullVersion$
* @mavengroupid $GroupId$
* @mavenartifactid $ArtifactId$
* @since 0.7
*/
public class JreProxyInstaller implements ProxyInstaller {
/** List of the functions' names that are not accepting a proxy as argument.
*/
private static final String[] SINGLE_ARGUMENT_UNPROTECTED_FUNCTION_NAMES = {
"compareTo", //$NON-NLS-1$
"equals", //$NON-NLS-1$
"overrides", //$NON-NLS-1$
"subclassOf", //$NON-NLS-1$
};
/** List of the functions' names that are not accepting a proxy as argument.
*/
static final Set<String> SINGLE_ARGUMENT_UNPROTECTED_FUNCTIONS = new HashSet<>(
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|
This script is used to remove the restart option from all policies in a specified category via the Jamf API.
Script is adapted from `purgeAllPoliciesInCategory.bash` by [Jeffrey Compton](https://twitter.com/igeekjsc)
Link: [https://github.com/igeekjsc/JSSAPIScripts/blob/master/purgeAllPoliciesInCategory.bash](https://github.com/igeekjsc/JSSAPIScripts/blob/master/purgeAllPoliciesInCategory.bash)
|
Washington (CNN) Travel restrictions, orders to stay home, TSA officers testing positive for coronavirus and public fear are killing demand for air travel, which could make a domestic travel ban under consideration by the Trump administration largely irrelevant.
The idea of grounding many or all domestic flights remains under consideration at the White House, where the administration's coronavirus task force is looking for ways to prevent people from congregating and spreading the virus.
The government's decision to restrict travel to China, South Korea, and much of Europe already brought a precipitous decline in airline service to overseas destinations.
Such a drastic move domestically could further cripple the nation's economy, and have negative effects such as preventing the flow of cargo, making it harder to ship medical supplies and other essential goods.
"Fauci is still pushing for it -- and maybe he's right," said one senior administration official, referring to Dr. Anthony Fauci of the National Institute of Allergy and Infectious Diseases, one of the most visible faces on the administration's task force. The NIAID did not immediately comment.
"We're not there yet. That doesn't mean never," the official continued. "But the President and a lot of us around him feel we should do everything we can to avoid it."
Dr. Deborah Birx, a member of the White House's coronavirus task force, said Thursday night on Fox News that President Donald Trump hadn't ruled out a federal shutdown.
"As President Trump has said from the beginning, everything is on the table. Every day we go over data, we review it and use science and data to drive policy and decision-making." Birx said.
A massive reduction in service is already happening before their eyes.
Last week triggered a "rapid deterioration" for airlines which led them to request financial relief from the government, explained an airlines source. Planes were flying 85-100% full pretty much across the board at the beginning of this year, and now they are closer to 50% full and in many cases much less, the official said. Airlines need planes to be about 65% full to break even and make the flight worth flying, the official added.
The topic of grounding all domestic flights was not raised in a call Trump held this week with the CEOs of major US airlines and air cargo carriers, according to a source familiar with the conversation.
Another person familiar with the discussions said the administration's coronavirus task force has not pressured airlines to completely shut down.
A 'virtual shutdown'
The airlines are parking hundreds of airplanes -- with American and Delta each parking around half their fleets -- and canceling flights en masse as travelers abandon their bookings faster than they make new reservations.
American said Thursday it plans to cancel 55,000 flights next month but warned it expects "demand to fall even more before it gets better."
The airlines do not plan to go to zero domestic flights, but it could "get pretty close to zero" so that it would be a "virtual shutdown," according to one of the industry sources.
One school of thought in the aviation industry: While there may not be a ban, per se, the economic conditions will likely continue to considerably limit the viability of operating domestic flights.
It's happening day by day, with airlines cutting capacity, and it's almost certain to continue.
The latest example came Thursday, when Minneapolis-based Compass Air, which operates flights on behalf of American and Delta, said it would cease to operate on April 7 because of falling demand in the wake of the coronavirus outbreak. Compass flies 6 million customers annually with an average of 280 departures per day to more than 40 destinations.
Feds to require flights on certain routes?
As airlines cut back, some within the industry believe that major routes will be mandated by the government, such as between Washington, DC and Los Angeles, according to an industry source.
That could lead to the elimination of service to smaller or mid-sized cities.
One of the possibilities, the industry source said, would be restricting flights to essential business travel only -- but airlines, at this point, are happy to take anyone who is healthy and willing to fly.
Airlines could also be forced to end service if the airports they fly in and out of stop operations.
On the heels of the airline industry's request for more than $50 billion in US government support, an industry group representing airports requested a $10 billion package from the government and warned it could default on bonds.
The Federal Aviation Administration told CNN it "does not permit airports that receive federal funds to shut down without agency approval."
Cargo needs
One of the factors keeping planes flying right now is the role that aviation plays in moving goods across the country.
"If airplanes don't fly, cargo doesn't fly," one administration official said. "We have to keep the transportation network up and running."
The International Air Transport Association, whose members include several US airlines, said this week it is urging governments around the world to "take urgent measures to ensure that air cargo will be available to support the global fight against COVID-19."
Sara Nelson, president of Association of Flight Attendants-CWA, told CNN a ban on domestic flights should be implemented only if health experts believe it truly necessary because "airlines provide the ability to move equipment and experts around."
Smooth air travel is necessary "in order to move goods and supplies in order to eradicate this," she said.
|
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---
abstract: 'A theoretical study is performed for the excitation of a single atom localized in the center of twisted light modes. Here we present the explicit dependence of excitation rates on critical parameters, such as the polarization of light, its orbital angular momentum projection, and the orientation of its propagation axis with respect to the atomic quantization axis. The effect of a spatial spread of the atom is also considered in detail. The expressions for transition rates obtained in this work can be used for any atom of arbitrary electronic configuration. For definiteness we apply them to the specific case of $^{2}S_{1/2} (F=0) \rightarrow\; ^{2}F_{7/2} (F=3, M=0)$ electric octupole (E3) transition in $^{171}$Yb$^{+}$ ion. Our analytical and numerical results are suitable for the analysis and planning of future experiments on the excitation of electric-dipole-forbidden transitions by twisted light modes in optical atomic clocks.'
author:
- 'S. A.-L. Schulz'
- 'A. A. Peshkov'
- 'R. A. Müller'
- 'R. Lange'
- 'N. Huntemann'
- 'Chr. Tamm'
- 'E. Peik'
- 'A. Surzhykov'
date: '\'
title: Generalized excitation of atomic multipole transitions by twisted light modes
---
\[sec:Introduction\] Introduction
=================================
Since the groundbreaking work of Allen *et al*. in 1992 [@Allen/PRA:1992], there has been growing interest in light beams with helical phase fronts. Such twisted (or vortex) beams have many attractive features which can be adapted to the needs of applications [@Yao/AOP:2011]. In particular, twisted photons carry a nonzero projection of the orbital angular momentum (OAM) onto the propagation direction and their intensity pattern has an annular character with an intensity minimum in the center [@Padgett/PT:2004]. These characteristic features make twisted light a valuable tool for various studies, ranging from the production of coherent superpositions of vortex states in Bose-Einstein condensates [@Kapale/PRL:2005] to the direct generation of twisted photons by ultrarelativistic electrons [@Chen/PRL:2018; @Bogdanov/PRD:2019] or intense vortex harmonics in a plasma [@Zhang/NJP:2016].
In recent years, much interest has been placed on the interaction of twisted light beams with single trapped atoms [@Surzhykov/PRA:2015; @Quinteiro/PRL:2017; @Schulz/PRA:2019]. A remarkable experiment by Schmiegelow and co-workers [@Schmiegelow/NC:2016] showed that if atoms are positioned near the low-intensity center of the beam, the twisted light can modify the selection rules and efficiently induce higher-order multipole transitions, in agreement with theoretical predictions [@Peshkov/PRA:2017; @Afanasev/NJP:2018]. These effects have been demonstrated on the electric quadrupole excitation of $^{40}$Ca$^{+}$ ions, resulting in characteristic population of magnetic sublevels. Moreover, the use of twisted light in this experiment has been shown to result in strong suppression of the AC-Stark shift in the dark beam center. This suppression together with the efficient excitation of non-dipole channels makes twisted light promising for studying and employing atomic clock transitions.
The application of twisted beams to the excitation of single trapped atoms requires a detailed theoretical analysis of the experimental geometry. A typical setup includes a trapped atom whose quantization axis is defined by an applied magnetic field. The atom interacts with a beam of light that is characterized by its polarization and propagation direction. Excitation rates are then strongly affected by the orientation of the atomic quantization axis relative to the propagation direction. Moreover, the strength of atomic transitions may be sensitive not only to the polarization state of the incident light, but also to the spatial spread of atomic position near the beam axis. As a first step towards analyzing such geometrical effects for perfectly localized atoms, recent work [@Solyanik-Gorgone/JOSAB:2019] considered a number of forbidden transitions induced by linearly polarized light.
In the present study, we lay down a general theoretical framework for any atom of arbitrary electronic configuration and for various polarization states of light. In addition, a realistic experimental scenario of atoms localized with a finite spatial spread is taken into account. Before discussing our approach for twisted light, in Sec. \[sec:plane\] we briefly recall the basic equations governing the excitation of atoms by conventional plane-wave radiation. Here we derive the rates for transitions between magnetic hyperfine sublevels and show that they are sensitive to the polarization of the light beam and to its orientation with respect to the atomic quantization axis. Later in Sec. \[sec:twisted\] we discuss the optical excitation by twisted light for the specific case of paraxial Bessel beams. General expressions are derived for the excitation of hyperfine transitions of a particular multipolarity by linearly, radially and azimuthally polarized beams. While the resulting formulas can be applied to an arbitrary atom or ion, in Sec. \[sec:results\] we consider the $^{2}S_{1/2} (F=0) \rightarrow\; ^{2}F_{7/2} (F=3)$ electric octupole (E3) transition in $^{171}$Yb$^{+}$, receiving much interest as a candidate for atomic clocks [@Godun/PRL:2014; @Sanner/N:2019]. Based on our calculations, we show that by choosing proper polarization states of incident twisted light, the transition rate can be significantly enhanced under certain orientations of the applied magnetic field when the atom is placed in the center of the beam. Similar enhancement can also be seen for the ion spatial spread of a few tens of nm. Sec. \[sec:summary\] provides concluding remarks.
Hartree atomic units ($\hbar = e = m_{e} =1,\; c=1/ \alpha$) are used throughout the paper.
\[sec:theory\]Theory
====================
\[sec:plane\]Excitation by plane-wave photons
---------------------------------------------
### \[sec:plane amplitude\]Transition amplitude
We begin by considering a single trapped atom exposed to a static magnetic field $\bm{B}$ determining the quantization $z_{\text{atom}}$ axis of the atom. Moreover, it is assumed that the atomic nucleus has nonzero spin $\bm{I}$, and hence atomic states $| \alpha F M \rangle$ are characterized by the total angular momentum $\bm{F} = \bm{I} + \bm{J}$, its projection $M$ on the atomic quantization axis, the total electron angular momentum $J$, and all additional quantum numbers $\alpha$. We focus on the atomic excitation process $| \alpha_{i} F_{i} M_{i} \rangle + \gamma \rightarrow | \alpha_{f} F_{f} M_{f} \rangle$ driven by a light field propagating at the angle $\theta$ with respect to the magnetic field. It is well known that all the properties of the excitation process can be traced back to the evaluation of the transition amplitude of the form [@Johnson:2007] $$\begin{aligned}
\label{eq:amp_pl_1}
\mathcal{M}_{M_f M_i}^{(\text{pl})} = \Bigg \langle \alpha_{f} F_{f} M_{f} \Bigg| \sum_{q} \bm{\alpha}_{q} \, \bm{A}_{\lambda}^{(\text{pl})} (\bm{r}_{q}) \Bigg| \alpha_{i} F_{i} M_{i} \Bigg \rangle \, .\end{aligned}$$ Here $q$ runs over all electrons in an atom, and $\bm{\alpha}_q$ denotes the vector of Dirac matrices for the $q$th particle. The incident field is assumed to be a circularly polarized plane wave with helicity $\lambda = \pm 1$. In the Coulomb gauge, the vector potential of this plane wave is given by $$\begin{aligned}
\label{eq:vec_pl_1}
\bm{A}_{\lambda}^{(\text{pl})} (\bm{r}) = \bm{e}_{\bm{k} \lambda} \, e^{i \bm{k} \bm{r}} \, ,\end{aligned}$$ with the polarization vector $\bm{e}_{\bm{k} \lambda}$ and frequency $\omega = kc$.
In order to evaluate the transition amplitude , it is convenient to use the multipole expansion of this vector potential $$\begin{aligned}
\label{eq:vec_pl_2}
\bm{e}_{\bm{k} \lambda} \, e^{i \bm{k} \bm{r}} =& \sqrt{2 \pi} \sum_{L M} \sum_{p = 0, 1} i^{L}[L]^{1/2} \, (i \lambda)^{p} \, \notag \\
&\times D^{L}_{M \lambda} (\phi_k, \theta_k, 0) \bm{a}^{p}_{L M} (\bm{r}) \, ,\end{aligned}$$ where $[L] = 2L + 1$ and $\bm{a}^{p}_{L M} (\bm{r})$ stands for magnetic $(p=0)$ or electric $(p=1)$ multipole components [@Rose:1957]. In addition, $D^{L}_{M \lambda}$ is the Wigner $D$-function which depends on the light propagation direction $\hat{\bm{k}} = \bm{k} / k = (\theta_k, \phi_k)$ with respect to the quantization $z$ axis of the entire system, $\theta_k$ and $\phi_k$ being the polar and azimuthal angles. For the further analysis, it is very important to choose this quantization axis in a convenient manner. When the light propagates not along the magnetic field, one can take either $\bm{B}$ or $\bm{k}$ vectors as the quantization $z$ axis of the entire system “atom $+$ light”. Although it is clear that the observables are independent of a particular choice of coordinate system, we choose here the light propagation ($z_{\text{light}}$) direction as the quantization $z$ axis, so that $\theta_k = \phi_k = 0^{\circ}$. This allows us to simplify Eq. by using the relation $D^{L}_{M \lambda} (0, 0, 0) = \delta_{M \lambda}$. On the other hand, we need to perform a rotation of the atomic states $| \alpha_{i} F_{i} M_{i} \rangle$ and $| \alpha_{f} F_{f} M_{f} \rangle$ originally defined in the coordinate system with the quantization $z_{\text{atom}}$ axis oriented along the magnetic field. Such a general transformation $$\begin{aligned}
\label{eq:rotation}
| \alpha F M \rangle_{\text{atom}} = \sum_{M'} d^{F}_{M' M} (\theta) | \alpha F M' \rangle_{\text{light}} \, \end{aligned}$$ can be performed by using the Wigner (small) $d$ functions [@Balashov:2000]. In this expression the state vector $| \alpha F M \rangle_{\text{atom}}$ describes the state quantized along the $z_{\text{atom}}$ axis, while $| \alpha F M' \rangle_{\text{light}}$ describes the state quantized along the $z_{\text{light}}$ axis. By using Eq. , we can rewrite the transition matrix element as $$\begin{aligned}
\label{eq:amp_pl_1p}
\mathcal{M}_{M_f M_i}^{(\text{pl})} =& \sum_{M'_i M'_f} d^{F_i}_{M'_i M_i} (\theta) d^{F_f}_{M'_f M_f} (\theta) \, \notag \\
&\times \Bigg \langle \alpha_{f} F_{f} M'_{f} \Bigg| \sum_{q} \bm{\alpha}_{q} \, \bm{A}_{\lambda}^{(\text{pl})} (\bm{r}_{q}) \Bigg| \alpha_{i} F_{i} M'_{i} \Bigg \rangle \, ,\end{aligned}$$ where all atomic and photonic states on the right-hand side are already defined with respect to the light quantization $z_{\text{light}}$ axis.
To proceed further, we assume that the electromagnetic field interacts only with atomic electrons and does not affect the nuclear spin. Therefore, it is natural to write the hyperfine wave functions $| \alpha F M' \rangle$ as a linear combination of the corresponding atomic $| \alpha J M'_J \rangle$ and nuclear $| I M'_I \rangle$ states [@Johnson:2007] $$\begin{aligned}
\label{eq:nuclear_atomic}
| \alpha F M' \rangle = \sum_{M'_J M'_I} \langle J M'_J, \, I M'_I | F M' \rangle | \alpha J M'_J \rangle | I M'_I \rangle \, .\end{aligned}$$ If we substitute this expression for the atomic states into Eq. and make use of the multipole expansion together with the Wigner-Eckart theorem, we find after some angular momentum algebra that the transition amplitude reduces to $$\begin{aligned}
\label{eq:amp_pl_2}
\mathcal{M}_{M_f M_i}^{(\text{pl})} =& \sum_{L p} C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} (p L) \,\, (i \lambda)^{p} \, \notag \\
&\times d^{L}_{\lambda \, \Delta M} (\theta) \, \langle F_i M_i, \, L \Delta M | F_f M_f \rangle \, ,\end{aligned}$$ where $\Delta M = M_f - M_i$ is the difference of the two angular momentum projections on $z_{\text{atom}}$ axis. Here the Clebsch-Gordan coefficients along with Wigner $d$ functions describe the geometry of the experiment, whereas the factors $C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} (p L)$ contain information about the coupling to a particular multipole of the electromagnetic field and are defined by $$\begin{aligned}
\label{eq:factor}
C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} &(p L) = \sqrt{2 \pi} \, i^{L} \, [L, F_{i}]^{1/2} \, (-1)^{J_{f} + I + F_{i} + L} \, \notag \\
&\times \left\{ \begin{array}{ccc}
F_f & F_i & L \\
J_i & J_f & I
\end{array} \right\}
\langle \alpha_f J_f || H_{\gamma} (pL) || \alpha_i J_i \rangle \, .\end{aligned}$$ Here, we have also introduced the following notation for the the reduced matrix element $$\begin{aligned}
\label{eq:reduced}
\langle \alpha_f J_f || H_{\gamma} (pL) || \alpha_i J_i \rangle = \Bigg \langle \alpha_{f} J_{f} \Bigg| \Bigg| \sum_{q} \bm{\alpha}_{q} \, \bm{a}_{L, q}^{p} \Bigg| \Bigg| \alpha_{i} J_{i} \Bigg \rangle \, ,\end{aligned}$$ which depends on the specific wave functions of the states.
As can be seen from Eq. , the transition amplitude includes a sum over all multipole $(p L)$ contributions. In atomic spectroscopy, however, we can usually restrict ourselves to only a leading multipole term allowed by the angular momentum and parity selection rules. Thus the transition matrix element is greatly simplified and can be written as $$\begin{aligned}
\label{eq:amp_pl_3}
\mathcal{M}_{M_f M_i}^{(\text{pl})} =& \, C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} (p L) \,\, (i \lambda)^{p} \, \notag \\
&\times d^{L}_{\lambda \, \Delta M} (\theta) \, \langle F_i M_i, \, L \Delta M | F_f M_f \rangle \, .\end{aligned}$$ This is a very good approximation for light neutral atoms or ions with small ionic charge of interest.
### \[sec:plane linear\]Transition rate for linearly polarized light
The formulas - were obtained for photons with definite helicity and therefore can be used to describe the excitation of atoms by circularly polarized light. However, it is also instructive to consider linearly polarized incident light. Along this way, we first need to construct the vector potential for linearly polarized radiation. For example, we can write a plane wave, which is linearly polarized parallel to the reaction $x$-$z$ plane defined by the vectors $\bm{k}$ and $\bm{B}$, as a superposition of the two circularly polarized waves according to $$\begin{aligned}
\label{eq:pl_h}
\bm{A}_{\parallel}^{(\text{pl})} (\bm{r}) = \frac{1}{\sqrt{2}} \left( \bm{A}_{\lambda = +1}^{(\text{pl})} + \bm{A}_{\lambda = -1}^{(\text{pl})} \right) = \bm{e}_{x} \, e^{i k z} \, .\end{aligned}$$ Similarly, a plane wave linearly polarized perpendicular to the reaction plane is defined by $$\begin{aligned}
\label{eq:pl_v}
\bm{A}_{\perp}^{(\text{pl})} (\bm{r}) = \frac{i}{\sqrt{2}} \left( \bm{A}_{\lambda = -1}^{(\text{pl})} - \bm{A}_{\lambda = +1}^{(\text{pl})} \right) = \bm{e}_{y} \, e^{i k z} \, .\end{aligned}$$ By using these formulas and the absolute-value-squared matrix elements , we can then introduce the normalized transition rates for absorption of parallel and perpendicular polarized plane-wave light $$\begin{aligned}
\label{eq:rate_pl_h}
&W_{\parallel}^{(\text{pl})} (\theta) \, \notag \\
&= \frac{N}{W^{(\text{pl})}_{\text{tot}}} \! \Bigg| \! \frac{1}{\sqrt{2}} \! \left[ \mathcal{M}_{M_f M_i}^{(\text{pl})} (\lambda \! = \! +1) + \mathcal{M}_{M_f M_i}^{(\text{pl})} (\lambda \! = \! -1) \right] \! \Bigg|^2 \, \notag \\
&= \frac{[L]}{8} \Big| i^{p} \, d^{L}_{+1 \, \Delta M} (\theta) + (-i)^{p} \, d^{L}_{-1 \, \Delta M} (\theta) \Big|^2 , \,\end{aligned}$$ and $$\begin{aligned}
\label{eq:rate_pl_v}
&W_{\perp}^{(\text{pl})} (\theta) \, \notag \\
&= \frac{N}{W^{(\text{pl})}_{\text{tot}}} \! \Bigg| \! \frac{i}{\sqrt{2}} \! \left[ \mathcal{M}_{M_f M_i}^{(\text{pl})} (\lambda \! = \! -1) - \mathcal{M}_{M_f M_i}^{(\text{pl})} (\lambda \! = \! +1) \right] \! \Bigg|^2 \, \notag \\
&= \frac{[L]}{8} \Big| - i^{p} \, d^{L}_{+1 \, \Delta M} (\theta) + (-i)^{p} \, d^{L}_{-1 \, \Delta M} (\theta) \Big|^2 \, ,\end{aligned}$$ where $N$ is some constant factor and $W^{(\text{pl})}_{\text{tot}}$ denotes the total plane-wave transition rate summed over photon polarizations and integrated over magnetic field angles $\theta$. Therefore, the expressions and are defined to be dimensionless and independent of line strengths. The combination of Wigner $d$ functions in the last lines of the expressions for $W_{\parallel}^{(\text{pl})} (\theta)$ and $W_{\perp}^{(\text{pl})} (\theta)$ in turn reflects the geometry of the excitation process. In fact, these formulas can be rewritten in terms of polynomials in the sine and cosine functions of $\theta$. For example, the explicit form of the normalized transition rates reads $$\begin{aligned}
\label{eq:rate_pl_ex}
W_{\parallel}^{(\text{pl})} (\theta) &= \frac{21}{32} \sin^2 \theta \, (1 - 5 \cos^2 \theta )^2 , \, \notag \\
W_{\perp}^{(\text{pl})} (\theta) &= 0 , \, \end{aligned}$$ where we assumed $\Delta M = 0$ for an E3 transition.
\[sec:twisted\]Excitation by twisted photons
--------------------------------------------
### \[sec:twisted amplitude\]Transition amplitude
![Geometry of the optical excitation of a single atom centered on the beam axis ($b=0$) by twisted light with the polarization vector $\bm{e}$. The angle $\theta$ determines the direction of the applied magnetic field $\bm{B}$ defining the quantization $z_{\text{atom}}$ axis of the atom with respect to the light propagation direction taken along the $z_{\text{light}}$ (or $z$) axis.[]{data-label="fig:geometry"}](geometry){width="0.99\linewidth"}
Having recalled the theory of atomic excitation by plane waves, we can start to discuss the excitation of atoms by twisted light. In this work, we consider a twisted beam with helicity $\lambda$, the longitudinal component $k_z$ of the linear momentum, the absolute value of the transverse momentum $ |\bm{k}_{\perp}| = \varkappa$, the photon energy $\omega = c \sqrt{k_z^2 + \varkappa^2}$, and the projection of the total angular momentum (TAM) $m_{\gamma}$. This so-called Bessel state is characterized by the vector potential [@Matula/JPB:2013] $$\begin{aligned}
\label{eq:vec_tw_2}
\bm{A}^{(\text{tw})} (\bm{r}) = \int a_{\varkappa m_{\gamma}} (\bm{k}_{\perp}) \, \bm{e}_{\bm{k} \lambda} \, e^{i \bm{k} \bm{r}} \, \frac{d^2 \bm{k}_{\perp}}{(2 \pi)^{2}} \, ,\end{aligned}$$ where the amplitude $a_{\varkappa m_{\gamma}} (\bm{k}_{\perp})$ is given by $$\begin{aligned}
\label{eq:vec_tw_amp}
a_{\varkappa m_{\gamma}} (\bm{k}_{\perp}) = \frac{2 \pi}{\varkappa} \, (-i)^{m_\gamma} \, e^{i m_\gamma \phi_k} \, \delta (k_{\perp} - \varkappa ) \, .\end{aligned}$$ As seen from Eq. , a Bessel beam can be represented as a superposition of plane waves whose wave vectors $\bm{k}$ are uniformly distributed upon the surface of a cone with an opening angle $\theta_{k} = \arctan (\varkappa / k_z)$.
We note that experiments usually deal with the light beams in the so-called paraxial approximation in which the transverse momentum of the photon is much smaller than its longitudinal momentum, i.e., $\varkappa \ll k_z$, and hence the opening angle $\theta_{k}$ is very small [@Matula/JPB:2013]. In this approximation, the vector potential of the Bessel beam after integration over $\bm{k}_{\perp}$ simplifies to
$$\begin{aligned}
\label{eq:vec_tw_1}
\bm{A}_{m_l \lambda}^{(\text{tw})} (\bm{r}) \approx \bm{e}_{\lambda} \, (-i)^{\lambda} J_{m_l}(\varkappa r_{\perp}) \, e^{i m_l \phi} \, e^{i k_z z} \, ,\end{aligned}$$
with $J_{m_l}(\varkappa r_{\perp})$ being the Bessel function of the first kind. Here $m_l = m_\gamma - \lambda$ can be interpreted as the projection of the orbital angular momentum (OAM) of light decoupled from the spin angular momentum (SAM) projection $\lambda$.
As in the case of plane-wave photons , the interaction between the atoms and the twisted light can be described by the matrix element $$\begin{aligned}
\label{eq:amp_tw_1}
\mathcal{M}_{M_f M_i}^{(\text{tw})} &= \Bigg \langle \alpha_{f} F_{f} M_{f} \Bigg| \sum_{q} \bm{\alpha}_{q} \, \bm{A}_{m_l \lambda}^{(\text{tw})} (\bm{r}_{q}) \Bigg| \alpha_{i} F_{i} M_{i} \Bigg \rangle \, \notag \\
&= \int a_{\varkappa m_{\gamma}} (\bm{k}_{\perp}) \, e^{-i \bm{k}_{\perp} \bm{b}} \, \notag \\
&\, \times \Bigg \langle \alpha_{f} F_{f} M_{f} \Bigg| \sum_{q} \bm{\alpha}_{q} \, \bm{e}_{\bm{k} \lambda} \, e^{i \bm{k} \bm{r}_{q}} \Bigg| \alpha_{i} F_{i} M_{i} \Bigg \rangle \frac{d^2 \bm{k}_{\perp}}{(2 \pi)^{2}} \, .\end{aligned}$$ Here the impact parameter $\bm{b} = (b_x, b_y, 0)$ specifies the position of a target atom with regard to the beam axis. The introduction of this parameter is necessary, since the Bessel beam has an inhomogeneous field distribution in the transverse plane, thereby making the excitation process very sensitive to $\bm{b}$. Calculations of the transition amplitude can again be simplified through use of the standard multipole expansion of a plane wave . Then, upon integrating over $k_{\perp}$ with the delta function $\delta (k_{\perp} - \varkappa )$ and making use of the integral representation of the Bessel function [@Peshkov/PRA:2017] $$\begin{aligned}
\label{eq:bessel}
&\int_{0}^{2 \pi} e^{i (m_{\gamma} - M) \phi_k - i \varkappa b \cos (\phi_k - \phi_b)} \, \frac{d \phi_k}{2 \pi} \, \notag \\
&= (-i)^{m_{\gamma} - M} e^{i (m_{\gamma} - M) \phi_b} J_{m_{\gamma} - M} (\varkappa b) \, ,\end{aligned}$$ we readily find, after some algebraic manipulations similar to those in Eqs. -, that $$\begin{aligned}
\label{eq:amp_tw_2}
&\mathcal{M}_{M_f M_i}^{(\text{tw})} (\bm{b}) = \, C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} (p L) \,\, (i \lambda)^{p} \, (-1)^{m_l + \lambda} \, \notag \\
& \,\,\,\,\,\,\, \times \langle F_i M_i, \, L \Delta M | F_f M_f \rangle \, \sum_{M} i^M \, e^{i (m_l + \lambda - M) \phi_b} \, \notag \\
&\,\,\,\,\,\,\, \times J_{m_l + \lambda - M} (\varkappa b) \, d^{L}_{M \, \lambda} (\theta_k) \, d^{L}_{M \, \Delta M} (\theta) \, ,\end{aligned}$$ where again the $C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} (p L)$ is given by Eq. and summation over multipoles $(p L)$ is restricted to the single leading term.
By comparing the transition amplitudes for plane waves and twisted light , we observe that the key difference between them arises from the summation over the projection quantum numbers $M$ in $\mathcal{M}_{M_f M_i}^{(\text{tw})}$. This sum contains the Bessel functions $J_{m_l + \lambda - M} (\varkappa b)$ and the exponential factors $\exp [i (m_l + \lambda - M) \phi_b]$ that describe the impact-parameter dependence of the matrix element. It is worth stressing that the transition amplitude for twisted light can be greatly simplified when the single atom is placed on the beam axis ($b=0$), namely $$\begin{aligned}
\label{eq:amp_tw_3}
&\mathcal{M}_{M_f M_i}^{(\text{tw})} (b = 0) = \, C_{\alpha_i J_i \alpha_f J_f}^{F_i F_f I} (p L) \,\, (i \lambda)^{p} \, (-i)^{m_l + \lambda} \, \notag \\
& \,\, \times \langle F_i M_i, \, L \Delta M | F_f M_f \rangle \, d^{L}_{m_l + \lambda , \, \lambda} (\theta_k) \, d^{L}_{m_l + \lambda , \, \Delta M} (\theta) \, .\end{aligned}$$ This equation explicitly expresses the fact that $\mathcal{M}_{M_f M_i}^{(\text{tw})}$ depends on the opening angle $\theta_k$, helicity $\lambda$, and OAM $m_l$ of twisted light, as well as on the angle $\theta$ between the light propagation direction and the external magnetic field \[cf. Fig. \[fig:geometry\]\].
### \[sec:twisted linear\]Transition rate for linear polarization
The formula shows how to calculate the amplitude for excitation by twisted light with definite helicity $\lambda$. Similar to before, we can again use this amplitude to analyze the absorption of linearly polarized twisted photons. This can be done easily within the paraxial approximation in which the OAM and SAM are independent from each other [@Matula/JPB:2013]. In analogy with plane waves, it is possible to construct the vector potential for twisted photons linearly polarized within the reaction $x$-$z$ plane defined by the magnetic field $\bm{B}$ direction and the light propagation $\bm{k}_z$ direction:
$$\begin{aligned}
\label{eq:tw_h}
\bm{A}_{\parallel}^{(\text{tw})} (\bm{r}) &= \frac{i}{\sqrt{2}} \left( \bm{A}_{m_l \, \lambda = +1}^{(\text{tw})} - \bm{A}_{m_l \, \lambda = -1}^{(\text{tw})} \right) \, \notag \\
&= \bm{e}_{x} \, J_{m_l}(\varkappa r_{\perp}) \, e^{i m_l \phi} \, e^{i k_z z} \, ,\end{aligned}$$
while for twisted photons polarized perpendicular to the reaction plane we find $$\begin{aligned}
\label{eq:tw_v}
\bm{A}_{\perp}^{(\text{tw})} (\bm{r}) &= \frac{1}{\sqrt{2}} \left( \bm{A}_{m_l \, \lambda = +1}^{(\text{tw})} + \bm{A}_{m_l \, \lambda = -1}^{(\text{tw})} \right) \, \notag \\
&= \bm{e}_{y} \, J_{m_l}(\varkappa r_{\perp}) \, e^{i m_l \phi} \, e^{i k_z z} \, .\end{aligned}$$ The intensity profile of these beams with an OAM $m_l = +2$ is shown in Figs. \[fig:int\_pol\] (a) and (b) together with the polarization vectors.
![Intensity profiles of paraxial Bessel beams of light of wavelength $467$ nm and opening angle $\theta_k = 7.5^{\circ}$. The directions of the electric field are indicated by black arrows: (a) parallel and (b) perpendicular linearly polarized twisted beams with OAM $m_l = +2$; (c) radially polarized beam; (d) azimuthally polarized beam.[]{data-label="fig:int_pol"}](int_pol){width="0.99\linewidth"}
By using the vector potential and the matrix element , we find the normalized transition rate for absorption of parallel polarized twisted light: $$\begin{aligned}
\label{eq:rate_tw_h}
W_{\parallel}^{(\text{tw})} (\theta, \bm{b}) = \frac{N}{W^{(\text{pl})}_{\text{tot}}} \Bigg| & \frac{i}{\sqrt{2}} \left[ \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l, \lambda \! = \! +1) \, \notag \right. \\
& \left. - \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l, \lambda \! = \! -1) \right] \Bigg|^2 \, .\end{aligned}$$ On the other hand, for perpendicular polarized twisted light we have $$\begin{aligned}
\label{eq:rate_tw_v}
W_{\perp}^{(\text{tw})} (\theta, \bm{b}) = \frac{N}{W^{(\text{pl})}_{\text{tot}}} \Bigg| & \frac{1}{\sqrt{2}} \left[ \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l, \lambda \! = \! +1) \, \notag \right. \\
& \left. + \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l, \lambda \! = \! -1) \right] \Bigg|^2 \, .\end{aligned}$$ If the atom is placed on the beam axis ($b=0$), these expressions simplify to $$\begin{aligned}
\label{eq:rate_tw_hv_b0}
W_{\parallel, \perp}^{(\text{tw})} (\theta, b = 0) &= \frac{[L]}{8} \Big| -i^{p+1} \, d^{L}_{m_l + 1 , \, +1} (\theta_k) \, d^{L}_{m_l + 1 , \, \Delta M} (\theta) \, \notag \\
& \mp (-i)^{p-1} \, d^{L}_{m_l - 1, \, -1} (\theta_k) \, d^{L}_{m_l - 1, \, \Delta M} (\theta) \Big|^2 \, ,\end{aligned}$$ where we have made use of Eq. . Moreover, using the explicit expressions of Wigner $d$ functions, we obtain $$\begin{aligned}
\label{eq:rate_tw_hv_b0_ex}
&W_{\parallel, \perp}^{(\text{tw})} (\theta, b = 0) \, \notag \\
&= \frac{21}{8192} \Big| 5 \sin^2 \theta_k \, (1 + \cos \theta_k) \, \sin^3 \theta \mp (1 - \cos \theta_k) \, \notag \\
& \;\;\; \times (1 - 10 \cos \theta_k - 15 \cos^2 \theta_k) \, (1 - 5 \cos^2 \theta) \, \sin \theta \Big|^2 \, ,\end{aligned}$$ which corresponds to $\Delta M = M_f - M_i = 0$ and $m_l = +2$ for an E3 transition.
### \[sec:twisted rad\_az\]Transition rate for radially and azimuthally polarized beams
With twisted light modes, it is possible to generate richer polarization patterns compared to plane waves [@Dorn/PRL:2003; @Tidwell/AO:1990]. For example, the so-called radially polarized beam, whose vector potential $$\begin{aligned}
\label{eq:tw_r}
\bm{A}_{\text{r}}^{(\text{tw})} (\bm{r}) &= -\frac{i}{\sqrt{2}} \left( \bm{A}_{m_l = -1 \, \lambda = +1}^{(\text{tw})} + \bm{A}_{m_l = +1 \, \lambda = -1}^{(\text{tw})} \right) \, \notag \\
&= \bm{e}_{r} \, J_{1}(\varkappa r_{\perp}) \, e^{i k_z z} \, \end{aligned}$$ can be constructed as a linear combination of two twisted beams with helicity $\lambda = \pm 1$ and OAM $m_l = \mp 1$ [@Quinteiro/PRA:2017]. The corresponding intensity profile and electric field directions are shown in Fig. \[fig:int\_pol\] (c). We see that in this case the electric field vector at any point on the beam profile is oriented in the radial direction $\bm{e}_{r}$. With Bessel beams we can also obtain another solution, namely the azimuthally polarized beam defined as $$\begin{aligned}
\label{eq:tw_az}
\bm{A}_{\text{az}}^{(\text{tw})} (\bm{r}) &= \frac{1}{\sqrt{2}} \left( \bm{A}_{m_l = +1 \, \lambda = -1}^{(\text{tw})} - \bm{A}_{m_l = -1 \, \lambda = +1}^{(\text{tw})} \right) \, \notag \\
&= \bm{e}_{\phi} \, J_{1}(\varkappa r_{\perp}) \, e^{i k_z z} \, ,\end{aligned}$$ where the polarization vector $\bm{e}_{\phi}$ implies that its electric field vector is always perpendicular to the radial vector, as depicted in Fig. \[fig:int\_pol\] (d). We note that both radially and azimuthally polarized beams do not have a well-defined OAM projection $m_l$; they can be seen as a superposition of two twisted modes with different OAM $m_l = \pm 1$ [@Quinteiro/PRA:2017].
Similarly to before, we can use the vector potential to calculate the transition rate for absorption of radiation of radial polarization for arbitrary impact parameters $$\begin{aligned}
\label{eq:rate_tw_r}
W_{\text{r}}^{(\text{tw})} (\theta, \bm{b}) = &\frac{N}{W^{(\text{pl})}_{\text{tot}}} \Bigg| -\frac{i}{\sqrt{2}} \left[ \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l \! = \! -1, \lambda \! = \! +1) \, \notag \right. \\
& \left. + \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l \! = \! +1 , \lambda \! = \! -1) \right] \Bigg|^2 \, .\end{aligned}$$ In the case of azimuthal polarization , we find $$\begin{aligned}
\label{eq:rate_tw_az}
W_{\text{az}}^{(\text{tw})} (\theta, \bm{b}) = &\frac{N}{W^{(\text{pl})}_{\text{tot}}} \Bigg| \frac{1}{\sqrt{2}} \left[ \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l \! = \! +1, \lambda \! = \! -1) \, \notag \right. \\
& \left. - \mathcal{M}_{M_f M_i}^{(\text{tw})} (m_l \! = \! -1 , \lambda \! = \! +1) \right] \Bigg|^2 \, .\end{aligned}$$ Again, these formulas are significantly simplified if one considers the atom with $b = 0$. By substituting Eq. into Eqs. and , we obtain the normalized transition rates $$\begin{aligned}
\label{eq:rate_tw_raz_b0}
&W_{\text{r,az}}^{(\text{tw})} (\theta, b = 0) = \frac{[L]}{8} \Big| d^{L}_{0 \, \Delta M} (\theta) \Big|^2 \, \notag \\
&\;\; \times \Big| (-i)^{p} \, d^{L}_{0 \, -1} (\theta_k) \pm i^{p} \, d^{L}_{0 \, +1} (\theta_k) \Big|^2 \, ,\end{aligned}$$ where we have used the fact that both twisted components have the TAM projection $m_{\gamma} = m_l + \lambda = 0$. In particular, the explicit expressions for $W_{\text{r,az}}^{(\text{tw})}$ are $$\begin{aligned}
\label{eq:rate_tw_raz_ex}
W_{\text{r}}^{(\text{tw})} (\theta, b = 0) =& \frac{21}{128} \sin^2 \theta_k \, (1 - 5 \cos^2 \theta_k)^2 \, \notag \\
&\times \cos^2 \theta \, (3 - 5 \cos^2 \theta)^2 \, , \notag \\
W_{\text{az}}^{(\text{tw})} (\theta, b = 0) =& \, 0 \, ,\end{aligned}$$ assuming that $\Delta M = 0$ and $m_l = +2$ for an E3 transition.
### \[sec:target\]Nonlocalized atoms
The transition rates for excitation by twisted light have been derived above for an atom whose position with respect to the beam axis is well-defined. Of course, this idealistic scenario is impossible to achieve in a real atom trap experiment. For example, in recent experiments [@Afanasev/NJP:2018; @Schmiegelow/NC:2016], a single laser-cooled $^{40}$Ca$^{+}$ ion trapped in a Paul trap had a thermal spatial spread of about $60$ nm. To account for this spatial distribution effect, we introduce the probability to find an atom at the distance $\bm{b}$ from the beam center: $$\begin{aligned}
\label{eq:distr}
f (\bm{b}) = \frac{1}{2 \pi \sigma^2} e^{-\frac{\bm{b}^2}{2 \sigma^2}} \, .\end{aligned}$$ This Gaussian distribution is assumed to be centered on the beam axis and characterized by the width $\sigma$. The mean transition rates are then obtained by integrating over the impact parameter $$\begin{aligned}
\label{eq:mean}
W^{(\text{tw})}_{\parallel, \perp, \text{r,az}} (\theta) = \int f (\bm{b}) \, W^{(\text{tw})}_{\parallel, \perp, \text{r,az}} (\theta, \bm{b}) \, d^2 \bm{b} \, .\end{aligned}$$ This formula enables us to understand how the excitation probability depends not only on the mutual orientation of photon and atomic axes, but also on the width $\sigma$ of the atomic spatial distribution.
### \[sec:lg\]Laguerre-Gaussian beams
![Normalized transition rate for absorption of plane-wave light linearly polarized parallel to the reaction plane (black solid line) as a function of tilt angle $\theta$ of the magnetic field for the $^{2}S_{1/2} (F_i = 0, \, M_i = 0) \rightarrow\; ^{2}F_{7/2} (F_f = 3 , \, M_f = 0)$ electric octupole (E3) transition in $^{171}$Yb$^{+}$. The transition rate for perpendicular polarized plane waves (red dashed line) vanishes identically for all angles $\theta$.[]{data-label="fig:pl"}](pl){width="0.76\linewidth"}
In this study, we present the theory of excitation of trapped atoms by Bessel light beams. In some recent experiments, however, another type of twisted light modes, namely Laguerre-Gaussian modes, are employed [@Peshkov/PRA:2017; @Schmiegelow/NC:2016]. While the detailed discussion of these modes is beyond the scope of our work, we mention here that both Bessel and Laguerre-Gaussian solutions behave like $r_{\perp}^{|m_l|} e^{i m_l \phi}$ near the optical vortex, i.e., for small $r_{\perp}$. This implies that the formulas derived above can be applied to the excitation by Laguerre-Gaussian beams of the same polarization and OAM if the spatial distribution of atoms is smaller than the characteristic size of the first bright ring of the beam, which is of the order of a few microns in our case \[cf. Fig. \[fig:int\_pol\]\].
\[sec:results\]Results and discussion
=====================================
In the previous sections, we obtained the formulas which allow us to calculate the (normalized) excitation rates for twisted light and plane waves. While the developed formalism can be applied to any atom or ion, we focus here on the $4f^{14} 6s \; ^{2}S_{1/2} \rightarrow \; 4f^{13} 6s^2 \; ^{2}F_{7/2} $ electric octupole (E3) transition in singly ionized ytterbium. This transition has attracted much experimental and theoretical attention as a candidate for a frequency standard [@Sanner/N:2019; @Biemont/PRL:1998]. For the specific case of $^{171}$Yb$^{+}$, we consider the initial and final hyperfine levels $F_i = 0$ and $F_f = 3$. A weak magnetic field is applied to split the hyperfine multiplet of the excited state by the Zeeman effect, making the individual $M_f$ sublevels distinguishable. In what follows, we concentrate on the transition between the $M_i = 0$ and $M_f = 0$ magnetic hyperfine sublevels that do not show a linear Zeeman effect.
![Normalized transition rates for absorption of parallel (black solid lines) and perpendicular (red dashed lines) linearly polarized twisted Bessel light with OAM $m_l = +1$ (top panel) and $m_l = +2$ (bottom panel) by a single $^{171}$Yb$^{+}$ ion placed on the beam axis ($b = 0$), while the opening angle is $\theta_k = 7.5^{\circ}$. All other parameters are as in Fig. \[fig:pl\].[]{data-label="fig:tw_m12_xy"}](tw_m12_xy){width="0.76\linewidth"}
![The same as Fig. \[fig:tw\_m12\_xy\], but for the radially polarized Bessel beam (green dashed line). The transition rate for the azimuthally polarized beam (orange solid line) equals zero for all angles $\theta$ if $b = 0$.[]{data-label="fig:ra"}](ra){width="0.76\linewidth"}
\[sec:results\_pw\]Excitation by plane waves
--------------------------------------------
Before considering the excitation of an $^{171}$Yb$^{+}$ ion by Bessel beams, we shall briefly review the results for plane waves [@Taylor:1996]. Fig. \[fig:pl\] shows the transition rates normalized to the factor $W^{\text{(pl)}}_{\text{tot}}$ for the $^{2}S_{1/2} (F_i = 0, \, M_i = 0) \rightarrow\; ^{2}F_{7/2} (F_f = 3 , \, M_f = 0)$ transition induced by plane-wave radiation with a wavelength of $467$ nm. Calculations are performed for the light polarized either parallel (black solid line) or perpendicular (red dashed line) to the reaction plane. As seen from Fig. \[fig:pl\], the transition rates and depend strongly on both the tilt angle $\theta$ of the magnetic field and the polarization of light. For example, the excitation rate $W_{\perp}^{(\text{pl})}$ vanishes identically for all angles $\theta$ when the incident light is perpendicular polarized \[cf. Eq. \]. In the case of parallel polarization, $W_{\parallel}^{(\text{pl})}$ exhibits oscillations and reaches maximum values at $\theta = 30^{\circ}$, $\theta = 90^{\circ}$, and $\theta = 150^{\circ}$.
\[sec:center\]Excitation by twisted light: atoms on the beam axis
-----------------------------------------------------------------
Having examined the excitation by linearly polarized plane waves, we can study the effects of twisted beams on transition probabilities. Again, we focus on paraxial Bessel beams polarized parallel or perpendicular to the reaction plane. Here the atom is assumed to be placed directly on the beam axis, $b = 0$. The corresponding transition rates are displayed in Fig. \[fig:tw\_m12\_xy\] for two OAM of incident light $m_l = +1$ (top panel) and $m_l = +2$ (bottom panel). It is apparent that the $\theta$ dependence of $W^{(\text{tw})}$ differs significantly from its plane-wave counterpart. In particular, while $W_{\perp}^{(\text{pl})}$ is identically zero for arbitrary orientation of the magnetic field, this is not the case for $W_{\perp}^{(\text{tw})}$. For example, for OAM projection $m_l = +1$, the normalized transition rate for twisted photons exhibits maximum values of $0.043$ at $\theta = 0^{\circ}$ and $180^{\circ}$. On the other hand, the positions of the absorption peaks for OAM $m_l = +2$ are shifted to $\theta = 35^{\circ}$ and $145^{\circ}$. It is worth stressing that the transition rate for twisted light polarized within the reaction plane $W^{(\text{tw})}_{\parallel}$ is also very sensitive to the OAM projection. For $m_l = +1$ the maxima occur at $\theta = 0^{\circ}$, $60^{\circ}$, $120^{\circ}$, and $180^{\circ}$, while for $m_l = +2$ there are maxima at $\theta = 30^{\circ}$, $90^{\circ}$, and $150^{\circ}$. As seen from Fig. \[fig:tw\_m12\_xy\], not only the angular pattern, but also the absolute values of transition rates depend on the OAM of light. They are reduced by almost two orders of magnitude when the OAM projection $m_l$ is increased from $+1$ to $+2$. This is caused by the reduction of the intensity of light near the vortex line as OAM increases [@Matula/JPB:2013; @Abramowitz:1964].
So far we have discussed the excitation of atoms by linearly polarized light. In order to further study the polarization dependence of the transition rates, we also consider radially and azimuthally polarized incident beams. The calculations for these nontrivial polarization states and for an atom located on the beam axis are displayed in Fig. \[fig:ra\]. This figure shows that the maximal excitation probability for radially polarized beam can be achieved by applying the external magnetic field along the light axis. In contrast, no excitation by azimuthally polarized beam is observed for $b = 0$. As will be demonstrated in the next section, this suppression is partially removed if the spatial spread of the trapped atom is not negligible with respect to the inverse transverse momentum $\varkappa^{-1}$ of the beam.
![Transition rates for absorption of parallel (top panel) and perpendicular (bottom panel) linearly polarized twisted Bessel light with OAM $m_l = +2$ and opening angle $\theta_k = 7.5^{\circ}$ when a single ion is placed on the beam axis (black solid lines), and when the centered ion has a spatial spread of $\sigma = 20$ nm (red dashed lines) or $\sigma = 50$ nm (blue dotted lines) in the beam center. All other parameters are as in Fig. \[fig:pl\].[]{data-label="fig:av_tw_m2_xy"}](av_tw_m2_xy){width="0.76\linewidth"}
\[sec:distr\]Excitation by twisted light: spatial spread of ions
----------------------------------------------------------------
The above calculations have been carried out for the atom positioned precisely at the beam center, $b=0$. Such an ideal scenario, however, is impossible to attain in real atom-trap experiments in which the atomic spatial spread has been found to be about 60 nm [@Schmiegelow/NC:2016]. We make use of Eq. for the Gaussian distribution to study the effect of atomic delocalization, and the corresponding transition rates are displayed in Fig. \[fig:av\_tw\_m2\_xy\] for Bessel beams linearly polarized parallel and perpendicular the reaction plane. Calculations have been done for OAM $m_l = +2$ and for atomic spatial distributions of width $\sigma = 20$ nm (red dashed lines) or $\sigma = 50$ nm (blue dotted lines) centered on the beam axis. In addition, these results are compared with idealized predictions for single atoms located exactly at the beam center (black solid lines). The atomic delocalization significantly affects the rates $W^{(\text{tw})}_{\parallel}$, as shown in the top panel of Fig. \[fig:av\_tw\_m2\_xy\]. For example, the oscillations of the transition rate become less pronounced at $\theta < 60^{\circ}$ and $\theta > 120^{\circ}$. The principal maximum of the transition rate remains unchanged and occurs for the perpendicular orientation of the trap magnetic field. The finite spatial spread of the atom also modifies the transition rates for absorption of Bessel photons polarized perpendicular to the reaction plane. As can be seen from the bottom panel of Fig. \[fig:av\_tw\_m2\_xy\], the rate $W^{(\text{tw})}_{\perp}$ is enhanced at $\theta < 45^{\circ}$ and $\theta > 135^{\circ}$, and the positions of the maxima become slightly shifted.
It should be noted that the spatial delocalization of the atom can strongly affect the transition rates also for other types of polarization. In particular, we see from Fig. \[fig:av\_tw\_az\] that while $W^{(\text{tw})}_{\text{az}}$ for azimuthal polarization vanishes identically when the atom is positioned precisely at $b=0$, the rate of photon absorption increases with the width of the atomic distribution $\sigma$. For example, if $\sigma = 50$ nm, $W^{(\text{tw})}_{\text{az}}$ reaches the maximum value of $2.3 \times 10^{-3}$ at $\theta = 30^{\circ}$ and $150^{\circ}$.
![The same as Fig. \[fig:av\_tw\_m2\_xy\], but for the azimuthally polarized Bessel beams.[]{data-label="fig:av_tw_az"}](av_tw_az){width="0.76\linewidth"}
\[sec:summary\]Summary and outlook
==================================
In summary, we have performed a theoretical study of the excitation of a single trapped atom by twisted light. Special attention has been paid to the dependence of the excitation rates on the polarization of incident light and on the orientation of the beam axis with respect to the atomic quantization axis, which is defined by the applied magnetic field. In order to investigate this geometrical dependence, we have employed first-order perturbation theory to describe the coupling between paraxial Bessel beams and trapped atoms. Based on this approach, we have derived simple analytical expressions for the excitation rates when considering linear, radial, and azimuthal polarization of incident light. While the theory is general and can be applied to any atom or ion, we have investigated the particular case of $^{2}S_{1/2} (F=0) \rightarrow\; ^{2}F_{7/2} (F=3, M=0)$ electric octupole transition in $^{171}$Yb$^{+}$. Our calculations have demonstrated that a proper choice of light polarization as well as of the mutual orientation of the beam direction and atomic quantization axis can strongly enhance this E3 transition. For a more accurate description of the excitation process we also took into account the effect of the atomic spatial distribution in a trap. It was found that the uncertainty in determination of atomic position significantly affects both the absolute value and the geometrical dependence of the transition rates. Thus, our study paves the way for understanding the optimal conditions for future experiments with trapped atoms and twisted photons.
\[sec:acknowledgments\]Acknowledgments {#secacknowledgmentsacknowledgments .unnumbered}
======================================
We gratefully acknowledge the support of the Braunschweig International Graduate School of Metrology B-IGSM and the DFG Research Training Group 1952 Metrology for Complex Nanosystems. This research was also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC-2123 QuantumFrontiers - 390837967 and within CRC 1227, Project S01.
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|
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>
Subframe for test browser_compartments.html (do not change this title)
</title>
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<body>
Subframe loaded.
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|
package com.minecolonies.api.research;
import com.minecolonies.api.research.effects.IResearchEffectManager;
import com.minecolonies.api.research.util.ResearchState;
/**
* Interface defining how a local research at a colony is. This represents how a colony stores researches they finished or started.
*/
public interface ILocalResearch
{
/**
* Getter for the progress of the research.
*
* @return the progress in ticks.
*/
int getProgress();
/**
* Getter of the id of the research.
*
* @return the String id.
*/
String getId();
/**
* Get the ResearchState of the research.
*
* @return the current state.
*/
ResearchState getState();
/**
* Get the string name of the branch.
*
* @return the branch name.
*/
String getBranch();
/**
* Getter for the research depth.
*
* @return the depth.
*/
int getDepth();
/**
* Set the current research state.
*
* @param value the state to set.
*/
void setState(ResearchState value);
/**
* Set the research progress.
*
* @param progress the progress to set.
*/
void setProgress(int progress);
/**
* Tick the research to execute it.
*
* @param effects the research effects class which holds the information of the colony.
* @param tree the research tree which holds the currently explored tree.
* @return true if effective.
*/
boolean research(IResearchEffectManager effects, ILocalResearchTree tree);
}
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Case: 09-30356 Document: 00511031771 Page: 1 Date Filed: 02/22/2010
IN THE UNITED STATES COURT OF APPEALS
FOR THE FIFTH CIRCUIT United States Court of Appeals
Fifth Circuit
FILED
February 22, 2010
No. 09-30356 Charles R. Fulbruge III
Summary Calendar Clerk
SALLY B. LAURENT,
Plaintiff - Appellant,
v.
MICHAEL J. ASTRUE, COMMISSIONER OF SOCIAL SECURITY,
Defendant - Appellee.
Appeal from the United States District Court
for the Eastern District of Louisiana
USDC No. 2:07-CV-3831
Before JOLLY, WIENER, and ELROD, Circuit Judges.
PER CURIAM:*
Sally B. Laurent appeals the district court’s order affirming the decision
of the Commissioner of Social Security (Commissioner) denying Laurent’s claims
for disability insurance benefits (DIB) and supplemental security income (SSI).
We affirm.
*
Pursuant to 5TH CIR . R. 47.5, the court has determined that this opinion should not
be published and is not precedent except under the limited circumstances set forth in 5TH CIR .
R. 47.5.4.
Case: 09-30356 Document: 00511031771 Page: 2 Date Filed: 02/22/2010
No. 09-30356
I.
Laurent applied to the Social Security Administration (SSA) for DIB and
SSI payments, based on multiple musculoskeletal impairments and the pain
resulting from those impairments. The SSA determined that Laurent was not
disabled and denied her applications.
Laurent requested a hearing, at which she represented herself. The
Administrative Law Judge (ALJ) heard testimony from Laurent and from a
Vocational Expert (VE). The ALJ concluded that Laurent was not disabled and
denied her claims for benefits. Laurent timely requested review from the
Appeals Council (AC), which denied review, and the ALJ’s decision thus became
the final decision of the Commissioner of Social Security. Laurent sought
judicial review of the Commissioner’s decision in the district court, which
affirmed the Commissioner’s decision. Laurent appeals.
II.
Title 42 U.S.C. § 405(g) limits our review of the Commissioner’s decision
to “(1) whether there is substantial evidence in the record to support the
decision, and (2) whether the decision comports with relevant legal standards.”
Brock v. Chater, 84 F.3d 726, 727-28 (5th Cir. 1996). “Substantial evidence is
more than a mere scintilla,” and is “such relevant evidence as a reasonable mind
might accept as adequate to support a conclusion.” Brown v. Apfel, 192 F.3d 492,
496 (5th Cir. 1999) (internal quotations omitted).
The Commissioner applies a five-step sequential evaluation process to
determine whether a claimant is entitled to disability benefits. 20 C.F.R. §§
404.1520, 416.920 (2006). If the Commissioner determines at any step that the
claimant is not disabled, the evaluation does not continue to the next step. Id.
The claimant carries the burden of proof in the first four steps of the analysis.
Muse v. Sullivan, 925 F.2d 785, 789 (5th Cir. 1991). Here, the ALJ ended the
evaluation after determining at step four that Laurent had the residual
2
Case: 09-30356 Document: 00511031771 Page: 3 Date Filed: 02/22/2010
No. 09-30356
functional capacity (RFC) to do her past relevant work as a bench assembler and
as a customer service representative.
Laurent challenges the ALJ’s determination that she is not disabled. On
appeal, she argues that the VE was incorrect as to the level of exertion her prior
job as a bench assembler requires, and that her customer service job did not
count as past relevant work because it did not constitute substantial gainful
activity (SGA) under 20 C.F.R. § 404.1574(b)(2). She therefore argues that she
is not able to perform her past relevant work and that the ALJ should have
continued to step five of the sequential evaluation process.
Laurent contends the ALJ improperly relied on the VE’s testimony that
her prior job as a bench assembler was sedentary because that testimony
conflicted with the Dictionary of Occupational Titles (DOT). However, in this
circuit, when a VE’s testimony conflicts with the DOT, “the ALJ may rely on the
vocational expert’s testimony provided that the record reflects an adequate basis
for doing so.” Carey v. Apfel, 230 F.3d 131, 146 (5th Cir. 2000). Further, “DOT
job descriptions should not be given a role that is exclusive of more specific
vocational expert testimony with respect to the effect of an individual claimant’s
limitations on his or her ability to perform a particular job.” Id. at 145. Here,
the VE testified that the bench assembler job was previously performed by
Laurent at the sedentary level, and that a person limited to sedentary exertion
who must alternate sitting and standing could perform the assembler job as he
had seen it performed. There is no indication that the VE’s testimony was
unreliable and Laurent does not point to evidence that the assembler job is not
sedentary, other than the DOT, so the ALJ’s reliance on the VE’s testimony was
proper.
Laurent does not challenge the VE’s testimony that she could perform her
previous work as a customer service representative, but argues on appeal that
her customer service job did not constitute SGA. However, Laurent
3
Case: 09-30356 Document: 00511031771 Page: 4 Date Filed: 02/22/2010
No. 09-30356
acknowledges in her reply brief that she earned $7570 as a customer service
representative in 2000, which exceeds the minimum required to constitute SGA.
20 C.F.R. § 404.1574(b)(2) Table 1. She does not dispute the Commissioner’s
calculation of her monthly earnings in that year. Laurent’s customer service
work does, therefore, constitute past relevant work. The opinions of two doctors
that she could perform a range of sedentary activities, which Laurent did not
rebut with any objective evidence or contrary medical opinion, is substantial
evidence that she could perform her prior sedentary jobs. The ALJ therefore did
not err in concluding at step four of the evaluation process that Laurent is not
disabled.
The judgment of the district court is
AFFIRMED.
4
|
Pages
Monday, May 21, 2012
Thoughts on The Avengers
Yeah, I know I'm late to the party. I don't know why it took me this long to see it, I was even planning on going to the midnight showing and then I got sick and all that jazz. But even though I'm late, it still looks to me like Superhero is the new black, and its always useful to analyze the current trends. Besides, I like black. And superheroes.
I will say up front that even though I like superheroes, they're not what you would call "my thing." I really, really enjoy superhero movies, but I'm much more likely to pick say Midnight in Paris over Spiderman or The Kings Speech over The Dark Knight. I guess its because its so easy to keep superheroes on this stereotypical, superficial level, and that bugs. However, Joss Whedon did a fantastic job of filling out character in The Avengers, so what I want to talk about is my three favorite Avengers and why they're so flippin awesome.
Iron Man: Who doesn't love Iron Man? (Who doesn't love Robert Downey Jr.). He's totally got the exciting bad boy exterior sensitive sweetheart interior thing going on. He's so absolutely smart and witty and hilarious. Albeit also absolutely cocky, which usually drives me nuts more than anything else, but he's cocky in the 'for humor' way as opposed to the 'you're all scum' way. I also have a tendency to favor superheroes who are super because of their own devices (i.e. Batman and Iron Man) over superheroes who are super because of some kind of supernatural something (i.e. Superman and Spiderman). Favorite line: "Shakespeare in the park? Doth mother know you weareth her drapes?" Did I mention Robert Downey Jr.?
Hulk: People kept saying Mark Ruffalo did a fantabulous job, and even with that my expectations were exceeded. I'm always a sucker for a middle-aged lonely damaged man, so of course I loved Hulk. You see his insecurities and sympathize deeply because of it, but then we also see him overcome those insecurities and kind of embrace his "other guy". Favorite line: "Yeah, last time I was in New York I kind of broke...Harlem."
Captain America: I think its Agent Coulson ("His first name is Agent.") who says that the people could use a little old fashioned, and that kind of sums up the big reason I love Captain America. It is so, so incredibly refreshing to me to see that kind of down-to-earth, home values kind of thing represented in a super hero. How I see it, that's sort of the closest to real-life superhero that they get. I love that in the face of a Norse god he'll say something like, "There's only one God, ma'am, and I don't think he dresses like that." That line almost made me squeal with love for CA and also Joss Whedon for writing it. I also loved "Last time I was in Germany and saw a man standing above everybody else, we ended up disagreeing." That whole Germany "There are always men like you" scene took my breath away with its awesomeness.
I do have two minor complaints. One general, one specific. I would have liked to see more women, including more women present for more than just their sex appeal, but Black Widow was still pretty kick butt and too few women is a thing with pretty much any super hero movie.
In this one particularly, though, I really wish they had done more with Loki. In the Thor movie he was so much more complex and developed, whereas in this one he felt a little one-dimensional. I like my villains a little less villain-y. But Tom Hiddleston is still fantastic and incredibly, incredibly beautiful.
So, thems my thoughts. Have you seen Avengers yet? I'm sure you're way ahead of me. What did you think?
Isn't it funny that these days saying "I finally saw it" means a few weeks after the initial release? I couldn't see it opening weekend b/c of family trip, but I saw it the Monday after opening weekend. Finally!
I agree on Loki. I was blown away by the actor in Thor. I'm like, who IS this guy?! He's like an alt-Johnny Weir of angst. I was transfixed by him and really happy he showed up in The Avengers.
An author blog I read posted some comments about the lack of women in The Avengers. The way she presented her argument annoyed me too much to provide a balanced comment, but your point is valid. We need to see more women in super hero movies who aren't just sexy or girlfriends getting rescued. Part of the issue with this is most superhero movies are based on actual comics which frequently feature women who are victims (the rescued girlfriends) or who use their sexitude to fight evil. In the case of The Avengers just "adding more women" isn't the answer because it should derive from the source material.
But kudos to Joss Whedon for using actress Cobie Smulders as a SHEILD agent to fill in transition scenes. I know he's a director who can be trusted to craft strong female characters, so I do expect more female presence in the next installment. There has to be one, this made like a gazillion dollars in three weeks. :)
I was torn on the female presence thing. On the one hand, Black Widow was seriously kick-butt. I mean, she is FREAKING AWESOME. Now that they've established her, I hope they do one or more movies focusing on her. She is definitely a very strong character here present for more than sex appeal.
On the other hand, I was disappointed with the portrayal of Pepper Potts. In previous movies, she was strong. In this one, she was gratuitous. What was with the tiny jean shorts? All she did in this movie was provide a great butt shot and show off an incredible set of very long legs.
I would have also liked to see Thor's lady-love. She's a smart character. Why didn't she get pulled in to SHIELD when Doctor whatshisface got turned into Loki's personal flying monkey?
I was happy that one of SHIELD's agents was female. I liked her in the chase scene. She was a good character. I also liked (and this was subtle) that the power source they were all flipping out about was apparently female.
Dammit...no I still have not seen it and it looks like another week before I do! I really want to see it but timing has been all bad since it came out. Glad you liked it and since I have not read anything but super good about this super hero movie I REALLY need to see it!
I absolutely love hearing from you! Thank you so, so much for your thoughts and comments, they really do make my day. Consider yourself awesome. Also, I do my best to respond to every comment within 24 hours, so I invite you to come back and continue the conversation :)
|
Purification, characterization, and cDNA cloning of a novel growth factor from the conditioned medium of NIH-Sape-4, an embryonic cell line of Sarcophaga peregrina (flesh fly).
A growth factor from the conditioned medium of NIH-Sape-4, an embryonic cell line of the flesh fly, was purified to homogeneity. This growth factor, termed IDGF, stimulated the proliferation of NIH-Sape-4 cells in an autocrine manner; it was a homodimer of a protein with a molecular mass of 52 kDa, and its specific activity was comparable with those of mammalian growth factors. Immunoblotting experiments revealed that unfertilized mature eggs of the flesh fly contained this growth factor, a certain level of which was maintained throughout embryonic development. Analysis of cDNA for this growth factor showed that this factor is a novel protein consisting of 553 amino acid residues. No significant sequence similarity was found between this factor and other proteins except atrial gland granule-specific antigen of Aplysia californica.
|
A road safety charity has condemned the sentence given to a motorist who knocked down and killed a seven-year-old boy while talking on her mobile phone.
However, the mother of Tydd St Mary Primary School pupil Seth Dixon has forgiven driver Amy Asker, who was fined just £90 and given five points on her driving licence.
The section of road where Seth Dixon, 7, was knocked over and killed.
Road safety campaigners branded the sentencing of Asker an ‘insult’ to the family of Seth.
He died just before Christmas 2014 from head injuries after he was hit by Ms Asker’s Ford Mondeo as he crossed a road outside his home.
Ms Asker (33) was fined £90 after admitting a charge of careless driving rather than the more serious offence of causing death by dangerous driving when she appeared before magistrates.
She was also ordered to pay a £20 victim surcharge and £85 costs.
Amy Asker
In Thursday’s Spalding Guardian we reported the inquest into Seth’s death, where it was heard that Ms Asker had been talking on the phone to a friend using its loud speaker when she hit Seth –known as Smiler.
Alice Bailey, campaigns adviser for road safety charity Brake, said: “The driver’s explanation and the subsequent fine and penalty points are an insult to the family.
“This tragic story illustrates why driving when distracted can be deadly.
“We’re calling on the government to make all phone use in vehicles illegal.
“Even when speaking on a hands free unit, your reaction times are 30 per cent slower than if you were at the current drink-drive limit in England and Wales.
“Having a conversation with a passenger in a car is very different. They can perceive hazards and understand the road conditions and behave accordingly.”
Seth was crossing the road outside his home in Tydd Gote to post a letter when the tragedy occurred on December 5, 2014.
The coroner heard that Ms Asker claimed she hadn’t seen Seth and only became aware of him on impact.
Asker, of Clapper Lane, Clenchwarton, near King’s Lynn, was driving her car at around 27mph in a 30mph zone at the time.
Coroner Paul Cooper recorded a narrative conclusion and said: “I am satisfied on the balance of probabilities that Ms Asker’s use of the mobile phone contributed to the cause of this child’s unfortunate death.”
Seth’s mother Alice Husband (42) said she hoped her son’s death would come as a strong warning to drivers not to use their phones behind the wheel.
|
1. Field of the Invention
The present invention relates to a monitoring camera system that performs transmission and reception of information or data to and from a monitoring camera and a sensor.
2. Description of the Related Art
A monitoring camera system that monitors an intruder entering a site of a house is conventionally known as an example of a communication system that performs transmission or reception of information or data with a sensor. For example, a monitoring camera system shown in Japanese Patent Unexamined Publication No. 2000-99862 includes a home server capable of recording a video or an audio, an infrared sensor, a video camera, and a microphone. When the infrared sensor detects an intruder, the home server records a video regarding the intruder and an audio regarding the intruder using the video camera and the microphone.
However, in Patent Unexamined Publication No. 2000-99862 described above, a setting value of the sensor including a threshold value used to determine that the sensor has detected a target (for example, an intruder) is not a value considering actual individual circumstances of a user, but is often uniformly set to a fixed value (default value), for example, in a specification or the like.
In other words, a case in which a user actually confirms an operation in which a sensor actually installed indoors, outdoors, or the like detects a target (for example, an intruder), and then, a setting value of the sensor is changed after actual use of the sensor is started is not assumed. Therefore, the setting value may not meet actual individual circumstances of the user, or the sensor may not operate as expected by the user.
Further, when the user changes the setting value (for example, sensitivity, and the threshold value) of the sensor into an appropriate setting value while actually confirming that the sensor detects the target (for example, an intruder), work of the user performing setting and changing while coming and going from and to an installation place of the sensor and an installation place of a receiver (for example, master device) that receives information (for example, information indicating abnormality) detected by the sensor occurs, and thus, there are problems in that complicated work is required for the user, and convenience for the user deteriorates. Particularly, when a large number of sensors are installed, an individual setting should be performed for each sensor, and setting work of the user increases. Further, work regarding a setting of a controlled device used in association with the sensor also increases.
|
Q:
Append contents of muliple tables - Visual FoxPro
I'm working with an accounting system with a Visual Foxpro backend. Every month, all of the invoices and payments are moved from the current invoices/payments table to a new table (in a different directory) with just that month's data. For example:
MainDBDir
currentInvoices.dbf (contains Dec invoices)
currentPayments.dbf (contains Dec payments)
2010Dir
NovDir
invoices.dbf (contains Nov2010 invoices)
payments.dbf (contains Nov2010 payments)
OctDir
invoices.dbf (contains Oct2010 invoices)
payments.dbf (contains Oct2010 payments)
I need to execute a queries on the last six months of data. Is there a way I can concatenate multiple tables (from multiple directories) in a single Visual Foxpro query?
I need something like this:
select * from concatenate(currentInvoices, 2010Dir/NovDir/invoices.dbf, 2010Dir/OctDir/invoices) where invoice_number like '12345'
I'd rather not execute a separate query for each table...
Thanks-
Jonathan
A:
You can concatenate the queries by using a union statement.
Example:
select * from currentInfoices.dbf
where invoice_number like '12345'
union
select * from "2010Dir\OctDir\invoices.dbf"
where invoice_number like '12345'
union
select * from "2010Dir\NovDir\invoices.dbf"
where invoice_number like '12345'
or
select *
from (select * from currentInfoices.dbf
union select * from "2010Dir\OctDir\invoices.dbf"
union select * from "2010Dir\NovDir\invoices.dbf") q
where invoice_number like '12345'
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The Final Kingdom – Part Five
After a great deal of consideration and thoughtful prayer, I have concluded that the final prophecy of Daniel, which I am about to start to try and explain (or at least simplify), is best dealt with from the perspective that the events which are described are still all in the future. Of course, we can squeeze past historical events into the prophecy and declare it fulfilled, but as we have already seen with the other prophecies, historical events can be squeezed into them even though they are just foreshadowing the things which are to come leading up to the return of the King, Yeshua.
It has occurred to me that the entire book of Daniel is much more than prophecy regarding the end times – there appears to be contained within a blueprint also. This blueprint teaches the church (and the Hebrews for that matter) how we, as followers of the One True God, ought to carry ourselves in times of great persecution. The events outlined in Daniel are coming our way, and sooner than any of us might believe. Before the end of this series, I will explain this matter fully. But for now, Here’s the start of a breakdown of Daniel chapters 10, 11, and 12. I won’t be able to get through it all in one sitting, so it will probably take two or three attempts. Please be patient.
In Part Four of this series I expressed my concern at what some translations of the Bible said in Daniel 10:1. Some appeared to find a way to use the phrase ‘great war‘ or ‘great tribulation‘, whilst others, in its place used the phrase ‘the appointed time was long‘. Having done some extensive research into this over the past few days I can now say that I believe ‘great war‘ or ‘great tribulation‘ to be the correct translation. I say this because the two words from which both translations are rendered are:
Tsaba (the T is silent) which every Hebrew dictionary lists as army, war, or warfare. It is listed as 6635 in Strong’s, so you can see for yourself, and it is used a total of 486 times in the Old Testament. Of those uses, on 35 occasions, it is to imply the word ‘war‘. On none of those 486 occasions does it get anywhere near to the idea of an ‘appointed time‘. I am not sure how anyone got to ‘appointed time‘ but they have and there must have been a reason for it. It is perhaps explained by the syntax of the first verse, which I will come onto shortly.
Gadol is the word from which some translations have rendered ‘long‘ and others ‘great‘. It is Strong’s 1419, which is an adjective used to describe the greatness of something. I can see how ‘long‘ may have been reached but, as its root word is ‘gadal‘ (1431) which means to ‘grow up‘ or ‘become great‘, may I suggest that ‘great‘ is correct. Or at least, more accurate.
Right, that’s a little bit of housekeeping out of the way.
Now, here’s the text.
You may well have noticed that the first verse of chapter ten is written in the third person. This may go some way to explaining why some translators have managed to get into the mess which they have. Daniel is an interesting book in terms of its composition. Much of it was written in Daniel’s native tongue of Hebrew, but there are some sections written in Aramaic, which was the language of the Chaldean people of Babylon. Aramaic was widely spoken by the Hebrew peoples after their return from exile in Babylon. That Daniel chose to write parts of the book in Aramaic possibly reflects that. What is clear, however, is that Daniel didn’t sit down and write it all in one go. It was recorded as events happened. It may have been that the final section was written just before his death. Remember, he was in captivity for over 70 years, which ages him at somewhere between 80-90 when Cyrus released the Hebrews. It is likely that Daniel, like many of his counterparts, decided that returning to a ruined Jerusalem at their age was not the most prudent thing to do, especially when so many of them had fully embraced the culture of Babylon. In fact, in the Jeremiah’s letter to them (found in Jeremiah 29), he actively encourages them to do so in verses 4-7.
With all of that in mind, it may have been that a third party did indeed write the opening verse of what we call chapter ten (Daniel didn’t write it in chapters – they were added in the Middle Ages), after Daniel had died, and as a way of explanation of its contents. If this is the case then whoever wrote it could have been saying that he had understanding of the vision because it is clear that Daniel didn’t at first. Of course, if the first verse was written as an epitaph, it could well have been saying that when Daniel died he had gained understanding of the vision.
When you read on, what becomes clear is that Daniel called upon his God, Yehovah, to bring him understanding of the vision. Why else would Daniel have been fasting and praying for three weeks? Many commentators have speculated that Daniel was actually mourning after receiving news about the state of Jerusalem. There is no evidence I can find to strengthen that view. It may well be true, but it remains speculation. Whatever the reason for Daniel’s three weeks of fasting and prayer, it is clear that the message Daniel received was in response to a question he had asked. I don’t believe that Daniel set out to fast for three weeks. The reading of it is that he determined that he would fast until he received an answer. We know from later on in the text (see Daniel 10:12) that from the moment that Daniel sought understanding, he was answered, but the answer was delayed for twenty-one days. There is a lesson for all of us here when seeking an answer for God – keep going until it arrives!
So, Daniel had been eating no meat or drinking no wine for a full three weeks when, one day, he was beside the River Tigris and saw a ‘certain man‘ when he looked up. This is a bit of a tough one because the description he gives is incredibly similar to the one of Yeshua given in the book of Revelation, but we know from this certain man’s own words that he had been detained by the Prince of Persia, which doesn’t sound like Yeshua – who after all could detain Him? Although, we have to remember that if it was Yeshua who was speaking to Daniel, it was in a pre-incarnate state and, therefore, before all power and authority had been given to Him. So, it is possible that the Prince of Persia (one of the beasts to whom a kingdom and power and authority had been given at that time) was able to detain Him. We will come back to that in a moment. First, let us deal with Daniel’s description of this certain man:
“I lifted my eyes and looked, and behold, a certain man clothed in linen, whose waist was girded with gold of Uphaz! His body was like beryl, his face like the appearance of lightning, his eyes like torches of fire, his arms and feet like burnished bronze in colour, and the sound of his words like the voice of a multitude.” [Daniel 10:5-6 NKJV]
If this were merely an angel (and I say ‘merely’ not in any degrading way but in context), which we know Daniel had encountered before and whom he didn’t described like this, why then did he do so on this occasion? Now take a look at the description which John gives in the Revelation:
“…One like the Son of Man, clothed with a garment down to the feet and girded about the chest with a golden band. His head and hair were white like wool, as white as snow, and His eyes like a flame of fire; His feet like fine brass, as if refined in a furnace, and His voice as the sound of many waters.” [Revelation 1:13b-15]
Remarkably similar, aren’t they? It is also interesting that both Daniel and John had the same reaction at the sight of Him – they both fell to the floor as though dead. And what adds weight to this being Yeshua is the description which Daniel tells of the reaction of the men who were with him – they didn’t see the vision but a great terror fell upon them. We see something similar with Paul’s companions on the Damascus road in Acts chapter nine.
There is a lot to get through, so I am going to pick out the really important parts. We learn from the text that from the moment Daniel sought understanding of the things which he had seen in a dream or vision, that God sent him an answer. Let us assume, for the moment, that God chose to send Yeshua, Himself, to reassure Daniel. Let’s assume that it was Yeshua who was held up in delivering that message by the ‘prince of the kingdom of Persia‘. Now, the question is, how could this ‘prince‘ contain the Son of God, let alone withstand Him for 21 days? I suspect that we have already answered that question in an earlier part of this series. This is no ordinary prince. In this usage the title prince is given to a spiritual ruler, or principality. If we take that all of the visions and dream contained within Daniel are connected, then we can see that the ‘prince of the kingdom of Persia‘ is a reference to one of the beasts, or spiritual entities, which have been given earthly power and authority.
If we take a look at the level of authority given to Nebuchadnezzar:
“You, O king, are a king of kings. For the God of heaven has given to you a kingdom, power, strength, and glory; and wherever the children of men swell, or the beasts of the field and the birds of the heaven, He has given them into your hand, and has made you ruler over them all…” [Daniel 2:37-38a]
If then, by the same rationale, the prince of the kingdom of Persia has been given a similar level of authority, then it is a little easier to understand why a pre-incarnate Yeshua was held up by him. Yeshua’s earthly authority wasn’t given until He walked the earth.
And staying with the idea of it being a spiritual entity which is actually given the power and authority, we must also apply this to Nebuchadnezzar. The power and authority which had been given to Nebuchadnezzar actually came from the prince of the kingdom of Babylon. We see this happening with Yeshua and His disciples – He gave to them the authority given to Him so that they could heal the sick and expel demons.
Back to the text. Yeshua explains to Daniel that He intends to make Daniel understand what must happen to his people in the latter days. It is clear from the Hebrew text that Yeshua is speaking of the final days. It is equally as clear that by ‘his people‘ Yeshua is speaking to Daniel of the Hebrews. It is worth mentioning also at this stage something that adds considerable gravity to it being Yeshua who is speaking at this stage. In the Revelation it is clearly Yeshua who speaks to John. He says to John this:
“Write the things which you have seen, and the things which are, and the things which will take place after this.” [Revelation 1:19]
After the initial messages for the seven churches of Asia Minor, Yeshua hands over to an angel. But, He states that what John is about to see concerns the things of the future first and then passes the responsibility of showing John what is clearly the very end of the earthly kingdoms and the establishment of the heavenly kingdom. My point is this – it appears that when it comes to the things of the last days, on occasions, Yeshua likes to be the messenger Himself, so that there can be no confusion about which He speaks.
Yeshua (back in Daniel 10) then asks Daniel if he knows why He has come to him. He doesn’t wait for an answer but says the following:
“And now I must return to fight with the prince of Persia; and when I have gone forth, indeed the prince of Yavan will come. But I will tell you what is inscribed in the Scripture of Truth. Yet there is one who holds with these things and that is Michael, your prince.” [Daniel 10:20b-21]
Let’s translate what that actually says.
“After I give you this message I will return to fight with the prince of the kingdom of Persia (who was probably holding up the return of the Hebrews to Isra’el). When I have return to the Father, then the prince of the kingdom of Yavan (that is in modern day Turkey) will arise to fight with the prince of the kingdom of Persia. Before I go I will tell you what is recorded in the books of God’s truth. There is only one here with me who holds with these truths and he is Michael, the prince of the kingdom of Isra’el.”
Now comes 11:1, which many avoid trying to explain:
“Also in the first year of Darius the Mede, I stood to be an encouragement to him and to strengthen him.” [Daniel 11:1]
Why did Yeshua say this?
Darius the Mede is only found, by this name, in the pages of Daniel. No historical account can be found of him. There were plenty of Medes called Darius but none which can be identified in this light. I have seen some research which suggests that Darius was an alternative name for Cyrus. Or it is possible that Darius was the Mede to whom Cyrus answered. Either way, we have Yeshua Himself reassuring Daniel that it was He who stood next to this Darius and encouraged him to set the Hebrews free.
Here follows the truth that Yeshua has said he would show Daniel from the time at the end. Please keep that in mind whilst we go through this. The events He speaks of all refer to the years leading up to the rise of the anti-Christ and the return of Yeshua, King of all kings.
“Behold, three more kings will arise in Persia, and then the fourth shall be far richer than them all; by his strength, through his riches, he shall stir up all against the realm of Yavan. Then a mighty king shall arise, who shall rule with great dominion and do according to his will.” [verses 2-3]
To paraphrase:
“From this time, there will be three more significant rulers of Persia, Then will come a fourth. Great wealth (probably from the control of Iranian oil) will bring him political strength, and he will stir up the people of the realm of Turkey (probably by invading their land). Then, in the land of Yavan (Turkey) a mighty ruler will arise (who is the large horn mentioned in Daniel 8). He will increase the size of his dominion and rule and do exactly as he pleases.”
“And when he has arisen, his kingdom shall be broken up and divided toward the four winds of heaven, but not among his posterity (people) nor according to his dominion with which he ruled; for his kingdom shall be uprooted, and given to others.” [verse 4]
“This large horn, ruler of Turkey, shall attack the ruler of Iran but he will be cut down before he can achieve all he plans. His kingdom and sphere of influence will be divided between the nations he conquered, so that there will be a Kingdom of the North; a Kingdom of the South; a Kingdom of the East; and a Kingdom of the West. None of his own people will succeed him.”
“Also the king of the South shall become strong, and so will one of his princes, who will gain power of him and have dominion, which will be very great.” [verse 5]
“In the south (possibly Egypt, Saudi Arabia, or Yemen) a ruler shall rise up from out of the large horn’s divided kingdom. To one of his spiritual princes who influences him shall be given even greater power.”
“And at the end of some years they shall join forces and the daughter of the king of the South shall go to the king of the North and make an agreement; but she shall not retain the power of her authority, and neither he nor his authority shall stand; but she shall be given up, with those who brought her, and with him who strengthened her in those times.” [verse 6]
Here’s where things start to get tricky to unravel and decipher. The verse basically says that after sometime (probably a set period of time), the king and the powerful prince of the South shall join forces. Whilst it says the ‘daughter‘ of the king of the South, it is unlikely to be a daughter as we know things. Often in prophetic Scripture the term daughter is used to describe both cities and a new and beloved generation. Throughout the book of Isaiah, Jerusalem is called ‘daughter‘. It requires some thinking outside the box. It may be that when the large horn falls and these four new kingdoms arise that they are not like anything we recognise today. It might well go back to ancient boundary and tribal lines of division. A new city or newly named region of the southern kingdom could easily be called a daughter.
If it was a city or a city-state that makes an agreement with the king of the North (which generally refers to Turkey or the region thereof), then because the verse describes the lack of power, it suggests that it could be a political move. It reads as if she (the daughter) will be betrayed and given over in some power tussle.
“But from a branch of her roots one shall arise in his place, who shall come with an army, enter the fortress of the king of the North, and deal with them and prevail. And he shall also carry their gods captive to Egypt, with their princes and their precious articles of silver and gold; and he shall continue more years than the king of the North.” [verses 7-8]
One of the city or city-states people shall rise up in place of the fallen king or prince. He will be given an army that will conquer the fortress of the northern kingdom. The word ‘princes‘ is deceptive here. On this occasion a better translation would have been molten images. I think that the verse is saying that the one who rises up from the root of the city or city-state will completely sack the North and take as plunder the things that it holds dear; its treasures. That might be wealth. It is likely to be people. If by this time there is widespread Sharia law implemented in the Middle East, then a medieval approach to warfare is likely to be readopted, as we have seen already with the likes of ISIL.
This time Egypt is named, but as a place of captivity which strengthens the idea that it will be people who are taken from the North. This power struggle between the North and the South seems to continue, but the new king of the South shall outlive the king of the North. The divide between these two nations could even be between Sunni and Shia Muslims.
The reading of the verses contained in the last three chapters of the book of Daniel are complicated to say the least. It is unclear how much time is covered, or how long each king or kingdom survives. I am going to break each section down into more manageable pieces, so the next few verse will be in the next instalment. I really don’t want to speculate about what is written there. It is clear from 12:4 that the words and the vision of these prophecies will have been sealed until the end times. I think around 10-15 years ago the Holy Spirit began the process of revealing the truths of the prophecies. There is still much more that remains hidden, but I firmly believe that the people whom God has prompted to have an interest in such writings will, if they seek Him for wisdom and understanding, be granted just that.
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(8/(-12))/(1/t)?
True
Suppose 4*r + 1124 = 4*n + 48, 3*n - 803 = 4*r. Is 2 a factor of n?
False
Suppose -1694 = -2*u + 4*f, -116*f + 117*f - 4279 = -5*u. Is 13 a factor of u?
False
Suppose 187 = 2*b - 879. Is 13 a factor of b?
True
Suppose 0 = -5*s - 3*k + 4 + 8, -k = 2*s - 4. Suppose b - 138 = -3*h - 2*b, -5*h - 4*b + 226 = s. Does 3 divide h?
True
Let j be 8/(-40) + (-102)/15. Let a(g) = -32*g - 20. Is 19 a factor of a(j)?
False
Is 11 a factor of (-386)/(-6) + 20/(-12)*-1?
True
Suppose -2*k = -7*k + 810. Suppose 498 = 4*b + k. Suppose -9*r + 13*r - b = 0. Is 4 a factor of r?
False
Let a = 33 - 62. Let j be 2/18 - 3470/45. Let o = a - j. Is o a multiple of 24?
True
Let s(o) = -16*o + 2. Suppose -5*p = 5, 7 + 1 = -3*i - 5*p. Let y be s(i). Suppose -l - y = -5*k, -k = -2*l + 6*l - 33. Does 2 divide l?
False
Let x(g) be the second derivative of g**3/6 + 13*g**2/2 - 2*g. Let w(u) = u**3 + 10*u**2 - 6. Let m be w(-10). Is 3 a factor of x(m)?
False
Let w(u) be the third derivative of -u**5/60 + u**4/3 - 7*u**3/6 - 7*u**2. Let b be w(5). Let i(c) = 2*c - 8. Is i(b) a multiple of 8?
True
Let k(i) = 84*i - 8. Let o be k(2). Suppose -53 = 3*b - 5*x - o, -2*b + 66 = 2*x. Does 4 divide b?
False
Is 15 a factor of 4/(-9 + 5) + 569?
False
Suppose -3*l + 5*l - 26 = 0. Suppose l*v = 10*v + 207. Is v a multiple of 12?
False
Let y(s) = 2*s**3 + 54*s**2 - 2*s + 13. Is 8 a factor of y(-24)?
False
Let f = 2102 + -1121. Is 9 a factor of f?
True
Let k = 9 + 11. Suppose k = 3*f - 7. Does 12 divide (f + -1)/(-4) + 50?
True
Let n(k) = -k. Let j(u) = -u**3 - 6*u**2 - 6*u - 6. Let m be j(-5). Let h(a) = 7*a + 1. Let v(l) = m*h(l) + 2*n(l). Is v(-1) a multiple of 8?
True
Does 7 divide (218/(-3))/((-12)/36)?
False
Let a(t) = -13*t + 10. Let u be a(-14). Suppose 0 = 4*p - 2*p - u. Is 12 a factor of p?
True
Suppose 0 = 5*c - 18 - 2, 0 = 2*r - 2*c + 46. Let l = -17 - r. Let d(w) = 15*w - 2. Does 14 divide d(l)?
True
Suppose 2*u - 523 - 73 = 0. Let f = 436 - u. Is 46 a factor of f?
True
Let s = 66 - 61. Suppose -70 - 1 = -u + s*n, -u - 2*n = -99. Is 7 a factor of u?
True
Let t = -830 + 1431. Is t a multiple of 14?
False
Let p(j) = 249*j**2 - 12*j + 15. Is p(3) a multiple of 10?
True
Let a be (-7918)/10 + ((-20)/(-25))/(-4). Is a/(-55)*75/6 a multiple of 18?
True
Let q(n) = 2*n**3 + 26*n**2 - 3*n - 1. Is q(-13) a multiple of 6?
False
Let x(y) = 78*y + 3. Let d be x(4). Suppose 0 = 2*z + 131 - d. Suppose -q = -3*h - h - 43, z = 2*q - 5*h. Is 17 a factor of q?
True
Let i be 61 + 0 + -2 - 1. Does 9 divide (48/3)/(-4) + i?
True
Let u = -1085 - -1105. Is u a multiple of 5?
True
Suppose -o - n - 2 = 1, 23 = 4*o - 3*n. Let a be (-2)/2 - 5*1. Let k = o - a. Is 3 a factor of k?
False
Suppose -5*q - 25 = 0, -2*k + 95 = 3*q - 68. Does 2 divide k?
False
Suppose 3*o + j - 13 = 0, -3*o + 9 = -5*j + 2. Suppose -4*n + 2*n = 2*m - o, 0 = 3*n - 5*m + 10. Suppose n = -u - 2*u + 78. Is u a multiple of 26?
True
Let z(d) = 17*d. Let o be z(-3). Let y = -25 - o. Suppose 5*n + 3*u - 9 = y, -4*n + 4*u = 4. Is n a multiple of 2?
True
Let d(f) = f**3 - 11*f**2 - 12*f + 6. Let z be d(13). Suppose 4*l + z = 4*w, -3*l = -w + 63 - 16. Is 8 a factor of w?
False
Suppose 2*v - 4*s = -2*s + 12, -s = -5*v + 14. Suppose 0 = -5*n + 5*q, 4 = 2*n - q + v. Suppose n*d - 5*j = 83, -2*j + 112 = 3*d - 7*j. Does 22 divide d?
False
Does 30 divide (-250)/(-4)*(7 - 253/55)?
True
Suppose 0 = -k + 5*k + 220. Let f = -39 - -29. Is f/k - (-64)/11 a multiple of 2?
True
Let a(q) = 29*q**2 - 16*q - 46. Is a(-13) a multiple of 83?
True
Is 5 a factor of -3*(565/3)/(-5)?
False
Let g = 11 - 3. Suppose 0 = -g*y + 277 + 115. Suppose -17 = 2*u - y. Does 3 divide u?
False
Let n(p) = p**2 + 7*p + 5. Suppose -2*m = -7 + 21. Let s be n(m). Suppose -3*u = -2*o + 44, -o + 2*u + 15 = -s. Does 8 divide o?
False
Suppose 4*n - 2956 + 962 = 5*v, 4*n - 4*v - 1992 = 0. Does 9 divide n?
False
Let k be ((-20)/6)/((-13)/(3159/18)). Suppose -2*t = -69 - k. Is t a multiple of 3?
True
Let n(u) = -6*u. Let x(z) = -36*z - 3. Let p(o) = -12*o - 1. Let b(d) = -7*p(d) + 2*x(d). Let i(l) = 4*b(l) + 9*n(l). Is 20 a factor of i(-6)?
True
Let f = -47 + 33. Let k(d) = -d + 31. Is k(f) a multiple of 15?
True
Let o be -1 + 1/1 + 2. Suppose -22 = -2*i - 4*k, 0 = 5*i + o*k - 10 - 13. Suppose g - 80 = -i*g. Does 10 divide g?
True
Suppose 3*j - 3338 = 27*p - 25*p, -4*p = j - 1108. Does 5 divide j?
False
Let v = -362 + 1030. Does 48 divide v?
False
Let d = 166 - 319. Does 36 divide 1726/8 - (d/36 - -4)?
True
Let z be (-6)/14 + (-211824)/252. Let q = -410 - z. Is 13 a factor of q?
False
Is 0/2 - 28*(-96)/8 a multiple of 14?
True
Suppose -4*z + 3 + 1 = 0, 5*m = -4*z + 539. Let q = 55 + -126. Let k = q + m. Does 16 divide k?
False
Suppose 2*j - 1 + 3 = 2*x, 2*j + 2 = -3*x. Suppose -11 = -3*o + 2*l, -2 = 2*l - x. Does 7 divide 8/12*10*o?
False
Suppose 0 = -5*y - 2*w + 85 + 65, -2*y = 4*w - 60. Let c = y + -42. Is 8 a factor of (-79)/(-3) + (-8)/c?
False
Let q be (-3)/(-6 - -3)*2. Is 20 a factor of 369/6 - (-1)/q?
False
Does 61 divide 2/9 - 59256/(-162)?
True
Let j(a) = -a**3 + a**2 - a. Is 36 a factor of j(-3)?
False
Let h be (1/(-3) + 1)*(2 + 1). Suppose 52 = 5*q + 2*g, -4*q + h*g = -2*g - 64. Does 12 divide q?
True
Let n(o) = o**3 + 19*o**2 - 123*o + 17. Is 4 a factor of n(-24)?
False
Suppose -7*v + 936 - 3582 = 0. Does 13 divide (12/(-14))/(6/v)?
False
Suppose -5*f - 306 = -u - 4*f, 326 = u + 4*f. Is u a multiple of 10?
True
Suppose -g = 4*g - 30. Suppose 0 = g*n - 5 - 13. Is 3 a factor of n?
True
Let r = -12 - -17. Suppose -r*s + 178 + 97 = 0. Suppose 3*g = -2*g + s. Does 11 divide g?
True
Let s(w) be the second derivative of w**5/20 + 17*w**4/12 - 2*w**3/3 - 35*w**2/2 + 7*w. Is 30 a factor of s(-17)?
False
Suppose -y - 1 = -5*n + 9, 3*y - 10 = -5*n. Does 14 divide (1698/(-15))/(n/(-5))?
False
Let t be 4/14 - 896/49. Let n be (t + 0)/((-6)/4). Suppose 150 = -7*v + n*v. Is v a multiple of 6?
True
Suppose -8*r = 22*r - 6480. Does 4 divide r?
True
Suppose 4*u - 39 + 3 = 0. Let y(w) = 271*w**2 - 1. Let c be y(-1). Suppose c = 12*o - u*o. Is o a multiple of 30?
True
Let c = 92 + -89. Is 8 a factor of (58 - -2) + (3 - c)?
False
Let b(z) = z - 2. Let g be b(2). Let r(h) = 9 + 1 - 6 - h. Does 4 divide r(g)?
True
Let z(x) = -7*x - 1. Suppose t = -0*t - 3. Is z(t) a multiple of 4?
True
Let f = -181 - -1525. Suppose 6*k + f = 12*k. Is k a multiple of 22?
False
Suppose -2*x + 8*v + 950 = 13*v, 4*x = -2*v + 1916. Does 8 divide x?
True
Suppose 0 = -4*n - 5*g + 4387, 0 = -60*n + 59*n - 2*g + 1096. Is n a multiple of 61?
True
Suppose 6*g - 26 = 5*g. Let j be g - 19 - (3 - -1). Suppose j*k = 2*k + 24. Is k a multiple of 24?
True
Is 36 a factor of 4*-1*(-1832)/16?
False
Suppose 11223 - 3447 = 8*r. Does 54 divide r?
True
Suppose -5*t + u + 93 = 0, 0*t + 2*u = -t + 12. Suppose 4*l = 34 + t. Suppose -2*z + 91 = -l. Does 31 divide z?
False
Suppose 13*q = 16*q. Suppose 17*u - 22*u + 65 = q. Does 3 divide u?
False
Let m(r) = 4*r**2 - 33*r - 10. Let y(p) = -p**2 - 17*p + 48. Let o be y(-19). Does 6 divide m(o)?
True
Let i be 1/(2 - 3) + 31. Let m = i + -24. Is m a multiple of 4?
False
Let f(n) = -16*n + 12. Let b be f(7). Let o = 160 + b. Does 20 divide o?
True
Let f(x) = 8*x**2 + 1. Let j be f(-1). Is 20/(-2)*(-5 + j/(-2)) a multiple of 4?
False
Let g(z) = 4*z**3 - 41*z**2 - 29*z + 16. Is g(13) a multiple of 35?
False
Let r(n) = -48*n**2 + 5*n + 7. Let m be r(-2). Let u = m + 464. Does 42 divide u?
False
Let a(n) = 3*n + 27. Let z be a(-8). Let w be (z + -4)/(2/(-8)). Is 10/w*134/5 a multiple of 22?
False
Let i = -66 - 70. Let y = 268 + i. Is 12 a factor of y?
True
Suppose 31*n - 23*n = 40. Suppose n*q = -f - 3, 0*f - 2*f + q + 16 = 0. Is 2 a factor of f?
False
Let t = 40 - 24. Let c be 216/(4*6/t). Suppose -3*i + c = i. Is i a multiple of 18?
True
Let j = 713 + 435. Is j a multiple of 28?
True
Suppose 7*c + 12 = 4*c. Does 13 divide c - -2*(-68)/(-8)?
True
Let a(b) be the second derivative of -3*b + 11/6*b**3 + 2*b**2 + 0 - 1/20*b**5 - 1/4*b**4. Is 23 a factor of a(-6)?
True
Suppose j = 3*k + 1056, 5*j - 3*k - 714 = 4626. Does 21 divide j?
True
Let v(a) = a**2 - 4*a - 107. Is 49 a factor of v(17)?
False
Let w(n) = n**3 - 5*n**2 + 2*n - 7. Let s be w(5). Suppose -4*r = -i - i - 186, -s*i = 15.
|
SMYRNA – Whitefield Academy families will see a shifting of top administrators over the next several months.
The school’s Board of Trustees announced this week they have selected the school’s current academic dean, Dr. Kevin Bracher, to replace Dr. John Lindsell as interim headmaster until they hire a permanent head.
Dr. Susan Banke, Whitefield’s upper school principal, is retiring at the end of the school year. Trustees are also searching for her replacement.
Lindsell turned in his resignation to the board Tuesday.
“For five wonderful years it has been my privilege to lead the school,” Lindsell said Friday, which was his last day. “Even in tough times, the school has advanced and much has been accomplished and the glory goes to God alone.”
He said he will leave behind “many sweet memories” of Whitefield school plays, concerts, football games, the Blue Crew, learning the intricacies of lacrosse, three state championships in basketball and tennis, commencement and Christmas breakfasts.
“Whitefield Academy has enriched my life, and for that I will be forever grateful,” he said.
Marsha Burke, the board’s chair, said Lindsell and his wife Stephanie welcomed a grandchild last month, and the couple decided to move to be closer to family.
She said Lindsell has helped lead a successful capital campaign in a difficult financial environment; construction and occupation of Morris Hall, Whitefield’s new upper school; academic success, which has led to Whitefield students having the highest SAT scores in Cobb; and a recent dual reaccreditation by SAIS/SACS.
“The Whitefield Academy community is particularly indebted to Dr. Lindsell for shepherding us through a difficult economic time and recruiting and promoting several outstanding staff members who are tremendous assets to Whitefield Academy,” Burke said. “We pray God’s blessings on him and Stephanie as they begin their next chapter.”
The board has formed a search committee to find Lindsell’s permanent replacement, but Bracher will take the reins in the meantime.
“I came to Whitefield Academy nearly six years ago because I was energized by the mission of the school and its people,” Bracher said. “I remain sold out to Whitefield’s mission and have enjoyed serving in positions of increasing responsibility for the community that has captured my heart. Leadership is serving others, and I can’t wait to continue serving alongside an incredibly experienced and talented leadership team.”
The board is also narrowing down its search for Banke’s replacement and hopes to name a new upper school principal in the next 30 days.
The longtime educator has been at Whitefield since 2006.
“We have an incredible slate of candidates for the upper school principal position,” said Whitefield spokesperson Elyse Hammett. “With that in the near future and looking throughout the region to see who the next headmaster will be, the future just looks really bright here at Whitefield.”
*We welcome your comments on the stories and issues of the day and seek to provide a forum for the community to voice opinions. All comments are subject to moderator approval before being made visible on the website but are not edited. The use of profanity, obscene and vulgar language, hate speech, and racial slurs is strictly prohibited. Advertisements, promotions, and spam will also be rejected. Please read our terms of service for full guides
|
Effectiveness of bicanalicular silicone intubation in the repair of canalicular lacerations.
In this series of 24 patients with 28 canalicular lacerations, bicanalicular silicone intubation is found to be an effective technique with 95% anatomic success. No statistically significant difference is noted in successful repair when comparing proximal, mid, and distal lacerations. There are no recognized cases of iatrogenic injury to either the injured or the uninjured canaliculus in this series. The repair of all canalicular lacerations is advocated.
|
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:default-content-type "json"
:auth-caching {:init {}
:ttl {:minutes 60}
:lru {:threshold 1000}
:dumpfile "data/cache/authz-dump.edn"}
:concept-caching {:init {}
:ttl {:hours 24}
:dumpfile "data/cache/concept-dump.edn"}
:cmr {
:access {:control {:protocol "https"
:host "cmr.sit.earthdata.nasa.gov"
:relative {:root {:url "/access-control"}}}}
:concept {
:variable {:version "1.1"}}
:echo {:rest {:protocol "https"
:host "cmr.sit.earthdata.nasa.gov"
:context "/legacy-services/rest"}}
:max-pagesize 2000
:opendap {:protocol "https"
:host "cmr.sit.earthdata.nasa.gov"
:public {:protocol "https"
:host "cmr.sit.earthdata.nasa.gov"}
:relative {:root {:url "/opendap"}}}
:search {:protocol "https"
:host "cmr.sit.earthdata.nasa.gov"
:relative {:root {:url "/search"}}}}
:giovanni {
:search {:protocol "https"
:host "giovanni.gsfc.nasa.gov"
:relative {:root {:url "/giovanni"}}}}
:edsc {
:search {:protocol "https"
:host "search.sit.earthdata.nasa.gov"
:relative {:root {:url "/search"}}}}
:httpd {
:port 3013
:entry-point-fn nil
:route-fns {
:api cmr.ous.app.routes.rest.core/all
:site cmr.ous.app.routes.site/all}
:pages {
:default-title "CMR OPeNDAP"}
:base-url "/opendap"
:docs "resources/public/docs"
:assets "resources/public/assets"
:rest-docs
{:base-url-template "%%OPENDAP_BASE_URL%%"
:source "resources/docs/rest-api/index.md"
:outdir "resources/public/docs/opendap/docs/current/rest-api"}
:skip-static #{"/opendap/docs"}
:replace-base-url #{"/opendap/docs/current/rest-api"
"/opendap/docs/current/reference/2000-usage.html"}
:index-dirs #{"/opendap/docs/1.0.0/marginalia"
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"/opendap/docs/current/rest-api"}
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:timeout 20000 ; milliseconds (20 seconds * 1000)
:heartbeat 200 ; milliseconds
}}
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|
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Most popular CAT
Cat Cat Dimen 6 Safety Boot In Honey (Size 8) on other UK sites
The Cat® Dimen 6" Safety Boot is a sturdy and durable safety boot with a steel toe cap and padded top. It has a yellow inner and the lace holes go all the way up to the ankle with four eyelets and two sets of hooks, giving you full ankle support to prevent twisting. There is a dual density polyurethane sole that provides an excellent level of slip resistance.
The Caterpillar Colorado is a favourite. Probably the ultimate rugged work boot. Offering a full grain leather upper or nubuck. This casual boot was built for working but is now a stylish key piece for men too! Boots have non slip rubber sole and mesh liing and sock. The famous motif is on the outside
This transparent cat safety net will protect your cat from tricky manoeuvres on the balcony or near to open windows. It is a great way to make balconies and open windows safe and the transparent material is virtually unnoticeable. It can be used indoors as well as outdoors and strong and durable as well as weather resistant and non-toxic. The mesh width is only 3 x 3 cm so it is suitable for
Passion is a dangerous adversary that weaves its treacherous threads amongst the members of a wealthy tycoons household. Murder and mania go hand in hand. Bruce the tycoons son has a strange obsession with his cat Samson. Samson has a vicious hatred of the family nurse Susan. Susan is plotting a murder but who is plotting to murder Susan?
Grab a place on the couch or go find a seat for youre in for a wonderful Dr. Seuss treat! The Cat in the Hat who goes by the name Is played by Mike Myers of comedy fame! It starts with two kids on a cold cold wet day there mum is at work and theyve no games to play! Then in walks the fun in the form of a Cat who pulls out the laughs from the brim of his hat. Things really get wild when The Cat
\Frontline Plus (Known as Frontline Combo) provides convenient and effective flea and tick control in dogs and cats, puppies and kittens. It is effective against all stages of the brown dog tick, the A\
Everyone has a pair of boots that are a go-to favourite and were certain that these wear-with-anything Chelsea boots will become yours. Crafted from chestnut brown leather theyre both versatile and comfortable too.
|
Q:
shutdown all the quartz jobs as soon as app server is shut down?
I have a web application in which I am running some jobs periodically so for that I am using quartz framework here. Below is how I am starting all my jobs:
As soon as the server gets started up, it calls postInit method autmatically. And then I start all my jobs and it works fine:
@PostConstruct
public void postInit() {
logger.logInfo("Starting all jobs");
StdSchedulerFactory factory = new StdSchedulerFactory();
try {
factory.initialize(App.class.getClassLoader().getResourceAsStream("quartz.properties"));
Scheduler scheduler = factory.getScheduler();
// starts all our jobs using quartz_config.xml file
scheduler.start();
} catch (SchedulerException ex) {
logger.logError("error while starting scheduler= ", ExceptionUtils.getStackTrace(ex));
}
}
@PreDestroy
public void shutdown() {
logger.logInfo("Shutting down all jobs");
}
Now I want to stop all the jobs that are running as soon as we try to shutdown the app server. So whenever we try to shutdown the app server, it will call shutdown method automatically. Now I need some way where we can shutdown all the jobs as soon as shutdown method is called. What is the best way by which I can shutdown all the jobs as soon as shutdown method is called?
Below is my "quartz.properties" file. Do I really need "quartz.properties" file since I guess I am using default values anyways I think?
#------------------------- Threads ---------------------------------#
# how many jobs we should run at the same time?
org.quartz.threadPool.threadCount=15
# ----------------------------- Plugins --------------------------- #
# class from where we should load the configuration data for each job and trigger.
org.quartz.plugin.jobInitializer.class=org.quartz.plugins.xml.XMLSchedulingDataProcessorPlugin
org.quartz.plugin.jobInitializer.fileNames = quartz_config.xml
org.quartz.plugin.jobInitializer.failOnFileNotFound = true
org.quartz.jobStore.class = org.quartz.simpl.RAMJobStore
A:
You can use Scheduler.shutdown() method as below and it is a good idea to externalize the quartz configuration even if you use the default parameters. This will make your code flexible.
private Scheduler scheduler;
@PostConstruct
public void postInit() {
logger.logInfo("Starting all jobs");
StdSchedulerFactory factory = new StdSchedulerFactory();
try {
factory.initialize(App.class.getClassLoader().getResourceAsStream("quartz.properties"));
scheduler = factory.getScheduler();
// starts all our jobs using quartz_config.xml file
scheduler.start();
} catch (SchedulerException ex) {
logger.logError("error while starting scheduler= ", ExceptionUtils.getStackTrace(ex));
}
}
@PreDestroy
public void shutdown() throws SchedulerException {
logger.logInfo("Shutting down all jobs");
scheduler.shutdown();
}
|
Q:
Highcharts : Export multiple charts to pdf in custom layout
I was trying to export multiple charts to a single pdf with the following layout.
It is working well as said in http://jsfiddle.net/BlackLabel/b0jnqd0c/
But when I try to export more number of charts, the entire charts are not exported. For example, if I change the lines in js fiddle code to :
$('#export-pdf').click(function() {
Highcharts.exportCharts([chart1, chart2, chart3, chart4, chart1, chart2, chart3, chart4], {
type: 'application/pdf'
});
});
And try to export 8 charts, my export pdf is missing the 8 charts and is restricted to 6 charts.
My requirement is to export the whole bunch of charts that are dynamically generated to pdf, there may be any number of charts.
Also as seen in image, the charts are not fit to pdf page.
A:
Would you like to achieve something like in the demo below? In the demo which I prepared, I tested exporting of 17 charts.
Highcharts.getSVG = function(charts) {
var svgArr = [],
top = 0,
width = 0,
endWidth = 0;
Highcharts.each(charts, function(chart) {
var svg = chart.getSVG(),
// Get width/height of SVG for export
svgWidth = +svg.match(
/^<svg[^>]*width\s*=\s*\"?(\d+)\"?[^>]*>/
)[1],
svgHeight = +svg.match(
/^<svg[^>]*height\s*=\s*\"?(\d+)\"?[^>]*>/
)[1];
svg = svg.replace(
'<svg',
'<g transform="translate(' + width + ', ' + top + ')" '
);
svg = svg.replace('</svg>', '</g>');
width += svgWidth;
endWidth = Math.max(endWidth, width)
if (width === 2 * svgWidth) {
width = 0;
top += svgHeight;
}
svgArr.push(svg);
});
top += 400;
return '<svg height="' + top + '" width="' + endWidth +
'" version="1.1" xmlns="http://www.w3.org/2000/svg">' +
svgArr.join('') + '</svg>';
};
Demo
|
In-situ measurements of low-level mercury vapor exposure from dental amalgam with zeeman atomic absorption spectroscopy.
Alongside food, emissions from amalgam fillings are an essential contribution to man's mercury burden. Previous methods for the determination of intraoral mercury vapor (Hg degrees ) release used principally some form of preconcentration of Hg on gold (film or wool), allowing relatively few measurements with unknown precision and sensitivity at selected times. Recently available computer-controlled Hg detectors operating on Zeeman atomic absorption spectroscopy (ZAAS) facilitate the direct real-time measurement of Hg degrees concentrations. It was the aim to adapt this method for a comparative investigation of emission processes from fillings in situ and from amalgam specimens in vitro. In addition to the ZAAS instrument, the apparatus consisted of a pump, magnetic valves, an electronic flow controller and a handle with a disposable mouth piece for aspiration of oral air. A programmable timer integrated the computer-controlled instrument operation and the data collection into a standard sampling protocol. A fast exponential decay of the emission was found after stimulation of amalgam specimens and of fillings in situ (halftimes 8.6 and 10.7 min). Precision was evaluated by a series of measurements on a single patient which indicated a consistently low coefficient of variation between 18% and 25%. After insertion of a few new fillings, sensitivity was high enough to detect a significant increase in emission against the background emission from the majority of old fillings. Zeeman-AAS in connection with a semi-automated sampling protocol and data storage provides precise in-situ measurements of Hg degrees emission from dental amalgam with real-time resolution. This facilitates the detailed exploration of the Hg degrees release kinetics and the applicability to large-scale studies.
|
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<div class="header">
<div class="summary">
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">GLM_GTC_matrix_transform<div class="ingroups"><a class="el" href="a00153.html">GTC Extensions (Stable)</a></div></div> </div>
</div><!--header-->
<div class="contents">
<p>Defines functions that generate common transformation matrices.
<a href="#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:gada6deb989d4b553fe0f7e3279f3afae1"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gada6deb989d4b553fe0f7e3279f3afae1"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gada6deb989d4b553fe0f7e3279f3afae1">frustum</a> (T left, T right, T bottom, T top, T near, T far)</td></tr>
<tr class="memdesc:gada6deb989d4b553fe0f7e3279f3afae1"><td class="mdescLeft"> </td><td class="mdescRight">Creates a frustum matrix with default handedness. <a href="a00169.html#gada6deb989d4b553fe0f7e3279f3afae1">More...</a><br /></td></tr>
<tr class="separator:gada6deb989d4b553fe0f7e3279f3afae1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga75b1c1d0ee1f80c1e873605adeb1838c"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga75b1c1d0ee1f80c1e873605adeb1838c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga75b1c1d0ee1f80c1e873605adeb1838c">frustumLH</a> (T left, T right, T bottom, T top, T near, T far)</td></tr>
<tr class="memdesc:ga75b1c1d0ee1f80c1e873605adeb1838c"><td class="mdescLeft"> </td><td class="mdescRight">Creates a left handed frustum matrix. <a href="a00169.html#ga75b1c1d0ee1f80c1e873605adeb1838c">More...</a><br /></td></tr>
<tr class="separator:ga75b1c1d0ee1f80c1e873605adeb1838c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gad0e184273bdacbe769e5cd81069e48ed"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gad0e184273bdacbe769e5cd81069e48ed"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gad0e184273bdacbe769e5cd81069e48ed">frustumRH</a> (T left, T right, T bottom, T top, T near, T far)</td></tr>
<tr class="memdesc:gad0e184273bdacbe769e5cd81069e48ed"><td class="mdescLeft"> </td><td class="mdescRight">Creates a right handed frustum matrix. <a href="a00169.html#gad0e184273bdacbe769e5cd81069e48ed">More...</a><br /></td></tr>
<tr class="separator:gad0e184273bdacbe769e5cd81069e48ed"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga79f704ad91a5f0d68abd88c66c8186e5"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga79f704ad91a5f0d68abd88c66c8186e5"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga79f704ad91a5f0d68abd88c66c8186e5">infinitePerspective</a> (T fovy, T aspect, T near)</td></tr>
<tr class="memdesc:ga79f704ad91a5f0d68abd88c66c8186e5"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a symmetric perspective-view frustum with far plane at infinite with default handedness. <a href="a00169.html#ga79f704ad91a5f0d68abd88c66c8186e5">More...</a><br /></td></tr>
<tr class="separator:ga79f704ad91a5f0d68abd88c66c8186e5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga47af534da2b28effa4c7945ec82ccd9d"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga47af534da2b28effa4c7945ec82ccd9d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga47af534da2b28effa4c7945ec82ccd9d">infinitePerspectiveLH</a> (T fovy, T aspect, T near)</td></tr>
<tr class="memdesc:ga47af534da2b28effa4c7945ec82ccd9d"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a left handed, symmetric perspective-view frustum with far plane at infinite. <a href="a00169.html#ga47af534da2b28effa4c7945ec82ccd9d">More...</a><br /></td></tr>
<tr class="separator:ga47af534da2b28effa4c7945ec82ccd9d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga79575023763df88dff1bf8255a42d0be"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga79575023763df88dff1bf8255a42d0be"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga79575023763df88dff1bf8255a42d0be">infinitePerspectiveRH</a> (T fovy, T aspect, T near)</td></tr>
<tr class="memdesc:ga79575023763df88dff1bf8255a42d0be"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a right handed, symmetric perspective-view frustum with far plane at infinite. <a href="a00169.html#ga79575023763df88dff1bf8255a42d0be">More...</a><br /></td></tr>
<tr class="separator:ga79575023763df88dff1bf8255a42d0be"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaf8eef81da1ad09f6a8920101c01eaae4"><td class="memTemplParams" colspan="2">template<typename T , precision P> </td></tr>
<tr class="memitem:gaf8eef81da1ad09f6a8920101c01eaae4"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gaf8eef81da1ad09f6a8920101c01eaae4">lookAt</a> (tvec3< T, P > const &eye, tvec3< T, P > const &center, tvec3< T, P > const &up)</td></tr>
<tr class="memdesc:gaf8eef81da1ad09f6a8920101c01eaae4"><td class="mdescLeft"> </td><td class="mdescRight">Build a look at view matrix based on the default handedness. <a href="a00169.html#gaf8eef81da1ad09f6a8920101c01eaae4">More...</a><br /></td></tr>
<tr class="separator:gaf8eef81da1ad09f6a8920101c01eaae4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gacd0c077ec7b58a575855e29cb5fb586d"><td class="memTemplParams" colspan="2">template<typename T , precision P> </td></tr>
<tr class="memitem:gacd0c077ec7b58a575855e29cb5fb586d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gacd0c077ec7b58a575855e29cb5fb586d">lookAtLH</a> (tvec3< T, P > const &eye, tvec3< T, P > const &center, tvec3< T, P > const &up)</td></tr>
<tr class="memdesc:gacd0c077ec7b58a575855e29cb5fb586d"><td class="mdescLeft"> </td><td class="mdescRight">Build a left handed look at view matrix. <a href="a00169.html#gacd0c077ec7b58a575855e29cb5fb586d">More...</a><br /></td></tr>
<tr class="separator:gacd0c077ec7b58a575855e29cb5fb586d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga2876d9313334980b94292d2ec169088e"><td class="memTemplParams" colspan="2">template<typename T , precision P> </td></tr>
<tr class="memitem:ga2876d9313334980b94292d2ec169088e"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga2876d9313334980b94292d2ec169088e">lookAtRH</a> (tvec3< T, P > const &eye, tvec3< T, P > const &center, tvec3< T, P > const &up)</td></tr>
<tr class="memdesc:ga2876d9313334980b94292d2ec169088e"><td class="mdescLeft"> </td><td class="mdescRight">Build a right handed look at view matrix. <a href="a00169.html#ga2876d9313334980b94292d2ec169088e">More...</a><br /></td></tr>
<tr class="separator:ga2876d9313334980b94292d2ec169088e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga65280251de6e38580110a0577a43d8f8"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga65280251de6e38580110a0577a43d8f8"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga65280251de6e38580110a0577a43d8f8">ortho</a> (T left, T right, T bottom, T top, T zNear, T zFar)</td></tr>
<tr class="memdesc:ga65280251de6e38580110a0577a43d8f8"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for an orthographic parallel viewing volume, using the default handedness. <a href="a00169.html#ga65280251de6e38580110a0577a43d8f8">More...</a><br /></td></tr>
<tr class="separator:ga65280251de6e38580110a0577a43d8f8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga45b1b64f99255c07119b4f1aaed04dd7"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga45b1b64f99255c07119b4f1aaed04dd7"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga45b1b64f99255c07119b4f1aaed04dd7">ortho</a> (T left, T right, T bottom, T top)</td></tr>
<tr class="memdesc:ga45b1b64f99255c07119b4f1aaed04dd7"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for projecting two-dimensional coordinates onto the screen. <a href="a00169.html#ga45b1b64f99255c07119b4f1aaed04dd7">More...</a><br /></td></tr>
<tr class="separator:ga45b1b64f99255c07119b4f1aaed04dd7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga71503df1e691b12cc2d45e64fd0628fe"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga71503df1e691b12cc2d45e64fd0628fe"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga71503df1e691b12cc2d45e64fd0628fe">orthoLH</a> (T left, T right, T bottom, T top, T zNear, T zFar)</td></tr>
<tr class="memdesc:ga71503df1e691b12cc2d45e64fd0628fe"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for an orthographic parallel viewing volume, using left-handedness. <a href="a00169.html#ga71503df1e691b12cc2d45e64fd0628fe">More...</a><br /></td></tr>
<tr class="separator:ga71503df1e691b12cc2d45e64fd0628fe"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gada0aaaee76f1fd3c272698c8eca735a1"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gada0aaaee76f1fd3c272698c8eca735a1"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gada0aaaee76f1fd3c272698c8eca735a1">orthoRH</a> (T left, T right, T bottom, T top, T zNear, T zFar)</td></tr>
<tr class="memdesc:gada0aaaee76f1fd3c272698c8eca735a1"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for an orthographic parallel viewing volume, using right-handedness. <a href="a00169.html#gada0aaaee76f1fd3c272698c8eca735a1">More...</a><br /></td></tr>
<tr class="separator:gada0aaaee76f1fd3c272698c8eca735a1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gac3613dcb6c6916465ad5b7ad5a786175"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gac3613dcb6c6916465ad5b7ad5a786175"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gac3613dcb6c6916465ad5b7ad5a786175">perspective</a> (T fovy, T aspect, T near, T far)</td></tr>
<tr class="memdesc:gac3613dcb6c6916465ad5b7ad5a786175"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a symetric perspective-view frustum based on the default handedness. <a href="a00169.html#gac3613dcb6c6916465ad5b7ad5a786175">More...</a><br /></td></tr>
<tr class="separator:gac3613dcb6c6916465ad5b7ad5a786175"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gae9146e2c550fc8646299e4b900238145"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gae9146e2c550fc8646299e4b900238145"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gae9146e2c550fc8646299e4b900238145">perspectiveFov</a> (T fov, T width, T height, T near, T far)</td></tr>
<tr class="memdesc:gae9146e2c550fc8646299e4b900238145"><td class="mdescLeft"> </td><td class="mdescRight">Builds a perspective projection matrix based on a field of view and the default handedness. <a href="a00169.html#gae9146e2c550fc8646299e4b900238145">More...</a><br /></td></tr>
<tr class="separator:gae9146e2c550fc8646299e4b900238145"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gae705a2f19c3ef5ef880bd6c92759cf2d"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gae705a2f19c3ef5ef880bd6c92759cf2d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gae705a2f19c3ef5ef880bd6c92759cf2d">perspectiveFovLH</a> (T fov, T width, T height, T near, T far)</td></tr>
<tr class="memdesc:gae705a2f19c3ef5ef880bd6c92759cf2d"><td class="mdescLeft"> </td><td class="mdescRight">Builds a left handed perspective projection matrix based on a field of view. <a href="a00169.html#gae705a2f19c3ef5ef880bd6c92759cf2d">More...</a><br /></td></tr>
<tr class="separator:gae705a2f19c3ef5ef880bd6c92759cf2d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga07cd8df791bf90dcb782645fe0b21261"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga07cd8df791bf90dcb782645fe0b21261"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga07cd8df791bf90dcb782645fe0b21261">perspectiveFovRH</a> (T fov, T width, T height, T near, T far)</td></tr>
<tr class="memdesc:ga07cd8df791bf90dcb782645fe0b21261"><td class="mdescLeft"> </td><td class="mdescRight">Builds a right handed perspective projection matrix based on a field of view. <a href="a00169.html#ga07cd8df791bf90dcb782645fe0b21261">More...</a><br /></td></tr>
<tr class="separator:ga07cd8df791bf90dcb782645fe0b21261"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga34048da27c559f1ac8e9550d169dd6f3"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga34048da27c559f1ac8e9550d169dd6f3"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga34048da27c559f1ac8e9550d169dd6f3">perspectiveLH</a> (T fovy, T aspect, T near, T far)</td></tr>
<tr class="memdesc:ga34048da27c559f1ac8e9550d169dd6f3"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a left handed, symetric perspective-view frustum. <a href="a00169.html#ga34048da27c559f1ac8e9550d169dd6f3">More...</a><br /></td></tr>
<tr class="separator:ga34048da27c559f1ac8e9550d169dd6f3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga5a4fa9f8ffabb2294e48a18bf8fa2f5f"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:ga5a4fa9f8ffabb2294e48a18bf8fa2f5f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga5a4fa9f8ffabb2294e48a18bf8fa2f5f">perspectiveRH</a> (T fovy, T aspect, T near, T far)</td></tr>
<tr class="memdesc:ga5a4fa9f8ffabb2294e48a18bf8fa2f5f"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a right handed, symetric perspective-view frustum. <a href="a00169.html#ga5a4fa9f8ffabb2294e48a18bf8fa2f5f">More...</a><br /></td></tr>
<tr class="separator:ga5a4fa9f8ffabb2294e48a18bf8fa2f5f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga9026c77505b99990f68826f27c267dc5"><td class="memTemplParams" colspan="2">template<typename T , precision P, typename U > </td></tr>
<tr class="memitem:ga9026c77505b99990f68826f27c267dc5"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga9026c77505b99990f68826f27c267dc5">pickMatrix</a> (tvec2< T, P > const &center, tvec2< T, P > const &delta, tvec4< U, P > const &viewport)</td></tr>
<tr class="memdesc:ga9026c77505b99990f68826f27c267dc5"><td class="mdescLeft"> </td><td class="mdescRight">Define a picking region. <a href="a00169.html#ga9026c77505b99990f68826f27c267dc5">More...</a><br /></td></tr>
<tr class="separator:ga9026c77505b99990f68826f27c267dc5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gad743556abd138264d4f06f4ca27f1d7e"><td class="memTemplParams" colspan="2">template<typename T , typename U , precision P> </td></tr>
<tr class="memitem:gad743556abd138264d4f06f4ca27f1d7e"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tvec3< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gad743556abd138264d4f06f4ca27f1d7e">project</a> (tvec3< T, P > const &obj, tmat4x4< T, P > const &model, tmat4x4< T, P > const &proj, tvec4< U, P > const &viewport)</td></tr>
<tr class="memdesc:gad743556abd138264d4f06f4ca27f1d7e"><td class="mdescLeft"> </td><td class="mdescRight">Map the specified object coordinates (obj.x, obj.y, obj.z) into window coordinates. <a href="a00169.html#gad743556abd138264d4f06f4ca27f1d7e">More...</a><br /></td></tr>
<tr class="separator:gad743556abd138264d4f06f4ca27f1d7e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga161b1df124348f232d994ba7958e4815"><td class="memTemplParams" colspan="2">template<typename T , precision P> </td></tr>
<tr class="memitem:ga161b1df124348f232d994ba7958e4815"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga161b1df124348f232d994ba7958e4815">rotate</a> (tmat4x4< T, P > const &m, T angle, tvec3< T, P > const &axis)</td></tr>
<tr class="memdesc:ga161b1df124348f232d994ba7958e4815"><td class="mdescLeft"> </td><td class="mdescRight">Builds a rotation 4 * 4 matrix created from an axis vector and an angle. <a href="a00169.html#ga161b1df124348f232d994ba7958e4815">More...</a><br /></td></tr>
<tr class="separator:ga161b1df124348f232d994ba7958e4815"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga8f062fcc07e2445500793f2803afebb0"><td class="memTemplParams" colspan="2">template<typename T , precision P> </td></tr>
<tr class="memitem:ga8f062fcc07e2445500793f2803afebb0"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga8f062fcc07e2445500793f2803afebb0">scale</a> (tmat4x4< T, P > const &m, tvec3< T, P > const &v)</td></tr>
<tr class="memdesc:ga8f062fcc07e2445500793f2803afebb0"><td class="mdescLeft"> </td><td class="mdescRight">Builds a scale 4 * 4 matrix created from 3 scalars. <a href="a00169.html#ga8f062fcc07e2445500793f2803afebb0">More...</a><br /></td></tr>
<tr class="separator:ga8f062fcc07e2445500793f2803afebb0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaee134ab77c6c5548a6ebf4e8e476c6ed"><td class="memTemplParams" colspan="2">template<typename T , precision P> </td></tr>
<tr class="memitem:gaee134ab77c6c5548a6ebf4e8e476c6ed"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gaee134ab77c6c5548a6ebf4e8e476c6ed">translate</a> (tmat4x4< T, P > const &m, tvec3< T, P > const &v)</td></tr>
<tr class="memdesc:gaee134ab77c6c5548a6ebf4e8e476c6ed"><td class="mdescLeft"> </td><td class="mdescRight">Builds a translation 4 * 4 matrix created from a vector of 3 components. <a href="a00169.html#gaee134ab77c6c5548a6ebf4e8e476c6ed">More...</a><br /></td></tr>
<tr class="separator:gaee134ab77c6c5548a6ebf4e8e476c6ed"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaed64bd81f5ecdab52fecbdf7f6b58194"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gaed64bd81f5ecdab52fecbdf7f6b58194"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gaed64bd81f5ecdab52fecbdf7f6b58194">tweakedInfinitePerspective</a> (T fovy, T aspect, T near)</td></tr>
<tr class="memdesc:gaed64bd81f5ecdab52fecbdf7f6b58194"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a symmetric perspective-view frustum with far plane at infinite for graphics hardware that doesn't support depth clamping. <a href="a00169.html#gaed64bd81f5ecdab52fecbdf7f6b58194">More...</a><br /></td></tr>
<tr class="separator:gaed64bd81f5ecdab52fecbdf7f6b58194"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaa50fce7f50b5d5da881ed30f5532a921"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr class="memitem:gaa50fce7f50b5d5da881ed30f5532a921"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tmat4x4< T, defaultp > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#gaa50fce7f50b5d5da881ed30f5532a921">tweakedInfinitePerspective</a> (T fovy, T aspect, T near, T ep)</td></tr>
<tr class="memdesc:gaa50fce7f50b5d5da881ed30f5532a921"><td class="mdescLeft"> </td><td class="mdescRight">Creates a matrix for a symmetric perspective-view frustum with far plane at infinite for graphics hardware that doesn't support depth clamping. <a href="a00169.html#gaa50fce7f50b5d5da881ed30f5532a921">More...</a><br /></td></tr>
<tr class="separator:gaa50fce7f50b5d5da881ed30f5532a921"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga82a558de3ce42cbeed0f6ec292a4e1b3"><td class="memTemplParams" colspan="2">template<typename T , typename U , precision P> </td></tr>
<tr class="memitem:ga82a558de3ce42cbeed0f6ec292a4e1b3"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL tvec3< T, P > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00169.html#ga82a558de3ce42cbeed0f6ec292a4e1b3">unProject</a> (tvec3< T, P > const &win, tmat4x4< T, P > const &model, tmat4x4< T, P > const &proj, tvec4< U, P > const &viewport)</td></tr>
<tr class="memdesc:ga82a558de3ce42cbeed0f6ec292a4e1b3"><td class="mdescLeft"> </td><td class="mdescRight">Map the specified window coordinates (win.x, win.y, win.z) into object coordinates. <a href="a00169.html#ga82a558de3ce42cbeed0f6ec292a4e1b3">More...</a><br /></td></tr>
<tr class="separator:ga82a558de3ce42cbeed0f6ec292a4e1b3"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<p>Defines functions that generate common transformation matrices. </p>
<p>The matrices generated by this extension use standard OpenGL fixed-function conventions. For example, the lookAt function generates a transform from world space into the specific eye space that the projective matrix functions (perspective, ortho, etc) are designed to expect. The OpenGL compatibility specifications defines the particular layout of this eye space.</p>
<p><<a class="el" href="a00071.html" title="GLM_GTC_matrix_transform ">glm/gtc/matrix_transform.hpp</a>> need to be included to use these functionalities. </p>
<h2 class="groupheader">Function Documentation</h2>
<a class="anchor" id="gada6deb989d4b553fe0f7e3279f3afae1"></a>
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<div class="memproto">
<table class="memname">
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::frustum </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Creates a frustum matrix with default handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
<tr><td class="paramname">near</td><td></td></tr>
<tr><td class="paramname">far</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::frustumLH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a left handed frustum matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
<tr><td class="paramname">near</td><td></td></tr>
<tr><td class="paramname">far</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::frustumRH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a right handed frustum matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
<tr><td class="paramname">near</td><td></td></tr>
<tr><td class="paramname">far</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::infinitePerspective </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a symmetric perspective-view frustum with far plane at infinite with default handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::infinitePerspectiveLH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a left handed, symmetric perspective-view frustum with far plane at infinite. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::infinitePerspectiveRH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a right handed, symmetric perspective-view frustum with far plane at infinite. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::lookAt </td>
<td>(</td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>eye</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>center</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>up</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Build a look at view matrix based on the default handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">eye</td><td>Position of the camera </td></tr>
<tr><td class="paramname">center</td><td>Position where the camera is looking at </td></tr>
<tr><td class="paramname">up</td><td>Normalized up vector, how the camera is oriented. Typically (0, 0, 1) </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- frustum(T const & left, T const & right, T const & bottom, T const & top, T const & nearVal, T const & farVal) frustum(T const & left, T const & right, T const & bottom, T const & top, T const & nearVal, T const & farVal) </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::lookAtLH </td>
<td>(</td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>eye</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>center</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>up</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Build a left handed look at view matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">eye</td><td>Position of the camera </td></tr>
<tr><td class="paramname">center</td><td>Position where the camera is looking at </td></tr>
<tr><td class="paramname">up</td><td>Normalized up vector, how the camera is oriented. Typically (0, 0, 1) </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- frustum(T const & left, T const & right, T const & bottom, T const & top, T const & nearVal, T const & farVal) frustum(T const & left, T const & right, T const & bottom, T const & top, T const & nearVal, T const & farVal) </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::lookAtRH </td>
<td>(</td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>eye</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>center</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>up</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Build a right handed look at view matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">eye</td><td>Position of the camera </td></tr>
<tr><td class="paramname">center</td><td>Position where the camera is looking at </td></tr>
<tr><td class="paramname">up</td><td>Normalized up vector, how the camera is oriented. Typically (0, 0, 1) </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- frustum(T const & left, T const & right, T const & bottom, T const & top, T const & nearVal, T const & farVal) frustum(T const & left, T const & right, T const & bottom, T const & top, T const & nearVal, T const & farVal) </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::ortho </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>zNear</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>zFar</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for an orthographic parallel viewing volume, using the default handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
<tr><td class="paramname">zNear</td><td></td></tr>
<tr><td class="paramname">zFar</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- glm::ortho(T const & left, T const & right, T const & bottom, T const & top) </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::ortho </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for projecting two-dimensional coordinates onto the screen. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- glm::ortho(T const & left, T const & right, T const & bottom, T const & top, T const & zNear, T const & zFar) </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::orthoLH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>zNear</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>zFar</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for an orthographic parallel viewing volume, using left-handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
<tr><td class="paramname">zNear</td><td></td></tr>
<tr><td class="paramname">zFar</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- glm::ortho(T const & left, T const & right, T const & bottom, T const & top) </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::orthoRH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>right</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>bottom</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>top</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>zNear</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>zFar</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for an orthographic parallel viewing volume, using right-handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">left</td><td></td></tr>
<tr><td class="paramname">right</td><td></td></tr>
<tr><td class="paramname">bottom</td><td></td></tr>
<tr><td class="paramname">top</td><td></td></tr>
<tr><td class="paramname">zNear</td><td></td></tr>
<tr><td class="paramname">zFar</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- glm::ortho(T const & left, T const & right, T const & bottom, T const & top) </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::perspective </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a symetric perspective-view frustum based on the default handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">far</td><td>Specifies the distance from the viewer to the far clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::perspectiveFov </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fov</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>width</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>height</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Builds a perspective projection matrix based on a field of view and the default handedness. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fov</td><td>Expressed in radians. </td></tr>
<tr><td class="paramname">width</td><td></td></tr>
<tr><td class="paramname">height</td><td></td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">far</td><td>Specifies the distance from the viewer to the far clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::perspectiveFovLH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fov</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>width</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>height</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Builds a left handed perspective projection matrix based on a field of view. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fov</td><td>Expressed in radians. </td></tr>
<tr><td class="paramname">width</td><td></td></tr>
<tr><td class="paramname">height</td><td></td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">far</td><td>Specifies the distance from the viewer to the far clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::perspectiveFovRH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fov</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>width</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>height</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Builds a right handed perspective projection matrix based on a field of view. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fov</td><td>Expressed in radians. </td></tr>
<tr><td class="paramname">width</td><td></td></tr>
<tr><td class="paramname">height</td><td></td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">far</td><td>Specifies the distance from the viewer to the far clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::perspectiveLH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a left handed, symetric perspective-view frustum. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">far</td><td>Specifies the distance from the viewer to the far clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::perspectiveRH </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>far</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a right handed, symetric perspective-view frustum. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">far</td><td>Specifies the distance from the viewer to the far clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::pickMatrix </td>
<td>(</td>
<td class="paramtype">tvec2< T, P > const & </td>
<td class="paramname"><em>center</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec2< T, P > const & </td>
<td class="paramname"><em>delta</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec4< U, P > const & </td>
<td class="paramname"><em>viewport</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<p>Define a picking region. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">center</td><td></td></tr>
<tr><td class="paramname">delta</td><td></td></tr>
<tr><td class="paramname">viewport</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Native type used for the computation. Currently supported: half (not recommanded), float or double. </td></tr>
<tr><td class="paramname">U</td><td>Currently supported: Floating-point types and integer types. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tvec3<T, P> glm::project </td>
<td>(</td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>obj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>model</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>proj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec4< U, P > const & </td>
<td class="paramname"><em>viewport</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<p>Map the specified object coordinates (obj.x, obj.y, obj.z) into window coordinates. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">obj</td><td>Specify the object coordinates. </td></tr>
<tr><td class="paramname">model</td><td>Specifies the current modelview matrix </td></tr>
<tr><td class="paramname">proj</td><td>Specifies the current projection matrix </td></tr>
<tr><td class="paramname">viewport</td><td>Specifies the current viewport </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Return the computed window coordinates. </dd></dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Native type used for the computation. Currently supported: half (not recommanded), float or double. </td></tr>
<tr><td class="paramname">U</td><td>Currently supported: Floating-point types and integer types. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::rotate </td>
<td>(</td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>angle</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>axis</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Builds a rotation 4 * 4 matrix created from an axis vector and an angle. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">m</td><td>Input matrix multiplied by this rotation matrix. </td></tr>
<tr><td class="paramname">angle</td><td>Rotation angle expressed in radians. </td></tr>
<tr><td class="paramname">axis</td><td>Rotation axis, recommended to be normalized. </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Supported: half, float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- rotate(tmat4x4<T, P> const & m, T angle, T x, T y, T z) </dd>
<dd>
- rotate(T angle, tvec3<T, P> const & v) </dd></dl>
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<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::scale </td>
<td>(</td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>v</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Builds a scale 4 * 4 matrix created from 3 scalars. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">m</td><td>Input matrix multiplied by this scale matrix. </td></tr>
<tr><td class="paramname">v</td><td>Ratio of scaling for each axis. </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- scale(tmat4x4<T, P> const & m, T x, T y, T z) </dd>
<dd>
- scale(tvec3<T, P> const & v) </dd></dl>
</div>
</div>
<a class="anchor" id="gaee134ab77c6c5548a6ebf4e8e476c6ed"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">GLM_FUNC_DECL tmat4x4<T, P> glm::translate </td>
<td>(</td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>v</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Builds a translation 4 * 4 matrix created from a vector of 3 components. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">m</td><td>Input matrix multiplied by this translation matrix. </td></tr>
<tr><td class="paramname">v</td><td>Coordinates of a translation vector. </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. <div class="fragment"><div class="line"><span class="preprocessor">#include <<a class="code" href="a00041.html">glm/glm.hpp</a>></span></div>
<div class="line"><span class="preprocessor">#include <<a class="code" href="a00071.html">glm/gtc/matrix_transform.hpp</a>></span></div>
<div class="line">...</div>
<div class="line">glm::mat4 m = <a class="code" href="a00169.html#gaee134ab77c6c5548a6ebf4e8e476c6ed">glm::translate</a>(<a class="code" href="a00156.html#gade0eb47c01f79384a6f38017ede17446">glm::mat4</a>(1.0f), <a class="code" href="a00156.html#gaa8ea2429bb3cb41a715258a447f39897">glm::vec3</a>(1.0f));</div>
<div class="line"><span class="comment">// m[0][0] == 1.0f, m[0][1] == 0.0f, m[0][2] == 0.0f, m[0][3] == 0.0f</span></div>
<div class="line"><span class="comment">// m[1][0] == 0.0f, m[1][1] == 1.0f, m[1][2] == 0.0f, m[1][3] == 0.0f</span></div>
<div class="line"><span class="comment">// m[2][0] == 0.0f, m[2][1] == 0.0f, m[2][2] == 1.0f, m[2][3] == 0.0f</span></div>
<div class="line"><span class="comment">// m[3][0] == 1.0f, m[3][1] == 1.0f, m[3][2] == 1.0f, m[3][3] == 1.0f</span></div>
</div><!-- fragment --> </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd>
<dd>
- translate(tmat4x4<T, P> const & m, T x, T y, T z) </dd>
<dd>
- translate(tvec3<T, P> const & v) </dd></dl>
</div>
</div>
<a class="anchor" id="gaed64bd81f5ecdab52fecbdf7f6b58194"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::tweakedInfinitePerspective </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a symmetric perspective-view frustum with far plane at infinite for graphics hardware that doesn't support depth clamping. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
</div>
<a class="anchor" id="gaa50fce7f50b5d5da881ed30f5532a921"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">GLM_FUNC_DECL tmat4x4<T, defaultp> glm::tweakedInfinitePerspective </td>
<td>(</td>
<td class="paramtype">T </td>
<td class="paramname"><em>fovy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>aspect</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>near</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T </td>
<td class="paramname"><em>ep</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Creates a matrix for a symmetric perspective-view frustum with far plane at infinite for graphics hardware that doesn't support depth clamping. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">fovy</td><td>Specifies the field of view angle, in degrees, in the y direction. Expressed in radians. </td></tr>
<tr><td class="paramname">aspect</td><td>Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height). </td></tr>
<tr><td class="paramname">near</td><td>Specifies the distance from the viewer to the near clipping plane (always positive). </td></tr>
<tr><td class="paramname">ep</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Value type used to build the matrix. Currently supported: half (not recommanded), float or double. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
</div>
<a class="anchor" id="ga82a558de3ce42cbeed0f6ec292a4e1b3"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">GLM_FUNC_DECL tvec3<T, P> glm::unProject </td>
<td>(</td>
<td class="paramtype">tvec3< T, P > const & </td>
<td class="paramname"><em>win</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>model</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tmat4x4< T, P > const & </td>
<td class="paramname"><em>proj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">tvec4< U, P > const & </td>
<td class="paramname"><em>viewport</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Map the specified window coordinates (win.x, win.y, win.z) into object coordinates. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">win</td><td>Specify the window coordinates to be mapped. </td></tr>
<tr><td class="paramname">model</td><td>Specifies the modelview matrix </td></tr>
<tr><td class="paramname">proj</td><td>Specifies the projection matrix </td></tr>
<tr><td class="paramname">viewport</td><td>Specifies the viewport </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Returns the computed object coordinates. </dd></dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Native type used for the computation. Currently supported: half (not recommanded), float or double. </td></tr>
<tr><td class="paramname">U</td><td>Currently supported: Floating-point types and integer types. </td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00169.html" title="Defines functions that generate common transformation matrices. ">GLM_GTC_matrix_transform</a> </dd></dl>
</div>
</div>
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Monday, June 28, 2010
A PAIR of counterfeiters who ran a £1 million pound illegal DVD copying operation in Milton Keynes have been jailed for a total of more than three years according to the Federation Against Copyright Theft.
(PRWeb UK/PRWEB ) June 28, 2010 -- A pair of counterfeiters who ran a £1 million pound illegal DVD copying operation in Milton Keynes have been jailed for a total of more than three years according to the Federation Against Copyright Theft.
Rosalba Stocec-Bot, a 28-year-old Romanian national, and Achilles Christian Ekedi-Tanenang, aged 36, from Cameroon, had both pleaded guilty to a 10 count indictment of Counterfeiting and Money Laundering, in a previous hearing at Luton Crown Court on June 3rd (Court reference: T20100209).
They appeared for sentence at Luton Crown Court on Friday June 25th and Stotec-Bec and Ekendi-Tanenang received 30 months and 15 months respectively.
The extensive investigation into the criminal activities of the defendants was started by Bedford Borough Trading Standards Service, operating on information received by the Federation Against Copyright Theft (FACT).
The investigation uncovered offences in both Bedford and Milton Keynes and was then taken on by Milton Keynes Council’s Trading Standards team, supported by Bedford Borough Trading Standards.
Films being sold included Harry Potter and the Half Blood Prince, The Hangover and Inglourious Basterds and box sets of TV series Friends, Lost and The Sopranos.
In July 2009, five properties across three counties were raided by Milton Keynes, Bedford Borough and Hertfordshire trading standards teams with support from FACT, ELSPA (Entertainment and Leisure Software Publishers Association), BPI (representing the UK recorded music industry) and local police forces.
The raids at addresses in Milton Keynes unearthed DVD manufacturing sites, with racks of DVD burners capable of producing 150 counterfeit discs in a matter of minutes.
Also at the addresses were over 67,000 discs ready for dispatch. A further 56,000 blank discs and associated material were taken from a storage site rented by Ekedi-Tanenang.
The two defendants were the masterminds behind a hugely successful site which sold counterfeit discs over the internet.
Notebooks found at Stocec-Bot’s house, in Peartree Bridge, Milton Keynes, showed the complexity of the operation, with multiple bank accounts, properties being bought and sold and money being transferred overseas to China and Romania.
The information contained in these books gave Stocec-Bot access to over 50 bank accounts many of which not in her name, allowing her to transfer money between accounts and concealing the trail of criminal profits.
A further investigation is being conducted by the Central Bedfordshire Financial Investigation Unit, a joint initiative between Central Bedfordshire Council and Bedford Borough Council, under the Proceeds of Crime Act. A Confiscation order will be sought to return the criminal proceeds, which are estimated at more than a £1m.
“Many consumers have been buying DVDs, such as Harry Potter, Sex and the City and Take That, from this couple not knowing that they were counterfeit and the industry will have lost huge revenues as a result.”
Kieron Sharp, FACT Director General, added, “After a long and very complex investigation started by FACT’s Internet Investigations team and pursued by Milton Keynes Trading Standards and Central Bedfordshire’s Financial Investigation Unit both of the key criminal masterminds behind an international counterfeiting conspiracy have been given prison sentences.
“This is one of the largest and most complex cases FACT has been involved in.
“The sophisticated nature of the operation was designed to try and hide the ultimate beneficiaries and the money trail led to China and other countries, as well as to money laundering in the UK using a property company as a front.
“The court has sent out a strong message that counterfeiting will be punished both with imprisonment and with eventual serious financial penalties.
“I would like to thank Milton Keynes, Central Bedfordshire and all those involved in this case for their efforts.”
About FACTThe Federation Against Copyright Theft is the UK’s leading trade organisation established to protect and represent the interests of the film, broadcasting and sports rights sectors against copyright and trademark infringements.
FACT works closely with statutory law enforcement agencies to combat all aspects of audio-visual theft including the increasing threat from online/internet-based piracy.
|
Q:
Multi-threaded tools
I am still pretty new to python scripting and am trying to speed up and smooth out some of my tools by adding multi-threading support. I feel like I may be miss-understanding some of the workflow theory here so feel free to redirect my mindset if I should be doing this another way. Basically what I am trying to do is the following:
==================================================================
###Pseudo-code -- I apologize if this does not follow existing conventions
main_function()
if do_stuff_function is not running:
Thread1 = new thread running do_stuff_function
do_stuff_function(args)
do some stuff
wait for 60 seconds (possibly using time.sleep())
end thread (tell main_function that the thread is done)
==================================================================
###Abridged code
def main(self):
check = True
index = 0
While index < 5:
if check == True:
check = False
thread1 = threading.Thread(target=self.doStuff, args=(self, index))
def do_stuff(self, index):
###Stuff happens here####
###iterate index and somehow return it (possibly a global variable)
time.sleep(60)
###somehow end the thread (still not entirely sure how to do that)
===================================================================
Notes:
-- This tool has a gui and it all tends to lock up and freeze if i run the time.sleep() in the main loop which is why I figured that multithreading would be a good solution (feel free to correct me if that is wrong). Or possibly a different way to wait that doesn't freeze the entire thread while waiting.
-- The program freezes in the while loop, is there a way to do this check without having to loop, possibly something like a callback (like a simulated button press when the do_stuff() function ends)?
-- I am also looking to try and add some error checking to this, so based on the results of do_stuff() return different error codes (just something to keep in mind).
I apologize if that is not enough info; feel free to ask for more specific info if you need it. Really guys, I appreciate all the help I can get, I am just trying to get a solid understanding of this stuff! Thanks!
A:
threads have some overhead and they all share the same CPU core, threads are good for waiting for user input or downloading files and other things where you are i/o limited, if you need more computing power I would suggest you use the multiprocessing module (see Multiprocessing vs Threading Python)
another problem with threads is that they 'lock up' because of the Global Interpreter Lock, this is because only 1 thread is allowed to write to memory at any one time, the absurd result is that to many threads brings down your program because they are all waiting to access memory
|
KYW editor Greg Orlandini and PSP editor Dan Walsh break down the big U.S.-Slovenia match, look ahead to the Algeria game, and evaluate the rest of the World Cup in their latest soccer podcast, recorded Saturday.
In the World Cup, there is a small reward for the team that only does well in a rivalry game, and a big reward for consistency. While the Americans have shown the ability to elevate their defensive game to match strong offenses like England, producing any kind of consistent attack is something they have yet to show.
|
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Boris Johnson has been offered a route to securing the pre-Christmas election that he has been seeking, through a plan that would only require the support of a simple majority of MPs.
With most Labour MPs still against the idea of a snap election, the prime minister looks set to lose his bid to secure a December poll on Monday in a vote that requires the backing of two-thirds of MPs. Other parties are also opposing an election until the EU has granted a three-month Brexit delay, although the DUP hinted on Saturday it could back the move.
However, in a sign that the coalition opposed to an election is under strain, the Liberal Democrats have drawn up a plan allowing Johnson to secure a December poll with a simple majority of MPs, with the support of Jo Swinson’s party and the SNP.
Under the one-page Lib Dem bill, the Fixed-Term Parliaments Act would be amended to state that the next election would take place on 9 December, three days earlier than under Johnson’s plans. It states that the new election date would be cancelled should the EU fail to grant a three-month Brexit extension.
The party is asking Johnson to adopt the bill and guide it through parliament between Tuesday and Thursday of this week, before dissolving parliament. It believes the timing of its plan means the prime minister would not be able to bring back his Brexit deal to the Commons before the election campaign starts – which he is currently threatening to do.
Swinson said last night: “Boris Johnson has missed his ‘do-or-die’ deadline and is now asking parliament to give him a general election and time for him to ram through his Brexit bill through parliament. That is a bad deal, and Liberal Democrats will not vote for it. We need to get Boris Johnson out of office, unlock the gridlock in parliament and give people the chance to vote to stay in the EU.
“A general election on our proposed timetable would take no-deal off the table, and give the public the chance to elect a Liberal Democrat government who will revoke article 50 or increase the number of MPs who support a People’s Vote.”
Party officials concede that the plan’s success lies in whether Johnson takes up the plan. However, it is a move that sees the Lib Dems shift support more clearly behind agitating for an early election.
Ian Blackford, the SNP’s leader in Westminster, gave his blessing to the plan on Saturday night. “I’m very keen that we work together on a mechanism, whether that be with Jo’s bill that we will support or any other mechanism – such as a vote of no confidence – to bring parliament to a speedy end and have an election as early as is possible,” he said.
The Lib Dems and SNP are also writing to Donald Tusk, president of the European Council, calling on Brussels to offer Britain a Brexit extension to the end of January next year.
The news comes with an Opinium poll for the Observer suggesting the Conservatives have a 16-point lead over Labour, which is split over an election.
Jeremy Corbyn said on Saturday that his party would “be very happy to fight an election once all vestiges of a no-deal exit from the EU have been taken off the table”. However, it remains unclear how that can be achieved. Figures on the left of the party are pushing to go to the polls, but Nick Brown, Labour’s chief whip, has warned Corbyn that scores of MPs would disobey any order to vote through an election.
Johnson repeated his demand on Saturday night for Labour to back his Brexit deal and vote for an early election and suggested that Brexit could drag on well into next year. He called on Labour to say how much more time it wanted to scrutinise his Brexit bill.
“Instead of grabbing this great new deal with both hands and helping move our country forward, parliament chose to ask for more tunnel,” said Johnson. “They agreed the deal but then they threw out the timetable. Unbelievably, Jeremy Corbyn then handed over the decision on what happens next to Brussels, so parliament’s delay could take us to 31 January at least.
“My worry is this parliament will just waste the next three months like it’s wasted the last three years.
“Parliament cannot hold the country hostage any longer. Millions of businesses and people cannot plan their futures, this paralysis is causing real damage and the country must move on in 2020.”
|
The 76th Golden Globe Awards are wrapped. “Green Book,” “Bohemian Rhapsody,” “Roma” and “The Kominsky Method” were among the big winners of the night. But the acceptance speeches were only a small part of the night’s most memorable moments, with others belonging to Emma Stone, Patricia Arquette and Oh, who pulled double duty as co-host and lead actress in a drama series winner. And if you’re already caught up on all the must-see moments from the show, dig through our after-party photos and dispatches to find out everything that happened after the cameras stopped rolling.
|
Targeted Analysis of Chromatin Events (TACE).
Visualization of meiotic chromatin from pollen mother cells has become an essential technique to study meiosis in the model plant Arabidopsis thaliana. Here we present an advanced cytogenetic method that combines improved immunocytology with chromosome painting, thereby generating a tool to quantitatively analyze localization of proteins to any given genomic region. Proteins involved in different processes such as DNA double-strand break formation and recombinational repair can be visualized on meiotic chromatin with the additional feature of assessing their abundance at specific chromosomal locations.
|
450 S.W.2d 634 (1970)
Clifford CURTIS, Appellant,
v.
The STATE of Texas, Appellee.
No. 42562.
Court of Criminal Appeals of Texas.
February 11, 1970.
Thomas E. Lucas, Houston (On Appeal Only), for appellant.
Carol S. Vance, Dist. Atty., Phyllis Bell and Allen Stilley, Asst. Dist. Attys., Houston, and Jim D. Vollers, State's Atty., Austin, for the State.
WOODLEY, Judge.
OPINION
The appeal is from a conviction for robbery by assault of Dan Reed Ellis, Jr. committed in the early morning hours of September 11, 1965, at the service station operated by the complainant Ellis, in the Northeast part of Houston. The appeal did not reach this court until September 30, 1969.
Trial was before a jury on a plea of not guilty. The punishment was assessed by the court at 35 years in the penitentiary.
The complainant's wife, seated in their automobile, witnessed the robbery of her husband which extended over a period of some 15 minutes, and testifying before the jury positively identified appellant as one of the two men who robbed her husband at gun point.
The complainant also identified appellant as one of the robbers but was not so positive in his identification. He fixed the time of the robbery as "between 2:30 and 3:00 A.M."
Appellant's court appointed counsel on appeal, in his supplemental brief filed in the trial court, urges as ground for reversal the contention that the case at bar is not distinguishable from the case of Rodriguez v. State, 170 Tex.Cr.R. 275, 340 S.W. 2d 61, on the basis of Rodriguez having appointed counsel and appellant having counsel of his own choosing as he concluded in his original brief, and urges that the mismanagement of the case at bar, as in the Rodriguez case, shows the denial of appellant's right to effective counsel and requires reversal.
The record reflects a docket entry: "Nov 4 1965 Court appoints S. Bostick" and list S. Bostick and S. Burns as attorneys for defendant. It also reflects that Sam Bostick and Sam Burns appeared as attorneys for the defendant and represented him at his trial.
*635 The record also reflects that Sam W. Bostick filed motion for new trial and that counsel S. Bostick and S. Burns appeared with appellant when sentence was pronounced and notice of appeal was given. Also the record reflects that after sentence and notice of appeal, appellant filed his sworn motion that he was "too poor to employ counsel to attend and appeal his cause" and prayed "that Sam W. Bostick or some other capable attorney be assigned to him as his attorney to attend and appeal his cause," and that such motion was granted the day it was sworn to and the court appointed Charles W. Gill as attorney to attend and appeal the case.
Thereafter counsel on appeal who filed appellant's brief was appointed by the court.
We find nothing in the record to show that Attorney Burns, who participated in the trial as counsel for appellant, was court-appointed.
There are other reasons why the majority opinion in Rodriguez v. State, supra, is not here applicable.
There is no showing in this record as to the experience or lack of experience or the education of either of appellant's trial counsel.
Appointed counsel did not testify that he did not have sufficient experience to properly defend an individual charged with an offense such as that for which his client was on trial, as did counsel for Rodriguez.
There is in the case at bar the novel situation where the victim of another robbery some 10 miles away was called by the defense for the purpose of proving an alibi.
The defense of alibi was also raised by another witness, a woman who testified that she was living with appellant at the time and he was at home with her on the night in question.
We cannot agree that a denial of effective aid of counsel is shown by appellant's counsel having called these witnesses in an effort to raise a reasonable doubt in the minds of the jurors as to appellant's presence at the time and place the robbery for which he was on trial was committed.
We note in this connection that had the issue of alibi been raised only by the testimony that he was at home in bed at the time of the robbery for which he was on trial, the state would not have been precluded from proving the other robbery committed within a short period of time. See Ferrell v. State, Tex.Cr.App., 429 S. W.2d 901; Owens v. State, Tex.Cr.App., 450 S.W.2d 324; Hawkins and Moore v. State, Tex.Cr.App., 450 S.W.2d 349; Parks v. State, Tex.Cr.App., 437 S.W.2d 554; 42 A.L.R.2d 854, 876.
We have examined the other grounds of error raised in appellant's motion for new trial and set out in appellant's brief and agree with counsel's conclusion that they do not require reversal of the conviction.
The judgment is affirmed.
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---
abstract: 'We develop a multi order parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where [*ortho-para*]{} distinction is valid. We apply our formalism to solid H$_2$ and D$_2$. We find an anomalous [*reentrant*]{} orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As temperature is increased the correlation increases along the phase boundary. We also find that even extremely small [*odd-J*]{} concentrations (1%) can trigger short-range orientational ordering.'
author:
- 'Bal[á]{}zs Het[é]{}nyi$^{1,3}$[^1], Sandro Scandolo$^{2,3}$, and Erio Tosatti$^{1,3}$'
title: 'Theoretical evidence for a reentrant phase diagram in [*ortho-para*]{} mixtures of solid H$_2$'
---
\[sec:intro\] Quantum effects dominate the low temperature ($T<200$K) phase diagram of solid molecular hydrogen in a wide range of pressures from ambient up to $\sim100$ GPa [@Silvera80; @Mao94]. In this regime the coupling between molecules is smaller than the molecular rotational constant, so quantum effects are generally described by means of weakly coupled quantum-rotor models [@VanKranendonk83]. Homonuclear molecules (H$_2$ and D$_2$) can assume only even or odd values of the rotational quantum number $J$, depending on the parity of the nuclear spin. Important differences exist in the phase diagrams of even-$J$ ([*para*]{}-H$_2$ and [*ortho*]{}-D$_2$), odd-$J$ ([*ortho*]{}-H$_2$ and [*para*]{}-D$_2$) and all-$J$ (HD) species. (For a summary of experimental results on the orientational ordering in H$_2$, D$_2$, and HD see Fig. 1b of reference .) At low pressure or high temperature, even-$J$ species are found in a rotationally disordered free-rotor state (phase I). Increasing pressure causes an increase of the intermolecular coupling, and eventually leads to an orientationally ordered state (phase II). Odd-$J$ systems on the other hand are orientationally ordered at low temperature and ambient pressure and remain ordered as pressure is increased. The stronger tendency of [*ortho*]{}-H$_2$ to order can be traced to the fact that its $J=1$ lowest rotational state allows for a spherically asymmetric ground state, unlike the $J=0$ ground state of even-$J$ species. The pressure-temperature phase diagram of HD exhibits a peculiar [*reentrant*]{} shape [@Moshary93]. Reentrance refers to phase diagrams where in some range of pressure the system reenters the disordered phase at ultra-low temperatures (see HD in Fig. \[fig:mf\]). The zero-temperature orientationally disordered phase is characterized by an energy gap against $J=1$ excitations. When this gap is sufficiently small and the temperature is finite, the thermally generated $J=1$ excitations suffice to induce ordering, which is then reentrant, as also shown by mean-field theory [@Freiman91; @Brodyanskii93; @Freiman98]. Reentrance is also found in models of two-dimensional rotors [@Simanek85], such as the quantum anisotropic planar rotor (QAPR) model [@Martonak97; @Muser98; @Hetenyi99].
High pressure experiments have focused mainly on the behavior of pure species. While understanding the orientational transition in [ *ortho*]{}-[*para*]{} mixtures of quantum rotors in two and three dimensions is a problem of long-standing theoretical and experimental interest [@Feldman95; @Harris85; @Sullivan87; @Goncharov96; @Hochli90; @Binder02; @Kokshenev96a; @Mazin97; @Goncharov01], less attention has been given at establishing the effects of [*ortho-para*]{} distinction. Exceptions [@Feldman95; @Goncharov96; @Mazin97; @Goncharov01] are the investigation of vibrons in [*ortho-para*]{} mixtures by Feldman [*et al.*]{} [@Feldman95] and a recent work by Goncharov [*et al.*]{} [@Goncharov96], where [*ortho*]{}-D$_2$ mixed with small amounts of [*para*]{}-D$_2$ indicated that the possibility of an orientationally frustrated phase between phases I and II (phase II’). Phase II’ persisted for a narrow pressure range ($\sim 2$GPa) for a thermally equilibrated [ *ortho-para*]{} mixture.
At ambient pressure hydrogen is known to enter gradually a phase of short-range order (orientational glass) [@Hochli90; @Binder02] when the concentration of [*ortho*]{} species is below $\sim 53$ % [@Harris85; @Sullivan87; @Hochli90]. Short-range order is believed to be a manifestation of the orientational frustration due to the random location of [*ortho*]{} molecules in the lattice, and eventually transforms into long-range order at [*ortho*]{} concentrations approaching unity. The pressure-induced increase of the intermolecular anisotropic coupling causes a decrease of the minimum concentration of [*ortho*]{} species required to trigger the orientational transition [@Silvera80]. At extremely high pressures ($\sim110$ GPa) orientational freezing is observed also in pure [*para*]{}-H$_2$, as stated above. Ambient pressure experiments on pure species as well as on samples with fixed concentration are possible because the rate of interconversion between [*para*]{} and [*ortho*]{} H$_2$ species is extremely slow at low pressure. Samples with fixed [*ortho*]{}-[*para*]{} concentration are prepared by letting the system thermalize at the corresponding temperature for very long times and experiments are then performed at any other temperature by rapid heating or quench ( [*rapid*]{} on the time scale of interconversion). At high pressures however the interconversion rate rises steeply [@Strzhemechny00]. At $58$ GPa, the highest pressures where the conversion rate has been measured, interconversion takes place in the time scale of seconds. While interconversion is still orders of magnitude slower than molecular rotation, the [*ortho-para*]{} distribution in this range of pressure is likely to be determined by thermal equilibrium. On the other hand [*ortho-para*]{} distinction is still valid.
Previous theoretical studies addressing quantum effects in compressed hydrogen (mean-field [@Freiman91; @Brodyanskii93; @Freiman98] or quantum Monte Carlo [@Kaxiras94; @Cui97; @Runge92; @Pollock94] studies) have in most cases neglected the distinction between even-$J$ and odd-$J$ species [@Kaxiras94], and in those cases where the distinction was explicitly considered, the analysis was restricted to pure even-$J$ or odd-$J$ species [@Cui97; @Runge92; @Pollock94]. On the other hand, theoretical modeling of mixed [*ortho*]{}-[*para*]{} systems [@Harris85; @Kokshenev96a; @Feldman95] at low pressure is generally limited to $J=0$/$J=1$ states. [@Harris85; @Kokshenev96a] This is not an accurate model for compressed H$_2$, as pressure and temperature cause a non-negligible admixture of rotational states with higher $J$’s in the ground state of both [*ortho*]{} and [*para*]{} species. A binary alloy model [@Feldman95] was also used to analyze the low-pressure vibrons in [*ortho-para*]{} mixtures.
In order to calculate the phase diagram of [*ortho-para*]{} mixtures of hydrogen in the solid phase we develop a multi order parameter (MOP) mean-field theory which accounts explicitly for [*ortho-para*]{} distinction in systems of coupled rotors. Our formalism enables us to treat a system of $\sim 3000$ molecules, which would be extremely computationally intensive with quantum Monte Carlo. Our formalism also includes correlations due to [*ortho-para*]{} distinction, a feature that is absent in standard mean-field theory. We apply the formalism to a system of coupled quadrupolar rotors whose centers of mass form a face-centered cubic lattice. We find that the phase line separating the orientationally disordered state (phase-I) from the orientationally ordered state is [*reentrant*]{} in the case of thermally equilibrated [*ortho-para*]{} mixtures for both H$_2$ and D$_2$. We also find that orientational order is short-ranged at low temperatures. The validity of our conclusion is supported by the fact that for the two-dimensional model mean-field theory [@Simanek85; @Martonak97] is in agreement with quantum Monte Carlo [@Muser98; @Hetenyi99] simulations on the overall shape of the phase diagram.
The Hamiltonian of a system of $N$ coupled quadrupolar quantum rotors interacting through a quadrupole-quadrupole potential can be written in the form $$\begin{aligned}
H &=& B \sum_{i=1}^N \hat{L_i}^2 + \frac{K}{2} \sum_{i<j}^N
\left( \frac{R_0}{R_{ij}} \right)^5 \\
& & \sum_{m,n} C(224;mn) Y_{2m} (\Omega_i) Y_{2n}(\Omega_j)
Y_{4m+n}^*(\Omega_{ij}), \nonumber
\label{eqn:H}\end{aligned}$$ where $B$ is the molecular rotational constant, $K$ is the coupling strength, $C(224;mn)$ are Clebsch-Gordan coefficients, $\Omega_i$ denote the coordinates of rotor $i$, and $\Omega_{ij}$ denote the direction of the vector connecting rotors $i$ and $j$. We define $R_0$ to be the nearest neighbor distance, $R_{ij}$ is the distance between molecules $i$ and $j$. Our MOP mean-field theory is based on the trial Hamiltonian $$\begin{aligned}
H_0 &=& B \sum_{i=1}^N \hat{L_i}^2 + K \sum_{i<j}^N \left(
\frac{R_0}{R_{ij}} \right)^5 \\ & & C(224;00) Y_{20}
(\Omega_i) \gamma_j Y_{40}^*(\Omega_{ij}), \nonumber
\label{eqn:H0}\end{aligned}$$ where $\gamma_i$ are parameters. Variation of the free-energy leads to the self-consistent expression $$\gamma_i = \langle Y_{20} (\Omega_i) \rangle_0.
\label{eqn:gamma}$$ Since the trial Hamiltonian in Eq. (\[eqn:H0\]) is a sum of single-rotor Hamiltonians, it follows that for each $\gamma_i$ in Eq. (\[eqn:gamma\]) the average needs to be performed over the corresponding coordinate $\Omega_i$ only. [*Ortho-para*]{} distinction can be implemented by restricting a particular average to be over odd-$J$ or even-$J$ states.
Since in this study we are only interested in the phase diagram we expand to first-order in the potential [@Simanek85]. Such an expansion is expected to be valid here, since the transition between the long-range ordered state and the disordered state is only weakly first-order [@Cui95]. Furthermore the transition between the short-range ordered state and the disordered state is known to be continuous at ambient pressure [@Harris85]. The resulting expression can be written $$\gamma_i = K 3 \sqrt{\frac{2}{35}} \Phi_i \sum_j \gamma_j \left(
\frac{R_0}{R_{ij}} \right)^5 Y_{40}(\Omega_{ij}),
\label{eqn:mtx}$$ where $\Phi_i$ is the phase correlator defined as $\Phi_i =
\int_0^{\beta} d \tau \langle Y_20(\Omega(0)) Y_{20} (\Omega(\tau))
\rangle_{free,i}$. The averaging is to be performed over a free rotor at inverse temperature $\beta$, and [*ortho-para*]{} distinction can be invoked by restricting the average as described above. Thus, for a given temperature and rotational constant, $\Phi_i$ can take on two values depending on whether rotor $i$ is odd-$J$ or even-$J$. Order will be signalled by non-zero solutions for $\gamma_i$, disorder by solutions in which all $\gamma_i$ are identically zero. The standard mean-field theory [@Freiman91; @Brodyanskii93] is automatically recovered for pure systems.
We calculated the phase diagrams for systems of fixed odd-$J$ fraction, as well as at the thermal equilibrium distribution, taking account of nuclear spin degeneracy. D$_2$ and H$_2$ differ by the values of the rotational constants ($2B_{D_2} = B_{H_2}$) and in the degeneracies of states. [ *Ortho*]{}([*para*]{}) H$_2$ is restricted to be odd-$J$(even-$J$) angular momentum and in D$_2$ the reverse. In our calculations for mixed systems, configurations of 2916 molecules on a face-centered cubic lattice were used. For a given odd-$J$ fraction 20 configurations are generated. A cutoff distance of 2.65 times the lattice constant is used, thus 134 nearest neighbors are included in the interaction calculation. The phase transition point is obtained by diagonalizing Eq. (\[eqn:mtx\]) (which is a matrix equation) and finding the lowest coupling constant for which a nonzero solution exists.
\[sec:results\] In Fig. \[fig:mf\] we present the results of standard mean-field theory phase diagrams of pure odd-$J$/even-$J$ of H$_2$ and D$_2$, and HD, all in excellent qualitative agreement with the experimental results (see Fig. 1b of reference ). The energy scale is defined to be the rotational constant of the H$_2$ molecule. The main difference between the phase diagrams of odd-$J$ and even-$J$ systems is accurately captured, namely that at low pressures odd-$J$ systems are always ordered, whereas even-$J$ systems order at finite pressures. As expected from experiment odd-$J$ D$_2$ orders at a lower coupling strength than odd-$J$ H$_2$, and the reentrant phase transition in HD is also well reproduced by mean-field theory [@Freiman91; @Brodyanskii93; @Freiman98].
In Fig. \[fig:mpmf\] the results of the formalism presented above are shown for solid H$_2$. As the [*ortho*]{} concentration is decreased the system tends towards disorder entering the ordered state at higher coupling constants for a given temperature. A noteworthy result of our calculations is that even at an [*ortho*]{} concentration of 1% the system enters an ordered state at coupling constants quite different from that of pure [ *para*]{} hydrogen, and that for any [*ortho*]{} concentration the ground state is always ordered. The 50% [*ortho*]{} system is very close to the pure [*ortho*]{} one. Our results are consistent with the phase diagram shown in Fig. 1 of Ref. in which the pure [*para*]{}-H$_2$ phase transition occurs at $\sim110$ GPa, and [*ortho*]{} containing samples show ordering at lower pressures.
In order to assess the nature of the ordering we calculated correlation functions of the local order parameters $\{\gamma_i\}$. This is an advantage of our multi order parameter formalism over the standard mean-field theory, since in single-site mean-field theory only phases of complete order or disorder are possible. In particular we have calculated $$G(r) = \langle (\gamma(0) \gamma(r))^2 \rangle.$$ The results along the phase line of the 10% [*ortho*]{} system of hydrogen are shown in Fig. \[fig:cf\]. The correlation increases along the phase boundary with increasing temperature indicating the onset of long-range order. The onset of long range order is due to the fact that [*ortho-para*]{} distinction ceases as temperature and coupling constant (pressure) are increased.
The orientational ordering of the system with [*ortho-para*]{} concentrations at thermal equilibrium is shown in Fig. \[fig:rnt\] along with the phase diagrams of the pure systems (also shown in Fig. \[fig:mf\]) for comparison. For H$_2$ and D$_2$ we calculated the phase diagrams via the multi order parameter mean-field theory presented here, and via the standard mean-field theory. The resulting phase diagrams indicate reentrance in both D$_2$ and H$_2$. Reentrance is also seen [@HetenyiUP] in the corresponding 2D model [@Martonak97]. Reentrance is stronger in the case of H$_2$, due to higher relative weight of odd-$J$ contribution (nuclear spin degeneracy), and higher rotational constant (stronger quantum effects). The correlation functions for different temperatures along the reentrant phase diagram are shown for H$_2$ in Fig. \[fig:cfrnt\]. As the temperature increases correlation increases along the phase boundary. At high temperatures ($T>1$) the order is definitely long-range. We conclude that short-range order may be present up to $T=0.75$. In the case of D$_2$ reentrance is less severe.
\[sec:conclusion\]
In summary we calculated the phase diagrams of solid hydrogen and its isotopes. We found that the I-II phase line is interspersed by another phase, likely to be orientationally frustrated, as suggested by the experiments of Goncharov [*et al.*]{} (Ref. ). For a thermal distribution of [*ortho-para*]{} rotors we find a reentrant phase diagram for both H$_2$ and D$_2$. At low temperatures the order is short-ranged. Most experimental signatures of the long-range ordered phase are well known, [@Silvera80; @Mao94] the short-range ordered phase may be seen by probing the distribution of the local order parameter. While nuclear magnetic resonance [@Harris85] is a useful probe, it may be difficult to apply at high pressure. The II‘ phase was found [@Goncharov96] by investigating the Raman vibronic shift and it is known to be sensitive in [*ortho-para*]{} mixtures [@Feldman95]. Rotational Raman lines are also sensitive to local order. Experimental studies to resolve the issues raised here would be helpful.
Work at SISSA/ICTP/Democritos was sponsored by MIUR FIRB RBAU071S8R004, FIRB RBAU01LX5H, and MIUR COFIN 2003, as well as by INFM. We acknowledge using resources of CINECA/HPC-Europa. We are grateful to Professor Y. A. Freiman for helpful discussions.
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[^1]: Present address:Institut für Theoretische Physik, Technische Universität Graz, Petersgasse 16, A-8010, Graz, Austria
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Estimation of toxicity of ionic liquids in Leukemia Rat Cell Line and Acetylcholinesterase enzyme by principal component analysis, neural networks and multiple lineal regressions.
Multiple linear regression (MLR), radial basis network (RB), and multilayer perceptron (MLP) neural network (NN) models have been explored for the estimation of toxicity of ammonium, imidazolium, morpholinium, phosphonium, piperidinium, pyridinium, pyrrolidinium and quinolinium ionic liquid salts in the Leukemia Rat Cell Line (IPC-81) and Acetylcholinesterase (AChE) using only their empirical formulas (elemental composition) and molecular weights. The toxicity values were estimated by means of decadic logarithms of the half maximal effective concentration (EC(50)) in microM (log(10)EC(50)). The model's performances were analyzed by statistical parameters, analysis of residuals and central tendency and statistical dispersion tests. The MLP model estimates the log(10)EC(50) in IPC-81 and AchE with a mean prediction error less than 2.2 and 3.8%, respectively.
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Francis Duggan
Your True Friends - Poem by Francis Duggan
You are down and out without any money and you've given up on all hopeAnd you think about ending your misery from a rafter beam dangling from a ropeAnd some of those you thought were good mates in your time of need not to be foundIt is then you know who your friends are your true friends will rally aroundAnd try to help you out of your troubles and offer you financial aidThough some of those who were your friends in the good times in your time of need from your life fadeA true friend will always stick by you a true friend will not see you downThough some may see you as a loser one of the poor souls of the Town, You had many friends in your good days such stories have been told beforeBut now that you've fallen on hard times you are not that well liked anymoreBut your real friends they will not ignore you and they will look on you as the samePerson you were when you were seen as successful though you don't have a coin to your name, In your time of need they stick by you as your friends are precious and rareThey will do their best for to help you and worry about your welfare
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Download Free Nursing E-Books for All Nurses Specialist All What You Need To Study Nursing All What You Need To Be Professional Nurse All What You Need To Continue Your Nursing Education Free Nursing Video Free PowerPoint Presentation
Sunday, March 27, 2011
To Comfort Always A Nurse's Guide to End-Of-Life Care
Caring for patients at the end of life s journey is challenging, but rewarding. To Comfort Always: A Nurse s Guide to End-of-Life Care prepares nurses to care for dying patients and their families by providing a primer that is both practical and insightful. From emotional needs such as relief of suffering to physical needs such as relief of pain, To Comfort Always supplies nurses what they need to know to deliver holistic, effective care. Linda Norlander brings her expertise in end-of-life care to this book that will serve as a valuable resource for nurses committed to comforting patients and families at one of life s most moving passages.
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Growth and nutritional status in residential center versus home-living children and adolescents with quadriplegic cerebral palsy.
To describe growth and nutrition in nonambulatory youth (<19 years of age) with cerebral palsy (CP) living in residential centers compared with similar youth living at home. A multicenter, cross-sectional, single observational assessment of 75 subjects living in a residential care facility compared with 205 subjects living at home. Primary outcome measures included anthropometric measures of height, weight, triceps, and subscapular skinfolds, and mid-upper-arm muscle area. Z scores were calculated from reference values for healthy children. Age, use of a feeding tube, and Gross Motor Functional Classification System (GMFCS) level were included as important confounders. Use of a feeding tube was associated with higher skinfold Z scores, and a significantly higher percentage of the residential subjects had a feeding tube. Height, weight, and arm-muscle area Z scores all diverged (negatively) from reference values with age, and the residential subjects were on average older than the home-living subjects. After controlling for age, GMFCS level and use of a feeding tube, residential living was associated with significantly greater weight, height, skinfold thicknesses, and mid-arm muscle area Z scores. Poor growth and nutrition in children with CP is a prevalent, important, and complex problem. Although factors intrinsic to the condition of CP likely play a significant role, it is also clear that environmental factors, including the living situation of the child, can have an impact.
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Q:
How to hook function in Joomla
I need to run my component(code) exactly after authorization (before page loading). Is there some features for it without changing source? Maybe some functions, like add_action in wordpress or something else?
A:
You probably want to create a plugin for this.
"Plugins provide functions which are associated with trigger events." (Joomla Wiki Plugin)
To listen to user events you must create a "User Plugin". To hook a function for user authorization see onUserLogin.
See the wiki page for more information about plugin developement.
Edit:
Since Joomla 1.5 an example of onUserLogin can be found in a plain Joomla CMS installation at plugins/user/joomla/joomla.php.
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Share
Ripple Labs and AML
FinCEN recently punished Ripple for failing to follow required BSA guidelines related to establishing AML policies. It’s unfortunate that an innovative company like Ripple Labs, whose intention is to create a low cost efficient payment clearing system would violate the law.
Certainly regulations exist to protect businesses and consumers, in this case from illegal payment transactions. Such an action puts doubt on the potential benefits of a new technology especially when combined with ‘Bitcoins’ that have also received negative publicity recently. It is important however, that what Ripple is doing is to establishing the payments infrastructure and not directly working the end clients, instead relying on the banking intermediary to conduct the appropriate sanction screening checks. However, it seems clear from a regulatory perspective that is not sufficient based on Ripple’s failure to file as an MSB.
Let’s hope innovation isn’t stifled by regulation. It’s a delicate balance, but one that needs to be tested in order to see improvement in the financial industry.
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An integrative approach considering acute symptoms and intensity ratings of chemosensory sensations during experimental exposures.
Even at low concentrations airborne chemicals can excite olfactory and trigeminal receptors and inform the organism about the presence of airborne chemicals. Acutely, malodors or sensory irritations might trigger symptoms (e.g., bad air quality, eye irritations) and in the long-run functional impairment of chemoreception might occur. In humans, knowledge about short-term adaptational processes and effects of exposure peaks on these systems is limited. Therefore, two different experiments with human volunteers were conducted. In experiment A exposures (4h) with fluctuating concentrations of 2-ethylhexanol (1.5, 10, 20ppm C(TWA)) were investigated, experiment B used similar but constant vapor concentrations. Olfactory- and trigeminal-mediated symptoms and intensities of odor, eye, and nasal irritations were recorded. All measures showed a dose-dependent response and peak exposure effects. In the course of the 4h exposures solely olfactory symptoms decreased. Nasal irritations remained nearly unchanged across the 4h, eye irritations slightly increased. Inter-individual differences related to the personality trait of self-reported chemical sensitivity had only minor effects on chemosensory symptoms in experiment B and no effect on intensity ratings in both experiments. Chemosensory effects seem to be amplified by exposure peaks and less adaptive than assumed.
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This program is conceptually very similar to hello.chpl, but it uses a more structured programming style,
explicitly defining a module, a configuration constant, and a
main() procedure.
The following statement declares a module named 'Hello'. If a
source file contains no module declarations, the filename minus its
.chpl extension serves as the module name for the code it
contains. Thus, 'hello' would be the automatic module name for the
previous hello.chpl example.
moduleHello{
This next statement declares a configuration constant named
message. The type is inferred to be a string since the
initializing expression is a string literal. Users may override
the default values of configuration constants and variables on the
executable's command-line. For example, we could change the
default message for a given run using the command line: ./hello--message="hiya!".
configconstmessage="Hello, world!";
Any top-level code in a module is executed as part of the module's
initialization when the program begins executing. Thus, in the
previous one-line hello.chpl, the presence
of a writeln() at the file scope formed the implicit hello
module's initialization and would be executed at program startup.
Since there was no explicit main() function or any other
top-level code, that's all that the program would do.
In this program, we define an entry point for the program by
defining a procedure named main(). This will be invoked after
this module and all the modules it uses are initialized.
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Differentiation of the female reproductive body in the colonial hydroidCampanularia flexuosa.
A comparison of two genetic stocks ofCampanularia flexuosa revealed consistent differences with respect to (1) the number of eggs present in the maturefemale reproductive body (gonangium), (2) the level on each upright stem at which the first gonangium forms, and (3) their preference for the formation of reproductive versusvegetative (side-branch) structures.Alterations in food intake established the optimum feeding level for maximal production of structurally normal gonangia and also showed differences between stocks in the effects of reduced food intake on gonangial versus vegetative growth.A staging series for gonangiogenesis was developed from observations of filling of the gonangium with primordial egg cells (PEC), gonangial elongation, funnel maturation and oogenesis.When upright segments bearing immature gonangia are isolated from the stolon the gonangia frequently resorb, transform into vegetative outgrowths, or form structurally abnormal gonangia bearing fewer germ cells than normal. These responses, and the observed accumulation of PEC at sites of presumptive gonangial outgrowth, support a stolonic origin hypothesis for PEC and implicate PEC and oocytes in the initiation, maintenance and maturation of structurally normal gonangia. In addition, continued differentiation of the gonangial structure appears to be necessary for oocyte maturation.Possible mechanisms for somatic and gametic cell recruitment, and the theoretical importance of cellular proliferation, aging, cell-shape changes, cell movement and cellular interactions in normal gonangial differentiation are discussed.
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Introduction {#Sec1}
============
In recent years, there has been an increase in the utilization of emergency departments (EDs) in many countries, including Saudi Arabia, as the number of patients keeps rising \[[@CR1], [@CR2]\]. Such an issue can be partly attributed to non-urgent presentations, which comprised approximately 50% of all ED cases in Saudi Arabia and Australia \[[@CR3], [@CR4]\]. In Saudi Arabia, non-urgent patients reported multiple reasons for visiting the ED including the lack of a regular primary healthcare provider, convenience and quick access, and the perception that they will receive better care \[[@CR5]\]. In addition, major delays in delivering care to patients in EDs have been reported in Riyadh (the capital city of Saudi Arabia) \[[@CR6]\]. All these factors can lead to ED overcrowding with consequences such as increased waiting time, impaired patient-centered care, and disrupted evaluation and treatment \[[@CR7]\].
Another component of this issue is triage, which is the assignment of priority to patients based on the level of urgency attached to their case \[[@CR7]\]. The main goal of triage is not to increase or decrease general waiting times, but to provide immediate care for those in most need \[[@CR8]\]. Therefore, triage leads to decreased waiting time for all patients except those in the lowest priority category \[[@CR9]\]. Long waiting times are not only associated with poor satisfaction, but can also negatively impact patients' perception of information, instructions, and the overall treatment \[[@CR10], [@CR11]\]. Decreasing waiting times is not an easily achievable aim; however, factors such as improving patient knowledge of how the assignment procedure works and communication of estimated waiting times can increase patients' satisfaction during ED visits \[[@CR10], [@CR12], [@CR13]\].
Additionally, patients' expectations regarding waiting times for laboratory or imaging results (conducted in the ED) appear to vary greatly. In one study, the interquartile range (IQR) for patients' time expectation for computed tomography (CT) scan results, for example, was 30 to 94 min \[[@CR14]\]. This variation could be attributed to a general lack of knowledge regarding such procedures.
A review of the literature revealed some studies that addressed patient awareness of ED triage. For example, Adeniji et al. reported that patients lack a good understanding of the triage \[[@CR15]\]. Meek et al. reached a similar conclusion and added that patients wanted to know more about the process \[[@CR16]\]. Additionally, Seibert (2014) found that only 33% of patients were aware of the definition of triage \[[@CR14]\].
To our knowledge, no studies have yet been conducted to evaluate ED patients' knowledge of triage in Saudi Arabia or the Middle East. Therefore, in this study, we aimed to assess ED visitors' knowledge of triage, to understand the factors influencing individuals' decisions to visit an ED and to explore the experiences of ED visitors to a tertiary hospital in Riyadh, Saudi Arabia.
Methods {#Sec2}
=======
Study setting, subjects, and design {#Sec3}
-----------------------------------
This cross-sectional study was conducted at the adult ED at King Abdulaziz Medical City, Riyadh, Saudi Arabia, which is a tertiary care hospital with a bed capacity of 1501 and a level I trauma center that receives approximately 220,000 ED visits each year. The ED follows the Canadian triage system which has 5 levels. Patients in the waiting area and meeting the inclusion criteria (classified as level 3, 4, or 5, age \> 14 years, Arabic speakers, and cognitively competent) were enrolled; patients who did not meet the inclusion criteria were excluded. In total, 334 patients participated in this study by filling a printed data collection form (DCF) during their waiting time.
Data collection form {#Sec4}
--------------------
A 31-question DCF was adopted from a previous published study conducted in the USA \[[@CR14]\]. To meet the requirements of our study subjects, the questionnaire was translated into Arabic. The survey was composed of two major sections. The first was designed to obtain demographics information such as age, sex, education level, and marital status. The second section focused on the use of primary health care facilities prior to the patient's ED visit, their understanding of ED triage system, the desire to be informed about the delays as well as common health problems (e.g., diabetes and heart attacks) during the waiting time, and the time patients expect to wait for results from some ED services, such as X-rays or CT scans.
Sample size {#Sec5}
-----------
Based on a literature review which estimated that 33% of the population were aware of the triage system, the margin of error and the confidence level of this study were 5% and 95%, respectively, and a minimum sample size of 334 was required to achieve statistical power \[[@CR14]\].
DCF piloting {#Sec6}
------------
In general, DCFs were filled within 5--15 min. This was dependent on the participant's answers (some "yes" answers required responses to additional questions), participant's enthusiasm (some intentionally answered "no" to avoid answering additional questions, or skipped some questions), and sometimes being called for treatment while filling the questionnaire. The team tried to overcome these obstacles by ensuring the participants' complete willingness to participate, as well as the ability to complete the survey after seeing the doctor. The Arabic version of the DCF was piloted and Cronbach's alpha was found to be 0.77.
Sampling technique {#Sec7}
------------------
Participants were allocated using a convenience sampling approach. Those patients in the waiting areas who fulfilled the aforementioned inclusion criteria were asked about their willingness to participate after the research team had provided a brief introduction about the study and confirmed their voluntary participation. Data were collected at any time (i.e., weekdays and weekends and morning, evening, and night shifts).
Data management and analysis {#Sec8}
----------------------------
The data were compiled using Microsoft Excel and then uploaded into the Statistical Package for the Social Sciences (IBM Corp. Released 2013, IBM SPSS Statistics for Windows, Version 22.0. Armonk, NY, USA) for analysis. Categorical variables (e.g., demographics) were represented as percentages and frequencies, while numerical variables (e.g., age) were summarized by calculating the mean and standard deviation. The prevalence, expressed in percentages, was calculated based on a 95% CI. Logistic regression was used to address the factors affecting patients' visit to the ED. All results were considered statistically significant at *P* value \< 0.05.
Ethical considerations {#Sec9}
----------------------
This study was approved by the International Review Board of King Abdullah International Medical Research Center, Riyadh, Saudi Arabia. Participants were assured that their participation would be voluntary and anonymous and would not affect the health services provided to them. All DCFs were attached with a consent form that included the research purpose as well as the participants' rights. All participants provided written informed consent to participate in this study.
Results {#Sec10}
=======
Baseline characteristics of study participants {#Sec11}
----------------------------------------------
The baseline characteristics of the respondents are shown in Table [1](#Tab1){ref-type="table"}. Most participants were in the 20--39 age groups (62%). The mean age was 32.9 years with a standard deviation of 11.67 years. Male and female participants were equally represented in the study population. Regarding education, 12% of respondents did not complete high school and the rest either completed high school (40%) or had a bachelor's degree or higher education (38%). Regarding occupation, 48% were unemployed, while 26% were employed in the military. Regarding marital status, 56% of the participants were married. Regarding income, 44% of respondents reported family income in the range 5000--9999 Saudi riyals, and 29% reported less than 5000 Saudi riyals. When asked about the chronicity of the presenting problem, only 30% said that the problem started on the day of the ED visit. Table 1Baseline characteristics of respondentsVariableCategory*N*%Age group (years)Mean ± SD (32.9 ± 11.67)Under 2027920--291053730--39712540--49491750 and over3412SexMale16550Female16350EducationDid not complete high school3712Completed high school12840Diploma3310Bachelor and higher12038OccupationUnemployed15048Private work134Health sector124Military sector8026Government sector (not health)3110Private sector (not health)176Other72Marital statusMarried18056Single12137Widowed/divorced237ResidenceIn Riyadh29189Outside Riyadh3611Family income/per month (Saudi Riyal)\< 500091295000--99991394410,000--14,9994414≥ 15,0003913When did this problem started?Today10130Not today23370Are you a patient waiting to be seen or a family memberPatient14746Family member16151Friend/co-worker103Do you have a primary care doctor or other health providerNo23284Yes4516Did you try to call your primary care doctor before coming to the ED?No2255Yes1845If yes, what did the office say?No appointments424Too sick---need to go to ED847Need further testing - that the doctor's office cannot do424Other16What is your main reason for coming to the emergency department?Regular care here8529Excellence in care12743Insurance reasons114Other financial reasons134My doctor told me to come3010Close to where I live/work2910*SD* standard deviation, *ED* emergency department
The use of primary care by ED visitors {#Sec12}
--------------------------------------
When asked whether they had a primary care provider (PCP), 84% answered "no." Of the remaining 16% that answered "yes," 45% tried to communicate with their PCP before visiting the ED. Of these, 47% were told they were too sick to be treated by the PCP and it was necessary to visit the ED.
ED visitors' expectations from the department {#Sec13}
---------------------------------------------
Patients' expectations from the ED are shown in Fig. [1](#Fig1){ref-type="fig"}. Of our respondents, 75% expressed their desire to be updated about any possible delays, and 73% wanted to know the cause of the delay. Additionally, 61% wanted more information on how the ED operates. Of these, 50% preferred the information to be delivered by a video playing in the waiting room, while 32% preferred handouts. The main reason for visiting the ED was excellence in care (43%) and having regular care in in the ED (29%). In terms of assessing the importance of various types of information provided during the waiting time, both general information about common illnesses (e.g., hypertension and diabetes) and information on serious medical conditions (e.g., stroke and heart attacks) were considered to be the most important by 81% and 80% of participants, respectively. Lastly, 77% of participants thought that it was important to know more information on the primary health care system and how to find a PCP. Fig. 1Patients expectations from the emergency department
Knowledge of the participants about the triage system in the ED {#Sec14}
---------------------------------------------------------------
Participants were asked if they knew why some patients are taken to the emergency room before others, even though they may not have waited as long. As shown in Table [2](#Tab2){ref-type="table"}, 40% of respondents answered "no." Among the 60% of participants who answered "yes," 50% provided the correct explanation. Furthermore, most respondents (79%) viewed this action as fair, while only 21% viewed it as unfair. When asked about if they knew the definition of triage system, only 11% of participants answered in the affirmative and provided the correct answer; of the remaining participants, 76% answered "no," or "yes" accompanied by an incorrect explanation. Lastly, participants were asked if they understood the function of a teaching hospital. Of 264 respondents, 71% answered "no" and 29% answered "yes." Additionally, 46% were aware that they were attending a teaching hospital, while and the other 54% were not. Table 2Knowledge of the participant about the triage system in the emergency departmentVariableCategory*N*%Do you know why some patients are taken to a room before others even though they may not have waited as long?Yes, with correct answer17051Yes, with incorrect answer or with no answer3210No13240Do you think this is fair?No6321Yes23679Do you know what triage means?Yes, with correct answer3711Yes, with incorrect answer or with no answer4313No25476Do you know what a teaching hospital is?No18771Yes7729Do you know if this hospital is a teaching hospital?No7254Yes6246
The mean time in minutes patients expect to wait for results of medical investigations and processes undertaken in the ED {#Sec15}
-------------------------------------------------------------------------------------------------------------------------
As shown in Fig. [2](#Fig2){ref-type="fig"}, the mean expected time for receipt of laboratory results was 69.3 min. The mean time patients expected to wait for imaging findings varied depending on modalities (X-ray and CT), with patients expected X-ray results to take less time to deliver. Results of an X-ray were expected within a mean time of 47.19 min, while CT results were expected within a mean time of 66.77 min. Consultation with another doctor was expected to take a mean time of 55.04 min. Making arrangements to provide a bed upstairs in the patient's home was expected to take the longest time, with a mean expectation of 100 min. Fig. 2The mean time in minutes patients expect to wait for results of medical investigations and processes undertaken in the ED
Univariate logistic regression analysis of the factors affecting the triage knowledge {#Sec16}
-------------------------------------------------------------------------------------
Participants who were under 20 years old were found to have a greater understanding of the triage system than those who were aged over 50 years (OR 2.21; 95% CI 0.44 to 11.11); however, this difference was not statically significant (*P* = 0.337). Moreover, there were no associations between patients' sex, level of education, occupation, marital status, living place or family income, and the knowledge of the triage system. Table [3](#Tab3){ref-type="table"} summarized the results of the univariate logistic regression model for identification of the factors affecting knowledge about the triage system among ED visitors. Table 3Logistic regression analysis of factors affecting patients' triage knowledgeVariableCategory*P* valueOR95% C. I for ORLowerUpperAge group (years)Under 200.3372.210.4411.1120--290.8471.120.353.6530--390.3681.650.554.9440--490.8851.080.373.1750 and over\*1SexMale0.0770.510.241.08Female\*1EducationIlliterate0.6341.310.443.92Completed high school0.8571.070.522.17Diploma0.5221.360.543.43Bachelor and higher\*1OccupationUnemployed0.5511.750.2810.94Private work0.1784.550.5041.34Health sector0.9470.920.099.39Military sector0.3742.450.3417.60Government sector (not health)0.7261.440.1911.25Private sector (not health)0.0786.870.8158.52Other\*1Marital statusMarried0.5140.710.252.00Single0.8840.910.263.23Widowed/divorced\*1ResidenceIn Riyadh0.9161.050.442.49Outside Riyadh\*1Family income (Saudi Riyal)\< 50000.4231.500.564.065000--99990.6621.230.493.06From 10,000--14,9990.930.960.342.69≥ 15,0001*CI* confidence interval, *OR* odds ratio\*Reference group
Discussion {#Sec17}
==========
Knowledge of triage systems among patients is not a widely investigated topic in the literature. The importance of addressing this issue lies in the fact that increased knowledge of triage systems is associated with increased patient satisfaction \[[@CR10], [@CR12], [@CR13]\]. Consequently, it is important to gain an understanding of patient satisfaction as well as the level of ED visitors' knowledge of the triage system and other factors that influence their experience during ED visits.
In this study, 61% of participants reported understanding why some patients are seen before others; of these participants, 83.6% where able to provide a correct explanation for their answers, while 16.4% failed to do so. These results are consistent with the findings of Seibert et al., who reported 68% of participants reported understanding this issue, of which 87% provided a correct explanation \[[@CR14]\]. Those who understood why some patients are seen before others were more likely to consider this situation to be fair, an association that was also reported to be significant by Seibert et al. \[[@CR14]\] After explaining triage to the participants, respondents in the study be Meek et al. reported a score of 6 on a 7-point scale for fairness \[[@CR15]\]. Furthermore, 24% of participants reported an understanding of the triage process, with 45% of these participants were able to provide a correct explanation; thus, only 11% of participants were able to define triage correctly. This number is much lower than the 33% reported in the USA and the 50% reported in Australia \[[@CR14], [@CR15]\]. These results indicate that the population in Saudi Arabia is as likely as those of other counties to know why some patients are seen before others in the ED, yet less likely to be able to correctly define triage. Furthermore, our findings indicate that patient satisfaction in directly related to their level of knowledge about triage.
Although the services provided by EDs have undergone improvements, some variations have been noted. Such variations may prompt some patients to choose one ED and avoid another. For instance, distance from the ED and presumed waiting time were the most influential factors in dictating patients' choice of ED \[[@CR17]\]; however, in this study, excellence of care and having regular care in an ED were the main reasons that influenced patients' decisions. Nearly 75% of patients stated the importance of receiving periodic updates about waiting time, with 69% of these preferring updates every 30 min. While 30 min was the shortest interval offered as an option in the present survey, the survey used by Cooke et al. included a 15-min interval option \[[@CR18]\]. A greater proportion of respondents in that study still preferred updates every 30 min (55%) compared with every 15 min (21%). More than 80% of participants viewed the provision of information about health education topics (e.g., diabetes, stroke) during the waiting time as important, which is consistent with the findings of a study conducted in the Boston \[[@CR19]\]. Lastly, 61% of participants wanted more information on how the ED operates, with 50% of these preferring the information to be delivered by a video playing in the waiting room. Educational videos during ED visits have been reported to be associated with increased patient satisfaction \[[@CR20]\].
Primary health care (PHC) plays an integral role in the quality of every sector in the health care system, including EDs. Overall health in communities, reduction in mortality, and health inequalities can be improved by providing high-quality primary care services \[[@CR21]\]. Accessing well-established PHC reduces ED's visits by approximately 50% and referrals to specialty care by 30% \[[@CR22]\]. Lack of regular access to PCPs is one of the reasons for ED overcrowding worldwide \[[@CR23], [@CR24]\]. An international study conducted by van den Berg et al. to investigate how the likelihood of attending an ED is related to accessibility of primary care showed the percentages of participants not having PCP in the following countries: 7.8% in Denmark, 10.7% in Belgium, 16.6% in Finland, 20.5% in England, 23.8% in Australia, 25.7% in Canada, 29% in Germany, 41% in Norway and Slovenia, 51.9% in Czech Republic, and 73.6% in Slovakia \[[@CR25]\]. Those percentages, not surprisingly, were below that identified in this study in Saudi Arabia, with almost 84% of ED visitors reporting a lack of access to PHC. Moreover, only half of those who had PCPs in this study attempted to communicate with their doctor prior to attending the ED. This finding is not accordance with the study by Afilalo et al. showing that 22% of ED patients had tried to contact their PCPs before attending the ED \[[@CR26]\]. Such apparent inconsistencies may be explained by variation in the health care systems in different countries. In Saudi Arabia, PHC was not a priority for the leading personalities in the health sector, which results in ED overcrowding. However, in 2016, the Saudi government announced a new plan (2030 vision) to encourage citizens to make use of PHC as a first step and by increasing family medicine residency training program opportunities all over the country \[[@CR27]\].
The mean time patients expected to wait for test results reported by participants in this study did not vary significantly from that of other studies, although different approaches were used to assess this variable. In this study, after excluding outliers, the mean times patients expected to wait for the results of laboratory tests, X-rays, and CT scans were 69, 47, and 61 min, respectively, whereas Seibert et al. reported 60 min for laboratory test results, 35 min for X-rays, and 60 min for CT scans \[[@CR15]\]. It is worth mentioning that the latter study reported the median expected times. In another study, 58% of patients reported expecting to receive their test results within 1 h \[[@CR18]\].
In this study, we used a convenient sample of ED visitors at a one tertiary hospital in Riyadh. Therefore, our study population cannot be representative of all ED visitors in Saudi Arabia or the Middle East. Moreover, non-Arabic speakers were not asked to participate in this study, which further limits the generalizability of our findings. Furthermore, variations in the work pressure and patient flow in the ED with time might influence our findings. However, the data were collected during different shifts (morning, evening, and night) on weekdays and weekends. Furthermore, the results could be skewed by the response rate of 80% and differences in patient waiting times during which the DCF was filled.
Conclusion {#Sec18}
==========
In conclusion, our population is not aware of triage. Efforts should be made to promote knowledge of triage. Additionally, only a small percentage of respondents said they have a primary care provider. It is important to provide access to primary care to community members. Finally, respondents in this study wanted more information regarding their visit and general information about health. These expectations should be met either by public health campaigns or educating material within the ED.
CI
: Confidence interval
CT
: Computerized tomography
DCF
: Data collection form
ED
: Emergency department
IQR
: Interquartile range
KAMC-ED
: King Abdulaziz Medical City -- Emergency Department
OR
: Odds ratio
PCP
: Primary care provider
PHC
: Primary health care
SD
: Standard deviation
**Publisher's Note**
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Not applicable.
NH contributed to the study design, data collection, data analysis, manuscript writing, and manuscript reviewing. FH contributed to the study design, data analysis, manuscript writing, and manuscript reviewing. AH contributed to the study design, data collection, manuscript writing, and manuscript reviewing. MS and MH contributed to the data collection, manuscript writing, and manuscript reviewing. EM contributed to the study design, data analysis, and manuscript reviewing. All authors read and approved the final manuscript.
This research received no grant from any funding agency in the public, commercial, or not-for-profit sectors.
Please contact author for data requests.
This study was approved by the institutional review board in King Abdullah International Medical Research Center (SP18/380/R). Informed consent was obtained from respondents prior to data collection.
Not applicable.
The authors declare that they have no competing interests.
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Champion Cleaners Dry Cleaning Blog - With Birmingham Area Happenings
Blood stains can be removed with products usually found in one's kitchen cabinet. Here are some home remedies for cleaning rugs, carpets and upholstery.
We all know that accidents will happen. Everyone will eventually do something that causes bleeding, and while household cuts and scrapes are usually nothing serious, we occasionally find ourselves in situations where it's necessary to remove blood stains out of the carpet or upholstery. Don't panic though. Blood can be removed and you no longer have to hide the spot on the carpet. Once you've bandaged your wound, act quickly. Time is the key factor in removing blood stains from carpet and upholstery. Follow these steps for the best results in blood stain removal on carpets and upholstery.
Step 1 - Blot and Absorb
First, blot the stain area with a damp cloth. Be sure not the rub the stain into the carpet. Rubbing will spread the stain and may cause it to set in deeper. Repeat this process until blotting does not remove any more blood. You can also blot the area with a baby wipe. Believe it or not, baby wipes are great at removing carpet stains.
Step 2 - Apply Diluted Detergent
Now mix one teaspoon of a neutral detergent - that is a detergent with no bleaches or alkalies - with one cup of warm water and gently blot. Be sure not to use hot water when working on the stain. Heat causes stains to set and will make it more difficult to clean.
Step 3 - Apply Diluted Amonia
After blotting with the detergent solution, mix one tablespoon of household ammonia to a cup of water and again gently blot until no more of the stain can be lifted. You can also try sponging the stain with hydrogen peroxide.
But remember that peroxide is a bleaching agent so you'll want to test the solution first on a hidden area of your carpet or furniture. Test any substance applied to rugs, carpet and upholstery to make sure there are no negative effects.
Household products provide an assortment of stain fighting home remedies. Vinegar is an awesome spot remover. Not only does it remove blood, but it also works well on pretty much any other common household stain.Don't forget the club soda, another tried and true home remedy. It creates bubbles which react with the blood to help loosen the stain. Sponge the stain as soon as possible with the soda and some cold water and then blot with a towel. Repeat as often as necessary.
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[Aromatase activity in lymphocytes of cancer patients and healthy subjects].
Conversion of androgens (aromatization) to estrogens in lymphocytes of cancer patients and healthy subjects in vitro was discovered. Aromatase activity in lymphocytes was comparable to that of fat and breast tumor tissues. It was completely suppressed in one out of two breast cancer patients receiving orimeten (aminoglutethimide). The activity in large bowel cancer was lower than in adenoma patients; however, the two groups were not balanced for age.
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Q:
WinForm RichTextBox text color changes too many characters
I have been working with an rtf box for a while in my winforms application running as a communcation interface between my external hardware device and my PC over serial. The issue I have is when using any example of colour change for a selection of text (that is sent before my actual command over serial) the echo back from my external device also has some text colour changed as well.
sending the symbol ';' I get the echo back and the reponse from my device all coloured in text.
;;[UART+ERROR]
My recieve event handler is the standard:
private void serialPort1_DataReceived(object sender, System.IO.Ports.SerialDataReceivedEventArgs e)
{
//fking threading
string rxString = serialPort1.ReadExisting(); // running on worker thread
this.Invoke((MethodInvoker)delegate
{
textLog.AppendText(rxString); // runs on UI thread
});
}
To write to the screen I used the example below (among many others I have also tried) to get working in my application. I am unsure what I am doing wrong.
private void AppendTextColor(RichTextBox box, Color color, string text)
{
int start = box.TextLength;
box.AppendText(text);
int end = box.TextLength;
// Textbox may transform chars, so (end-start) != text.Length
box.Select(start, end - start);
{
box.SelectionColor = color;
// could set box.SelectionBackColor, box.SelectionFont too.
}
box.SelectionLength = 0; // clear
}
A:
Your Select() call leaves the SelectionStart property at the start of the appended text instead of end of the text. You could restore it like you did for SelectionLength, but the simpler way to do it is:
private static void AppendTextColor(RichTextBox box, Color color, string text) {
box.SelectionStart = box.Text.Length; // Optional
var oldcolor = box.SelectionColor;
box.SelectionColor = color;
box.AppendText(text);
box.SelectionColor = oldcolor;
}
Note the // Optional comment, it isn't needed when the user cannot edit the text.
Do beware that you have a very serious fire-hose problem in your code. You are calling Invoke() at a very high rate, liable to cause the UI thread to start burning 100% core when the box starts filling up. Easy to tell when that happens, you can't see updates anymore and your program stops responding to input. Buffering in the DataReceived event handler is required, using ReadLine() instead of ReadExisting() is usually the simple way to get there. And use BeginInvoke() instead, Invoke() is very likely to cause the SerialPort.Close() call to deadlock.
|
# The MIT License
#
# Copyright (c) 2004-2009, Sun Microsystems, Inc., Kohsuke Kawaguchi, Sung Kim, id:cactusman
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
add\ description=\uC0C1\uC138 \uB0B4\uC6A9 \uC785\uB825
edit\ description=\uB0B4\uC6A9 \uC218\uC815
|
import Danmaku from '../../src/index.js';
describe('destroy API', function() {
it('should release memory', function(done) {
var container = document.getElementById('test-container');
var danmaku = new Danmaku({
container: container
});
danmaku.emit({ text: 'Flip Flapper' });
setTimeout(function() {
danmaku.destroy();
assert.equal(0, container.childNodes.length);
assert.equal(null, danmaku.comments);
assert.equal(null, danmaku.container);
danmaku.destroy();
done();
}, 100);
});
});
|
Q:
rename directories containing left/right square
To rename directories containing left & right squares you can use:
shopt -s globstar
rename -n 's/\(|\[|\]|\)//g' **
This will rename everything with [ & ] from the directory you're in and recursive..
but I need to execute this as a nemo.action script, and can't get it to work.
(Basically a normal bash script)
My current script is:
#!/bin/bash
shopt -s globstar
rename "$@" 's/\(|\[|\]|\)//g' **
where $@ is /media/sf_Mediaserver3/Untitled Folder/[ hdjue] [kskk]
where the [ hdjue] [kskk] (just random letters) is the starting folder that I want to rename and the following files/folders...
This doesn't work of course, and now I have to go to the parent directory and run the first lines, but that would process ALL directories in the parent directory, not only the
[ hdjue] [kskk] anybody got any idea how to solve this?
it almost seems like the rename function can't handle a start directory?
And if possible, remove all spaces (replace with . (dot)), and make the filename/directory lowercase, to simplify the compatibility with external/internal requests..
A:
The requirement here, as I understand it, is to remove all instances of the [ and ] characters from files and directories at and under the specified paths.
The difficulty is to avoid renaming the directory while it's still being traversed. The globstar ** lists items from the root down rather than depth first, so given an example such as a a/b a/b/c, renaming a will mean that the paths to a/b and a/b/c are no longer valid. The find option can handle this with its -depth, but that requires a different approach
#!/bin/bash
#
find "$@" -depth -name '*[[\]]*' -print0 |
while IFS= read -d '' -r item
do
path="${item%/*}" file="${item##*/}" # Separate path and file name parts
name="${file//[[\]]/}" # Generate new file name
name="${name// /.}" # Comment: space becomes dot
name="${name,,}" # Comment: lowercase name
echo mv -f "$item" "$path/$name" # Rename
done
Remove echo (or supplement it) when you are happy the script will do what you expect.
I've used -print0 in conjunction with the -d '' option for read to handle files with really strange filenames (including those with newlines and non-printing characters). You can remove both if you want to see what is going on - or if your implementations don't support them - but the script then becomes less robust
The modifiers when assigning the variables path, file, and name match using globs (not regular expressions). A single modifier (%, #, /) means a shortest or single match; a double modifier (%%, ##, //) means a longest match or multiple matches. It is all documented in the bash man page but here is my explanation with context:
${item%/*} The % indicates that the shortest match to the glob pattern should be removed from the end of the value of $item. So for a/b/c we would remove text matching /* leaving a/b
${item##*/} The ## indicates that the longest match to the glob pattern should be removed from the beginning of the value of $item. So for a/b/c we would remove text matching */ leaving c
${file//[[\]]/} The // indicates that multiple replacements of the glob should be replaced with the text following the next /, i.e. nothing. The glob is a square-bracketed collection of the two characters [ and ], meaning "either [ or ]". So for ab[cd]ef[gh we would end up with abcdefgh
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ARVADA, Colo. — She was a memorable figure in this western Denver suburb, a teenager wearing a traditional Muslim headscarf and dress, sitting alone on a park swing or walking into a Christian church with a backpack and notebook.
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One of the challenging aspects of moving is what to do with all of the “junk” that you own. This isn’t trash, per se, but the stuff that you find strewn throughout your house once everything else is packed. These items are things that would look at home in a junk drawer, things you’ve been holding onto that never found a proper home, and things that defy easy categorization. The following are just a few ideas on how to handle the moving detritus.
What to do with your drawer junk when moving
The first thing you should do when you empty out your drawers is to sort through everything and toss what you don’t need. Once you’ve sorted out the actual trash, you’re probably going to be left with small items that could have some use at some point in the future, like rubber bands, loose batteries and more. Take these items and sort them in small Ziploc bags to keep them together during the move.
Once you start unpacking, you’ll want to organize items so that you don’t end up having random clutter again. Pick up some drawer dividers that allow you to separate small items. This way, you can have a section for receipts, coupons and notes, a section for loose batteries, rubber bands and paper clips and a section for pens, pencils and markers.
Make sure that the dividers are shallow so that they don’t end up overflowing with these items. Also, don’t get lazy. If items have a proper place in your household that isn’t the junk drawer, put them away in their right place. The more organized it remains, the more likely you are to find the items you need and to use them regularly so that it’s no longer a “junk” drawer.
On a larger scale, junk drawers teach us how to purge what we don’t need, organize what we have, and identify our lazy habits. Most homes don’t look like magazine covers, because people actually live in them. Clutter, unwanted items, and items without a home are bound to build up, but you can come up with a system to keep everything orderly.
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king 1 e, 1 z, and 1 f?
2/5
Two letters picked without replacement from {u: 3, p: 3, f: 7, l: 4, n: 1}. Give prob of picking 1 n and 1 f.
7/153
What is prob of picking 1 q and 1 s when two letters picked without replacement from ngsssqos?
1/7
Calculate prob of picking 2 z when two letters picked without replacement from zzwmwmzzzzzm.
7/22
Four letters picked without replacement from bbbmbbbbmbbm. Give prob of picking 1 m and 3 b.
28/55
Calculate prob of picking 3 r when three letters picked without replacement from ccrcoccrror.
4/165
Three letters picked without replacement from xxxxjxxxjj. What is prob of picking 2 j and 1 x?
7/40
Two letters picked without replacement from kxrqjxjjqrxqxjxxxq. Give prob of picking 1 r and 1 k.
2/153
Three letters picked without replacement from wmwmwmwmmy. What is prob of picking 3 m?
1/12
Calculate prob of picking 1 p and 1 q when two letters picked without replacement from {p: 1, q: 4, n: 1, f: 1, r: 1}.
1/7
Two letters picked without replacement from {i: 2, k: 1, p: 2, g: 1, f: 2}. What is prob of picking 2 f?
1/28
Two letters picked without replacement from {c: 3, i: 1, e: 4, y: 1, s: 5}. Give prob of picking 1 e and 1 i.
4/91
Three letters picked without replacement from gggvggjejjgeggegggeg. What is prob of picking 1 g and 2 e?
6/95
What is prob of picking 1 u, 2 b, and 1 o when four letters picked without replacement from bbuouukuob?
4/35
Three letters picked without replacement from {m: 1, e: 1, x: 1, k: 1, c: 1}. What is prob of picking 1 c, 1 k, and 1 x?
1/10
Four letters picked without replacement from {v: 5, s: 13}. What is prob of picking 1 s and 3 v?
13/306
Four letters picked without replacement from vwwwvwavvvv. What is prob of picking 2 w, 1 a, and 1 v?
6/55
What is prob of picking 2 r and 1 j when three letters picked without replacement from jtkzjthrrzjjzrk?
12/455
Two letters picked without replacement from {h: 3, w: 2, u: 2, f: 2, j: 2, v: 1}. Give prob of picking 1 v and 1 w.
1/33
What is prob of picking 3 b when three letters picked without replacement from bibbbbbbbbbbbbbbii?
455/816
Two letters picked without replacement from {f: 2, t: 2, n: 5}. Give prob of picking 1 n and 1 t.
5/18
Four letters picked without replacement from {q: 8, d: 11, w: 1}. Give prob of picking 2 d and 2 q.
308/969
Three letters picked without replacement from {e: 5, h: 7, u: 4}. Give prob of picking 2 u and 1 e.
3/56
Three letters picked without replacement from dzadrddzk. Give prob of picking 1 d, 1 z, and 1 r.
2/21
Calculate prob of picking 2 n when two letters picked without replacement from nnddnnnzdzny.
5/22
Calculate prob of picking 1 q and 1 m when two letters picked without replacement from qqmmqmzqmm.
4/9
What is prob of picking 1 k and 2 q when three letters picked without replacement from {d: 4, v: 6, l: 1, q: 2, k: 3}?
3/560
Calculate prob of picking 2 m when two letters picked without replacement from {m: 5, n: 3}.
5/14
Two letters picked without replacement from ufuauffuuuuaf. What is prob of picking 1 u and 1 f?
14/39
What is prob of picking 2 u when two letters picked without replacement from uvus?
1/6
Three letters picked without replacement from sssskskskkksss. What is prob of picking 2 k and 1 s?
45/182
What is prob of picking 1 h and 1 o when two letters picked without replacement from {i: 1, l: 2, h: 1, j: 6, t: 1, o: 4}?
4/105
Calculate prob of picking 1 q, 2 x, and 1 z when four letters picked without replacement from bbbbcqbbcbbbqxxbqzs.
1/1292
What is prob of picking 1 u and 3 r when four letters picked without replacement from ryiriririuiyi?
4/715
What is prob of picking 3 w when three letters picked without replacement from incwwwnnwicniicnnnn?
4/969
Two letters picked without replacement from rrddddrd. Give prob of picking 2 r.
3/28
What is prob of picking 1 m, 2 g, and 1 z when four letters picked without replacement from hygmggtymzmggzth?
3/91
Two letters picked without replacement from plpwuiiwpis. What is prob of picking 1 s and 1 i?
3/55
Four letters picked without replacement from qqqqggqgggqqgg. What is prob of picking 2 g and 2 q?
63/143
Calculate prob of picking 2 b and 1 q when three letters picked without replacement from {q: 1, b: 17}.
1/6
Calculate prob of picking 1 m and 3 p when four letters picked without replacement from {m: 9, p: 7}.
9/52
Calculate prob of picking 1 y, 1 e, and 1 i when three letters picked without replacement from ceiicyw.
2/35
Calculate prob of picking 2 h when two letters picked without replacement from hrhaxaxhahxhrbarrar.
10/171
Four letters picked without replacement from kkraaankanhahnnuhn. What is prob of picking 1 r, 1 k, 1 a, and 1 h?
1/68
Three letters picked without replacement from lmemeqmvelglmm. What is prob of picking 3 m?
5/182
Three letters picked without replacement from rnrgrnjjrnjrn. Give prob of picking 1 g and 2 j.
3/286
What is prob of picking 1 u and 1 s when two letters picked without replacement from {o: 1, y: 1, s: 3, u: 2, c: 3, b: 1}?
6/55
Two letters picked without replacement from rpupyr. What is prob of picking 1 y and 1 r?
2/15
Calculate prob of picking 4 o when four letters picked without replacement from oovvoo.
1/15
Calculate prob of picking 2 v and 1 o when three letters picked without replacement from {v: 9, o: 6, d: 3, b: 1}.
72/323
Two letters picked without replacement from {q: 2, n: 1}. What is prob of picking 2 q?
1/3
Two letters picked without replacement from {b: 1, z: 1, o: 1, l: 2, a: 2, y: 2}. What is prob of picking 1 y and 1 b?
1/18
Four letters picked without replacement from clcccccccccllccccc. What is prob of picking 3 l and 1 c?
1/204
Calculate prob of picking 3 b and 1 c when four letters picked without replacement from cbcncbnbnnc.
2/165
What is prob of picking 1 t and 1 n when two letters picked without replacement from {t: 3, u: 3, o: 1, b: 1, h: 2, n: 1}?
3/55
Calculate prob of picking 3 u when three letters picked without replacement from ututvvtu.
1/56
Three letters picked without replacement from {s: 3, w: 1, g: 1, q: 1, y: 1, u: 6}. Give prob of picking 1 y, 1 q, and 1 u.
3/143
Two letters picked without replacement from rcccrcrcccrccccrrc. Give prob of picking 2 c.
22/51
Three letters picked without replacement from {p: 2, c: 2}. What is prob of picking 1 c and 2 p?
1/2
Three letters picked without replacement from {j: 1, k: 1, c: 2, l: 2}. Give prob of picking 2 c and 1 j.
1/20
Calculate prob of picking 2 z when two letters picked without replacement from {j: 5, z: 3}.
3/28
Three letters picked without replacement from {g: 3, v: 1}. Give prob of picking 1 v and 2 g.
3/4
Three letters picked without replacement from {a: 2, x: 4}. What is prob of picking 3 x?
1/5
Calculate prob of picking 2 c when two letters picked without replacement from caoccaacaa.
2/15
Three letters picked without replacement from djfvfdoj. What is prob of picking 1 v, 1 f, and 1 j?
1/14
Calculate prob of picking 1 g and 1 q when two letters picked without replacement from sqssqseqsgqqqsegqqg.
8/57
Two letters picked without replacement from {z: 4, p: 1, f: 5, v: 1}. What is prob of picking 1 v and 1 z?
4/55
Two letters picked without replacement from {d: 6, q: 3, m: 4}. Give prob of picking 1 d and 1 m.
4/13
Calculate prob of picking 1 p and 1 s when two letters picked without replacement from fpffppfsppppppfpfpp.
4/57
What is prob of picking 1 j, 1 h, and 1 t when three letters picked without replacement from {j: 1, t: 1, a: 1, v: 2, h: 1, k: 1}?
1/35
Four letters picked without replacement from kxoxkojoixxoopx. What is prob of picking 1 k, 1 i, and 2 o?
4/273
Calculate prob of picking 2 v, 1 o, and 1 q when four letters picked without replacement from {q: 1, v: 4, o: 8}.
48/715
Four letters picked without replacement from {f: 9, e: 7}. What is prob of picking 4 e?
1/52
Two letters picked without replacement from {v: 5, g: 8}. What is prob of picking 2 g?
14/39
Two letters picked without replacement from moggqmqze. What is prob of picking 1 q and 1 o?
1/18
What is prob of picking 1 f, 1 y, and 1 b when three letters picked without replacement from {j: 1, y: 1, b: 1, s: 2, f: 1, w: 1}?
1/35
Two letters picked without replacement from {l: 1, x: 2, e: 1, y: 1}. What is prob of picking 1 l and 1 x?
1/5
Calcula
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Buy Locks are the largest online supplier of ERA Security products. We offer extremely competitive prices to both the public and trade. Buy Locks supply a complete range of ERA door locks, ERA window locks and door accessories.
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#!/bin/bash
exec 2>&1
source /etc/environment
BUNDLE_EXEC="<%= node[:languages][:ruby][:bin_dir] %>/bundle exec"
APP_ROOT="<%= node[:kafka][:contrib][:deploy][:root] %>/current"
KAFKA_CONTRIB="${APP_ROOT}/bin/kafka"
APP="<%= @options[:app_type] %>"
HADOOP_HOME="<%= @options[:hadoop_home] %>"
KAFKA_HOME="<%= @options[:kafka_home] %>"
CONFIG_FILE="${APP_ROOT}/config/<%= @options[:app_name] %>.properties"
TOPIC="<%= @options[:topic] %>"
EXTRA_OPTS="<%= @options[:app_options] %>"
cd $APP_ROOT
exec chpst -u <%= @options[:run_as_user] %> $BUNDLE_EXEC $KAFKA_CONTRIB $APP -f $CONFIG_FILE -t $TOPIC $EXTRA_OPTS --kafka_home=${KAFKA_HOME} --hadoop_home=${HADOOP_HOME}
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Ian Winchester
Ian Winchester (born 27 May 1973) is a discus thrower from New Zealand.
He finished tenth at the 1992 World Junior Championships, eighth at the 1998 World Cup and fifth at the 1998 Commonwealth Games (where he also finished eighth in shot put) He also competed at two World Championships (1997, 1999) as well as the 2000 Summer Olympics without reaching the final round.
His personal best throw is 65.03 metres, achieved in May 2002 in Salinas. This is the current national record, and makes him the third best discus thrower in Oceania after Australians Werner Reiterer and Wayne Martin.
Achievements
Personal bests
References
Category:1973 births
Category:Living people
Category:New Zealand male discus throwers
Category:Athletes (track and field) at the 2000 Summer Olympics
Category:Olympic athletes of New Zealand
Category:Athletes (track and field) at the 1998 Commonwealth Games
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WD-50, one of the biggest-name restaurants in New York, plans to close at the end of November 2014, and there's no explanation as to why.
Chef Wylie Dufresne, largely regarded as one of the more creative and boundary-pushing chefs in the business, has been at the helm of WD-50 for 11 years now — it's where he made his mark, propelling the restaurant to tremendous success. In 2010, S. Pellegrino listed it as one of the World's 50 Best Restaurants. Dufresne himself has been called the "Mad Scientist" of food, an appropriate title considering this is the man who figured out how to fry mayonnaise.* This is a guy who takes tremendous joy in breaking down the component parts of foods just so he can rebuild them in crazy new ways like a kid with Legos and an active imagination, and whose kitchen at WD-50 has an enormous entrance specifically designed to allow customers to watch him and his chefs at work.
He's also, somewhat antithetically for a big-name chef, known as a nice guy and generally very well-liked within the business. Yesterday, though, he tweeted that WD-50's last night of business would be at the end of November:
Nov 30 will be our final night of service at wd50. Come celebrate with us for the next 173 days. Stay tuned!! pic.twitter.com/DGnbfkkrV6
There really isn't much information on this at this point. There are some rumors that there's a new building going up at the site of the restaurant, so it's possible this is merely a prelude to relocation, but no one knows anything for sure, and Dufresne has resisted all media attempts to find out more in the past day.
One thing's for sure, though: whatever he does next, he's not going to want for customers.
*When asked if he was doing it because it sounded like a cool idea and he'd be the first to do so, Dufresne responded, "No, I'm doing it because it's delicious." After reading that article, I'm a little bit in love with Wylie Dufresne.
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Q:
Import package & type
Here is my problem and my project structure
src
|-->config
|--> config.go
|-->otherPackage
|--> otherFile.go
|-->main.go
I have a type on config.go that I would like to use in otherFile.go
But when I tried to add it to the import here theses issues:
imported and not used.
undefined: Config
Although I use it in the function declaration
function(target float64, entries [2]float64, config Config)
What is the problem with this?
I tried to import it with
import (
"fmt"
"math"
"../config"
)
A:
You cannot "import from a package". All you can do is "import the whole package". That means if you import "full/import/path/of/foo" and that package declared itself to be called foo via package foo at the beginning, then everything in this package has to be qualified by foo:
foo.Config
If you package is called config than declaring a variable config will shaddow the whole package: so you have to:
Rename the config variable to e.g. cfg
Reference Config from package config with its qualified name config.Config
|
Q:
Render control programmatically (using LoadControl) while adhering the page lifecycle
I'm trying to use LoadControl to get a custom control in code for programmatic rendering purposes. However I notice that the OnInit method of my custom control is not being called. Am I missing an essential step here?
//Loading the control
Page h = HttpContext.Current.Handler as Page;
UserControl userControl = (UserControl)h.LoadControl(pathToControl);
h.Controls.Add((Control)userControl);
//Rendering the control
StringWriter stringWriter = new StringWriter();
HtmlTextWriter writer = new HtmlTextWriter((TextWriter) stringWriter);
userControl.RenderControl(writer);
var result = stringWriter.ToString();
This is where the code above is called
[ScriptService]
public partial class Ajax : System.Web.UI.Page
{
protected void Page_Load(object sender, EventArgs e)
{
}
[WebMethod]
[ScriptMethod(ResponseFormat = ResponseFormat.Json)]
public static object AjaxMethod(string productCode) {
//here...
}
}
A:
So you are making a PageMethods call to the server, and want to stream back the markup for a custom control update, is what it looks like. PageMethods do not execute a lifecycle, therefore it will never fire the OnInit event handler. People have used this same technique using JQuery or an HTTP handler, and some examples of how they did it was here:
how can we load usercontrol using generic handler?
http://weblogs.asp.net/sanjeevagarwal/archive/2008/07/22/Dynamically-create-ASP.NET-user-control-using-ASP.NET-Ajax-and-Web-Service.aspx
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EUGENE — Oregon men’s basketball committed three of the athletic department’s seven self-reported NCAA secondary violations in 2018-19.
Ducks basketball assistant coach Kevin McKenna committed two of the men’s basketball team’s three violations, baseball committed two violations and former football defensive coordinator Jim Leavitt and softball coach Melyssa Lombardi each committed one, according to records provided to The Oregonian/OregonLive on Monday in response to a Freedom of Information Act request.
A men’s basketball recruit participated in an open gym workout during a recruiting dead period in which McKenna was present and a basketball recruit took an impermissible unofficial visit last summer during a recruiting quiet period.
The third men’s basketball violation involved an official visitor photoshoot at a competition site, though the name of the individual involved is redacted.
Baseball director of operations Jamie Walton was cited for two violations for a recruit driving for an official visit they were not cleared to take and for a player participating in an alumni game before receiving certification as eligible.
Leavitt posed for a photo with a recruit during an evaluation period.
Lombardi was cited for an official visitor taking part in a photoshoot at a competition site.
The document the University of Oregon released to the Oregonian/OregonLive doesn’t specify the penalties to each coach involved, though five of the violations are listed as “closed” with one of McKenna’s and the unnamed men’s basketball violation designated as “submitted.”
Typically, recruiting related NCAA secondary violations require a coaching staff member or school to forego contact with the specific recruit involved or from all on or off-campus recruiting for a set period of time.
Oregon NCAA secondary violations in 2018-19 (7 total)
Men’s basketball: 3
Baseball: 2
Football: 1
Softball: 1
|
---
abstract: 'We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.'
address:
- 'Ghent University, SYSTeMS Research Group, Technologiepark 914, 9052 Zwijnaarde, Belgium.'
- 'IDSIA, Galleria 2, 6928 Manno (Lugano), Switzerland'
author:
- Gert de Cooman
- Filip Hermans
- Alessandro Antonucci
- Marco Zaffalon
title: 'Epistemic irrelevance in credal nets: the case of imprecise Markov trees'
---
Introduction {#sec:introduction}
============
The last twenty years have witnessed a rapid growth of *graphical models* in the fields of artificial intelligence and statistics. These models combine graphs and probability to address complex multivariate problems in a variety of domains, such as medicine, finance, risk analysis, defence, and environment, to name just a few.
Much has been done also on the front of imprecise probability. In particular, *credal nets* [@cozman2000] have been and still are the subject of intense research. A credal net creates a global model of a domain by combining local uncertainty models using some notion of independence, and then uses this to do inference. The local models represent uncertainty by closed convex sets of probabilities, also called *credal sets*.
The notion of independence used with credal nets in the vast majority of cases is that of *strong independence* (with some exceptions in [@campos2007b]). Loosely speaking, two variables $X,Y$ are strongly independent if the credal set for $(X,Y)$ can be regarded as originating from a number of precise models in each of which $X$ and $Y$ are stochastically independent. Strong independence is closely related to the *sensitivity analysis* interpretation of credal sets, which regards an imprecise model as arising out of partial ignorance of a precise one.
In the particular case of credal nets, strong independence leads to a mathematical equivalence: a credal net model is equivalent to a model consisting of a set of Bayesian nets, each with the same graph but with different values for the parameters. The sensitivity analysis interpretation is then that there is some (kind of ideal) Bayesian net model of the problem under consideration, and the graph of such a net is known. But, for some reason, the net’s parameters are not known precisely, and that is why one considers the set of all the Bayesian nets that are consistent with the partial specification of the parameters. Common causes for the existence of partial knowledge are the cost of, and time constraints on, eliciting parameters, and disagreement amongst a group of experts consulted for that purpose. Non-ignorable missing data can be another reason, in case the parameters are inferred from a data set [@zaffalon2009].
The sensitivity analysis interpretation of imprecise-probability models, and hence strong independence, is not always applicable. A notable case arises when one wishes to model an expert’s beliefs: it is then not always tenable that there should be some ideal Bayesian net that models these beliefs, and that it is only because of our limited resources that we cannot define it precisely. Rather, it seems more reasonable to concede that expert knowledge may be *inherently* imprecise to some extent.[^1] This simple observation makes the sensitivity analysis interpretation fail, and hence it makes strong independence an inadequate model, in general, for such a situation.[^2]
An alternative and attractive approach to expressing irrelevance that is not committed to the sensitivity analysis interpretation is offered by *epistemic irrelevance* [@walley1991]: we say that $X$ is epistemically irrelevant to $Y$ if observing $X$ does not affect our beliefs about $Y$. In other words, by making an epistemic irrelevance assessment, a subject states that her belief model about $Y$ does (or will) not change after receiving information about $X$. When the belief model is a precise probability, both epistemic irrelevance and strong independence reduce to the usual (stochastic) independence.[^3] But when the model is a set of probabilities, this is no longer the case, because in contradistinction with strong independence, epistemic irrelevance is a property *of this set* that cannot be explained using properties of the precise probabilities in the set. Epistemic irrelevance is defined directly in terms of a subject’s belief model (the set of probabilities). For this reason, it is very well suited for a behavioural theory of imprecise probability. Contrary to strong independence, it is not a symmetrical notion: generally speaking, the epistemic irrelevance of $X$ to $Y$ does not entail the epistemic irrelevance of $Y$ to $X$. It is also weaker than strong independence, in the sense that strong independence implies epistemic irrelevance: sets of probabilities that correspond to assessments of epistemic irrelevance usually include those related to strong independence assessments. It therefore does not lead to overconfident inferences when the sensitivity analysis interpretation is not justified.
At this point, the question we address in this paper should be clear: can we define credal nets based on epistemic irrelevance, and moreover create an exact algorithm to perform efficient inferences with them? We give a fully positive answer to this question in the special case that
the graph under consideration is a directed tree, and
the related variables assume finitely many values.
The intuitions that showed us the way towards this result originated in previous work done by some of us on imprecise probability trees [@cooman2007d] and imprecise Markov chains [@cooman2008].
How do we address this problem?
In Section \[sec:markov-trees\], we discuss some preliminary graph-theoretic notions, and define the local uncertainty models that will be used at each node of a tree. These models are formalised through the language of *coherent lower previsions* [@walley1991]. We discuss how such local models will give rise to a global uncertainty model, which plays the same role as the joint mass function built by the chain rule in a Bayesian net. Based on the global model, we state the Markov condition that defines the imprecise-probability interpretation of our credal trees. As announced before, this Markov condition involves epistemic irrelevance rather than strong independence.
In Section \[sec:independent-natural-extension\], we take a brief detour to discuss in general terms how to combine marginal models into joint ones using irrelevance assessments, in a way that is as conservative as possible. We do so because the notion of so-called *epistemic independence*, which arises out of a symmetrisation of epistemic irrelevance, has so far been defined in the literature only for the case of two variables. We define and discuss the *independent natural extension* of a number of marginals. This is the most conservative joint model that arises out of the marginals and epistemic independence alone. Moreover, we show that the independent natural extension has a very important *strong factorisation* property, which has a crucial part in our algorithm for updating credal trees under epistemic irrelevance.
In Section \[sec:joint\], we turn to the problem of constructing the most conservative global model based only on the local models in the tree and our Markov condition. We show that this task can be achieved by a recursive construction that proceeds from the leaves to the root of the tree using two operations: the *independent natural extension* discussed in Section \[sec:independent-natural-extension\], and the *marginal extension*, defined and studied in [@walley1991; @miranda2006b]. We also show that all uncertainty models we consider, the local ones as well as the global ones that we create, satisfy a consistency criterion that generalises (and is based on the same ideas as) the usual consistency criterion in Bayesian nets: they are (separately and jointly) *coherent* [@walley1991; @miranda2008a; @miranda2009a; @williams2007] (see in particular [@miranda2009b Section 8.1]). This is an important rationality requirement.
We briefly comment on some of the graphical separation criteria induced by epistemic irrelevance in Section \[sec:separation\]. We then go on to develop and justify an algorithm for making inferences on credal trees under epistemic irrelevance in Section \[sec:algorithm\]. The algorithm is used to *update* the tree: it computes posterior beliefs about a *target* variable in the tree conditional on the observation of other variables, which are called *instantiated*, meaning that their value is determined. It can in particular be used for treating the model as an expert system.
Our algorithm is based on message passing, as are the traditional algorithms that have been developed for precise graphical models. It has some remarkable properties:
it works in time linear in the number of nodes in the tree;
it natively computes posterior lower and upper *previsions* (or expectations) rather than probabilities;
it is the first algorithm developed for credal nets that exclusively uses the formalism of coherent lower previsions; and
it is shown that, under very mild conditions, using the tree for updating beliefs cannot lead to inferences that are inconsistent with the local models we have started from, nor with one another.
We give a step-by-step example of the way inferences can be done using our algorithm in Section \[sec:example\]. We also comment there on the intriguing relationship between the failure of certain classical separation properties in our framework, and dilation [@herron1997; @seidenfeld1993].
The last part of the paper focuses on numerical simulations. In Section \[sec:comparison\] we empirically measure the amount of imprecision introduced by using epistemic irrelevance rather than strong independence in a credal tree, when propagating inferences backwards (towards the root) from instantiated nodes to the target node. Indeed, it can be shown [@cooman2007d] that there is *no difference* between inferences that go forward from instantiated nodes to the target node under strong independence and epistemic irrelevance. In Section \[sec:application\] we present an application of our algorithm to on-line character recognition. We learn the probabilities from data and compare the predictions of our approach with those of its precise probability counterpart. The results are encouraging: they show that the tree can be used for real applications, and that the imprecision it originates is justified.
In order to keep this paper reasonably short, we have to assume the reader has a good working knowledge of the basics of Peter Walley’s [@walley1991] theory of coherent lower previsions. This is needed in particular for the most important proofs, collected in the Appendix. For a fairly detailed discussion of the coherence notions and results needed in the context of this paper, we refer to recent work by Enrique Miranda [@miranda2008a; @miranda2009a].
Credal trees under epistemic irrelevance {#sec:markov-trees}
========================================
Basic notions and notation.
---------------------------
We consider a rooted and directed discrete tree with finite width and depth. We call ${T}$ the set of its nodes $s$, and we denote the *root*, or initial, node by ${\square}$. For any node $s$, we denote its *mother node* by ${m(s)}$. Of course, ${\square}$ has no mother node, and we use the convention ${m({\square})}=\emptyset$. Also, for each node $s$, we denote the set of its *children* by ${C_{}(s)}$, and the set of its *siblings* by ${S(s)}$. Clearly, ${S({\square})}=\emptyset$, and if $s\neq{\square}$ then ${S(s)}={C_{}({m(s)})}\setminus\{s\}$. If ${C_{}(s)}=\emptyset$, then we call $s$ a *leaf*, or *terminal node*. We denote by ${{T}^\lozenge}\coloneqq{\{s\in{T}\colon{C_{}(s)}\neq\emptyset\}}$ the set of all non-terminal nodes.
For nodes $s$ and $t$, we write $s{\sqsubseteq}t$ if *$s$ precedes $t$*, i.e., if there is a directed segment in the tree from $s$ to $t$. The relation ${\sqsubseteq}$ is a special partial order on the set ${T}$. ${A(s)}\coloneqq{\{t\in{T}\colont{\sqsubset}s\}}$ denotes the chain of *ancestors* of $s$, and ${D(s)}\coloneqq{\{t\in{T}\colons{\sqsubset}t\}}$ its set of *descendants*. Here $s{\sqsubset}t$ means that $s{\sqsubseteq}t$ and $s\neq t$. We also use the notation ${{\uparrow}s}\coloneqq{A(s)}\cup\{s\}$ for the chain (segment) connecting ${\square}$ and $s$, and ${{\downarrow}s}\coloneqq{D(s)}\cup\{s\}$ for the sub-tree with root $s$. Similarly, we let ${{\uparrow}S}\coloneqq\bigcup{\{{{\uparrow}s}\colons\in S\}}$ and ${{\downarrow}S}\coloneqq\bigcup{\{{{\downarrow}s}\colons\in S\}}$ for any subset $S\subseteq {T}$. For any node $s$, its set of non-parent non-descendants is given by ${\overline{s}}\coloneqq{T}\setminus({{\{{m(s)}\}}}\cup{{\downarrow}s})$.
With each node $s$ of the tree, there is associated a variable ${X_{s}}$ assuming values in a non-empty finite set ${\mathcal{X}_{s}}$. We denote by ${\mathcal{L}({\mathcal{X}_{s}})}$ the set of all real-valued maps (also called *gambles*) on ${\mathcal{X}_{s}}$. We extend this notation to more complicated situations as follows. If $S$ is any subset of ${T}$, then we denote by ${X_{S}}$ the tuple of variables whose components are the ${X_{s}}$ for all $s\in S$. This new joint variable assumes values in the finite set ${\mathcal{X}_{S}}\coloneqq\times_{s\in S}{\mathcal{X}_{s}}$, and the corresponding set of gambles is denoted by ${\mathcal{L}({\mathcal{X}_{S}})}$. [^4] Generic elements of ${\mathcal{X}_{s}}$ are denoted by ${x_{s}}$ or ${z_{s}}$. Similarly for ${x_{S}}$ and ${z_{S}}$ in ${\mathcal{X}_{S}}$. Also, if we mention a tuple ${z_{S}}$, then for any $t\in S$, the corresponding element in the tuple will be denoted by ${z_{t}}$. We assume all variables in the tree to be logically independent, meaning that the variable ${X_{S}}$ may assume *all* values in ${\mathcal{X}_{S}}$, for all $\emptyset\subseteq S\subseteq{T}$.
We will frequently use the simplifying device of identifying a gamble $f_S$ on ${\mathcal{X}_{S}}$ with its *cylindrical extension* to ${\mathcal{X}_{U}}$, where $S\subseteq U\subseteq{T}$. This is the gamble $f_U$ on ${\mathcal{X}_{U}}$ defined by $f_U({x_{U}})\coloneqq f_S({x_{S}})$ for all ${x_{U}}\in{\mathcal{X}_{U}}$. To give an example, if $\mathcal{K}\subseteq{\mathcal{L}({\mathcal{X}_{{T}}})}$, this trick allows us to consider $\mathcal{K}\cap{\mathcal{L}({\mathcal{X}_{S}})}$ as the set of those gambles in $\mathcal{K}$ that depend only on the variable ${X_{S}}$. As another example, this device allows us to identify the gambles ${\mathbb{I}_{{{\{{x_{S}}\}}}}}$ and ${\mathbb{I}_{{{\{{x_{S}}\}}}\times{\mathcal{X}_{{T}\setminus S}}}}$, and therefore also the events ${{\{{x_{S}}\}}}$ and ${{\{{x_{S}}\}}}\times{\mathcal{X}_{{T}\setminus S}}$. More generally, for any event $A\subseteq{\mathcal{X}_{S}}$, we can identify the gambles ${\mathbb{I}_{A}}$ and ${\mathbb{I}_{A\times{\mathcal{X}_{{T}\setminus S}}}}$, and therefore also the events $A$ and $A\times{\mathcal{X}_{{T}\setminus S}}$. In the same spirit, a lower prevision on all gambles in ${\mathcal{L}({\mathcal{X}_{S}})}$ can be identified with a lower prevision defined on the set of corresponding gambles on ${\mathcal{X}_{{T}}}$, a subset of ${\mathcal{L}({\mathcal{X}_{{T}}})}$.
Throughout the paper, we consider (conditional) lower previsions as models for a subject’s beliefs about the values that certain variables in the tree may assume. We use a systematic notation for such (conditional) lower previsions. Let $I,O\subseteq{T}$ be *disjoint* sets of nodes with $O\neq\emptyset$, then we generically[^5] denote by ${{\underline{{V}}}_{O}(\cdot\vert{X_{I}})}$ a *conditional lower prevision*, defined on the set of gambles ${\mathcal{L}({\mathcal{X}_{I\cup O}})}$.[^6] For every gamble $f$ on ${\mathcal{X}_{I\cup O}}$ and every ${x_{I}}\in{\mathcal{X}_{I}}$, ${{\underline{{V}}}_{O}(f\vert{x_{I}})}$ is the lower prevision (or lower expectation, or a subject’s supremum buying price) for/of the gamble $f$, conditional on the event that ${X_{I}}={x_{I}}$. We interpret ${{\underline{{V}}}_{O}(f\vert{X_{I}})}$ as a real-valued map (gamble) on ${\mathcal{X}_{I}}$ that assumes the value ${{\underline{{V}}}_{O}(f\vert{x_{I}})}$ in the element ${x_{I}}$ of ${\mathcal{X}_{I}}$. The conjugate *conditional upper prevision* ${{\overline{{V}}}_{O}(\cdot\vert{X_{I}})}$ is defined on ${\mathcal{L}({\mathcal{X}_{I\cup O}})}$ by ${{\overline{{V}}}_{O}(f\vert{X_{I}})}\coloneqq-{{\underline{{V}}}_{O}(-f\vert{X_{I}})}$ for all gambles $f$ on ${\mathcal{X}_{I\cup O}}$.
We will always implicitly assume that all conditional models ${{\underline{{V}}}_{O}(\cdot\vert{X_{I}})}$ we use are *separately coherent*, meaning that:
1. \[item:separate:coherence:apg\] ${{\underline{{V}}}_{O}(f\vert{x_{I}})}\geq\min_{{z_{O}}\in{\mathcal{X}_{O}}}f({x_{I}},{z_{O}})$ for all $f\in{\mathcal{L}({\mathcal{X}_{I\cup O}})}$ and all ${x_{I}}\in{\mathcal{X}_{I}}$ \[accepting partial gains\];
2. \[item:separate:coherence:superadd\] ${{\underline{{V}}}_{O}(f_1+f_2\vert{x_{I}})}\geq {{\underline{{V}}}_{O}(f_1\vert{x_{I}})}+{{\underline{{V}}}_{O}(f_2\vert{x_{I}})}$ for all $f_1,f_2\in{\mathcal{L}({\mathcal{X}_{I\cup O}})}$ and all ${x_{I}}\in{\mathcal{X}_{I}}$ \[super-additivity\];
3. \[item:separate:coherence:nnhom\] ${{\underline{{V}}}_{O}(\lambda f\vert{x_{I}})}=\lambda{{\underline{{V}}}_{O}(f\vert{x_{I}})}$ for all $f\in{\mathcal{L}({\mathcal{X}_{I\cup O}})}$, all non-negative real $\lambda$ and all ${x_{I}}\in{\mathcal{X}_{I}}$ \[non-negative homogeneity\].
By combining SC\[item:separate:coherence:apg\]–SC\[item:separate:coherence:nnhom\], it follows that for all $f\in{\mathcal{L}({\mathcal{X}_{I\cup O}})}$, ${x_{I}}\in{\mathcal{X}_{I}}$ and ${z_{O}}\in{\mathcal{X}_{O}}$: $$\min_{{z_{O}}\in{\mathcal{X}_{O}}}f({x_{I}},{z_{O}})
\leq{{\underline{{V}}}_{O}(f\vert{x_{I}})}
\leq{{\overline{{V}}}_{O}(f\vert{x_{I}})}
\leq\max_{{z_{O}}\in{\mathcal{X}_{O}}}f({x_{I}},{z_{O}}).$$ If we let $f$ be the indicator ${\mathbb{I}_{{{\{{z_{I}}\}}}}}$ of the set ${{\{{z_{I}}\}}}$ in these inequalities, they reduce to the following, intuitively obvious, property:[^7]
1. \[item:separate:coherence\] ${{\underline{{V}}}_{O}({{{\{{z_{I}}\}}}\times{\mathcal{X}_{O}}}\vert{x_{I}})}={{\overline{{V}}}_{O}({{{\{{z_{I}}\}}}\times{\mathcal{X}_{O}}}\vert{x_{I}})}={{\mathbb{I}_{\{{x_{I}}\}}}}({z_{I}})$ for all ${x_{I}},{z_{I}}\in{\mathcal{X}_{I}}$.
From SC\[item:separate:coherence:apg\], SC\[item:separate:coherence:superadd\] and SC\[item:separate:coherence\] we can also derive that, with obvious notations: $$\label{eq:separate:coherence}
{{\underline{{V}}}_{O}(f\vert{x_{I}})}
={{\underline{{V}}}_{O}({{\mathbb{I}_{\{{x_{I}}\}}}}f\vert{x_{I}})}
={{\underline{{V}}}_{O}(f({x_{I}},\cdot)\vert{x_{I}})}
\text{ for all gambles $f$ on ${\mathcal{X}_{I\cup O}}$ and ${x_{I}}\in{\mathcal{X}_{I}}$},$$ where $f({x_{I}},\cdot)$ is a partial map defined on ${\mathcal{X}_{O}}$. This implies that ${{\underline{{V}}}_{O}(\cdot\vert{X_{I}})}$ is completely determined by its behaviour on (cylindrical extensions of maps in) ${\mathcal{L}({\mathcal{X}_{O}})}$.
Hereafter, we will frequently introduce conditional lower previsions of the type ${{\underline{{V}}}_{O}(\cdot\vert{X_{I}})}$ as if they are defined on ${\mathcal{L}({\mathcal{X}_{O}})}$, simply because that is a very natural thing to do: such a conditional lower prevision is usually interpreted as representing beliefs about the variable ${X_{O}}$, conditional on values of the variable ${X_{I}}$. But the reader should keep in mind that, by the separate coherence property , ${{\underline{{V}}}_{O}(\cdot\vert{X_{I}})}$ can (and should) always be uniquely extended to the larger domain ${\mathcal{L}({\mathcal{X}_{I\cup O}})}$.
As soon as we consider a number of such conditional lower previsions ${{\underline{{V}}}_{O_k}(\cdot\vert{X_{I_k}})}$, $k=1,\dots,n$, they should satisfy more stringent consistency criteria than that each of them should be separately coherent: they should also be consistent with one another in the sense of Walley’s *(joint) coherence* [@walley1991 Section 7.1.4(b)]. For more details about this much more involved type of coherence, we refer also to [@miranda2008a; @miranda2009a].
Finally, let us introduce one of the most important concepts for this paper, that of epistemic irrelevance. We describe the case of conditional irrelevance, as the unconditional version of epistemic irrelevance can easily be recovered as a special case.[^8]
Consider three disjoint subsets $C$, $I$, and $O$ of $N$, where both $I$ and $O$ are non-empty. When a subject judges ${X_{I}}$ to be *epistemically irrelevant to ${X_{O}}$ conditional on ${X_{C}}$*, he assumes that if he knows the value of ${X_{C}}$, then learning in addition which value ${X_{I}}$ assumes in ${\mathcal{X}_{I}}$ will not affect his beliefs about ${X_{O}}$. More formally, assume that a subject has a separately coherent conditional lower prevision ${{\underline{{V}}}_{O}(\cdot\vert{X_{C}})}$ on ${\mathcal{L}({\mathcal{X}_{O}})}$. If he assesses ${X_{I}}$ to be epistemically irrelevant to ${X_{O}}$ conditional on ${X_{C}}$, this implies that he can infer from his model ${{\underline{{V}}}_{O}(\cdot\vert{X_{C}})}$ a conditional model ${{\underline{{V}}}_{O}(\cdot\vert{X_{C\cup I}})}$ on ${\mathcal{L}({\mathcal{X}_{O}})}$ given by $${{\underline{{V}}}_{O}(f\vert{x_{C\cup I}})}\coloneqq{{\underline{{V}}}_{O}(f\vert{x_{C}})}
\text{ for all $f\in{\mathcal{L}({\mathcal{X}_{O}})}$ and all ${x_{C\cup I}}\in{\mathcal{X}_{C\cup I}}$.}$$
Local uncertainty models.
-------------------------
We now add a *local uncertainty model* to each of the nodes $s$. If $s$ is not the root node, i.e. has a mother ${m(s)}$, then this local model is a (separately coherent) conditional lower prevision ${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ on ${\mathcal{L}({\mathcal{X}_{s}})}$: for each possible value ${z_{{m(s)}}}$ of the variable ${X_{{m(s)}}}$ associated with its mother ${m(s)}$, we have a coherent lower prevision ${{\underline{{Q}}}_{s}({\cdot}\vert{z_{{m(s)}}})}$ for the value of ${X_{s}}$, conditional on ${X_{{m(s)}}}={z_{{m(s)}}}$. In the root, we have an unconditional local uncertainty model ${{\underline{{Q}}}_{{\square}}}$ for the value of ${X_{{\square}}}$. ${{\underline{{Q}}}_{{\square}}}$ is a (separately) coherent lower prevision on ${\mathcal{L}({\mathcal{X}_{{\square}}})}$. We use the common generic notation ${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ for all these local models.[^9]
Global uncertainty models. {#sec:criteria}
--------------------------
We intend to show in Section \[sec:joint\] how all these local models ${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ can be combined into *global uncertainty models*. We generically denote such global models using the letter $P$. More specifically, we want to end up with an unconditional joint lower prevision ${\underline{{P}}}\coloneqq{\underline{{P}}}_{{{\downarrow}{\square}}}={\underline{{P}}}_{{T}}$ on ${\mathcal{L}({\mathcal{X}_{{T}}})}$ for all variables in the tree, as well as conditional lower previsions ${{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}$ on ${\mathcal{L}({\mathcal{X}_{{{\downarrow}S}}})}$ for all non-terminal nodes $s$ and all non-empty $S\subseteq{C_{}(s)}$.
In this list, the only item that needs more explanation concerns the Markov-type conditions that the tree structure encodes. This is what we turn to now.
The interpretation of the graphical model. {#sec:graphical:interpretation}
------------------------------------------
In classical Bayesian nets, the graphical structure is taken to represent the following assessments: for any node $s$, conditional on its parent variables, its non-parent non-descendant variables are epistemically irrelevant to it (and therefore also independent).
In the present context, we assume that the tree structure embodies the following conditional irrelevance assessment, which turns out to be equivalent with the conditional independence assessment above in the special case of a Bayesian tree.
1. Consider any node $s$ in the tree, any subset $S$ of its set of children ${C_{}(s)}$, and the set ${\overline{S}}\coloneqq\bigcap_{c\in S}{\overline{c}}$ of their common non-parent non-descendants. Then *conditional on the mother variable ${X_{s}}$, the non-parent non-descendant variables ${X_{{\overline{S}}}}$ are assumed to be epistemically irrelevant to the variables ${X_{{{\downarrow}S}}}$ associated with the children in $S$ and their descendants.*
This interpretation turns the tree into a *credal tree under epistemic irrelevance*, and we also introduce the term *imprecise Markov tree* (IMT) for it. For the global models we are considering here, CI has the following consequences. It implies that for all $s\in{{T}^\lozenge}$, all non-empty $S\subseteq{C_{}(s)}$ and all $I\subseteq{\overline{S}}$, we can infer from ${{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}$ a model ${{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{{\{s\}}\cup{I}}})}$, where for all ${z_{{\{s\}}\cup I}}\in{\mathcal{X}_{{\{s\}}\cup I}}$, with obvious notations:[^10] $$\label{eq:irrelevance}
{{\underline{{P}}}_{{{\downarrow}S}}({f}\vert{z_{{\{s\}}\cup{I}}})}
\coloneqq{{\underline{{P}}}_{{{\downarrow}S}}({f(\cdot,{z_{I}})}\vert{z_{s}})}
\text{ for all gambles $f$ in ${\mathcal{L}({\mathcal{X}_{{{\downarrow}S}\cup I}})}$},$$ where $f(\cdot,{z_{I}})$ denotes a partial map of $f$, defined on ${\mathcal{X}_{{{\downarrow}S}}}$.
We discuss some of the separation properties that accompany this interpretation in Section \[sec:separation\]. For now, we focus on two immediate consequences that will help us go from local to global models in Section \[sec:joint\].
First, consider some node $s$. Then CI tells us that for any two children $c_1,c_2\in{C_{}(s)}$ of $s$, the variable ${X_{{{\downarrow}c_1}}}$ is epistemically irrelevant to the variable ${X_{{{\downarrow}c_2}}}$, conditional on ${X_{s}}$.
+=\[->,semithick\] \[grow=down,level distance=30,sibling distance=25\] child [node [${X_{{{\downarrow}c_1}}}$]{}]{} child [node [$\dots$]{}]{} child [node [${X_{{{\downarrow}c_2}}}$]{}]{};
It even tells us that for any two disjoint non-empty sets $S_1\subseteq{C_{}(s)}$ and $S_2\subseteq{C_{}(s)}$ of children of $s$, the variable ${X_{{{\downarrow}S_1}}}$ is epistemically irrelevant to ${X_{{{\downarrow}S_2}}}$, conditional on ${X_{s}}$. We conclude that, conditional on a node, all its children $c$ (and the variables associated with their sub-trees ${{\downarrow}c}$) are *epistemically independent* [@walley1991 Chapter 9], in the specific sense to be discussed in the next section.
Next, consider some non-terminal node $s$ different from ${\square}$, and its mother variable ${X_{{m(s)}}}$. We infer from CI that this mother variable ${X_{{m(s)}}}$ is epistemically irrelevant to the variable ${X_{{{\downarrow}{C_{}(s)}}}}$ conditional on ${X_{s}}$:
+=\[->,semithick\] at (0,0) [${X_{{m(s)}}}$]{} \[grow=down,level distance=30,sibling distance=25\] child [node [${X_{s}}$]{} child [node [${X_{{{\downarrow}c_1}}}$]{}]{} child [node [$\dots$]{}]{} child [node [${X_{{{\downarrow}c_n}}}$]{}]{}]{}; at (3,-1) [or equivalently, ]{}; at (6,0) [${X_{{m(s)}}}$]{} \[grow=down,level distance=30\] child [node [${X_{s}}$]{} child [node [${X_{{{\downarrow}{C_{}(s)}}}}$]{}]{}]{};
Independent natural extension {#sec:independent-natural-extension}
=============================
Let us make a small digression on epistemic independence, which will help us in our discussion further on. The material in this section is based on work that some of us have published elsewhere [@cooman2009b], and we refer to that paper for more details and proofs for the results mentioned in this section.
Independent products. {#sec:indnatex}
---------------------
Suppose we have a number of (separately) coherent marginal lower previsions ${\underline{P}_{n}}$ on ${\mathcal{L}({\mathcal{X}_{n}})}$ representing beliefs about the values that each of a finite number of (logically independent) variables ${X_{n}}$ assume in the respective non-empty finite sets ${\mathcal{X}_{n}}$, $n\in N$, where $N$ is some non-empty finite set.
We want to construct a joint lower prevision ${\underline{P}_{N}}$ on ${\mathcal{L}({\mathcal{X}_{N}})}$, where ${\mathcal{X}_{N}}=\times_{n\in N}{\mathcal{X}_{n}}$, that coincides with the marginals ${\underline{P}_{n}}$ on their respective domains ${\mathcal{L}({\mathcal{X}_{n}})}$, and such that this ${\underline{P}_{N}}$ reflects the following structural assessments: for any disjoint proper subsets $O$ and $I$ of $N$, the variables ${X_{I}}$ are epistemically irrelevant to the variables ${X_{O}}$. In other words, learning the value of any number of these variables would not affect beliefs about the remaining variables. We then call the variables ${X_{n}}$, $n\in N$, *epistemically independent*.
Generally speaking, such irrelevance assessments are useful because they allow us to turn unconditional into conditional lower previsions. In particular, for any disjoint proper subsets $O$ and $I$ of $N$, we can use the epistemic irrelevance assessment of ${X_{I}}$ to ${X_{O}}$ to infer from the joint lower prevision ${\underline{P}_{N}}$ a conditional lower prevision ${\underline{P}_{O}({\cdot}\vert{X_{I}})}$ on ${\mathcal{L}({\mathcal{X}_{{O\cup{I}}}})}$ given by: $${\underline{P}_{O}({h}\vert{z_{I}})}
\coloneqq{\underline{P}_{N}}(h(\cdot,{z_{I}}))
\text{ for all gambles $h$ on ${\mathcal{X}_{{O\cup{I}}}}$ and all ${z_{I}}\in{\mathcal{X}_{I}}$}.$$ So we can use the symmetrised assessment of epistemic independence of the variables ${X_{n}}$, $n\in N$ to infer from ${\underline{P}_{N}}$ the following family of conditional lower previsions: $${\mathcal{I}({\underline{P}_{N}})}
\coloneqq{\{{\underline{P}_{O}({\cdot}\vert{X_{I}})}\colon\text{$O$ and $I$ disjoint proper subsets of $N$}\}}.$$ This idea leads to the definition of an independent product, which generalises the existing notion for (precise) probability models.
\[def:independent:product\] A (separately) coherent lower prevision ${\underline{P}_{N}}$ on ${\mathcal{L}({\mathcal{X}_{N}})}$ that coincides with the marginal lower previsions ${\underline{P}_{n}}$ on their domains ${\mathcal{L}({\mathcal{X}_{n}})}$, $n\in N$ and that is coherent with the family of conditional lower previsions ${\mathcal{I}({\underline{P}_{N}})}$ is called an *independent product*[^11] of these marginals ${\underline{P}_{n}}$.
It turns out that there always is a point-wise smallest independent product:
\[prop:independent-factorising\] Any collection of (separately) coherent lower previsions ${\underline{P}_{n}}$ on ${\mathcal{L}({\mathcal{X}_{n}})}$, $n\in N$, has a point-wise smallest independent product. We call it their *independent natural extension* and denote it by $\otimes_{n\in N}{\underline{P}_{n}}$. Moreover, $\otimes_{n\in N}{\underline{P}_{n}}$ is a strongly factorising coherent lower prevision on ${\mathcal{L}({\mathcal{X}_{N}})}$.
Strong factorisation is strongly linked with independent products, and will play a crucial part in our development of an algorithm for updating an imprecise Markov tree in Section \[sec:algorithm\]. It is defined as follows:
We call a (separately) coherent lower prevision ${\underline{P}_{N}}$ on ${\mathcal{L}({\mathcal{X}_{N}})}$ *strongly factorising* if for all disjoint proper subsets $O$ and $I$ of $N$, all $g\in{\mathcal{L}({\mathcal{X}_{O}})}$ and all non-negative $f\in{\mathcal{L}({\mathcal{X}_{I}})}$, ${\underline{P}_{N}}(fg)={\underline{P}_{N}}(f{\underline{P}_{N}}(g))$.
As another important example, the so-called *strong product* $\times_{n\in N}{\underline{P}_{n}}$ [@cozman2000] of marginal lower previsions ${\underline{P}_{n}}$ is strongly factorising.[^12]
As a consequence of the separate coherence of the joint lower prevision ${\underline{P}_{N}}$, the right-hand side of the equality in this definition can be rewritten as: $${\underline{P}_{N}}(f{\underline{P}_{N}}(g))
=
\begin{cases}
{\underline{P}_{N}}(f){\underline{P}_{N}}(g)
&\text{ if ${\underline{P}_{N}}(g)\geq0$}\\
{\overline{P}_{N}}(f){\underline{P}_{N}}(g)
&\text{ if ${\underline{P}_{N}}(g)\leq0$},
\end{cases}$$ which explains where the term ‘factorising’ comes from. In particular, for any (separately) coherent strongly factorising joint lower prevision ${\underline{P}_{N}}$, we see that for any partition $N_1$, …, $N_m$ of $N$: $$\label{eq:events-factorising}
{\underline{P}_{N}}(\times_{k=1}^mA_k)=\prod_{k=1}^m{\underline{P}_{N}}(A_k)
\text{ and }
{\overline{P}_{N}}(\times_{k=1}^mA_k)=\prod_{k=1}^m{\overline{P}_{N}}(A_k),$$ where $A_k\subseteq{\mathcal{X}_{I_k}}$ for $k=1,\dots,m$.
The independent natural extension has very interesting and non-trivial *marginalisation and associativity properties*. Consider any non-empty subset $R$ of $N$, then the independent natural extension $\otimes_{r\in R}{\underline{P}_{r}}$ of the marginals ${\underline{P}_{r}}$, $r\in R$ coincides with the restriction of $\otimes_{n\in N}{\underline{P}_{n}}$ to the set of gambles ${\mathcal{L}({\mathcal{X}_{R}})}$: $$\label{eq:marginalisation}
\left(\otimes_{r\in R}{\underline{P}_{r}}\right)(g)
=\left(\otimes_{n\in N}{\underline{P}_{n}}\right)(g)
\text{ for all gambles $g$ on ${\mathcal{X}_{R}}$}.$$ Moreover, for any partition $N_1$ and $N_2$ of $N$, we have that $$\label{eq:associativity}
\otimes_{n\in N}{\underline{P}_{n}}
=\left(\otimes_{n_1\in N_1}{\underline{P}_{n_1}}\right)\otimes\left(\otimes_{n_2\in N_2}{\underline{P}_{n_2}}\right),$$ so $\otimes_{n\in N}{\underline{P}_{n}}$ is the independent natural extension of its ${\mathcal{X}_{N_1}}$-marginal $\otimes_{n_1\in N_1}{\underline{P}_{n_1}}$ and its ${\mathcal{X}_{N_2}}$-marginal $\otimes_{n_2\in N_2}{\underline{P}_{n_2}}$.
Regular extension
-----------------
As a next step, suppose we want to condition a separately coherent and strongly factorising joint ${\underline{P}_{N}}$ on observations of the type ${X_{I}}={z_{I}}$, where $I$ is some proper subset of $N$. In other words, we want to find conditional lower previsions ${\underline{P}_{O}({\cdot}\vert{X_{I}})}$ on ${\mathcal{L}({\mathcal{X}_{{I\cup{O}}}})}$ that are (jointly) coherent with the joint lower prevision ${\underline{P}_{N}}$. To this end, we calculate the so-called *regular extension* as follows. Consider ${z_{I}}$ in ${\mathcal{X}_{I}}$. When ${\overline{P}_{N}}({{\{{z_{I}}\}}})>0$, $${\underline{R}({h}\vert{z_{I}})}
\coloneqq\max{\{\mu\in{\mathbb{R}}\colon{\underline{P}_{N}}({{\mathbb{I}_{\{{z_{I}}\}}}}[h-\mu])\geq0\}},$$ where $O$ is any non-empty subset of $N\setminus I$ and $h$ is any gamble on ${\mathcal{X}_{{I\cup{O}}}}$. When ${\overline{P}_{N}}({{\{{z_{I}}\}}})=0$, ${\underline{R}({\cdot}\vert{x_{I}})}$ is *vacuous*, meaning that ${\underline{R}({h}\vert{z_{I}})}=\min_{{x_{O}}\in{\mathcal{X}_{O}}}h({z_{I}},{x_{O}})$ for all gambles $h$ on ${\mathcal{X}_{{I\cup{O}}}}$.
Generally speaking, coherence only determines ${\underline{P}_{O}({\cdot}\vert{z_{I}})}$ uniquely if ${\underline{P}_{N}}({{\{{z_{I}}\}}})>0$, and in that case regular extension yields this uniquely coherent conditional lower prevision: ${\underline{P}_{O}({\cdot}\vert{z_{I}})}={\underline{R}({\cdot}\vert{z_{I}})}$. When ${\underline{P}_{N}}({{\{{z_{I}}\}}})=0$, regular extension is still coherent, and it even still characterises the coherent ${\underline{P}_{O}({\cdot}\vert{z_{I}})}$, because these all lie between the vacuous lower prevision and ${\underline{R}({\cdot}\vert{z_{I}})}$. For more details about this regular extension, we refer to [@walley1991 Appendix J] and [@miranda2009a Section 4].
If the joint ${\underline{P}_{N}}$ is strongly factorising, we get: $$\begin{aligned}
{\underline{P}_{N}}({{\mathbb{I}_{\{{x_{I}}\}}}}[h-\mu])
&={\underline{P}_{N}}({{\mathbb{I}_{\{{x_{I}}\}}}}{\underline{P}_{N}}(h({x_{I}},\cdot)-\mu))\\
&=
\begin{cases}
{\underline{P}_{N}}({{\{{x_{I}}\}}})[{\underline{P}_{N}}(h({x_{I}},\cdot))-\mu]
&\text{ if ${\underline{P}_{N}}(h({x_{I}},\cdot))\geq\mu$}\\
{\overline{P}_{N}}({{\{{x_{I}}\}}})[{\underline{P}_{N}}(h({x_{I}},\cdot))-\mu]
&\text{ if ${\underline{P}_{N}}(h({x_{I}},\cdot))\leq\mu$},
\end{cases}\end{aligned}$$ so we conclude that, quite interestingly, $$\label{eq:regular-extension-factorising}
{\underline{R}({h}\vert{x_{I}})}={\underline{P}_{N}}(h({x_{I}},\cdot))
\text{ as soon as ${\overline{P}_{N}}({{\{{x_{I}}\}}})>0$}.$$ In other words, the conditional lower previsions found by regular extension of a strongly factorising joint satisfy all epistemic irrelevance conditions present in an assessment of epistemic independence. We shall have occasion to use this idea several times in the course of this paper, especially in the proofs.
Conditionally independent products. {#sec:condindnatex}
-----------------------------------
To end this section, we generalise the notion of an independent product to that of a conditionally independent product. In this case we have a number of ‘marginal’ conditional lower previsions ${\underline{P}_{n}(\cdot\vert{Y})}$ on ${\mathcal{L}({\mathcal{X}_{n}})}$ representing beliefs (conditional on a variable ${Y}$ in a finite set ${\mathcal{Y}}$) about the values that each of a finite number of (logically independent) variables ${X_{n}}$ assume in the respective non-empty finite sets ${\mathcal{X}_{n}}$, $n\in N$.
We want to construct a conditional lower prevision ${\underline{P}_{N}(\cdot\vert{Y})}$ on ${\mathcal{L}({\mathcal{X}_{N}})}$, where ${\mathcal{X}_{N}}=\times_{n\in N}{\mathcal{X}_{n}}$, that coincides with the marginal conditional lower previsions ${\underline{P}_{n}(\cdot\vert{Y})}$ on their respective domains ${\mathcal{L}({\mathcal{X}_{n}})}$, and such that this ${\underline{P}_{N}(\cdot\vert{Y})}$ reflects the following structural assessments: for any disjoint proper subsets $O$ and $I$ of $N$, the variables ${X_{I}}$ are epistemically irrelevant to the variables ${X_{O}}$, *conditional on ${Y}$*. In other words, if the value of ${Y}$ was known, then learning the value of any number of these variables would not affect beliefs about the remaining variables. We then call the variables ${X_{n}}$, $n\in N$ *epistemically independent, conditional on ${Y}$*.
Generally speaking, such conditional irrelevance assessments are useful because they allow us to turn lower previsions conditional on ${Y}$ alone into other, more involved conditional lower previsions. In particular, for any disjoint proper subsets $O$ and $I$ of $N$, we can use the epistemic irrelevance assessment of ${X_{I}}$ to ${X_{O}}$ conditional on ${Y}$ to infer from the joint lower prevision ${\underline{P}_{N}(\cdot\vert{Y})}$ a conditional lower prevision ${\underline{P}_{O}({\cdot}\vert{X_{I}},{Y})}$ on ${\mathcal{L}({\mathcal{X}_{{O\cup{I}}}})}$ \[or equivalently on ${\mathcal{L}({\mathcal{X}_{{O\cup{I}}}\times{\mathcal{Y}}})}$\] given by: $${\underline{P}_{O}({h}\vert{z_{I}},{y})}
\coloneqq{\underline{P}_{N}(h(\cdot,{z_{I}})\vert{y})}
\text{ for all gambles $h$ on ${\mathcal{X}_{{O\cup{I}}}}$ and all ${z_{I}}\in{\mathcal{X}_{I}}$}.$$ So we can use the symmetrised assessment of epistemic independence of the variables ${X_{n}}$, $n\in N$ conditional on ${Y}$ to infer from the ${\underline{P}_{N}(\cdot\vert{Y})}$ the following family of conditional lower previsions: $${\mathcal{I}({\underline{P}_{N}(\cdot\vert{Y})})}
\coloneqq{\{{\underline{P}_{O}({\cdot}\vert{X_{I}},{Y})}\colon\text{$O$ and $I$ disjoint proper subsets of $N$}\}}.$$ This idea leads to the definition of a conditionally independent product.
\[def:conditionally:independent:product\] A (separately) coherent conditional lower prevision ${\underline{P}_{N}(\cdot\vert{Y})}$ on ${\mathcal{L}({\mathcal{X}_{N}})}$ that coincides with the ‘marginal’ conditional lower previsions ${\underline{P}_{n}(\cdot\vert{Y})}$ on their domains ${\mathcal{L}({\mathcal{X}_{n}})}$, $n\in N$ and that is coherent with the family of conditional lower previsions ${\mathcal{I}({\underline{P}_{N}(\cdot\vert{Y})})}$ is called a *conditionally independent product* of these marginals ${\underline{P}_{n}(\cdot\vert{Y})}$.
It turns out that there always is a point-wise smallest conditionally independent product:
\[prop:conditionally:independent-factorising\] Any collection of (separately) coherent conditional lower previsions ${\underline{P}_{n}(\cdot\vert{Y})}$ on ${\mathcal{L}({\mathcal{X}_{n}})}$, $n\in N$, has a point-wise smallest conditionally independent product. We call it their *conditionally independent natural extension* and denote it by $\otimes_{n\in N}{\underline{P}_{n}(\cdot\vert{Y})}$.
The notation we use for the conditionally independent natural extension is appropriately suggestive: for each ${y}$ in ${\mathcal{Y}}$, $\otimes_{n\in N}{\underline{P}_{n}(\cdot\vert{y})}$ is indeed the independent natural extension of the marginal lower previsions ${\underline{P}_{n}(\cdot\vert{y})}$. This implies that each $\otimes_{n\in N}{\underline{P}_{n}(\cdot\vert{y})}$ is a strongly factorising coherent lower prevision on ${\mathcal{L}({\mathcal{X}_{N}})}$.
We are now ready to go back to our discussion of imprecise Markov trees.
Constructing the most conservative joint {#sec:joint}
========================================
Let us show how to construct specific global models for the variables in the tree, and argue that these are the most conservative coherent models that extend the local models and express all conditional irrelevancies , encoded in the imprecise Markov tree. In Section \[sec:algorithm\], we will use these global models to construct and justify an algorithm for updating the imprecise Markov tree.
The crucial step lies in the recognition that any tree can be constructed recursively from the leaves up to the root, by using basic building blocks of the following type:
+=\[->,semithick\] =\[->,thick,dotted,draw=blue!50\] (xm) [${X_{{m(s)}}}$]{} \[grow=down,level distance=30,sibling distance=25\] child [node (xs) [${X_{s}}$]{} child [node (xc1) [${X_{{{\downarrow}c_1}}}$]{}]{} child [node (xc2) [${X_{{{\downarrow}c_2}}}$]{}]{} child [node (dots) [$\dots$]{}]{} child [node (xcn) [${X_{{{\downarrow}c_n}}}$]{}]{}]{}; (xsmodel) [${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$]{}; (xckmodel) [${{\underline{{P}}}_{{{\downarrow}c_k}}({\cdot}\vert{X_{s}})}$]{}; (xs) – (xsmodel); (xcn) – (xckmodel);
The global models are then also constructed recursively, following the same pattern. In what follows, we first derive the recursion equations for these global models in a heuristic manner. The real justification for using the global models thus derived is then given in Theorem \[theo:global-models\].
Consider a node $s$ and suppose that, in each of its children $c\in{C_{}(s)}$, we already have a global conditional lower prevision ${{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}$ on ${\mathcal{L}({\mathcal{X}_{{{\downarrow}c}}})}$ \[or equivalently, on ${\mathcal{L}({\mathcal{X}_{{\{s\}}\cup{{\downarrow}c}}})}$\].
Given that, conditional on ${X_{s}}$, the variables ${X_{{{\downarrow}c}}}$, $c\in{C_{}(s)}$ are epistemically independent \[see Section \[sec:graphical:interpretation\], condition CI\], the discussion in Section \[sec:independent-natural-extension\] leads us to combine the ‘marginals’ ${{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}$, $c\in{C_{}(s)}$ into their point-wise smallest conditionally independent product (conditionally independent natural extension) $\otimes_{c\in{C_{}(s)}}{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}$, which is a conditional lower prevision ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$ on ${\mathcal{L}({\mathcal{X}_{{{\downarrow}{C_{}(s)}}}})}$ \[or equivalently, on ${\mathcal{L}({\mathcal{X}_{{{\downarrow}s}}})}$\]:
+=\[->,semithick\] =\[->,thick,dotted,draw=blue!50\] (xm) [${X_{{m(s)}}}$]{} \[grow=down,level distance=30,sibling distance=25\] child [node (xs) [${X_{s}}$]{} child [node (xc) [${X_{{{\downarrow}{C_{}(s)}}}}$]{}]{}]{}; (xsmodel) [${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$]{}; (xcmodel) [$\otimes_{c\in{C_{}(s)}}{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}\eqqcolon{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$]{}; (xs) – (xsmodel); (xc) – (xcmodel);
Next, we need to combine the conditional models ${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ and ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$ into a global conditional model about ${X_{{{\downarrow}s}}}$. Given that, conditional on ${X_{s}}$, the variable ${X_{{m(s)}}}$ is epistemically irrelevant to the variable ${X_{{{\downarrow}{C_{}(s)}}}}$ \[see Section \[sec:graphical:interpretation\], condition CI\], we expect ${\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}(\cdot\vert{X_{{\{{m(s)},s\}}}})$ and ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$ to coincide \[this is a special instance of Eq. \]. The most conservative (point-wise smallest) coherent way of combining the conditional lower previsions ${\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}(\cdot\vert{X_{{\{{m(s)},s\}}}})$ and ${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ consists in taking their *marginal extension*[^13] ${{\underline{{Q}}}_{s}({{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}(\cdot\vert{X_{{\{{m(s)},s\}}}})}}\vert{X_{{m(s)}}})}={{\underline{{Q}}}_{s}({{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}}\vert{X_{{m(s)}}})}$; see [@miranda2006b; @walley1991] for more details. Graphically:
+=\[->,semithick\] =\[->,thick,dotted,draw=blue!50\] (xm) [${X_{{m(s)}}}$]{} \[grow=down,level distance=30,sibling distance=25\] child [node (xs) [${X_{{{\downarrow}s}}}$]{}]{}; (xsmodel) [${{\underline{{Q}}}_{s}({{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}}\vert{X_{{m(s)}}})}\eqqcolon{{\underline{{P}}}_{{{\downarrow}s}}({\cdot}\vert{X_{{m(s)}}})}$]{}; (xs) – (xsmodel);
Summarising, and also accounting for the case $s={\square}$, we can construct a global conditional lower prevision ${{\underline{{P}}}_{{{\downarrow}s}}({\cdot}\vert{X_{{m(s)}}})}$ on ${\mathcal{L}({\mathcal{X}_{{{\downarrow}s}}})}$ by backwards recursion: $$\begin{aligned}
{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}
&\coloneqq\otimes_{c\in{C_{}(s)}}{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}
\label{eq:backwards-nine}\\
{{\underline{{P}}}_{{{\downarrow}s}}({\cdot}\vert{X_{{m(s)}}})}
&\coloneqq{{\underline{{Q}}}_{s}({{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}}\vert{X_{{m(s)}}})}
={{\underline{{Q}}}_{s}({\otimes_{c\in{C_{}(s)}}{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}}\vert{X_{{m(s)}}})},
\label{eq:backwards-global}\end{aligned}$$ for all $s\in{{T}^\lozenge}$. If we start with the ‘boundary conditions’ $$\label{eq:boundary-condition}
{{\underline{{P}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}\coloneqq{{\underline{{Q}}}_{t}({\cdot}\vert{X_{{m(t)}}})}
\text{ for all leaves $t$},$$ then the recursion relations and eventually lead to the global joint model ${{\underline{{P}}}_{{\square}}}={{\underline{{P}}}_{{{\downarrow}{\square}}}({\cdot}\vert{X_{{m({\square})}}})}$, and to the global conditional models ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$ for all non-terminal nodes $s$. For any subset $S\subseteq{C_{}(s)}$, the global conditional model ${{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}$ can then be defined simply as the restriction of the model ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$ on ${\mathcal{L}({\mathcal{X}_{{{\downarrow}{C_{}(s)}}}})}$ to the set ${\mathcal{L}({\mathcal{X}_{{{\downarrow}S}}})}$: $$\label{eq:backwards-restrict}
{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{X_{s}})}\coloneqq {{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({g}\vert{X_{s}})}
\text{ for all gambles $g$ on ${\mathcal{X}_{{{\downarrow}S}}}$}.$$ It follows from the discussion in Section \[sec:independent-natural-extension\] that, alternatively \[see Eq. \], $$\label{eq:backwards-nine-restrict}
{{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}
=\otimes_{c\in S}{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{s}})}.$$ For easy reference, we will in what follows refer to this collection of global models as the *family of global models ${\mathcal{T}(\underline{P})}$,* so $${\mathcal{T}(\underline{P})}
\coloneqq\{{{\underline{{P}}}_{}}\}\cup
{\{{{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}\colons\in{{T}^\lozenge}\text{ and non-empty }S\subseteq{C_{}(s)}\}}.$$
We end this section by discussing a number of interesting properties for the family of global models ${\mathcal{T}(\underline{P})}$ we can derive in this way. Let us call any real functional $\Phi$ on ${\mathcal{L}({\mathcal{X}_{}})}$ *strictly positive* if $\Phi({{\mathbb{I}_{\{{x_{}}\}}}})>0$ for all ${x_{}}\in{\mathcal{X}_{}}$.
\[prop:global:positivity\] If all the local models ${{\overline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$, $s\in{T}$ are strictly positive, then so are all the global models in ${\mathcal{T}(\underline{P})}$.
\[prop:global:positivity:too\] Consider any non-empty subset $E$ of ${T}$ and any ${x_{E}}\in{\mathcal{X}_{E}}$. If ${\overline{{P}}}({{\{{x_{E}}\}}})>0$ then also ${{\overline{{P}}}_{{{\downarrow}c}}({{{\{{x_{E\cap{{\downarrow}c}}}\}}}}\vert{x_{e}})}>0$ for all $e\in E$ and all $c\in{C_{}(e)}$.[^14]
Before we formulate the most important result in this section (and arguably, in this paper), we provide some motivation. Suppose we have some family of global models $${\mathcal{T}(\underline{V})}
\coloneqq\{{{\underline{{V}}}_{}}\}\cup
{\{{{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}\colons\in{{T}^\lozenge}\text{ and non-empty }S\subseteq{C_{}(s)}\}}$$ associated with the tree. How do we express that such a family is compatible with the assessments encoded in the tree?
First of all, we require that our global models should extend the local models:
1. \[item:global:local\] For each $s\in{T}$, ${{\underline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ is the restriction of ${{\underline{{V}}}_{{{\downarrow}s}}({\cdot}\vert{X_{{m(s)}}})}$ to ${\mathcal{L}({\mathcal{X}_{s}})}$.
The second requirement is that our models should satisfy the rationality requirement of coherence:
1. \[item:global:coherence\] The (conditional) lower previsions in ${\mathcal{T}(\underline{V})}$ are jointly coherent.
The third requirement requires more explanation: the global models should reflect all epistemic irrelevancies encoded in the graphical structure of the tree. Naively, we would want condition to be satisfied. The problem is that only the right-hand side in Eq. , involving the model ${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}$ is directly available to us. To get to the left-hand side involving the model ${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{{\{s\}}\cup{I}}})}$, one naive approach would be to ‘condition the joint model ${{\underline{{V}}}_{}}={{\underline{{V}}}_{T}}$ on the variable ${X_{{\{s\}}\cup I}}$’. But we have seen in Section \[sec:indnatex\] that given a joint model, coherence in general only determines the conditional models uniquely, provided that the *lower probability* of the conditioning event is non-zero. This is a fairly strong condition, and in what follows we would generally prefer to work with the much weaker condition that the *upper probability* of the conditioning event is non-zero.[^15] Since in that case the left-hand side of Eq. need not be uniquely determined from the joint ${{\underline{{V}}}_{}}$ by coherence, this approach becomes unfeasible.
Nevertheless, as soon as we realise that all we can reasonably require from our models is that they should be coherent, the right approach readily suggests itself:[^16] we should require that if we use the available models ${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{s}})}$ to *define* the models ${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{{\{s\}}\cup{I}}})}$ through the epistemic irrelevance condition , then the result should still be coherent:
1. \[item:global:irrelevance\] If we define the conditional lower previsions ${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{{\{s\}}\cup{I}}})}$, $s\in{{T}^\lozenge}$, $S\subseteq{C_{}(s)}$ and $R\subseteq{\overline{S}}$ through the epistemic irrelevance requirements $${{\underline{{V}}}_{{{\downarrow}S}}({f}\vert{z_{{\{s\}}\cup{R}}})}
\coloneqq{{\underline{{V}}}_{{{\downarrow}S}}({f(\cdot,{z_{R}})}\vert{z_{s}})}
\text{ for all gambles $f$ in ${\mathcal{L}({\mathcal{X}_{{{\downarrow}S}\cup R}})}$},$$ then all these models together should be (jointly) coherent with all the available models in the family ${\mathcal{T}(\underline{V})}$.
And there is a final requirement, which guarantees that all inferences we make on the basis of our global models are as conservative as possible, and are therefore based on no other considerations than what is encoded in the tree:
1. \[item:global:smallest\] The models in the family ${\mathcal{T}(\underline{V})}$ are dominated (point-wise) by the corresponding models in all other families satisfying requirements [T\[item:global:local\]]{}–[T\[item:global:irrelevance\]]{}.
It turns out that the family of models ${\mathcal{T}(\underline{P})}$ we have been constructing above satisfy all these requirements.
\[theo:global-models\] If all local models ${{\overline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ on ${\mathcal{L}({\mathcal{X}_{s}})}$, $s\in{T}$ are strictly positive, then the family of global models ${\mathcal{T}(\underline{P})}$, obtained through Eqs. –, constitutes the point-wise smallest family of (conditional) lower previsions that satisfy [T\[item:global:local\]]{}–[T\[item:global:irrelevance\]]{}. It is therefore the unique family to also satisfy [T\[item:global:smallest\]]{}. Finally, consider any non-empty set of nodes $E\subseteq{T}$ and the corresponding conditional lower prevision derived by applying regular extension:[^17] $${\underline{R}({f}\vert{x_{E}})}
\coloneqq\max{\{\mu\in{\mathbb{R}}\colon{{\underline{{P}}}_{{{\downarrow}T}}}({{\mathbb{I}_{\{{x_{E}}\}}}}[f-\mu])\ge0\}}
\text{ for all $f\in{\mathcal{L}({\mathcal{X}_{T}})}$ and all ${x_{E}}\in{\mathcal{X}_{E}}$}.$$ Then the conditional lower prevision ${\underline{R}({\cdot}\vert{X_{E}})}$ is (jointly) coherent with the global models in the family ${\mathcal{T}(\underline{P})}$.
The last statement of this theorem guarantees that if we use regular extension to *update the tree* given evidence ${X_{E}}={x_{E}}$, i.e., derive conditional models ${\underline{R}({\cdot}\vert{x_{E}})}$ from the joint model ${{\underline{{P}}}_{}}={{\underline{{P}}}_{{{\downarrow}T}}}$, such inferences will always be coherent. This is of particular relevance for the discussion in Section \[sec:algorithm\], where we derive an efficient algorithm for updating the tree using regular extension. It implies in particular that our algorithm produces coherent inferences.
Some separation properties {#sec:separation}
==========================
Without going into too much detail, we would like to point out some of the more striking differences between the separation properties in imprecise Markov trees under epistemic irrelevance, and the more usual ones that are valid for Bayesian nets [@pearl1988], which, by the way, are also inherited from Bayesian nets by credal nets under strong independence [@cozman2000].
It is clear from the interpretation of the graphical model described in Section \[sec:graphical:interpretation\] that we have the following simple separation results:
+=\[->,semithick\] (xi1) [${X_{i_1}}$]{} \[grow=right,sibling distance=25\] child [node (xi2) [${X_{i_2}}$]{} child [node (xt) [${X_{t}}$]{}]{}]{};
+=\[->,semithick\] (xi2) [${X_{i_2}}$]{} child\[grow=left,sibling distance=25\] [node (xi1) [${X_{i_1}}$]{}]{} child\[grow=right,sibling distance=25\] [node (xt) [${X_{t}}$]{}]{};
where in both cases, *${X_{i_2}}$ separates ${X_{t}}$ from ${X_{i_1}}$*: when the value of ${X_{i_2}}$ is known, additional information about the value of ${X_{i_1}}$ does not affect beliefs about the value of ${X_{t}}$. In this figure, between $i_1$ and $i_2$, and between $i_2$ and $t$, there may be other nodes, but the arrows along the path segment through these nodes should all point in the indicated directions. The underlying idea is that $t$ is a (descendant of some) child $c$ of $i_2$, and conditional on the mother $i_2$ of $c$, the non-parent non-descendant $i_1$ of $c$ is epistemically irrelevant to $c$ and all of its descendants.
On the other hand, and in contradistinction with what we are used to in Bayesian nets, we will not generally have separation in the following configuration:
+=\[<-,semithick\] (xi1) [${X_{i_1}}$]{} \[grow=right,sibling distance=25\] child [node (xi2) [${X_{i_2}}$]{} child [node (xt) [${X_{t}}$]{}]{}]{};
where *${X_{i_2}}$ does not necessarily separate ${X_{t}}$ from ${X_{i_1}}$*. We will come across a simple counterexample in Section \[sec:example\]. Where does this difference with the case of Bayesian nets originate? It is clear from the reasoning above that ${X_{i_2}}$ separates ${X_{i_1}}$ from ${X_{t}}$: conditional on ${X_{i_2}}$, ${X_{t}}$ is epistemically irrelevant to ${X_{i_1}}$. For precise probability models, irrelevance generally implies symmetrical independence, and therefore this will generally imply that conditional on ${X_{i_2}}$, ${X_{i_1}}$ is epistemically irrelevant to ${X_{t}}$ as well. But for imprecise probability models no such symmetry is guaranteed [@couso1999b], and we therefore cannot infer that, generally speaking, ${X_{i_2}}$ will separate ${X_{i_1}}$ from ${X_{t}}$. *As a general rule, we can only infer separation if the arrows point from the ‘separating’ variable ${X_{i_2}}$ towards the ‘target’ variable ${X_{t}}$.*
A fast algorithm for updating in an imprecise Markov tree {#sec:algorithm}
=========================================================
We now consider the case where we are interested in making inferences about the value of the variable ${X_{t}}$ in some *target node* $t$, when we know the values ${x_{E}}$ of the variables ${X_{E}}$ in a set $E\subseteq{T}\setminus\{t\}$ of *evidence nodes*; see for instance Fig \[fig:mtree\].
The formulation of the problem.
-------------------------------
If we assume that the values of the remaining variables are *missing at random*, then we can do this by conditioning the joint ${\underline{{P}}}$ obtained above on the available evidence ‘${X_{E}}={x_{E}}$’; see for instance [@cooman2004b; @zaffalon2009].
We will address this problem by updating the lower prevision ${\underline{{P}}}$ to the lower prevision ${{\underline{{R}}}_{t}({\cdot}\vert{x_{E}})}$ on ${\mathcal{L}({\mathcal{X}_{t}})}$ using *regular extension* [@walley1991 Appendix J]: $$\label{eq:regular}
{{\underline{{R}}}_{t}({g}\vert{x_{E}})}=\max{\{\mu\in{\mathbb{R}}\colon{\underline{{P}}}({{\mathbb{I}_{\{{x_{E}}\}}}}[g-\mu])\geq0\}}$$ for all gambles $g$ on ${\mathcal{X}_{t}}$, *assuming that ${\overline{{P}}}({{\{{x_{E}}\}}})>0$*. Theorem \[theo:global-models\] guarantees that such inferences are coherent. Sufficient conditions on the local models for this positivity assumption to hold are given in Proposition \[prop:global:positivity\].
Consider the map $$\rho_g\colon{\mathbb{R}}\to{\mathbb{R}}\colon\mu\mapsto{\underline{{P}}}({{\mathbb{I}_{\{{x_{E}}\}}}}[g-\mu]).$$ We can infer from the separate coherence of ${\underline{{P}}}$ that ${\lvert\rho_g(\mu_1)-\rho_g(\mu_2)\rvert}\leq{\lvert\mu_1-\mu_2\rvert}{\overline{{P}}}(\{{x_{E}}\})$ for all $\mu_1,\mu_2\in{\mathbb{R}}$, which implies that $\rho_g$ is (Lipschitz) continuous. Separate coherence of ${\underline{{P}}}$ also guarantees that $\rho_g$ is concave and non-increasing. Hence ${\{\mu\in{\mathbb{R}}\colon\rho_g(\mu)\geq0\}}=(-\infty,{{\underline{{R}}}_{t}({g}\vert{x_{E}})}]$, which shows that the supremum that we should have [*a priori*]{} used in is indeed a maximum. ${{\underline{{R}}}_{t}({g}\vert{x_{E}})}$ is the right-most zero of $\rho_g$, and it is, again by separate coherence of ${\underline{{P}}}$, guaranteed to lie between the smallest value $\min g$ and the largest value $\max g$ of $g$. If moreover ${\underline{{P}}}({{\{{x_{E}}\}}})>0$, then separate coherence of ${\underline{{P}}}$ implies that ${{\underline{{R}}}_{t}({g}\vert{x_{E}})}$ is the unique zero of $\rho_g$. If on the other hand ${\underline{{P}}}({{\{{x_{E}}\}}})=0$, then $(-\infty,{{\underline{{R}}}_{t}({g}\vert{x_{E}})}]$ is the set of all zeros of $\rho_g$. It appears that any algorithm for calculating ${{\underline{{R}}}_{t}({g}\vert{x_{E}})}$ will benefit from being able to calculate the values of $\rho_g$, or even more simply check their signs, efficiently.
Calculating the values of $\rho_g$ recursively. {#sec:calculating-rho}
-----------------------------------------------
We now recall from Section \[sec:joint\] that the joint ${\underline{{P}}}$ can be constructed recursively from leaves to root. The idea we now use is that calculating $\rho_g(\mu)={\underline{{P}}}({{\mathbb{I}_{\{{x_{E}}\}}}}[g-\mu])$ becomes easier if we graft the structure of the tree onto the argument $g^\mu\coloneqq{{\mathbb{I}_{\{{x_{E}}\}}}}[g-\mu]$ as follows. Define $$g^\mu_s
\coloneqq
\begin{cases}
{{\mathbb{I}_{\{{x_{s}}\}}}}&\text{if $s\in E$}\\
g-\mu&\text{if $s=t$}\\
1&\text{if $s\in{T}\setminus(E\cup\{t\})$},
\end{cases}$$ then $g^\mu_s\in{\mathcal{L}({\mathcal{X}_{s}})}$ and $g^\mu=\prod_{s\in{T}}g^\mu_s$. Also define, for any $s\in{T}$, the gamble $\phi^\mu_s$ on ${\mathcal{X}_{{{\downarrow}s}}}$ by $\phi^\mu_s\coloneqq\prod_{u\in{{\downarrow}s}}g^\mu_u$. Then $$\phi^\mu_{\square}=g^\mu
\text{ and }
\phi^\mu_s\geq0\text{ if $s{\not\sqsubseteq}t$},$$ and $$\label{eq:function-branching}
\phi^\mu_s=g^\mu_s\prod_{c\in{C_{}(s)}}\phi^\mu_c
\text{ for all $s\in{T}$},$$ where we use the convention that any product over an empty set of indices equals one. Eq. is the argument counterpart of Eq. . Also, if $s{\not\sqsubseteq}t$ then $g^\mu_s$ and $\phi^\mu_s$ do not depend on $\mu$, nor on $g$. Indeed, in that case $$\label{eq:function-branching-too}
\phi^\mu_s={{\mathbb{I}_{\{{x_{E\cap{{\downarrow}s}}}\}}}}.$$
### First, let us consider the nodes $s{\not\sqsubseteq}t$. {#first-let-us-consider-the-nodes-snotsqsubseteqt. .unnumbered}
We define the *messages* ${{\underline{{\pi}}}_{s}}$ and ${{\overline{{\pi}}}_{s}}$ recursively by $$\label{eq:lower-upper-messages}
{{\underline{{\pi}}}_{s}}
\coloneqq{{\underline{{Q}}}_{s}\bigg({g^\mu_s
\smashoperator{\prod_{c\in{C_{}(s)}}}{{\underline{{\pi}}}_{c}}}\Big\vert{X_{{m(s)}}}\bigg)}\\
\text{ and }
{{\overline{{\pi}}}_{s}}
\coloneqq{{\overline{{Q}}}_{s}\bigg({g^\mu_s
\smashoperator{\prod_{c\in{C_{}(s)}}}{{\overline{{\pi}}}_{c}}}\Big\vert{X_{{m(s)}}}\bigg)}.$$ We summarise such a pair by the notation: ${{\underline{\overline{{\pi}}}}_{s}}\coloneqq{{\underline{\overline{{Q}}}}_{s}({g^\mu_s\prod_{c\in{C_{}(s)}}{{\underline{\overline{{\pi}}}}_{c}}}\vert{X_{{m(s)}}})}\coloneqq({{\underline{{\pi}}}_{s}},{{\overline{{\pi}}}_{s}})$. Then there are two possibilities: $${{\underline{\overline{{\pi}}}}_{s}}=
\begin{cases}
{{\underline{\overline{{Q}}}}_{s}({{{\{{x_{s}}\}}}}\vert{X_{{m(s)}}})}\smashoperator{\prod_{c\in{C_{}(s)}}}{{\underline{\overline{{\pi}}}}_{c}}({x_{s}})
&\text{ if $s\in E$}\\
{{\underline{\overline{{Q}}}}_{\prod_{c\in{C_{}(s)}}}\bigg({{\smashoperator[r}\Big\vert{X_{{m(\prod_{c\in{C_{}(s)}})}}}\bigg)}{{\underline{\overline{{\pi}}}}_{c}}}]{s}
&\text{ if $s\notin E$}.
\end{cases}$$ The messages ${{\underline{{\pi}}}_{s}}$ and ${{\overline{{\pi}}}_{s}}$ are gambles on ${\mathcal{X}_{{m(s)}}}$, and can therefore be seen as tuples of real numbers, with as many components ${{\underline{\overline{{\pi}}}}_{s}}({x_{{m(s)}}})$ as there are elements ${x_{{m(s)}}}$ in ${\mathcal{X}_{{m(s)}}}$. They are all non-negative. As their notation suggests, they do not depend on the choice of $g$ or $\mu$, but only (at most) on which nodes are *instantiated*, i.e., belong to $E$, and on which value ${x_{E}}$ the variable ${X_{E}}$ for these instantiated nodes assumes.
It then follows from Eqs. and and the strong factorisation property[^18] that \[see the Appendix for a proof\] $$\label{eq:algorithm-off-backbone}
{{\underline{{P}}}_{{{\downarrow}s}}({\phi^\mu_s}\vert{X_{{m(s)}}})}={{\underline{{\pi}}}_{s}}
\text{ and }
{{\overline{{P}}}_{{{\downarrow}s}}({\phi^\mu_s}\vert{X_{{m(s)}}})}={{\overline{{\pi}}}_{s}}.$$
### Next, we turn to nodes $s{\sqsubseteq}t$. {#next-we-turn-to-nodes-ssqsubseteqt. .unnumbered}
Define the messages ${{\pi}_{s}^{\mu}}$ by $$\label{eq:messages-on-backbone-1}
{{\pi}_{s}^{\mu}}\coloneqq{{\underline{{Q}}}_{s}({\psi^\mu_s}\vert{X_{{m(s)}}})},$$ where the gambles $\psi^\mu_s$ on ${\mathcal{X}_{s}}$ are given by the recursion relations: $$\label{eq:messages-on-backbone-2}
\psi^\mu_t
\coloneqq\max\{g-\mu,0\}\smashoperator{\prod_{c\in{C_{}(t)}}}{{\underline{{\pi}}}_{c}}
+\min\{g-\mu,0\}\smashoperator{\prod_{c\in{C_{}(t)}}}{{\overline{{\pi}}}_{c}},$$ and for each ${\square}\neq s{\sqsubseteq}t$, so ${m(s)}$ exists, $$\label{eq:messages-on-backbone-3}
\psi^\mu_{{m(s)}}
\coloneqq
\bigg[
\max\{{{\pi}_{s}^{\mu}},0\}\smashoperator{\prod_{c\in{S(s)}}}{{\underline{{\pi}}}_{c}}
+\min\{{{\pi}_{s}^{\mu}},0\}\smashoperator{\prod_{c\in{S(s)}}}{{\overline{{\pi}}}_{c}}
\bigg]
g^\mu_{{m(s)}}.$$ The messages ${{\pi}_{s}^{\mu}}$ are again tuples of real numbers, with one component ${{\pi}_{s}^{\mu}}({x_{{m(s)}}})$ for each of the possible values ${x_{{m(s)}}}$ of ${X_{{m(s)}}}$.[^19] They do depend on the choice of $g$ or $\mu$, as well as on which nodes are instantiated and on which value ${x_{E}}$ the variable ${X_{E}}$ for these instantiated nodes assumes.
It then follows from Eqs. and and the strong factorisation property of the local independent products that \[see the Appendix for a proof\] $$\label{eq:algorithm-in-target}
{{\underline{{P}}}_{{{\downarrow}s}}({\phi^\mu_s}\vert{X_{{m(s)}}})}={{\pi}_{s}^{\mu}}
\text{ and of course }\rho_g(\mu)={{\pi}_{{\square}}^{\mu}}.$$ We conclude that we can find the value of $\rho_g(\mu)$ by a backwards recursion method consisting in passing messages up to the root of the tree, and in transforming them in each node using the local uncertainty models; see Eqs. and –.
There is a further simplification, because we are not necessarily interested in the actual value of $\rho_g(\mu)$, but rather in its sign. It arises whenever there are instantiated nodes above the target node: $E\cap{A(t)}\neq\emptyset$. Let in that case $e_t$ be the greatest element of the chain $E\cap{A(t)}$, i.e., the instantiated node closest to and preceding the target node $t$, and let $s_t$ be its successor in the chain ${{\uparrow}t}$; see for instance Fig. \[fig:mtree\]. If we let $$\lambda_g(\mu)
\coloneqq\max\{{{\pi}_{s_t}^{\mu}}({x_{e_t}}),0\}
\smashoperator{\prod_{c\in{S(s_t)}}}{{\underline{{\pi}}}_{c}}({x_{e_t}})
+\min\{{{\pi}_{s_t}^{\mu}}({x_{e_t}}),0\}
\smashoperator{\prod_{c\in{S(s_t)}}}{{\overline{{\pi}}}_{c}}({x_{e_t}}),$$ then it follows from Eq. \[with $s=s_t$ and ${m(s)}=e_t$\] that $\psi^\mu_{e_t}={{\mathbb{I}_{\{{x_{e_t}}\}}}}\lambda_g(\mu)$. If we now continue to use Eqs. and until we reach the root of the tree, we eventually find that[^20] $$\label{eq:simplification}
\rho_g(\mu)
=
\begin{cases}
{\underline{{P}}}({{\{{x_{E}}\}}})\lambda_g(\mu)
&\text{ if $\lambda_g(\mu)\geq0$}\\
{\overline{{P}}}({{\{{x_{E}}\}}})\lambda_g(\mu)
&\text{ if $\lambda_g(\mu)\leq0$}.
\end{cases}$$ Since we assumed from the outset that ${\overline{{P}}}({{\mathbb{I}_{\{{x_{E}}\}}}})>0$, we gather from Eq. that ${{\underline{{R}}}_{t}({g}\vert{x_{E}})}=\max{\{\mu\in{\mathbb{R}}\colon\lambda_g(\mu)\geq0\}}$. Moreover, by combining Eqs. and with Proposition \[prop:global:positivity:too\], we find that ${{\overline{{\pi}}}_{c}}({x_{e_t}})={{\overline{{P}}}_{{{\downarrow}c}}({{{\{{x_{E\cap{{\downarrow}c}}}\}}}}\vert{x_{e_t}})}>0$ for all $c\in{S(s_t)}$, and therefore $\lambda_g(\mu)\geq0{\Leftrightarrow}{{\pi}_{s_t}^{\mu}}({x_{e_t}})\geq0$. Hence ${{\underline{{R}}}_{t}({g}\vert{x_{E}})}=\max{\{\mu\in{\mathbb{R}}\colon{{\pi}_{s_t}^{\mu}}({x_{e_t}})\geq0\}}$.
We conclude that in order to update the tree in the situation described above, we can perform all calculations on the sub-tree ${{\downarrow}s_t}$, where the new root $s_t$ has local model ${{\underline{{Q}}}_{s_t}({\cdot}\vert{x_{e_t}})}$. This is also borne out by the discussion of the separation properties in Section \[sec:separation\].
An algorithm.
-------------
at (7,-2) [ ; & ;\
;& ;\
; & ;\
]{}; (root) at (0,0) [ ${\square}$]{}; (x1) at ($(root)+(-100:\afstand)$) [${X_{1}}$]{}; (x2) at ($(root)+( -15:\afstand)$) [${X_{2}}$]{}; (x3) at ($ (x2)+(-40:\afstand)$) [${X_{3}}$]{}; (x4) at ($ (x3)+(-110:\afstand)$) [${X_{4}}$]{};
(x5) at ($ (x4)+(-140:\afstand)$) [${X_{5}}$]{}; (x15) at ($ (x4)+(170:\afstand)$) [${X_{15}}$]{}; (x6) at ($ (x5)+(-140:\afstand)$) [${X_{6}}$]{}; (x7) at ($ (x5)+(-80:\afstand)$) [${X_{7}}$]{}; (x8) at ($ (x7)+(-45:\afstand)$) [${X_{8}}$]{}; (x9) at ($ (x7)+(-100:\afstand)$) [${X_{9}}$]{}; (x16) at ($ (x6)+(-150:\afstand)$) [${X_{16}}$]{};
(x10) at ($ (x4)+(-40:\afstand)$) ; (x11) at ($ (x10)+(-100:\afstand)$) [${X_{11}}$]{}; (x12) at ($ (x10)+(-35:\afstand)$) [${X_{12}}$]{}; (x14) at ($ (x12)+(-35:\afstand)$) [${X_{14}}$]{}; (x13) at ($ (x12)+(-100:\afstand)$) [${X_{13}}$]{}; (root) – (x1); (root) – (x2); (x2) – (x3); (x3) – (x4); (x4) – (x5); (x5) – (x6); (x5) – (x7); (x7) – (x8); (x7) – (x9); (x6) – (x16); (x4) – (x15); (x4) – (x10); (x10) – (x11); (x10) – (x12); (x12) – (x13); (x12) – (x14);
We now convert these observations into a workable algorithm.
Using regular extension and message passing, we are able to compute ${{\underline{{R}}}_{t}({g}\vert{x_{E}})}$: we
choose any $\mu\in[\min{g},\max{g}]$;
calculate the value of $\lambda_g(\mu)$ by sending messages from the terminal nodes towards the root; and
repeat this in some clever way to find the maximal $\mu$ that will make this $\lambda_g(\mu)$ zero.
But we have seen above that this naive approach can be sped up by exploiting
the separation properties of the tree, and
the independence of $\mu$ (and $g$) for some of the messages, namely those associated with nodes that do not precede the target node $t$.
For a start, as we are only interested in the sign of $ \rho_g(\mu)$ \[or equivalently, that of $\lambda_g(\mu)$\], which we have seen is determined by the sign of ${{\pi}_{s_t}^{\mu}}({x_{e_t}})$, we only have to take into consideration nodes that strictly follow $e_t$.
The next thing a smarter implementation of the algorithm can do, is determine the *trunk* ${\tilde{{T}}}$ of the tree: those nodes that precede the queried node $t$ and strictly follow the greatest observed node $e_t$ preceding $t$. We can define the trunk more formally as follows: ${\tilde{{T}}}\coloneqq{{\uparrow}t}\cap{{\downarrow}{C_{}(e_t)}}$. For the tree in Fig. \[fig:mtree\] for instance, where the darker ${X_{10}}$ is the queried variable and the lighter nodes $\{2,6,7,8,9,11,14,15\}$ are instantiated, the trunk is given by ${\tilde{{T}}}=\{3,4,10\}$, and indicated by bolder arrows.
(x4s) at (2,-10) [${X_{4}}$]{}; (Pi) at ($(x4s)+(30:\afstand)$) [${{\underline{\overline{{\Pi}}}}_{4}}={{\underline{\overline{{\pi}}}}_{5}}{{\underline{\overline{{\pi}}}}_{14}}$]{}; (x5s) at ($ (x4s)+(-140:\afstand)$) [${X_{5}}$]{}; (x14s) at ($ (x4s)+(170:\afstand)$) [${X_{14}}$]{}; (x6s) at ($ (x5s)+(-140:\afstand)$) [${X_{6}}$]{}; (x7s) at ($ (x5s)+(-80:\afstand)$) [${X_{7}}$]{}; (x8s) at ($ (x7s)+(-45:\afstand)$) [${X_{8}}$]{}; (x9s) at ($ (x7s)+(-100:\afstand)$) [${X_{9}}$]{}; (x16s) at ($ (x6s)+(-150:\afstand)$) [${X_{16}}$]{}; (x4s) – (x5s); (x4s) – (x14s); (x5s) – (x6s); (x5s) – (x7s); (x7s) – (x8s); (x7s) – (x9s); (x6s) – (x16s);
[ ]{}; at ($ (m)!0.1!-90:(x5s) $) [${{\underline{\overline{{\pi}}}}_{5}}={{\underline{\overline{{Q}}}}_{5}({{{\underline{\overline{{\pi}}}}_{6}}{{\underline{\overline{{\pi}}}}_{7}}}\vert{X_{4}})}$]{}; [ ]{}; at ($ (m)!0.1!90:(x6s) $) [${{\underline{\overline{{Q}}}}_{6}({{\{{x_{6}}\}}}\vert{X_{5}})}={{\underline{\overline{{\pi}}}}_{6}}$]{}; [ ]{}; at ($ (m)!0.0!90:(x7s) $) [${{\underline{\overline{{\pi}}}}_{7}}={{\underline{\overline{{Q}}}}_{7}({{\{{x_{7}}\}}}\vert{X_{5}})}{{\underline{\overline{{\pi}}}}_{8}}{{\underline{\overline{{\pi}}}}_{9}}$]{}; [ ]{}; at ($ (m)!0.1!90:(x8s) $) [${{\underline{\overline{{\pi}}}}_{8}}={{\underline{\overline{{Q}}}}_{8}({{\{{x_{8}}\}}}\vert{X_{7}})}$]{}; [ ]{}; at ($ (m)!0.0!90:(x9s) $) [${{\underline{\overline{{\pi}}}}_{9}}={{\underline{\overline{{Q}}}}_{9}({{\{{x_{9}}\}}}\vert{X_{7}})}$]{}; [ ]{}; at ($ (m)!0.0!90:(x14s) $) [${{\underline{\overline{{\pi}}}}_{14}}$]{}; [ ]{}; at ($ (m)!0.1!90:(x16s) $) [$1={{\underline{\overline{{\pi}}}}_{16}}$]{};
(x4s) – (Pi.south west);
We have a special interest in the nodes that constitute the trunk, because only they will send messages to their mother nodes that actually depend on $\mu$. As a consequence, all other nodes (all descendants of the trunk that are not in the trunk themselves) send messages that have to be calculated only once. This implies that we can summarise all the $\mu$-independent messages by propagating all of them until they reach the trunk. The $\mu$-independent messages ${{\underline{\overline{{\pi}}}}_{s}}$ that arrive in a trunk node $s$ can be represented more succinctly by their point-wise products ${{\underline{\overline{{\Pi}}}}_{s}}\coloneqq\prod_{c\in{{C_{}(s)}}\setminus{\tilde{{T}}}}{{\underline{\overline{{\pi}}}}_{c}}$, because Eqs. and only depend on them through on these products.
This means that for every trunk node $s\in{\tilde{{T}}}$, we have to find the lower (upper) messages of every child $c$ of $s$ that is not in the trunk itself. Both ${{\underline{{\pi}}}_{c}}$ and ${{\overline{{\pi}}}_{c}}$ can be calculated recursively using Eq. , where the recursion starts at the leaves and moves up to (but stops right before) the trunk. In the leaves, the local lower and upper previsions of the indicator of the evidence are sent upwards if the leaf is instantiated; if not the constant 1 is sent up, which is equivalent to deleting the node from the tree. We could envisage removing *barren nodes* (all of whose descendants are uninstantiated, such as ${X_{1}}$, ${X_{13}}$, ${X_{16}}$ in the example tree above) from the tree beforehand, but we believe the computational overhead created by the search for them will void the gain.
(x2b) at (4,2) [${x_{e_t}}$]{}; (x3b) at ($ (x2b)+(-40:\afstand)$) [${X_{s_t}}$]{}; (x4b) at ($ (x3b)+(-90:\afstand)$) [${X_{4}}$]{}; (x10b) at ($ (x4b)+(-90:\afstand)$) ; (x3b) – (x4b); (x4b) – (x10b); [ ]{}; at ($ (m)!0.1!-90:(x3b) $) [${{\pi}_{s_t}^{\mu}}({x_{e_t}})
={{\underline{{Q}}}_{s_t}({\underbrace{\max\{{{\pi}_{s_t}^{\mu}},0\}{{\underline{{\Pi}}}_{s_t}}
+\min\{{{\pi}_{s_t}^{\mu}},0\}{{\overline{{\Pi}}}_{s_t}}}_{\psi^\mu_{s_t}}}\vert{x_{e_t}})}$]{}; [ ]{}; at ($ (m)!0.1!90:(x4b) $) [${{\pi}_{4}^{\mu}}={{\underline{{Q}}}_{4}({\underbrace{\max\{{{\pi}_{t}^{\mu}},0\}{{\underline{{\Pi}}}_{4}}
+\min\{{{\pi}_{t}^{\mu}},0\}{{\overline{{\Pi}}}_{4}}}_{\psi^\mu_{4}}}\vert{X_{s_t}})}$]{}; [ ]{}; at ($ (m)!0.1!90:(x10b) $) [${{\pi}_{t}^{\mu}}={{\underline{{Q}}}_{t}({\underbrace{\max\{g-\mu,0\}{{\underline{{\Pi}}}_{t}}
+\min\{g-\mu,0\}{{\overline{{\Pi}}}_{t}}}_{\psi^\mu_t}}\vert{X_{4}})}$]{};
The only recursion that is still left to do, is the calculation of the $\mu$-dependent messages ${{\pi}_{s}^{\mu}}$ along the trunk. As demonstrated in Fig. \[fig:joint\], we can calculate ${{\pi}_{s_t}^{\mu}}(e_t)$ using the following recursion formula: $${{\pi}_{s}^{\mu}} \coloneqq
\begin{cases}
{{\underline{{Q}}}_{s}({\max\{g-\mu,0\}{{\underline{{\Pi}}}_{s}}+\min\{g-\mu,0\}{{\overline{{\Pi}}}_{s}}}\vert{X_{{m(s)}}})}
&s=t,\\
{{\underline{{Q}}}_{s}({\max\{{{\pi}_{c_t}^{\mu}},0\}{{\underline{{\Pi}}}_{s}}+\min\{{{\pi}_{c_t}^{\mu}},0\}{{\overline{{\Pi}}}_{s}}}\vert{X_{{m(s)}}})}
&s\in{\tilde{{T}}}\setminus\{t\}\text{ and }{C_{}(s)}\cap{\tilde{{T}}}={\{c_t\}}.
\end{cases}$$ These formulas are reformulations of Eqs. –, where the influence of the ${{\underline{\overline{{\Pi}}}}_{}}$ has been made explicit.
Since we now know how to calculate ${{\pi}_{s_t}^{\mu}}(e_t)$, we can tackle the final problem: find the maximal $\mu$ for which ${{\pi}_{s_t}^{\mu}}(e_t)=0$. In principle, a secant root-finding method could be used, but using the concavity and non-increasing character of ${{\pi}_{s_t}^{\mu}}(e_t)$ as a function of $\mu$, we can speed up the calculation of the maximal root drastically as shown in Fig. \[fig:rootfinding\].
(-0.1,0) – (1.5,0) node\[right\] [$\mu$]{}; (-0.08,-0.4) – (-0.08,0.5) node\[left\] [$\rho_g(\mu)$]{}; plot (,[0.4-exp(4\*)/60]{}); (0.1,[0.4-exp(4\*0.1)/60]{}) – (0.65,[0.4-exp(4\*0.65)/60]{}) – ([((24-exp(4\*0.65))\*0.1-(24-exp(4\*0.1))\*0.65)/(exp(4\*0.1)-exp(4\*0.65))]{},0); (1.0,[0.4-exp(4\*1.0)/60]{}) – (0.95,[0.4-exp(4\*0.95)/60]{}) – ([((24-exp(4))\*0.95-(24-exp(4\*0.95)))/(exp(4\*0.95)-exp(4))]{},0); (0.65,[0.4-exp(4\*0.65)/60]{}) – ([((24-exp(4\*0.65))\*0.95-(24-exp(4\*0.95))\*0.65)/(exp(4\*0.95)-exp(4\*0.65))]{},0) – (0.95,[0.4-exp(4\*0.95)/60]{}); ([ln(24)/4]{},0) circle (0.3pt) node\[above,xshift=4pt\] [$t$]{}; (0.1,[0.4-exp(4\*0.1)/60]{}) circle (0.3pt) node \[above\] [$(a,\rho_g(a))$]{}; (0.65,[0.4-exp(4\*0.65)/60]{}) circle (0.3pt) node \[above right\] [$(b,\rho_g(b))$]{}; (0.95,[0.4-exp(4\*0.95)/60]{}) circle (0.3pt) node \[right,yshift=2pt\] [$(c,\rho_g(c))$]{}; (1.0,[0.4-exp(4\*1.0)/60]{}) circle (0.3pt) node \[right,yshift=-0pt\] [$(d,\rho_g(d))$]{}; ([((24-exp(4\*0.65))\*0.95-(24-exp(4\*0.95))\*0.65)/(exp(4\*0.95)-exp(4\*0.65))]{},0) circle (0.2pt) node \[below left\] [$p$]{}; ([((24-exp(4))\*0.95-(24-exp(4\*0.95)))/(exp(4\*0.95)-exp(4))]{},0) circle (0.2pt) node \[below right,xshift=+4pt\] [$q$]{}; ([((24-exp(4\*0.65))\*0.1-(24-exp(4\*0.1))\*0.65)/(exp(4\*0.1)-exp(4\*0.65))]{},0) circle (0.2pt) node \[below right\] [$r$]{}; at (2.5,0)
$p\coloneqq\nicefrac{\rho_g(c) b-\rho_g(b) c}{\rho_g(c)-\rho_g(b)}$;\
$m\coloneqq c$;$t\coloneqq\nicefrac{p+m}{2}$;\
[**while** ]{} $m-p>\mathit{tol}$ [ **and** ]{}$\rho_g(t)\neq0.0$\
$\quad\text{\bf if }\rho_g(t)>0$\
$\qquad a\coloneqq b;\; b\coloneqq t$;\
$\qquad s\coloneqq\nicefrac{\rho_g(a)b-\rho_g(b)a}{\rho_g(a)-\rho_g(b)}$;\
$\quad\text{\bf else}$\
$\qquad d\coloneqq c;\; c\coloneqq t$;\
$\qquad s\coloneqq\nicefrac{\rho_g(c) d-\rho_g(d) c}{\rho_g(c)-\rho_g(d)}$;\
$\quad p\coloneqq\nicefrac{\rho_g(c)b-\rho_g(b)c}{\rho_g(c)-\rho_g(b)}$;\
$\quad m\coloneqq\min\{m,s\}$;$t\coloneqq\nicefrac{p+m}{2}$;
;
Let us briefly discuss the complexity of our algorithm. Consider for a start that for a fixed $\mu$ each node makes a single local computation and then propagates the result to its mother node: this implies that, with $\mu$ fixed, the algorithm is linear in the number of nodes. Iterating on $\mu$ then amounts to multiplying such a linear complexity with the number of iterations. This number depends on the function $g$, as the iterations are made to compute the root of a function that is known to belong to the real interval $[\min g,\max g]$. If we assume that the bisection algorithm is employed to find the root—for the sake of simplicity—and let $r\coloneqq\max g-\min g$ be the range of the function, then the number of iterations is bounded by $\log_2\frac{r}{\mathit{tol}}+1$, where $\mathit{tol}$ is some fixed tolerance. In other words, the number of iterations is linear in the number $b$ of bits needed to represent $r$ in base 2. This means that the overall complexity of the algorithm is $O(b\cdot|T|)$, taking into account that the computational complexity of our root-finding algorithm must be lower than for the bisection (and actually also for the secant) algorithm. Since $b$ will be a small number[^21] in most cases (e.g. when the focus is on probabilities), we simply refer to the complexity of our algorithm as linear in the number of nodes.
A simple example involving dilation {#sec:example}
===================================
We present a very simple example that allows us to
follow the inference method discussed above in a step-by-step fashion;
see that there are separation properties for credal nets under strong independence that fail for credal trees under epistemic irrelevance; and
see that in that case we will typically observe dilation.
Consider the following imprecise Markov chain:
+=\[->,semithick\] =\[->,thick,dotted,draw=blue!50\] (x1) [${X_{1}}$]{} \[grow=right,level distance=35\] child [node (x2) [${X_{2}}$]{} child [node (x3) [${X_{3}}$]{}]{}]{}; (x1info) [?]{}; (x2info) [${x_{2}}$]{}; (x3info) [${x_{3}}$]{}; (x1) – (x1info); (x2info) – (x2); (x3info) – (x3);
To make things as simple as possible, we suppose that ${\mathcal{X}_{1}}=\{a,b\}$ and that ${{\underline{{Q}}}_{1}}$ is a linear (or precise, or expectation-like) model ${{Q}_{1}}$ with mass function ${q}$. We also assume that ${{\underline{{Q}}}_{2}({\cdot}\vert{X_{1}})}$ is a linear model ${{Q}_{2}({\cdot}\vert{X_{1}})}$ with conditional mass function ${{q}({\cdot}\vert{X_{1}})}$. We make no such restrictions on the local model ${{\underline{{Q}}}_{3}({\cdot}\vert{X_{2}})}$. We also use the following simplifying notational device: if we have three real numbers $\underline{\kappa}$, $\overline{\kappa}$ and $\gamma$, we let $${\underline{\overline{\kappa}}\langle\gamma\rangle}
\coloneqq\underline{\kappa}\max\{\gamma,0\}+\overline{\kappa}\min\{\gamma,0\}.$$ We observe ${X_{2}}={x_{2}}$ and ${X_{3}}={x_{3}}$, and want to make inferences about the target variable ${X_{1}}$: for any $g\in{\mathcal{L}({\mathcal{X}_{1}})}$, we want to know ${{\underline{{R}}}_{1}({g}\vert{x_{\{2,3\}}})}$. Letting ${\underline{{r}}}\coloneqq{{\underline{{R}}}_{1}({\{a\}}\vert{x_{\{2,3\}}})}$ and ${\overline{{r}}}\coloneqq{{\overline{{R}}}_{1}({\{a\}}\vert{x_{\{2,3\}}})}$, we infer from the separate coherence of ${{\underline{{R}}}_{1}({\cdot}\vert{x_{{\{2,3\}}}})}$ that it suffices to calculate ${\underline{{r}}}$ and ${\overline{{r}}}$, because $${{\underline{{R}}}_{1}({g}\vert{x_{\{2,3\}}})}=g(b)+{\underline{\overline{{r}}}\langleg(a)-g(b)\rangle}.$$ We let $g^\mu=[{\mathbb{I}_{{\{a\}}}}-\mu]{{\mathbb{I}_{\{{x_{2}}\}}}}{{\mathbb{I}_{\{{x_{3}}\}}}}$, and apply the approach of the previous section. We see that the trunk $\tilde{{T}}=\{1\}$, and the instantiated leaf node $3$ sends up the messages ${{\underline{\overline{{\pi}}}}_{3}}={{\underline{\overline{{Q}}}}_{3}({{{\{{x_{3}}\}}}}\vert{X_{2}})}$ to the instantiated node $2$, which transforms them into the messages $${{\underline{\overline{{\pi}}}}_{2}}
={{\underline{\overline{{Q}}}}_{2}({{{\{{x_{2}}\}}}}\vert{X_{1}})}{{\underline{\overline{{\pi}}}}_{3}}({x_{2}})
\eqqcolon{{q}({{x_{2}}}\vert{X_{1}})}{\underline{\overline{{q}}}},$$ where we let ${{q}({{x_{2}}}\vert{X_{1}})}\coloneqq{{\underline{\overline{{Q}}}}_{2}({{{\{{x_{2}}\}}}}\vert{X_{1}})}$ and ${\underline{\overline{{q}}}}\coloneqq {{\underline{\overline{{\pi}}}}_{3}}({x_{2}})$. These messages are sent up to the (target) root node $t=1$, which transforms them into the message ${{\pi}_{1}^{\mu}}={{Q}_{1}}(\psi^\mu_1)$ with $\psi^\mu_1={{q}({{x_{2}}}\vert{X_{1}})}{\underline{\overline{{q}}}\langle{\mathbb{I}_{{\{a\}}}}-\mu\rangle}$. If we also use that $0\leq\mu\leq 1$, this leads to $${{\underline{{P}}}_{1}}(g^\mu)
={{\pi}_{1}^{\mu}}
={q}(a){q}({x_{2}}\vert a){\underline{{q}}}[1-\mu]
+{q}(b){q}({x_{2}}\vert b){\overline{{q}}}[-\mu],$$ so we find after applying regular extension that $$\begin{aligned}
{\underline{{r}}}&={{\underline{{R}}}_{1}({\{a\}}\vert{x_{\{2,3\}}})}
=\frac{{q}(a){q}({x_{2}}\vert a){\underline{{q}}}}
{{q}(a){q}({x_{2}}\vert a){\underline{{q}}}+{q}(b){q}({x_{2}}\vert b){\overline{{q}}}}\\
{\overline{{r}}}&={{\overline{{R}}}_{1}({\{a\}}\vert{x_{\{2,3\}}})}
=\frac{{q}(a){q}({x_{2}}\vert a){\overline{{q}}}}
{{q}(a){q}({x_{2}}\vert a){\overline{{q}}}+{q}(b){q}({x_{2}}\vert b){\underline{{q}}}}.\end{aligned}$$ When ${\underline{{q}}}={\overline{{q}}}$, which happens for instance if the local model for ${X_{3}}$ is precise, then we see that, with obvious notations, $$\label{eq:precise}
{\overline{{r}}}={\underline{{r}}}=\frac{{q}(a){q}({x_{2}}\vert a)}
{{q}(a){q}({x_{2}}\vert a)
+{q}(b){q}({x_{2}}\vert b)}
\eqqcolon p(a\vert{x_{2}})$$ and therefore ${X_{2}}$ indeed separates ${X_{3}}$ from ${X_{1}}$. But in general, letting $\alpha\coloneqq{q}(a){q}({x_{2}}\vert a)$ and $\beta\coloneqq{q}(b){q}({x_{2}}\vert b)$, we get $${\overline{{r}}}-p(a\vert{x_{2}})
=\frac{\alpha\beta}{\alpha+\beta}
\frac{{\overline{{q}}}-{\underline{{q}}}}
{\alpha{\overline{{q}}}+\beta{\underline{{q}}}}
\text{ and }
p(a\vert{x_{2}})
-{\underline{{r}}}=\frac{\alpha\beta}{\alpha+\beta}
\frac{{\overline{{q}}}-{\underline{{q}}}}
{\alpha{\underline{{q}}}+\beta{\overline{{q}}}}.$$ As soon as ${\overline{{q}}}>{\underline{{q}}}$, ${X_{2}}$ no longer separates ${X_{3}}$ from ${X_{1}}$, and we witness *dilation* [@herron1997; @seidenfeld1993] because of the additional observation of ${X_{3}}$!
Numerical comparison with strong independence {#sec:comparison}
=============================================
Strong independence implies epistemic irrelevance, and hence inferred (lower-upper) probability intervals for imprecise Markov trees with epistemic irrelevance will include those obtained assuming strong independence. This suggests that our algorithm could also be used also as a tool to make conservative (also called outer) approximations of the computations made in a credal tree under strong independence. This could be an important application of our algorithm since at the moment it is unclear whether or not updating probabilities in a tree is a polynomial task under strong independence. If it were not, addressing the problem would definitely benefit from the availability of fast approximations.
With this idea in mind, we make a preliminary empirical exploration of the quality of the approximation. As noted in Section \[sec:separation\], the two models have different separation properties: this is particularly important when evidence is back-propagated from leaves to root. For this reason, we compare posterior probability intervals for the root variable of a *chain* where only the leaf node is instantiated.
Fig. \[fig:strvsepi\] reports the results of this comparison for chains with binary nodes, randomly generated local models, and variable length (from 5 up to 100 nodes). The algorithm in Section \[sec:algorithm\] has been used to compute the posterior probability intervals in the chains under epistemic irrelevance, while the *2U algorithm* [@fagiuoli1998] was used for updating in the chains under strong independence. The inferred probability intervals for the former turn out to be clearly wider, and the mean difference between the two intervals is about $0.3$ irrespective of the length of the chain, at least for chains with more than ten nodes.
For non-binary nodes there are no efficient algorithms known for updating chains with strong independence. We used the procedure in [@campos2005] to update chains with less than seven ternary nodes and credal sets with three randomly generated extreme points in the strong independence case. A similar difference between the posterior intervals was observed also in these cases. For longer chains, updating for the chain under strong independence is too slow and no comparison can be made. In summary, there is a non-negligible difference between inferences based on the two notions of ‘independence’. This means that the epistemic approximations to the strong case could be quite crude in practise. However, their being outer (that is, safe) approximations together with their light complexity could still make of them very useful tools, whenever the strong independence approach is deemed necessary or appropriate.
(0.0,0) – (105,0) node\[right\] ; (0.0,0.0) – (0.0,45) node\[left\] ; /in [0/0, 25/25 , 50/50 , 75/75 , 100/100]{} (0pt,4pt) – (0pt,-4pt) node\[below\] [$\xtext$]{}; /in [10/.10, 20/.20, 30/.30 , 40/.40]{} (4pt,0pt) – (-4pt,0pt) node\[left\] [$\ytext$]{}; plot\[xscale=1.0/1.0,yscale=1.0/1.0,smooth,mark=x,mark size=10pt\] file [data.table]{};
An application {#sec:application}
==============
The tree topology of the graphs considered in this paper is expressive enough to model useful and interesting problems. These problems can then be solved efficiently by means of the algorithm described in the previous sections. We make this point clearer with an example application about character recognition. This is also an opportunity to illustrate the differences between the traditional, precise-probability, approach to the problem and the imprecise-probability one. Most notably, these differences arise because the imprecise-probability methods come with the inherent ability to suspend judgement when the information available is deemed insufficient to reliably recognise a character, whereas the precise-probability ones do not.
Imprecise hidden Markov models
------------------------------
Hidden Markov models (HMMs) [@rabiner1989] are popular tools for modelling a sequence of hidden variables that generate a related sequence of observable variables. These are respectively referred to as the *generative* and *observable* sequences. HMMs have applications in many areas of signal processing, and more specifically in speech and text recognition.
Both the generative and the observable sequence are described by sets of variables over the same domain ${\mathcal{X}_{}}$, denoted respectively by ${X_{s_1}}$, …, ${X_{s_n}}$ and ${X_{o_1}}$, …, ${X_{o_n}}$. The independence assumptions between these variables, which characterise HMMs, are those corresponding to the tree structure below. Informally, this topology states that every element of the generative sequence depends only on its predecessor, while each observation depends only on the corresponding element of the generative sequence.
+=\[->,semithick\] =\[draw,->,semithick\] (x1) [${X_{s_1}}$]{} \[grow=right,level distance=40\] child [node (x2) [${X_{s_2}}$]{} child [node (x) [$\dots$]{} child [node (xn) [${X_{s_n}}$]{}]{}]{}]{}; (o1) [${X_{o_1}}$]{}; (o2) [${X_{o_2}}$]{}; (o) [$\dots$]{}; (on) [${X_{o_n}}$]{}; (x1) – (o1); (x2) – (o2); (xn) – (on); ; ;
A local uncertainty model should be defined for each variable. In the case of precise probabilistic assessments, this corresponds to linear (precise, or expectation-like) versions of the local models ${{\underline{{Q}}}_{s_1}}$, ${{\underline{{Q}}}_{s_{k+1}}({\cdot}\vert{X_{s_k}})}$ and ${{\underline{{Q}}}_{o_k}({\cdot}\vert{X_{s_k}})}$, $k=1,\dots,n$, where the conditional models are assumed to be *stationary*, i.e., independent of $k$. These model, respectively, beliefs about the first state in the generative sequence, the transitions between adjacent states, and the observation process.
Bayesian techniques for learning from multinomial data are usually employed for identifying these models. But, especially if only few data are available, other methods leading to imprecise assessments, such as the *imprecise Dirichlet model* (IDM, [@walley1996b]), might offer a more realistic model of the local uncertainty. For example, for the unconditional local model ${{\underline{{Q}}}_{s_1}}$, applying the IDM leads to the following simple identification: $$\label{eq:idm}
{{\underline{{Q}}}_{s_1}}(\{x_1\})=\frac{n^{s_1}_{x_1}}{s+\sum\limits_{x\in{\mathcal{X}_{}}}n^{s_1}_{x}}
\quad
{{\overline{{Q}}}_{s_1}}(\{x_1\})=\frac{s+n^{s_1}_{x_1}}{s+\sum\limits_{x\in{\mathcal{X}_{}}}n^{s_1}_{x}},$$ where $n^{s_1}_{x_1}$ counts the units in the sample for which ${X_{s_1}}=x_1$, and $s$ is a (positive real) hyper-parameter that expresses the degree of caution in the inferences. For the conditional local models, we can proceed similarly. This leads to the identification of an *imprecise HMM*, a special credal tree under epistemic irrelevance, like the ones introduced in Section \[sec:markov-trees\].
Generally speaking, the algorithm described in Section \[sec:algorithm\] can be used for computing inferences with such imprecise HMMs. Below, we address the more specific problem of *on-line recognition*, which consists in the identification of the most likely value of ${X_{s_n}}$, given the evidence for the whole observational sequence ${X_{o_1}}={x_{o_1}}$, …, ${X_{o_n}}={x_{o_n}}$. For precise local models, this problem requires the computation of the state $\tilde{x}_{s_n}\coloneqq\operatorname{argmax}_{{x_{s_n}}\in{\mathcal{X}_{}}}P(\{{x_{s_n}}\}\vert{x_{o_1}},\dots,{x_{o_n}})$ that is most probable after the observation. For imprecise local models different criteria can be adopted; see [@troffaes2007] for an overview. We consider *maximality*: we order the states by ${x_{s_n}}>{z_{s_n}}$ if and only if $\underline{P}({{\mathbb{I}_{\{{x_{s_n}}\}}}}-{{\mathbb{I}_{\{{z_{s_n}}\}}}}\vert{x_{o_1}},\dots,{x_{o_n}})>0$, and we look for the *undominated* or *maximal* states under this order. This may produce *indeterminate* predictions: the set of undominated states may have more than one element.
On-line character recognition
-----------------------------
As a very first application of the imprecise HMM, we have considered a *character recognition* problem.[^22] A written text was regarded as a generative sequence, while the observable sequence was obtained by artificially corrupting the text. This is a model for a not perfectly reliable observation process, such as the output of an OCR device. The local models were identified using the IDM, as in , by counting the occurrences of single characters and the ‘transitions’ from one character to another in the generative sequence, and by matchings between the elements of the two sequences. By modelling text as a generative sequence, we obviously ignore any dependence there might be between a character and its $n$-th predecessor, for any $n\geq 2$. A better, albeit still not completely realistic, model would resort to using $n$-grams (i.e., clusters of $n$ characters with $n\geq2$) instead of monograms. Such models might lead to higher accuracy, but they need larger data sets for their quantification, because of the exponentially larger number of possible transitions for which probabilities have to be estimated. The figure below depicts how on-line recognition through HMM might apply to this setup.
+=\[ed\] (x1) [${X_{s_1}}$]{} \[level distance=35\] child\[grow=down\] [node\[observed\] (o1) [${X_{o_1}}$]{}]{} child\[grow=right\] [node\[nd\] (x2) [${X_{s_2}}$]{} child\[grow=down\] [node\[observed\] (o2) [${X_{o_2}}$]{}]{} child\[grow=right\] [node\[target\] (x3) child\[grow=down\] [node\[observed\] (o3) [${X_{o_3}}$]{}]{}]{}]{}; (xi) [**I**]{}; ; ; (xv) [**V**]{}; ; (oi) [**I**]{}; ; ; (ov) [**V**]{}; ;
The performance of the precise model can be characterised by its *accuracy* (the percentage of correct predictions) alone. The imprecise HMM requires more indicators. We follow [@corani2008] in using the following:
determinacy
: percentage of determinate predictions,
set-accuracy
: percentage of indeterminate predictions containing the right state,
single accuracy
: percentage of correct predictions computed considering only determinate predictions, and
indeterminate output size
: average number of states returned when the prediction is indeterminate over number of possible states.
----------------------------------------------------------------------------------- -- --
**Precise HMM\
Accuracy & $93.96 \%$ & $(\nicefrac{7275}{7743})$\
Accuracy (if imprecise indeterminate)& $64.97\%$& $(\nicefrac{243}{374})$\
\
**Imprecise HMM\
Determinacy& $95.17\%$ & $(\nicefrac{7369}{7743})$\
Set-accuracy& $93.58\%$ & $(\nicefrac{350}{374})$\
Single accuracy& $95.43\%$ & $(\nicefrac{7032}{7369})$\
Indeterminate output size& $2.97$ out of $21$ classes & $(\nicefrac{1112}{374})$\
\
****
----------------------------------------------------------------------------------- -- --
: Precise vs. imprecise HMMs. Test results obtained by twofold cross-validation on the first two chants of Dante’s *Divina Commedia* and $n=2$. Quantification is achieved by IDM with $s=2$ and Perks’ prior modified as suggested in [@zaffalon2001 Section 5.2]. The single-character output by the precise model is then guaranteed to be included in the set of characters the imprecise HMM identifies.[]{data-label="tab:results"}
The recognition using our algorithm is fast: it never takes more than one second for each character. Table \[tab:results\] reports descriptive values for a large set ($7743$) of simulations, and a comparison with precise model performance. Imprecise HMMs guarantee quite accurate predictions. In contrast with the precise model, there are ‘indeterminate’ instances for which they do not output a single state. Yet, this happens rarely, and even then we witness a remarkable reduction in the number of undominated states (from the $21$ letters of the Italian alphabet to less than $3$). Interestingly, the instances for which the imprecise probability model returns more than one state appear to be ‘difficult’ for the precise probability model: the accuracy of the precise models displays a strong decrease if we focus only on these instances, while the imprecise models here display basically the same performance as for other instances, by returning about three characters instead of a single one.
Conclusions {#sec:conclusion}
===========
We have defined imprecise-probability (or credal) trees using Walley’s notion of epistemic irrelevance. Credal trees generalise tree-shaped Bayesian nets in two ways: by allowing the parameters of the tree to be imprecisely specified, and moreover by replacing the notion of stochastic independence with that of epistemic irrelevance. Our focusing on epistemic irrelevance is the most original aspect of this work, as this notion has received limited attention so far in the context of credal nets.
We have focused in particular on developing an efficient exact algorithm for updating beliefs on the tree. Like the algorithms developed for precise graphical models, our algorithm works in a distributed fashion by passing messages along the tree. It computes lower and upper conditional previsions (expectations) with a complexity that is linear in the number of nodes in the tree. This is remarkable because until now it was unclear whether an algorithm with the features described above was at all feasible: in fact, epistemic irrelevance is most easily formulated using coherent lower previsions, which have never before been used as such in practical applications of credal nets. Moreover, it is at this point not clear that epistemic irrelevance is as ‘well-behaved’ as strong independence is with respect to the graphoid axioms for propagation of probability in graphical models [@cozman2005b; @moral2005b].[^23] Our results therefore appear very encouraging, and seem to have the potential to open up new avenues of research in credal nets.
On a more theoretical side, we have also shown that our credal trees satisfy the important rationality requirement of coherence. This has been established under the assumption that the *upper* probability of any possible observation in the tree is positive, which is a very mild requirement. The same assumption also allowed us to show that all inferences made by updating the tree will be coherent with each other as well as with the local uncertainty models in the nodes of the tree.
On the applied side, we have presented an application of the credal tree model to the problem of character recognition, where the parameters of the model are inferred from data. The empirical results are positive, especially because they show that our credal trees are able to make more reliable predictions than their precise-probability counterparts.
Where to go from here? There are many possible avenues for future research.
It would be very useful to be able to extend the algorithm at least to so-called *polytrees*, which are substantially more expressive graphs than trees are. This could be a difficult task to achieve. In fact, updating credal nets based on strong independence is an NP-hard task when the graph is more general than a tree [@campos2005a]. Similar problems might affect the algorithms for credal nets based on irrelevance.
For applications, it would be very important to develop statistical methods specialised for credal nets under irrelevance that avoid introducing excessive imprecision in the process of inferring probabilities from data. This could be achieved, for instance, by using a single global IDM over the variables of the tree rather than many local ones, as we did in our experiments.
Another research direction could be concerned with trying to strengthen the conclusions that epistemic trees lead to. There might be cases where our Markov condition based on epistemic irrelevance is too weak as a structural assessment. We have discussed situations where this type of Markov condition systematically leads to a dilation of uncertainty when updating beliefs with observations, and indicated that this dilation is related to the (lack of) certain separation properties induced by epistemic irrelevance on a graph. Dilation might not be desirable in some applications, and we could be called upon to strengthen the model in order to rule out such behaviour. One way to address the issue of dilation—but not necessarily the easiest—could consist in adding additional irrelevance statements to the model, other than those derived from the Markov condition. An easier avenue could be based on designing assumptions that together with the Markov condition lead to some stronger separation properties, while not necessarily requiring them to match the common ones used in Bayesian nets.
Acknowledgements {#acknowledgements .unnumbered}
================
Research by De Cooman and Hermans was supported by Flemish BOF project 01107505 and SBO project 060043 of the IWT-Vlaanderen. Research by Antonucci and Zaffalon has been partially supported by the Swiss NSF grants n. 200020-116674/1 and n. 200020-121785/1. This paper has benefited from discussions with Serafín Moral, Fabio G. Cozman and Cassio P. de Campos, and from the generous comments provided by two anonymous referees.
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Proofs of important results {#sec:app}
===========================
In this Appendix, we justify formulas and , and give proofs for Propositions \[prop:global:positivity\] and \[prop:global:positivity:too\], and Theorem \[theo:global-models\].
Let us define the gambles $${{\varpi}_{s}^{\mu}}\coloneqq{{\underline{{P}}}_{{{\downarrow}s}}({\phi^\mu_s}\vert{X_{{m(s)}}})}\in{\mathcal{L}({\mathcal{X}_{{m(s)}}})},\quad s{\sqsubseteq}t$$ and, with obvious notations, $${{\underline{\overline{{\varpi}}}}_{s}}\coloneqq{{\overline{\underline{{P}}}}_{{{\downarrow}s}}({\phi^\mu_s}\vert{X_{{m(s)}}})}\in{\mathcal{L}({\mathcal{X}_{{m(s)}}})},\quad s{\not\sqsubseteq}t.$$ Let the chain ${{\uparrow}t}$ be given by $\{t_1,\dots,t_r\}$, where $t_1\coloneqq{\square}$, $t_r\coloneqq t$ and $t_k\coloneqq{m(t_{k+1})}$ for $k=1,\dots,r-1$. If we apply the recursion equation in $s=t_1$ and take into account the separate coherence and the strong factorisation of the conditionally independent natural extension ${{\underline{{P}}}_{{{\downarrow}{C_{}(t_1)}}}({\cdot}\vert{X_{t_1}})}$, we see that $$\label{eq:justification:one}
{{\varpi}_{t_1}^{\mu}}
={{\varpi}_{{\square}}^{\mu}}
=\rho_g(\mu)
={{\underline{{P}}}_{}}(\phi^\mu_{t_1})
={{\underline{{Q}}}_{t_1}}(\psi^\mu_{t_1}),$$ where \[provided that $t_1\neq t$ and therefore $r>1$\] $$\begin{aligned}
\psi^\mu_{t_1}
&\coloneqq{{\underline{{P}}}_{{{\downarrow}{C_{}(t_1)}}}({\phi^\mu_{t_1}}\vert{X_{t_1}})}
={{\underline{{P}}}_{{{\downarrow}{C_{}(t_1)}}}\bigg({{g^\mu_{t_1}\smashoperator{\prod_{c\in{C_{}(t_1)}}}\phi^\mu_c}}\Big\vert{X_{t_1}}\bigg)}
=g^\mu_{t_1}{{\underline{{P}}}_{{{\downarrow}{C_{}(\prod_{c\in{C_{}(t_1)}})}}}\bigg({{\smashoperator[r}\Big\vert{X_{\prod_{c\in{C_{}(t_1)}}}}\bigg)}\phi^\mu_c}]{t_1}\notag\\
&=g^\mu_{t_1}{{\underline{{P}}}_{{{\downarrow}{C_{}(t_2)}}}\bigg({{{{\underline{{P}}}_{{{\downarrow}t_1}}({\phi^\mu_{t_2}}\Big\vert{X_{t_2}}\bigg)}{t_1}
\smashoperator{\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}}}\phi^\mu_c}}\vert{X_{=}})}g^\mu_{t_1}{{\underline{{P}}}_{{{\downarrow}{C_{}(t_1)}}}\bigg({{{{\varpi}_{t_2}^{\mu}}
\smashoperator{\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}}}\phi^\mu_c}}\Big\vert{X_{t_1}}\bigg)}\notag\\
&=\bigg[
\max\{{{\varpi}_{t_2}^{\mu}},0\}
{{\underline{{P}}}_{{{\downarrow}{C_{}(\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}})}}}\bigg({{\smashoperator[r}\Big\vert{X_{\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}}}}\bigg)}\phi^\mu_c}]{t_1}
+\min\{{{\varpi}_{t_2}^{\mu}},0\}
{{\overline{{P}}}_{{{\downarrow}{C_{}(\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}})}}}\bigg({{\smashoperator[r}\Big\vert{X_{\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}}}}\bigg)}\phi^\mu_c}]{t_1}
\bigg]g^\mu_{t_1}\notag\\
&=\bigg[
\max\{{{\varpi}_{t_2}^{\mu}},0\}
\smashoperator{\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}}}{{\underline{{\varpi}}}_{c}}
+\min\{{{\varpi}_{t_2}^{\mu}},0\}
\smashoperator{\prod_{c\in{C_{}(t_1)}\setminus{\{t_2\}}}}{{\overline{{\varpi}}}_{c}}
\bigg]g^\mu_{t_1}. \label{eq:justification:two}
\end{aligned}$$ Similarly, we find that $$\label{eq:justification:three}
{{\varpi}_{t_2}^{\mu}}
={{\underline{{P}}}_{{{\downarrow}t_2}}({\phi^\mu_{t_2}}\vert{X_{t_1}})}
={{\underline{{Q}}}_{t_2}({\psi^\mu_{t_2}}\vert{X_{t_1}})},$$ where \[provided that $t_2\neq t$ and therefore $r>2$\] in a completely similar way as above $$\label{eq:justification:four}
\psi^\mu_{t_2}
\coloneqq{{\underline{{P}}}_{{{\downarrow}{C_{}(t_2)}}}({\phi^\mu_{t_2}}\vert{X_{t_2}})}
=\bigg[
\max\{{{\varpi}_{t_3}^{\mu}},0\}
\smashoperator{\prod_{c\in{C_{}(t_2)}\setminus{\{t_3\}}}}{{\underline{{\varpi}}}_{c}}
+\min\{{{\varpi}_{t_3}^{\mu}},0\}
\smashoperator{\prod_{c\in{C_{}(t_2)}\setminus{\{t_3\}}}}{{\overline{{\varpi}}}_{c}}
\bigg]g^\mu_{t_2}.$$ We can go on in this way until we come to $t_r=t$: $$\label{eq:justification:five}
{{\varpi}_{t_r}^{\mu}}
={{\underline{{P}}}_{{{\downarrow}t_r}}({\phi^\mu_{t_r}}\vert{X_{t_{r-1}}})}
={{\underline{{Q}}}_{t_r}({\psi^\mu_{t_r}}\vert{X_{t_{r-1}}})},$$ where, using the separate coherence and the strong factorisation of the conditionally independent natural extension ${{\underline{{P}}}_{{{\downarrow}{C_{}(t_r)}}}({\cdot}\vert{X_{t_r}})}$, $$\begin{aligned}
\psi^\mu_{t}
=\psi^\mu_{t_r}
&\coloneqq{{\underline{{P}}}_{{{\downarrow}{C_{}(t_r)}}}({\phi^\mu_{t_r}}\vert{X_{t_r}})}
={{\underline{{P}}}_{{{\downarrow}{C_{}(t_r)}}}\bigg({{g^\mu_{t_r}\smashoperator{\prod_{c\in{C_{}(t_r)}}}\phi^\mu_c}}\Big\vert{X_{t_r}}\bigg)}
={{\underline{{P}}}_{{{\downarrow}{C_{}(\smashoperator)}}}\bigg({{[g-\mu}\Big\vert{X_{\smashoperator}}\bigg)}{\prod_{c\in{C_{}(t_r)}}}\phi^\mu_c}]{t_r}\notag\\
&=\max\{g-\mu,0\}{{\underline{{P}}}_{{{\downarrow}{C_{}(\prod_{c\in{C_{}(t_r)}})}}}\bigg({{\smashoperator[r}\Big\vert{X_{\prod_{c\in{C_{}(t_r)}}}}\bigg)}\phi^\mu_c}]{t_r}
+\min\{g-\mu,0\}{{\overline{{P}}}_{{{\downarrow}{C_{}(\prod_{c\in{C_{}(t_r)}})}}}\bigg({{\smashoperator[r}\Big\vert{X_{\prod_{c\in{C_{}(t_r)}}}}\bigg)}\phi^\mu_c}]{t_r}\notag\\
&=\max\{g-\mu,0\}\smashoperator{\prod_{c\in{C_{}(t)}}}{{\underline{{\varpi}}}_{c}}
+\min\{g-\mu,0\}\smashoperator{\prod_{c\in{C_{}(t)}}}{{\overline{{\varpi}}}_{c}}.\label{eq:justification:six}
\end{aligned}$$ Clearly, if we can prove that ${{\underline{\overline{{\varpi}}}}_{s}}={{\underline{\overline{{\pi}}}}_{s}}$ for all $s{\not\sqsubseteq}t$, it will follow from the considerations above that also ${{\varpi}_{s}^{\mu}}={{\pi}_{s}^{\mu}}$ for all $s{\sqsubseteq}t$, and then the proof is complete. This is what we now set out to do. Consider any $s{\not\sqsubseteq}t$. Then applying the recursion equation and taking into account the separate coherence and the strong factorisation of the conditionally independent natural extension ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$, we see that, provided $s$ is not a terminal node, and with obvious notations, $$\label{eq:justification:seven}
{{\underline{\overline{{\varpi}}}}_{s}}
={{\overline{\underline{{P}}}}_{{{\downarrow}s}}({\phi^\mu_{s}}\vert{X_{{m(s)}}})}
={{\underline{\overline{{Q}}}}_{s}({\overline{\underline{\psi}}_s}\vert{X_{{m(s)}}})},$$ where $$\begin{aligned}
\overline{\underline{\psi}}_{s}
&\coloneqq{{\overline{\underline{{P}}}}_{{{\downarrow}{C_{}(s)}}}({\phi^\mu_{s}}\vert{X_{s}})}
={{\overline{\underline{{P}}}}_{{{\downarrow}{C_{}(s)}}}\bigg({{g^\mu_{s}\smashoperator{\prod_{c\in{C_{}(s)}}}\phi^\mu_c}}\Big\vert{X_{s}}\bigg)}
=g^\mu_{s}{{\overline{\underline{{P}}}}_{{{\downarrow}{C_{}(\prod_{c\in{C_{}(s)}})}}}\bigg({{\smashoperator[r}\Big\vert{X_{\prod_{c\in{C_{}(s)}}}}\bigg)}\phi^\mu_c}]{s}\notag\\
&=g^\mu_s\smashoperator{\prod_{c\in{C_{}(s)}}}
{{\overline{\underline{{P}}}}_{{{\downarrow}c}}({\phi^\mu_c}\vert{X_{s}})}
=g^\mu_s\smashoperator{\prod_{c\in{C_{}(s)}}}{{\underline{\overline{{\varpi}}}}_{c}}.\label{eq:justification:eight}
\end{aligned}$$ If on the other hand $s$ is a terminal node, then we can use Eq. to find that $$\label{eq:justification:nine}
{{\underline{\overline{{\varpi}}}}_{s}}
={{\overline{\underline{{P}}}}_{{{\downarrow}s}}({\phi^\mu_{s}}\vert{X_{{m(s)}}})}
={{\underline{\overline{{Q}}}}_{s}({\phi^\mu_{s}}\vert{X_{{m(s)}}})}
={{\underline{\overline{{Q}}}}_{s}({g^\mu_{s}}\vert{X_{{m(s)}}})}
= {{\underline{\overline{{\pi}}}}_{s}},$$ where the last equality follows from Eq. . Now combine Eqs. – and use recursion to complete the proof.
Fix any ${x_{{T}}}$ in ${\mathcal{X}_{{T}}}$. We need to prove that ${{\overline{{P}}}_{}}({{\{{x_{T}}\}}})>0$ and that ${{\overline{{P}}}_{{{\downarrow}S}}({{{\{{x_{{{\downarrow}S}}}\}}}}\vert{z_{s}})}>0$ for all $s\in{{T}^\lozenge}$, non-empty $S\subseteq{C_{}(s)}$ and ${z_{s}}\in{\mathcal{X}_{s}}$. Our argumentation is similar to a special case of the one in Section \[sec:calculating-rho\]. We use the notation established there, but with in particular $g\coloneqq\mu+1$, $t\coloneqq{\square}$ and $E\coloneqq{T}$. This implies that $g^\mu={{\mathbb{I}_{\{{x_{T}}\}}}}$, $g^\mu_s={{\mathbb{I}_{\{{x_{s}}\}}}}$ and $\phi^\mu_s={{\mathbb{I}_{\{{x_{{{\downarrow}s}}}\}}}}$. In accordance with Eq. , we define the messages ${{\overline{{\pi}}}_{s}}\in{\mathcal{L}({\mathcal{X}_{{m(s)}}})}$ and ${{\overline{{\lambda}}}_{s}}\in{\mathcal{L}({\mathcal{X}_{s}})}$ recursively by: $$\label{eq:global:positivity}
{{\overline{{\lambda}}}_{s}}\coloneqq\prod_{c\in{C_{}(s)}}{{\overline{{\pi}}}_{c}}
\text{ and }
{{\overline{{\pi}}}_{s}}
\coloneqq{{\overline{{Q}}}_{s}({{{\mathbb{I}_{\{{x_{s}}\}}}}{{\overline{{\lambda}}}_{s}}}\vert{X_{{m(s)}}})}
={{\overline{{\lambda}}}_{s}}({x_{s}}){{\overline{{Q}}}_{s}({{{\{{x_{s}}\}}}}\vert{X_{{m(s)}}})},
\quad s\in{T}$$ with, as before by convention ${{\overline{{\lambda}}}_{s}}\coloneqq1$ in all leaves $s$. The last equality follows from the separate coherence of the local models ${{\overline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ and the fact that all messages ${{\overline{{\pi}}}_{s}}$ and ${{\overline{{\lambda}}}_{s}}$ are non-negative. It is clear from the recursion equations and \[see also Eq. , the proof is completely similar to that of Eqs. and given above\] that ${{\overline{{P}}}_{{{\downarrow}s}}({{{\{{x_{{{\downarrow}s}}}\}}}}\vert{X_{{m(s)}}})}={{\overline{{\pi}}}_{s}}$, for all $s\in{T}$, and that ${{\overline{{P}}}_{{{\downarrow}{C_{}(s)}}}({{{\{{x_{{{\downarrow}{C_{}(s)}}}}\}}}}\vert{X_{s}})}={{\overline{{\lambda}}}_{s}}$ for all $s\in{{T}^\lozenge}$. Similarly, it follows from Eq. , conjugacy and the strong factorisation property of the conditionally independent natural extension that ${{\overline{{P}}}_{{{\downarrow}S}}({{{\{{x_{{{\downarrow}S}}}\}}}}\vert{X_{s}})}=\prod_{c\in S}{{\overline{{\pi}}}_{c}}$ for all $s\in{{T}^\lozenge}$ and all non-empty $S\subseteq{C_{}(s)}$. So we have to prove that all values (all components) of all messages ${{\overline{{\pi}}}_{s}}$, $s\in{T}$ are (strictly) positive. This follows at once from the recursion equation and the assumed strict positivity of the local models ${{\overline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$.
Our argumentation is similar to a special case of the one in Section \[sec:calculating-rho\]. We also use notation similar to that established there, with in particular $g\coloneqq\mu+1$ and $t\coloneqq{\square}$. In accordance with Eq. , we define the messages ${{\overline{{\pi}}}_{s}}\in{\mathcal{L}({\mathcal{X}_{{m(s)}}})}$ and ${{\overline{{\lambda}}}_{s}}\in{\mathcal{L}({\mathcal{X}_{s}})}$ recursively by: $$\label{eq:global:positivity:too}
{{\overline{{\lambda}}}_{s}}\coloneqq\prod_{c\in{C_{}(s)}}{{\overline{{\pi}}}_{c}},
\quad s\in{T}$$ and $$\label{eq:global:positivity:ttoo}
{{\overline{{\pi}}}_{s}}\coloneqq
\begin{cases}
{{\overline{{\lambda}}}_{s}}({x_{s}}){{\overline{{Q}}}_{s}({{{\{{x_{s}}\}}}}\vert{X_{{m(s)}}})}
&\text{ if $s\in E$}\\
{{\overline{{Q}}}_{s}({{{\overline{{\lambda}}}_{s}}}\vert{X_{{m(s)}}})}
&\text{ if $s\in{T}\setminus E$}.
\end{cases}$$ with, as before by convention ${{\overline{{\lambda}}}_{s}}\coloneqq1$ in all leaves $s$. All these messages are non-negative by construction. It is clear from the recursion equations and \[see also Eq. , the proof is completely similar to that of Eqs. and given above\] that ${{\overline{{P}}}_{{{\downarrow}s}}({{{\{{x_{E\cap{{\downarrow}s}}}\}}}}\vert{X_{{m(s)}}})}={{\overline{{\pi}}}_{s}}$ for all $s\in{T}$. Now it follows from the recursion equations and and the assumption ${\overline{{P}}}({{\{{x_{E}}\}}})={{\overline{{\pi}}}_{{\square}}}>0$ that ${{\overline{{\lambda}}}_{e}}({x_{e}})>0$ for all $e\in E$. Again applying Eq. , we find that indeed ${{\overline{{\pi}}}_{c}}({x_{e}})>0$ for all $c\in{C_{}(e)}$.
Our proof of Theorem \[theo:global-models\] relies heavily on a very convenient coherence result proved by Enrique Miranda [@miranda2009a Theorem 6], which we relate here to make the paper more self-contained. We use the notations established in the context of Section \[sec:independent-natural-extension\].
\[theo:blessyouquique\] Let ${\underline{{P}}}$ be a (separately) coherent lower prevision on ${\mathcal{L}({\mathcal{X}_{N}})}$, and consider $m$ disjoint pairs of subsets $O_k$ and $I_k$ of $N$, $k=1,\dots,m$. Assume that ${\overline{{P}}}({{\{{x_{I_k}}\}}})>0$ for all ${x_{I_k}}\in{\mathcal{X}_{I_k}}$, $k=1,\dots,m$ and use regular extension to define the conditional lower previsions ${\underline{R}({\cdot}\vert{X_{I_k}})}$ on ${\mathcal{L}({\mathcal{X}_{O_k}})}$, for $k=1,\dots,m$. Then the (conditional) lower previsions ${\underline{{P}}}$, ${\underline{R}({\cdot}\vert{X_{I_1}})}$, …, ${\underline{R}({\cdot}\vert{X_{I_m}})}$ are (jointly) coherent.
We begin by showing that the family of models ${\mathcal{T}(\underline{P})}$ satisfies requirements T\[item:global:local\]–T\[item:global:irrelevance\].
To prove T\[item:global:local\], consider any $s\in{T}$, and any $f\in{\mathcal{L}({\mathcal{X}_{s}})}$, then it follows from separate coherence that ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({f}\vert{X_{s}})}=f$, and therefore we infer from the recursion equation that indeed ${{\underline{{P}}}_{{{\downarrow}s}}({f}\vert{X_{{m(s)}}})}={{\underline{{Q}}}_{s}({{{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({f}\vert{X_{{m(s)}}})}}}\vert{X_{s}})}={{\underline{{Q}}}_{s}({f}\vert{X_{{m(s)}}})}$.
Next, we turn to the proof of T\[item:global:coherence\] and T\[item:global:irrelevance\]. Consider any $s\in{{T}^\lozenge}$, $S\subseteq{C_{}(s)}$ and $R\subseteq{\overline{S}}$. Let ${x_{{\{s\}}\cup R}}\in{\mathcal{X}_{{\{s\}}\cup R}}$ and $f\in{\mathcal{L}({\mathcal{X}_{{{\downarrow}S}\cup{\{s\}}\cup R}})}$. We calculate the following regular extension of the joint: $$\label{eq:coherence-rext-new-one}
{\underline{R}({f}\vert{x_{{\{s\}}\cup R}})}
=\max{\{\mu\in{\mathbb{R}}\colon{\underline{{P}}}({{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu])\geq0\}}.$$ Consider that $${{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu]={{\mathbb{I}_{\{{x_{s}}\}}}}{{\mathbb{I}_{\{{x_{R}}\}}}}[g-\mu],$$ where $g\coloneqq f(\cdot,{x_{s}},{x_{R}})\in{\mathcal{L}({\mathcal{X}_{{{\downarrow}S}}})}$. Let $t_2$ be the unique child of $t_1\coloneqq{\square}$ such that $s\in{{\downarrow}t_2}$ \[assuming of course that $s\neq t_1={\square}$\]. By using separate coherence, recursion equations , and , and the strong factorisation property \[see Proposition \[prop:independent-factorising\]\] of the conditionally independent natural extension, in a way similar to the argumentation in Section \[sec:calculating-rho\], we see that $$\begin{aligned}
{\underline{{P}}}({{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu])
&={{\underline{{Q}}}_{t_1}}({{\underline{{P}}}_{{{\downarrow}}}}({{{{\mathbb{I}_{\{{x_{R\setminus{{\downarrow}t_2}}}\}}}}{{\underline{{P}}}_{{{\downarrow}}}}({{{{\mathbb{I}_{\{{x_{s}}\}}}}{{\mathbb{I}_{\{{x_{R\cap{{\downarrow}t_2}}}\}}}}[g-\mu}\vert{X_{}}\vert{X_{)}})}}
{{C_{}(t_1)}}{t_1}}]{{C_{}(t_1)}}{t_1})\\
&={{\underline{{Q}}}_{t_1}}({{\underline{{P}}}_{{{\downarrow}}}}({{h_2{{\underline{{P}}}_{{{\downarrow}}}}({{{{\mathbb{I}_{\{{x_{s}}\}}}}{{\mathbb{I}_{\{{x_{R\cap{{\downarrow}t_2}}}\}}}}[g-\mu}\vert{X_{}}\vert{X_{)}})}}{t_2}{t_1}}]
{{C_{}(t_1)}}{t_1})\\
&={{\underline{{P}}}_{{{\downarrow}t_1}}}(h_2{{\underline{{P}}}_{{{\downarrow}}}}({{{{\mathbb{I}_{\{{x_{s}}\}}}}{{\mathbb{I}_{\{{x_{R\cap{{\downarrow}t_2}}}\}}}}[g-\mu}\vert{X_{]}})}{t_2}{t_1}),\end{aligned}$$ where $h_2\coloneqq{{\mathbb{I}_{\{{x_{R\setminus{{\downarrow}t_2}}}\}}}}\geq0$. Similarly, let $t_3$ be the unique child of $t_2$ such that $s\in{{\downarrow}t_3}$ \[assuming of course that $s\neq t_2$\]. Then we see in the same way as above that $${{\underline{{P}}}_{{{\downarrow}}}}({{{{\mathbb{I}_{\{{x_{s}}\}}}}{{\mathbb{I}_{\{{x_{R\cap{{\downarrow}t_2}}}\}}}}[g-\mu}\vert{X_{]}})}{t_2}{t_1}
={{\underline{{P}}}_{{{\downarrow}}}}({{h_3{{\underline{{P}}}_{{{\downarrow}}}}({{{{\mathbb{I}_{\{{x_{s}}\}}}}{{\mathbb{I}_{\{{x_{R\cap{{\downarrow}t_3}}}\}}}}[g-\mu}\vert{X_{}}\vert{X_{)}})}}{t_3}{t_2}}]{t_2}{t_1},$$ where $h_3\coloneqq{{\mathbb{I}_{\{{x_{R\setminus{{\downarrow}t_3}}}\}}}}\geq0$. Continuing in this way, we eventually come to the conclusion that $$\label{eq:coherence-new-one}
{\underline{{P}}}({{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu])
=\underline{G}({{\underline{{P}}}_{{{\downarrow}{C_{}()}}}}({{h{{\mathbb{I}_{\{{x_{s}}\}}}}[g-\mu}\vert{X_{}}})}]{s}),$$ where $h\coloneqq{{\mathbb{I}_{\{{x_{R\cap{{\downarrow}{C_{}(s)}}}}\}}}}={{\mathbb{I}_{\{{x_{R\cap({{\downarrow}{C_{}(s)}}\setminus{{\downarrow}S})}}\}}}}$, and where the real functional $\underline{G}$ on ${\mathcal{L}({\mathcal{X}_{s}})}$ is essentially constructed as follows. Consider the segment $t_1t_2\dots t_{r-1}t_r$ connecting ${\square}$ and $s$, i.e. $t_r\coloneqq s$, $t_{r-1}\coloneqq{m(t_r)}$, …, $t_{k}\coloneqq{m(t_{k+1})}$, …, $t_1\coloneqq{m(t_{2})}={\square}$. Then there are non-negative $h_k$ on ${\mathcal{X}_{{{\downarrow}t_k}}}$ such that for all $f\in{\mathcal{L}({\mathcal{X}_{s}})}$, $\underline{G}(f)=f_1$, where $f_r\coloneqq f$ and $f_{k}\coloneqq{{\underline{{P}}}_{{{\downarrow}t_{k+1}}}({{h_{k+1}f_{k+1}}}\vert{X_{t_k}})}$, $k=1,\dots,r-1$. \[If $r=1$, or in other words $s=t_1={\square}$, just let $\underline{G}\coloneqq{{\underline{{P}}}_{{{\downarrow}{\square}}}}$.\] In other words, the functional $\underline{G}$ results from recursively multiplying with non-negative maps and applying global conditional lower previsions. As such, $\underline{G}$ is non-negatively homogeneous and super-additive \[because the successive multiplication and composition preserves these properties\]. In addition, it does not depend on $g$ nor $\mu$. If we use the separate coherence of ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$, the strong factorisation, associativity and marginalisation properties of the conditionally independent natural extension ${{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({\cdot}\vert{X_{s}})}$ \[see Proposition \[prop:independent-factorising\], Eqs. and , and the recursion equations and \], and the separate coherence of the conditional lower prevision ${{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{x_{s}})}$, we get: $$\begin{aligned}
{{\underline{{P}}}_{{{\downarrow}}}}({{h{{\mathbb{I}_{\{{x_{s}}\}}}}[g-\mu}\vert{X_{]}})}{{C_{}(s)}}{s}
&={{\mathbb{I}_{\{{x_{s}}\}}}}{{\underline{{P}}}_{{{\downarrow}}}}({{h[g-\mu}\vert{x_{]}})}{{C_{}(s)}}{s}\notag\\
&={{\mathbb{I}_{\{{x_{s}}\}}}}
\begin{cases}
{{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({h}\vert{x_{s}})}[{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}-\mu]
&\text{if ${{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\geq\mu$}\\
{{\overline{{P}}}_{{{\downarrow}{C_{}(s)}}}({h}\vert{x_{s}})}[{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}-\mu]
&\text{if ${{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\leq\mu$}.
\end{cases}
\label{eq:coherence-new-two}
\end{aligned}$$ Combining Eqs. and , and invoking the non-negative homogeneity of the real functional $\underline{G}$, this leads to: $${\underline{{P}}}({{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu])
=
\begin{cases}
\underline{G}({{\mathbb{I}_{\{{x_{s}}\}}}}){{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({h}\vert{x_{s}})}[{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}-\mu]
&\text{if ${{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\geq\mu$}\\
\overline{G}({{\mathbb{I}_{\{{x_{s}}\}}}}){{\overline{{P}}}_{{{\downarrow}{C_{}(s)}}}({h}\vert{x_{s}})}[{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}-\mu]
&\text{if ${{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\leq\mu$},
\end{cases}$$ where we let $\overline{G}({{\mathbb{I}_{\{{x_{s}}\}}}})\coloneqq-\underline{G}(-{{\mathbb{I}_{\{{x_{s}}\}}}})$. By letting $f=\mu\pm1$ \[and therefore also $g=\mu\pm1$\] in this expression, we derive in particular that $${\underline{{P}}}({{\{{x_{{\{s\}}\cup R}}\}}})
=\underline{G}({{\mathbb{I}_{\{{x_{s}}\}}}}){{\underline{{P}}}_{{{\downarrow}{C_{}(s)}}}({h}\vert{x_{s}})}
\text{ and }
{\overline{{P}}}({{\{{x_{{\{s\}}\cup R}}\}}})
=\overline{G}({{\mathbb{I}_{\{{x_{s}}\}}}}){{\overline{{P}}}_{{{\downarrow}{C_{}(s)}}}({h}\vert{x_{s}})},$$ and therefore also $${\underline{{P}}}({{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu])\\
=
\begin{cases}
{\underline{{P}}}({{\{{x_{{\{s\}}\cup R}}\}}})[{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}-\mu]
&\text{if ${{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\geq\mu$}\\
{\overline{{P}}}({{\{{x_{{\{s\}}\cup R}}\}}})[{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}-\mu]
&\text{if ${{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\leq\mu$}.
\end{cases}$$ Since we have assumed that all local models ${{\overline{{Q}}}_{s}({\cdot}\vert{X_{{m(s)}}})}$ are strictly positive, we gather from Proposition \[prop:global:positivity\] that ${\overline{{P}}}({{\{{x_{{\{s\}}\cup R}}\}}})>0$, and therefore $${\underline{{P}}}({{\mathbb{I}_{\{{x_{{\{s\}}\cup R}}\}}}}[f-\mu])\geq0
{\Leftrightarrow}{{\underline{{P}}}_{{{\downarrow}S}}({g}\vert{x_{s}})}\geq\mu.$$ This allows us to infer from Eq. that $$\label{eq:coherence-rext-new-two}
{\underline{R}({f}\vert{x_{{\{s\}}\cup R}})}
={{\underline{{P}}}_{{{\downarrow}S}}({f(\cdot,{x_{s}},{x_{R}})}\vert{x_{s}})}
\text{ for all $f\in{\mathcal{L}({\mathcal{X}_{{{\downarrow}S}\cup{\{s\}}\cup R}})}$ and ${x_{{\{s\}}\cup R}}\in{\mathcal{X}_{{\{s\}}\cup R}}$}.$$ If we now combine Eq. with Theorem \[theo:blessyouquique\], we see that both T\[item:global:coherence\] and T\[item:global:irrelevance\] hold.
To complete the proof, we consider T\[item:global:smallest\]. Consider any family of models ${\mathcal{T}(\underline{V})}$ that satisfies conditions T\[item:global:local\]–T\[item:global:irrelevance\]. Then we want to show that $$\label{eq:dominance-one}
{{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}\geq{{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}
\text{ for all $t\in{{T}^\lozenge}$ and all non-empty $S\subseteq{C_{}(s)}$}$$ and $$\label{eq:dominance-two}
{{\underline{{V}}}_{}}\geq{{\underline{{P}}}_{}}.$$ The proof proceeds in a recursive (inductive) fashion. Since the ${{\underline{{V}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}$ satisfy T\[item:global:local\], we infer in particular that $${{\underline{{V}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}={{\underline{{P}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}={{\underline{{Q}}}_{t}({\cdot}\vert{X_{{m(t)}}})}
\text{ for all terminal nodes $t$}.$$ It is therefore clearly sufficient to prove the following statement for all non-terminal nodes $t\in{{T}^\lozenge}$: $$\label{eq:induction-step}
(\forall c\in{C_{}(t)})
({{\underline{{V}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}\geq{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})})
{\Rightarrow}\left\{
\begin{aligned}
&{{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}\geq{{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}
\text{ for all non-empty $S\subseteq{C_{}(t)}$}\\
&{{\underline{{V}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}\geq{{\underline{{P}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}.
\end{aligned}
\right.$$ This is what we now set out to do. Fix any non-terminal node $t\in{{T}^\lozenge}$ and any non-empty $S\subseteq{C_{}(t)}$, and assume that ${{\underline{{V}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}\geq{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}$ for all $c\in{C_{}(t)}$.
First of all, define for any disjoint proper subsets $I$ and $O$ of $S$, the conditional lower previsions ${{\underline{{V}}}_{{{\downarrow}O}}({\cdot}\vert{X_{{\{t\}}\cup{{\downarrow}I}}})}$ through: $${{\underline{{V}}}_{{{\downarrow}O}}({f}\vert{x_{{\{t\}}\cup{{\downarrow}I}}})}
={{\underline{{V}}}_{{{\downarrow}O}}({f(\cdot,{x_{{{\downarrow}I}}})}\vert{x_{t}})}
\text{ for all $f\in{\mathcal{L}({\mathcal{X}_{{{\downarrow}O}\cup{{\downarrow}I}}})}$ and all ${x_{{\{t\}}\cup{{\downarrow}I}}}\in{\mathcal{X}_{{\{t\}}\cup{{\downarrow}I}}}$}.$$ Then we infer from T\[item:global:irrelevance\] \[with $S=O$, $s=t$ and $R={{\downarrow}I}\subseteq{\overline{O}}$\] that all these conditional lower previsions are in particular (jointly) coherent with the conditional lower prevision ${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}$. If we recall Definition \[def:conditionally:independent:product\] \[with $N={\{{{\downarrow}c}\colonc\in S\}}$ and ${Y}={X_{t}}$\], we conclude that ${{\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}({\cdot}\vert{X_{t}})}$ is a conditionally independent product of the ‘marginals’ ${{\underline{{V}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}$, $c\in S$, which therefore dominates the smallest such independent product: $${{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}
\geq\otimes_{c\in S}{{\underline{{V}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}$$ and therefore, using the assumption, we infer from this inequality that $$\label{eq:other-step-two}
{{\underline{{V}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})}
\geq\otimes_{c\in S}{{\underline{{V}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}
\geq\otimes_{c\in S}{{\underline{{P}}}_{{{\downarrow}c}}({\cdot}\vert{X_{t}})}
={{\underline{{P}}}_{{{\downarrow}S}}({\cdot}\vert{X_{t}})},$$ where we have also used, successively, the monotonicity property of the conditionally independent natural extension \[see [@cooman2009b] for a proof\] and the recursion equations and .
Next, define the conditional lower prevision ${\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}(\cdot\vert{X_{{\{{m(t)},t\}}}})$ on ${\mathcal{L}({\mathcal{X}_{{{\{{m(t)}\}}}\cup{{\downarrow}t}}})}$ through: $$\begin{gathered}
\label{eq:other-step-three}
{\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}(f\vert{x_{{\{{m(t)},t\}}}})
\coloneqq
{{\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}({f({x_{{m(t)}}},{x_{t}},\cdot)}\vert{x_{t}})}\\
\text{for all $f\in{\mathcal{L}({\mathcal{X}_{{{\{{m(t)}\}}}\cup{{\downarrow}t}}})}$ and all ${x_{{\{{m(t)},t\}}}}\in{\mathcal{X}_{{\{{m(t)},t\}}}}$}.
\end{gathered}$$ Then we infer from T\[item:global:irrelevance\] \[with $s=t$, $S={C_{}(t)}$ and $R={{\{{m(t)}\}}}\subseteq{\overline{{C_{}(t)}}}$\] that this conditional lower prevision ${\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}(\cdot\vert{X_{{\{{m(t)},t\}}}})$ is in particular (jointly) coherent with the conditional lower prevision ${{\underline{{V}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}$ defined on ${\mathcal{L}({\mathcal{X}_{{{\{{m(t)}\}}}\cup{{\downarrow}t}}})}$. We then see that for all $g\in{\mathcal{L}({\mathcal{X}_{{{\downarrow}t}}})}$: $$\begin{aligned}
{{\underline{{V}}}_{{{\downarrow}t}}({g}\vert{X_{{m(t)}}})}
&\geq{{\underline{{V}}}_{{{\downarrow}t}}({{{\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}(g\vert{X_{{\{{m(t)},t\}}}})}}\vert{X_{{m(t)}}})}\\
&={{\underline{{V}}}_{{{\downarrow}t}}({{{{\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}({g}\vert{X_{{m(t)}}})}}}\vert{X_{t}})}
={{\underline{{Q}}}_{t}({{{{\underline{{V}}}_{{{\downarrow}{C_{}(t)}}}({g}\vert{X_{{m(t)}}})}}}\vert{X_{t}})}\\
&\geq{{\underline{{Q}}}_{t}({{{{\underline{{P}}}_{{{\downarrow}{C_{}(t)}}}({g}\vert{X_{{m(t)}}})}}}\vert{X_{t}})}\\
&={{\underline{{P}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}.
\end{aligned}$$ The first equality follows from Eq. , the second one holds because the global models ${{\underline{{V}}}_{{{\downarrow}t}}({\cdot}\vert{X_{{m(t)}}})}$ satisfy T\[item:global:local\], and the third one follows from recursion equation . The first inequality follows if we apply Walley’s Marginal Extension Theorem[^24] [@walley1991 Theorem 6.7.2] in the formulation of [@miranda2006b Theorem 4]. The second inequality follows from the inequality and the non-decreasing character of ${{\underline{{Q}}}_{t}({\cdot}\vert{X_{{m(t)}}})}$, which follows from separate coherence. This completes our proof that T\[item:global:smallest\] is also satisfied.
The last part of the proof follows at once from Eqs. \[with $R=\emptyset$\], and Theorem \[theo:blessyouquique\].
[^1]: For a detailed argumentation and exposition of this point of view, we refer to [@walley1991 Chapter 5].
[^2]: Obviously, there will be special cases where strong independence is justified in order to model an expert’s knowledge. Moreover, strong independence could provide a good approximation to more accurate models, even when it is not entirely appropriate. This is something that seems to deserve further investigation.
[^3]: If we ignore issues related to events with probability zero.
[^4]: \[fn:empty-product\] For any subset $S$ of ${T}$, ${\mathcal{X}_{S}}$ is defined formally as the set of all maps ${x_{S}}$ of $S$ to $\bigcup_{s\in S}{\mathcal{X}_{s}}$, such that ${x_{S}}(s)={x_{s}}\in{\mathcal{X}_{s}}$ for all $s\in S$. So when $S=\emptyset$, the empty product ${\mathcal{X}_{\emptyset}}$ is defined as the set of all maps from $\emptyset$ to $\emptyset$, which is a singleton. The corresponding variable ${X_{\emptyset}}$ can then only assume this single value, so there is no uncertainty about it. ${\mathcal{L}({\mathcal{X}_{\emptyset}})}$ can be identified with the set ${\mathbb{R}}$ of real numbers.
[^5]: Besides the letter $V$, we will also use the letters $P$, $Q$ and $R$.
[^6]: In keeping with the observation in footnote \[fn:empty-product\], we also allow $I=\emptyset$, which means conditioning on the variable ${X_{I}}={X_{\emptyset}}$, which can only assume one single value. This means that ${{\underline{{V}}}_{O}(\cdot\vert{X_{\emptyset}})}\eqqcolon{\underline{{V}}}_{O}$ effectively becomes an unconditional lower prevision on ${\mathcal{L}({\mathcal{X}_{O\cup\emptyset}})}={\mathcal{L}({\mathcal{X}_{O}})}$. This a very useful device that allows us to use the same generic notation for both conditional and unconditional lower previsions.
[^7]: For any event $A\subseteq{\mathcal{X}_{I\cup O}}$, we denote ${{\underline{{V}}}_{O}({\mathbb{I}_{A}}\vert{x_{I}})}$ also as ${{\underline{{V}}}_{O}(A\vert{x_{I}})}$ and call this real number the (conditional) lower *probability* of $A$. Similarly ${{\overline{{V}}}_{O}(A\vert{x_{I}})}\coloneqq{{\overline{{V}}}_{O}({\mathbb{I}_{A}}\vert{x_{I}})}$ is the (conditional) upper *probability* of $A$.
[^8]: It suffices, in the discussion below, to let $C=\emptyset$. As we indicated in footnote \[fn:empty-product\], this makes sure the variable ${X_{C}}$ has only one possible value, so conditioning on that variable amounts to not conditioning at all.
[^9]: We can do this because ${X_{{m({\square})}}}={X_{\emptyset}}$ has only one possible value, so conditioning on that variable amounts to not conditioning at all.
[^10]: For leaves $s$, the corresponding irrelevance condition is trivial, as the set ${C_{}(s)}$ of children of $s$ is empty.
[^11]: In [@cooman2009b], we distinguish between many-to-many and many-to-one independent products. It is not necessary to make this distinction here, but whenever we use the term ‘independent product’ in the present paper, we implicitly refer to the more stringent many-to-many version introduced there.
[^12]: This type of independent product comes to the fore in a study of credal nets under strong independence.
[^13]: Marginal extension is, in the special case of precise probability models, also known as the law of total probability, or the law or iterated expectations.
[^14]: Observe that this holds trivially also if $E\cap{{\downarrow}c}=\emptyset$, because then ${\mathcal{X}_{E\cap{{\downarrow}c}}}={\mathcal{X}_{\emptyset}}$ is a singleton \[see footnote \[fn:empty-product\]\] whose upper probability should be $1$ by separate coherence.
[^15]: As the results in [@cooman2009b] suggest, it might be possible to go even further, and prove a counterpart to Theorem \[theo:global-models\] with no positivity restrictions on the local models. We leave this as an avenue for future research, however.
[^16]: This is also the approach implicit in Definition \[def:independent:product\], as well as the one used in [@cooman2009b]. It coincides with the usual, naive approach as soon as all the relevant conditional models are uniquely determined from the joint by coherence.
[^17]: If we look at the proof of this result in the Appendix, it is not hard to see that similar statements can be made about the (joint) coherence of the regular extensions ${\underline{R}({\cdot}\vert{X_{E_k}})}$ for any finite collection $E_k$, $k=1,\dots,n$ of sets of nodes.
[^18]: \[fn:doesntmatter\]This, together with the course of reasoning leading to Eq. , shows that the results of updating the tree (and the algorithm we are deriving) in this way will be exactly the same *for any way* of forming a product of the local models for the children of $s$, *provided only that this product is strongly factorising*. For instance, replacing the conditionally independent natural extension with the strong product in Eq. will lead to exactly the same inferences. Of course, this should not be taken to mean that our algorithm also works for updating credal trees under strong independence.
[^19]: If $s$ is the root node, then ${m(s)}=\emptyset$ and ${{\pi}_{s}^{\mu}}$ is a single real number, which by Eq. is equal to $\rho_g(\mu)$. See also footnote \[fn:empty-product\].
[^20]: Actually, we easily derive that $\rho_g(\mu)
=a\max\{\lambda_g(\mu),0\}+b\min\{\lambda_g(\mu),0\}$, where $a$ and $b$ are real constants that do not depend on $g$ and $\mu$. Letting $g\coloneqq\mu\pm1$ then allows us to identify the constants $a$ and $b$.
[^21]: It could be argued that $b$ should be bounded given the finiteness of a computer’s way to represent numbers.
[^22]: For a more involved application, related to aircraft trajectory model tracking, see [@antonucci2009].
[^23]: Unlike credal nets based on strong independence, a credal net based on epistemic irrelevance cannot generally be seen as equivalent with a set of Bayesian nets *with the same graphical structure*: if it were, then all separation properties of Bayesian nets would simply be inherited, and we have seen in Section \[sec:example\] that such is not the case.
[^24]: Recall that this is a coherence result that generalises the so-called Law of Iterated Expectations to coherent lower previsions.
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