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Q:
List all files in a directory except for an extension
I wonder how do I show all files in a directory with the exception of an extension.
Example: .bat
My code:
Dir /ah-d /b /s "%temp%" >>"Temp.TxT"
Result:
Folder123
image.jpg
TESTE.bat
abc.TMP
Result I want:
Folder123
image.jpg
abc.TMP
Note: The other files may vary extensions.
A:
You can filter the output by piping to FINDSTR, rejecting lines that end with your extension.
The /L option treats the search as a literal search (as opposed to a regular expression). The /E option only matches if at end of line. The /I option makes it case insensitive. The /V option inverts the search, keeping lines that don't match, filtering out the lines that do match
dir /ah-d /b /s "%temp%" | findstr /live .bat >>"temp.txt"
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#!/bin/bash
set -eo pipefail
source ./0-params.sh
### SQL SERVER
# Create a logical server in the resource group
echo "Creating a Azure SQL Server instance $SERVERNAME in $DB_RG."
az sql server create \
--name $SERVERNAME \
--resource-group $DB_RG \
--location $LOCATION \
--admin-user $DBUSER \
--admin-password $DBPASS \
-o table &> $base_source_path/../setup/log/2-database.log
# Configure a firewall rule for the server
echo "Allowing Azure IPs to the Azure SQL Server instance."
az sql server firewall-rule create \
--resource-group $DB_RG \
--server $SERVERNAME \
-n AllowAllAzureIPs \
--start-ip-address $startip \
--end-ip-address $endip \
-o table &>> $base_source_path/../setup/log/2-database.log
# Create a database in the server with zone redundancy as true
echo "Creating the $DATABASENAME database on $SERVERNAME."
az sql db create \
--resource-group $DB_RG \
--server $SERVERNAME \
--name $DATABASENAME \
--service-objective S0 \
--zone-redundant false \
-o table &>> $base_source_path/../setup/log/2-database.log
# Load Data
echo "Loading starting data in $DATABASENAME on $SERVERNAME."
sqlcmd \
-S tcp:$SERVERNAME.database.windows.net,1433 \
-d tailwind \
-U $DBUSER \
-P $DBPASS \
-i ~/source/tailwind-traders/sql_server/tailwind_ss.sql &>> $base_source_path/../setup/log/2-database.log
# ### PostgreSQL
# SKU=B_Gen5_1
# # Create the PostgreSQL service
# az postgres server create \
# --resource-group $DB_RG \
# --name $SERVERNAME \
# --location $LOCATION \
# --admin-user $DBUSER \
# --admin-password $DBPASS \
# --sku-name $SKU \
# --version 10.0
# # Open up the firewall so we can access
# az postgres server firewall-rule create \
# --resource-group $DB_RG \
# --server $SERVERNAME \
# --name AllowAllAzureIPs \
# --start-ip-address $startip \
# --end-ip-address $endip
# echo "Creating the Tailwind database..."
# # Load data
# pushd ~/source/tailwind-traders/postgres/
# psql "postgres://$DBUSER%40$SERVERNAME:$DBPASS@$SERVERNAME.postgres.database.azure.com/postgres" -c "CREATE DATABASE tailwind;"
# psql "postgres://$DBUSER%40$SERVERNAME:$DBPASS@$SERVERNAME.postgres.database.azure.com/tailwind" -f tailwind.sql
# popd
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|
Peyto
Peyto may refer to:
Peyto Lake
Peyto Peak
Peyto Glacier
William Peyto (disambiguation) |
Q:
Unsupervised classification - feature vectors are obtained
I need to classify commercial products. You know what price comparison engines does.
We have obtained the feature vectors. They are not the best yet pretty good. My last step is classifying them without knowing how many clusters there are. So algorithms like k-means won't work since they require how many classes there are.
So here example set of feature vectors. They are in order here (as an example) but i need an algorithm which does not depend on any order.
#################################################
47 - ddr2;asus;1066;g41;am;p5qpl;775;
48 - g41;p5qpl;asus;am;ddr2;vga;anakart;
49 - intel;anakart;ddr2;1066;p5qpl;asus;am;
50 - p5qpl;ddr2;asus;am;g41;vga;anakart;
51 - ddr2;asus;1066;g41;am;p5qpl;775;
52 - g41;p5qpl;1066;am;ddr2;asus;anakart;
53 - p5qpl;ddr2;1066;am;g41;asus;sata;
54 - g41;p5qpl;1066;am;asus;ddr2;sata;
###################################################
55 - engtx480;asus;384bit;2di;gddr5;vga;16x;
56 - 2di;karti;384bit;asus;engtx480;ekran;pci;
57 - asus;engtx480;2di;vga;gddr5;384bit;16x;
58 - 2di;karti;engtx480;384bit;asus;gddr5;1536mb;
59 - engtx480;asus;384bit;2di;gddr5;vga;16x;
60 - engtx480;asus;384bit;2di;gddr5;vga;16x;
####################################################
61 - ray;blu;ihbs112;siyah;bulk;dvd;sata;
62 - ihbs112;ray;blu;on;lite;yazici;kutusuz;
63 - ihbs112;blu;ray;lite;on;siyah;bulk;
64 - blu;ihbs112;ray;lite;on;siyah;yazici;
65 - liteon;ihbs112;bd;yazma;hizi;12x;max;
66 - ihbs112;ray;blu;on;lite;bulk;dvd;
67 - etau108;dvd;siyah;lite;on;rw;ihbs112;
68 - ihbs112;liteon;bd;yazma;hizi;12x;max;
69 - ihbs112;ray;blu;lite;on;siyah;bulk;
#####################################################
When a human look it is easy to classify products with just using these feature vectors. But i need to achieve it via an algorithm. And also i need to achieve it with an algorithm which does not requires any prior information just uses feature vectors.
From the above feature vector set the 47-54 is a cluster , 55-60 another cluster and 61-69 another cluster (each cluster means a commercial product in real life). So the algorithm need to classify these correctly with just using these kind of feature vectors.
The algorithm can not be depended on the line order of the feature vectors or how many classes there will be. We don't know anything and we just have feature vectors.
Waiting your suggestions about this classification problem. Thank you.
A:
Adaptive Resonance Theory is the short answer to your question. Unlike KMeans you dont need to set the number of clusters in advance. The input is a set of feature vectors either binary (ART 1 Algorithm) or continuous (ART -2A, ARTMAP etc.) and the output is classification of documents in clusters.
|
"This is the violet hour, the hour of hush and wonder, when the affectations glow and valor is reborn, when the shadows deepen along the edge of the forest and we believe that, if we watch carefully, at any moment we may see the unicorn."
Monday, September 17, 2012
These days, I *surface* up out of the Opera House to enjoy a free day! Last Saturday, I did just that with a new-found friend, Birgit. She is a German Journalist who is doing a feature interview with one of our *Rigolettos*. We met at a Dress Rehearsal....and swapped *Opera Backstage Stories*... then, much to my surprise, she invited me to go sailing with her! Of course, I said yes! Now, I am a Sea-lover to be sure, but I have NEVER sailed in San Francisco on our choppy waters. But, *armed* with Ginger Capsules (to prevent sea-sickness), I met Birgit at the San Francisco Sailing Company.I arrived a bit early so I could photograph the *infamous* Sea Lions at Pier 39. All was still and relatively quiet...very few tourists up and about ..
Even this fellow was sound asleep!
But, this BIG GUY was wide awake! And so were his friends!
I met Birgit and we found our Ship, the Santa Maria.
It was one of those typical San Francisco *Summer* Days....sunshine to the East, thick fog to the West.
We boarded, along with fifteen other *brave souls* - and set off..
The Bay Bridge and some fog and blue skies!
Alcatraz
Coit Tower and foggy skies..
Headed West...towards the Fog-Shrouded Golden Gate....
Nearing the Bridge.... it was really cold and windy, and the waves were beginning to intensify!
Oh what fun. It looked cold tho. We used to sale in SO CAL when I lived there. Not to far out in the sea tho. mostly around Newport Harbor but that could get pretty hairy with so many Sunday sailor's. lol Nice you made a new friend to share this adventure with..Love the Seals too.
boy you sure are brave. i'm not a boat person and those waters looked rough. but how neat to see the city from a boat. glad you found a new friend. (have had a hard time with my internet connection lately and also doing so much detailed work has left me not wanting to blog much.) but I miss you and all my friends.
Follow La Luna's Silver Path Across the Heavens
Prayers for our World
Help Feed Animals in Shelters - Click Here Daily to Help!
Wonderful Reads
Welcome!
About Me
A lover of all of life's beauties - music, poetry, nature, animals, the ever-changing moon, the smell of jasmine at twilight. Thunder and lightning in the Summertime. The smell of Pinon after the rain. Running through crisp, multi-coloured Autumn leaves with my favourite Chocolate Lab, Walking in the first snowfall of Winter and tasting snow on my tongue. Believing in the power of love - no matter what... |
Q:
Which one is the true statement?
All five statements below are true.
None of the four statements below are true.
Both of the statements above are true.
Exactly one of the three statements above is true.
None of the four statements above are true.
None of the five statements above are true.
A:
This is the line of thought I followed:
Statement #3
is impossible because of #1 and #2 contradicting each other (let's consider only the last three statements, for simplicity). So, #3 must be false.
As a consequence,
#1 must be false.
If #4 were true, then #2 must be true (by exclusion), but this would imply that #4 itself is false. Then,
#4 is false.
If #5 were true,
then #2 must be false. So far, this holds. If #5 were false, then #2, by exclusion, must be true. But this implies that #3 is true too, which is a contradiction, as seen above.Then #5 is true, and #2 is false.
Accordingly,
#6 is false because it being true would imply that #5 is false.
In conclusion,
there is only one true statement, as said in the title, and is #5.
A:
True statement is
5th statement
Reason
1 is false(only 5 is true)
2 is false(5 is true)
3 is false(both above are false)
4 is false(all are false)
6 is false(5is true)
A:
Another nice way to approach this puzzle is by constructing chains of implications. We know there's only one true statement, so if one statement implies another one, then it's false.
Firstly, $3\Rightarrow1\Rightarrow6\Rightarrow5$, so $3$ and $1$ and $6$ are false.
Since $3$ and $1$ are not true, $4\Leftrightarrow2$, so they're both false.
The only option left is $5$, so this is the answer.
|
Wayne Rooney’s first game as permanent England captain is unlikely to live long in the memory for any other reason but the skipper did score the penalty to earn a 1-0 victory over Norway.
A half-full Wembley was not exactly treated to a classic but what about Rooney’s performance? We used statistics to track the striker’s game in Wednesday night’s friendly, including his match-winning spot-kick.
5TH MINUTE
Having started like he means business, sprinting after a Jack Wilshere long ball but drifting offside, Rooney decides not to pull rank at a free-kick from around 25 yards from goal. He instead lets Leighton Baines take the set-piece and the left-back sends the ball over the crossbar.
12TH MINUTE
Rooney catches Norway centre-back Havard Nordtveit in the face with a stray arm when challenging for an aerial ball and is involved in a long chat with the referee. Rooney has only had five touches of the ball, with goalkeeper Joe Hart (two) the only England player to have seen less of the ball.
19TH MINUTE
Shortly after attempting to set the tone by positively chasing down Norway right-back Omar Elabdellaoui, Rooney receives the ball in the penalty area with his back to goal. Unfortunately his control lets him down and he then misplaces an attempted pass to Jordan Henderson. Rooney’s passing success rate stands at 70 per cent.
30TH MINUTE
After half-an-hour played, Rooney has had 15 touches of the ball, attempted 10 passes at a success rate of 70%. All of these statistics are less than any other England outfield player. Rooney has also not attempted any shots.
HALF-TIME
Just a few minutes after an inaccurate crossfield pass, Rooney’s half comes to an end with England drawing 0-0 with Norway. Rooney’s passing has improved to a 75% success rate but it is still less than any of his outfield team-mates, as is his total of touches (24). He has attempted one shot but it does not hit the target. He has also contributed 100% of the game's two offsides.
52ND MINUTE
Having not had a touch to change his statistics since the start of the second half, Rooney shows a burst of speed as he chases after a through ball. But Norway goalkeeper Orjan Haskjold comes out of his area to clear.
68TH MINUTE
Following a foul on Raheem Sterling, England are awarded a penalty and Rooney converts the spot-kick with power. He places the penalty forcefully to the right-hand side of Haskjold. England’s skipper punches the air in celebrating a goal which makes him his country’s fourth top goalscorer, moving ahead of Michael Owen, with 41.
69TH MINUTE
Sixty seconds after scoring the penalty, Rooney’s game is over as he is substituted, presumably to be rested. Rooney’s contribution included 29 touches, only five in his time on the field in the second half, and two shots, one of which – the penalty goal – was on target. The forward played 20 passes at a success rate of 75%.
FORMER ENGLAND CAPTAIN TERRY BUTCHER’S VERDICT...
“I do not know [where Rooney is going to fit in]. I look upon this as a big problem for the manager, because Sterling had the sort of game you wanted Rooney to have. He [Sterling] was supplying through balls for Daniel Sturridge; he was supplying lots of good ammunition from the left-hand side. When he [Sterling] does drift around in that central midfield area in behind the striker, where Rooney does play, he is much more effective than Rooney. The only thing Rooney did in the game, for me, was score the penalty. He is a match-winner in that respect. But it was through Sterling and his pace that he got the penalty.” |
Q:
Cannot export Azure SQL database
When I try to export my database via the 'Export' button in the Azure portal, I get the following error:
Error encountered during the service operation.
Could not extract package from specified database.
The element DataSyncEncryptionKey_8d263adb59574052847134070b69d73d is not supported in Microsoft Azure SQL Database v12.
Though I did at one point try the DataSync service, I never ended up using it and am certainly not using it now. I regret even trying this service because it created schemas in my database that I do not know how to remove completely.
Now, it seems that these schemas are preventing me from exporting my database.
At the very least, it would be nice to resolve this error. However, it would be better if I could remove all traces of the DataSync service.
Please note that I have already used the script in the accepted solution to this question: How to remove SQL Azure Data Sync objects manually. That removed the DataSync schema but I am still left with the 'dss' and 'TaskHosting' schemas.
I have also tried emailing support, as recommended by the accepted solution in this thread: https://social.msdn.microsoft.com/Forums/azure/en-US/8b68b44b-c98a-4b38-8aab-36a30a7fafd9/the-element-datasyncencryptionkeyid-is-not-supported-in-microsoft-azure-sql-database-v12-when?forum=ssdsgetstarted. That email simply bounced back.
Additionally, if I go into Azure portal, it does not show any sync groups or sync agents whatsoever.
A:
First off, let me thank @alberto-morillo for his help. There is a good chance the SQL Agent would have worked had the situation been different.
In the end, I contacted Azure Support and they gave me the following script. Everything worked fine afterwards.
declare @n char(1)
set @n = char(10)
declare @triggers nvarchar(max)
declare @procedures nvarchar(max)
declare @constraints nvarchar(max)
declare @views nvarchar(max)
declare @FKs nvarchar(max)
declare @tables nvarchar(max)
declare @udt nvarchar(max)
-- triggers
select @triggers = isnull( @triggers + @n, '' ) + 'drop trigger [' + schema_name(schema_id) + '].[' + name + ']'
from sys.objects
where type in ( 'TR') and name like '%_dss_%'
-- procedures
select @procedures = isnull( @procedures + @n, '' ) + 'drop procedure [' + schema_name(schema_id) + '].[' + name + ']'
from sys.procedures
where schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
-- check constraints
select @constraints = isnull( @constraints + @n, '' ) + 'alter table [' + schema_name(schema_id) + '].[' + object_name( parent_object_id ) + '] drop constraint [' + name + ']'
from sys.check_constraints
where schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
-- views
select @views = isnull( @views + @n, '' ) + 'drop view [' + schema_name(schema_id) + '].[' + name + ']'
from sys.views
where schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
-- foreign keys
select @FKs = isnull( @FKs + @n, '' ) + 'alter table [' + schema_name(schema_id) + '].[' + object_name( parent_object_id ) + '] drop constraint [' + name + ']'
from sys.foreign_keys
where schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
-- tables
select @tables = isnull( @tables + @n, '' ) + 'drop table [' + schema_name(schema_id) + '].[' + name + ']'
from sys.tables
where schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
-- user defined types
select @udt = isnull( @udt + @n, '' ) +
'drop type [' + schema_name(schema_id) + '].[' + name + ']'
from sys.types
where is_user_defined = 1
and schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
order by system_type_id desc
print @triggers
print @procedures
print @constraints
print @views
print @FKs
print @tables
print @udt
exec sp_executesql @triggers
exec sp_executesql @procedures
exec sp_executesql @constraints
exec sp_executesql @FKs
exec sp_executesql @views
exec sp_executesql @tables
exec sp_executesql @udt
GO
declare @n char(1)
set @n = char(10)
declare @functions nvarchar(max)
-- functions
select @functions = isnull( @functions + @n, '' ) + 'drop function [' + schema_name(schema_id) + '].[' + name + ']'
from sys.objects
where type in ( 'FN', 'IF', 'TF' )
and schema_name(schema_id) = 'dss' or schema_name(schema_id) = 'TaskHosting' or schema_name(schema_id) = 'DataSync'
print @functions
exec sp_executesql @functions
GO
--update
DROP SCHEMA IF EXISTS [dss]
GO
DROP SCHEMA IF EXISTS [TaskHosting]
GO
DROP SCHEMA IF EXISTS [DataSync]
GO
DROP USER IF EXISTS [##MS_SyncAccount##]
GO
DROP ROLE IF EXISTS [DataSync_admin]
GO
DROP ROLE IF EXISTS [DataSync_executor]
GO
DROP ROLE IF EXISTS [DataSync_reader]
GO
declare @n char(1)
set @n = char(10)
--symmetric_keys
declare @symmetric_keys nvarchar(max)
select @symmetric_keys = isnull( @symmetric_keys + @n, '' ) + 'drop symmetric key [' + name + ']'
from sys.symmetric_keys
where name like 'DataSyncEncryptionKey%'
print @symmetric_keys
exec sp_executesql @symmetric_keys
-- certificates
declare @certificates nvarchar(max)
select @certificates = isnull( @certificates + @n, '' ) + 'drop certificate [' + name + ']'
from sys.certificates
where name like 'DataSyncEncryptionCertificate%'
print @certificates
exec sp_executesql @certificates
GO
print 'Data Sync clean up finished'
|
Q:
Sencha Touch 2 cross-domain login
Is it possible to do a cross-domain login using the Sencha Touch 2 and Spring Security ?
A:
You can achieve that with Restful Web Services. You can build a restful web service with Spring, and Spring Security can handle both authentication and authorization. I believe this is the only way, since you can't redirect pages that are not in the same domain with a regular Spring Security authetication. To make the application works cross-domain, you'll need this lib http://software.dzhuvinov.com/cors-filter.html.
|
Q:
Recursive function with array
I have an array with the following example definition:
segments = [["000", "001", "002"], ["110", "111", "112"], ["210", "211", "212"]]
This array can have any number of elements and each element will have an array.
I am trying to generate the following output:
000-110-210
000-110-211
000-110-212
000-111-210
000-111-211
000-111-212
000-112-210
000-112-211
000-112-212
001-110-211
001-110-212
001-111-210
001-111-211
001-111-212
001-112-210
001-112-211
001-112-212
.
.
.
I cannot figure out the logic to get this done.
A:
You can use Array#product:
combined = segments[0].product(*segments[1..-1])
#=> [["000", "110", "210"], ["000", "110", "211"], ["000", "110", "212"],
# ["000", "111", "210"], ["000", "111", "211"], ["000", "111", "212"],
# ["000", "112", "210"], ["000", "112", "211"], ["000", "112", "212"],
# ["001", "110", "210"], ["001", "110", "211"], ["001", "110", "212"],
# ["001", "111", "210"], ["001", "111", "211"], ["001", "111", "212"],
# ["001", "112", "210"], ["001", "112", "211"], ["001", "112", "212"],
# ["002", "110", "210"], ["002", "110", "211"], ["002", "110", "212"],
# ["002", "111", "210"], ["002", "111", "211"], ["002", "111", "212"],
# ["002", "112", "210"], ["002", "112", "211"], ["002", "112", "212"]]
Or more explicitly (if the number of arrays is fixed):
combined = segments[0].product(segments[1], segments[2])
Use join to join the sub arrays:
combined.map { |arr| arr.join('-') }
#=> ["000-110-210", "000-110-211", "000-110-212", ...]
|
Validation of Functional Assessment for Liver Resection Considering Venous Occlusive Area after Extended Hepatectomy.
Previous studies demonstrated that liver function in a veno-occlusive region is approximately 40% of that in a non-veno-occlusive region after hepatectomy with excision of major hepatic vein. We validated the preoperative assessment of future remnant liver (FRL) function based on 40% decreased function of the veno-occlusive region. Sixty patients who underwent hepatectomy with excision of major hepatic vein were analyzed. The FRL functions of the veno-occlusive and non-veno-occlusive regions were calculated with 99mTc-galactosyl human serum albumin scintigraphy single-proton emission computed tomography fusion system and SYNAPSE VINCENT® preoperatively. Risk assessment for hepatectomy was evaluated based on indocyanine green retention at 15 min, and patients with insufficient FRL function were described as marginal. The median volume and function of the veno-occlusive region per whole liver were 111 ml and 11.0%, respectively. When the function of the veno-occlusive region was presumed as 0%, 40%, and 100%, the FRL function was 62.5%, 68.4%, and 75.0% and 21, 15, and 7 patients were classified as marginal, respectively. When the function of the veno-occlusive region was presumed as 40%, the posthepatectomy liver failure (PHLF) rate of marginal patients was significantly higher than that of safe patients (46.7% vs 8.9%, P = 0.002). Multivariable analysis indicated that marginal FRL function based on 40% decreased function of the veno-occlusive region was the only independent risk factor for PHLF (odds ratio 8.97, P = 0.002) after extended hepatectomy. Assessment of preoperative FRL function based on 40% decreased function of the veno-occlusive region may have high validity. |
export enum UserFileThemeEnum {
Light = <any>'light',
Dark = <any>'dark'
}
|
First Morning in Ireland
Waking up in Ireland
I woke up early my first morning in Ireland. The effects of jet lag made it a restless night and, when there was just enough light to see soft shapes in the room, I looked over to the bedside table. There was no bedside clock and, as I had no watch or phone or device of any kind, I could only guess at the time. I decided to end the struggle of going back to sleep and get up. When I looked out the second floor window of the farmhouse B&B, there was only a hint of morning through the thick fog. Even though I could see very little, something compelled me outside and I crept slowly out of bed to quietly get dressed. Trying not to wake up my wife, or anyone else in the house, I snuck out the door, along the hallway, and down the stairs.
Dressed in a thick Aran jumper to cut the cold, I closed the main door to the house and walked along the path of small white stones that cut through the dewy grass. I could just make out the narrow country lane below. There was only quiet, save for the crunch of gravel; the fog muffled any other sound of the farm and I found a weathered bench that faced out towards the hills. I sat down, warming my hands with my breath, and watched the fog slowly lift. I still had no idea how early it was, as I hugged myself to keep warm, but I wasn’t bothered. I couldn’t see it yet, but I knew I was close to the Neolithic site of Newgrange.
The fog slowly lifted, exposing more of the greenery that defines Ireland, and I watched the trees reveal themselves like lost soldiers, tucked against the old stone walls. Lost in the magic of the morning, I was suddenly jolted into the present when an orange tabby cat jumped onto my lap. She nestled herself in to keep warm, and together we watched as the first beams of sun slowly washed the world in light. I could soon make out the white outer wall of Newgrange and I imagined what the early inhabitants must have felt on mornings such as this one, as they gathered together to perform the ancient rites.
As the sun burned off the last of the fog, marking the end of that mystical time of the day when the borders between our world and the Otherworld were softened, the cat jumped off my lap and went in search of birds and mice. Before me lay a patchwork blanket of green fields and I could hear the morning bustle of farmhands heading out towards the back of the property. I went inside to see if Paula was awake.
She was still in bed but her eyes were open. She blinked a few times before asking, “Have you been up long?”
“Just for a bit,” I lied. “Are you ready for some breakfast?”
Written by: Chris Brauer
Chris Brauer lives in British Columbia, Canada where he splits his time between writing and teaching. He has recently completed a travel memoir about living in the Sultanate of Oman, and is currently working on a book about his travels in Ireland. He is also working on his first collection of poetry.
All Photo Credits: Chris Brauer
For more ITKT travel stories about Ireland
For more ITKT travel stories about Europe
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10,000 Miles with my Dead Father's Ashes is coming out September 18, 2018, and we are giving away travel and books for the first seven months and all book buyers get fun free gifts. Sign up here to learn more.
So, what do you do when you lose your father's ashes before the scattering? Find out here! And it is all set in Andalucia, southern Spain. |
Snoopy Baby Shower Ideas
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CAIRNS CITY WEBCAM - LIVE STREAM
The Cairns City Webcam is located on the Pacific Hotel Rooftop.
The cam shows a live stream of Cairns inner city and includes views of the Cairns Marina, Reef Fleet Terminal, Casino, Cairns Esplanade & Parklands.
The view changes every 30 - 60 seconds seconds.
In the afternoon you can see the Reef Vessels returning from their Day Tours and thousands of flying foxes making their way across the inlet. |
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"title":"MDN Web Docs - X-Frame-Options"
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{
"url":"https://www.owasp.org/index.php/Clickjacking_Defense_Cheat_Sheet",
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"notes":"Partial support refers to not supporting the `ALLOW-FROM` option.\r\nThe `X-Frame-Options` header has been obsoleted by [the `frame-ancestors` directive](https://www.w3.org/TR/CSP2/#directive-frame-ancestors) from Content Security Policy Level 2.",
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|
e second derivative of i(k) wrt k.
-100*k**3
Let g(w) be the second derivative of 10*w + 2/21*w**7 + 0 + 0*w**2 + 0*w**6 + 0*w**4 + 5/3*w**3 + 0*w**5. Find the second derivative of g(t) wrt t.
80*t**3
Let u(j) = -j + 13. Suppose f - 31 = -4*c, 58 = 4*f - f + 5*c. Let y be u(f). Find the third derivative of -14*q**2 - q**3 + 4*q**y + 7*q**2 wrt q.
-6
Let n(m) = -m**3 - m + 2. Let d be n(0). What is the third derivative of 4357 - 4357 + 37*p**d - 21*p**6 wrt p?
-2520*p**3
Let f(o) = 2*o**4 + 3*o**3 + 6*o**2 - 315*o - 746. Let w(b) = -2*b**4 - 4*b**3 - 8*b**2 + 316*b + 746. Let r(c) = -4*f(c) - 3*w(c). Differentiate r(h) wrt h.
-8*h**3 + 312
Find the third derivative of -146*j**3 - 205*j**2 + 3*j**3 + 26*j**3 wrt j.
-702
What is the derivative of -13*w**3 - 11*w**3 + 27 + 80 + w + 12*w - 6*w wrt w?
-72*w**2 + 7
Let p(g) be the first derivative of 317*g**4/4 - 374*g - 239. What is the first derivative of p(t) wrt t?
951*t**2
Let f(c) be the second derivative of 10*c**7/7 - 20*c**3 - 7*c - 1. What is the second derivative of f(t) wrt t?
1200*t**3
What is the third derivative of -58*x**2 + 11*x - 34*x**6 + 22*x**6 - 10*x wrt x?
-1440*x**3
Let m be (-8)/(-6)*99/(-6). Let p be 60/33 - 4/m. What is the derivative of 4*o**p - o**2 - 5*o**2 - 4 + 6 wrt o?
-4*o
Let x(q) = 529*q**4 + 7*q**3 + 562. Let i(h) = 530*h**4 + 6*h**3 + 560. Let a(l) = 7*i(l) - 6*x(l). Differentiate a(w) with respect to w.
2144*w**3
Let z(t) = 2*t**2 + 48*t - 8. Let k be z(-25). What is the first derivative of -u**3 + 4*u**4 - 43*u**4 + 8*u**4 - k wrt u?
-124*u**3 - 3*u**2
Let f(t) be the third derivative of 0 + 0*t**6 + 7/24*t**4 + 1/42*t**8 + 0*t**7 - 3*t**2 + 0*t**5 + 0*t**3 + 0*t. Find the second derivative of f(a) wrt a.
160*a**3
Let k(t) be the third derivative of -53*t**8/84 + 121*t**4/24 + 3*t**2 + 2. Find the second derivative of k(w) wrt w.
-4240*w**3
Let k(w) = 313*w**4 + 8*w**3 + 8*w**2 + 104. Let v(b) = -2*b**4 + 2*b**3 + 2*b**2. Let h(u) = -k(u) + 4*v(u). What is the derivative of h(m) wrt m?
-1284*m**3
Let d(x) be the third derivative of -4*x**7/15 + x**6/60 - 23*x**4/24 + x**3/6 - 33*x**2. What is the second derivative of d(l) wrt l?
-672*l**2 + 12*l
Let v(z) be the first derivative of 3*z**6/5 - 5*z**3/6 + 12*z - 12. Let l(n) be the first derivative of v(n). Find the second derivative of l(u) wrt u.
216*u**2
Suppose 2 = -3*v + 11. What is the first derivative of -46 - 9*k**3 + 27*k**4 - 6*k**v - 26*k**4 wrt k?
4*k**3 - 45*k**2
Let f(u) be the second derivative of 13*u**6/30 + u**3/3 - 61*u**2/2 - 4*u + 40. What is the derivative of f(y) wrt y?
52*y**3 + 2
Let w(c) = -c**4 - c**3 - c**2. Let z(o) = 82*o**4 - 3*o**3 - 3*o**2 - 23. Let v(g) = 3*w(g) - z(g). Find the first derivative of v(j) wrt j.
-340*j**3
Let f be (-50)/(-6) - (-28)/42. What is the third derivative of -f*q**3 - 11*q**2 + q**2 + 3*q**3 wrt q?
-36
Let j(a) = 2*a**2 - 5*a - 1. Let p be 14/4 - 9/18. Let u be j(p). Find the third derivative of -o**4 + 10*o**4 + 2*o**u + 3*o**2 wrt o.
216*o
Suppose 5*d - 27 = 13. Let a = d + -3. What is the first derivative of -3 - o**2 + a - 5 wrt o?
-2*o
Let s be 10/(-2*3/(-9)). Let t = -9 + s. Find the third derivative of 6*n**t - 13*n + 13*n + 3*n**2 wrt n.
720*n**3
Let q(r) be the second derivative of -r**6/6 - 7*r**5/10 - 43*r**4/4 - r + 51. What is the third derivative of q(g) wrt g?
-120*g - 84
Let w(k) = k**2 - k + 5. Let r be w(0). Suppose -r*z = -3*z - 4. Find the second derivative of 7*s + 12*s**z - 7*s - s wrt s.
24
Let d be (1 - 28/10)/(90/(-750)). Find the second derivative of 15*r + 2*r**3 - d*r**3 + 5*r**3 - 12*r**3 wrt r.
-120*r
Let q(d) be the second derivative of 51*d**5/20 + 2*d**4/3 + 9*d**2/2 + 74*d. What is the third derivative of q(u) wrt u?
306
Suppose 1 = 5*u - 9. Let m(a) be the second derivative of -1/2*a**u - 4*a + 1/3*a**3 + 0. Find the first derivative of m(b) wrt b.
2
Let r(g) be the second derivative of 451*g**4/12 - 133*g**3/3 + g**2/2 - 451*g. What is the second derivative of r(n) wrt n?
902
Differentiate -24 + 27493*o**3 - 170*o**4 - 27493*o**3 with respect to o.
-680*o**3
Let c(f) = 242*f**3 - 3*f**2 - 36*f + 5. Let t(h) = -485*h**3 + 5*h**2 + 72*h - 9. Let a(b) = 5*c(b) + 3*t(b). What is the second derivative of a(n) wrt n?
-1470*n
Find the second derivative of 6*n**3 + 1647*n - 2949*n + 32*n**2 + 1571*n wrt n.
36*n + 64
Let s(k) = -k**3 - k**2 - k. Let u(x) = 5*x**3 - 2*x**2 + 4*x + 16. Let m(w) = 6*s(w) + u(w). Find the second derivative of m(j) wrt j.
-6*j - 16
Suppose -100 = -13*o - 7*o. Find the second derivative of -2*v**o + 5*v**5 - 12*v**5 - 23*v**5 + 7*v wrt v.
-640*v**3
Let a(c) be the second derivative of c**5/20 + 3*c**4/2 - 33*c**2/2 + 93*c. What is the derivative of a(k) wrt k?
3*k**2 + 36*k
Let x = -58 - -71. Find the third derivative of 0*u**2 + x*u**4 - 12*u**2 + 0*u**2 wrt u.
312*u
Suppose 0*x - r + 11 = 3*x, 4*x - r = 10. Suppose 3*a - 5 = -l + 8, 0 = -2*l - 5*a + 23. What is the derivative of -i**2 + l + 0 + x wrt i?
-2*i
What is the third derivative of -10*p**5 + 36*p**5 + 142*p**5 + 2*p**2 + 129*p**5 - 93 - 41*p**5 wrt p?
15360*p**2
Let l = -41 + 58. What is the derivative of -15*h - 8 + 12*h**3 + l*h**3 + 15*h wrt h?
87*h**2
What is the second derivative of -l + 18*l**4 + 3*l**2 + 3*l - 11*l**2 - 13 + 6*l**2 wrt l?
216*l**2 - 4
Let s(w) be the second derivative of -w**8/14 - w**6 - w**4/4 + 25*w**2 - 605*w. Find the third derivative of s(t) wrt t.
-480*t**3 - 720*t
Suppose 4*m + 61 = 77. What is the derivative of 7 + 3*p + m*p**2 - 6*p - p + 2*p wrt p?
8*p - 2
Let c(s) be the first derivative of s**6 - 9*s**5/5 + 93*s**2 - 160. Find the second derivative of c(v) wrt v.
120*v**3 - 108*v**2
Let h(r) = 132*r**4 - 31*r**2 - 8*r + 6. Let t(c) = -130*c**4 + 31*c**2 + 7*c - 5. Let x(i) = -5*h(i) - 6*t(i). What is the third derivative of x(j) wrt j?
2880*j
Let o(g) be the third derivative of -g**6/60 + 37*g**5/60 + 27*g**3 - 293*g**2. Differentiate o(i) with respect to i.
-6*i**2 + 74*i
Let j = 301 + -301. Let a(i) be the third derivative of 0*i**4 + j - 4/3*i**3 + 0*i + 1/10*i**5 + 3*i**2. Differentiate a(n) wrt n.
12*n
Find the third derivative of 98*d**2 + 6455*d**3 + 3*d**4 - 2*d**5 - 3*d**4 - 6505*d**3 wrt d.
-120*d**2 - 300
Let y(l) be the second derivative of -35*l**4/12 - 3*l**3/2 - 3*l**2/2 - 23*l + 2. Find the second derivative of y(g) wrt g.
-70
Differentiate 236 - 168 + 307 + 468 + 31 + 423*o**3 wrt o.
1269*o**2
Suppose 5*v - 1 = -3*o, 5*v + o - 3 = 2*v. Find the third derivative of 2*s + 17*s**6 - 66*s**2 - 2*s + 50*s**v wrt s.
2040*s**3
Find the first derivative of 18*f - 3*f**4 + 21 + 8 - 44*f wrt f.
-12*f**3 - 26
Let k be (-7)/(-2) - 5/(-10). Find the third derivative of 2*c**k + 5*c**2 + 6*c**4 - c**2 + 9*c**2 wrt c.
192*c
Find the third derivative of 8 - 3 - 3 - 7*y**2 - 2*y**3 - 8*y**2 - 6*y**6 wrt y.
-720*y**3 - 12
Suppose -12*a + 6 = -10*a. What is the second derivative of z**3 + 23*z**4 + 7*z**3 - 28*z - 8*z**a wrt z?
276*z**2
Let x(h) = 2*h. Let n(m) = 95*m + 46. Let i(j) = -2*n(j) - 4*x(j). Find the first derivative of i(k) wrt k.
-198
Suppose g + 26 - 34 = 0. What is the third derivative of -792*d**2 + 799*d**2 + 4*d**3 + g*d**3 wrt d?
72
Let h(i) be the second derivative of 18*i**3 + 23*i**2/2 + 108*i. Differentiate h(y) with respect to y.
108
Let f(k) = -10*k**3 - 30*k + 33*k - 4*k**2 - 2*k**2. Let y(d) = d**2. Let o(x) = -f(x) - 6*y(x). Find the second derivative of o(z) wrt z.
60*z
What is the third derivative of 142*q**5 - 18*q**3 + 31*q**2 - 145*q**5 - 3*q + 3*q + 2 wrt q?
-180*q**2 - 108
Let m(s) = 7*s**3 + 30*s**2 + 6. Let k(t) = -t**2 + t**3 - 5*t**2 - 4 + 3 + 5*t**2. Let y(x) = 6*k(x) + m(x). Find the third derivative of y(f) wrt f.
78
Let u(n) = -n**2 + 12*n + 5. Let t be u(10). Let b be t/4 + (-5)/20. Find the third derivative of 0*z**6 - 4*z**6 + 0*z**b - 3*z**2 + z**2 wrt z.
-480*z**3
What is the derivative of -799*y + 106*y + 83*y + 102*y + 619 wrt y?
-508
Let v = 34 + -27. Find the second derivative of -18*l**4 + 9*l**4 - 31*l**4 - v*l + 5*l**4 wrt l.
-420*l**2
Suppose 3*c + 8 = -r, -17 = -2*r + 4*c + 7. What is the first derivative of z**r + 18 + 461*z**3 - 461*z**3 wrt z?
4*z**3
Let o(b) be the second derivative of -23*b**3/6 + 23*b**2 - 34*b. Let w(f) = -68*f + 139. Let |
[Development of the frontal sinus after frontocranial remodeling for craniostenosis in infancy].
General considerations about frontal sinus development are discussed. This retrospective radiological study concerns 90 craniosynostoses among 850 cases operated in the Cranio-Facial Unit (1976-88, Hôpital Necker des Enfants Malades, Paris, France). The incidence of frontal sinus development is compared between a control group and the craniosynostoses group with a mean age at surgery of 3 years and a mean follow-up of 6.5 years. Pneumatization of the frontal bone seemed to vary according to the type of surgery and the age at review, but was not linked to sex and age at surgery. A classification of fronto-cranial remodelling is suggested. |
Preventing sentinel events caused by family members.
As long as there are human beings involved in health care, there will be errors. Sometimes these errors are minor, and some can lead to significant morbidity and mortality. At times, the errors are caused by family members who mean well, but may cause further problems and possibly death. This article discusses as few case studies, potential errors, and strategies critical-care nurses can use to prevent these errors. |
Catholic priests go online to net followers
Father Nigel Barrett and Father Warner D’Souza are no conventional Catholic priests. To engage with parishioners in Malad and Bandra respectively, they scrap on Orkut, run Facebook groups, send parish updates through e-posters and text messages as well as write blogs to engage the youth in discussions, reports Aarefa Johari.
Father Nigel Barrett and Father Warner D’Souza are no conventional Catholic priests.
To engage with parishioners in Malad and Bandra respectively, they scrap on Orkut, run Facebook groups, send parish updates through e-posters and text messages as well as write blogs to engage the youth in discussions about religious, civic, social and political issues.
“The best way to reach today’s youth is to meet them where they are — on social networking sites,” said D’Souza (38), among a growing number of city priests embracing new media.
D’Souza has more than 400 fans on each of his Bandra parish-related Facebook communities.
“Young people hesitate to approach priests in the institution of the church. They are more comfortable opening up within the anonymity of the net,” said Barrett (42), from Malad’s Orlem Church, who reaches out to parishioners over Google chat. The online forum has attracted more youngsters to community activities.
“I used to think parish work was only for the elders,” said 24-year-old Erita D’Souza, who learned that her parish needed youth volunteers only after she started following Barrett online in her college days. “Now I have joined Sunday school and the local choir.”
Although Barrett has kept pace with changing technology ever since he was ordained 12 years ago, this year — the Year of the Priests for all Catholics — the need to adopt new media in communication has become a central concern for priests after the Pope urged them last month to use technology to spread the word. |
In addition to a deep Bonneville team, other teams in the mix included Century, Rigby and perennial wrestling powerhouses Blackfoot and Pocatello. The top four wrestlers in each weight class qualified for the state meet scheduled this Friday and Saturday.
Preston snared two individual district championships with seniors Cameron Dietrich and Devin Porter.
For the full story subscribe to The Preston Citizen: in print or online. |
Q:
Java putting set into map
Whats the quickest way to put a set into a map?
public class mySet<T>
{
private Map<T, Integer> map;
public mySet(Set<T> set)
{
Object[] array = set.toArray();
for(int i =0; i< array.length; i++)
{
T v = (T)array[i];
map.put(v, 1);
}
}
}
Right now, I just converted set into an array and loop through the array and putting them in one by one. Is there any better way to do this?
A:
One options would be this:
for (T value : set) {
map.put(value, 1);
}
|
<?xml version="1.0" encoding="UTF-8"?>
<ui version="4.0">
<class>DownloadDialog</class>
<widget class="QDialog" name="DownloadDialog">
<property name="geometry">
<rect>
<x>0</x>
<y>0</y>
<width>263</width>
<height>144</height>
</rect>
</property>
<property name="font">
<font>
<pointsize>12</pointsize>
</font>
</property>
<property name="windowTitle">
<string>Download</string>
</property>
<widget class="QProgressBar" name="progressBar">
<property name="geometry">
<rect>
<x>20</x>
<y>30</y>
<width>231</width>
<height>23</height>
</rect>
</property>
<property name="maximum">
<number>0</number>
</property>
<property name="value">
<number>-1</number>
</property>
</widget>
<widget class="QLabel" name="label">
<property name="geometry">
<rect>
<x>20</x>
<y>70</y>
<width>53</width>
<height>15</height>
</rect>
</property>
<property name="text">
<string>Bytes:</string>
</property>
</widget>
<widget class="QLabel" name="label_2">
<property name="geometry">
<rect>
<x>20</x>
<y>110</y>
<width>41</width>
<height>16</height>
</rect>
</property>
<property name="text">
<string>ETA:</string>
</property>
</widget>
<widget class="QLabel" name="bytesLabel">
<property name="geometry">
<rect>
<x>80</x>
<y>70</y>
<width>171</width>
<height>16</height>
</rect>
</property>
<property name="text">
<string>--- of ---</string>
</property>
</widget>
<widget class="QLabel" name="etaLabel">
<property name="geometry">
<rect>
<x>80</x>
<y>110</y>
<width>171</width>
<height>16</height>
</rect>
</property>
<property name="text">
<string>--- h --- m</string>
</property>
</widget>
<widget class="QLabel" name="label_3">
<property name="geometry">
<rect>
<x>20</x>
<y>90</y>
<width>53</width>
<height>15</height>
</rect>
</property>
<property name="text">
<string>Speed:</string>
</property>
</widget>
<widget class="QLabel" name="speedLabel">
<property name="geometry">
<rect>
<x>80</x>
<y>90</y>
<width>161</width>
<height>16</height>
</rect>
</property>
<property name="text">
<string>--- mbit</string>
</property>
</widget>
</widget>
<resources/>
<connections/>
</ui>
|
The present invention claims priority from Japanese Patent Application No. 10-321378 filed Oct. 28, 1999, the contents of which are incorporated herein by reference.
1. Field of the Invention
The present invention relates to a brain wave data processing device used for processing brain wave data to detect distinctive patterns, and more particularly to a brain wave data processing device which averages brain wave data in which distinguishing patterns are detected in individual brain wave data obtained in a single trial, and to a computer readable storage medium in which a program to realize this brain wave data processing device is loaded.
2. Description of Related Art
When an excitation or event is added to a subject (trial), an electric potential evoked by the added excitation or event (evoked potential) would occur in the brain and spinal cord of the subject. In particular, a potential variation occurred in a cerebral cortex with a constant time relation to an excitation or event is referred to as an event-related potential (ERP). Such a potential or potential variation is generally observed as brain wave data, and used as effective data to know the mechanism of, for example, feeling, perception, and psychological phenomenon, or to find a position of an injury. However, the amplitude of the potential variations involved with the trial is considerably smaller than that of rhythmic, ordinary brain waves, so that a signal occurred from one observation is often indistinct. Therefore, a method has been devised in which multiple trials are performed under the same conditions and the brain wave data obtained from each trial are added and averaged with the time of excitation (event) as a reference point, causing components of the rhythmic, ordinary brain waves to be canceled, so that only the evoked potential obtained by the excitation (event) is extracted. This technique is referred to as an averaging method.
Incidentally, as a technique to process an unsteady signal which changes over time to analyze whether or not a distinguishing component is included, in these days, attention has focused on the wavelet conversion. An example of the brain wave data subjected to the wavelet conversion in a single trial includes the reference xe2x80x9cP300 Single Trial Storage Processing Based on Wavelet Conversionxe2x80x9d by Masatoshi Nakamura, Yasushi Hisatomi, Naoshi Sugikou, Shigeto Nishida, Yoshio Ikeda, and Hiroshi Shibasaki (Proceedings of the fifteenth SICE Kushu branch congress, pp. 355-358, Nov. 23, 1996). However, the device by Nakamura et al. provides only the wavelet conversion and inverse wavelet conversion with respect to the brain wave data, and includes only the filtering function to eliminate noises in live data. Further, although they have attempted to restrict parameters included in the wavelet conversion according to the result of filtering to the live data, the reliability of the result can not be expected, because they use a formula model as a true waveform. In addition, they have examined wavelet conversion parameters only in limited ranges, so that a considerable amount of information contained in the live data may have been lost. The largest problem of the report by Nakamura et al. is that how to use the waveforms subjected to filtering process (the waveform data subjected to the wavelet conversion and inverse wavelet conversion) is not mentioned. After all, the device by Nakamura et al. may be considered not to reach the practical stage yet, although the attempt to analyze the brain wave data using the wavelet conversion and inverse wavelet conversion can be found.
When the averaging of the brain wave data is determined by the averaging method and the evoked potential, such as the event-related potential (ERP), is observed, in the past, an enormous period of time was required in order to extract distinguishing patterns from individual brain wave data to obtain the averaging of the brain wave data. The reason for it is that the work of extracting the patterns was all performed by the inspection of an experimenter (or a decipherer of the brain wave).
It is an object of the present invention to provide a method for analyzing brain wave data which can automate the work to extract distinguishing patterns from brain wave to reduce the load of the experimenter and improve the quality and reliability of the brain wave data obtained as well as the efficiency of the work for analyzing the brain wave data.
In addition, as described above, in the past, a concrete application of the wavelet conversion for the brain wave data was not made clear, however, it is also another object of the present invention to exhibit concrete applications. Accordingly, the present invention exhibits the averaging of the brain wave data as a concrete application of the wavelet conversion, and also it is an object of the present invention to provide a device which performs the averaging without significantly losing the information of original waveform data by considering not only the waveform data itself as with the prior art but also whole of values of the wavelet conversion parameters, when the results of the wavelet conversion are compared and examined.
The brain wave data processing device according to the present invention comprises, in a brain wave data processing device detecting distinguishing patterns from individual brain wave data obtained in a single trial, a brain wave data storage means for storing digital brain wave data, a wavelet conversion means for subjecting the digital brain wave data read out from the brain wave data storage means to wavelet conversion to determine a wavelet coefficient, a wavelet coefficient surface output means for outputting the wavelet coefficient as function values of a scale parameter and a shift parameter in the wavelet conversion, a wavelet coefficient window parameter setting means for setting a wavelet coefficient window, a wavelet coefficient window means for extracting a predetermined area based on the wavelet coefficient window from a wavelet coefficient surface defined by the scale parameter, shift parameter, and wavelet coefficient, and a brain wave data discriminating means for discriminating whether or not the predetermined area has been extracted from the wavelet coefficient surface by the wavelet coefficient window means for individual digital brain wave data.
The brain wave data processing device according to the present invention may further be provided with a brain wave data averaging means for averaging only the digital brain wave data from which the predetermined area is extracted in the wavelet coefficient surface and a pattern latency extraction means for determining a vertex latency of distinguishing patterns included only in the digital brain wave data from which the predetermined area is extracted in the wavelet coefficient surface.
In the present invention, the brain wave data in which the distinguishing patterns have been detected, for example, by inspection are previously prepared and the corresponding wavelet coefficient surface is determined from these brain wave data, and the wavelet coefficient window may be set according to the shape and value of this wavelet coefficient surface. Although various types are considered as a mother wavelet in the wavelet conversion, Mexican Hat can be exhibited as a desirable one.
According to the present invention, the wavelet coefficient surface is the result of subjecting the brain wave data to the wavelet conversion, and by subjecting this wavelet coefficient surface to the wavelet coefficient window, it is discriminated whether or not a predetermined area is extracted in the wavelet coefficient surface, so that all the processing from the measurement of the brain wave data to the discrimination of whether distinguishing patterns exist in the brain wave data can be automatically performed.
Furthermore, by providing a brain wave data averaging means, all the processing from the measurement of the brain wave data to the averaging process can be automatically executed, and by providing a pattern latency extraction means, a vertex latency of the extracted pattern can be automatically determined. |
// Copyright (C) 2017 Jérôme Leclercq
// This file is part of the "Nazara Development Kit"
// For conditions of distribution and use, see copyright notice in Prerequisites.hpp
#pragma once
#ifndef NDK_COMPONENTS_PHYSICSCOMPONENT3D_HPP
#define NDK_COMPONENTS_PHYSICSCOMPONENT3D_HPP
#include <Nazara/Physics3D/RigidBody3D.hpp>
#include <NDK/Component.hpp>
#include <memory>
namespace Ndk
{
class PhysicsComponent3D;
using PhysicsComponent3DHandle = Nz::ObjectHandle<PhysicsComponent3D>;
class NDK_API PhysicsComponent3D : public Component<PhysicsComponent3D>
{
friend class CollisionComponent3D;
friend class PhysicsSystem3D;
public:
inline PhysicsComponent3D();
PhysicsComponent3D(const PhysicsComponent3D& physics);
~PhysicsComponent3D() = default;
inline void AddForce(const Nz::Vector3f& force, Nz::CoordSys coordSys = Nz::CoordSys_Global);
inline void AddForce(const Nz::Vector3f& force, const Nz::Vector3f& point, Nz::CoordSys coordSys = Nz::CoordSys_Global);
inline void AddTorque(const Nz::Vector3f& torque, Nz::CoordSys coordSys = Nz::CoordSys_Global);
inline void EnableAutoSleep(bool autoSleep);
inline void EnableNodeSynchronization(bool nodeSynchronization);
inline Nz::Boxf GetAABB() const;
inline Nz::Vector3f GetAngularDamping() const;
inline Nz::Vector3f GetAngularVelocity() const;
inline float GetGravityFactor() const;
inline float GetLinearDamping() const;
inline Nz::Vector3f GetLinearVelocity() const;
inline float GetMass() const;
inline Nz::Vector3f GetMassCenter(Nz::CoordSys coordSys = Nz::CoordSys_Local) const;
inline const Nz::Matrix4f& GetMatrix() const;
inline Nz::Vector3f GetPosition() const;
inline Nz::Quaternionf GetRotation() const;
inline bool IsAutoSleepEnabled() const;
inline bool IsMoveable() const;
inline bool IsNodeSynchronizationEnabled() const;
inline bool IsSleeping() const;
inline void SetAngularDamping(const Nz::Vector3f& angularDamping);
inline void SetAngularVelocity(const Nz::Vector3f& angularVelocity);
inline void SetGravityFactor(float gravityFactor);
inline void SetLinearDamping(float damping);
inline void SetLinearVelocity(const Nz::Vector3f& velocity);
inline void SetMass(float mass);
inline void SetMassCenter(const Nz::Vector3f& center);
inline void SetMaterial(const Nz::String& materialName);
inline void SetMaterial(int materialIndex);
inline void SetPosition(const Nz::Vector3f& position);
inline void SetRotation(const Nz::Quaternionf& rotation);
static ComponentIndex componentIndex;
private:
inline void ApplyPhysicsState(Nz::RigidBody3D& rigidBody) const;
inline void CopyPhysicsState(const Nz::RigidBody3D& rigidBody);
inline Nz::RigidBody3D* GetRigidBody();
inline const Nz::RigidBody3D& GetRigidBody() const;
void OnAttached() override;
void OnComponentAttached(BaseComponent& component) override;
void OnComponentDetached(BaseComponent& component) override;
void OnDetached() override;
void OnEntityDestruction() override;
void OnEntityDisabled() override;
void OnEntityEnabled() override;
struct PendingPhysObjectStates
{
Nz::Vector3f angularDamping;
Nz::Vector3f massCenter;
bool autoSleep;
bool valid = false;
float gravityFactor;
float linearDamping;
float mass;
};
std::unique_ptr<Nz::RigidBody3D> m_object;
PendingPhysObjectStates m_pendingStates;
bool m_nodeSynchronizationEnabled;
};
}
#include <NDK/Components/PhysicsComponent3D.inl>
#endif // NDK_COMPONENTS_PHYSICSCOMPONENT3D_HPP
|
Accommodation summary
Popis
Ověřeno společností Wimdu
Translated by Google Translate
Show original version.
Visit us and get the real feel for Berlin! The studio lays in the heart of Kreuzberg - the district that never sleeps. You will live in between the famous Oranienstraße and Warschauer Straße and will get an impression of the original Berlin. The neighborhood offers you a huge variety of bars, restaurants, clubs and also supermarkets. And as it is typical for Berlin: there is something for every taste! Görlitzer Park, which is a park famous for its multi cultural atmosphere, is only two minutes away and gives you the opportunity to relax or to have a barbecue. Next train station (line 1) is five minutes by feet. It gives you a very good transportation in every important area from Berlin. The historical center is reachable in 10 Minutes or the Hauptbahnhof in 15 Minutes.
The studio is located in a very calm and pretty courtyard. With its high ceilings (3,80 m), its big rooms and its original wooden floor it has the classical charm of a berlin style apartment.
The living/bedroom offers a comfortable sleeping couch for two people, a separate floor with a queen size bed, flat screen TV, stereo system, eating nook, DVD player and large double windows. Free internet access is also available.
The kitchen is fully equipped and for example includes a cooking top, a refrigerator, a sink and pots and pans.
The tiled bathroom has a sink, toilet and a shower. Fresh towels and beddings are always included in our price!
If you have any more questions please feel free to ask!
Podrobnosti
Ohodnoďte tomuto hostiteli i další ubytování
Dear Ben,
the stay in Berlin went very well. The apartment was provided with everything it needed and it was very clean.
I would point out that in the apartament there was not the key to the waste delivery. We did the separate collection of waste and we have minimized the undifferentiated waste
We booked your apartment looking at the map of Berlin, (we did'nt know the city) and when we arrived we found that to get to public transport from the apartament it was necessary walking one kilometer and one kilometer to come back (Italians are not very athelics), the neighborhood was very nice. I recommend the apartament.
Tanti saluti.
Angela from the city of Bologna (Italia) |
Q:
How to Ensure Efficiency on Nested Select Query?
Mysql is not my strongest language! But I'm happy to have produced something that gives proper results which would otherwise involve three separate (php) queries.
Yet I'm not certain this is ideal. Here is the query:
SELECT * FROM
(
(SELECT sum(price) AS day FROM sales WHERE sold_date > DATE_SUB(NOW(), INTERVAL 1 DAY)) as day,
(SELECT sum(price) AS week FROM sales WHERE sold_date > DATE_SUB(NOW(), INTERVAL 1 WEEK)) as week,
(SELECT sum(price) AS month FROM sales WHERE sold_date > DATE_SUB(NOW(), INTERVAL 1 MONTH)) as month
)
WHERE 1
And it gives this beautiful result:
+--------+---------+----------+
| day | week | month |
+--------+---------+----------+
| 356.00 | 2393.00 | 11026.00 |
+--------+---------+----------+
I couldn't be happier.
Yet with a large database, I'm concerned this query structure might be too much?
How can I ensure this is not destined to be a resource hog?
A:
Your query might be surprisingly efficient. You can, however, try this with conditional aggregation:
select sum(case when sold_date > DATE_SUB(NOW(), INTERVAL 1 DAY) then price else 0 end) as "day",
sum(case when sold_date > DATE_SUB(NOW(), INTERVAL 1 WEEK) then price else 0 end) as "week",
sum(case when sold_date > DATE_SUB(NOW(), INTERVAL 1 MONTH) then price else 0 end) as "month"
from sales
where sold_date > DATE_SUB(NOW(), INTERVAL 1 MONTH);
Having an index on sales(sold_date) should help the query. An index on sales(sold_date, price) should be even better.
|
To spank or not to spank: For most American parents, it isn’t a question.
The majority of U.S. children have been spanked at some time in their life, despite a robust body of evidence that suggests spanking a child leads to problems in the future.
The latest evidence of the negative effects of spanking comes from researchers at Columbia University. After analyzing data from more than 1,500 families, they found that children who are spanked in early childhood are not only more likely to be aggressive as older children, they are also more likely to do worse on vocabulary tests than their peers who had not been spanked.
The study was published this week in the journal Pediatrics.
While several studies have found a connection between spanking and aggressive behavior, the finding that spanking could be linked to cognitive ability is somewhat new.
“Only a few studies have looked at the cognitive effects of spanking,” said Michael MacKenzie, an associate professor at Columbia University and lead author of the study. “We are still trying to learn if spanking has a direct effect on early brain development, or if families that spank more are less likely to read to their kids and use more complex language.”
In this latest study, MacKenzie analyzed data collected from more than 1,500 families as part of the Fragile Families and Child Well-Being Study (FFCW). The study followed children from 20 U.S. cities from birth to age 10. Most of the kids were born between 1998 and 2000.
Parents were asked questions about their child’s behavior and whether they had spanked their children within the past month. The answer was frequently yes: 57% of mothers and 40% of fathers reported spanking their children when they were 3 years old, as did 52% of mothers and 33% of fathers when their children were 5 years old.
When these kids turned 9, parents were asked to assess their behavior. The researchers also gave the children a test that measured their vocabulary.
The FFCW study also collected other data that might influence a 9-year old’s behavior and performance on the vocabulary test, including the age of the mother when the child was born, the mother’s self-reported stress levels, her intelligence scores, and her own impulsivity. The researchers also knew whether the child had a low birth weight and what his or her temperament was like during the first year of life, among other things. The researchers factored all of these into their analysis.
“If you were just to compare kids who were spanked and not spanked, the differences may not relate to the spanking, because the families that do spank may look different from non-spanking families in lots of ways,” said MacKenzie.
But even when the researchers controlled for these differences, " we still saw that spanking is an influencing factor in future behaviors.”
The researchers found a clear connection between spanking at age 5 and the child’s behavior at age 9. Compared to children who were never spanked by their mothers, those who were spanked at least twice a week scored 2.66 points higher on a test of aggression and rule-breaking, while those who were spanked less frequently scored 1.17 points higher, according to the study. To get a sense of how much extra aggression that is, boys tend to score 1 point higher on this test than girls, MacKenzie said.
The effects of spanking by fathers were different. Compared with children who were never spanked by their dads, those who were spanked at least twice a week scored 5.7 points lower on a vocabulary test, the researchers found. To put that in perspective, MacKenzie noted that children whose moms dropped out of high school score 2.6 points lower on this test, on average, than children whose moms finished college.
MacKenzie believes that this research shows a need for public health officials and pediatricians to reexamine how they are talking about spanking.
“Spanking is still the typical experience for most kids,” he said. “We have to start being more thoughtful about how we present this information for parents in a way that they can receive it.”
So many parents have a hard time accepting that spanking is truly bad for kids, probably because they were spanked as children and think they turned out OK.
“The decision to spank is tied to most parents’ own rearing experiences,” said MacKenzie. “It is intimately tied to family history.”
Follow me on Twitter to stay up to date on studies related to parenting.
ALSO:
Researchers: Regular bedtimes lead to better behaved kids
Depressed moms, depressed offspring: An unbroken chain?
Grouchy, angry, irritable and depressed: the hard cases, study says |
Maine's highest court on Tuesday rejected a national anti-gay marriage group's latest bid to shield the identities of the donors who contributed to its effort to defeat the state's gay marriage law in 2009.
The National Organization for Marriage had sought permission to delay submitting a campaign finance report that the Maine Commission on Governmental Ethics and Election Practices ordered it to file last year when it fined the group $50,250 for its involvement in overturning the law supporting same-sex marriage six years ago.
But the Maine Supreme Judicial Court said Tuesday that NOM can't put off filing the report and revealing its donor list until after the court considers the group's challenge of the commission's ruling because the justices said it's unlikely that the Washington D.C.-based organization will win its appeal.
"Enough is enough," Mills said in a statement. "NOM has fought for almost six years to skirt the law and to shield the names of the out-of-state donors who bank-rolled their election efforts. The time has come for them to finally comply with state law like everyone else."
After Maine's same-sex marriage law was overturned at the ballot box in 2009, it was legalized again by voters in 2012.
Maine's ethics commission ruled last year that the group broke the law by not registering as a ballot question committee and not filing campaign finance reports despite playing a central role in the 2009 referendum. The commission said the group gave nearly $2 million to Stand for Marriage Maine, the political action committee that led the repeal effort.
NOM has already paid the fine, which is thought to be the largest campaign finance penalty in state history.
But the group maintains that it followed the law, arguing that none of its donations were raised specifically for the purposes of defeating Maine's same-sex marriage law. The group, which has long fought in Maine courts to keep its donor list secret, said that revealing their identities will make people weary to contribute in the future.
Brian Brown, president of NOM, said Tuesday that he needs to discuss the decision with his lawyer to determine the group's next steps. But he said he believes that NOM is being unfairly penalized by the commission and the court because of its views on marriage.
"These are all unjust, illegitimate decisions," Brown said. "It does not bode well for the body politic when the judges and the ethics commission get to punish those they disagree with."
The supreme court acknowledged that forcing NOM to disclose their donor list will likely make the group's appeal of the commission's decision moot.
But the justices said that NOM hasn't put forward any persuasive constitutional challenges to the commission's decision or shown that the panel made any errors in reaching its conclusion, and therefore, hasn't proven that it will has a good chance of succeeding in its appeal.
The content contained on the web site has been prepared by BLN as a service to the internet community and is not intended to constitute legal advice or a substitute for consultation with a licensed legal professional in a particular case. Law Firm Website Design by Law Promo |
Actress/director Sarah Polley detailed how senility shattered a long-married couple in her directorial debut, the 2006 film “Away From Her.”
Now, Polley is moving in a more audacious direction, examining what happens when a perfectly happy married woman meets a man with whom she has a laboratory full of chemistry?
It’s a love triangle without overt villains, a story with a love struck couple stretching marital bonds to the breaking point while never dismissing the institution or its cultural value.
“Take This Waltz” may be challenging, but it’s not with structural defects. Polley’s dialogue can be cloying and overstated – that is, when the situations aren’t comically obvious and manipulative. Michelle Williams’ latest bravura turn holds this triangle together, letting us feel her anguish and longing in ways that tug at our hearts while her character comes to a series of shattering realizations.
Margot and Lou (Williams and Seth Rogen) live a contented life in a warmly captured Toronto neighborhood. They tease each other with violent jokes, trot out funny accents as part of their foreplay rituals and live to snuggle themselves to sleep.
Margot meets a handsome man (Luke Kirby) at such a park, and the two immediately share a warm, fizzy chemistry. They later sit next to each other on a plane (rom-com coincidence!) where their sexually charged bickering continues. It’s instant attraction, and when they part she sheepishly tells him she’s married, and both parties assume that will be that.
But Daniel just so happens to live a few feet away from Margot’s house, and when he hauls out his human-powered rickshaw each morning (precious alert!) she can’t help but rise early to see him off.
What follows is a tentative relationship made of stolen moments and not so chance encounters. They both know it’s wrong, but proximity and curiousity win out nearly every time.
Williams began her career on “Dawson’s Creek,” the kind of potboiler that leaves many actors wanting for work upon cancellation. She’s not a traditional beauty, yet her talent lies in laying her characters bare for our inspection. Watching her fall in love is to witness acting by degrees. You can see her heart flutter, hear her pulse quicken.
When Daniel describes what he would do to her should they ever dare to consummate their passions Williams melts before his eyes, and ours. It could be the most erotic movie moment of the year, even though no one removes so much as a sock or scarf.
Rogen puts aside his raunchy comedy mannerisms – although his staccato pot laugh remains – to make Lou the kind of man most woman would adore unconditionally. Will it be enough?
Polley’s story stumbles badly in the final moments, from a ridiculously arranged montage to a subplot lugging co-star Sarah Silverman’s character back into the picture to assist the resolution. The bruised feelings and tenderness Polley’s film generate remain, growing stronger during the thorny emotional climax.
“Take This Waltz” will linger In your thoughts, even as its tropes and imperfections quickly fade away. |
CAGE, a cancer/testis antigen, induces c-FLIP(L) and Snail to enhance cell motility and increase resistance to an anti-cancer drug.
Cancer associated gene (CAGE) regulates expression of epithelial-mesenchymal transition (EMT)-related proteins through extracellular regulated kinase (ERK), Akt and nuclear factor kappaB (NF-kB) in mouse B16F10 melanoma cells. Snail, a EMT-related protein, mediates the effect of CAGE on the induction of matrix metalloproteinase-2 (MMP-2) and cancer cell motility. C-Flice inhibitory protein mediates the effect of CAGE on the induction of MMP-2 and cell motility by the induction of Snail. CAGE was shown to protect cells against celastrol, an anti-cancer agent. Celastrol-resistant B16F10 melanoma cells had a higher expression level of c-FLIP(L) and Snail as compared with a sensitive cell line. |
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Dogs are nothing if not expressive. Anyone who's ever owned a dog knows how emotive they are; from puppy-dog eyes begging you for a piece of your sandwich, to the guilty look they give you when they-know-you-know they've done something naughty. This means that dogs have some of the best reaction faces of any animal, so we scoured the internet for some of the best ones. |
Tuning the brain for motherhood: prolactin-like central signalling in virgin, pregnant, and lactating female mice.
Prolactin is fundamental for the expression of maternal behaviour. In virgin female rats, prolactin administered upon steroid hormone priming accelerates the onset of maternal care. By contrast, the role of prolactin in mice maternal behaviour remains unclear. This study aims at characterizing central prolactin activity patterns in female mice and their variation through pregnancy and lactation. This was revealed by immunoreactivity of phosphorylated (active) signal transducer and activator of transcription 5 (pSTAT5-ir), a key molecule in the signalling cascade of prolactin receptors. We also evaluated non-hypophyseal lactogenic activity during pregnancy by administering bromocriptine, which suppresses hypophyseal prolactin release. Late-pregnant and lactating females showed significantly increased pSTAT5-ir resulting in a widespread pattern of immunostaining with minor variations between pregnant and lactating animals, which comprises nuclei of the sociosexual and maternal brain, including telencephalic (septum, nucleus of the stria terminalis, and amygdala), hypothalamic (preoptic, paraventricular, supraoptic, and ventromedial), and midbrain (periaqueductal grey) regions. During late pregnancy, this pattern was not affected by the administration of bromocriptine, suggesting it to be elicited mostly by non-hypophyseal lactogenic agents, likely placental lactogens. Virgin females displayed, instead, a variable pattern of pSTAT5-ir restricted to a subset of the brain nuclei labelled in pregnant and lactating mice. A hormonal substitution experiment confirmed that estradiol and progesterone contribute to the variability found in virgin females. Our results reflect how the shaping of the maternal brain takes place prior to parturition and suggest that lactogenic agents are important candidates in the development of maternal behaviours already during pregnancy. |
'use strict';
const gulp = tars.packages.gulp;
const plumber = tars.packages.plumber;
const concat = tars.packages.concat;
const notifier = tars.helpers.notifier;
const pagesAndDataFilesProcessing = require(`${tars.root}/tasks/html/helpers/pages-and-data-files-processing`);
/**
* concat data for components and some other sources to one file
*/
module.exports = () => {
return gulp.task('html:concat-mocks-data', () => {
return gulp
.src(
[
`./markup/pages/**/*.${tars.templater.ext}`,
`!./markup/pages/**/_*.${tars.templater.ext}`,
`./markup/${tars.config.fs.componentsFolderName}/**/data/data.js`,
`${tars.config.devPath}temp/symbols-data-template.js`,
],
{ allowEmpty: true },
)
.pipe(
plumber({
errorHandler(error) {
notifier.error(
`An error occurred while concating ${tars.config.fs.componentsFolderName}'s data.`,
error,
);
},
}),
)
.pipe(pagesAndDataFilesProcessing())
.pipe(concat('mocksData.js', { newLine: ',\n\n' }))
.pipe(gulp.dest(`${tars.config.devPath}temp/`))
.pipe(notifier.success(`Data for ${tars.config.fs.componentsFolderName} ready`));
});
};
|
The present invention relates to a defect substitution method of a disc-shaped recording medium having a sector structure, and to an apparatus for recording and reproducing data on a disc-shaped recording medium using said defect substitution method, and more specifically relates to an optical disc defect management method of an optical disc in a recording system in which error detection and correction coding spans a plurality of sectors, and to an optical disc recording and reproducing apparatus.
High speed random access is possible with disc-shaped recording media, and a high recording density can be achieved by formatting a disc with a narrow data track pitch and bit pitch. Disc-shaped recording media can be generally categorized based on differences in the applicable recording method as either a magnetic disc or optical disc, and can be further classified as either a fixed type or removable type media based on differences in the method whereby the medium is mounted in the recording/reproducing apparatus during use. The smallest recording unit of the physical recording area to which data is generally recorded on disc-shaped recording media is called a xe2x80x9csector.xe2x80x9d Sectors that cannot be used for data storage also occur in disc-shaped recording media as a result of defects during manufacture or damage occurring after manufacture. In addition to data writing errors occurring as a result of writing data sectors that are defective as a result of damage to the disc-shaped recording medium itself, data writing errors attributable to the operating environment can also occur as described below.
Optical discs, of which the DVD is typical, have been widely used in recent years as a large capacity recording medium because of their high recording density. Further advances in recording density have also been achieved to further increase storage capacity. Optical discs, however, are typically manufactured from low rigidity materials such as polycarbonate, and even disc deflection resulting from the dead weight of the disc cannot be ignored. In addition, this type of optical disc is commonly used as a replaceable, removable recording medium. For use, the disc is inserted into a recording and reproducing apparatus and mounted on a rotating spindle, and the positioning precision of the disc therefore cannot be assured.
It is also common to directly insert optical discs into the recording and reproducing apparatus without housing the disc in a protective case. Even when used housed in such a protective case, however, the entire recording medium is exposed during recording and reproducing because the protective case is not airtight. That is, optical disc recording media have essentially no shielding against the ambient environment. It should be noted that the problems specific to optical recording media reside in the point that these media are different from the hard disc recording media, including both low recording density fixed discs and removable hard discs, which are also a magnetic storage medium.
In addition to problems associated with their rigidity, mounting precision, and low airtightness, when an optical disc recording medium is inserted into a recorder and recorded or played, normal recording and reproducing can be inhibited by variations in the relative position to the optical pickup, or by foreign matter in the air interfering with the laser from the optical pickup. In such cases, data reading and writing can be obstructed through a wide band of the recording area, and burst mode recording and reproduction errors occur easily, as a result of the narrow track pitch and dot pitch enabling high density recording, even if there are no disc defects or damage to the information sector of the optical disc recording medium. While such burst-mode recording and reproducing problems occur easily in optical disc recording media, they are also found in the above-noted magnetic recording media and are common to all types of disc-shaped recording medium.
xe2x80x9cRecording defectxe2x80x9d is a general term for the inability to record as a result of a defect or damage to the recording medium itself or the conditions under which the disc is used. If a recording defect occurs when recording data to a particular sector, data is recorded continuously to the recording medium by saving the data to a reserved recording sector area, which is reserved separately from the normal data recording sectors, no matter what the cause of the recording defect. This operation of recording to a reserved sector area data that should be recorded to the sector in which a recording defect occurred is called xe2x80x9calternative recording,xe2x80x9d and the reserved sector area used for alternative recording is called an xe2x80x9calternative area.xe2x80x9d
In consideration for the above-noted problems, an object of the present invention is therefore to provide a defect management method whereby the size of the required alternative area can be suppressed and a disc-shaped recording medium can be efficiently used, and to provide a recording and reproducing apparatus for a disc-shaped recording medium.
A disc-shaped recording medium recording and reproducing apparatus for recording data by sector unit to a disc-shaped recording medium having a structure with a plurality of recording sectors, said disc-shaped recording medium recording and reproducing apparatus characterized by comprising: a coding means for error detection and correction coding said data twice, in row and column directions, and segmenting said data into sector units; a means for recording data coded in sector units to a sector in a first recording area of said disc-shaped recording medium; a defective sector discrimination means for reproducing said sector to discriminate whether the sector is a defective sector; and a defective sector substitution means for, when said sector is determined to be a defective sector, recording data recorded to a defective sector to an alternative sector in a second recording area disposed on said disc-shaped recording medium. |
WASHINGTON (Reuters) - AT&T told a federal judge late Thursday it should reject any request by the U.S. Justice Department to force it to divest its DirecTV unit or Turner networks as part of approving its proposed $85.4 billion acquisition of Time Warner Inc.
FILE PHOTO: A combination photo shows the Time Warner shares price at the New York Stock Exchange and AT&T logo in New York, NY, U.S., on November 15, 2017 and on October 23, 2016 respectively. REUTERS/Lucas Jackson (L) and REUTERS/Stephanie Keith/File Photos
The publication of the closing briefs from both sides brings to end the trial over a deal which took on broader political significance immediately after it was announced in October 2016.
President Donald Trump, a frequent critic of Time Warner’s CNN network, attacked the deal on the campaign trail last year, vowing that as president the Justice Department would block it.
Last week, a Justice Department attorney said Judge Richard Leon should consider requiring AT&T to make a “partial divestiture.”
The Justice Department had urged AT&T last year to divest either DirecTV, the largest pay TV company with more than 20 million subscribers, or TimeWarner’s Turner networks because the government said AT&T could use Time Warner content as a “weapon” to raise prices.
The Justice Department had demanded divestitures because it argued that ATT would have the ability to raise prices on Time Warner content for pay TV rivals.
“Divestitures here would destroy the very consumer value this merger is designed to unlock. Divesting DirecTV would eliminate the price decrease for millions of DirecTV consumers predicted by the government itself, and divesting Turner would eliminate the content innovations and the advertising benefits that put downward pressure on Turner prices,” the company said in a court filing.
Leon is expected to decide by June 12 whether to approve the merger. The Justice Department has said it is illegal because consumers would end up paying more for television while AT&T and Time Warner say they need the deal to compete with internet titans like Facebook Inc and Netflix Inc
“The government did not even begin to make a credible case that the merger would likely harm competition, substantially or even just a little,” AT&T said in its closing brief. “This is not a close case. The government failed to meet its burden for multiple independent reasons.”
The Justice Department’s final brief was filed under seal late Thursday and a redacted version has not yet been made public.
The government argued the deal would mean that consumers will pay more since AT&T could elect to raise prices for Time Warner content to other pay TV companies, like Charter Communications or Cox. The Justice Department has also said that AT&T could refuse to license the content to new, cheaper online services.
AT&T, for its part, has argued that Time Warner’s licensing fees were too valuable for the company to forego. Time Warner reported better-than-expected quarterly revenue in late April, an increase of 10 percent to $3.34 billion, because of advertisers associated with college basketball games.
AT&T sought to assuage critics by offering to submit to third-party arbitration any disagreement with distributors over the pricing for Time Warner’s networks and to promise not to black out programing during arbitration. The offer is good for seven years.
Judge Leon, who asked few questions during the trial, asked witnesses several times if they felt the arbitration proposal was adequate.
Leon rejected a request by AT&T to force the Justice Department to turn over records that could have shed light on whether Trump pressured the Justice Department to try to block the deal. |
Two-photon fluorescence imaging super-enhanced by multishell nanophotonic particles, with application to subcellular pH.
A novel nanophotonic method for enhancing the two-photon fluorescence signal of a fluorophore is presented. It utilizes the second harmonic (SH) of the exciting light generated by noble metal nanospheres in whose near-field the dye molecules are placed, to further enhance the dye's fluorescence signal in addition to the usual metal-enhanced fluorescence phenomenon. This method enables demonstration, for the first time, of two-photon fluorescence enhancement inside a biological system, namely live cells. A multishell hydrogel nanoparticle containing a silver core, a protective citrate capping, which serves also as an excitation quenching inhibitor spacer, a pH indicator dye shell, and a polyacrylamide cladding are employed. Utilizing this technique, an enhancement of up to 20 times in the two-photon fluorescence of the indicator dye is observed. Although a significant portion of the enhanced fluorescence signal is due to one-photon processes accompanying the SH generation of the exciting light, this method preserves all the advantages of infrared-excited, two-photon microscopy: enhanced penetration depth, localized excitation, low photobleaching, low autofluorescence, and low cellular damage. |
Listen to Vaas—the insane pirate at the center of open-world first-person-shooter Far Cry 3—bitch about the bass-heavy tracks that pop up in damn near every big-budget video game trailer. Yes, he's naked some of the time but don't let his total nudity distract you from the truth of his words. "All these f***ing games playing the exact same f***ing beats…" Preach it, Vaas. |
The news about Joe Biden has taken on a completely surreal quality. For a long time, the headlines were about his declining mental state, which is becoming hard to ignore. This was bizarre enough in a presumptive Democrat candidate for the presidency.
Then, Tara Reade dropped a bombshell, alleging that the same politician known for publicly groping and sniffing women and children had sexually assaulted her. The media assiduously ignored Reade's allegations as long as they could and eventually reported on them only to dismiss both Reade and the allegations.
The media's worst nightmare came true, though, when corroborating evidence about Reade's allegations started piling up. It was easy enough to downplay corroboration when it came from her brother and a friend. Of course they'd side with her. But when a phone call from Reade's mother to The Larry King Show in 1993 — a time contemporaneous with the event — popped up and Mom was talking about her daughter's problems with a "prominent senator," things got dicey.
The nightmare reached Stephen King proportions yesterday, when two women who knew Reade in the mid-1990s, not long after the alleged assault, reported that Reade had told them about the assault. While the fact that she told them shortly after she left Biden's office does not prove that he attacked her, it certainly proves that she's not creating the story out of whole cloth today for some nefarious purpose. By contrast, Christine Blasey Ford, a pro-abortion fanatic, first started telling the story about Brett Kavanaugh when he was touted as a possible Supreme Court nominee during the Bush presidency, decades after the event had allegedly happened.
Lynda LaCasse, who intends to vote for Biden no matter what he did, was Reade's neighbor and friend in 1995 or 1996. She told Business Insider that she remembers Reade telling her about Biden's conduct two or three years before:
LaCasse told Insider that in 1995 or 1996, Reade told her she had been assaulted by Biden. "I remember her saying, here was this person that she was working for and she idolized him," LaCasse said. "And he kind of put her up against a wall. And he put his hand up her skirt and he put his fingers inside her. She felt like she was assaulted, and she really didn't feel there was anything she could do." LaCasse said that she remembers Reade getting emotional as she told the story. "She was crying," she said. "She was upset. And the more she talked about it, the more she started crying. I remember saying that she needed to file a police report." LaCasse said she does not recall whether Reade supplied any other details, like the location of the alleged assault or anything Biden may have said. "I don't remember all the details," LaCasse said. "I remember the skirt. I remember the fingers. I remember she was devastated."
As if that's not enough, Lorraine Sanchez, with whom Reade worked from 1994 to 1996, also heard from Reade that something happened in D.C.:
"[Reade said] she had been sexually harassed by her former boss while she was in DC," Sanchez said, "and as a result of her voicing her concerns to her supervisors, she was let go, fired." Sanchez said she does not recall if Reade offered details about the sort of harassment she allegedly suffered, or if she named Biden. "What I do remember," Sanchez said, "is reassuring her that nothing like that would ever happen to her here in our office, that she was in a safe place, free from any sexual harassment."
Michelle Goldberg, a New York Times writer known for using different standards for Biden and Kavanaugh, says the new evidence is a "nightmare" — not because a woman suffered at Biden's hands, but because it hurts Biden's chances at the White House:
This is the most persuasive corroborating evidence that has come out so far. What a nightmare. https://t.co/u4yPbEElaf — Michelle Goldberg (@michelleinbklyn) April 27, 2020
Goldberg is frightened, but the Washington Post is still valiantly spinning, this time claiming that these new facts are merely partisan amplification of “efforts” to “question” Biden’s behavior:
Developments in allegations against Biden amplify efforts to question his behavior https://t.co/OWXvnKzvvN — Post Politics (@postpolitics) April 28, 2020
What does amplify the problem is that someone remembered a video from last year in which Kamala Harris said she believes those Biden accusers who complained about unwanted touching. Scratch her off Biden's list of possible female choices for vice president. Maybe Biden can expand his explorations by looking at so-called transgender women.
So far, though, Biden's response to the allegation has simply been to deny it in a formal statement. The media have refrained from asking him any questions about it.
Meanwhile, Biden's latest campaign video gives more fuel to the speculation that he is so lost in dementia that he can no longer speak for himself. He doesn’t even look like Jill Biden's ventriloquist dummy here because his lips aren't moving. Instead, he just looks like a dummy: |
Legg Mason Inc. increases quarterly dividend
Legg Mason Inc. on Tuesday announced a quarterly divided of 13 cents per share, an 18 percent increase. The Baltimore-based money manager said the dividend will be paid on July 8 for those who are shareholders as of June 11.
When it comes to generating income from investments, Americans' expectations for returns are significantly higher than what they are actually earning, according to a survey released this morning by Legg Mason Inc.
Nearly a year after being acquired by rival Men's Wearhouse in a contentious takeover struggle, Jos. A. Bank Clothiers will lay off 122 employees at the company's corporate headquarters in Hampstead, a company spokesman said Monday. |
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Gottfried turns around Wolfpack quickly
A year ago, N.C. State was on Day 5 of what would turn out to be a 21-day coaching search, a final wearying coda to a season that went nowhere. Mark Gottfried’s name wasn’t even on the radar at that point.
On Monday, Gottfried sat inside his office at the Dail Center watching video of Kansas on an iPad. The Wolfpack’s players had the day off. Gottfried did not. He was scouting, planning, going on radio shows and preparing to travel to St. Louis for the NCAA Tournament’s Midwest Regional.
A year ago, people didn’t know where the program was headed, who the coach was going to be, which players would be back. In less than 12 months, Gottfried not only has taken N.C. State back to the NCAA Tournament for the first time in six years, but beat two higher-seeded teams to advance to a regional that also includes North Carolina.
“Honestly, I didn’t know what to expect,” N.C. State forward Richard Howell said. “But I am grateful for the situation, that coach Gottfried came in. I feel like it’s a blessing. The amount of confidence he has in us is unbelievable. I feel like that’s why we’re so good.”
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It’s a turnaround of Homeric proportions, not just for the program, but for the coach. Gottfried resigned in midseason at his alma mater Alabama 2 1/2 years ago and spent two full seasons adrift in that coaching purgatory known as “television analyst,” unsure if he’d ever find the right opportunity to get back into the game.
He felt stranded in his daily routine with no players, no staff, no practices, only milk and eggs to pick up at the supermarket. It’s hard to feel stranded when your phone overflows with 79 text messages, as Gottfried’s did after Sunday’s win against Georgetown.
He had been through this before, on Jim Harrick’s staff at UCLA when it took over a program with unparalleled tradition that had fallen on hard times and won a national title. He didn’t take any template from that, no road map to rebuilding, just a belief that if it was once great, it can be great once again.
Some of this isn’t witchcraft. Gottfried upgraded the schedule significantly, which helped land an at-large bid to the NCAA Tournament. N.C. State athletics director Debbie Yow agreed to make funds available to give Gottfried essentially his choice of assistants. He used that money to bring in a solid Xs-and-Os guy with head-coaching experience in Bobby Lutz, two strong recruiters in Orlando Early and Rob Moxley and a new strength coach in Joe Alejo.
And, perhaps most important, they all found a team eager to get to work. When Gottfried took the job, junior forward Scott Wood, in his first meeting with the coach, told him he didn’t want to be part of any “rebuilding year.”
“I don’t want to just play to get better,” Wood told Gottfried. “I think we’ve got the talent and the pieces that we could be a dominant team.”
Gottfried quickly saw why there was all that talk about an ACC title when C.J. Leslie committed during the summer of 2010. The raw talent was there; it was just very raw.
“These guys had never accomplished anything in college basketball,” said Harrick, Gottfried’s mentor. “Most guys on scholarship are cocky without being confident. That’s what these guys were. I watched them walk off the floor Sunday, and they were confident without being cocky. I like that. That’s the way you want your players.”
Under former coach Sidney Lowe, N.C. State wasn’t a poorly coached team. It was a lightly coached team. He was an NBA guy, and he expected players to prepare and motivate themselves. Gottfried and his staff have added structure and held players accountable, but for every kick in the pants, there’s been a pat on the back, in varying degrees for each player.
They’ve embraced Leslie — “Just by calling him ‘Calvin,’ that broke the ice between the two,” Harrick observed — challenged Howell to improve his fitness, bolstered Wood’s confidence and empowered point guard Lorenzo Brown, the team’s most important player, to run the offense.
Related stories from Wichita Eagle
“Sometimes, it’s uncomfortable,” Gottfried said. “But I think those guys came to a point where they really decided to trust our staff, Calvin especially. Some guys, it takes longer. We’re all different. Some guys trust you right off the bat. Other guys, there’s a wall where you can’t penetrate that wall. And you can feel it. But I think there’s been a lot of trust back and forth.”
If those were the pieces, Gottfried brought some of the glue to put them together. He brought notebooks he’d filled during his time as a television analyst, approaching the games he called like he was scouting opponents, all filed under the heading, “If I get another job…”
That job came along last spring. Yow pursued a number of candidates without success, even sending out an email to Wolfpack Club members that apologized for how long the search was taking and warned it might take a little longer.
“We have not tried to sugarcoat the challenge of rebuilding our basketball program,” Yow wrote in the email. “Our absence for five consecutive years from the NCAA Tournament was noted by each coach as evidence that the program is in poor shape and will require a special effort to rebuild.”
A day later, she sprung a surprise: Gottfried. The results have exceeded even Yow’s wildest hopes.
“I think this ‘special effort’ is a little further advanced at this point than I had envisioned, absolutely,” Yow said Monday.
“He’s been masterful at changing the whole culture and bringing out the best in these young men. It has been a process, not an event. This has been day to day for a year, and he’s done a terrific job.”
With a top-10 recruiting class coming in next season, many Wolfpack fans already were looking forward to the future. That was before the future, to everyone’s enduring surprise, turned out to be now. |
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Located 3 blocks from Plaza de Armas Square, VIP House The Garden and more offers accommodations in Cusco. Free WiFi access is available. Some rooms here feature a private bathroom, a TV and garden views. A daily breakfast is included. At VIP House The Garden guests will find a 24-hour front desk, a garden and a terrace. Other facilities offered at the property include a shared lounge, a games room and a tour desk. The property is located 3 blocks from San Cristobal Park. |
Recently, a novel scheme for mapping the quantum state of a light field onto an atomic ensemble was proposed [@EITPRA] in which the electromagnetically induced transparency plays a major role. This “storage of light” technique enables us to overcome the difficulty of localizing photons which are mainly used as carriers of quantum information. While the storage and retrieval of a single photon state has already been realized, [@DLCZ-EIT; @Kuz] it has not been demonstrated for a squeezed vacuum. It should be noted that the former experiment can be performed conditionally whereas the latter should be demonstrated in deterministic manner and is thus sensitive to field loss. Mapping the squeezed state onto an atomic ensemble is a critical task not only for quantum information processing but also for ultra-precise measurement of atomic spins.
To perform such an experiment, it is necessary to generate a high-level squeezed vacuum resonant on an atomic transition. By utilizing KNbO$_3$ crystals, a squeezed vacuum has already been generated resonant on the Cs D-lines (852 nm, 894 nm) and the interaction between the atoms and the squeezed vacuum has also been investigated intensively [@ESP92]. However, there have been relatively few experiments done on the generation of a squeezed vacuum resonant on the Rb D-lines (780 nm, 795 nm), while Rb has played an important role in quantum information processing along with Cs. So far experiments have been limited to -0.9 dB squeezing with quasi-phase-matched MgO:LiNbO$_3$ waveguides [@AKA-PRL] and -0.85 dB squeezing with the self-rotation of Rb itself [@self-rotation]. Note that the KNbO$_3$ crystal which is useful at the Cs resonance line cannot be utilized at the Rb one [@F1]. In this letter we demonstrate -2.75 dB squeezing at 795 nm using a periodically-poled KTiOPO$_4$ (PPKTP) crystal [@F1; @F2], which to the best of our knowledge, is the highest squeezing obtained at the Rb D$_1$ line.
Figure \[Abst\_E\_setup\] shows the experimental setup. A continuous-wave Ti:Sapphire laser (Coherent, MBR 110) at 795 nm was employed in this experiment. The beam from the Ti:Sapphire laser was phase-modulated by an electro-optic modulator (EOM). This modulation was utilized to lock a cavity for frequency doubling and a cavity for squeezing using the FM sideband method [@Drever83].
![Experimental setup. ISO: optical isolator, EOM: electro optic modulator, OPO: sub-threshold degenerate optical parametric oscillator, HBS: 50:50 beam splitter, PT: partial transmittance mirror, HD: balanced homodyne detector, PD: photodiode, SM: single mode fiber.[]{data-label="Abst_E_setup"}](a.eps)
The frequency doubler had a bow-tie type ring configuration with two spherical mirrors (radius of curvature of 100 mm) and two flat mirrors. One of the flat mirrors (PT1) had a reflectivity of $90 \%$ at 795 nm and was used as the input coupler, while the other mirrors were high-reflectivity coated. All the mirrors had reflectivities of less than $5 \%$ at 397.5 nm. A 10 mm long PPKTP crystal (Raicol Crystals) was used for second harmonic generation. Figure \[b\] shows the dependence of the blue output power on the fundamental laser power incident on the frequency doubler. The output from the frequency doubler was stable over tens of minutes provided the fundamental power was less than 290 mW.
![ Second-harmonic output power versus incident laser power.[]{data-label="b"}](b.eps)
The generated 397.5 nm beam pumped a degenerate optical parametric oscillator (OPO) that also had a bow-tie type ring configuration using two spherical mirrors (radius of curvature of 50 mm) and two flat mirrors. One of the flat mirrors (PT2) had a reflectivity of $90 \%$ at 795 nm and was used as the output coupler. The round trip cavity length was $l = 600 mm$ and a beam waist radius inside the crystal was $20$ $\mu m$. A 10 mm long PPKTP crystal was again used for parametric down conversion. The OPO was driven below the parametric oscillation threshold $P_{th} = 150 \mathrm{mW}$, which was derived theoretically from the nonlinear efficiency of the crystal $E_{NL} = 0.023 \mathrm{W^{-1}}$, the intra-cavity loss $L = 0.0173$, and the transmittance of the input coupler $T = 0.10$ using the following expression $
P_{th} = (T + L)^2/(4 E_{NL}).
$
The IR beam from the OPO squeezer was split into four beams: an alignment beam, a probe beam, a lock beam, and a local oscillator beam for homodyne detection. The alignment beam was an auxiliary beam and was used for aligning the cavity, measuring the intra-cavity loss, and matching the spatial mode of the pump beam with the OPO cavity. For the last application, the alignment beam was converted to the second harmonic using the OPO and used as a reference beam. This reference second harmonic beam propagated in the opposite direction to the pump beam and represented the OPO cavity mode. This meant that by matching the spatial mode of the reference beam with that of the pump beam, the pump beam could be matched with the OPO cavity mode.
The probe beam was utilized to measure the classical parametric gain. This was done by injecting the beam into the OPO cavity through a high-reflection flat mirror and detecting the transmitted probe beam from the output coupler with a photodiode (PD3).
The lock beam was also injected into the cavity through a high-reflection flat mirror in the counter propagating mode to the probe beam. The transmitted lock beam from the output coupler was detected with a photodiode (PD2) and the error signal for locking the cavity length was extracted using the FM sideband method.
The generated squeezed light was combined with a local oscillator (LO) at a half-beam splitter (HBS) and detected by a balanced homodyne detector (HD). The HD had two photodiodes (Hamamatsu photonics, S-3590 with anti-reflection coating) that had a quantum efficiency of $98 \% $. The output of the HD was measured at the sideband component of $1 \mathrm{MHz}$ using a spectrum analyzer. The circuit noise level of the homodyne detector was 14.0 dB below the shot noise level.
Figure \[Abst\_E\_sv\_exp\] shows the measured quantum noise levels at a pump power of 61 mW as the local oscillator phase was scanned. The noise level was measured with a spectrum analyzer in zero-span mode at 1 MHz, with a resolution bandwidth of 100 kHz and a video bandwidth of 30 Hz. The squeezing level of $-2.75 \pm 0.14 \mathrm{dB}$ and the anti-squeezing level of $+7.00 \pm 0.13 \mathrm{dB}$ were observed, where the standard deviation was estimated from a fitting based on eq. (\[Abst\_E\_sqv\]).
![Measured quantum noise levels.(i) Local oscillator beam phase was scanned.(ii) Shot noise level. Noise levels are displayed as the relative power compared to the shot noise level (0 dB). The settings of the spectrum analyzer were, zero-span mode at 1 MHz, resolution bandwidth = 100 kHz, video bandwidth = 30 Hz.[]{data-label="Abst_E_sv_exp"}](c.eps)
The variance of the output mode $S$ can be modeled using [@ESP92; @Collett84] $$\begin{aligned}
S = 1 + 4 \alpha \rho x \left[ \frac{\cos^2 \theta}{(1 - x)^2 + 4 \Omega^2} - \frac{\sin^2 \theta}{(1 + x)^2 + 4 \Omega^2} \right], \label{Abst_E_sqv}\end{aligned}$$ where $\theta$ is the relative phase between the squeezed light and LO, $\alpha$ and $\rho$ are the detection efficiency and the OPO escape efficiency, respectively. The detection efficiency $\alpha$ is the product of the photodiode quantum efficiency $\eta$, and the homodyne efficiency $\xi^2$ (where $\xi$ is the visibility between the output and the local oscillator mode): $\alpha = \eta \xi^2$. The OPO escape efficiency can be written as $
\rho = T/(T+L),
$ where $T$ and $L$ are the transmission of the output coupler and the intra-cavity loss, respectively. The pump parameter $x$ is defined by the pump power $P_{pump}$ and the oscillation threshold $P_{th}$, and is expressed using the parametric gain $G$ by $
x \equiv (P_{pump} / P_{th})^{1/2}
= 1 - 1/G^{1/2}.
$ The detuning parameter $\Omega$ is given by the ratio of the measurement frequency $\omega$ to the OPO cavity decay rate $\gamma = c(T+L)/l$, i.e. $\Omega = \omega / \gamma$, where $c$ is the speed of light.
In our setup, $\eta = 0.99$ and $\xi = 0.91$, therefore $\alpha = 0.82$. $T = 0.10$ and $L = 0.0173$ yield $\rho = 0.85$. Note that our crystal made no measurable difference to the intra-cavity loss in the presence of the pump beam [@F1]. The detuning parameter was $\Omega = 0.107$. The classical parametric gain of $G = 5.3$ measured with a 61 mW pump light yields $x = 0.57$. With these values, eq. (\[Abst\_E\_sqv\]), predicts theoretical squeezing / anti-squeezing levels of $-4.4 \mathrm{dB}$ and $+8.9 \mathrm{dB}$, respectively. This theoretical squeezing / anti-squeezing levels are become to $-4.1 \mathrm{dB}$ and $+8.7 \mathrm{dB}$ by accounting for the effect of the circuit noise.
We repeated the above measurement and analysis for various pump powers. The results are summarized in Fig. \[d\]. There is a similar discrepancy from the theoretical values for both squeezing and anti-squeezing data. This discrepancy can not be explained by simply introducing unknown field loss, because a squeezing is theoretically much sensitive to the field loss compared to an anti-squeezing. In the current setup, the spatial mode of the incident probe beam was not perfectly matched to that of the OPO cavity. Therefore, thermal lens effect caused by injection of the blue pump beam could modify the cavity mode and increase (or decrease) the transmittance of the probe beam. When we measured the parametric gain $G$, we set the transmittance of the probe beam without the pump beam to unity. If the thermal lens effect discussed above had occurred, measured parametric gain should be corrected. Introducing about 10$\%$ correction for the value of $G$ and considering unknown field loss, the discrepancy between theoretical values and squeezing/anti-squeezing data can be explained. The observed squeezing level became slightly degraded when the pump power reached 70 mW, which could be explained by mixing of the highly anti-squeezed component with the observed quadrature noise due to the temporal fluctuation in the LO phase.
![Squeezing and anti-squeezing levels for several powers of the pump beam. The circles and squares indicate measured values, while $+$ and $\times$ indicate theoretical values which are calculated using the parametric gains.[]{data-label="d"}](d.eps)
In conclusion, we observed $-2.75 \pm 0.14 \mathrm{dB}$ squeezing and $+7.00 \pm 0.13 \mathrm{dB}$ anti-squeezing at 795 nm, which corresponds to the D$_1$ transition of Rb atoms. It should be possible to achieve a higher squeezing level by increasing visibility of the homodyne system and reducing the phase fluctuation by stabilizing the setup actively. While electromagnetically induced transparency was observed with the squeezed vacuum in our previous work [@AKA-PRL], neither slow propagation nor storage could be realized due mainly to the low squeezing level. The squeezing level obtained in this study was much higher than that previously obtained with the PPLN waveguide and we thus believe that storage of the squeezed vacuum should be achievable with the current setup.
We gratefully acknowledge G. Takahashi, N. Takei, H. Yonezawa, and K. Wakui for their valuable comments and stimulating discussions. This work was supported by Grant-in-Aid for Young Scientists (A), and a 21st Century COE Program at Tokyo Tech “Nanometer-Scale Quantum Physics” by MEXT.
[99]{} M. Fleischhauer and M. D. Lukin, Phys. Rev. A [**65**]{} 022314 (2002) M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, nature (London) [**438**]{} 837 (2005). T. Chanèliere, D. N. Matsukevich, S. D. Jenkins, S. -Y. Lan, T. A. B. Kennedy, and A. Kuzmich, nature (London) [**438**]{} 833 (2005). E. S. Polzik, J. Carri, and H. J. Kimble, Appl. Phys. B [**55,**]{} 279 (1992). D. Akamatsu, K. Akiba, and M. Kozuma, Phys. Rev. Lett. [**92,**]{} 203602 (2004). J. Ries, B. Brezger, and A. I. Lvovsky, Phys. Rev. A [**68,**]{} 025801 (2003). S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, quant-ph/0602036 T. Aoki, G. Takahashi, and A. Furusawa, quant-ph/0511239 R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B [**31,**]{} 97 (1983). M. J. Collett and C. W. Gardiner, Phys. Rev. A [**30,**]{} 1386 (1984).
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Does histologic grading of inflammation in bone marrow predict the response of aplastic anaemia patients to antithymocyte globulin therapy?
We tested the hypothesis of teVelde and Haak that the degree of bone marrow inflammation in aplastic anaemia might correlate with an immunological process responsive to immunosuppressive therapy. 120 patients with aplastic anaemia but no suitable marrow donor were treated with horse antithymocyte globulin (ATG) and 53 who had matched sibling donors with bone marrow transplants. Pretreatment bone marrow histology in methacrylate and paraffin specimens was graded by degree of inflammatory infiltrate in a four-tiered system. High grade (II-III) was compared to low (O-I) as a correlate of response to ATG. Complete and partial response to ATG was seen in 50% of patients with high grade marrow and 31% of patients with low grade marrow (P = 0.099). Only one of four patients with grade III inflammation responded significantly to ATG treatment. Median survival following ATG therapy was similar in both groups as well. There was a significantly lower median age in the patients with low grade (24.5 years) versus high grade (37.5 years) inflammation (P = 0.016). Grade also had no prognostic value in the marrow transplant group. |
Q:
Is it possible to cast a type parameter?
According to the Implicit converting Logic which enables something like:
string str = "something";
Object o = str ;
I was expecting that assigning a Dictionary<string, string> to Dictionary<string, Object> would be possible, but this is not the case.
Is it possible to explicity cast the string value to Object without having to iterate through the keyValuePair-items?
EDIT1: replaced all Boxing/Unboxing words with converting and casting as comments and answers mention this isnt Boxing issue.
Thank you all
A:
Typecasting doesn't help you there but you can convert one to another with LINQ:
Dictionary<string, object> newDict;
newDict = dict.ToDictionary(pair => pair.Key, pair => (object)pair.Value);
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The Role of Soluble CD40L Ligand in Human Carcinogenesis.
The role of CD40/CD40L in carcinogenesis is widely examined. The mechanisms linking the CD40/CD40L system and the soluble form of CD40 ligand (sCD40L) with neoplasia are nowadays a topic of intensive research. CD40L and sCD40L belong to the TNF superfamily and are molecules with a proinflammatory role. A variety of cells express CD40L such as the immune system cells, the endothelial cells and activated platelets. Although many medications such as statins have been shown to reduce sCD40L, it is still debated whether specific treatments targeting the CD40/CD40L system will prove to be effective against carcinogenesis in the near future. A comprehensive search of the Pubmed Database was conducted for English-language studies using a list of key words. At diagnosis, serum samples of patients with neoplasia contained higher levels of sCD40L than healthy controls, suggesting that sCD40L may play a predictive role in human carcinogenesis. Patients with neoplasia had higher circulating sCD40L levels and it is likely that sCD40L may have a predictive role. It is still unclear whether sCD40L can be used as a therapeutic target. |
---
abstract: 'Let $A$ be a commutative comodule algebra over a commutative bialgebra $H$. The group of invertible relative Hopf modules maps to the Picard group of $A$, and the kernel is described as a quotient group of the group of invertible grouplike elements of the coring $A\ot H$, or as a Harrison cohomology group. Our methods are based on elementary $K$-theory. The Hilbert 90 Theorem follows as a corollary. The part of the Picard group of the coinvariants that becomes trivial after base extension embeds in the Harrison cohomology group, and the image is contained in a well-defined subgroup $E$. It equals $E$ if $H$ is a cosemisimple Hopf algebra over a field.'
address:
- 'Faculty of Engineering Sciences, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium'
- 'Faculty of Engineering Sciences, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium'
author:
- 'S. Caenepeel'
- 'T. Guédénon'
title: The relative Picard group of a comodule algebra and Harrison cohomology
---
[^1]
Introduction {#introduction .unnumbered}
============
Let $l$ be a cyclic Galois field extension of $k$. The Hilbert 90 Theorem tells us that every cocycle in $Z^1(C_p,l^*)$ is a coboundary. There exist various generalizations of this result. For example, if we have a Galois extension $B\to A$ of commutative rings, with Galois group $G$, then the cohomology group $H^1(G,\GG_m(A))$ is isomorphic to ${{\rm Pic}}(A/B)$, the kernel of the natural map from the Picard group of $B$ to the Picard group of $A$, see for example [@DI]. Now we can ask the following question: suppose that $G$ acts on $A$ as a group of isomorphisms. Can we still give an algebraic interpretation of $H^1(G,\GG_m(A))$? A second problem is whether there is any relation between $H^1(G,\GG_m(A))$ and the Picard group of the ring of invariants $B=A^G$.\
In this note, we will discuss these two problems in a more general situation: we will assume that $A$ is a commutative $H$-comodule algebra, with $H$ an arbitrary commutative bialgebra over a commutative ring $k$. We then ask for an algebraic interpretation of the first Harrison cohomology group $H^1_{\rm Harr}(H,A,\GG_m)$ (with notation as in [@C2]). If $H$ is finitely generated and projective, then this Harrison cohomology group is isomorphic to a Sweedler cohomology group $Z^1_{\rm Harr}(H,A,\GG_m)$, and if $H=\ZZ G$ with $G$ a finite group, then it reduces to the cohomology group $H^1(G,\GG_m(A))$.\
We proceed as follows: we introduce the relative Picard group ${{\rm Pic}}^H(A)$ as the Grothendieck group of the category of invertible relative Hopf modules. The forgetful functor to the category of invertible $A$-modules induces a K-theoretic exact sequence, linking the Picard group of $A$, the relative Picard group, and the groups of unit elements of $A$ and the coinvariants $B=A^{{\rm co}H}$; the middle term in the sequence can be computed, and it is the group of invertible grouplike elements of the coring $A\ot H$. We show also that these grouplike elements are precisely the Harrison cocycles, and it follows from the exactness of the sequence that the first Harrison cohomology group is the kernel of the map ${{\rm Pic}}^H(A)\to {{\rm Pic}}(A)$, answering our first question.\
Then we observe that there is a similar exact sequence associated to the induction functor $\dul{{{\rm Pic}}}(B)\to \dul{{{\rm Pic}}}(A)$, and that the two exact sequences fit into a commutative diagram. If $A$ is a faithfully flat Hopf Galois extension of $B$, then the categories of $B$-modules and relative Hopf modules are equivalent, hence ${{\rm Pic}}(B)\cong{{\rm Pic}}^H(A)$, and we recover Hilbert 90. In general, we have an injection ${{\rm Pic}}(A/B)\to H^1_{\rm Harr}(H,A,\GG_m)$, and we can describe a subgroup of $H^1_{\rm Harr}(H,A,\GG_m)$ that contains the image of ${{\rm Pic}}(A/B)$. The image is precisely this subgroup if $H$ is a cosemisimple Hopf algebra over a field $k$.\
A special situation is the following: let $k$ be an algebraically closed field, $A$ a finitely generated commutative normal $k$-algebra, and $G$ a connected algebraic group acting rationally on $A$. Then $A$ is an $H$-comodule algebra, with $H$ the affine coordinate ring of $G$. In this case, our exact sequence was given by Magid in [@23], but apparently the author of [@23] was not aware of the connection to Harrison cohomology, grouplike elements of corings and the generalized Hilbert 90 Theorem.\
In [Section \[se:4\]]{}, we study the Harrison cocycles (or the grouplike elements in $A\ot H$) in some particular cases. First we look at the situation considered by Magid in [@23], and then it turns out that the grouplike elements of $G(A\ot H)$ are induced by the grouplike elements of $H$. In the situation where $A$ is a $\ZZ$-graded commutative $k$-algebra, the relative Picard group turns out to be the graded Picard group ${{\rm Pic}}_g(A)$ studied by the first author in [@C1]. If $A$ is reduced, then the grouplike elements of $A\ot H$ can also be described using the grouplikes of $H$, according to a result in [@C1].
Preliminary results
===================
[\[se:1\]]{}
The language of corings
-----------------------
[\[se:1.1\]]{} Relative Hopf modules can be viewed as comodules over a coring. This will be used in the sequel, and this is why we briefly recall some properties of corings. Recall that an $A$-coring is a comonoid in the monoidal category ${}_A{\mathcal{M}}_A$ of $A$-bimodules. Thus an $A$-coring $\CCC$ is an $A$-bimodule together with two $A$-bimodule maps $$\Delta_\CCC :\ \CCC\to \CCC\otimes_A\CCC \quad
\hbox{and}\quad \varepsilon_\CCC:\ \CCC\to A$$ satisfying the usual coassociativity and counit properties. We refer to [@4; @5; @6; @15; @26] for a detailed discussion of corings. $$G(\CCC)=\{X\in \CCC~|~\Delta_\CCC(X)=X\ot_A X~{\rm and}~\varepsilon_\CCC(X)=1\}$$ is the set of grouplike elements of $\CCC$. A right $\CCC$-comodule $M$ is a right $A$-module together with a right $A$-linear map $\rho_M :\ M\rightarrow M\otimes_A \CCC$ satisfying $$(M\otimes_A\varepsilon_\CCC)\circ \rho_M=M, \quad \hbox{and} \quad
(M\otimes_A\Delta_{\CCC})\circ \rho_M=(\rho_M \otimes_A \CCC)\circ \rho_M.$$ A morphism of right $\CCC$-comodules $f :\ M \to N$ is an $A$-linear map $f$ such that $$\rho_N \circ f=(f\otimes_A\CCC)\circ \rho_M.$$ ${\mathcal{M}}^\CCC$ will be the category of right $\CCC$-comodules and comodule morphisms. We have the following interpretation of the grouplike elements of $\CCC$.
[\[le:1.1\]]{} Let $\CCC$ be an $A$-coring. Then there is a bijective correspondence between $G(\CCC)$ and the set of maps $\rho:\ A\to A\ot_A\CCC=\CCC$ making $A$ into a right $\CCC$-comodule. The coaction $\rho_X$ corresponding to $X\in G(\CCC)$ is given by $$\rho_X(a)=Xa.$$ With this notation, $A^X=(A,\rho_X)\cong A^Y= (A,\rho_Y)$ as right $\CCC$-comodules if and only if there exists an invertible $b\in A$ such that $\rho_Y(b)=Yb=bX$.
The first part is well-known (and straightforward), see for example [@5]. Let $f:\ A^X\to A^Y$ be a right $\CCC$-colinear isomorphism. Then $f(a)=ba$ for some $b\in A$, which is invertible since $f$ is an isomorphism. The fact that $f$ is $\CCC$-colinear tells us that $$Yb=\rho_Y(f(1))=(f\ot_A\CCC)(\rho_X(1))=bX.$$ The converse property is obvious.
Relative Hopf modules
---------------------
[\[se:1.2\]]{} Let $H$ be a bialgebra over a commutative ring $k$, and $A$ a right $H$-comodule algebra. Throughout this note, we will assume that $H$ and $A$ are commutative. Then $A$ is a commutative algebra and we have a right $H$-coaction $\rho$ on $A$ such that $$\rho(ab)=a_{[0]}b_{[0]}\ot a_{[1]}b_{[1]},$$ for all $a,b\in A$. Here we use the Sweedler-Heyneman notation for the coaction $\rho$: $\rho(a)=a_{[0]}\ot a_{[1]}$, with summation implicitely understood. For the comultiplication on $H$, we use the notation $\Delta(h)=h_{(1)}\ot h_{(2)}$.\
A relative Hopf module $M$ is a $k$-module, together with a right $A$-action and a right $C$-coaction $\rho_M$ such that $$\rho_M(ma)=m_{[0]}a_{[0]}\ot m_{[1]}a_{[1]},$$ for all $a\in A$ and $m\in M$. The category of relative Hopf modules and $A$-linear $H$-colinear maps will be denoted by ${\mathcal{M}}^H_A$. The coinvariant submodule $M^{{\rm co}H}$ of $M\in {\mathcal{M}}^H_A$ is defined by $$M^{{\rm co}H}=\{m\in M~|~\rho_M(m)=m\ot 1\}.$$ $A^{{\rm co}H}=B$ is a $k$-subalgebra of $A$, and $M^{{\rm co}H}$ is a $B$-module. We obtain a functor $(-)^{{\rm co}H}:\ {\mathcal{M}}^H_A\to {\mathcal{M}}_B$, that has a left adjoint $T=-\ot_BA:\ {\mathcal{M}}_B\to {\mathcal{M}}^H_A$. The right $H$-coaction on $N\ot_BA$ is $N\ot_B \rho$. The unit $u$ and counit $c$ of the adjunction are given by the following formulas, for $N\in{\mathcal{M}}_B$ and $M\in {\mathcal{M}}^H_A$: $$u_N :\ N \to (N\otimes _{B}A )^{{\rm co}H},~~ u_N(n)=n \otimes 1;$$ $$c_M :\ M^{{\rm co}H}\otimes_{B}A \to M,~~ c_{M}(m\otimes a)=ma.$$ $A$ is called a Hopf algebra extension of $B=A^{{\rm co}H}$ if the canonical map $${\rm can}:\ A\ot_B A\to A\ot H,~~{\rm can}(a\ot_B b)=ab_{[0]}\ot b_{[1]}$$ is an isomorphism. If $A$ is a faithfully flat Hopf Galois extension, then the adjunction $(-\ot_B A,(-)^{{\rm co}H})$ is a pair of inverse equivalences. We refer to [@11; @24; @27] for a detailed discussion of Hopf algebras and relative Hopf modules.\
$\CCC=A\ot H$ is a coring, with structure maps $$a'(b\ot h)a=a'ba_{[0]}\ot ha_{[1]}$$ $$\Delta_{\CCC}(a\ot h)=(a\ot h_{(1)})\ot_A(1\ot h_{(2)})$$ $$\varepsilon_{\CCC}(a\ot h)=a\varepsilon(h)$$ The category ${\mathcal{M}}^{A\ot H}$ is isomorphic to the category ${\mathcal{M}}_A^H$ of relative Hopf modules; we refer to [@4; @6] for full detail. Note that $X=\sum_i a_i \otimes h_i \in G(A\ot H)$ if and only if $${\label{eq:grouplike1}}
\sum_i (a_i \otimes {h_i}_{(1)} \otimes {h_i}_{(2)})=\sum_{i,j} (a_i{a_j}_{[0]} \otimes
h_i{a_j}_{[1]}\otimes h_j)\quad
\hbox{and} \quad \sum a_i\varepsilon(h_i)=1.$$ $A\ot H$ is also a commutative algebra, with multiplication $$(a\ot h)(b\ot k)=ab\ot hk.$$ The product of two grouplike elements is a grouplike element, and $1_A\ot 1_H$ is grouplike, hence $G^i(A\ot H)$, the set of invertible grouplike elements, is an abelian group. Also observe that an invertible grouplike element is precisely a normalized Harrison 1-cocycle (see for example [@C2 Sec. 9.2] for the definition of the Harrison complex).\
Let $H$ be a finitely generated projective cocommutative Hopf algebra, and $A$ a commutative left $H$-module algebra. Then $H^*$ is a commutative Hopf algebra, and $A$ is a right $H^*$-comodule algebra. If $\sum_i a_i\ot f_i\in A\ot H^*$ is an invertible grouplike element (or a normalized Harrison cocycle), then $${\label{eq:Sweedler1}}
\phi:\ H\to A,~~\phi(h)=\sum_i a_if_i(h),$$ is a normalized Sweedler $1$-cocycle, this means that $\phi(1_H)=1_A$, and the cocycle condition $${\label{eq:Sweedler2}}
\phi(hh')=\sum_i(h_{(1)}.(\phi(h')))\phi(h_{(2)}),$$ is satisfied. This gives a bijective correspondence between Harrison and Sweedler cocycles, see [@C2 Prop. 9.2.3]. For the definition of the Sweedler complex, see [@S2] or [@C2 Sec. 9.1]. In the case where $H=kG$, with $G$ a finite group, Sweedler cohomology reduces to group cohomology.
Elementary algebraic K-theory
-----------------------------
[\[se:1.3\]]{} Let $({\mathcal{C}},\ot, I)$ and $({\mathcal{D}},\ot, J)$ be skeletally small symmetric monoidal categories, and let $F:\ {\mathcal{C}}\to {\mathcal{D}}$ be a cofinal, strong monoidal functor. Then we can consider the Grothendieck and Whitehead groups of ${\mathcal{C}}$ and ${\mathcal{D}}$, and we have an exact sequence connecting them (see for example [@Bass Ch. VII]): $${\label{eq:K1}}
K_1{\mathcal{C}}\rTo^{K_1F} K_1{\mathcal{D}}\rTo^{d}K_1\ul{\phi F}\rTo^{g}
K_0{\mathcal{C}}\rTo^{K_0F} K_0{\mathcal{D}}.$$ $C\in {\mathcal{C}}$ is called invertible if there exists $C'\in {\mathcal{C}}$ such that $C\ot C'\cong I$. If all elements of ${\mathcal{C}}$ and ${\mathcal{D}}$ are invertible, then the description of the five groups in [(\[eq:K1\])]{} and the connecting maps simplifies (see [@C2 App. C]). $K_0{\mathcal{C}}$ is the group of isomorphism classes of objects in ${\mathcal{C}}$ and $K_1{\mathcal{C}}\cong {{\rm Aut}\,}_{{\mathcal{C}}}(I)$ (which is then an abelian group). Let $\ul{\Psi F}$ be the following category: objects are couples $(C,\alpha)$, with $C\in {\mathcal{C}}$ and $\alpha:\ F(C)\to J$ an isomorphism in ${\mathcal{D}}$. A morphism between $(C,\alpha)$ and $(C',\alpha')$ is an isomorphism $f:\ C\to C'$ in ${\mathcal{C}}$ such that $\alpha'= F(f)\circ \alpha$. $\ul{\Psi F}$ is monoidal, every object is invertible and $K_1\ul{\phi F}\rTo^{g}\cong K_0\ul{\Psi F}$. The maps $d$ and $g$ are given as follows: $d(\alpha)=[(I,\alpha)]$ and $g[(C,\alpha)]=[C]$.\
A typical example is the following: For a commutative ring $A$, let $\dul{{{\rm Pic}}}(A)$ be the category of invertible $A$-modules. If $i:\ B\to A$ is a morphism of commutative rings, then we have cofinal strongly monoidal functor $$G=-\ot_B A:\ \dul{{{\rm Pic}}}(B)\to \dul{{{\rm Pic}}}(A),$$ and [(\[eq:K1\])]{} takes the form $${\label{eq:K2}}
1\to \GG_m(B)\to\GG_m(A)\rTo^{d'}K_1\ul{\phi G}\rTo^{g'} {{\rm Pic}}(B)\to {{\rm Pic}}(A).$$
The relative Picard group
=========================
[\[se:2\]]{} If $M,N\in {\mathcal{M}}_A^H$, then $M\ot_A N\in {\mathcal{M}}_A^H$, with right $H$-coaction $$\rho_{M\ot_AN}(m\ot_An)=m_{[0]}\ot_A n_{[0]}\ot m_{[1]}n_{[1]}.$$ So we have a symmetric monoidal category $({\mathcal{M}}_A^H,\ot_A,A)$. Let $\dul{{{\rm Pic}}}^H(A)$ be the full subcategory consisting of invertible objects. ${{\rm Pic}}^H(A)=K_0\dul{{{\rm Pic}}}^H(A)$, the group of isomorphism classes of relative Hopf modules, will be called the relative Picard group of $A$ and $H$. The isomorphism class in ${{\rm Pic}}^H(A)$ represented by an invertible relative Hopf module $M$ will be denoted by $\{M\}$. This new invariant fits into an exact sequence:
[\[pr:2.1\]]{} We have an exact sequence $${\label{eq:2.1.1}}
1\to \GG_m(B)\to\GG_m(A)\rTo^{d}G^i(A\ot H)\rTo^{g} {{\rm Pic}}^H(A)\to {{\rm Pic}}(A).$$
This result can be proved in two ways: a first possibility is to show that [(\[eq:2.1.1\])]{} is precisely the exact sequence [(\[eq:K1\])]{}, associated to the functor $\dul{{{\rm Pic}}}^H(A)\to \dul{{{\rm Pic}}}(A)$ forgetting the $H$-coaction. Let us present an easy direct proof.\
The map $\GG_m(B)\to\GG_m(A)$ is the natural inclusion. Take $a\in A$ invertible, and let $d(a)=X=a^{-1}a_{[0]}\ot a_{[1]}$. $X$ is grouplike, since $a^{-1}a_{[0]}\varepsilon(a_{[1]})=1$, and $$\begin{aligned}
X\ot_A X&=&
(a^{-1}a_{[0]}\ot a_{[1]})\ot_A(b^{-1}b_{[0]}\ot b_{[1]})\\
&=&a^{-1}a_{[0]}(b^{-1})_{[0]}b_{[0]}\ot a_{[1]}(b^{-1})_{[1]}b_{[1]}\ot b_{[2]}\\
&=&a^{-1}b_{[0]}\ot b_{[1]}\ot b_{[2]}\\
&=& (a^{-1}b_{[0]}\ot b_{[1]})\ot_A(1\ot b_{[2]})=\Delta(X),\end{aligned}$$ where we identified $(A\ot H)\ot_A(A\ot H)=A\ot H\ot H$ and we wrote $a=b$. The inverse of $X$ is $X^{-1}=a(a^{-1})_{[0]}\ot (a^{-1})_{[1]}$, so $X\in G^i(A\ot H)$.\
If $d(a)=a^{-1}a_{[0]}\ot a_{[1]}=1_A\ot 1_H$, then $a_{[0]}\ot a_{[1]}=a\ot 1_H$, so $a\in B$, and the sequence is exact at $\GG_m(A)$.\
For $X\in G^i(A\ot H)$, let $g(X)=A^X$, with notation as in [Lemma \[le:1.1\]]{}. $g$ is multiplicative: take $X=\sum_i a_i\ot h_i$ and $Y=\sum_j b_j\ot k_j$ in $G^i(A\ot H)$, then $A^X\ot_AA^Y=A$ as an $A$-bimodule, with comultiplication given by $\rho_{A^X\ot_AA^Y}(1)=\sum_{i,j} a_i\ot_A b_j\ot h_ik_j=XY$, as needed.\
If $g(X)=\{A\}$ in ${{\rm Pic}}^H(A)$, then there exists an $H$-colinear $A$-linear isomorphism $f:\ A^X\to A$. Then $f(1)=a$ is invertible in $A$, and, since $f$ is $H$-colinear, $a_{[0]}\ot a_{[1]}=\rho(a)=(f\ot H)(X)=aX$, so $X=a^{-1}a_{[0]}\ot a_{[1]}=d(a)$, and the sequence is also exact at $G^i(A\ot H)$.\
The exactness of the sequence at ${{\rm Pic}}^H(A)$ follows from [Lemma \[le:1.1\]]{}.
[\[re:2.2\]]{} Let $H=k\ZZ$, and let $A$ be a commutative $\ZZ$-graded $k$-algebra. Then ${{\rm Pic}}^H(A)={{\rm Pic}}_g(A)$, the graded Picard group of $A$, as introduced in [@C1], see also [@CVO]. The exact sequence [(\[eq:2.1.1\])]{} reduces to the exact sequence in [@C1 Prop. 2.1].
The map $d:\ \GG_m(A)\rTo^{d}G^i(A\ot H)$ is precisely the map $\GG_m(A)\to \GG_m(A\ot H)$ in the Harrison complex. From [Proposition \[pr:2.1\]]{}, we therefore obtain immediately:
[\[co:2.3\]]{} With $H$ and $A$ as in [Proposition \[pr:2.1\]]{}, we have an isomorphism of abelian groups $${{\rm Pic}}^H(A)\cong H^1_{\rm Harr}(H,A,\GG_m).$$
This is the promised algebraic interpretation of the first Harrison cohomology group. Note that there are no flatness or projectivity assumptions on $H$ or $A$. We have Hilbert 90 as an easy consequence.
[\[co:2.4\]]{} [**(Hilbert 90)**]{} Let $H,A,B$ be as in [Proposition \[pr:2.1\]]{}. If $A$ is a faithfully flat $H$-Galois extension of $B$, then we have an isomorphism of abelian groups $${{\rm Pic}}(A/B)\cong H^1_{\rm Harr}(H,A,\GG_m).$$
From the fact that the monoidal categories ${\mathcal{M}}_B$ and ${\mathcal{M}}^H_A$ are equivalent, it follows that ${{\rm Pic}}(B)\cong{{\rm Pic}}^H(A)$.
Take the exact sequences [(\[eq:K2\])]{} and [(\[eq:2.1.1\])]{}, and observe that they fit into a commutative diagram $$\begin{diagram}
1&\rTo^{} &\GG_m(B)&\rTo^{}&\GG_m(A)&\rTo^{d'}&K_1\ul{\phi G}&\rTo^{g'}& {{\rm Pic}}(B)&\rTo^{}& {{\rm Pic}}(A)\\
&&\dTo_{=}&&\dTo_{=}&&&&\dTo_{j}&&\dTo_{=}\\
1&\rTo^{} &\GG_m(B)&\rTo^{}&\GG_m(A)&\rTo^{d}&G^i(A\ot H)&\rTo^{g}& {{\rm Pic}}^H(A)&\rTo^{}& {{\rm Pic}}(A)
\end{diagram}$$ The map $j$ maps $[N]\in {{\rm Pic}}(B)$ to $\{N\ot_B A\}\in {{\rm Pic}}^H(A)$. Using the Five Lemma, we find a map $i:\ K_1\ul{\phi G}\to G^i(A\ot H)$.
[\[le:2.5\]]{} With notation as above, the maps $i$ and $j$ are injective.
From the fact that $u$ is a natural transformation between additive endofunctors of the category of $B$-modules, and since $u_B$ is an isomorphism, it follows that $u_N:\ N\to
(N\ot_B A)^{{\rm co}H}$ is an isomorphism if $N$ is finitely generated and projective as a $B$-module. So if $N\ot_B A\cong A$, then $N\cong (N\ot_B A)^{{\rm co}H}\cong A^{{\rm co}H}=B$, and $j$ is injective. The injectivity of $i$ then follows from an easy diagram chasing argument.
Our next aim is to characterize the image of $i$. This will be the topic of [Section \[se:3\]]{}; it will turn out that we obtain nice results in the case where $H$ is cosemisimple.
Coinvariantly generated relative Hopf modules
=============================================
[\[se:3\]]{} Some of our results will be more specific if we assume that $H$ is a cosemisimple Hopf algebra over a field $k$. Recall that $H$ is cosemisimple if there exists a left integral $\phi$ on $H^*$ such that $\phi(1)=1$ (see e.g. [@26]). In this case, the coinvariants functor $(-)^{{\rm co}H}:\ {\mathcal{M}}_A^H\to {\mathcal{M}}_B$ is exact, see [@24 Lemma 2.4.3].
A relative Hopf module $M$ is called [*coinvariantly generated*]{} if $c_M$ is surjective, or, equivalently, if $M=M^{{\rm co}H}A$. If $M$ is coinvariantly generated, and finitely generated as an $A$-module, then we can find a finite set $\{m_1,\cdots,m_n\}\in M^{{\rm co}H}$ that generates $M$.
It follows immediately from the properties of adjoint functors that $N\ot_BA$ is coinvariantly generated, for every $N\in {\mathcal{M}}_B$; in particular, $A$ is coinvariantly generated. We also have the following:
[\[le:3.1\]]{} Let $M\in {\mathcal{M}}^H_A$ and $N\in {\mathcal{M}}_B$. If $M$ is an epimorphic image of $N\otimes_BA$ in ${\mathcal{M}}^H_A$, then $M^{{\rm co}H}=0$ implies that $M=0$.
If $M^{{\rm co}H}=0$, then ${{\rm Hom}}_A^H(N\otimes_B A, M)={{\rm Hom}}_B(N, M^{{\rm co}H})=0$. But ${{\rm Hom}}_A^H(N\otimes_B A, M)$ contains the epimorphism of relative Hopf modules $N\otimes_B A\rightarrow M$, so $M=0$.
If $N$ is an epimorphic image of $M$ in ${\mathcal{M}}^H_A$, and if $M$ is coinvariantly generated, then $N$ is also coinvariantly generated.
[\[le:3.2\]]{} Assume that $H$ is a cosemisimple Hopf algebra over a field $k$. If $N\in {\mathcal{M}}_B$ is projective, then $N\ot_B A$ is projective in ${\mathcal{M}}^H_A$.
See [@9 Prop. 2.5].
[\[le:3.3\]]{} Let $k$ be a field.
1. The forgetful functor ${\mathcal{M}}^H_A\to{\mathcal{M}}_A$ preserves projectives;
2. if $H$ is cosemisimple, then the forgetful functor also reflects projectivity of finitely generated modules.
\(1) Take $M\in {\mathcal{M}}^H_A$ projective, and consider the epimorphism $p:\ M\ot A\to M$, $p(m\ot a)=ma$ in ${\mathcal{M}}^H_A$. The exact sequence $$0\to {{\rm Ker}\,}p\to M\ot A\rTo^{p}M\to 0$$ splits in ${\mathcal{M}}^H_A$, since $M$ is a projective object, and a fortiori in ${\mathcal{M}}_A$. Hence $M$ is a direct factor of $M\ot A$, which is a projective $A$-module, so $M$ is also a projective $A$-module.\
(2) Let $M,N$ be a relative Hopf modules, and assume that $M$ is finitely generated and projective in ${\mathcal{M}}_A$. According to [@9 Prop. 4.2], ${{\rm Hom}}_A(M,N)\in {\mathcal{M}}_A^H$, and it is easy to show that ${{\rm Hom}}_A(M,N)^{{\rm co}H}={{\rm Hom}}_A^H(M,N)$. It follows that the functor ${{\rm Hom}}_A^H(M,-):\ {\mathcal{M}}_A^H\to {\mathcal{M}}$ is exact, since it is the composition of the exact functors ${{\rm Hom}}_A(M,-):\ {\mathcal{M}}^H_A\to {\mathcal{M}}^H$ ($M\in {\mathcal{M}}_A$ is projective) and $(-)^{{\rm co}H}:\ {\mathcal{M}}^H\to {\mathcal{M}}$ ($H$ is cosemisimple).
[\[le:3.4\]]{} Let $H$ be a cosemisimple Hopf algebra over a field $k$, and take $P,Q\in {\mathcal{M}}^H_A$ finitely generated as $A$-modules. Assume that $Q$ is a projective object of ${\mathcal{M}}^H_A$. Then every epimorphism $f:\ P\to Q$ in ${\mathcal{M}}^H_A$ has a right inverse in ${\mathcal{M}}^H_A$.
It is clear that ${{\rm Hom}}_A(Q,P)$ and ${{\rm Hom}}_A(Q,Q)$ are right $H$-comodules, and the map $f^*={{\rm Hom}}_A(Q,f):\ {{\rm Hom}}_A(Q,P)\to {{\rm Hom}}_A(Q,Q)$ is right $H$-colinear. It follows from [Lemma \[le:3.3\]]{} that $Q$ is projective as an $A$-module, so $f^*$ is surjective. Since $f^*$ is $H$-colinear, it restricts to a surjection $${{\rm Hom}}_A^H(Q,P)={{\rm Hom}}_A(Q,P)^{{\rm co}H}\to {{\rm Hom}}_A^H(Q,Q)={{\rm Hom}}_A(Q,Q)^{{\rm co}H}.$$ Take a preimage $g\in {{\rm Hom}}_A^H(Q,P)$ of the identity map ${\rm id}_Q$ on $Q$. Then $f\circ g={\rm id}_Q$, and the result follows.
For $M\in {\mathcal{M}}_A$, we will denote the dual module by $M^*={{\rm Hom}}_A(M,A)$.
[\[pr:3.5\]]{} Let $H$ be cosemisimple, and assume that $P\in {\mathcal{M}}^H_A$ is coinvariantly generated and finitely generated projective as an $A$-module. Then
1. $P^{{\rm co}H}$ is a finitely generated projective $B$-module;
2. $P^*$ is coinvariantly generated;
3. the map $c_P$ is an isomorphism in ${\mathcal{M}}^H_A$.
\(1) As we have seen, there exist $p_1, p_2,\cdots, p_n \in P^{{\rm co}H}$ such that $P=\sum_i p_iA$. Set $F=A^n$ and let $f:\ F\ \to P$ be the $A$-linear map given by $f(a_1, a_2, ... , a_n)=\sum_i p_ia_i$. Then $F\in {\mathcal{M}}^H_A$ and $f$ is an epimorphism in ${\mathcal{M}}^H_A$. By [Lemma \[le:3.4\]]{}, there exists a monomorphism $g\in {{\rm Hom}}_A(P ,
F)$ such that $f\circ g={\rm id}_P$. The restriction of $g$ to $P^{{\rm co}H}$ is then a $B$-linear right inverse of the restriction of $f$ to $F^{{\rm co}H}$, and $F^{{\rm co}H}=B^{n}$, and we obtain (1).
\(2) The map $g^*={{\rm Hom}}_A(g , A):\ F^*\to P^*$ is surjective and $H$-colinear. The fact that $F^*$ is coinvariantly generated then implies that $P^*$ is also coinvariantly generated.
\(3) Consider the natural transformation $t:\ (-)^{{\rm co}H}\ot_BA\to (-)$ given by $$t_P:\ P^{{\rm co}H} \ot_BA\rightarrow P,~~t_P(p\otimes a)= pa.$$ The map $t_A$ is an isomorphism, so $t_F$ is an isomorphism by additivity. It follows that $t_P$ is an isomorphism, since $F=P\oplus {{\rm Ker}\,}f$ as $H$-comodules.
Let $X=\sum_i a_i\ot h_i\in G(A\ot H)$, and write $$A_X=\{a\in A~|~\rho(a)=aX=\sum_i aa_i\ot h_i\},$$ and $$A_X^i=\{a\in A_X~|~a~{\rm is~invertible}\}.$$ Observe that $${{\rm Im}\,}(d)=\{X\in G^i(A\ot H)~|~A_X^i\neq \emptyset\}$$ and $$A_{1\ot 1}=A^{{\rm co}H}.$$ Furthermore, $A_XA_Y\subset A_{XY}$: take $a\in A_X$ and $b\in A_Y$, then $\rho(a)=aX=\sum_i aa_i\ot h_i$, $\rho(b)=bY=\sum_j bb_j\ot k_j$ and $\rho(ab)=a_{[0]}b_{[0]}\ot a_{[1]}b_{[1]}=\sum_{i,j} aa_ibb_j\ot h_ik_j=abXY$. Also $A_X^i\cap A_Y^i=\emptyset$ if $X\neq Y$.
[\[le:3.6\]]{} The set $$E=\{X\in G^i(A\ot H)~|~AA_X=A~{\rm and}~AA_{X^{-1}}=A\}$$ is a subgroup of $G^i(A\ot H)$ containing ${{\rm Im}\,}(d)$.
If $X\in {{\rm Im}\,}(d)$, then there exists an invertible $a\in A_X$, and then $AA_X=A$. since $X^{-1}\in {{\rm Im}\,}(d)$, we also have $AA_{X^{-1}}=A$, hence $X\in E$. It is clear that $1\ot 1\in E$. If $X,Y\in E$, then $AA_{XY}\supset AA_XA_Y=AA_Y=A$, and, in a similar way, $AA_{(XY)^{-1}}=A$, hence $XY\in E$. Finally, if $X\in E$, then obviously $X^{-1}\in E$.
[\[pr:3.7\]]{} Consider the injective map $j:\ {{\rm Pic}}(B)\to {{\rm Pic}}^H(A)$. If $H$ is a cosemisimple Hopf algebra over a field $k$, then $${{\rm Im}\,}(j)=\{\{M\}\in {{\rm Pic}}^H(A)~|~M~\hbox{is coinvariantly generated}\}.$$
$M\ot_B A$ is coinvariantly generated, so ${{\rm Im}\,}(j)$ is contained in the desired set. If $H$ is cosemisimple, and $\{N\}\in {{\rm Pic}}^H(A)$, with $N$ coinvariantly generated, then $N=(N^{{\rm co}H})\ot_BA\in {{\rm Im}\,}(j)$, by [Proposition \[pr:3.5\]]{}(3).
[\[le:3.8\]]{} Take $X\in G^i(A\ot H)$. Then $A^X$ is coinvariantly generated if and only if $AA_{X^{-1}}=A$. If $H$ is cosemisimple, then this is also equivalent to $X\in E$.
The first statement follows from the fact that $(A^X)^{{\rm co}H}=A_{X^{-1}}$. Indeed, $a\in (A^X)^{{\rm co}H}$ if and only if $\rho_X(a)=Xa=a\ot 1$, if and only if $\rho(a)=(1\ot 1)a=X^{-1}(a\ot 1)=aX^{-1}$, which means that $a\in A_{X^{-1}}$.\
Let $H$ be cosemisimple. Note that $(A^X)^*\cong A^{X^{-1}}$ as relative Hopf modules. If $A^X$ is coinvariantly generated, then so is $A^{X^{-1}}$, by [Proposition \[pr:3.5\]]{}, and then $X\in E$.
Now we are able to prove the main result of this Section.
[\[th:3.9\]]{} Consider the monomorphism $i:\ K_1\ul{\phi G}\to G^i(A\ot H)$ introduced in [Lemma \[le:2.5\]]{}.\
Then ${{\rm Im}\,}(i)\subset E$ and ${{\rm Im}\,}(i)= E$ if $H$ is a cosemisimple Hopf algebra over a field $k$. In this situation, ${{\rm Pic}}(A/B)\cong E$.
Take $[(M,\alpha)] \in
K_0\ul{\psi G}$, and let $i[(M,\alpha)]=X\in G^i(A\ot H)$. Then $\{A^X\}=j(g'[(M,\alpha)])=j([M])=\{M\ot_BA\}$, hence $A^X$ is coinvariantly generated and $AA_{X^{-1}}=A$, by [Lemma \[le:3.8\]]{}. In a similar way, $i([(M,\alpha)]^{-1})=X^{-1}$, and $A^{X^{-1}}\cong M^*\ot_B A$ is coinvariantly generated, so $AA_X=A$, again by [Lemma \[le:3.8\]]{}. This proves that $X\in E$.\
Assume now that $H$ is cosemisimple, and take $X\in E$. It follows from [Lemma \[le:3.8\]]{} that $A^X$ is coinvariantly generated, and from [Proposition \[pr:3.7\]]{} that $A^X=M\ot_B A$ for some $M\in \dul{{{\rm Pic}}}(B)$. Since the image of $M$ in ${{\rm Pic}}(A)$ is trivial, $[M]=g'[(M,\alpha)]$ for some $(M,\alpha)\in {\mathcal{C}}$. Write $i[(M,\alpha)]=Y$. Then $X=Yd(a)$, for some $a\in \GG_m(A)$. Consider the map $\alpha':\ M\ot_BA\to A$, $\alpha'(m\ot b)=a^{-1}\alpha(m\ot b)$. Then $i[(M,\alpha')]=X$.
On the grouplike elements
=========================
[\[se:4\]]{} We have an injective map $i:\ G(H)\to G(A\ot H)$, $i(g)=1_A\ot g$. Everything simplifies if $i$ is an isomorphism. We discuss two situations in which this is (almost) the case.
Recall that a commutative algebra which is an integral domain is called normal if it is integrally closed in its field of fractions.
[\[pr:4.11\]]{} Let $k$ be an algebraically closed field, $A$ a finitely generated commutative normal $k$-algebra and $G$ a connected algebraic group acting rationally on $A$. Let $H$ be the affine coordinate ring of $G$, and $\chi(G)$ be the group of characters of $G$. Then $$G(A\otimes H)=\{1 \otimes \phi~|~\phi \in G(H)=\chi(G)\}.$$
Let $x=\sum_i a_i \otimes f_i \in G(A \otimes H)$. Then we have $${\label{eq:4.11.1}}
\sum_i (a_i \otimes {f_i}_{(1)} \otimes {f_i}_{(2)})=\sum_{i,j} (a_i{a_j}_{[0]} \otimes
(f_i*{a_j}_{[1]})\otimes f_j)$$ and $\sum a_i\varepsilon(f_i)=1$. The map $$\alpha:\ A\ot H\to{{\rm Hom}}(kG,A),~~\alpha(a\ot f)(g)=af(g)$$ is injective. Let $\phi=\alpha(x)$. Using [(\[eq:4.11.1\])]{}, we compute for all $g,g'\in G$ that $$\begin{aligned}
&&\hspace*{-15mm}
\phi(gg')=\sum_i a_if_i(gg')=\sum_i a_i{f_i}_{(1)}(g){f_i}_{(2)}(g')\\
&=&\sum_{i,j} (a_i{a_j}_{[0]}((f_i*{a_j}_{[1]})(g))f_j(g')=
\sum_{i,j} a_i{a_j}_{[0]}f_i(g){a_j}_{[1]}(g)f_j(g')\\
&=&\sum_{i,j} (g.a_j)f_j(g')a_if_i(g)=\sum_{i,j}
g.(a_jf_j(g'))a_if_i(g)\\
&=&(g.(\phi(g')))\phi(g).\end{aligned}$$ From the second equality, we have $1=\sum_i a_if_i(1_G)=\phi(1_G)$. For every $g\in G$, $\phi(g)$ is invertible in $A$, with inverse $g.(\phi(g^{-1}))$. By the proof of [@21 Prop. 1b, p. 46], $\phi(g)\in k$ for every $g\in G$, so $\phi \in\chi(G)$. Now $\chi(G)=G(H)\subset H$ (see [@19 p. 25]), so it follows in particular that $\phi\in H$. For all $g\in G$ we now have that $$\alpha(1\ot \phi)(g)=\phi(g)=\sum_i a_if_i(g)=\alpha(x)(g),$$ hence $x=1\ot \phi$, by the injectivity of $\alpha$.
Now consider the situation from [Remark \[re:2.2\]]{}: $H=k\ZZ\cong k[X,X^{-1}]$, and $A$ is a commutative $\ZZ$-graded algebra. In this situation $A\ot H=A\ot k[X,X^{-1}]$. Grouplike elements in $A\ot H$ can be constructed as follows. Let $1=e_1+\cdots+e_n$ with the $e_i$ orthogonal idempotents, and take $d_1,\cdots, d_n\in \ZZ$. Then $\sum_{i=1}^n e_i\ot X^{d_i}$ is a grouplike element in $A\ot k[X,X^{-1}]$. In this way, we have an embedding of ${\mathcal{C}}({{\rm Spec}\,}(A),\ZZ)$, the continuous functions from ${{\rm Spec}\,}(A)$ (with the Zariski topology) to $\ZZ$ (with the discrete topology), into $G(A\ot k[X,X^{-1}])$. The first author was amazed to see that one of his first results, [@C1 Theorem 2.3], can be restated in such a way that it becomes a result about corings. Recall that a commutative ring is called reduced if it has no nontrivial nilpotents.
[\[pr:gr\]]{} Let $A$ be a reduced $\ZZ$-graded commutative $k$-algebra. Then the map ${\mathcal{C}}({{\rm Spec}\,}(A),\ZZ)\to G(A\ot k[X,X^{-1}])$ is a bijection.
[\[ex:gr2\]]{} (cf. [@C1 Example 2.6]) [Proposition \[pr:gr\]]{} does not hold if $A$ contains nilpotent elements; this is related to the fact that there exist non-homogeneous units in this situation. Let $A=k[x]$, with $x^2=0$, and put a $\ZZ$-grading on $A$ by taking $\deg (x)=1$. Then $1+ax\in \GG_m(A)$, and $d(1+ax)=(1-ax)\ot 1+ax\ot X$ is a grouplike element in $G(A\ot k[X,X^{-1}])$ which is not in the image of ${\mathcal{C}}({{\rm Spec}\,}(A),\ZZ)$.
[99]{} H. Bass, “Algebraic K-Theory", Benjamin, New York, 1968.
T. Brzeziński, The structure of corings. Induction functors, Maschke-type theorem, and Frobenius and Galois properties, [*Algebr. Representat. Theory*]{} [**5**]{} (2002), 389–410.
T. Brzeziński, The structure of corings with a grouplike element, [*Banach Center Publ.*]{} [**61**]{} (2003), 21–35.
T. Brzeziński and R. Wisbauer, “Corings and comodules", [*London Math. Soc. Lect. Note Ser.*]{} [**309**]{}, Cambridge University Press, Cambridge, 2003.
S. Caenepeel, A cohomological interpretation of the graded Brauer group I, [*Comm. Algebra*]{} [**11**]{} (1983), 2129–2149.
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S. Caenepeel and T. Guédénon, Projectivity of a relative Hopf module over the subring of coinvariants, in “Hopf algebras", J. Bergen, S. Catoiu and W. Chin (eds.), [*Lect. Notes Pure Appl. Math.*]{} [**237**]{}, Marcel Dekker, New York, 2004, 97–108.
S. Caenepeel and F. Van Oystaeyen, Brauer groups and the cohomology of graded rings, [*Monographs and Textbooks in Pure and Appl. Math.*]{} [**121**]{}, Marcel Dekker, New York, 1988.
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[^1]: Research supported by the project G.0278.01 “Construction and applications of non-commutative geometry: from algebra to physics" from FWO Vlaanderen
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Tumor cell cytostasis by macrophages and antibody in vitro. II. Isolation and characterization of suppressed cells.
Tumor cells in a cytostatic state caused by macrophages and antibody were isolated. Such suppressed cells excluded vital dye, incorporated uridine and leucine, and metabolized glucose. They did not, however incorporate thymidine, nor did they resume cell division in culture. During prolonged culture, these cells eventually died. In this system, cytostasis was an all-or-nothing phenomenon at the level of the individual cell. Once in the cytostatic state tumor cells did not resume proliferation. |
Q:
Asus Touchscreen Laptop Linux. Would it work?
I got an Asus touchscreen laptop with Windows 8 pre-installed. If dual boot is a problem, can I just purge Windows 8, and make it a Linux only system without sacrificing the touchscreen feature?
A:
Yes, your ASUS Laptop will work with Ubuntu. I think the touchscreen will work since this video on YouTube shows a ASUS Vivobook with Ubuntu 12.10 with the touchscreen in action. If you have a Vivobook or something similar, more than likely it will work.
You can dual boot if you want. Keep in mind that your ASUS laptop came with Windows 8, which means it may come with a security feature called "UEFI Secure Boot" or "Secure Boot" for short. You will need to disable "Secure Boot" in order to get the laptop to boot from removable media, like CD's, DVD's and USB Drives.
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Application of an emulsified polycolloid substrate biobarrier to remediate petroleum-hydrocarbon contaminated groundwater.
Emulsified polycolloid substrate (EPS) was developed and applied in situ to form a biobarrier for the containment and enhanced bioremediation of a petroleum-hydrocarbon plume. EPS had a negative zeta potential (-35.7 mv), which promoted its even distribution after injection. Batch and column experiments were performed to evaluate the effectiveness of EPS on toluene containment and biodegradation. The EPS-to-water partition coefficient for toluene (target compound) was 943. Thus, toluene had a significant sorption affinity to EPS, which caused reduced toluene concentration in water phase in the EPS/water system. Groundwater containing toluene (18 mg/L) was pumped into the three-column system at a flow rate of 0.28 mL/min, while EPS was injected into the second column to form a biobarrier. A significant reduction of toluene concentration to 0.1 mg/L was observed immediately after EPS injection. This indicates that EPS could effectively contain toluene plume and prevent its further migration to farther downgradient zone. Approximately 99% of toluene was removed after 296 PVs of operation via sorption, natural attenuation, and EPS-enhanced biodegradation. Increase in total organic carbon and bacteria were also observed after EPS supplement. Supplement of EPS resulted in a growth of petroleum-hydrocarbon degrading bacteria, which enhanced the toluene biodegradation. |
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Marvin Rees officially takes over as Bristol Mayor
It was an historic moment as Labour's Marvin Rees was sworn in as Bristol's new elected mayor. He promptly made the first promise of his new job: "Under my leadership, I want to set up a city office in which I hope you will all play a full part. It's here that your expertise and priorities can come together to deliver the city we all want and need."
The ceremony concluded a weekend of results which saw Labour take control of the city council for the first time in 13 years.
George Ferguson handed the reigns to Marvin Rees and said he was quitting politics Credit: ITV News
Mr Rees' victory, over two rounds, overturned the result of the only previous contest in 2012. The man who won then, the independent George Ferguson, said he was now quitting politics after a turbulent time in office:
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Mr Ferguson, famous for his red trousers, made an immediate mark by changing the name of council headquarters to City Hall, and vigorously championed the new Arena and Metrobus schemes. But he also pressed ahead with unpopular policies like 20 mile an hour speed limits and residents' parking zones.
Labour was able to use all-out council elections to underpin Mr Rees's campaign, and leader Jeremy Corbyn came to congratulate him in person, Mr Corbyn told ITV News: "Marvin has an ability to unite the city, he has good vision about the city but above all he has this human spirit which brings people together."
Marvin Rees grew up in Lawrence Weston in north west Bristol Credit: ITV News
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Mr Rees told ITV News that growing up in Lawrence Weston, he never imagined he would one day be Mayor: |
#
# Copyright (c) 2019. JetBrains s.r.o.
# Use of this source code is governed by the MIT license that can be found in the LICENSE file.
#
from ._configuration import *
__all__ = _configuration.__all__
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c ŭ
[**On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation.** ]{}
S. M. Sergeev\
Branch Institute for Nuclear Physics, Protvino 142284, Russia.\
E-mail: sergeev\[email protected]
[[**[Abstract]{}**]{}: A sort of two dimensional linear auxiliary problem for the complex of 3D $R$ – operators associated with the Zamolodchikov – Bazhanov – Baxter statistical model is proposed. This problem resembles the problem of the local Yang – Baxter equation but does not coincide with it. The formulation of the auxiliary problem admits a notion of a “fusion”, and usual local Yang – Baxter equation appears among other results of this “fusion”. ]{}
[**[Key words:]{}**]{} Tetrahedron equation, $\,2+1\,$ integrability, local Yang – Baxter equation.
Introduction
============
Well known shortcoming of the three dimensional integrability, connected with the tetrahedron equation, is the remarkable poverty of the models. Actually, there exists only one nontrivial complex of solutions of the tetrahedron equation, which has statistical mechanics, field theory and “classical” (i. e. functional) forms. In the statistical mechanics, when the number of states is finite, the model is called Zamolodchikov – Bazhanov – Baxter model [@zam-solution; @bb-first]. It is known almost everything (except the most complicated aspects, concerning the structure of eigenstates of the transfer matrices and the correlation functions) about this model, namely: the partition function [@baxter-pf; @bb-first], the vertex – IRF correspondence [@mss-vertex; @mss-psi], affine Toda field theory [@kr-ats] and field theory operator $R$ – matrix [@fk-qd; @sbm-qd], and the transition from the infinite number of the states to finite one [@br-qd; @sbm-qd], and finally, the functional $R$ – operator as the sequence of the permutation relations for the field theory $R$ – matrix [@sbm-qd; @ms-modified]. Here one should mention that there exists an hierarchy of the operator $R$ – matrices which corresponds to several partial specifications of the spectral parameters of ZBB matrix weights. There must exist a reverse way, obtaining of more complicate $R$-s in the hierarchy in terms of simplest (some sort of the fusion). Also one may mention the interpretation of the projection of 3D operator $R$ – matrices in terms of a representation of some specific Drinfeld double [@double].
From the other hand side there are a lot of solutions of the functional tetrahedron equation. Moreover, we’ve got infinitely many such solutions [@korepanov-diss] [*versus*]{} one specific given by the complex mentioned above.
Recall that usually the functional tetrahedron solution appears when one considers so – called local Yang – Baxter equation (LYBE) [@maillet], which is a proper generalization of the zero curvature condition for two dimensional system. Namely, let $L_{i,j}(\vec x)$ be matrices of weights of the Yang – Baxter type, and $\vec x$ stands for their formal parameters. Then LYBE $$\label{lybe}
L_{12}(\vec x)\c L_{13}(\vec y)\c L_{23}(\vec z)\;=\;
L_{23}(\ac{\vec z})\c L_{13}(\ac{\vec y})\c L_{12}(\ac{\vec x})\;,$$ when it is nondegenerative with respect to $\ac{\vec x},\ac{\vec y},\ac{\vec z}$, gives the functional map from $\{\vec x,\vec y,\vec z\}$ to $\{\ac{\vec x},\ac{\vec y},\ac{\vec z}\}$ by $$\ds
\ac{\vec x}\;=\;\vec r_1(\vec x,\vec y,\vec z)\;,\;\;\;
\ac{\vec y}\;=\;\vec r_2(\vec x,\vec y,\vec z)\;,\;\;\;
\ac{\vec z}\;=\;\vec r_3(\vec x,\vec y,\vec z)\;,$$ Usually the functional operator $R_{i,j,k}$, giving this map, is introduced: $$R_{i,j,k}\c\phi(\vec x_i,\vec x_j,\vec x_k)\;=\;
\phi(\ac{\vec x}_i,\ac{\vec x}_j,\ac{\vec x}_k)\;,$$ $$\ds
\ac{\vec x}_i=\vec r_1(\vec x_i,\vec x_j,\vec x_k),\;\;\;
\ac{\vec x}_j=\vec r_2(\vec x_i,\vec x_j,\vec x_k),\;\;\;
\ac{\vec x}_k=\vec r_3(\vec x_i,\vec x_j,\vec x_k)\;,$$ where $\phi$ is an arbitrary function. Considering the quadrilateral formed by six $L$-s $$\begin{aligned}
&\ds
L_{12}(\vec x_1)\c L_{13}(\vec x_2)\c L_{23}(\vec x_3)\c
L_{14}(\vec x_4)\c L_{24}(\vec x_5)\c L_{34}(\vec x_6)\;=
&\nonumber\\
&\ds
=\;L_{34}(\vec y_6)\c L_{24}(\vec y_5)\c L_{14}(\vec y_4)\c
L_{23}(\vec y_3)\c L_{13}(\vec y_2)\c L_{12}(\vec y_1)\;,
&\end{aligned}$$ one obtains rhs by two different ways, first starting from $L_{12}L_{13}L_{24}$, second starting from $L_{23}L_{24}L_{34}$. This gives the equivalence of two successive applications of $R_{i,j,k}$: $$\begin{aligned}
&\ds \phi[\vec y_1,\vec y_2,\vec y_3,\vec y_4,\vec y_5,\vec y_6]\;=
&\nonumber\\
&\ds R_{123}\c
\Biggl(R_{145}\c
\Bigl( R_{246}\c
\bigl( R_{356}\c
\phi[\vec x_1,...,\vec x_6]\bigr)\Bigr)\Biggr)
\;=&\nonumber\\
&\ds=\;
R_{356}\c
\Biggl(R_{246}\c
\Bigl(R_{145}\c
\bigl(R_{123}\c
\phi[\vec x_1,...,\vec x_6]\bigr)\Bigr)\Biggr)
\;.&\end{aligned}$$ This is the functional tetrahedron equation (FTE). [^1]
In the case when the local weights $L_{a,b}(\vec x)$ have the structure of the ferro-electric type free fermion model’s weights, the irreducible part of eq. (\[lybe\]) can be extracted in the form of Korepanov’s equation $$\label{korepanov}
X_{12}(\vec x)\c X_{13}(\vec y)\c X_{23}(\vec z)\;=\;
X_{23}(\ac{\vec z})\c X_{13}(\ac{\vec y})\c X_{12}(\ac{\vec x})\;,$$ where ‘$\c$’ means the matrix multiplication of $$\begin{aligned}
&\ds X_{12}(\vec x)\;=\;
\left(\begin{array}{ccc}
a(\vec x)& b(\vec x)& 0\\
c(\vec x)& d(\vec x)& 0\\
0 & 0 & 1
\end{array}\right)\;,
&\nonumber\\
&\ds X_{13}(\vec x)\;=\;
\left(\begin{array}{ccc}
a(\vec x)& 0& b(\vec x)\\
0& 1& 0\\
c(\vec x)& 0& d(\vec x)
\end{array}\right)\;,
&\nonumber\\
&\ds X_{23}(\vec x)\;=\;
\left(\begin{array}{ccc}
1& 0& 0\\
0& a(\vec x)& b(\vec x)\\
0& c(\vec x)& d(\vec x)
\end{array}\right)\;,&\end{aligned}$$ $a(\vec x),...,d(\vec x)$ are in general some [*matrix*]{} functions. Eq. (\[korepanov\]) and its connection with the functional tetrahedron equation was investigated in [@korepanov-diss] in most general case. There was proven that there exists a wide class of the solutions of FTE associated with eq. (\[korepanov\]). A subset of the solutions of FTE was described in [@rmk-lybe], [@ks-fun] and resently in [@oneparam]. These are the cases when $a,b,c,d$ are some numeric functions of single variable $x$. Nevertheless, the solution of FTE associated with the ZBB complex is still not described in terms of LYBE (moreover, we suspect, this is impossible at least in terms of the Korepanov’s equation (\[korepanov\])).
So, [**what we wished to say by this long introduction.**]{} From one hand side a plenty of the solutions of FTE exist, these solutions are associated with LYBE (LYBE makes FTE obvious), but we have no skill to quantize them. From the other hand side, only one model is the whole complex, i. e. it exists in the statistical mechanics form, field theory form and a functional transformation form, moreover, there exists a well defined way to obtain the statistical mechanics and the field theory from the functional form, but we do not know a sort of a linear problem (like LYBE) for this.
In this paper we try to give the answer to all these questions. We suggest some formulation of two dimensional system associated with 2D lattice, which is not Yang – Baxter type system (i. e. we do not interpret the vertices as matrices of weights or anything equivalent), but nevertheless the usual graphic pictures remain as well as a sort of zero curvature condition, FTE and so on. Our formulation resembles the electric networks, when the star – triangle equivalence gives the electric network solution of FTE (well described in terms of Korepanov’s equation [@rmk-lybe; @oneparam]) but originally this equivalence is not LYBE at all, it is just a resoldering of the resistances. What we suggest, it is just a proper generalization of Kirchhoff’s rules in terms of arbitrary 2D networks formed by rectangular vertices. Such formulation is not equivalent to the usual LYBE-s in general. The functional transformation corresponding to ZBB complex is a partial case of our functional transformation. There is a sort of fusion in the system proposed, and the ferro-electric case is just a subspace of a partial case of fused system.
Formulation of the system and $R$ – operator
============================================
Consider $2D$ graphs formed by the usual oriented rectangular vertices. Each vertex has four adjacent fields. Assign to these fields some variables, [*currents*]{}, for the vertex shown in fig. \[fig-vertex\] denote them $J,J';\Phi,\Phi'$. Suppose these current are additive for any field of the $2D$ network, and for any closed field let the sum of the currents belonging to this field and corresponding to the surrounding vertices be zero (it is supposed that all the currents assigned to any vertex flow into this vertex) – see fig. \[fig-lhs\] and considerations for it for an example. Suppose also the currents assigned to the vertex $V_k$ obey some condition, $V_k(J_k,J'_k,\Phi_k,\Phi'_k)=0$ (obviously, this condition must be a set of linear relations homogeneous with respect to the currents). Thus, for any network there appears some condition for currents. Two networks are equivalent if their such conditions coincide. For example, the evolution of 2D network is given by the condition of the equivalence of the left hand side type and right hand side type graphs, as it is drawn in fig. (\[fig-ybe\]). Solving such equivalence condition with respect to the parameters of $V_k'$ in rhs, we obtain a solution of FTE.
Now fix the form of $V(J,J',\Phi,\Phi')$ (a sort of Ohm’s law): $$\begin{aligned}
\label{ohm}
&\ds
\Phi \;=\;i\,\w\,\cdot\,J\;,\;\;\;\;
\Phi'\;=\;-i\,u\,\cdot\,J\;,&\nonumber\\
&\ds
\Phi\;=\;-i\,\u\,\cdot\,J'\;,\;\;\;\;
\Phi'\;=\;i\,w\,\cdot\,J'\;,\end{aligned}$$ with the primitive “zero – curvature” condition: $$u^{-1}\c w^{}\;=\;\w^{\,-1}\c \u^{}\;.$$ Surely, invertible elements $u,w,\u,\w$ are treated as the parameters of the vertex $V$. Note also that this is not unique choice of $V(J,J',\Phi,\Phi')$, we may for example suppose two of the currents to be independent. Such cases we do not investigate here.
(350,150) (100,0)
(150,150) (15,75)[(1,0)[120]{}]{} (75,15)[(0,1)[120]{}]{} (75,75) (100,100)[$\ds J'$]{} (100,40)[$\ds \Phi'$]{} (40,100)[$\ds \Phi$]{} (40,40)[$\ds J$]{}
(450,200) (00,0)
(200,200) (75,0)[(0,1)[200]{}]{} (37.5,25)[(3,2)[150]{}]{} (187.5,75)[(-3,2)[150]{}]{} (75,50) (75,150) (150,100) (85,155)[$V_{12}$]{} (85,30)[$V_{23}$]{} (140,115)[$V_{13}$]{} (50,180)[$x$]{} (25,95)[$y'$]{} (50,15)[$z$]{} (125,155)[$z'$]{} (125,35)[$x'$]{} (185,95)[$y$]{}
(220,95)[$\ds =$]{} (250,0)
(200,200) (125,0)[(0,1)[200]{}]{} (12.5,75)[(3,2)[150]{}]{} (162.5,25)[(-3,2)[150]{}]{} (50,100) (125,50) (125,150) (40,115)[$\ac V_{13}$]{} (135,55)[$\ac V_{12}$]{} (135,130)[$\ac V_{23}$]{} (75,155)[$x$]{} (5,95)[$y'$]{} (75,40)[$z$]{} (140,180)[$z'$]{} (140,15)[$x'$]{} (170,95)[$y$]{}
(300,200) (50,0)
(200,200) (75,0)[(0,1)[200]{}]{} (37.5,25)[(3,2)[150]{}]{} (187.5,75)[(-3,2)[150]{}]{} (75,50) (75,150) (150,100) (55,175)[$J'_1$]{} (85,155)[$\Phi'_1$]{} (55,135)[$\Phi_1$]{} (80,120)[$J_1$]{} (145,120)[$J'_2$]{} (145,70)[$J_2$]{} (175,95)[$\Phi'_2$]{} (120,95)[$\Phi_2$]{} (50,55)[$\Phi_3$]{} (55,20)[$J_3$]{} (80,75)[$J'_3$]{} (80,35)[$\Phi'_3$]{}
Consider now the Baxter – type correspondence. Let the outer currents be $x,y,z,x',y',z'$ as it is shown in fig. \[fig-ybe\]. Left – hand side is drawn in fig. (\[fig-lhs\]). There $J_k,J'_k,\Phi_k,\Phi'_k$ are connected by (\[ohm\]). Conservation of the currents for closed field is $$J_1+\Phi_2+J'_3\;=\;0\;,$$ and given outer currents are $$\begin{aligned}
&\ds J'_1\;=\;x\,,\;\;\; \Phi'_2\;=\; y\,,\;\;\;
J_3\;=\;z\,,&\nonumber\\
&\ds J_2+\Phi'_3\;=\;x'\,,\;\;\;
\Phi_1+\Phi_3\;=\; y'\,,\;\;\;
\Phi'_1+J'_2\;=\;z'\,.&\end{aligned}$$ These with (\[ohm\]) give the following system: $$\begin{aligned}
&\ds u_1^{-1}\c w^{}_1\c x \;+\;
\u^{}_2\c w_2^{-1}\c y \;+\;
w_3^{-1}\c u^{}_3\c z\;=\;0\;,&\nonumber\\
&\ds
x'\;=\;i\,u_2^{-1}\c y \;-\; i\,u^{}_3\c z\;,
&\nonumber\\
&\ds
y'\;=\;-i\,\u_1^{}\c x \;+\; i\,\w_3^{}\c z\;,
&\nonumber\\
&\ds
z'\;=\;i\, w_1^{}\c x \;-\; i\, w_2^{-1}\c y\;.&\label{lhs}\end{aligned}$$ Thus two of the currents are independent, and the rest four one can express in terms of the independent.
Analogous consideration for the right – hand side with primed parameters of the vertices dives $$\begin{aligned}
&\ds
\aw_1^{-1}\c \au_1^{}\c x' \;+\;
\aw_2^{}\c \nau_2^{-1}\c y' \;+\;
\au_3^{-1}\c \aw_3^{}\c z'\;=\;0\;,&\nonumber\\
&\ds
x\;=\;i\,\nau_2^{-1}\c y' \;-\; i\,\nau_3^{}\c z'\;,
&\nonumber\\
&\ds
y\;=\;-i\,\au_1\c x' \;+\; i\, \aw_3^{}\c z'\;,
&\nonumber\\
&\ds
z\;=\;i\,\naw_1\c x' \;-\; i\, \naw_2^{-1}\c y'\;.&\label{rhs}\end{aligned}$$ Let now rhs (\[rhs\]) be equivalent to lhs (\[lhs\]). This gives eight equations for the parameters of $V_k$ and $\ac V_k$. The solution is following: introduce $$\begin{aligned}
\ds
\Lambda_1 &=&
u_1^{-1}\c w_1^{}\;+\;
\u_3^{\,-1}\c \u_1^{}\;+\;
\u_2^{}\c w_1^{}\;,
\nonumber\\
\ds
\Lambda_2 &=&
\u_2^{}\c w_2^{-1}\;+\;
w_3^{-1}\c u_2^{-1}\;+\;
u_1^{-1}\c w_2^{-1}\;
\nonumber\\
\ds
\Lambda_3 &=&
w_3^{-1}\c u_3^{}\;+\;
\w_2^{}\c u_3^{}\;+\;
\w_1^{\,-1}\c \w_3^{}\;,\end{aligned}$$ and let $\Omega_i$, defined up to an ambiguity $\Omega_i\rightarrow\acute\omega\c\Omega_i$, obey $$\begin{aligned}
\ds
\Omega_1\c [\,u_2^{-1}\c\Lambda_2^{-1}\c u_1^{-1}\,]
&=&
\Omega_2\c [\,\u_1^{ }\c\Lambda_1^{-1}\c \u_2^{ }\,]\;,
\nonumber\\
\ds
\Omega_2\c [\,\w_3^{ }\c\Lambda_3^{-1}\c\w_2^{ }\,]
&=&
\Omega_3\c [\,w_2^{-1}\c\Lambda_2^{-1}\c w_3^{-1}\,]\;,
\nonumber\\
\ds
\Omega_3\c [\,w_1^{ }\c\Lambda_1^{-1}\c\u_3^{\,-1}\,]
&=&
\Omega_1\c [\,u_3^{ }\c\Lambda_3^{-1}\c\w_1^{\,-1}\,]\;,\end{aligned}$$ where any of this equations is the rather nontrivial sequence of two other, then $$\begin{aligned}
&\ds
\aw_1^{}\;=\;w_2^{}\c \Omega_3^{-1}
\;,\;\;\;
\au_1^{}\;=\;\Lambda_2^{-1}\c w_3^{-1}
\;,&\nonumber\\
&\ds
\naw_1^{}\;=\;\Lambda_3^{-1}\c \w_2^{}
\;,\;\;\;
\nau_1^{}\;=\;\w_3^{\,-1}\c \Omega_2^{-1}
\;,&\label{one}\end{aligned}$$ $$\begin{aligned}
&\ds
\aw_2^{}\;=\;\Omega_3^{}\c w_1^{}
\;,\;\;\;
\au_2^{}\;=\; \Omega_1^{}\c u_3^{}
\;,&\nonumber\\
&\ds
\naw_2^{}\;=\;\w_1^{}\c \Lambda_3^{}
\;,\;\;\;
\nau_2^{}\;=\;\u_3^{}\c \Lambda_1^{}
\;,&\label{two}\end{aligned}$$ $$\begin{aligned}
&\ds
\aw_3^{}\;=\;\Lambda_2^{-1}\c u_1^{-1}
\;,\;\;\;
\au_3^{}\;=\;u_2^{}\c \Omega_1^{-1}
\;,&\nonumber\\
&\ds
\naw_3^{}\;=\;\u_1^{\,-1}\c\Omega_2^{-1}
\;,\;\;\;
\nau_3^{}\;=\;\Lambda_1^{-1}\c\u_2^{}
\;.&\label{three}\end{aligned}$$ This map has the gauge degrees of the freedom, one degree in lhs and one in rhs. Namely, the system is unchanged if one change lsh as follows $$\begin{aligned}
&\ds
u_1^{}\rightarrow u_1^{}\c\omega^{-1}\;,\;\;\;\;
\w_1^{}\rightarrow \w_1^{}\c\omega^{-1}\;,
&\nonumber\\
&\ds
\u_2^{}\rightarrow \omega\c\u_2^{}\;,\;\;\;\;
\w_2^{}\rightarrow \omega\c\w_2^{}\;,
&\nonumber\\
&\ds
\u_3^{}\rightarrow \u_3^{}\c\omega^{-1}\;,\;\;\;\;
w_3^{}\rightarrow w_3^{}\c\omega^{-1}\;,
&\end{aligned}$$ and rhs (this is the above mentioned shift of $\Omega$-s) $$\begin{aligned}
&\ds
\nau_1^{}\rightarrow \nau_1^{}\c\acute\omega^{-1}\;,\;\;\;\;
\aw_1^{}\rightarrow \aw_1^{}\c\acute\omega^{-1}\;,
&\nonumber\\
&\ds
\au_2^{}\rightarrow \acute\omega\c\au_2^{}\;,\;\;\;\;
\aw_2^{}\rightarrow \acute\omega\c\aw_2^{}\;,
&\nonumber\\
&\ds
\au_3^{}\rightarrow \au_3^{}\c\acute\omega^{-1}\;,\;\;\;\;
\naw_3^{}\rightarrow \naw_3^{}\c\acute\omega^{-1}\;.
&\label{themap}\end{aligned}$$ Thus we obtain the map $R(\ac\omega,\omega)$, $$R_{1,2,3}(\ac\omega,\omega)\;:\;
\{V_1(\omega),V_2(\omega),V_3(\omega)\}\rightarrow
\{\ac V_1(\ac\omega),\ac V_2(\ac\omega),\ac V_3(\ac\omega)\}\;,$$ where $\{\ac V_k\}$ are given by (\[themap\]) and the gauge ambiguity is expressed via the dependence of $R$ on $\omega,\ac\omega$. This $R$ gives the correspondence between two “one dimensional” orbits in the spaces of in- and out state spaces. A fixing of the gauge means a rule comparing points on these orbits. Thus in FTE there exist three-parameters in-orbit and three-parameters out-orbit. Even if the points on in- and -out orbits of the quadrilateral are fixed, there still are one-parameter freedoms in left and right hand sides of FTE.
Partial cases
=============
Mention now a possible algebraization of the system (\[one\]–\[three\]). Suppose the parameters of $V_{12}$, $V_{13}$ and $V_{23}$ commute. Demand that the parameters of $\ac V_{12}$, $\ac V_{13}$, $\ac V_{23}$ also commute. This immediately gives $$\w\c w\;=\;w\c\w\;=\;k^2\;,\;\;\;\;
\u\c u\;=\;u\c\u\;=\;q^{-1}k^2\;,$$ where $k^2$ is a center, and $$u\c w\;=\;q\; w\c u\;.$$ Expressions for $\Omega$-s are $$\ds
\Omega_1\;=\;f^{-2}{k_2^2\over k_3^2}\c\Lambda_1^{-1}
\;,\;\;\;
\Omega_2\;=\;f^{-2}{1\over k_1^2k_3^2}\c\Lambda_2^{-1}
\;,\;\;\;
\Omega_3\;=\;f^{-2}{k_2^2\over k_1^2}\c\Lambda_3^{-1}
\;,$$ where $f$ is also a center. When $k$-s conserve, i. e. $f=1$, the map (\[one\]–\[three\]) can be realized by the known complete operator $R$ – matrix [@sbm-qd; @ms-modified].
To make it clear, put $q=1$, i. e. $u,w,\u,\w$ are numbers. Then change $$\ds u=>ku\,,\;\;\; w=>kw\,,\;\;\; \u=>k/u\,,\;\;\; \w=>k/w\,,$$ Hence $$\ds
\ac k_1\;=\;k_1f\,,\;\;\;\;
\ac k_2\;=\;{k_2\over f}\,,\;\;\;
\ac k_3\;=k_3f\,,$$ and $$\begin{aligned}
&\ds
\ac w_1\;=\;{f\over k_2}\;
{k_3\,w_1w_2+k_1\,w_2u_3+k_1k_2k_3\,u_3w_3\over w_3}\;,
&\nonumber\\
&\ds
\ac u_1\;=\;{k_2\over f}\;
{u_1u_2w_2\over k_1\,u_1w_2+k_3\,u_2w_3+k_1k_2k_3\,u_1w_3}\;,
&\nonumber\\
&\ds
\ac w_2\;=\;{k_2\over f}\;
{w_1w_2w_3\over k_3\,w_1w_2+k_1\,w_2u_3+k_1k_2k_3\,u_3w_3}\;,
&\nonumber\\
&\ds
\ac u_2\;=\;{k_2\over f}\;
{u_1u_2u_3\over k_3\,w_1u_2+k_1\,u_2u_3+k_1k_2k_3\,u_1w_1}\;,
&\nonumber\\
&\ds
\ac w_3\;=\;{k_2\over f}\;
{u_2w_2w_3\over k_1\,u_1w_2+k_3\,u_2w_3+k_1k_2k_3\,u_1w_3}\;,
&\nonumber\\
&\ds
\ac u_3\;=\;{f\over k_2}\;
{k_3\,w_1u_2+k_1\,u_2u_3+k_1k_2k_3\,u_1w_1\over u_1}\;.
&\label{old}\end{aligned}$$ If we choose $f=1$, so that it is possible to put $k=1$, then the map (\[old\]) is explicitly the complete functional map of ZBB complex (see [@ms-modified] for a table of two – parameters functional maps, all the examples there are just several specifications of eq. (\[old\]) with respect to $k$-s, and the case $(iv)$ there is explicitly (\[old\]).)
FTE is the sequence of FTE just for $k$-s. Another possibility of choosing $f$ is the situation when $u_i=w_i=1$ is the stationary point of the map (\[old\]), this gives the electric network form of $f$: $$f\;=\;{k_2\over k_1+k_3+k_1k_2k_3}\;.$$ One more possibility is to choose $f$ as it is for the Onsager’s model.
A “fusion”
==========
(400,200) (100,0)
(200,200) (100,0)[(0,1)[200]{}]{} (0,75)[(1,0)[200]{}]{} (0,125)[(1,0)[200]{}]{} (100,75) (100,125) (45,30)[$J$]{}(45,170)[$\Phi$]{} (145,30)[$\Phi'$]{}(145,170)[$J'$]{} (45,95)[$x$]{}(145,95)[$x'$]{} (110,130)[$V_\alpha$]{}(110,80)[$V_\beta$]{}
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(200,200) (25,0)[(1,2)[100]{}]{} (175,0)[(-1,2)[100]{}]{} (0,25)[(1,0)[200]{}]{} (0,75)[(1,0)[200]{}]{} (100,150)(110,145)[$1$]{} (37.5,25)(27.5,30)[$5$]{} (62.5,75)(52.5,80)[$3$]{} (137.5,75)(142.5,80)[$2$]{} (162.5,25)(167.5,30)[$4$]{}
(250,0)
(200,200) (75,0)[(1,2)[100]{}]{} (125,0)[(-1,2)[100]{}]{} (0,125)[(1,0)[200]{}]{} (0,175)[(1,0)[200]{}]{} (100,50)(110,45)[$1$]{} (37.5,175)(17.5,180)[$3$]{} (62.5,125)(42.5,130)[$5$]{} (137.5,125)(152.5,130)[$4$]{} (162.5,175)(177.5,180)[$2$]{}
(220,100)[$=$]{}
Consider a double vertex formed by two vertices, $V_\alpha$ and $V_\beta$ as it is shown in fig. (\[fig-LL\]). Denote this object as $V_{<\alpha,\beta>}$. Let the outer currents be $J,J',\Phi,\Phi'$ and $x,x'$. They obey four relations, $$\begin{aligned}
&\ds
J'\;=\;i\,\u_\alpha^{\,-1}\,\Phi\;,\;\;\;\;
\Phi'\;=\;-i\,u_\beta^{}\,J\;,
&\nonumber\\
&\ds
x\;=\;i\w_\beta^{}\,J-i\w_\alpha^{\,-1}\,\Phi\;,
\;\;\;
x'\;=\;-w_\beta^{-1}u_\beta^{}\,J-w_\alpha^{}\u_\alpha^{\,-1}\,\Phi\;,
&\end{aligned}$$ so that only two of the currents are independent. Let them be $J$ and $x$, then $$\begin{aligned}
&\ds
x'\;=\;-(\u_\beta^{-1}+u_\alpha^{})\w_\beta^{}\,J-i u_\alpha^{}\,x\;,
&\nonumber\\
&\ds
J'\;=\;i\u_\alpha^{\,-1}\w_\alpha^{}\w_\beta^{}\,J-\u_\alpha^{\,-1}
\w_\alpha^{}\,x\;,
&\nonumber\\
&\ds
\Phi\;=\;\w_\alpha^{}\w_\beta^{}\,J+i\w_\alpha^{}\,x\;,\;\;\;
\Phi'\;=\;-iu_\beta^{}\,J\;.
&\end{aligned}$$ Consider the transformation of a pair of such double vertices, $V_{<2,4>}$ and $V_{<3,5>}$, as it is shown in fig. (\[fig-double\]). In terms of $R$ operators, this transformation is given by $R_{123}\c R_{145}$. One can impose an invariant condition for left and right hand sides of (\[fig-double\]), namely, consider the condition when in $V_{<\alpha,\beta>}$ the “edge” currents, $x$ and $x'$, are proportional, i. e. $\u_\beta^{\,-1}+u_\alpha^{}=0$, so that $x'=-iu_\alpha^{} x$. Obviously, if the “edge” current flows through the left hand side of (\[fig-double\]), then it has to flow through the right hand side of (\[fig-double\]). This means that if one imposes in the left hand side the conditions $$\label{xx}
u_2^{}+\u_4^{\,-1}\;=\;0\;,\;\;\;\;
u_3^{}+\u_5^{\,-1}\;=\;0\;,$$ then one obtains $$\label{yy}
\au_2^{}+\nau_4^{\,-1}\;=\;0\;,\;\;\;\;
\au_3^{}+\nau_5^{\,-1}\;=\;0\;,$$ i. e. (\[xx\]) is the ideal of $R_{123}\c R_{145}$. For this simple system this fact can be easily verified directly.
(400,200) (100,0)
(200,200) (25,75)[(1,0)[150]{}]{} (25,125)[(1,0)[150]{}]{} (75,25)[(0,1)[150]{}]{} (125,25)[(0,1)[150]{}]{} (75,75) (75,125) (125,75) (125,125) (55,135)[$\beta$]{} (55,55)[$\alpha$]{} (135,55)[$\gamma$]{} (135,135)[$\delta$]{} (5,95)[$x$]{} (95,5)[$y$]{} (175,95)[$x'$]{} (95,175)[$y'$]{} (160,160)[$J'$]{} (30,30)[$J$]{} (30,160)[$\Phi$]{} (155,30)[$\Phi'$]{}
Consider now more complicated case of the quadrat (see fig. (\[fig-quad\]). Call this object $V_{<\alpha,\beta,\gamma,\delta>}$. In this case three currents are independent, choose them be $J$, $x$ and $y$. Solving the system $$\begin{aligned}
&\ds
x\;=\;i\,\w_\alpha^{}\,J\,-\,i\,\w_\beta^{\,-1}\Phi\;,\;\;\;
x'\;=\;i\,w_\gamma^{}\,J'\,-\,i\,w_\delta^{-1}\,\Phi'\;,
&\nonumber\\
&\ds
y\;=\;i\,u_\delta^{-1}\,\Phi'\,-\,i\,u_\alpha^{}\,J\;,\;\;\;
y'\;=\;i\,\u_\beta^{\,-1}\,\Phi\,-\,i\,\u_\gamma^{}\,J'\;,
&\nonumber\\
&\ds
w_\alpha^{-1}u_\alpha^{}\,J+w_\beta^{}\u_\beta^{\,-1}\,\Phi+
u_\gamma^{-1}w_\gamma^{}\,J'+\u_\delta^{}w_\delta^{-1}\,\Phi'\;=\;0\;,
&\end{aligned}$$ we obtain $$\begin{aligned}
&\ds
J'\;=\;-w_\gamma^{-1}u_\gamma^{}\,(\chi\,J
\,+\,i\,u_\beta^{}\,x\,-\,i\,\w_\delta^{}\,y)\;,
&\nonumber\\
&\ds
\Phi\;=\;\w_\beta^{}\,\w_\alpha^{}\,J\,+\,i\,\w_\beta^{}\,x\;,\;\;\;
\Phi'\;=\;u_\delta^{}\,u_\alpha^{}\,J\,-\,i\,u_\delta^{}\,y\;,
&\nonumber\\
&\ds
x'\;=\;-\,i\,(w_\delta^{-1}u_\delta^{}u_\alpha^{}\,+\,u_\gamma^{}\,\chi)\,J
\,+\,u_\gamma^{}\,u_\beta^{}\,x
\,-\,(u_\gamma\,+\,\u_\delta^{\,-1})\,\w_\delta^{}\,y\;,
&\nonumber\\
&\ds
y'\;=\;i\,(\u_\beta^{\,-1}\w_\beta^{}\w_\alpha^{}\,+\,\w_\gamma^{}\,\chi)\,J
\,-\,(w_\beta^{-1}\,+\,\w_\gamma^{})\,u_\beta^{}\,x\,+\,
\w_\gamma^{}\w_\delta^{}\,y\;,
&\end{aligned}$$ where $$\chi\;=\;w_\alpha^{-1}u_\alpha^{}\,+\,
u_\beta^{}\w_\alpha^{}\,+\,
\w_\delta^{}u_\alpha^{}\;.$$ Consider the intertwining of three copies of $V_{<\alpha,\beta,\gamma,\delta>}$: $$\begin{aligned}
&\ds
\Re_{1,2,3}\;:\;
V_{<\alpha_1,\beta_1,\gamma_1,\delta_1>}\,,\,
V_{<\alpha_2,\beta_2,\gamma_2,\delta_2>}\,,\,
V_{<\alpha_3,\beta_3,\gamma_3,\delta_3>}
&\nonumber\\
&\ds
\;\rightarrow\;
\ac V_{<\alpha_1,\beta_1,\gamma_1,\delta_1>}\,,\,
\ac V_{<\alpha_2,\beta_2,\gamma_2,\delta_2>}\,,\,
\ac V_{<\alpha_3,\beta_3,\gamma_3,\delta_3>}\;,&\end{aligned}$$ so that $$\begin{aligned}
&\ds
\Re_{1,2,3}\;=\;
R_{\alpha_1,\beta_2,\gamma_3}\c
R_{\delta_1,\gamma_2,\gamma_3}\c
R_{\beta_1,\beta_2,\beta_3}\c
R_{\gamma_1,\gamma_2,\beta_3}\c
&\nonumber\\
&\ds
R_{\alpha_1,\alpha_2,\delta_3}\c
R_{\delta_1,\delta_2,\delta_3}\c
R_{\beta_1,\alpha_2,\alpha_3}\c
R_{\gamma_1,\delta_2,\alpha_3}\;.
&\end{aligned}$$ Imposing the condition of independence of $x',y'$ on $J$, we obtain the ideal of the corresponding complicated $\Re$: $$\label{ideal}
w_\delta^{-1}u_\delta^{}u_\alpha^{}\,+\,u_\gamma^{}\,\chi\;=\;0\;,\;\;\;\;
\u_\beta^{\,-1}\w_\beta^{}\w_\alpha^{}\,+\,\w_\gamma^{}\,\chi\;=\;0\;.$$ Next, ignoring the “edge” currents at all (i. e. putting them zeros), so that $$\begin{aligned}
&\ds
\Phi\;=\;\w_\beta\c\w_\alpha\c J\;=\;
\u_\beta\c \u_\gamma\c J'\;,
&\nonumber\\
&\ds
\Phi'\;=\;u_\delta\c u_\alpha\c J\;=\;
w_\delta\c w_\gamma\c J'\;,
&\end{aligned}$$ we obtain on the surface of (\[ideal\]) the morphism $$V_\alpha\times V_\beta\times V_\gamma\times
V_\delta\Leftrightarrow V$$ where $$\begin{aligned}
&\ds
\overline U \;=\;i\,\u_\beta^{}\u_\gamma^{}\;,\;\;\;\;
\overline W \;=\;-i\,\w_\beta^{}\w_\alpha^{}\;,
&\nonumber\\
&\ds
U \;=\; i\,u_\delta^{}u_\alpha^{}\;,\;\;\;\;
W \;=\; -i\,w_\delta^{}w_\gamma^{}\;.
&\label{fusion}\end{aligned}$$ Obviously, all these manipulations resemble the fusion for the two dimensional models. For an operator formulation, when $R$ – operators can be expressed in terms of quantum dilogarithms of $w_i,u_i$, the ideals (\[ideal\]) mean the operator projectors commuting with $\Re$.
Note that one can ignore the face currents and consider only $x,y\rightarrow x',y'$. Thus one obtains exactly the formulation of the free fermionic $6$-vertex type, that was considered in [@oneparam]. Most complete formulation is, of course, the formulation with the face – edge currents.
Discussion
==========
In this notes we have proposed some algebraical toy which can be interpreted as a intertwining problem for the complex of $R$ – operators associated with ZBB statistical model. Obvious is only one advantage of this toy: a sort of a “fusion”. A nonsense (or again an advantage) of this toy is also obvious: the gauge ambiguity. One can fix this ambiguity in different ways, so that $3D$ $R$ – operators gain some non – quantized functional part.
Nevertheless, we guess that our system would lead to something more general then known set of the solutions of the tetrahedron equation. A naïve way to obtain other $R$ – matrices is to regard the elements $u_k,w_k,\u_k,\w_k$ as matrices of the same structure, and hence noncommutative for different $k$-s. Give only one example: consider the case when $$\ds u\;=\;w\;=\;\u\;=\;\w\;=\;
\left(\begin{array}{cc}
0 & k \\ 1/s & 0\end{array}\right)\;,$$ that is the simplest generalization of the pure electric network system so as the gauge ambiguity is canceled, then the rather nontrivial map $$\begin{aligned}
&\ds
k'_1\;=\;{k_2s_3\over s_1+k_2+s_3}\,,\;\;\;
s'_1\;=\;k_3+s_2+{s_2k_3\over k_1}\,,
&\nonumber\\
&\ds
k'_2\;=\;k_1+k_3+{k_1k_3\over s_2}\,,\;\;\;
s'_2\;=\;{s_1s_3\over s_1+k_2+s_3}\,,
&\nonumber\\
&\ds
k'_3\;=\;{s_1k_2\over s_1+k_2+s_3}\,,\;\;\;
s'_3\;=\;k_1+s_2+{k_1s_2\over k_3}\,
&\end{aligned}$$ is obtained.
[**Acknowledgments**]{}: I should like to thank Yu. G. Stroganov, H. E. Boos, V. V. Mangazeev, G. P. Pron’ko, F. W. Nijhoff and especially Rinat Kashaev and Igor Korepanov for many fruitful discussions.
The work was partially supported by the grant of the Russian Foundation for Fundamental research No 95 – 01 – 00249.
[10]{}
A. B. Zamolodchikov. “Tetrahedron equations and the relativistic $S$ matrix of straight strings in $2+1$ dimensions”. , [**79**]{}, 489-505, 1981.
V. V. Bazhanov and R. J. Baxter. “New solvable lattice models in three dimensions”. , [**69**]{}, 453-485, 1992.
R. J. Baxter. “The Yang – Baxter equations and the Zamolodchikov model”. , [**18D**]{}, 321-347, 1986.
S. M. Sergeev V. V. Mangazeev and Yu. G. Stroganov. “The vertex formulation of the Bazhanov – Baxter model”. , Vol. 82, Nos 1/2, 1996.
S. M. Sergeev H. E. Boos, V. V. Mangazeev and Yu. G. Stroganov. “$\Psi$ – vectors for three-dimensional models”. , Vol. 11, No. 6, pp. 491-498, 1996.
R. M. Kashaev and N. Yu. Reshetikhin. “Affine Toda field theory as a 3-dimensional integrable system”. , 1995.
L.D. Faddeev and R.M. Kashaev. “Quantum dilogarithm”. , [**A9**]{}, 1994.
V. V. Bazhanov S. M. Sergeev and V. V. Mangazeev. “Quantum dilogarithm and the tetrahedron equation”. , 95-141, 1995.
V.V. Bazhanov and N.Yu. Reshetikhin. “Remarks on the quantum dilogarithm”. , [**28**]{}, 1995.
S. M. Sergeev J.-M. Maillard. “Three dimensional integrable models based on modified tetrahedron equations and quantum dilogarithm.”. , submitted to Phys. Lett. B., 1997.
S. M. Sergeev. “Two – dimensional $R$ – matrices – descendants of three dimensional $R$ – matrices.”. , Vol. 12, No. 19, pp. 1393 – 1410., 1997.
I. G. Korepanov. “Algebraic integrable dynamical systems, $2+1$ - dimensional models in wholly discrete space – time, and inhomogeneous models in $2$ - dimensional statistical physics”. , 1995.
J. M. Maillet and F. W. Nijhoff, “Multidimensional Lattice Integrability and the Simplex Equations”, in Proceedings of the Como Conference on Nonlinear Evolution Equations: Integrability and Spectral Methods, eds. A. Degasperis, A. P. Fordy and M. Lakshmanan, pp. 537 – 548, Manchester University Press, 1990\
J.-M. Maillet and F. W. Nijhoff, “Integrability for multidimensional lattice models”, B224 (1989) 389-396.\
J.-M. Maillet. “Integrable systems and gauge theories”. , 18B, pp. 212-241., 1990.
I. G. Korepanov. “Tetrahedral Zamolodchikov algebras corresponding to Baxter’s $L$ – operators”. , [**154**]{}, 85-97, 1993.
R. M. Kashaev. “On discrete three – dimensional equations associated with the local Yang – Baxter relation”. , 35, 389-937, 1996.
S. M. Sergeev R. M. Kashaev. “On pentagon, ten-term, and tetrahedron relations”. , submitted to Commun. Math. Phys., 1996.
S. M. Sergeev. “ Solutions of the functional tetrahedron equation connected with the local Yang – Baxter equation for the ferro-electric.”. , 1997.
[^1]: Here one should mention the successful attempt to obtain 3D $R$ – matrix directly from the similar consideration of the Zamolodchikov – type algebra for two dimensional $L^\alpha_{i,j}$, where $\alpha$-s – indices of 3D $R$ – matrix [@korepanov]. This $R$ – matrix obtained appeared to be some special case of the $R$ – matrix for ZBB model.
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Jordan Phillips Will Have The Biggest Impact Of Any Miami Dolphins Rookie In 2015
By Nik Zirounis
Trevor Ruszkowski-USA TODAY Sports
The Miami Dolphins had seven choices in the 2015 NFL Draft held this past spring. Miami’s biggest catch was former Louisville Cardinals wide receiver DeVante Parker with the 14th pick. After two weeks of training camp and one exhibition game, it will instead be Jordan Phillips, chosen 38 picks after Parker, who will be the Dolphins’ breakout rookie this season.
There was some discussion amongst draft experts that Phillips should be a late first round selection. The ex-Oklahoma Sooners’ lineman has outstanding size at 6-foot-6 and 330 pounds. He has a great combination of power and speed. He has even famously done back flips on the practice field at Oklahoma. What was not to like?
The knock on the sizeable ex-Sooner was his motor wasn’t always humming. Phillips would tend to take plays off and not give it his all in some games against lesser competition. Pro coaches and scouts hate that kind of talk and it sent Phillips’ stock into decline. That’s why he was available twenty picks into the second round.
Every negative thing said about Phillips has been erased in Miami’s training camp. All reports are that he has been working hard and doesn’t seem lazy at all. He has used his size to bludgeon offensive linemen in practice and blew up a helpless Chicago Bears blocker on a play during the first preseason game.
Phillips is still vying for a starting defensive tackle spot next to superstar Ndamukong Suh. Although incumbent Earl Mitchell is the favorite to return to his starting roost, Phillips may have slipped past free agent acquisition C.J. Mosley as Mitchell’s biggest challenger. Whoever starts next to Suh will benefit from having single blocking. That will allow that player the opportunity to put up some nice numbers.
Even if Phillips is relegated to second string status, he will be on the field enough to make some big plays. Parker, meanwhile, should probably take half the season to be as productive as a first round wide receiver should be. Heaven forbid, but there is a chance that Parker may not fully recover from his injury or become comfortable in the Dolphins’ offense at all this year.
Fourth round draft pick Jamil Douglas has an outside chance at starting at one of the two vacant guard positions. Odds are he fills in on occasion, thus eliminating him from having any huge impact in year one and stealing Phillips’ spotlight.
Miami’s quartet of fifth round picks probably won’t tip the scales away from Phillips’ favor, either. Running back Jay Ajayi has the best opportunity of the bunch, but he was absent from the Dolphins’ game in Chicago and has looked outmatched so far in camp. Cornerback Bobby McCain was climbing the depth chart ladder before falling back versus the Bears. Defensive backs Cedric Thompson and Tony Lippett are developmental players.
One last good thing that Phillips has going for him is that he won’t be asked to carry the load on this potentially outstanding defense. Suh will anchor the group up front and defensive ends Cameron Wake and Olivier Vernon are already established NFLstars. That gives Phillips the freedom to stay in control and let his enormous talent do the talking. It will also allow him to be the Dolphins’ best rookie in 2015.
Nik Zirounis is an NFL/Dolphins writer for RantSports.com. Follow him on Twitter @realnikz and like him on Facebook. |
Add dry ingredients to mug, and mix well. Add the egg and mix thoroughly. Pour in the milk and oil and mix well. Add the chocolate chips (if using) and vanilla extract, and mix again. Put your mug in the microwave and cook for 3 minutes at 1000 watts (high). The cake will rise over the top of the mug, but don't be alarmed! Allow to cool a little, and tip out onto a plate if desired.
EAT! (This can serve 2 if you want to feel slightly more virtuous).Why is this the most dangerous cake recipe in the world? Because now we are all only ever 5 minutes away from chocolate cake at any time of the day or night!
EnjoyDebbiex
Back tomorrow with a box set of notecards template and a little desk note set :)
Been a bit of a non blogger of late but recently decided to start again, was looking for inspiration both for blogging and crafting and found your blog. Just came across this post of the dangerous cake and went straight to the kitchen to try it out. OMG A-MAZING!!! I just made it for my hubby (who currently has flu and off food) and it went down a treat!!! There will be a link to your blog when I start blogging again, loving your cards and box tutorials!! Frances x |
by
Tomorrow the National Hockey Leagues version of Christmas will take place. Teams in the playoff hunt (or teams who are very close to a playoff spot) typically become “buyers” this time of year. These teams will usually end up trading away prospects and/or draft picks to the teams who sit at the bottom of the rankings (the “sellers”) and in return the buyers pick up better than average NHL players they feel will add something to the current makeup of their team.
The Carolina Hurricanes were labeled sellers as early as December. Their most valuable trade assets were forward Tuomo Ruutu and defenseman Tim Gleason who had their fates all but sealed. Tim Gleason was going to end being traded to the Philadelphia Flyers and Tuomo Ruutu could have ended up on a few different teams (Detroit seemed to be one of the front runners.) But that didn’t end up happening, in a move that surprised many, the Carolina Hurricanes ended up resigning Ruutu and Gleason to four year deals.
By choosing to keep Gleason and Ruutu the Hurricanes, in effect, closed the door on picking up any more high round draft picks or top rated prospects this season. It also opened the option for the Hurricanes to try and resign fellow Unrestricted Free Agents Bryan Allen and Jaroslav Spacek. Both players bring something that makes them worthwhile to keep around.
Jaroslav Spacek came in with very low expectations from fans, but after 25 games with the Hurricanes, he has 3 goals and 6 assists and is a plus one. The 38 year old defenseman has over 850 NHL games over the course of his career and that veteran experience is certainly a benefit not only to the team each night but to 24 year old Jamie McBain and 19 year old Justin Faulk who usually end up getting paired with him. Of course Rutherford will gauge how interested Spacek is when presented with the idea of staying with the team (former teammate and now head coach Kirk Muller will likely also try to apply the pressure) but Spacek will also be given the option of going to a contender if that opportunity should arise.
Bryan Allen is the second oldest blueliner (behind Spacek) at 31 years old, but compared to most of the Hurricane defensive crop he’s having one of the better seasons. Averaging 19:12 minutes per game he is only one of three defensemen to have a positive plus – minus record. He’s ranked 9th in the league for blocked shots and (I said this at the time the Hurricane acquired him) the 6’5’’ 226lbs defenseman fits the physical mold of the type of defenseman the Hurricanes need (and if the trade him don’t have a ready replacement for.)
According to Chip Alexander, who covers the Hurricanes for the Raleigh News & Observer, General Manager Jim Rutherford spoke with Allen’s agent today about possibly resigning and said that it “wasn’t going to happen.” Now things could change between now and the end of tomorrow, and Rutherford has been wrong on these things before (Jussi Jokinen wasn’t originally supposed to stick around), but if Allen does get traded I think we will see Spacek stay (and vice versa.)
I’ll be available all day tomorrow and will have an blog post up where you can comment on trade happening throughout the day, I’ll include my thoughts and bring you the latest Hurricane news.
Your call: Which players will the Hurricanes end up trading?
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Check out our Blog Roll (some good ORIGINAL hockey content) + I’d like to shout our one of my favorite affiliates Sharks Circle! If your looking for good independent NHL coverage check out Sharks Circle (don’t let the name fool you, you don’t have to be a Sharks fan to enjoy.)
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MINNEAPOLIS — Red Sox righty Rick Porcello wants to stay in Boston. He loves pitching for the Red Sox. He reportedly tried to negotiate a hometown discount during spring training. He recognizes New England as his home and has a house in southern Vermont.
President of baseball operations Dave Dombrowski gave Chris Sale a five-year, $145-million extension during spring training after re-signing Nathan Eovaldi in free agency for four years, $68 million
Porcello, meanwhile, remains unsigned as his free agency looms at the end of the 2019 season.
The righty pitched 7 scoreless innings, allowing four hits and one walk while striking out eight here at Target Field on Monday. He led the Red Sox 2-0 over the Twins.
The Red Sox should pay Porcello. He’s Boston’s most durable starting pitcher and he’s a clubhouse leader who receives enormous respect from his peers.
“Those three guys, they mean a lot to me in the clubhouse: David (Price), Chris (Sale) and Rick," Red Sox manager Alex Cora said after the victory Monday. "Whenever I have a message or whatever, they’re the ones that are always in the office and we talk about it. And they take care of that stuff in there. And in their own way, too. They’re very different.
“He’s been great,” Cora added about Porcello. "He’s a guy that I got to meet (before the 2018 season). Remember, he flew with me to Puerto Rico the first time I went down there with the supplies. We connected right away. And he's been amazing for us."
Porcello is the type of veteran the Red Sox need at times when things aren’t going well — like this season. Boston improved to a season-high six games over .500 here Monday but this has been a challenging year for Cora’s club.
Just look at how Porcello handled himself in his first year with Boston when he posted a 4.92 ERA and received enormous scrutiny.
Many players in his situation have felt resentment toward Boston, the fan base and media while playing out the remainder of their lucrative contracts.
But Porcello wants to stay here beyond his current contract. That tells you a lot about his personality and how he can help younger pitchers as they transition to the majors.
“We’ve got fans paying a lot of money for tickets. And when you’re going out there and making a lot of money and not performing, you deserve to hear it,” Porcello told MassLive.com in April. "So I don’t think I’ve ever taken that personally here. I completely understand it. If I was a fan watching, I probably would have booed myself.”
Porcello had an 11.12 ERA after his first three starts this year. He has a 3.30 ERA (76 1/3 innings, 28 earned runs) in his past 12 starts.
“He’s been great,” Cora said. “He didn’t have a good start to the season, but he kept working on his craft, making adjustments.”
At this point, the Red Sox seem more likely to offer Porcello a qualifying offer. And he probably would be wise to accept it.
If he declined it, he likely would be in the same position that Dallas Keuchel was this past offseason. Keuchel turned down a $17.9 million qualifying offer from the Astros. He went unsigned until after the 2019 June Draft because no teams wanted to give up the compensation draft pick tied to his qualifying offer.
Teams can’t offer the same player a qualifying offer two years in a row, And so Porcello would be able to enter free agency after the 2020 without being tied to a compensation draft pick.
Maybe the Red Sox will come to their senses in the meantime and re-sign their durable leader. |
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Alright you fucken nerds........
After a good, long run, we have decided to close our forums in an effort to refocus attention to other sections of the site. Fortunately for you all, we're living in a time where discussion of a favorite topic now has a lot of homes. So we encourage you all to bring your ravenous love for discussion to Chuck's official Facebook, Twitter, Tumblr and Instagram. And, as always, you can still post comments on all News updates. Thank you for your loyalty and passion over the years. These changes will happen June 1.
If they do, then it is a potential box office bomb. Average people don't want to see a movie end like that.
If they don't, all nerds everywhere will spit fire, and obviously we've proved that nerds are not insiginifcant at the box office or at generating good press.
well, to his credit, Leonidas didn't live at the end of 300, but yeah, unless they do a kill bill type thing and break it into two movies of about 2 1/2 hours apiece, it's going to suck. But it will be damn pretty to look at so i'll see it regardless. Plus it'll probably have some kickass trailers before it too!
Anyone know the song from the trailer off hand? Actually works pretty well with the clips.
Yeah, it is a Smashing Pumpkin's song called "The End is the Beginning is the End", it's the last track from the Batman and Robin soundtrack as well, funny enough. The Beginning is the End is the Beginning is also that song, just another version of it.
The trailer was beautiful btw. And as for staying true to the ending, it's looking like they are. It also seems that the lead designer of the Cloverfield monster is the one designing the (OMG SPOILERS) squid monster thing according to fan sites.
From what scripts people have been able to get from the movie, it does look like they jacked around with the story a bit, but we'll never know until it is out of course. They recently released some more pictures that look stunning as well, I'll see if I can find them.
This movie is going to blow, I'm sorry. It just is. They're going to make it into the X-Men and we will all fuckin' cry.
That's what I've been afraid of ever since they thought of making it a movie. How in the bleedin hell are they going to capture Dr's view of time? You can't have that experience through film, you just can't.
Also, thanks everyone for agreeing that X-Men sucked. It totally did and I hate people who won't admit it.
But this doesn't stop me from getting all excited. We all know we're going to see it, regardless of how suspicious we are of it. We're either going to be happy and sad at the same time that we were right and it's crap, or we're going to see it and be dissapointed/surprised that it wasn't crap.
Here's a great fan site for the movie. Currently has an interview with Matthew Goode about his role as Oxymandias and how he's putting his own "spin" to his past.../groan. We should be getting new clips/info from the San Diego Comic Con tomorrow as well.
Oh yeah, and here's a pin-up of Sally Jupiter they released from the movie.
i feel a little better about this film after seeing zach snyder on comic-con saying how if the best he does is just make a three hour commercial for the book he'd be perfectly happy with that. That's really about the best that can be done with a movie of this.
Here's a bunch of comic con posters they released. No real news about the movie though, just the things we could already figure out. It's staying pretty true to the comic, but does have some original parts and has a hard R rating. The clip they showed had more images directly from the comic, Rorschach discovering Comedian's secret costume nook, more graphic Mr. Manhatten blowing up people, Silk Spectre unvieling the Owl Ship, Comedian getting slashed by the Vietnamese woman, etc.
Important Disclaimer: Although this is Chuck Palahniuk’s official website, we are in essence, more an official ‘fansite.’ Chuck Palahniuk himself does not own nor run this website. Nor did he create it. It was started by Dennis Widmyer, who is the webmaster and editor of most of the content. Chuck Palahniuk himself should not be held accountable nor liable for any of the content posted on this website. The opinions expressed in the news updates, content pages and message boards are not the opinions of Chuck Palahniuk nor his publishers. If you are trying to contact Chuck Palahniuk, sending emails to this website will not get you there. You should instead, take the more professional route of contacting his publicist at Doubleday. |
Q:
Visual Studio 2015 - Compiler giving Stack Overflow on big fluent call
I have a code like this:
SomeObject.MakeFluent()
.AddProperty(new MyProperty() { ... })
.AddProperty(new MyProperty() { ... })
.AddProperty(new MyProperty() { ... })
.AddProperty(new MyProperty() { ... })
.AddProperty(new MyProperty() { ... })
//[+1024 times]
.AddProperty(new MyProperty() { ... });
On compile, I get a csc.exe error, stack overflow. If I change the chained method call to:
var fluentAux = SomeObject.MakeFluent();
fluentAux.AddProperty(new MyProperty() { ... });
fluentAux.AddProperty(new MyProperty() { ... });
fluentAux.AddProperty(new MyProperty() { ... });
The code above works fine.
Is there a way to configure max stack call on VS2015's C# compiler? I ask because on VS2013, this issue doesn't happen.
Has the VS2015 compiler become less resilient?
Note: The COMPILER is returning 'stack overflow', not my program.
A:
Opened, as suggested by @DaveShaw, an issue on github:
https://github.com/dotnet/roslyn/issues/9795
|
Image: Getty / Gizmodo
Google fired software engineer James Damore on Monday after his 10-page anti-diversity screed went viral within the company. According to emails obtained by Gizmodo, and accounts from four individuals who attended a Ph.D program retreat with Damore, this is not the first time he offended his peers with sexist ideologies.
According to emails provided to Gizmodo, Andrew Murray and Tim Mitchison, the co-directors of the Systems Biology Program at Harvard—which Damore attended for two years before leaving the program and starting his career at Google—issued a formal apology to a number of students for a student skit performed at the 2012 Systems Biology Program Retreat. According to two sources, Damore was the primary performer in the skit.
In an email dated October 15, 2012, nine days after the conclusion of the retreat, Murray and Mitchison wrote that the skit “presented material that offended many members of our community” and emphasized that even in the context of a humorous skit, “targeting any group within the program that can be defined by gender, by ethnicity, by sexual orientation, or by religious orientation, is never acceptable.”
The stated purpose of the retreat is “to bring our community together to learn about current research in systems biology,” according to a description on the Systems Biology Ph.D program website. A photo reviewed by Gizmodo confirmed that Damore was present on the 2012 retreat, along with over 35 other adults.
A source who spoke under the condition of anonymity because they did not want their name associated with the current controversy surrounding Damore said that Damore participated in the writing, arranging, casting, and performing of the skit, which they described as “sexist” in nature. According to the source, a short humorous skit is typically performed by students during the annual retreat, and while they described the skits as typically a “roast,” they emphasized that “the goal is not to offend.” Damore participated in the writing of the skit, along with other program students, but according to two sources, Damore was the primary performer during the skit when it was performed. The source noted that in the “particular year in which James played a role organizing, [the skit] was particularly offensive to women.”
Three sources allege that Damore told what they characterized as a masturbation-related joke during the course of the performance, which fell flat and offended some in the audience. However, two sources attributed the backlash to the performance not to any malice on the part of Damore, but instead to his awkward delivery.
Multiple sources also allege that the skit was viewed as problematic among many individuals in the department and that a number of people were offended by the specific masturbation joke. The administration later issued the formal apology to the group for the skit overall.
An email with the subject line “Final Skit Brainstorming,” dated October 4, 2012, shows Damore emailed others in the program to finalize the skit and decide casting.
Over a year later, in a final email, dated November 21, 2013 with the subject line “I’m Leaving Harvard,” announced Damore’s departure from Harvard. In it, he said he “had too much fun [over the] summer,” referring to a Google internship he completed, and announced he would be taking a job at Google in December of that year.
When contacted for comment on Damore’s tenure at Harvard and any backlash related to the skit in question, a spokesperson from Harvard’s communications office responded, “As a policy, we do not comment on individual students.”
Andrew Murray, Tim Mitchison, and James Damore did not respond to multiple requests for comment.
Do you have a tip about what’s going on at Google? Email the author of this story: [email protected]. |
642 P.2d 1178 (1982)
56 Or.App. 478
STATE of Oregon, Respondent,
v.
Kenneth Owen TROW, Appellant.
No. 79-06-31954; CA 19840.
Court of Appeals of Oregon.
Argued and Submitted June 17, 1981.
Decided March 22, 1982.
Reconsideration Denied April 27, 1982.
*1179 Charles J. Merten, Portland, argued the cause for appellant. With him on the brief was Merten & Saltveit, Portland.
Thomas H. Denney, Asst. Atty. Gen., Salem, argued the cause for respondent. With him on the brief were Dave Frohnmayer, Atty. Gen., and William F. Gary, Deputy Sol. Gen., Salem.
Before BUTTLER, P.J., and WARDEN and WARREN, JJ.
WARREN, Judge.
Defendant appeals his conviction after jury trial for unlawful use of a vehicle. ORS 164.135. We affirm.
Defendant was indicted by secret indictment in June, 1979:
"The above-named defendant is accused by the Grand Jury of Multnomah County, State of Oregon, by this indictment of the crime of UNAUTHORIZED USE OF VEHICLE committed as follows:
"The said defendant, between February 20, 1979 and March 24, 1979, in the County of Multnomah, State of Oregon, did unlawfully and intentionally use a vehicle, to-wit: a 1966 Chrysler, Oregon License No. CFD 158, owned by Leonard Mohler and Michael I. Luce, the said defendant having custody of the said vehicle pursuant to an agreement between the said defendant and Leonard Mohler and Michael I. Luce whereby the said defendant was to perform for compensation *1180 a specific service for Leonard Mohler and Michael I. Luce involving the repair of said vehicle, said use being without the consent of Leonard Mohler and Michael I. Luce, and for the said defendant's own purpose in a manner constituting a gross deviation from the agreed purpose, contrary to the Statutes in such cases made and provided and against the peace and dignity of the State of Oregon.
"* * *."
Defendant moved to dismiss and, alternatively, for a hearing equivalent to a preliminary hearing before trial. Those motions were denied.
In September, 1979, defendant petitioned the Supreme Court for a writ of mandamus, seeking to compel the circuit court either to dismiss the indictment or to grant defendant a hearing equivalent to a preliminary hearing or to show cause why it had not done so. Defendant then demurred to the indictment. In October, the Supreme Court issued an alternative writ of mandamus, ordering the circuit court to show cause why it had not granted defendant's motion. The circuit court overruled the demurrer in November.
Defendant next moved in the Supreme Court for an order staying the trial in the circuit court until further order of the Supreme Court on the petition for mandamus. On December 11, 1979, the Supreme Court granted the stay "pending the issuance of [its] decision." An opinion dismissing the petition was handed down on June 3, 1980, 289 Or. 265, 611 P.2d 1169 (1980), and an opinion denying defendant's petition for rehearing was filed September 23, 289 Or. 673, 616 P.2d 496 (1980). However, the mandate dissolving the stay was not issued by the Supreme Court until November 20, and was not received in Portland until November 21, 1980.
On November 18, 1980, trial commenced. Just before jury selection, defendant moved for an order requiring one of the victims, Michael Luce, to submit to a defense interview and for a continuance until that interview was completed. The motion was denied.
Mohler testified that the Chrysler had belonged to his deceased wife, that Automotive Emporium had repaired the car in the summer of 1978, and warranted that work, and that he understood that he would not have to pay for any later work done on the car under that warranty. Mohler said that his wife had died in September, 1978, just before he agreed to sell the car to Luce. He had gone on an 18-month drunk after her death, during which he drank every day until he "felt better." He lived near defendant's business and often went there to talk to defendant but was not sure of the content of those conversations, because he had been "upset" during that period. Mohler did remember that he wanted to sell the Chrysler for about $600 and that defendant had told him that he could get Mohler more than $600 for the car.
Luce testified for the state that, in early 1979, he had orally contracted to purchase the Chrysler from Mohler and had taken the car to Automotive Emporium for minor electrical work. After telling people there that he was "interested in buying" the car and after determining that they would honor a warranty of work done for Mohler the previous summer, Luce left the car for repair. He subsequently learned that the car had been used by Automotive Emporium as a loaner. He had not authorized defendant or anyone else to use the car as a loaner.
Defendant testified that he was general manager of Automotive Emporium, Inc. He said that Mohler had been in need of money and had told defendant that he planned to sell the car for $600. Defendant said that he told Mohler in late 1978 or early 1979 that defendant could get more than $600 for the car and that, if he could not, he would buy it himself for Automotive Emporium's use as a loaner. Defendant had not given money to Mohler for the car before using the car as a loaner, because, he said, he was waiting for Mohler to deliver the title. As a result of defendant's use of the vehicle as a loaner, the car was left dirty and damaged.
*1181 Defendant first contends that the trial court was without jurisdiction to try him before the mandate had issued in the collateral mandamus case. The Supreme Court had stayed this case pending issuance of its decision, not of its mandate. It issued its decision June 3, 1980, and denied rehearing September 23, 1980. Its mandate did not issue until November 20, 1980, two days after trial began, five and one-half months after its original decision and nearly two months after it denied rehearing.
Although the parties did not include in the record any premandate document evidencing notice of the Supreme Court's decision, we presume that defendant received notice before September 23, 1980, in order to have petitioned for the rehearing denied that day.
The question is not of notice but of jurisdiction. We hold that the stay was dissolved no later than September 23, 1980, by the terms of the Supreme Court's order re-entered that day. Cf. State v. Houghton, 45 Or. 110, 111-112, 75 P. 887 (1904) (on retrial after reversal on appeal, judgment reversing and ordering new trial gives trial court authority to proceed; mandate is merely official evidence). The trial court had jurisdiction to try defendant on November 18, 1980.[1]
The trial court did not err in overruling defendant's demurrer to the indictment for lack of specificity. The indictment tracked the language of ORS 164.135(1)(b)[2] and charged defendant with intentional "use" for his own purpose of a specific vehicle, without the owner's consent and "in a manner constituting a gross deviation from the agreed purpose" of "perform[ing] for compensation a specific service * * * involving repair" of the car. That was sufficient
"* * * (1) to inform the accused of the nature and character of the criminal offense * * * with sufficient particularity to enable him to make his defense, (2) to identify the offense so as to enable the accused to avail himself of his conviction or acquittal thereof in the event that he should be prosecuted further for the same cause, and (3) to inform the court of the facts charged * * *." State v. Smith, 182 Or. 497, 500, 188 P.2d 998 (1948), quoted in State v. Sanders, 280 Or. 685, 687-88, 572 P.2d 1307 (1972).
Definition of intentional misuse as deviation from the agreed purpose of repair was enough. Just as the exception carved in Sanders for burglary indictments does not require allegation of elements of the crime intended upon unlawful entry, so here misuse need not be defined beyond "gross deviation" from the agreed purpose of repair. State v. Sanders, supra, 280 Or. at 690, 572 P.2d 1307.[3]
*1182 Defendant's third assignment is denial of his motion for a post-indictment "preliminary hearing." Defendant's equal protection arguments were raised and found wanting in State v. Clark, 291 Or. 231, 630 P.2d 810, cert. den. ___ U.S. ___, 102 S.Ct. 640, 70 L.Ed.2d 619 (1981), and State v. Edmonson, 291 Or. 251, 630 P.2d 822 (1981). As in those cases, defendant here has not shown how, if at all, he was denied
"`individually, or [as a member of] a class * * *, the equal privilege of a preliminary hearing with other citizens of the state similarly situated.' * * * In other words, defendant's constitutional claim requires a showing how the choice of procedure is administered, and whether it offers or denies preliminary hearings to individual defendants, or to social, geographic, or other classes of defendant (apart from the `classification' formed by the choice itself) purely haphazardly or otherwise on terms that have no satisfactory explanation * * *." 291 Or. at 253-254, 630 P.2d 822 (quoting State v. Clark, supra, 291 Or. at 243, 630 P.2d 810). (Emphasis added.)
Defendant also claims that grand juries no longer serve their intended function as an alternative to probable cause hearings and, therefore, that grand jury indictments violate due process. Although conceivably a grand jury could be so manipulated as to deny due process, defendant has not shown that his grand jury was so manipulated or that all grand juries are so manipulated.
Defendant next contends that the trial court should have granted his motion to require Luce to submit to a defense interview. Luce's decision not to talk to the defense was his own. The prosecution did not advise or suggest that he should not talk to the defense. Defendant was afforded both discovery of Luce's statement to police and full cross-examination at trial. He had no absolute right to compel Luce to speak with defense counsel, State v. York, 291 Or. 535, 541, 632 P.2d 1261 (1981), and has not shown prejudice or inability to cross-examination the reluctant witness. The trial court did not abuse its discretion.
Defendant's fifth and sixth assignments are the trial court's denials of his motions for acquittal and directed verdict. At trial, defendant's ground was insufficient evidence to prove criminal intent, gross deviation from intended purpose, or a claim of right to the car in another superior to defendant's.[4]
Defendant's own testimony was that he had not paid Mohler for the car or received title from Mohler before he lent the car; he had agreed to buy the car if he could not otherwise sell it for Mohler. That was evidence that his "claim of right" was not superior to that of the victims.
The state presented evidence that the intended purpose was repair. Defendant's evidence was that he was Mohler's agent to sell the car; he did not offer evidence that loaning the car to his customers was within the scope of the claimed agency. It was for the jury to determine if defendant's use of the vehicle as a loaner was a gross deviation.
Defendant's final assignment is that the court erred in excluding his wife's testimony about two telephone conversations she had overheard in the winter of 1978-79. Defendant offered the testimony to show his state of mind. The court sustained the state's hearsay objection after defendant's offer of proof. Mrs. Trow would have testified that she had overheard defendant's end of his telephone conversations with his accountant and with Mohler.[5] Defendant *1183 does not dispute that the evidence was hearsay but argues that the testimony was relevant and admissible to show his mental state as to whether he felt he had authority to use the car.
The offer of proof at most corroborated defendant's and another witness' testimony. Any error in excluding this evidence, offered for a non-hearsay purpose, was harmless. As discussed above, even if the jury believed defendant's version of the facts, he did not establish that he bought the car from Mohler or that he had a claim of right to use the car as a loaner before he actually bought it. The proffered testimony does nothing to dispute the element of an agreed purpose of repair; in fact, it shows that defendant had not bought the car and that, if he had told Mohler of plans to use the car as a loaner, they were plans so to use the car after he bought it.
Affirmed.
NOTES
[1] Defendant did not object before or at trial that he was without notice, or the court without jurisdiction, because the mandate had not yet issued. Subject matter jurisdiction is not waived for failure to object before or at trial. Objections to notice or other defenses and objections are waived if not timely raised: no later than the responsive pleading in some cases and never later than at trial, except for subject matter jurisdiction. ORCP 21. Defendant waived any valid objection to lack of mandate. Cf. Dickson v. King, 151 Or. 512, 514, 49 P.2d 367 (1935) (proceeding to trial, when counsel knew that mandate was on file with trial court clerk but had not been entered in lower court journal, waived objection to proceeding before entry, such objection is not jurisdictional.)
[2] ORS 164.135(1)(b) provides:
"A person commits the crime of unauthorized use of a vehicle when:
"* * *
"(b) Having custody of a vehicle, boat or aircraft pursuant to an agreement between himself or another and the owner thereof whereby he or another is to perform for compensation a specific service for the owner involving the maintenance, repair or use of such vehicle, boat or aircraft, he intentionally uses or operates it, without consent of the owner, for his own purpose in a manner constituting a gross deviation from the agreed purpose * *."
[3] Sanders does require allegation of the specific crime intended in order to give notice of the criminal intent the defendant is charged to have had. We need not reach the question here whether this indictment would have been sufficient to specify intent had it not specified the nature of the "specific service."
[4] On appeal, defendant argues for the first time that there was no evidence that defendant was to perform a service for compensation, an element of the crime, because the only compensation involved was for the original repair in May, 1978. Even if this could be construed as raised below under the issue of gross deviation from the intended purpose, there was evidence that the car was to be repaired under a warranty for past, paid work.
[5] The offer of proof of the telephone conversations was:
"Q. What was the conversation [with the accountant]?
"A. Ken explained to him that or asked him if he remembered the Chrysler we worked on, he had, because he comes down to our shop quite a bit, he remembered it from the summer because Ken talked to him about Mohler because he felt so darn sorry for him, he just said: You remember that '66 Chrysler? And Don said: Yes. And Ken said: Well, I am trying to help Mr. Mohler sell it because his wife died recently and he has got all sorts of problems and he can't drive and he says if I can't sell it for more than 600 I am going to buy it from him but, you know, it's really a good car, just put whatever amount of money to front end, working on it, and, you know, one of his daughters needed, because he was looking for a car for one of his daughters, Donna then, and asked if one of the daughters or maybe a client that he had might need the car.
"Q. Okay. With respect to the phone conversation that you heard Mr. Trow's half of it, would you tell first of all why it is that you think Mr. Mohler was on the other end, and then what the substance of the conversation was that you heard?
"A. Well, I heard Ken remark Leonard a couple of times. He calls him by his first name and he was talking about the Chrysler and he was telling him be foolish to sell it now, that he should be able to get more than $600 out of it, and it was a good car and all that. If he tried to shop it around, see if he could get more money and if, you know, at least would buy it himself for 600 and use it as a loaner if he needed to."
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Image en médecine {#sec1}
=================
Nous rapportons le cas d'une patiente jeune âgée de 33 ans qui présente depuis 2 ans des arthralgies avec des œdèmes des quatre membres aggravés par la survenue d'un hippocratisme digital et une ostéo-arthropathie hypertrophiante (OAH) secondaire ou syndrome de Pierre-Marie Bamberger. Dans le cadre du bilan étiologique, un scanner thoraco abdominal a objectivé la présence d'une volumineuse masse tissulaire d\'allure tumorale de 11.5 cm massivement excavée pulmonaire au niveau du lobe supérieur droit avec large extension locorégionale et à distance. L'aspect histologique et immuno histochimique a été compatible avec un adénocarcinome pulmonaire primitif. La patiente a été mise sous chimiothérapie palliative avec début de régression des œdèmes. L'ostéo-arthropathie hypertrophiante ou syndrome de Pierre-Marie Bamberger est un syndrome paranéoplasique qui peut précéder un carcinome brochique dans 25% des cas. Il associe un hippocratisme digital (déformation des doigts en baguette de tambour, ramollissement de la matrice unguéale, et l'ongle, avec bombement et une déformation en verre de montre) et une augmentation de volume des articulations des os des mains et des pieds. Sur le plan radiologique, il se manifeste par un développement accru du périoste au niveau des diaphyses distales des os longs et au niveau des phalanges. Ces déformations ostéo-articulaires sont douloureuses, associées à des désordres neuro-vasculaires avec œdème important pouvant être responsable d'une impotence fonctionnelle. Le traitement étiologique suffit à faire régresser les déformations et les œdèmes comme le cas de cette patiente.
{#f0001}
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Change of isoenzyme pattern during long-term polyxenic cultivation of Entamoeba histolytica.
Isoenzymes of phosphoglucomutase and hexokinase were repeatedly evaluated using starch gel electrophoresis in polyxenic cultures of Entamoeba histolytica. In two out of 18 strains spontaneous changes of isoenzyme patterns were recorded. While originally they were categorized into virulent group of zymodemes, following isoenzyme analysis classified them as non-virulent. The relation between virulence and isoenzyme pattern is questionable. |
Q:
Store and check multiple $_SESSION
I have 3 objects with same variable but rendered with diferent values.
001 - Title one
002 - Title two
003 - Title three
I need to check on another block of page if this first three are the same. The only thing that comes to mind is store this variables in a $_SESSION. So far so good. The problem is that it only stores last value (obviously).
CODE
/* -- block one --*/
session_start();
$_SESSION['lasttitle'] = $item->getTitle;
echo $item->getTitle(); //rendering 1st object
echo $item->getTitle(); //rendering 2nd object
echo $item->getTitle(); //rendering 3rd object
/* -- block two --*/
session_start();
$last3 = $_SESSION['lasttitle'];
if($item->getTitle() != $last3) {
//don't render last 3
}
A:
$_SESSION['lastTitles'][] = $item->getTitle();
$_SESSION['lastTitles'] = array_slice($_SESSION['lastTitles'], -3);
..
if (in_array($item->getTitle(), $_SESSION['lastTitles'])) ..
This stores an array of the last three titles, and checks whether a title is in this array.
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A delicious thought occurs -- that our persecutors will soon have egg all over their faces. All we now need is icing on the cake. What a bonus it would be to see Sarkozy bite the dust in the French presidential elections in May, and for Angela Merkel to be similarly humbled next year.
Keep your fingers crossed.
Please sign in or register with Independent.ie for free access to Opinions. |
Q:
What is the Firefox/Javascript chrome module - documentation?
Every time i Google i get the Chrome browser - grr! But I'm trying to understand this:
use another mechanism via the chrome module. See OS.File and/or the MDN File I/O snippets.
Where can i find documentation for this Firefox+Javascript module?
How to Append to a file in a Firefox add-on?
A:
Updated my answer in that other question. I was talking about the SDK chrome module, which is just a way to access Components and with that the XPCOM services and components, so basically what every "old school" XUL add-on gets.
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When you’re in the market for a new furnace, the first and most important consideration will be the furnace size. Misjudging the size of the furnace you need can lead to higher energy bills, reduced indoor comfort and a shorter life for your new system. Learning how to size a furnace is not a do-it-yourself project and since you’ll need to use a licensed HVAC contractor to install the unit, it’s best to start with a professional who has the tools available to size your furnace accurately.
HVAC contractors use a detailed method called Manual J to accurately size heating systems, since sizing is so important. The software executes a thorough load calculation of your home, and it will determine what size furnace you need based your home’s size, energy efficiency, household occupancy and preferred temperatures.
The software lets the HVAC contractor adjust the factors that contribute to the heating load, so you can learn if increasing your insulation and sealing air leaks would allow you to install a smaller system, which will cost less initially and throughout its usable lifetime.
Installing too large a system results in short cycling, which increases wear and tear, along with insufficiently heated spaces indoors. Too small a system won’t warm your home as well during our coldest weather.
The output from Manual J will tell you how many BTUs (British thermal units) that you need. Besides improving your home’s energy efficiency, you can also choose a system that’s smaller based on its overall efficiency, known as AFUE (annual fuel utilization efficiency).
The AFUE is expressed as the percentage of fuel the furnace uses to create heat versus wasted up the chimney. AFUE ratings run from 80 percent, the least efficient, and go as high as 98 percent. High efficiency furnaces cost more initially but will pay for themselves in reduced heating costs, especially in our climate.
If you’d like to learn more about how to size a furnace, contact the pros at Meyer’s Company, Inc. We’ve provided trusted HVAC services for Griffith, Munster, Highland, St John, Scheriville and Gary since 1951.
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One high-ranking executive suggested Hunter will get some two or three-year offers as a free agent. The outfielder ranked 20th on MLBTR's list of top 50 free agents.
Evaluators were puzzled by the Nationals’ decision not to make Jackson a qualifying offer. An offer would have set them up for draft pick compensation or another affordable one-year deal.
GMs and agents expect Pagan to get multiple offers for three years. A four or five-year deal doesn’t seem out of reach for the center fielder.
Some rival officials expected the Rangers to make Napoli a one-year qualifying offer and set themselves up for draft pick compensation.
Brad Ausmus, one of the top managerial prospects in MLB, told Olney that it’s important for managers to remember how difficult it is to play at the highest level. “The managers who understood the patience involved are the managers who have related to the players best on teams I have been a part of, and garnered their respect,” Ausmus said.
The Padres have had some extension talks with Chase Headley, Olney reports. While both sides are interested in a deal, it’s hard to value Headley following his impressive second half performance.
The Padres will focus on adding starting pitching this offseason, Olney reports. Rival executives like San Diego’s pitching depth, but GM Josh Byrnes will still pursue additions. |
.class final Lcom/tencent/mm/wallet_core/ui/EditHintView$2;
.super Landroid/text/method/NumberKeyListener;
.source "SourceFile"
# annotations
.annotation system Ldalvik/annotation/EnclosingClass;
value = Lcom/tencent/mm/wallet_core/ui/EditHintView;
.end annotation
.annotation system Ldalvik/annotation/InnerClass;
accessFlags = 0x0
name = null
.end annotation
# instance fields
.field final synthetic mjl:Lcom/tencent/mm/wallet_core/ui/EditHintView;
# direct methods
.method constructor <init>(Lcom/tencent/mm/wallet_core/ui/EditHintView;)V
.locals 0
.prologue
.line 481
iput-object p1, p0, Lcom/tencent/mm/wallet_core/ui/EditHintView$2;->mjl:Lcom/tencent/mm/wallet_core/ui/EditHintView;
invoke-direct {p0}, Landroid/text/method/NumberKeyListener;-><init>()V
return-void
.end method
# virtual methods
.method protected final getAcceptedChars()[C
.locals 1
.prologue
.line 489
const/16 v0, 0xa
new-array v0, v0, [C
fill-array-data v0, :array_0
return-object v0
:array_0
.array-data 2
0x31s
0x32s
0x33s
0x34s
0x35s
0x36s
0x37s
0x38s
0x39s
0x30s
.end array-data
.end method
.method public final getInputType()I
.locals 1
.prologue
.line 485
const/4 v0, 0x3
return v0
.end method
|
The Chicago Bears are going all in on their young running backs after deciding not to re-sign veteran Matt Forte.
The team has so much faith in running backs Jeremy Langford and Ka’Deem Carey that they never even offered a new contract to Forte. General manager Ryan Pace told CBS Chicago going with the two young runners is best for the team:
“Really it was just the confidence we have in our younger backs and treating (Forte) with respect.”
Head coach John Fox has similar faith in the two:
#Bears coach Fox on parting ways w/ Matt Forte: "What allowed us to make that decision was the confidence we had in our younger backs." — Chicago Bears (@ChicagoBears) February 24, 2016
Langford had a pair of good games against the Rams and Chargers while filling in for the injured Forte, putting up 324 yards from scrimmage in those contests. The rookie finished 2015 with 537 yards and six touchdowns.
Carey showed good power and speed when he was given opportunities during his second NFL season. He ended up with 159 yards and a pair of touchdowns in 2015.
It’s expected that Langford will become the feature back in 2016, with Carey spelling him on occasion. The Bears could supplement the two through free agency or the draft.
Fox: Running backs will have “earn” playing time. New world with Matt Forte gone. — Around The NFL (@AroundTheNFL) February 24, 2016
It’s not at all surprising the Bears did not offer Forte a contract as many expected the team to move on. The confidence in the young talent should be welcome news to Bears fans.
Still, replacing a player who would probably fall in line behind only Walter Payton as the best running back in Bears history will be no small task. |
/*
* Copyright 2012-2020 the original author 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
*
* https://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 org.springframework.boot.configurationprocessor.fieldvalues.javac;
import java.lang.reflect.Method;
/**
* Base class for reflection based wrappers. Used to access internal Java classes without
* needing tools.jar on the classpath.
*
* @author Phillip Webb
*/
class ReflectionWrapper {
private final Class<?> type;
private final Object instance;
ReflectionWrapper(String type, Object instance) {
this.type = findClass(instance.getClass().getClassLoader(), type);
this.instance = this.type.cast(instance);
}
protected final Object getInstance() {
return this.instance;
}
@Override
public String toString() {
return this.instance.toString();
}
protected Class<?> findClass(String name) {
return findClass(getInstance().getClass().getClassLoader(), name);
}
protected Method findMethod(String name, Class<?>... parameterTypes) {
return findMethod(this.type, name, parameterTypes);
}
protected static Class<?> findClass(ClassLoader classLoader, String name) {
try {
return Class.forName(name, false, classLoader);
}
catch (ClassNotFoundException ex) {
throw new IllegalStateException(ex);
}
}
protected static Method findMethod(Class<?> type, String name, Class<?>... parameterTypes) {
try {
return type.getMethod(name, parameterTypes);
}
catch (Exception ex) {
throw new IllegalStateException(ex);
}
}
}
|
RTI Compressed Air Filtration
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The manufacture of many types of work pieces requires the substantial planarization of at least one surface of the work piece. Examples of such work pieces that require a planar surface include semiconductor wafers, optical blanks, memory disks, and the like. Without loss of generality, but for ease of description and understanding, the following description of the invention will focus on applications to only one specific type of work piece, namely a semiconductor wafer. The invention, however, is not to be interpreted as being applicable only to semiconductor wafers.
One commonly used technique for planarizing the surface of a work piece is the chemical mechanical planarization (CMP) process. In the CMP process a work piece, held by a work piece carrier, is pressed against a polishing surface in the presence of a polishing slurry, and relative motion (rotational, orbital, linear, or a combination of these) between the work piece and the polishing surface is initiated. The mechanical abrasion of the work piece surface combined with the chemical interaction of the slurry with the material on the work piece surface ideally produces a planar surface.
The construction of the carrier and the relative motion between the polishing pad and the carrier head have been extensively engineered in an attempt to achieve a uniform removal of material across the surface of the work piece and hence to achieve the desired planar surface. For example, the carrier may include a flexible membrane or membranes that contacts the back or unpolished surface of the work piece and accommodates variations in that surface. One or more pressure zones or chambers (separated by pressure barriers) may be provided behind the membrane(s) so that different pressures can be applied to various locations on the back surface of the work piece to cause uniform polishing across the front surface of the work piece.
However, the pressure distribution across the back surface of the wafer for conventional carriers often is not sufficiently controllable during the CMP process. Thus, as illustrated in FIG. 1, a work piece with an initial non-planar profile, such as a profile 10, that is planarized by a conventional carrier will have a non-planar surface profile similar to a profile 12 after the CMP process, although a substantially planar surface is desired. Further, conventional carriers do not provide sufficient control of the pressure zones to permit a desired non-planar profile to be achieved. In addition, to the extent the planarization process can be adjusted during CMP, such as, for example, by increasing or decreasing pressures in the adjustable pressure zones, the adjustment(s) typically takes place toward the end of the CMP process, thus resulting in over-correction.
Accordingly, it is desirable to provide a method for controlling the pressures of adjustable pressure zones of a work piece carrier during CMP to achieve substantially planar, or desired non-planar, profiles. In addition, it is desirable to provide a method for controlling the CMP process sufficiently early in the process to prevent over-correction. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description of the invention and the appended claims, taken in conjunction with the accompanying drawings and this background of the invention. |
When errors are detected in I/O operations for a drive, error handling is generally performed with respect to the entire drive. For instance, when drive errors are detected, the entire drive might be marked as “End of Life” (EOL) or as unavailable. In this case, the upper layer logic unit needs to reconstruct all data stored on the entire failed drive. As a result, error handling for the entire drive proves time-consuming and may reduce the service life of the drive and system stability significantly. |
What pent up wildness have you released?
” At Christmas, we celebrate the birth of things that save us. Sometimes salvation can come as much from freedom and letting go as from creation. What pent up wildness have you released? How has that saved you or someone else” -Order of Service, Christmas Eve
Release
Solstice, Christmas, New Years. All of these holidays turn my introspective self even deeper inwards. As I sat in the service Christmas Eve and contemplated the questions above, I was filled with gratitude. I was overwhelmed by gratitude. I’m not going to lie, it’s been a hard year. It’s been a year of feeling everything from despair to ecstasy. It’s been a year of giving up things that once were life giving. It’s been a year of opening my hands to let things fall apart, flow through and disintegrate. And it has been the restructuring and nurturing the new wild imagination that has been ignited in my heart. It has been a year of healing. It has been a year of reunion and connection. It has been a year of reaching far outside of myself and deep into myself at the same time.
I had a difficult conversation once with my father; one in a string of difficult conversations about faith. He wanted to know what I believed about Jesus. He wanted to know if I believed Jesus saved me, was the Savior. The answer was true for me then and now, but unsatisfying for my father. I believe that if we take the teachings and actions of Jesus seriously and model our lives after it, we are saved from many many things. Above all, this year has been about bringing myself into greater alignment with the Source of All. I have been working and praying and acting with intention to bring forth the unique work that I have been put on earth to carry out. It saves me every day, this work. It saves my hope and vision for the world, for my children. It saves me from giving up in the face of violence, hatred and division. I have released my heart into the world and this saves me every day. And it breaks me open over and over. It brings me to tears in the face of horror and the face of beauty. It changes the whole world. It changes everything. |
"""Worker Remote Control Bootstep.
``Control`` -> :mod:`celery.worker.pidbox` -> :mod:`kombu.pidbox`.
The actual commands are implemented in :mod:`celery.worker.control`.
"""
from celery import bootsteps
from celery.utils.log import get_logger
from celery.worker import pidbox
from .tasks import Tasks
__all__ = ('Control',)
logger = get_logger(__name__)
class Control(bootsteps.StartStopStep):
"""Remote control command service."""
requires = (Tasks,)
def __init__(self, c, **kwargs):
self.is_green = c.pool is not None and c.pool.is_green
self.box = (pidbox.gPidbox if self.is_green else pidbox.Pidbox)(c)
self.start = self.box.start
self.stop = self.box.stop
self.shutdown = self.box.shutdown
super().__init__(c, **kwargs)
def include_if(self, c):
return (c.app.conf.worker_enable_remote_control and
c.conninfo.supports_exchange_type('fanout'))
|
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Blind Woman's Curse (UK - BD RB)
Marcus kicks some technical ass but then a black cat stares at him. GULP!
Feature
Blind Woman’s Curse (also known as Black Cat's Revenge) is a thrilling Yakuza film featuring Meiko Kaji in her first major role. Playing Akemi, the dragon tattooed leader of the Tachibana Yakuza clan, the deadly fighter slashes the eyes of an opponent and a black cat appears, to lap the blood from the gushing wound. The cat along with the Akemi’s victim go on to pursue Akemi s gang in revenge, leaving a trail of dead Yakuza girls and their dragon tattoos skinned from their bodies.
Video
The image here, though obviously aged (the film was release in 1970) still manages to look dead pretty in that classic Japanese cinema way. Colours, especially reds leap off of the screen and the blue/grey looks of the film do a lot to make the character’s skin and exotic tattoos look detailed and sometimes really quite vivid.
The presentation here is noticeably sharp and clean, with some pretty good black levels and outside of the odd hazier elements, that usually leads to a cut to another scene everything holds up throughout. The cool blue tint to the film reduces a lot of the effect that the natural light might provide in the exterior scenes but it still makes for a stylised look that works and enables colours from the set designs to thrive as they really do draw attention to themselves.
There are some darker scenes that introduce a little more grain and grub to the otherwise good looking presentation but for the most part this is a film that boosts all the right elements to celebrate the super stylised look of the film and for me at least, most everything looked great, even with the odd element that seemed a little compared to the sharper elements of the frame.
Audio
The audio track, which is an uncompressed mono PCM affair is a tad scratchy in places but is still relatively well layered and strong in all the right places. Dialogue is sometimes a little muffled but never anything all that distracting, the battles sound great with those fake but awesome swords and slashes reaching out of the mono limitations and the score, while a little lost in the mix sometimes still has its fair share of high points. There’s not a lot more to say about the audio here. It does what it needs to do and feels much cleaner than you’d expect without losing its original dynamics.
Extras
The commentary with Japanese Cinema expert Jasper Sharp is a calm, detailed affair and is packed with detail. I genuinely felt like i learnt a ton of new things as i came away from the film and got plenty of knowledge about the Ghost Cat sub genre of Japanese film. This is a great track and does a great job at promoting other films in connected to Blind Woman’s Curse even with the thinnest of links.
Next up is the Trailer, as series of Stray Cat Rock Trailers and in the retail version a reversible sleeve and a collector’s booklet but I didn’t get to have a look at these with my review disc.
Overall
Blind Woman’s Curse is kooky and odd and has some really strange little moments but Meiko Kaji is a furious lead that draws you in with her killer stares and emotion fueled responses. The disc looks great for its age and has HD tweaks in all the right places. The audio is also pretty great despite its limitations even though the extras are thin the detailed commentary track more than makes up for anything lacking here.
Note: The images below are taken from the Blu-ray release and resized for the page. Full-resolution captures are available by clicking individual images, but due to .jpg compression they are not necessarily representative of the quality of the transfer.
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/*
Copyright 2016 The Kubernetes 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 photon_pd
import (
"fmt"
"os"
"path"
"path/filepath"
"strings"
"time"
"github.com/golang/glog"
"k8s.io/apimachinery/pkg/types"
"k8s.io/kubernetes/pkg/api/v1"
"k8s.io/kubernetes/pkg/cloudprovider/providers/photon"
"k8s.io/kubernetes/pkg/util/exec"
"k8s.io/kubernetes/pkg/util/mount"
"k8s.io/kubernetes/pkg/volume"
volumeutil "k8s.io/kubernetes/pkg/volume/util"
)
type photonPersistentDiskAttacher struct {
host volume.VolumeHost
photonDisks photon.Disks
}
var _ volume.Attacher = &photonPersistentDiskAttacher{}
var _ volume.AttachableVolumePlugin = &photonPersistentDiskPlugin{}
func (plugin *photonPersistentDiskPlugin) NewAttacher() (volume.Attacher, error) {
photonCloud, err := getCloudProvider(plugin.host.GetCloudProvider())
if err != nil {
glog.Errorf("Photon Controller attacher: NewAttacher failed to get cloud provider")
return nil, err
}
return &photonPersistentDiskAttacher{
host: plugin.host,
photonDisks: photonCloud,
}, nil
}
// Attaches the volume specified by the given spec to the given host.
// On success, returns the device path where the device was attached on the
// node.
// Callers are responsible for retryinging on failure.
// Callers are responsible for thread safety between concurrent attach and
// detach operations.
func (attacher *photonPersistentDiskAttacher) Attach(spec *volume.Spec, nodeName types.NodeName) (string, error) {
hostName := string(nodeName)
volumeSource, _, err := getVolumeSource(spec)
if err != nil {
glog.Errorf("Photon Controller attacher: Attach failed to get volume source")
return "", err
}
glog.V(4).Infof("Photon Controller: Attach disk called for host %s", hostName)
// TODO: if disk is already attached?
err = attacher.photonDisks.AttachDisk(volumeSource.PdID, nodeName)
if err != nil {
glog.Errorf("Error attaching volume %q to node %q: %+v", volumeSource.PdID, nodeName, err)
return "", err
}
PdidWithNoHypens := strings.Replace(volumeSource.PdID, "-", "", -1)
return path.Join(diskByIDPath, diskPhotonPrefix+PdidWithNoHypens), nil
}
func (attacher *photonPersistentDiskAttacher) VolumesAreAttached(specs []*volume.Spec, nodeName types.NodeName) (map[*volume.Spec]bool, error) {
volumesAttachedCheck := make(map[*volume.Spec]bool)
volumeSpecMap := make(map[string]*volume.Spec)
pdIDList := []string{}
for _, spec := range specs {
volumeSource, _, err := getVolumeSource(spec)
if err != nil {
glog.Errorf("Error getting volume (%q) source : %v", spec.Name(), err)
continue
}
pdIDList = append(pdIDList, volumeSource.PdID)
volumesAttachedCheck[spec] = true
volumeSpecMap[volumeSource.PdID] = spec
}
attachedResult, err := attacher.photonDisks.DisksAreAttached(pdIDList, nodeName)
if err != nil {
glog.Errorf(
"Error checking if volumes (%v) are attached to current node (%q). err=%v",
pdIDList, nodeName, err)
return volumesAttachedCheck, err
}
for pdID, attached := range attachedResult {
if !attached {
spec := volumeSpecMap[pdID]
volumesAttachedCheck[spec] = false
glog.V(2).Infof("VolumesAreAttached: check volume %q (specName: %q) is no longer attached", pdID, spec.Name())
}
}
return volumesAttachedCheck, nil
}
func (attacher *photonPersistentDiskAttacher) WaitForAttach(spec *volume.Spec, devicePath string, _ *v1.Pod, timeout time.Duration) (string, error) {
volumeSource, _, err := getVolumeSource(spec)
if err != nil {
glog.Errorf("Photon Controller attacher: WaitForAttach failed to get volume source")
return "", err
}
if devicePath == "" {
return "", fmt.Errorf("WaitForAttach failed for PD %s: devicePath is empty.", volumeSource.PdID)
}
// scan scsi path to discover the new disk
scsiHostScan()
ticker := time.NewTicker(checkSleepDuration)
defer ticker.Stop()
timer := time.NewTimer(timeout)
defer timer.Stop()
for {
select {
case <-ticker.C:
glog.V(4).Infof("Checking PD %s is attached", volumeSource.PdID)
checkPath, err := verifyDevicePath(devicePath)
if err != nil {
// Log error, if any, and continue checking periodically. See issue #11321
glog.Warningf("Photon Controller attacher: WaitForAttach with devicePath %s Checking PD %s Error verify path", devicePath, volumeSource.PdID)
} else if checkPath != "" {
// A device path has successfully been created for the VMDK
glog.V(4).Infof("Successfully found attached PD %s.", volumeSource.PdID)
// map path with spec.Name()
volName := spec.Name()
realPath, _ := filepath.EvalSymlinks(devicePath)
deviceName := path.Base(realPath)
volNameToDeviceName[volName] = deviceName
return devicePath, nil
}
case <-timer.C:
return "", fmt.Errorf("Could not find attached PD %s. Timeout waiting for mount paths to be created.", volumeSource.PdID)
}
}
}
// GetDeviceMountPath returns a path where the device should
// point which should be bind mounted for individual volumes.
func (attacher *photonPersistentDiskAttacher) GetDeviceMountPath(spec *volume.Spec) (string, error) {
volumeSource, _, err := getVolumeSource(spec)
if err != nil {
glog.Errorf("Photon Controller attacher: GetDeviceMountPath failed to get volume source")
return "", err
}
return makeGlobalPDPath(attacher.host, volumeSource.PdID), nil
}
// GetMountDeviceRefs finds all other references to the device referenced
// by deviceMountPath; returns a list of paths.
func (plugin *photonPersistentDiskPlugin) GetDeviceMountRefs(deviceMountPath string) ([]string, error) {
mounter := plugin.host.GetMounter()
return mount.GetMountRefs(mounter, deviceMountPath)
}
// MountDevice mounts device to global mount point.
func (attacher *photonPersistentDiskAttacher) MountDevice(spec *volume.Spec, devicePath string, deviceMountPath string) error {
mounter := attacher.host.GetMounter()
notMnt, err := mounter.IsLikelyNotMountPoint(deviceMountPath)
if err != nil {
if os.IsNotExist(err) {
if err := os.MkdirAll(deviceMountPath, 0750); err != nil {
glog.Errorf("Failed to create directory at %#v. err: %s", deviceMountPath, err)
return err
}
notMnt = true
} else {
return err
}
}
volumeSource, _, err := getVolumeSource(spec)
if err != nil {
glog.Errorf("Photon Controller attacher: MountDevice failed to get volume source. err: %s", err)
return err
}
options := []string{}
if notMnt {
diskMounter := &mount.SafeFormatAndMount{Interface: mounter, Runner: exec.New()}
mountOptions := volume.MountOptionFromSpec(spec)
err = diskMounter.FormatAndMount(devicePath, deviceMountPath, volumeSource.FSType, mountOptions)
if err != nil {
os.Remove(deviceMountPath)
return err
}
glog.V(4).Infof("formatting spec %v devicePath %v deviceMountPath %v fs %v with options %+v", spec.Name(), devicePath, deviceMountPath, volumeSource.FSType, options)
}
return nil
}
type photonPersistentDiskDetacher struct {
mounter mount.Interface
photonDisks photon.Disks
}
var _ volume.Detacher = &photonPersistentDiskDetacher{}
func (plugin *photonPersistentDiskPlugin) NewDetacher() (volume.Detacher, error) {
photonCloud, err := getCloudProvider(plugin.host.GetCloudProvider())
if err != nil {
glog.Errorf("Photon Controller attacher: NewDetacher failed to get cloud provider. err: %s", err)
return nil, err
}
return &photonPersistentDiskDetacher{
mounter: plugin.host.GetMounter(),
photonDisks: photonCloud,
}, nil
}
// Detach the given device from the given host.
func (detacher *photonPersistentDiskDetacher) Detach(deviceMountPath string, nodeName types.NodeName) error {
hostName := string(nodeName)
pdID := deviceMountPath
attached, err := detacher.photonDisks.DiskIsAttached(pdID, nodeName)
if err != nil {
// Log error and continue with detach
glog.Errorf(
"Error checking if persistent disk (%q) is already attached to current node (%q). Will continue and try detach anyway. err=%v",
pdID, hostName, err)
}
if err == nil && !attached {
// Volume is already detached from node.
glog.V(4).Infof("detach operation was successful. persistent disk %q is already detached from node %q.", pdID, hostName)
return nil
}
if err := detacher.photonDisks.DetachDisk(pdID, nodeName); err != nil {
glog.Errorf("Error detaching volume %q: %v", pdID, err)
return err
}
return nil
}
func (detacher *photonPersistentDiskDetacher) WaitForDetach(devicePath string, timeout time.Duration) error {
ticker := time.NewTicker(checkSleepDuration)
defer ticker.Stop()
timer := time.NewTimer(timeout)
defer timer.Stop()
for {
select {
case <-ticker.C:
glog.V(4).Infof("Checking device %q is detached.", devicePath)
if pathExists, err := volumeutil.PathExists(devicePath); err != nil {
return fmt.Errorf("Error checking if device path exists: %v", err)
} else if !pathExists {
return nil
}
case <-timer.C:
return fmt.Errorf("Timeout reached; Device %v is still attached", devicePath)
}
}
}
func (detacher *photonPersistentDiskDetacher) UnmountDevice(deviceMountPath string) error {
return volumeutil.UnmountPath(deviceMountPath, detacher.mounter)
}
|
This invention relates generally to surgical devices and, more particularly, to an improved elastic surgical ring clip and an improved ring loader for placing one or more elastic surgical rings onto the distal end of a ring applicator device. The elastic surgical ring clip is made of an elastic material and is configured so as to provide a clip having significantly increased, compressive or elastic strength. The ring loader includes a conically shaped ring expander onto which elastic surgical rings are loaded and a ring dilator having a plurality of fingers which engage the ring and push it up and over the ring expander and onto the distal end of a ring applicator device.
There are several prior art patents which disclose somewhat related elastic surgical clips and loading devices. The more relevant patents in the prior art include U.S. Pat. No. 4,167,188 issued to Coy L. Lay, deceased et al and my own prior U.S. Pat. No. 4,548,201. The Lay patent is directed to an elastic band designed and dimensioned for tying off human fallopian tubes or similar, anatomical tubular members. My prior patent shows an improved, elastic ligating ring clip and a ring loader for placing elastic rings onto the distal end of a ring applicator device including a conical ring expander and a ring dilator in the form of thin, flexible posts joined in pairs radiating from a deformable, elastic ring engaging aperture.
Nothing in the prior art discloses the surgical clip constructions of this invention which include an elastic body of a configuration which imparts greatly increased compressive or elastic strength to the elastic clip and a ring loader for placing one or more elastic surgical ring clips onto the distal end of a ring applicator device including a conical ring expander and a conical ring dilator having a plurality of fingers for pushing each ring along and over the expander and onto the distal end of a ring applicator device. |
Diseases of the Internet
When it comes to the most-searched topic for Web queries, there’s no doubt that sex tops the list; but, bearing in mind that health-related matters take up 2% of all queries on the search engines, its not surprising that there are a variety of internet-related ailments that can result out of this!
Internet addiction has been around for years. How do you know if you’re already addicted or rapidly tumbling toward trouble? Take this Internet Addiction Test here.
Cyberchondria - aggravated by Self-diagnosis Web-sites which have 90% of the diagnoses where patients die within one week!
Cyberchondria(aka internet self-diagnosis) is another condition first coined in 2000 and refers to the practice of leaping to dire conclusions while researching health matters online. If that severe headache haunting you in the morning led you to the Web search-engine and convinced you that it is caused by a brain tumour, then the likely diagnosis is probably cyberchondria. People tend to look at the first few results in the search-engine and that froms the basis for them to probe further. For instance, a search on ‘headaches’ could lead to ‘brain tumours’ or ‘meningitis’. The phenomenon has become so pervasive that Microsoft did its own study on the causes of cyberchondria (see here).
My advice? While its good for people to know what’s going on in their body, make sure you look at reputable sites only and even then, look at them after your doctor has told you what you have (this will give you a reasonable launching pad to look at other likely possibilities- what doctors call differential diagnoses).
Gosh, I was one. Had this bleeding gum. Worried sick if it was cancer (and I’m not even a smoker). Went on the net. More alarmed. Worry, worry for about 2 weeks before I found courage to go to the dentist. It was a simple case of overbrushing!
Never again am I going to look up health things on the net! |
The Best Headlamps
This category of gear is one of the most important, considering that a headlamp is one of the fundamental pieces of gear in a pack. While it’s certainly possible to navigate the wilderness at night without a light, having a powerful and reliable lamp can mean the difference between breaking camp at dusk, or keeping on going well after the sun dips behind the horizon. However, comparing headlamps is a bit trickier than it seems.
Headlamps are used for a wide variety of activities, which makes it challenging to compare different brands and models. Some headlamps are designed for short burn times with priority on power, like those for mountain biking, fishing, and kayak touring. Meanwhile, other headlamps are designed for long burn times with flexible settings, such as those intended for spelunking, adventure racing, and mountaineering. This makes for a lot of diversity in features in addition to a broad range of pricing. Fortunately, price does not always mean better performance.
In our tests below, we selected the best headlamp that takes into account all of the features together. However, each headlamp offers unique advantages for specific activities, so make sure to read all of the reviews to select one that will fit all that’s planned, and don’t forget to bring a backup.
The HL7R is a simple headlamp with a lot of power and is rechargeable via USB. It has one of the most uniform light outputs we’ve seen on the flood setting and a powerful spot beam but its short battery life requires it to be recharged regularly.
The Black Diamond Icon Polar is the expedition headlamp. It is designed to withstand extreme conditions with a variety of useful modes and has a long battery life. But all those features take some time to figure out and the many straps and wires tangle easily.
The Olympia EX 550 is the most powerful lamp we tested with a caveat. It has bulletproof construction and is easy to use; unfortunately, it burns through batteries surprisingly fast and uses a type (CR123A) that you may not find outside of specialty electronics stores.
The Petal Nao features the most visibility among the headlamps we tested. It sports a USB recharging plug and a light sensor that controls brightness to prevent getting blinded. Unfortunately, the lamp tested well under claimed battery life and less than advertised brightness, with a couple other bugs.
The Princeton Tec Sync is an affordable general use headlamp with great battery life and solid construction. However, it is not as bright as advertised and bobbles around during high impact activities. It was the least-bright lamp that we tested.
Navigation:
Review Results
Brightness
Using a light meter that measures lux, each of these lamps were tested to determine the furthest distance at which they registered 1 and 10 lux, both directly in front of the beam and at a 10 degree angle from the line of the beam to determine peripheral brightness. For reference, 1 lux is about the brightness of a standard paper match, seen from the distance of one foot. However, even with this method, this category was challenging to test because of the variety of light quality projected from each lamp.
At the extremes, the lights vary in beam focus quite drastically. Compare the Mammut X-Shot, which measured 1 lux all the way to 132 feet directly in front, while only projecting 1 lux to 35 feet when measured 10 degrees off the center beam, a ratio of nearly 4 to 1. On the other hand, the COAST HL7R reached 78 feet directly in front, while reaching 40 feet at 10 degrees; a ratio of 2 to 1. For this rating, the lamps were all tested at max power with their beams focused, where it was possible, to obtain the maximum distance.
The ratio in the preceding paragraph provides insight into the quality of light measured by distribution. With traditional bulbs, a light shined on a wall produces a distribution that is noticeably brighter in the center, a dim ring around that, and a bright ring near the edges which then softly diffuses. However, with LED technology, combined with advanced lens shaping, it is possible to produce a perfectly uniform circle of light with a distinct edge.
The insight drawn from a distribution analysis has to do with light efficiency. A light that produces a diffuse edge, with a noticeable amount of ambient light, comes at the cost of power that could have been aimed toward the center beam. So, a light such as the Princeton Tec Sync is considerably dimmer than other lights, while illuminating an area so broad it appears almost like a bulb. On the other hand, the COAST HL7R captures all of the light produced by the bulb and distributes it only inside a very defined circle, doing it so evenly that any distortions and abnormalities are undetectable to the human eye. The technology in the HL7R results in the brightest beam possible over the area upon which the light shines, maximizing the power from the batteries.
Our tests took both of these factors into consideration in selecting a headlamp that provides the most versatility across outdoor activities. While it is certainly attractive to have a bright beam, this often comes at the cost of battery life and size. In addition, when moving the head using a light with an uneven distribution, illuminated objects appear to “shift.” More weight was placed on the quality of the beam because it is often objectively more important to accurately see the task at hand, than it is to see far away objects.
Let’s compare two very different lights. The light projected from the Petzl NAO produced some of the most light among the lamps; it scored high in both distance and peripheral illumination. The light projected from the HL7R, on the other hand, was a perfectly uniform disc and movement of the head had no impact on the brightness of any individual spot so long as it remained in the illuminated area. Ultimately, the distance carried enough weight for the Nao to beat the HL7R in this rating. However, the HL7R scored very high because we were most impressed with what it was able to do with the light it did produce.
Battery Life
The lamps were turned on and a camera captured photos at set increments of time until the bulbs no longer shined enough light to be reasonably detectable. This ended up being about 0.3 lux at 10 feet, equivalent to the brightness of a mobile phone screen at that distance. Each lamp was either fully charged or loaded with new batteries and they were not turned off until depleted. The photos were then compiled into time-lapse videos to demonstrate the quality of the beam as the battery power degrades.
While battery life was the primary consideration, another factor we considered was whether the batteries were rechargeable. Headlamps are used for a very wide variety of reasons, with one of the most important being the amount of time a light stays on. If camping for longer than one night, having a lamp that doesn’t require spare batteries is always preferable. However, most people carry power banks now that allow for small devices to be recharged via USB. As a result, the ability for a light to be recharged weighed favorably, with bonus points to any lamp that had rechargeable batteries that could be swapped out for spares.
There are two additional considerations that push the lamps one way or the other.One is whether the lamp shut off completely once the batteries depleted, or if it continued to dim until light was no longer detectable. The second is whether the headlamps met the expectations set by the manufacturer of predicted run-time.
This rating can best be demonstrated with the following examples. Take the Olympus EX 550, which scored poorly with a rating of 3. This lamp has a short battery life at just over three hours, it shuts off completely once the battery is dead, and it uses a very expensive and rare type of battery. No one would argue that this combination makes the EX 550 beg for an upgrade. On the other hand, the COAST HL7R has a similar battery life with just under 3 hours, but it dims as the battery is drained, the battery life is markedly extended with a lower power output, the headlamp can be recharged via USB, and it comes packaged with rechargeable AAA batteries that can be swapped out instantly for fresh backups. While the run-time on the HL7R gave it a low score to start, these other advantages produce a meaningful advantage.
Comfort
Comfort was a major factor in the test, as one must wear the lamps for an extended period of time. The selection of headlamps provided a wide variety of methods to keep the lamp on, as well as different ways of distributing the components. For the purposes of the review, headlamp straps were tested a little loose, in a way they would be comfortable for several days in a row of putting the headlamp on around dusk and wearing it for a few hours until crawling into a sleeping bag. We often tighten up a headlamp and sacrifice some comfort during an activity like trail running. In other cases, the headlamp is strapped to a helmet, and comfort is a non-issue. Ultimately, because comfort is such a subjective category, this rating was influenced by the following factors.
First, and most importantly, was whether the headlamp had any obvious features that made it stand out from others and how that came into play. An example is the Petzl Nao which has stiff plastic that is designed to distribute the pressure. Unfortunately, sharp edges that don’t perfectly fit the shape of the wearer’s head place pressure at specific points, ironically causing discomfort and leaving a visible mark on the skin after even short periods of use.
Second, a headlamp is worn while doing things like hiking, climbing, biking, etc., so a another factor was whether the lamp stayed put during impact activities. Headlamps with top straps performed particularly well, as this additional stabilization prevented them from bobbling up and down. On the other hand, lamps such as the Princeton Tec Sync experienced problems. The weight of the Sync is concentrated away from the attachment point on a swivel. This causes the entire mechanism to roll up or down during most any impact.
A third consideration is weight distribution. The bobbing action in the previous paragraph is mitigated in other models such as the Mammut X-shot, where the battery pack is placed on the rear of the lamp. The distribution of weight minimized the amount of force that is experienced by the lamp and prevents noticeable bobbing. Weight distribution also plays a part in comfort directly. There is a noticeable difference in a lamp like the Olympia EX 550, which is essentially a large metal block on the front of the head, and models such as the COAST HL7R that distribute the weight evenly in the front and back of the head. The feeling of even weight distribution creates a subtle confidence that any sudden jarring action won’t toss the headlamp off the head and into a dark crevasse or down the cliff.
This bobbling action ties into the fourth consideration, which is whether the headlamp can be operated with one hand. The Sync best demonstrates this because when we tried to change the setting, the entire lamp would rotate with the switch. This means it lost points because we needed to use two hands; one to hold the body of the lamp steady, and the other to rotate the switch to our desired setting.
And finally, the last consideration was whether the peripherals caused discomfort. This is evident in the Black Diamond Icon Polar that has backpack straps on a battery pack that is connected to the headlamp by a rubber coated metal wire. While there is certainly reason for this design, it did require some logistical consideration when putting layers on and taking them off. In addition, the wire tugged gently as we turned our heads because it would inevitably become taut between clothing layers or the backpack.
Ease of Use
The Ease of Use rating is very important because it can mean the difference between turning the lamp on without frustration, or fumbling around until the user rips it off their head to examine the controls. However, it is not just the operation, but also the overall design that makes it easy to pick up and turn on seamlessly.
An initial component is the overall design of each headamp and how easy it is to put on. For example, the Petzl Nao has thin strings that sometimes twist in a pack and become tangled, this can be further complicated if the USB battery pack is detached and the power cable is unplugged. For a first-time user, this configuration can take several minutes to figure out. Another headlamp that deserves a mention is the Black Diamond Icon Polar due to the battery pack with backpack straps which loop around the power cord. We have yet to figure out a neat way to pack it, other than stuffing it into its own baggie so that the Icon does not get tangled amongst other items in the pack. On the other hand, plain strap lamps like the Princeton Tec Sync are so simple the only thing that can go wrong is putting it on upside down—but even then, it will still work.
The next component of this rating is in the operation of the light. Some lights, such as the Olympia EX 550, have one button that cycles through simple settings; off, on, and strobe. This is ideal because so long as the wearer can find the button, they can get the light on. However, for more complicated functions such as dimming, multi-colored lights, and locking the lamp, figuring out the press sequence on one button becomes frustrating.
The selection of headlamps we tested offered solutions on easy operation to varying degrees of satisfaction. The worst offender is the Black Diamond Icon Polar. This lamp literally operates more than five functions through a variety of button press combinations; lock/unlock, on/off, dim, high setting, low setting, red light, dim red light, and strobe. I have owned the Icon for several years now and still get lost. A headlamp that is somewhere in between is the Petzl Nao. The Nao has a knob that twists, but has a short delay that causes confusion when turning on and off. In addition, there is often no noticeable difference between the high power and Reactive Lighting settings. At least Petzl programmed the lock-out function in the Nao to activate by twisting the knob in the opposite direction.
Additional considerations were the ease of use of the button, switch, or lever on each headlamp. The Mammut X-Shot lost out because, although the buttons are easy to find, the rubber button cover is larger than the actual switch underneath. This means that pressing the button does not always activate the light. This consideration also takes into account whether the headlamp can be operated with winter gloves or mittens. The Princeton Tec Sync, for example, was difficult to operate with a heavy mitt, and moisture on the knob made operation slippery.
Features
The Features rating was the most diverse category of testing. Some lamps were packed with features, while others did not have any. It would be unfair to praise a lamp simply because it has additional features, that would mean more features results in a better lamp. So, this rating assumed all the lamps are even from the start, and features weighed towards the rating based on whether they added to the overall experience of the lamp, or made no sense and frustrated the user.
There are a couple examples that illustrate the way this rating played out. The Olympia EX 550 is the simplest lamp. Its features are a lock out function and a strobe. Both of these are useful, in particular the lock out function is welcome in a lamp where each 3 hours costs over $10. However, they do not add much value to the lamp overall and bump it from a 5 to a 6. On the other hand, the Black Diamond Icon Polar is packed full of features that make it the best expedition lamp. In spite of the frustrations with comfort and ease of use, this lamp offers a set of features that set it apart from the rest; specifically, a separate battery pack that is protected from extreme temperatures and offers a larger power bank with AA batteries, a red light that also dims, and a lock out that flashes blue when engaged.
Review Conclusion
Headlamps were originally a light attached by a strap to the head, but in today’s specialized technical environment the headlamp has become a precision instrument. The design of a headlamp makes it advantageous in some situations, and a distraction in others. Our tests were designed to identify the headlamp that achieved the highest overall score, making it the best headlamp for a wide variety of uses. However, each lamp has unique features that can make it the best tool for the job depending on the activity it is chosen for. For example, even though it ranked 5th, the Mammut X-Shot is an excellent choice for climbing.
The difference in the headlamps selected for this review was also very broad. For example, the lamps varied from the latest technology with the Petzl Nao featuring the Reactive Lighting technology, to the simple, tried and true models like the Princeton Tec Sync and Olympia EX 550 that just turned on and off. However, in the end, this aspect did not predict the rankings. The simple-to-use COAST HL7R took the top spot, and the similarly simple Sync scored the lowest.
In fact, no single rating was predictive of the final standings. All of the brands are established in the lighting world, and these were the top picks of 2015 with no surprises that caused any individual headlamp to fail. However, we definitely identified some challenges with the designs that we hope are addressed in future generations. Specifically, it would be great to see rechargeable and removable batteries with a USB port on each model. For a lamp like the Olympia EX 550, this may have brought it to the top of the pack.
Please keep in mind that each lamp has its own advantages. We recommend reading each review carefully.
Testing Methods
The Visibility Mini-Rating (Brightness Test):
For the purposes of this review, we determined the maximum distance at which the light meter reads values of 10 lux and 1 lux in two positions:
directly ahead of the lamp in the primary beam
10º off of the center of the primary beam to measure peripheral illumination
The results provide a measure of balance in each model of headlamp. A balanced headlamp provides both clear illumination at the focus of the beam where the user is usually looking, as well as peripheral illumination that provides context in the area around that focus. An unbalanced headlamp strains the eyes because it requires additional effort to interpret the contrasting dark and light areas.
An example of an unbalanced headlamp is using a narrow beam while mountain biking. The contrast of the high intensity center to the much darker peripheral causes vision to process longer. As the brain tries to read both dark areas and highly illuminated areas, reaction time lags and the rider is unable to respond to features on the trail. Sometimes it is as if they can’t see them at all. So, a narrow beam headlamp is not a good choice for a mountain biker.
Run Time Testing
The lamps were turned on and a camera captured photos at set increments of time until the bulbs no longer shined enough light to be reasonably detectable. This ended up being about 0.3 lux at 10 feet, equivalent to the brightness of a mobile phone screen at the same distance. Each lamp was either fully charged or loaded with new batteries and they were not turned off until depleted. The photos were then compiled into time-lapse videos to demonstrate the quality of the beam as the battery power degrades and can be viewed in each of the the videos in the individual reviews.
Comfort
The basic test for comfort is putting the headlamp on. However, to prevent prejudice, a number of factors were taken into account to provide an objective analysis. One consideration was the way the weight was distributed and whether the lamp felt unbalanced with all the weight on the front or rear. As mentioned above, a lamp with all of its weight in the front can make a person feel nervous if they are performing an activity that can produce a jarring impact and knock the lamp off. A second consideration was complexity of the design. For example, the Black Diamond Icon Polar had several components that affected how the lamp feels when it is put on and caused varying levels of discomfort. The next consideration was whether any odd features made the lamp comfortable or uncomfortable. For example, the Petzl Nao’s sharp plastic corners leave visible marks on the skin. Secondary considerations are how the lamp behaves during high impact activities; whether it bobbles, and whether it can easily be operated with one hand.
Ease of Use
For this rating, intuitiveness and accident prevention were the deciding factors. Before the test could begin, we looked at how easy it was to put the headlamp on. This sounds simple, but we encountered models like the Black Diamond Icon Polar that had multiple straps, cords, and cables. Once we got to turning the lights on, the lamps that scored the highest had operation that was intuitive and simple. The COAST HL7R’s button that performs a limited number of simple functions scored the highest. On the other hand, the Icon Polar’s single button that performs all 5+ functions in complex combinations of presses, got the lowest score. Additional considerations were taken into account with regard to how the button, lever, or knob worked and where it was placed, as well as whether it could be operated with gloves.
Features
This category is a sort of catch all for aspects of the lamps that did not fit into any of the other ratings. Points were either added or subtracted depending on the functionality and usefulness or the un-intuitiveness or distracting nature of a feature. For features that added to the value of the headlamp, such as the Reactive Lighting technology of the Petzl Nao, the score was advanced. On the other hand, features that took away from the utility of a lamp lowered the score.
About This Category of Product
On Brightness and the Lux
The lux is a standard unit used as a measure of intensity, as perceived by the human eye, of light that hits or passes through a surface. It is designed specifically to illustrate human brightness perception. The following is a table of lux value of surfaces under different illumination:
Illuminance (lux)
Surface illuminated by:
0 lux
Moonless, overcast night sky
0.27-1.0 lux
Full moon on a clear night
10-15 lux
Candle light
50 lux
Family living room lights
80 lux
Office building hallway
100 lux
Very dark overcast day
320-500 lux
Office lighting
400 lux
Sunrise or sunset on a clear day
1000 lux
Overcast day, typical TV studio lighting
10,000-25,000 lux
Full daylight (not direct sun)
32,000-100,000 lux
Direct sunlight
https://en.wikipedia.org/wiki/Lux
Lux value range is used in architecture to set brightness levels in different types of rooms. For example: a large school lecture classroom is said to have adequate lighting if a light meter records 150 to 300 lux, whereas a research room requires 200 to 750 lux for comfortable reading conditions. For a space where simple tasks are performed such as passing through or identifying large objects, (as in a warehouse, garage, or fire escape), only 30 to 70 lux is required. |
1. The Field of the Invention
The present invention is directed to an electrical interconnection for attachment to a substrate. More specifically, the present invention is directed to an electrical interconnection between a contact area of a substrate and a contact area of a die and a method of forming the same.
2. Present State of the Art
Integrated circuits have for years been universally used in computer applications, as well as other high-tech applications such as communications and military technologies. A primary concern with integrated circuits has long been the electrical interconnection between the bond pad of a die and the bond pad of a semiconductive substrate. In the context of this document, the term xe2x80x9csemiconductive substratexe2x80x9d is defined to mean any construction comprising semiconductive material, including but not limited to bulk semiconductive material such as a semiconductive wafer, either alone or in assemblies comprising other materials thereon, and semiconductive material layers, either alone or in assemblies comprising other materials. The term xe2x80x9csubstratexe2x80x9d refers to any supporting structure including but not limited to the semiconductor substrates described above. In the context of this document, the term xe2x80x9cdiexe2x80x9d is defined as a chip or other electronic component part, either passive or active, discrete or integrated.
Bond pads have typically been used to provide electrically conductive metal contact areas on semiconductor substrates in integrated circuits. Bond pads used in integrated circuits have historically been composed of an aluminum-copper alloy, wherein the copper typically comprises less than about 0.5% of the alloy. Aluminum is an excellent metal for bond pad formation due to its superior adhesion qualities, high thermal stability, and ease of workability (i.e., in etching processes). Although aluminum bond pads are the semiconductor industry standard, aluminum readily oxidizes, even at room temperature, to form aluminum oxide (Al2O3). Oxides of conductive metals, whether it be aluminum, copper or other conductive metals, sharply increase the contact resistance of the metal and decrease the electrical connection and the efficiency of the bond pad. Hence, while aluminum bond pads exhibit excellent electrical conductivity, unprotected aluminum bond pads readily react to form aluminum oxide which exhibits very high contact resistance and results in a poor interconnection between the bond pad of a die and the bond pad of a substrate.
Several processes have been proposed for removing aluminum oxide from aluminum bond pads in electrical interconnect formation. For instance, it is known to clean aluminum oxide off of aluminum bond pads by sputter-etching in a vacuum tight sputtering chamber and then sputtering a barrier metal, such as TiW, TiN and NiCr, onto the clean aluminum bond pad. A noble metal, such as gold, is then sputtered onto the barrier metal to provide an inert, oxide free surface. While this metallization scheme successfully removes the oxide formed on the aluminum bond pad, this process unfortunately requires the semiconductor die pads and bond pads to be extensively handled. Extensive handling often results in contamination of, and damage to, the electrical connection. Furthermore, the gold plating of the semiconductor die pad is an elaborate process that is difficult, expensive and time consuming.
Another process commonly referred to as the xe2x80x9czincate processxe2x80x9d activates the aluminum bond pads using a xe2x80x9czincate solutionxe2x80x9d and then deposits a layer of nickel and a layer of gold on the bond pad to preserve the electrical connection. The zincate solution, consisting of zinc oxide and sodium hydroxide, dissolves an aluminum oxide formed on the aluminum bond pad to clean the same, and also deposits a thin layer of zinc over the clean aluminum bond pad. A thin nickel phosphorous barrier layer is then deposited over the zinc. A layer of gold is added to the surface of the nickel phosphorous layer to provide an oxide free surface. Although the zincate process effectively reduces the contact resistance stemming from oxide formation, the zincate process is considered to be too expensive for typical mass production processes.
In view of the drawbacks of the presently used electrical interconnection between the bond pad of a chip and the bond pad of a substrate, it is readily apparent that there exists a need for an affordable, reliable, highly conductive electrical interconnection for attachment to a substrate and an affordable method for forming an electrical interconnection for attachment to a substrate.
In accordance with the invention as embodied and broadly described herein, there is provided an electrical interconnection for attachment to a substrate and a method for forming an electrical interconnection to a substrate. The electrical interconnection in the present invention comprises a first metal layer, a first diffusion barrier layer on the first metal layer, a second metal layer on the first diffusion barrier layer, an organometallic layer on the second metal layer, and an electrical interconnect layer on the organometallic layer.
Once the oxide formed on the first metal layer is removed, a first diffusion barrier layer is formed on the first metal layer. The first diffusion barrier layer prevents diffusion of the first metal layer and the second metal layer therethrough. In a preferred embodiment, the first metal layer is composed of aluminum and the second metal layer is composed of copper. The first diffusion barrier layer prevents the aluminum and the copper from diffusing and adversely effecting the electrical interconnection.
The organometallic layer is preferably formed by contacting the second metal layer with an organic material to form a organometallic layer. The organometallic layer formed is preferably a copper azole such as Cu+(azolexe2x88x92) and Cu++(azolexe2x88x92)2). The organometallic layer prevents oxidation of the second metal layer which is preferably copper.
The electrical interconnection device of the present invention may be combined with an additional substrate to form an electrical interconnection between a first substrate and a second substrate, for example, as in an integrated circuit. The electrical interconnect of the present invention has a low contact resistance and creates a good electrical interconnect to bond a die to another substrate, such as a supporting substrate. |
Q:
Unregister uwp background task
I register a background task and I try to unregister it again when a certain setting is deactivated. But I only found information about register and scheduling tasks. Is there no way to this?
A:
is this what you are looking for?
var tasks = BackgroundTaskRegistration.AllTasks;
foreach(var task in tasks)
{
// You can check here for the name
string name = task.Value.Name;
task.Value.Unregister(true);
}
|
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<div class="textblock"><p>AngelScript requires the application developer to register the interface that the scripts should use to interact with anything outside the script itself.</p>
<p>It's possible to register <a class="el" href="doc_register_func.html">global functions</a> and <a class="el" href="doc_register_prop.html">global properties</a> that can be used directly by the scripts.</p>
<p>For more complex scripts it may be useful to register new <a class="el" href="doc_register_type.html">object types</a> to complement the built-in data types.</p>
<p>AngelScript doesn't have a <a class="el" href="doc_strings.html">built-in string type</a> as there is no de-facto standard for string types in C++. Instead AngelScript permits the application to register its own preferred string type, and a <a class="el" href="classas_i_script_engine.html#ac238aa44f91bad0b9025d956c5555575">string factory</a> that the script engine will use to instanciate the strings.</p>
<p>There is also no default built-in array type as this too is something that most developers may want to have their own version of. The array type is registered as a <a class="el" href="doc_adv_template.html">template</a>, which is then set as the <a class="el" href="classas_i_script_engine.html#ac9451feece1297eba8d1649036039e82">default array type</a>. A standard <a class="el" href="doc_addon_array.html">array add-on</a> is provided for those that do not want to implement their own array type.</p>
<p><a class="el" href="classas_i_script_engine.html#ae2d89b82561b7f9843f35693c664589f">Class interfaces</a> can be registered if you want to guarantee that script classes implement a specific set of class methods. Interfaces can be easier to use when working with script classes from the application, but they are not necessary as the application can easily enumerate available methods and properties even without the interfaces.</p>
<p><a class="el" href="classas_i_script_engine.html#a03c1a2cc23ae4b742c927f3472a1a4f7">Function definitions</a> can be registered when you wish to allow the script to pass function pointers to the application, e.g. to implement callback routines.</p>
<p><a class="el" href="classas_i_script_engine.html#abed6e77f2a532c8a4f528650fa137d37">Enumeration types</a> and <a class="el" href="classas_i_script_engine.html#addb24466769dc52be96c7e37d5305245">typedefs</a> can also be registered to improve readability of the scripts. </p>
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I hate being the third wheel in my friends’ relationships. Here’s why.
Frankly, I think that entire mindset is bullshit.
One of the biggest fights I’ve ever gotten into with a friend was over a boy.
But it wasn’t for reasons you might think.
I’ve always only had a few close friends. I’m a notoriously anxious person and I don’t particularly enjoy meeting new people, so I was never a social butterfly. While I don’t have a large circle of friends, I adore and am fiercely loyal to my core group.
In high school, one of these friends started dating one of our mutual acquaintances. It felt like almost instantly I had gone from seeing her multiples times a week to never seeing her at all. Up until that point, we had been extremely close.
[bctt tweet=”It all changes the moment they get a boyfriend or a girlfriend.” username=”wearethetempest”]
When we first were introduced back in sophomore year, we bonded over a shared love of the movie Say Anything and campy, offbeat 80’s pop culture. Our friendship blossomed from simply sitting at the same lunch table, to having hushed discussions while squished together on her tiny twin mattress during Saturday night sleepovers. When she entered this new relationship, suddenly the person I traded so many of my deepest secrets with was disappearing and I couldn’t understand why.
The hurt I felt quickly turned into bitterness and I lashed out in the only way I knew how. If she was going to ignore me and fade out of my life, I was going do the same exact thing to her. It was our senior year of high school, and unfortunately, we spent a majority of that time not speaking at all.
This was the first time that a close friend of mine began blowing me off for their significant other, but it was not the last. Throughout college and even now, I’ve begun to recognize a pattern. While my friends are single, I see them all the time. We grab a quick lunch at our local Asian fusion restaurant. Or a cheeky hump-day drink to get us through the week. However, it all changes the moment they get a boyfriend or a girlfriend. Then it’s like I have to a slay dragon, cross a moat, and promptly submit a ten page, double-spaced proposal in order to make any kind of plans with them.
As someone who doesn’t know if she’ll ever get into a romantic relationship herself, this pattern scares me because not only is this behavior common within our society, it is expected. We’re very much expected to have one partner who we’ll settle down with and eventually marry. It’s why traditions like bachelor and bachelorette parties still exist. The night before our wedding, we’re supposed to go out with our friends and have one last hurrah because it will all change the moment “I do” crosses our lips.
Frankly, I think that entire mindset is bullshit.
I’m sick of people privileging romantic relationships over platonic ones.
This way of thinking implies that platonic relationships aren’t as important because there is no sex or romantic love involved. As a result, there is also the implication that if a person does not enter a romantic relationship, then their lives are inherently less valid or unfulfilled. Which is, of course, completely untrue.
On a more personal level, however, I think I have the biggest gripe with the misconception that a platonic friendship cannot be as intimate as a romantic one. Physical intimacy is not the only kind that exists.
When I think of the type of intimacy that exists within my own life, I immediately think about my best friend. I talk to her every single day and she frequently acts as my sounding board. I share with her my hopes, dreams, fears, anxieties, and everything that falls in those murky in-between spaces. I’ve freely told her information about myself that no one else knows.
That alone is a form of intimacy.
As I get older, I’ve started to accept the fact that perhaps I’ll always experience this tug of war between my friends and their significant others. Especially as the race down the aisle grows closer and closer. I just hope that my friends can recognize that a romantic relationship and marriage is not the be-all-end-all of interpersonal connection.
My friendships are just as important, valid, and necessary for a full and thriving life – on both sides of the relationship. |
Q:
ASP.net checkbox always checked
<asp:CheckBox ID="isSubscribed" runat="server" /> Subscribe to mailing list?<br /><br />
<asp:Button runat="server" CssClass="btn" ID="btnPrefUpdate" OnClick="updatePrefs" Text="Update" /><br /><br />
This fires in the code behind:
protected void updatePrefs(object sender, EventArgs e)
{
Response.Write(isSubscribed.Checked);
Response.End();
}
But it's always coming out as true! Whether it is checked or not! I know I'm doing it wrong, could someone show me how to access this value properly?
A:
like @Curt said, it looks to me like you have something in your page_load. if you set the value in Page_Load make sure it is inside the following if statement
if(!Page.isPostBack)
{
isSubscribed.Checked = true;
}
|
Q:
How to know library is debug library or release?
I am using mysql cpp library .
I checkout the recent copy from there bzr trunk and
used cmake to generate library .
First time I used release mode and second time I used debug mode to build.
The both library have
a mysql_debug.cpp
U mysql_debug
Is there a way to check in program (C or C++ code) or using nm that library is Release library or Debug library
A:
I have seen false negatives with nm so I do not trust it. When I want to check to see if an object file has debug info I run objdump -x on the object file or library and look to see if there are headers that say dbg, stabs, or dwarf. This is not the most elegant solution by any means, but it has never been wrong and it is real easy to see the difference in when you have a debug and release build to compare.
|
Q:
How to use embedded resource in ASP.Net?
I'm practicing to use embedded resource in ASP.Net. I wrote a javascript file, put it into a C# class library and change It's Build Action Property to Embedded Resource. In my web project, I added reference to the that class library. I want to use that javascript file in my web pages but i don't know how? please help me
Thanks
A:
My problem was resolved.
Anybody can accomplish as following steps:
- Add a class library to your solution
- Add the resource files which you want to embed
- Register your resource in AssemblyInfo.cs
[assembly: System.Web.UI.WebResource("A.B.C", "D")]
with:
A is your class library name
B is the folder's name which contain your resource file
C is the resource files'name
D is the content type of your resource ("text/javascript" or another)
In the code behind file of the asp.net page you include the resource:
string scriptLocation = Page.ClientScript.GetWebResourceUrl(typeof(the empty class' name which added before), "A.B.C");
Page.ClientScript.RegisterClientScriptInclude("A.B.C", scriptLocation);
test what you have done
|
The 35Amp GX200 Smart Chip offers a power range of 5W to 200W and a voltage output of 0.5V to 7.0V—making the SnowWolf-200W Box Mod a high-performance, temperature-controlled machine. The SnowWolf can be used with either Kanthal or Nickel wire. The atomizer coil resistance range is 0.05 to 2.5 Ohms, and the device is capable of handling those Super Sub Ohm tanks and RDA builds while still taking advantage of extremely high watts. A black glass face paired with a stainless steel body give the device a sleek look and modern finish. |
Archive for the ‘Fun Spring Activities’ Category
When you are learning about birds in the spring, a fun activity you can do with your kids is to make your own nest. Your kids can “fly” around the yard as if they were birds, searching for materials from which to build their nest.
You want to start with a base, or a place to build your nest. You can grab one of those pottery dishes that go under a large potted plant. Or grab a tray from your kitchen. Or you can just build your nest on the ground or in a tree.
Materials you can gather to make your own nest:
twigs and sticks
dead leaves
moss and lichen
wheat stalks
dead grass
bark from trees
dead weeds
fluff from flowers
wet mud
How to put together your nest:
You will want to mix some dirt and water to create your glue. Birds sometimes use spider webs or other sticky plants to keep their nest together instead of mud, but many birds use mud.
Start arranging your dry grass, leaves, pine needles, twigs and other debris into a nest shape. Use the mud to glue it all together. Make it nice and soft by adding moss and fluff to line the inside of the nest.
Now you can place some oval-shaped rocks into the nest to make it look like a bird laid eggs there.
When my daughter was in the hospital for her spinal surgery last year, someone gave her a gift of a “Tea Party in a Bag.” I thought this idea was wonderful! The woman from my mom’s church placed some delicious tea party snacks and dishes into a cloth bag. Whenever my daughter wanted a tea party, all she would have to do is open the bag and set out the dishes and treats!
We did need to heat up some water for the tea, but that’s pretty easy to do. You will want to make sure to include an assortment of tea bags to choose from, if you are wanting to assemble your own “Tea Party in a Bag.”
The dishes can be toy dishes or real teacups and a teapot. Since I had real dishes, we used the toy dishes from the bag as decorations for the table. If you want to get real teapots and teacups, you can buy them in second hand shops or yard sales inexpensively.
You might want to include a lace tablecloth or other table covering, but this is optional. You might also want to include pretty decorations, like the cloth flowers that were included in our package.
Make sure the tea party treats are in sealed containers or bags. That way if the girl wants to wait for a month or two before having the tea party, the treats will not be stale. Store-bought cookies, cakes, miniature pies, or nuts would all be appropriate for inclusion in your tea party bag.
My daughter invited a friend over, and we had a fun time with our tea party. This was a blessing to me as a mom because I was so exhausted from having stayed up all night at the hospital for several days, and I loved having an easy activity that required nothing from me but the heating up of water. A great gift!
Gardening with kids is a joy! The kids can see a plant growing up out of the soil into a large and beautiful plant. Getting fresh air and sunshine is good for children, and they are more likely to eat fruits and vegetables when they grow their own plants.
First you will want to find a plot of ground for your child to plant his or her garden. There was a small square plot at the front of our house, and my son chose that space for a small tomato plant. If you look at the picture above, last year his plant grew to ten times the size in just three months! The tomatoes tasted wonderful. He wanted to sell them, but they were just too good. So into his mouth they popped.
This year my son wanted to plant strawberry plants. I told him that a contained area is great for strawberry plants, which tend to take over the whole yard like a weed. The strawberry plants thrived as well.
Tips for Gardening with Kids
Make sure that the soil is rich in the area where your child is planting. You will want to dig out the bad soil and replace it with good gardening soil.
Don’t forget to water your plants. You might want to place a note on the refrigerator to remind your child to water the plants.
Let the child choose the plants. This way they will be more interested in the growth and produce of their plants.
Choose plants that are native to your area. You are more likely to succeed if the plants are indigenous to the area. You can find those in local nurseries rather than big chain stores that ship their plants from outside your state.
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[Resistance to beta-lactam antibiotics and aminoglycosides in gram negative bacteria. 1. Molecular and genetic characterization of R-factors (author's transl)].
With frequent use of aminoglycoside antimicrobials and beta-lactam antibiotics in hospitals in the last few years, the number of bacterial strains resistant to these chemotherapeutics increased. Lately, strains of E. coli, Klebsiella, Enterobacter, Serratia, Proteus and Pseudomonas resistant to many antimicrobials (ampicillin, carbenicillin, cephalothin, chloramphenicol, gentamycin, tobramycin, sisomycin, neomycin, paromomycin, kanamycin, streptomycin, spectinomycin, tetracycline, sulphonamides) were isolated from patients of the university hospital in Zuerich. The resistant phenotype of two representative strains (Klebsiella pneumoniae 1 and Serratia marcescens 2) could be transferred by mixed cultivation to E. coli K-12. Multiple resistance of strain 1, and addition, could be transferred to Salmonella typhimurium, Serratia marcescens, Providencia, Proteus mirabilis and Klebsiella pneumoniae in varying frequencies. Transfer to Pseudomonas aeruginosa, however, could not be achieved. Spontaneous instability of resistance was observed in 0.15% of the cells of an overnight brothe culture and in 90% of the cells of a three months old culture. Conjugation, instability and the response to the sex phages MS-2 and If-1 suggested that resistance was mediated by a monomolecular R-factor, belonging to the fi+-type. This suggestion was confirmed by molecular characterization of the resistance plasmids. After transfer of the R-factors of K. pneumoniae 1 (R-FK 1) and Serratia marcescens 2 (R-FK2) into E. coli K-12, plasmid DNA was labelled with (methyl-3H) thymidine, and isolated by isopycnic centrifugation in cesiumchlorid-ethidium-bromide. Analysis of plasmid DNA then was carried out by sedimentation in a 5-20% neutral sucrose gradient together with reference plasmids of known molecular weights and sedimentation constants. The analysis revealed that R-FK1 had a molecular weight of 54 X 10(6) and R-FK2 of 50 X 10(6) daltons. The values were confirmed by contour length measurements of open circular forms with an electron microscope. A comparison of the sedimentation profile of labelled plasmid DNA from strain 1 and 14C-labelled DNA of E. coli K-12 (R-FK1) showed that the wild-type strain contained, besides the large resistance plasmid, at least two smaller "cryptic" plasmids. These smaller plasmid molecules were also found in antibiotic susceptible variants of strain 1, which did not contain the 54 X 10(6) dalton plasmid molecule, responsible for the resistant phenotype. The number of copies of R-FK1 in E. coli K-12 was determined to be 2, indicating stringent control of replication. It is discussed that the growing number of isolations of strains of Escherichia, Klebsiella, Serratia, Proteus, Providencia and Pseudomonas, exhibiting the same resistance phenotype, results from the spread of the R-factor described above among the hospital bacterial flora. |
Iraq army, militants fight over oil refinery | USA NOW
The Iraq army is claiming it has stopped an attack on the nation's largest oil refinery. The news comes only hours after inital reports stated that Sunni militants had taken control of the Beiji refinery.
http://archive.dnj.com/VideoNetwork/3629636006001/Iraq-army-militants-fight-over-oil-refinery-USA-NOWhttp://archive.dnj.com/VideoNetwork/3629636006001/Iraq-army-militants-fight-over-oil-refinery-USA-NOWhttp://bc_gvpc.edgesuite.net/img/963482463001/201406/2796/963482463001_3629510308001_thumbnail-for-video-3629443528001.jpgIraq army, militants fight over oil refinery | USA NOWThe Iraq army is claiming it has stopped an attack on the nation's largest oil refinery. The news comes only hours after inital reports stated that Sunni militants had taken control of the Beiji refinery.4vpcbestviolence in IraqGas PricesInternational newsbaiji oil refineryUSANOWNational NewsUSA NOWtroops in IraqNewsOil prices01:03 |
---
abstract: 'We consider topological Markov chains (also called Markov shifts) on countable graphs. We show that a transient graph can be extended to a recurrent graph of equal entropy which is either positive recurrent of null recurrent, and we give an example of each type. We extend the notion of [*local entropy*]{} to topological Markov chains and prove that a transitive Markov chain admits a measure of maximal entropy (or [*maximal measure*]{}) whenever its local entropy is less than its (global) entropy.'
author:
- Sylvie Ruette
title: 'On the Vere-Jones classification and existence of maximal measures for countable topological Markov chains '
---
Introduction {#introduction .unnumbered}
============
In this article we are interested in connected oriented graphs and topological Markov chains. All the graphs we consider have a countable set of vertices. If $G$ is an oriented graph, let $\Gamma_G$ be the set of two-sided infinite sequences of vertices that form a path in $G$ and let $\sigma$ denote the shift transformation. The [*Markov chain*]{} associated to $G$ is the (non compact) dynamical system $(\Gamma_G,\sigma)$. The entropy $h(G)$ of the Markov chain $\Gamma_G$ was defined by Gurevich; it can be computed by several ways and satisfies the Variational Principle [@Gur1; @Gur2].
In [@Ver1] Vere-Jones classifies connected oriented graphs as transient, null recurrent or positive recurrent according to the properties of the series associated with the number of loops, by analogy with probabilistic Markov chains. To a certain extent, positive recurrent graphs resemble finite graphs. In [@Gur1] Gurevich shows that a Markov chain on a connected graph admits a measure of maximal entropy (also called [*maximal measure*]{}) if and only if the graph is positive recurrent. In this case, this measure is unique and it is an ergodic Markov measure.
In [@Sal2; @Sal3] Salama gives a geometric approach to the Vere-Jones classification. The fact that a graph can (or cannot) be “extended” or “contracted” without changing its entropy is closely related to its class. In particular a graph with no proper subgraph of equal entropy is positive recurrent. The converse is not true [@Sal3] (see also [@uFie] for an example of a positive recurrent graph with a finite valency at every vertex that has no proper subgraph of equal entropy). This result shows that the positive recurrent class splits into two subclasses: a graph is called [*strongly positive recurrent*]{} if it has no proper subgraph of equal entropy; it is equivalent to a combinatorial condition (a finite connected graph is always strongly positive recurrent). In [@Sal2; @Sal3] Salama also states that a graph is transient if and only if it can be extended to a bigger transient graph of equal entropy. We show that any transient graph $G$ is contained in a recurrent graph of equal entropy, which is positive or null recurrent depending on the properties of $G$. We illustrate the two possibilities – a transient graph with a positive or null recurrent extension – by an example.
The result of Gurevich entirely solves the question of existence of a maximal measure in term of graph classification. Nevertheless it is not so easy to prove that a graph is positive recurrent and one may wish to have more efficient criteria. In [@GZ2] Gurevich and Zargaryan give a sufficient condition for existence of a maximal measure; it is formulated in terms of exponential growth of the number of paths inside and outside a finite subgraph. We give a new sufficient criterion based on local entropy.
Why consider local entropy? For a compact dynamical system, it is known that a null local entropy implies the existence of a maximal measure ([@New], see also [@Bow4] for a similar but different result). This result may be strengthened in some cases: it is conjectured that, if $f$ is a map of the interval which is $C^r$, $r>1$, and satisfies $h_{top}(f)>h_{loc}(f)$, then there exists a maximal measure [@Buz]. Our initial motivation comes from the conjecture above because smooth interval maps and Markov chains are closely related. If $f\colon [0,1]\to [0,1]$ is $C^{1+\alpha}$ (i.e. $f$ is $C^1$ and $f'$ is $\alpha$-Hölder with $\alpha>0$) with $h_{top}(f)>0$ then an oriented graph $G$ can be associated to $f$, $G$ is connected if $f$ is transitive, and there is a bijection between the maximal measures of $f$ and those of $\Gamma_G$ [@Buz; @Buz4]. We show that a Markov chain is strongly positive recurrent, thus admits a maximal measure, if its local entropy is strictly less that its Gurevich entropy. However this result does not apply directly to interval maps since the “isomorphism” between $f$ and its Markov extension is not continuous so it may not preserve local entropy (which depends on the distance).
The article is organized as follows. Section \[sec:background\] contains definitions and basic properties on oriented graphs and Markov chains. In Section \[sec:classification\], after recalling the definitions of transient, null recurrent and positive recurrent graphs and some related properties, we show that any transient graph is contained in a recurrent graph of equal entropy (Proposition \[prop:transient-recurrent\]) and we give an example of a transient graph which extends to a positive recurrent (resp. null recurrent) graph. Section \[sec:maximal-measure\] is devoted to the problem of existence of maximal measures: Theorem \[theo:hloc-maximal-measure\] gives a sufficient condition for the existence of a maximal measure, based on local entropy.
Background {#sec:background}
==========
Graphs and paths
----------------
Let $G$ be an oriented graph with a countable set of vertices $V(G)$. If $u,v$ are two vertices, there is at most one arrow $u\to v$. A [*path*]{} of length $n$ is a sequence of vertices $(u_0,\cdots,u_n)$ such that $u_i\to u_{i+1}$ in $G$ for $0\leq i<n$. This path is called a [*loop*]{} if $u_0=u_n$. We say that the graph $G$ is [*connected*]{} if for all vertices $u,v$ there exists a path from $u$ to $v$; in the literature, such a graph is also called [*strongly connected*]{}.
If $H$ is a subgraph of $G$, we write $H\subset G$; if in addition $H\not=G$, we write $H{\subseteq_{\mbox{\rm \hspace{-0.5em}{\scriptsize /}
}}\hspace{-0.3em}}G$ and say that $H$ is a [*proper subgraph*]{}. If $W$ is a subset of $V(G)$, the set $V(G)\setminus W$ is denoted by $\overline{W}$. We also denote by $W$ the subgraph of $G$ whose vertices are $W$ and whose edges are all edges of $G$ between two vertices in $W$.
Let $u,v$ be two vertices. We define the following quantities.
- $p_{uv}^G(n)$ is the number of paths $(u_0,\cdots,u_n)$ such that $u_0=u$ and $u_n=v$; $R_{uv}(G)$ is the radius of convergence of the series $\sum p_{uv}^G(n)z^n$.
- $f_{uv}^G(n)$ is the number of paths $(u_0,\cdots,u_n)$ such that $u_0=u$, $u_n=v$ and $u_i\not=v$ for $0<i<n$; $L_{uv}(G)$ is the radius of convergence of the series $\sum f_{uv}^G(n)z^n$.
Let $G$ be an oriented graph. If $G$ is connected, $R_{uv}(G)$ does not depend on $u$ and $v$; it denoted by $R(G)$.
If there is no confusion, $R(G)$ and $L_{uv}(G)$ will be written $R$ and $L_{uv}$. For a graph $G'$ these two radii will be written $R'$ and $L'_{uv}$.
Markov chains {#subsec:markov-chain}
-------------
Let $G$ be an oriented graph. $\Gamma_G$ is the set of two-sided infinite paths in $G$, that is, $$\Gamma_G=\{(v_n)_{n\in\IZ} \mid \forall n\in \IZ, v_n\to v_{n+1}
\mbox{ in } G \}\subset (V(G))^{\IZ}.$$ $\sigma$ is the shift on $\Gamma_G$. The [*(topological) Markov chain*]{} on the graph $G$ is the system $(\Gamma_G,\sigma)$.
The set $V(G)$ is endowed with the discrete topology and $\Gamma_G$ is endowed with the induced topology of $(V(G))^{\IZ}$. The space $\Gamma_G$ is not compact unless $G$ is finite. A compatible distance on $\Gamma_G$ is given by $d$, defined as follows: $V(G)$ is identified with $\IN$ and the distance $D$ on $V(G)$ is given by $
D(n,m)=\left|\frac{1}{2^n}-\frac{1}{2^m}\right|$. If $\bar u=(u_n)_{n\in\IZ}$ and $\bar v=(v_n)_{n\in\IZ}$ are two elements of $\Gamma_G$, $$d(\bar u,\bar v)=\sum_{n\in\IZ}
\frac{D(u_n,v_n)}{2^{|n|}}\leq 3.$$
The Markov chain $(\Gamma_G,\sigma)$ is [*transitive*]{} if for any non empty open sets $A,B\subset \Gamma_G$ there exists $n>0$ such that $\sigma^n(A)\cap
B\not=\emptyset$. Equivalently, $\Gamma_G$ is transitive if and only if the graph $G$ is connected. In the sequel we will be interested in connected graphs only.
Entropy {#subsec:def-entropy}
-------
If $G$ is a finite graph, $\Gamma_G$ is compact and the topological entropy $h_{top}(\Gamma_G,\sigma)$ is well defined (see e.g. [@DGS] for the definition of the topological entropy). If $G$ is a countable graph, the [*Gurevich entropy*]{} [@Gur1] of $G$ is given by $$h(G)=\sup\{h_{top}(\Gamma_H,\sigma)\mid H\subset G, H \mbox{ finite}\}.$$
This entropy can also be computed in a combinatorial way, as the exponential growth of the number of paths with fixed endpoints [@Gur2].
Let $G$ be a connected oriented graph. Then for any vertices $u,v$ $$h(G)=\lim_{n\to+\infty}\frac{1}{n}\log p_{uv}^G(n)=-\log R(G).$$
Another way to compute the entropy is to compactify the space $\Gamma_G$ and then use the definition of topological entropy for compact metric spaces. If $G$ is an oriented graph, denote the one-point compactification of $V(G)$ by $V(G)\cup\{\infty\}$ and define $\overline{\Gamma}_G$ as the closure of $\Gamma_G$ in $(V(G)\cup\{\infty\})^{\IZ}$. The distance $d$ naturally extends to $\overline{\Gamma}_G$. In [@Gur1] Gurevich shows that this gives the same entropy; this means that there is only very little dynamics added in this compactification. Moreover, the Variational Principle is still valid for Markov chains [@Gur1].
Let $G$ be an oriented graph. Then $$h(G)=h_{top}(\overline{\Gamma}_G,\sigma)=\sup\{h_{\mu}(\Gamma_G)\mid \mu
\ \sigma\mbox{-invariant probability measure}\}.$$
On the classification of connected graphs {#sec:classification}
=========================================
Transient, null recurrent, positive recurrent graphs
----------------------------------------------------
In [@Ver1] Vere-Jones gives a classification of connected graphs as transient, null recurrent or positive recurrent. The definitions are given in Table \[tab:classification\] (lines 1 and 2) as well as properties of the series $\sum p_{uv}^G(n)z^n$ which give an alternative definition.
------------------------------------------------------------- --------------- ------------ ------------------
transient null positive
recurrent recurrent
[1.5ex]{}${\displaystyle}\sum_{n>0} f^G_{uu}(n)R^n$ $<1$ $1$ $1$
[1.5ex]{}${\displaystyle}\sum_{n>0} nf^G_{uu}(n)R^n$ $\leq+\infty$ $+\infty$ $<+\infty$
[1.5ex]{}${\displaystyle}\sum_{n\geq 0} p^G_{uv}(n)R^n$ $<+\infty$ $+\infty$ $+\infty$
[1.5ex]{}${\displaystyle}\lim_{n\to+\infty} p^G_{uv}(n)R^n$ $0$ $0$ $\lambda_{uv}>0$
[1.5ex]{} $R=L_{uu}$ $R=L_{uu}$ $R\leq L_{uu}$
------------------------------------------------------------- --------------- ------------ ------------------
: properties of the series associated to a transient, null recurrent or positive recurrent graph $G$; these properties do not depend on the vertices $u,v$ ($G$ is connected). \[tab:classification\]
In [@Sal2; @Sal3] Salama studies the links between the classification and the possibility to extend or contract a graph without changing its entropy. It follows that a connected graph is transient if and only if it is strictly included in a connected graph of equal entropy, and that a graph with no proper subgraph of equal entropy is positive recurrent.
In [@Sal2] Salama claims that $L_{uu}$ is independent of $u$, which is not true; in [@Sal3] he uses the quantity $L=\inf_u L_{uu}$ and he states that if $R=L$ then $R=L_{uu}$ for all vertices $u$, which is wrong too (see Proposition 3.2 in [@GurS]). It follows that in [@Sal2; @Sal3] the statement “R=L” must be interpreted either as “$R=L_{uu}$ for some $u$” or “$R=L_{uu}$ for all $u$” depending on the context. This encouraged us to give the proofs of Salama’s results in this article.
In [@Sal3] Salama shows that a transient or null recurrent graph satisfies $R=L_{uu}$ for all vertices $u$; we give the unpublished proof due to U. Fiebig [@uFie].
\[prop:transient-R=L\] Let $G$ be a connected oriented graph. If $G$ is transient or null recurrent then $R=L_{uu}$ for all vertices $u$. Equivalently, if there exists a vertex $u$ such that $R<L_{uu}$ then $G$ is positive recurrent.
For a connected oriented graph, it is obvious that $R\leq L_{uu}$ for all $u$, thus the two claims of the Proposition are equivalent. We prove the second one.
Let $u$ be a vertex of $G$ such that $R<L_{uu}$. Let $F(x)=\sum_{n\geq 1}f_{uu}^G(n)x^n$ for all $x\geq 0$. If we break a loop based in $u$ into first return loops, we get the following formula: $$\label{eq:P(x)-F(x)}
\sum_{n\geq 0}p_{uu}^G(n)x^n=\sum_{k\geq 0}(F(x))^k.$$ Suppose that $G$ is transient, that is, $F(R)<1$. The map $F$ is analytic on $[0,L_{uu})$ and $R<L_{uu}$ thus there exists $R<x<L_{uu}$ such that $F(x)<1$. According to Equation (\[eq:P(x)-F(x)\]) one gets that $\sum_{n\geq 0}p_{uu}^G(n)x^n<+\infty$, which contradicts the definition of $R$. Therefore $G$ is recurrent. Moreover $R<L_{uu}$ by assumption, thus $\sum_{n\geq 1} nf_{uu}^G(n)R^n<+\infty$, which implies that $G$ is positive recurrent.
A connected oriented graph is called [*strongly positive recurrent*]{} if $R<L_{uu}$ for all vertices $u$.
\[lem:recurrent-R\] Let $G$ be a connected oriented graph and $u$ a vertex.
1. $R<L_{uu}$ if and only if $\,\sum_{n\geq 1}f_{uu}^G(n)L_{uu}^n>1$.
2. If $G$ is recurrent then $R$ is the unique positive number $x$ such that $\sum_{n\geq 1}f_{uu}^G(n)x^n=1$.
Use the fact that $F(x)=\sum_{n\geq 1}f_{uu}^G(n)x^n$ is increasing.
The following result deals with transient graphs [@Sal2].
Let $G$ be a connected oriented graph of finite positive entropy. Then $G$ is transient if and only if there exists a connected oriented graph $G'{\supseteq_{\mbox{\rm \hspace{-0.65em}{\scriptsize /}
}}\hspace{-0.15em}}G$ such that $h(G')=h(G)$. If $G$ is transient then $G'$ can be chosen transient.
The assumption on the entropy implies that $0<R<1$. Suppose first that there exists a connected graph $G'{\supseteq_{\mbox{\rm \hspace{-0.65em}{\scriptsize /}
}}\hspace{-0.15em}}G$ such that $h(G')=h(G)$, that is, $R'=R$. Fix a vertex $u$ in $G$. The graph $G$ is a proper subgraph of $G'$ thus there exists $n$ such that $f_{uu}^G(n)<f_{uu}^{G'}(n)$, which implies that $$\sum_{n\geq 1}f_{uu}^G(n)R^n<\sum f_{uu}^{G'}(n){R'}^n\leq 1.$$ Therefore $G$ is transient.
Now suppose that $G$ is transient and fix a vertex $u$ in $G$. One has $\sum_{n\geq 1} f_{uu}^G(n)R^n<1$. Let $k\geq 2$ be an integer such that $$\sum_{n\geq 1} f_{uu}^G(n)R^n+R^k<1.$$ Define the graph $G'$ by adding a loop of length $k$ based at the vertex $u$; one has $R'\leq R$ and $$\label{eq:G'-G-transient}
\sum_{n\geq 1}f_{uu}^{G'}(n){R'}^n\leq
\sum_{n\geq 1}f_{uu}^{G'}(n){R}^n=
\sum_{n\geq 1}f_{uu}^{G}(n){R}^n+R^k<1.$$ Equation (\[eq:G’-G-transient\]) implies that $R\leq L_{uu}'$ and also that the graph $G'$ is transient, so $R'=L_{uu}'$ by Proposition \[prop:transient-R=L\]. Then one has $L_{uu}'=R'\leq R\leq L_{uu}'$ thus $R=R'$.
In [@Sal3] Salama proves that if $R=L_{uu}$ for all vertices $u$ then there exists a proper subgraph of equal entropy. We show that the same conclusion holds if one supposes that $R=L_{uu}$ for some $u$. The proof below is a variant of the one of Salama. The converse is also true, as shown by U. Fiebig [@uFie].
\[prop:R<=L\] Let $G$ be a connected oriented graph of positive entropy.
1. If there is a vertex $u$ such that $R=L_{uu}$ then there exists a connected subgraph $G'{\subseteq_{\mbox{\rm \hspace{-0.5em}{\scriptsize /}
}}\hspace{-0.3em}}G$ such that $h(G')=h(G)$.
2. If there is a vertex $u$ such that $R<L_{uu}$ then for all proper subgraphs $G'$ one has $h(G')<h(G)$.
i\) Suppose that $R=L_{uu}$. If $u_0=u$ is followed by a unique vertex, let $u_1$ be this vertex. If $u_1$ is followed by a unique vertex, let $u_2$ be this vertex, and so on. If this leads to define $u_n$ for all $n$ then $h(G)=0$, which is not allowed.
Let $u_k$ be the last built vertex; there exist two distinct vertices $v,v'$ such that $u_k\to v$ and $u_k\to v'$. Let $G_1'$ be the graph $G$ deprived of the arrow $u_k\to v$ and $G_2'$ the graph $G$ deprived of all the arrows $u_k\to w$, $w\not=v$. Call $G_i$ the connected component of $G_i'$ that contains $u$ ($i=1,2$); obviously $G_i{\subseteq_{\mbox{\rm \hspace{-0.5em}{\scriptsize /}
}}\hspace{-0.3em}}G$. For all $n\geq 1$ one has $$f_{uu}^G(n)=f_{u_ku}^G(n-k)=f_{u_ku}^{G_1}(n-k)+f_{u_ku}^{G_2}(n-k),$$ thus there exists $i\in\{1,2\}$ such that $L_{uu}=L_{u_ku}^{G_i}$. One has $$R\leq R(G_i)\leq L_{u_ku}(G_i)=L_{uu}=R,$$ thus $R=R(G_i)$, that is, $h(G)=h(G_i)$.
ii\) Suppose that $R<L_{uu}$ and consider $G'{\subseteq_{\mbox{\rm \hspace{-0.5em}{\scriptsize /}
}}\hspace{-0.3em}}G$. Suppose first that $u$ is a vertex of $G'$. The graph $G$ is positive recurrent by Proposition \[prop:transient-R=L\] so $\sum_{n\geq 1}f_{uu}^G(n)R^n=1$. Since $G'{\subseteq_{\mbox{\rm \hspace{-0.5em}{\scriptsize /}
}}\hspace{-0.3em}}G$ there exists $n$ such that $f_{uu}^{G'}(n)<f_{uu}^G(n)$, thus $$\label{eq:G'-G-recurrent}
\sum_{n\geq 1} f_{uu}^{G'}R^n<1.$$ Moreover $L_{uu}'\geq L_{uu}$. If $G'$ is transient then $R'=L_{uu}'$ (Proposition \[prop:transient-R=L\]) thus $R'\geq L_{uu}>R$. If $G'$ is recurrent then $\sum_{n\geq 1}f_{uu}^{G'}{R'}^n=1$ thus $R'>R$ because of Equation (\[eq:G’-G-recurrent\]). In both cases $R'>R$, that is, $h(G')<h(G)$.
Suppose now that $u$ is not a vertex of $G'$ and fix a vertex $v$ in $G'$. Let $(u_0,\ldots,u_p)$ a path (in $G$) of minimal length between $u=u_0$ and $v=u_p$, and let $(v_0,\ldots, v_q)$ be a path of minimal length between $v=v_0$ and $u=v_q$.
If $(w_0=v,w_1,\ldots, w_n=v)$ is a loop in $G'$ then $$(u_0=u,u_1,\ldots,u_p=w_0,w_1,\ldots,w_n=v_0,v_1,\ldots,v_q=u)$$ is a first return loop based in $u$ in the graph $G$. For all $n\geq 0$ we get that $p_{vv}^{G'}(n)\leq f_{uu}^G(n+p+q)$, thus $R'\geq L_{uu}>R$, that is, $h(G')<h(G)$.
The following result gives a characterization of strongly positive recurrent graphs. It is a straightforward corollary of Proposition \[prop:R<=L\] (see also [@uFie]).
\[theo:strongly-positive-recurrent\] Let $G$ be a connected oriented graph of positive entropy. The following properties are equivalent:
1. for all $u$ one has $R<L_{uu}$ (that is, $G$ is strongly positive recurrent),
2. there exists $u$ such that $R<L_{uu}$,
3. $G$ has no proper subgraph of equal entropy.
Recurrent extensions of equal entropy of transient graphs {#subsec:exR=L}
---------------------------------------------------------
We show that any transient graph $G$ can be extended to a recurrent graph without changing the entropy by adding a (possibly infinite) number of loops. If the series $\sum n f_{vv}^G(n)R^n$ is finite then the obtained recurrent graph is positive recurrent (but not strongly positive recurrent), otherwise it is null recurrent.
\[prop:transient-recurrent\] Let $G$ be a transient graph of finite positive entropy. Then there exists a recurrent graph $G'\supset G$ such that $h(G)=h(G')$. Moreover $G'$ can be chosen to be positive recurrent if $\,\sum_{n>0} nf_{uu}^G(n)R^n<+\infty$ for some vertex $u$ of $G$, and $G'$ is necessarily null recurrent otherwise.
The entropy of $G$ is finite and positive thus $0<R<1$ and there exists an integer $p$ such that $\frac{1}{2}\leq pR<1$. Define $\alpha=pR$. Let $u$ be a vertex of $G$ and define $D=1-\sum_{n\geq 1} f_{uu}^G(n)R^n$; one has $0<D<1$. Moreover $$\sum_{n\geq 1} \alpha^n\geq \sum_{n\geq 1} \frac{1}{2^n}=1,$$ thus $$\label{eq:series}
\sum_{n\geq k+1}\alpha^n=\alpha^k\sum_{n\geq 1}\alpha^n\geq \alpha^k.$$
We build a sequence of integers $(n_i)_{i\in I}$ such that $2\sum_{i\in I} \alpha^{n_i}=D$. For this, we define inductively a strictly increasing (finite or infinite) sequence of integers $(n_i)_{i\in I}$ such that for all $k\in I$ $$\sum_{i=0}^k \alpha^{n_i} \leq \frac{D}{2} <
\sum_{i=0}^k \alpha^{n_i} + \sum_{n>n_k} \alpha^n.$$
– Let $n_0$ be the greatest integer $n\geq 2$ such that $\sum_{k\geq n} \alpha^k >\frac{D}{2}$. By choice of $n_0$ one has $\sum_{n\geq n_0+1} \alpha^n \leq \frac{D}{2}$, thus $\alpha^{n_0}\leq\frac{D}{2}$ by Equation (\[eq:series\]). This is the required property at rank $0$.
– Suppose that $n_0,\cdots,n_k$ are already defined. If $\sum_{i=0}^k \alpha^{n_i}=
\frac{D}{2}$ then $I=\{0,\cdots,k\}$ and we stop the construction. Otherwise let $n_{k+1}$ be the greatest integer $n >n_k$ such that $$\sum_{i=0}^k \alpha^{n_i}+\sum_{j\geq n} \alpha^j > \frac{D}{2}.$$ By choice of $n_{k+1}$ and Equation (\[eq:series\]), one has $$\alpha^{n_{k+1}}\leq \sum_{j\geq n_{k+1}+1} \alpha^j\leq
\frac{D}{2}-\sum_{i=0}^k \alpha^{n_i}.$$ This is the required property at rank $k+1$.
Define a new graph $G'\supset G$ by adding $2p^{n_i}$ loops of length $n_i$ based at the vertex $u$. Obviously one has $R'\leq R$, and $\sum_{i\in I}(pR)^{n_i}=\frac{D}{2}$ by construction. Therefore $$\label{eq:sum=1}
\sum_{n\geq 1} f_{uu}^{G'}(n)R^n=
\sum_{n\geq 1} f_{uu}^G(n)R^n+\sum_{i\in I}2(pR)^{n_i}=1.$$ This implies that $R\leq L_{uu}'$. If $G'$ is transient then $\sum_{n\geq 1} f_{uu}^{G'}(n){R'}^n<1$ and $R'=L_{uu}'$ by Proposition \[prop:transient-R=L\], thus $R\leq R'$ and Equation (\[eq:sum=1\]) leads to a contradiction. Therefore $G'$ is recurrent. By Lemma \[lem:recurrent-R\](ii) one has $R'=R$, that is, $h(G')=h(G)$. In addition, $$\sum_{n\geq 1} n f_{uu}^{G'}(n)R^n=
\sum_{n\geq 1} n f_{uu}^G(n)R^n+\sum_{i\in I} n_i \alpha^{n_i}$$ and this quantity is finite if and only if $\sum n f_{uu}^G(n)R^n$ is finite. In this case the graph $G'$ is positive recurrent.
If $\sum n f_{uu}^G(n)R^n=+\infty$, let $H$ be a recurrent graph containing $G$ with $h(H)=h(G)$. Then $H$ is null recurrent because $$\sum_{n\geq 1} n f_{uu}^{H}(n)R^n\geq \sum_{n\geq 1} n f_{uu}^G(n)R^n=+\infty.$$
\[ex:R=L\] We build a positive (resp. null) recurrent graph $G$ such that $\sum f_{uu}^G(n)L_{uu}^n=1$ and then we delete an arrow to obtain a graph $G'\subset G$ which is transient and such that $h(G')=h(G)$. First we give a description of $G$ depending on a sequence of integers $a(n)$ then we give two different values to the sequence $a(n)$ so as to obtain a positive recurrent graph in one case and a null recurrent graph in the other case.
Let $u$ be a vertex and $a(n)$ a sequence of non negative integers for $n\geq 1$, with $a(1)=1$. The graph $G$ is composed of $a(n)$ loops of length $n$ based at the vertex $u$ for all $n\geq 1$ (see Figure \[fig:G-G’\]). More precisely, define the set of vertices of $G$ as $$V=\{u\}\cup\bigcup_{n=1}^{+\infty}\{v_k^{n,i} \mid 1\leq i\leq a(n),
1\leq k\leq n-1\},$$ where the vertices $v_k^{n,i}$ above are distinct. Let $v_0^{n,i}=v_n^{n,i}=u$ for $1\leq i\leq a(n)$. There is an arrow $v_k^{n,i}\to v_{k+1}^{n,i}$ for $0\leq k\leq n-1, 1\leq i\leq a(n), n\geq 1$ and there is no other arrow in $G$. The graph $G$ is connected and $f_{uu}^G(n)=a(n)$ for $n\geq 1$.
![the graphs $G$ and $G'$; the bold loop (on the left) is the only arrow that belongs to $G$ and not to $G'$, otherwise the two graphs coincide. \[fig:G-G’\]](markov-fig1bis.eps)
The sequence $(a(n))_{n\geq 2}$ is chosen such that it satisfies $$\label{eq:=1}
\sum_{n\geq 1} a(n)L^n=1,$$ where $L=L_{uu}>0$ is the radius of convergence of the series $\sum a(n)z^n$. If $G$ is transient then $R=L_{uu}$ by Proposition \[prop:transient-R=L\], but Equation (\[eq:=1\]) contradicts the definition of transient. Thus $G$ is recurrent. Moreover, $R=L$ by Lemma \[lem:recurrent-R\](ii).
The graph $G'$ is obtained from $G$ by deleting the arrow $u\to u$. Obviously one has $L_{uu}'=L$ and $$\sum_{n\geq 1} f_{uu}^{G'}(n)L^n=1-L<1.$$ This implies that $G'$ is transient because $R'\leq L_{uu}'$. Moreover $R'=L_{uu}'$ by Proposition \[prop:transient-R=L\] thus $R'=R$, that is, $h(G')=h(G)$.
Now we consider two different sequences $a(n)$.
[**1)**]{} Let $a(n^2)=2^{n^2-n}$ for $n\geq 1$ and $a(n)=0$ otherwise. Then $L=\frac{1}{2}$ and $$\sum_{n\geq 1}f_{uu}^G(n)L^n=\sum_{n\geq 1}2^{n^2-n}\frac{1}{2^{n^2}}=
\sum_{n\geq 1}\frac{1}{2^n}=1.$$ Moreover $$\sum_{n\geq 1}nf_{uu}^G(n)L^n=\sum_{n\geq 1} \frac{n^2}{2^n}<+\infty,$$ hence the graph $G$ is positive recurrent.
[**2)**]{} Let $a(1)=1$, $a(2^n)=2^{2^n-n}$ for $n\geq 2$ and $a(n)=0$ otherwise. One can compute that $L=\frac{1}{2}$, and $$\sum_{n\geq 1}f_{uu}^G(n)L^n=
\frac{1}{2}+ \sum_{n\geq 2}2^{2^n-n}\frac{1}{2^{2^n}}
=\frac{1}{2}+\sum_{n\geq 2}\frac{1}{2^n}
=1.$$ Moreover $$\sum_{n\geq 1}nf_{uu}^G(n)L^n
=\frac{1}{2}+\sum_{n\geq 2} 2^n\frac{1}{2^n}=+\infty$$ hence the graph $G$ is null recurrent.
Let $G$ be transient graph of finite entropy. Fix a vertex $u$ and choose an integer $k$ such that $\sum_{n\geq k}R^n<1-\sum_{n\geq 1}f_{uu}^G(n)R^n$. For every integer $n\geq k$ let $m_n=\lfloor R^{-n}\rfloor$, add $\lfloor R^{-(m_n-n)}\rfloor$ loops of length $m_n$ based at the vertex $u$ and call $G'$ the graph obtained in this way. It can be shown that the graph $G'$ is transient, $h(G')=h(G)$ and $\sum_{n\geq 1}
nf_{uu}^{G'}R'^n=+\infty$. Then Proposition \[prop:transient-recurrent\] implies that every transient graph is included in a null recurrent graph of equal entropy.
In the more general setting of thermodynamic formalism for countable Markov chains, Sarig puts to the fore a subclass of positive recurrent potentials which he calls strongly positive recurrent [@Sar4]; his motivation is different, but the classifications agree. If $G$ is a countable oriented graph, a [*potential*]{} is a continuous map $\phi\colon \Gamma_G\to \IR$ and the [*pressure*]{} $P(\phi)$ is the analogous of the Gurevich entropy, the paths being weighted by $e^{\phi}$; a potential is either transient or null recurrent or positive recurrent. Considering the null potential $\phi\equiv 0$, we retrieve the case of (non weighted) topological Markov chains. In [@Sar4] Sarig introduces a quantity $\Delta_u[\phi]$; $\phi$ is transient (resp. recurrent) if $\Delta_u[\phi]<0$ (resp. $\Delta_u[\phi]\geq 0$). The potential is called [*strongly positive recurrent*]{} if $\Delta_u[\phi]>0$, which implies it is positive recurrent. A strongly positive recurrent potential $\phi$ is stable under perturbation, that is, any potential $\phi+t\psi$ close to $\phi$ is positive recurrent too. For the null potential, $\Delta_u[0]=\log\left(\sum_{n\geq 1} f_{uu}(n)L^n\right)$, thus $\Delta_u[0]>0$ if and only if the graph is strongly positive recurrent (Lemma \[lem:recurrent-R\] and Theorem \[theo:strongly-positive-recurrent\]). In [@GurS] strongly positive recurrent potentials are called [*stable positive*]{}.
Examples of (non null) potentials which are positive recurrent but not strongly positive recurrent can be found in [@Sar4]; some of them resemble much the Markov chains of Example \[ex:R=L\], their graphs being composed of loops as in Figure \[fig:G-G’\].
Existence of a maximal measure {#sec:maximal-measure}
==============================
Positive recurrence and maximal measures
----------------------------------------
A Markov chain on a finite graph always has a maximal measure [@Par], but it is not the case for infinite graphs [@Gur1]. In [@Gur2] Gurevich gives a necessary and sufficient condition for the existence of such a measure.
\[theo:Gurevic\] Let $G$ be a connected oriented graph of finite positive entropy. Then the Markov chain $(\Gamma_G,\sigma)$ admits a maximal measure if and only if the graph is positive recurrent. Moreover, such a measure is unique if it exists, and it is an ergodic Markov measure.
In [@GZ2] Gurevich and Zargaryan show that if one can find a finite connected subgraph $H \subset G$ such that there are more paths inside than outside $H$ (in term of exponential growth), then the graph $G$ has a maximal measure. This condition is equivalent to strong positive recurrent as it was shown by Gurevich and Savchenko in the more general setting of weighted graphs [@GurS].
Let $G$ be a connected oriented graph, $W$ a subset of vertices and $u,v$ two vertices of $G$. Define $t_{uv}^W(n)$ as the number of paths $(v_0,\cdots,v_n)$ such that $v_0=u,
v_n=v$ and $v_i\in W$ for all $0<i<n$, and put ${\displaystyle}\tau_{uv}^W=\limsup_{n\to+\infty} \frac{1}{n}\log t_{uv}^W(n)$.
\[theo:GZ-et-reciproque\] Let $G$ be a connected oriented graph of finite positive entropy. If there exists a finite set of vertices $W$ such that $W$ is connected and for all vertices $u,v$ in $W$, $\tau_{uv}^{\overline{W}}\leq h(W)$, then the graph $G$ is strongly positive recurrent.
For graphs that are not strongly positive recurrent the entropy is mainly concentrated near infinity in the sense that it is supported by the infinite paths that spend most of the time outside a finite subgraph (Proposition \[prop:entropy-infinity\]). This result is obtained by applying inductively the construction of Proposition \[prop:R<=L\](i). As a corollary, there exist “almost maximal measures escaping to infinity” (Corollary \[cor:entropy-infinity\]). These two results are proven and used as tools to study interval maps in [@BR], but they are interesting by themselves, that is why we state them here.
\[prop:entropy-infinity\] Let $G$ be a connected oriented graph which is not strongly positive recurrent and $W$ a finite set of vertices. Then for all integers $n$ there exists a connected subgraph $G_n\subset G$ such that $h(G_n)=h(G)$ and for all $w\in W$, for all $0\leq k<n$, $f_{ww}^{G_n}(k)=0$.
\[cor:entropy-infinity\] Let $G$ be a connected oriented graph which is not strongly positive recurrent. Then there exists a sequence of ergodic Markov measures $(\mu_n)_{n\geq 0}$ such that $\lim_{n\to+\infty}h_{\mu_n}(\Gamma_G,\sigma)=h(G)$ and for all finite subsets of vertices $W$, ${\displaystyle}\lim_{n\to+\infty}
\mu_n\left(\{(u_n)_{n\in\IZ}\in \Gamma_G\mid u_0\in W\}\right)=0$.
Local entropy and maximal measures {#subsec:hloc-mesure-max}
----------------------------------
For a compact system, the [*local entropy*]{} is defined according to a distance but does not depend on it. One may wish to extend this definition to non compact metric spaces although the notion obtained in this way is not canonical.
Let $X$ be a metric space, $d$ its distance and let $T\colon X\to X$ be a continuous map.
The [*Bowen ball*]{} of centre $x$, of radius $r$ and of order $n$ is defined as $$B_n(x,r)=\{y\in X\mid d(T^ix,T^iy)<r , 0\leq i< n\}.$$
$E$ is a $(\delta,n)$-separated set if $$\forall y,y'\in E, y\not=y', \exists 0\leq k<n,\ d(T^k y, T^k y')\geq
\delta.$$ The maximal cardinality of a $(\delta,n)$-separated set contained in $Y$ is denoted by $s_n(\delta,Y)$.
The local entropy of $(X,T)$ is defined as ${\displaystyle}h_{loc}(X)=\lim_{{\varepsilon}\to 0}h_{loc}(X,{\varepsilon})$, where $$h_{loc}(X,{\varepsilon})=\lim_{\delta\to 0} \limsup_{n\to+\infty}
\frac{1}{n}\sup_{x\in X}\log s_n(\delta,B_n(x,{\varepsilon})).$$
If the space $X$ is not compact, these notions depend on the distance. When $X=\Gamma_G$, we use the distance $d$ introduced in Section \[subsec:markov-chain\]. The local entropy of $\Gamma_G$ does not depend on the identification of the vertices with $\IN$.
Let $\Gamma_G$ be the topological Markov chain on $G$ and $\overline{\Gamma}_G$ its compactification as defined in Section \[subsec:markov-chain\]. Then $h_{loc}(\Gamma_G)=
h_{loc}(\overline{\Gamma}_G)$.
Let $\bar u=(u_n)_{n\in\IZ} \in \overline{\Gamma}_G$, ${\varepsilon}>0$ and $k\geq 1$. By continuity there exists $\eta>0$ such that, if $\bar v\in \overline{\Gamma}_G$ and $d(\bar u,\bar v)<\eta$ then $d(\sigma^i(\bar u),\sigma^i(\bar v))<{\varepsilon}$ for all $0\leq i<k$. By definition of $\overline{\Gamma}_G$ there is $\bar v\in \Gamma_G$ such that $d(\bar u,\bar v)<\eta$, thus $\bar u\in B_k(\bar v,{\varepsilon})$, which implies that $B_k(\bar u,{\varepsilon})\subset B_k(\bar v,2{\varepsilon})$. Consequently $h_{loc}(\overline{\Gamma}_G,{\varepsilon})\leq h_{loc}(\Gamma,2{\varepsilon})$, and $h_{loc}(\overline{\Gamma}_G)\leq h_{loc}(\Gamma_G)$. The reverse inequality is obvious.
We are going to prove that, if $h_{loc}(\Gamma_G)<h(G)$, then $G$ is strongly positive recurrent. First we introduce some notations.
Let $G$ be an oriented graph. If $V$ is a subset of vertices, $H$ a subgraph of $G$ and $\bar{u}=(u_n)_{n\in\IZ}\in \Gamma_G$, define $${{\cal C}}^{H}(\bar u,V)=\{(v_n)_{n\in\IZ}\in \Gamma_H\mid
\forall n\in\IZ, u_n\in V\Rightarrow (v_n=u_n),
u_n\not\in V\Rightarrow v_n\not\in V\}.$$ If $S\subset \Gamma_G$ and $p,q\in\IZ\cup\{-\infty,+\infty\}$, define $$[S]_{p}^{q}=\{(v_n)_{n\in\IZ}\in \Gamma_G\mid
\exists (u_n)_{n\in\IZ}\in S,\forall p\leq n\leq q, u_n=v_n\}.$$
\[lem:C-Bn\] Let $G$ be an oriented graph on the set of vertices $\IN$.
1. If $V\supset \{0,\cdots,p+2\}$ then for all $\bar u\in\Gamma_G$ and all $n\geq 1$, ${{\cal C}}^G(\bar u,V)\subset B_n(\bar u,2^{-p}).$
2. If $\bar u=(u_n)_{n\in\IZ}$ and $\bar v=(v_n)_{n\in\IZ}$ are two paths in $G$ such that $(u_0,\cdots,u_{n-1})
\not=(v_0,\cdots,v_{n-1})$ and $u_i,v_i\in\{0,\cdots,q-1\}$ for $0\leq i\leq n-1$ then $(\bar u,\bar v)$ is $(2^{-q},n)$-separated.
\(i) Let $\bar u=(u_n)_{n\in\IZ}\in\Gamma_G$. If $\bar v=(v_n)_{n\in\IZ}\in
{{\cal C}}^G(\bar u,V)$, then $D(u_j,v_j)\leq 2^{-(p+2)}$ for all $j\in\IZ$. Consequently for all $0\leq i<n$ $$d(\sigma^i(\bar u),\sigma^i(\bar v))
=\sum_{k\in\IZ}\frac{D(u_{i+k},v_{i+k})}{2^{|k|}}
\leq \sum_{k\in\IZ}\frac{2^{-(p+2)}}{2^{|k|}}
\leq 3\cdot 2^{-(p+2)}< 2^{-p}.$$
\(ii) Let $0\leq i\leq n-1$ such that $u_i\not= v_i$. By hypothesis, $u_i,v_i\leq q-1$. Suppose that $u_i<v_i$. Then ${\displaystyle}d(\sigma^i (\bar u),\sigma^i (\bar v))\geq D(u_i,v_i)=
2^{-u_i}(1-2^{-(v_i-u_i)})\geq 2^{-q}$.
\[theo:hloc-maximal-measure\] Let $G$ be a connected oriented graph of finite entropy on the set of vertices $\IN$. If $h_{loc}(\Gamma_G)<h(G)$, then the graph $G$ is strongly positive recurrent and the Markov chain $(\Gamma_G,\sigma)$ admits a maximal measure.
Fix $C$ and ${\varepsilon}>0$ such that $h_{loc}(\Gamma_G,{\varepsilon})<C<h(G)$. Let $p$ be an integer such that $2^{-(p-1)}<{\varepsilon}$. Let $G'$ be a finite subgraph $G'$ such that $h(G')>C$ and let $V$ be a finite subset of vertices such that $V$ is connected and contains the vertices of $G'$ and the vertices $\{0,\cdots,p\}$. Define $W=\overline{V}$, $V_q=\{n\leq q\}$ and $W_q=V_q\setminus V=W\cap V_q$ for all $q\geq 1$.
Our aim is to bound $t_{uu'}^{W}(n)=t_{uu'}^{\overline {V}}(n)$. Choose $u,u'\in V$ and let $(w_0,\cdots,w_{n_0})$ be a path between $u'$ and $u$ with $w_i\in V$ for $0\leq i\leq n_0$. Fix $n\geq 1$. One has ${\displaystyle}t_{uu'}^W(n)=\lim_{q\to+\infty} t_{uu'}^{W_q}(n)$.
Fix $\delta_0>0$ such that $$\forall \delta\leq\delta_0,\limsup_{n\to+\infty}\frac{1}{n}
\sup_{\bar v\in\Gamma_G}\log s_n(\delta,B_n(\bar v,{\varepsilon}))<C.$$ Take $q\geq 1$ arbitrarily large and $\delta\leq \min\{\delta_0,
2^{-(q+1)}\}$. Choose $N$ such that $$\forall n\geq N, \forall \bar v\in\Gamma_G, \frac{1}{n}\log
s_n(\delta,B_n(\bar v,{\varepsilon}))<C.
\label{eq:N}$$
If $t_{uu'}^{W_q}(n)\not=0$, choose a path $(v_0,\cdots,v_n)$ such that $v_0=u, v_n=u'$ and $v_i\in W_q$ for $0<i<q$. Define $\bar v^{(n)}=(v^{(n)}_i)_{i\in\IZ}$ as the periodic path of period $n+n_0$ satisfying $v^{(n)}_i=v_i$ for $0\leq i\leq n$ and $v^{(n)}_{n+i}=w_i$ for $0\leq i\leq n_0$.
Define the set $E_q(n,k)$ as follows (see Figure \[fig:Eq\]): $$E_q(n,k)=\left[{{\cal C}}^{V_q}(\bar v^{(n)},V)\right]_0^{k(n+n_0)}\cap
\left[\bar v^{(n)}\right]_{-\infty}^{0}\cap
\left[\bar v^{(n)}\right]_{k(n+n_0)}^{+\infty}.$$
![The set $E_q(n,k)$ ($k=2$ on the picture): $\bar{v}^{(n)}$ (in solid) is a periodic path, $\bar u$ (in dashes) is a element of $E_q(n,k)$. Between the indices $0$ and $k(n+n_0)$, $\bar v^{(n)}$ and $\bar u$ coincide when $v^{(n)}_i$ is in $V$ and $\bar v^{(n)}$ and $\bar u$ are in $W_q$ at the same time. Before $0$ or after $k(n+n_0)$, the two paths coincide\[fig:Eq\].](markov-fig3bis.eps)
The paths in $E_q(n,1)$ are exactly the paths counted by $t_{uu'}^{W_q}(n)$ which are extended outside the indices $\{0,\cdots,n\}$ like the path $\bar v^{(n)}$, thus $\# E_q(n,1)=t_{uu'}^{W_q}(n)$. Similarly, $\# E_q(n,k)=\left(t_{uu'}^{W_q}(n)\right)^k$.
By definition, $E_q(n,k)\subset {{\cal C}}^G(\bar v^{(n)},V)$ and $\{0,\cdots,p\}\subset V$ thus $E_q(n,k)\subset B_{k(n+n_0)}(\bar v^{(n)},{\varepsilon})$ by Lemma \[lem:C-Bn\](i). Moreover, if $(w_i)_{i\in\IZ}$ and $(w_i')_{i\in\IZ}$ are two distinct elements of $E_q(n,k)$, there exists $0\leq i <k(n+n_0)$ such that $w_i\not=w_i'$ and $w_i,w_i'\leq q$, thus $E_q(n,k)$ is a $(\delta,k(n+n_0))$-separated set by Lemma \[lem:C-Bn\](ii). Choose $k$ such that $k(n+n_0)\geq N$. Then by Equation (\[eq:N\]) $$\# E_q(n,k)\leq s_{k(n+n_0)}(\delta,B_{k(n+n_0)}(\bar v^{(n)},{\varepsilon}))
< e^{k(n+n_0)C}.$$ As $\# E_q(n,k)=\left(t_{uu'}^{W_q}(n)\right)^k$, one gets $t_{uu'}^{W_q}(n)<e^{(n+n_0)C}$. This is true for all $q\geq 1$, thus $$t_{uu'}^W(n)=\lim_{q\to +\infty}t_{uu'}^{W_q}(n)\leq e^{(n+n_0)C}$$ and $$\tau_{uu'}^W=\tau_{uv'}^{\overline{V}}\leq C<h(V).$$ Theorem \[theo:GZ-et-reciproque\] concludes the proof.
Define the entropy at infinity as $h_{\infty}(G)=\lim_{n\to+\infty}h(G\setminus G_n)$ where $(G_n)_{n\geq 0}$ is a sequence of finite graphs such that $\bigcup_n G_n=G$. The local entropy satisfies $h_{loc}(\Gamma_G)\geq h_{\infty}(G)$ but in general these two quantities are not equal and the condition $h_{\infty}(G)<h(G)$ does not imply that $G$ is strongly positive recurrent. This is illustrated by Example \[ex:R=L\] (see Figure \[fig:G-G’\]).
[10]{}
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Sylvie [Ruette]{} – Institut de Mathématiques de Luminy – CNRS UPR 9016 – 163 avenue de Luminy, case 907 – 13288 Marseille cedex 9 – France\
[*E-mail :*]{} [[email protected]]{}
|
Video files primarily come in two types: with a file header, and without a file header. The file header records global information of the video file, for example, size and duration of each frame, position of a key frame, and so on. A video file without a file header is composed of many video file packages. Although there is no dedicated header for storing the global information of the file, information such as the position of the key frame and a timestamp is stored in specific video file packages.
Video dragging is a common operation performed when a user watches a video. In the process of watching the video, the user can drag a progress bar to locate the current playing position of the video quickly so as to find a segment of interest quickly. Because a client has to start decoding and playing from the position of the key frame of the video, a player needs to locate the key frame of the video in the process of dragging the video.
In the prior art, the video dragging operation depends on the file header of the video file. By parsing the file header, the position information of all key frames of the video file stored in the file header is obtained, and video data that begins with a key frame is sent to the client, where the key frame is the closest to a position from which the video is requested to be dragged, and the client decodes and plays the video data, thereby completing the video dragging operation. However, if the video file of a specific format has no file header, the video file cannot be played after being dragged, so the video file can only be played sequentially.
In addition, in the prior art, a server generally uses a fragmented buffer architecture for storing video files. Under this architecture, for a video, the server only stores a part of segments of the video. In the process of dragging the video, if a target position of dragging goes beyond the range of the video segments stored on the server, the dragging operation cannot be completed, which deteriorates user experience. |
# Bouvet Island
---
description: Lykketoppen, -54.4362/3.3138
components:
country: Bouvet Island
country_code: bv
expected: |
Bouvet Island, Norway
|
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