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Irene Tracey
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Career
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Awards and honours In 2008, Tracey was awarded the triennial Patrick Wall Medal from the Royal College of Anaesthetists and in 2009 was made a Fellow of the Royal College of Anaesthetists (FRCA) for her contributions to the discipline. She won the Suffrage Science award in 2014. In 2015 she was elected a Fellow of the Academy of Medical Sciences (FMedSci) and in 2017 won the Feldberg Foundation prize, followed in 2018 by the British Neuroscience Association’s Outstanding Contribution to Neuroscience award. In 2020, Tracey was elected a member of the Academia Europaea (MAE), and in 2022 she has been elected an honorary fellow of The Physiological Society. In the 2022 New Year Honours List, Tracey was appointed a Commander of the Order of the British Empire (CBE) by Queen Elizabeth II for services to medical research. She received her CBE from Charles III at Windsor Castle on 16 November 2022 during the first Investiture held by His Majesty following his Accession. In 2023 she was elected a Fellow of the Royal Society.
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Irene Tracey
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Career
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Publications Tracey has published over 200 original papers; Semantic Scholar lists her as a contributor to over 400 publications including the following publications: Pain 2012 Refresher Courses: 14th World Congress on Pain Pain: A Ladybird Expert Book Wall & Melzack's Textbook of Pain: Expert Consult Dissociating Pain from Its Anticipation in the Human Brain Exacerbation of Pain by Anxiety Is Associated with Activity in a Hippocampal Network Imaging how attention modulates pain in humans using functional MRI The Cerebral Signature for Pain Perception and Its Modulation A common neurobiology for pain and pleasure Neurocognitive aspects of pain perception Multidisciplinary research priorities for the COVID-19 pandemic: a call for action for mental health science Public engagement As part of her passion for public understanding of science, Tracey has made numerous media appearances, including on BBC Radio 4's All in the Mind.She has created and presented two radio programmes about pain: From Agony to Analgesia, a two-episode BBC programme in 2017, and The Anatomy of Pain, a four-part, BBC Discovery series in 2018.Tracey's work on pain has also featured in two BBC Horizon TV documentaries; a Science Museum exhibition in London; public lectures at DANA, the Oxford Museum of Natural History, and the Cheltenham Science Festival; and articles in New Scientist, BBC Science Focus, and Good Housekeeping.The Lancet and The New Yorker have both run profiles of her. She was interviewed by Jim Al-Khalili in April 2019 for BBC Radio 4’s The Life Scientific. She was also listed in The Times’ Life Sciences Global Power List in 2020.
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Irene Tracey
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Personal life
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Tracey married the climate physicist Myles Allen in 1994 and has three children.
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GNAT2
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GNAT2
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Guanine nucleotide-binding protein G(t) subunit alpha-2 is a protein that in humans is encoded by the GNAT2 gene.
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GNAT2
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Function
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Transducin is a 3-subunit guanine nucleotide-binding protein (G protein) which stimulates the coupling of rhodopsin and cGMP-phosphodiesterase during visual impulses. The transducin alpha subunits in rods and cones are encoded by separate genes. This gene encodes the alpha subunit in cones.
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Gluteal tuberosity
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Gluteal tuberosity
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The gluteal tuberosity is the lateral one of the three upward prolongations of the linea aspera of the femur, extending to the base of the greater trochanter. It serves as the principal insertion site for the gluteus maximus muscle.
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Gluteal tuberosity
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Structure
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The gluteal tuberosity is the lateral prolongation of three prolongations of the linea aspera that extending superior-ward from the superior extremity of the linea aspera on the posterior surface of the femur.The gluteal tuberosity takes the form of either an elongated depression or a rough ridge. It extends from the linea aspera nearly vertically superior-ward to the base of the greater trochanter. Its superior part is often elongated to form a roughened crest, upon which a more or less prominent rounded tubercle - the third trochanter - is occasionally developed.
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Gluteal tuberosity
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Structure
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Attachments The gluteal tuberosity is the principal site of insertion of the gluteus maximus muscle, accepting the muscle's tendon (the gluteus maximus muscle additionally also inserts onto the iliotibial tract).
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Computers & Geosciences
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Computers & Geosciences
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Computers & Geosciences is a scientific journal published monthly by Elsevier on behalf of the International Association for Mathematical Geosciences. It contains research and review papers in computing applied to geosciences. Its impact factor is 3.372.
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Wilting
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Wilting
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Wilting is the loss of rigidity of non-woody parts of plants. This occurs when the turgor pressure in non-lignified plant cells falls towards zero, as a result of diminished water in the cells. Wilting also serves to reduce water loss, as it makes the leaves expose less surface area. The rate of loss of water from the plant is greater than the absorption of water in the plant. The process of wilting modifies the leaf angle distribution of the plant (or canopy) towards more erectophile conditions.
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Wilting
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Wilting
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Lower water availability may result from: drought conditions, where the soil moisture drops below conditions most favorable for plant functioning; the temperature falls to the point where the plant's vascular system cannot function; high salinity, which causes water to diffuse from the plant cells and induce shrinkage; saturated soil conditions, where roots are unable to obtain sufficient oxygen for cellular respiration, and so are unable to transport water into the plant; or bacteria or fungi that clog the plant's vascular system.Wilting diminishes the plant's ability to transpire and grow. Permanent wilting leads to plant death. Symptoms of wilting and blights resemble one another.
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Wilting
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Wilting
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The plants may recover during the night when evaporation is reduced as the stomata closes.In woody plants, reduced water availability leads to cavitation of the xylem.
Wilting occurs in plants such as balsam and holy basil. Wilting is an effect of the plant growth-inhibiting hormone, abscisic acid.
With cucurbits, wilting can be caused by the squash vine borer.
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COVID-19 pandemic in Venezuela
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COVID-19 pandemic in Venezuela
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The COVID-19 pandemic in Venezuela was a part of the worldwide pandemic of coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first two cases in Venezuela were confirmed on 13 March 2020; the first death was reported on 26 March. However, the first record of a patient claiming to have symptoms of coronavirus disease dates back to 29 February 2020, with government officials suspecting that the first person carrying the virus could have entered the country as early as 25 February.Venezuela is particularly vulnerable to the wider effects of the pandemic because of its ongoing socioeconomic and political crisis causing massive shortages of food staples and basic necessities, including medical supplies. The mass emigration of Venezuelan doctors has also caused chronic staff shortages in hospitals.To prevent the spread of the disease into Venezuela, the governments of Brazil and Colombia temporarily closed their borders with Venezuela. The Colombian government had placed 1 October as a tentative date for reopening the border.In February 2021, Venezuela started vaccinations with the Russian Sputnik V COVID-19 vaccine and a vaccine produced by the Chinese company Sinopharm. It aimed to vaccinate 70 percent of the population by the end of 2021. An academic survey found that by the 1 September 2021, 10% of the Venezuelan population was fully vaccinated. By the end of 2021, Venezuela had administered 30,049,714 doses of vaccine, about 52.7% of the country's population.
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COVID-19 pandemic in Venezuela
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Background
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In January, Venezuela's Ministry of Popular Power for Health announced that the Rafael Rangel National Institute of Hygiene (Spanish: Instituto Nacional de Higiene Rafael Rangel) in Caracas would act as the observatory for non-influenza respiratory viruses, including coronaviruses in humans. It is the only health institution in the country with the ability to diagnose respiratory viruses and to operate logistically across the 23 states, the Capital District and the Federal Dependencies of Venezuela.In February, the Venezuelan government announced that the country had imposed epidemiological surveillance, restrictions and a plan to detect individuals with COVID-19 at the Simón Bolívar International Airport in Maiquetía, Venezuela's main international airport. They said Venezuela would receive diagnostic kits for the virus strain from the Pan American Health Organization (PAHO).
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COVID-19 pandemic in Venezuela
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Timeline
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Timeline of 2020 March Venezuela reported its first official cases of coronavirus disease on 13 March 2020. However, several days earlier a suspected case became controversial due to the state treatment of a whistleblower. On 7 March, Fe y Alegría reported that a suspicious medical case was registered in Zulia: a 31-year-old who was not from Venezuela was examined at the Pedro Iturbe Hospital and later transferred to the University Hospital of Maracaibo. The patient had apparent symptoms and was discharged days later. The state governor, Omar Prieto, asked the Public Ministry to investigate a University of Zulia professor, Freddy Pachano, for bringing attention to the suspected case in the state, and the NGO Espacio Público condemned Prieto for ordering such an investigation. Nicolás Maduro declared a ban on protests on 12 March before cases were confirmed in Venezuela to prevent the spread of the outbreak, as well as a ban on flights from Europe and Colombia.The first cases, two on 13 March, were registered in the state of Miranda. Colombian president Iván Duque closed the border with Venezuela effective from the next day. On 14 March, the official number of cases rose by eight (to ten), and had spread across four states (Miranda, Apure, Aragua and Cojedes). Communication Minister Jorge Rodríguez announced that flights from Panama and the Dominican Republic to the country would be suspended for 30 days, beginning on 15 March.Stay-at-home orders were announced on 15 March, when the country registered another seven cases, and introduced the next day across six states and the Caracas area. The orders were dubbed "collective quarantine"; there are exceptions for transportation, health, and delivery of food. It was on the first day of the quarantine across six states, 16 March, that Argentina's ambassador in Venezuela, Eduardo Porretti, tested positive for the virus, and Nicolás Maduro announced that sixteen new cases were confirmed, bringing the total to 33. Based on this, Maduro extended the quarantine to the entire country.When Venezuela went into lockdown on 17 March, authorities in Brazil partially closed their border with Venezuela. Brazilian Health Minister Luiz Henrique Mandetta had urged closure of the border due to Venezuela's collapsing health system. Venezuelan Vice President Delcy Rodríguez announced three more cases the same day. In the afternoon, a patient that would later test positive for coronavirus fled from a hospital in Propatria, in west Caracas.On 18 March, Delcy Rodríguez reported that the numbers of cases had not changed since the previous day. By 21 March, the government reported 70 confirmed cases in the country.Economic measures to deal with the consequences of the pandemic were announced on 22 March, along with seven more cases. Rent and credit payments were suspended for six months, accompanied by compensation in local currency for property owners and medium-sized businesses. The measures also extended a 2015 policy that prevents companies from firing employees through December 2020. The government said that no household would have their utilities cut off. The government also took over payment of wages for workers in non-essential companies that were not operating during the national emergency and gave workers in the informal sector a one-off social security payment.The first confirmed death from the disease was announced on 26 March. Another death was reported the next day. Also on 27 March, Delcy Rodríguez met with Prime Minister of Trinidad and Tobago Keith Rowley, with the meeting focused on the strategy being deployed in both countries to combat the pandemic. There was also controversy on this day when NGO PROVEA revealed that around ninety people coming from Cúcuta, Colombia, were forcefully isolated on 25 March by the National Guard in Barqusimeto, Lara, without food or proper sanitary conditions.
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COVID-19 pandemic in Venezuela
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Timeline
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April Information Minister Jorge Rodríguez first reported that there were more recoveries than new infections in Venezuela on 11 April. Delcy Rodríguez and Nicolás Maduro announced an extension of the national quarantine and state of alarm for 30 days.After a sudden rise of the number of cases in Margarita Island, Nicolás Maduro announced a curfew the entire state of Nueva Esparta on 19 April. 41 of the cases at the time, were related to Roberto Vahlis Baseball Academy. Some of its member had just arrived from Dominican Republic by plane.A 29-year-old man was killed by two gunshots to the head during riots in Upata, Bolívar state, caused by food and fuel shortages that were exacerbated by the lockdown since mid-March. The message "Murió por hambre" (He died of hunger) was written in chalk besides the pool of blood that he left. Colectivos participated in the police operation to repress the riots, who used their motorcycles despite the fuel shortages. At least two people were injured and thirty others were arrested.
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COVID-19 pandemic in Venezuela
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Timeline
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May Delcy Rodríguez reported the first cases of COVID-19 in Amazonas and Carabobo on 10 May. That left Delta Amacuro as the only unaffected state at that moment.Nicolás Maduro, on 12 May, extended the lockdown for 30 more days. The restrictions to national flights were also extended 30 days by the national aeronautics institute INAC (Spanish: Instituto Nacional de Aeronáutica Civi).The first patient with COVID-19 in Delta Amacuro was reported on 13 May. As of that date, all states of Venezuela have reported at least a case of COVID-19.Mid May, Maracaibo reports a major outbreak of cases related to Las Pulgas, a popular market. The market was closed.After 34 days without a death report, a new deceased by COVID-19 was reported on 26 May.
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COVID-19 pandemic in Venezuela
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Timeline
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June The easing of the lockdown started on 1 June, with gyms and shopping centers opening. Schools, courts and bars remain closed.As of 9 June the Venezuelan government had reduced re-emigrations to 400 per day, three days a week, a reduction of 80% from previous levels.The state of alarm was extended a third time for an additional month on 12 June.Opposition and health care workers in Maracaibo announced on the fourth week of June that hospitals in the city were filled and dozens of doctors and nursed were infected. William Barrientos, a surgeon and opposition legislator, said that 40 health workers were infected with the virus. A nurse died in the Maracaibo Military Hospital. The authorities enabled 20 small and midsized hotels in Maracaibo to treat patients. Measures were increased in Zulia, Caracas and eight other states.
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COVID-19 pandemic in Venezuela
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Timeline
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July Diosdado Cabello, vice-president of the United Socialist Party of Venezuela and president of the pro-government Constituent National Assembly announced he tested positive for COVID-19 on 9 July.Tareck El Aissami, the Minister of Petroleum and Omar Prieto, the Governor of Zulia also tested positive on 10 July.A member of the National Constituent Assembly and the Governor of the Capital District, Darío Vivas tested positive for COVID-19 on 19 July.
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COVID-19 pandemic in Venezuela
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Timeline
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August Venezuela Minister of Communication and Information Jorge Rodríguez tested positive for COVID-19 on 13 August. On the same day, Darío Vivas died of COVID-19 at the age of 70.
Timeline of 2021 February In February 2021, Venezuela started vaccinating health care workers with the Russian Sputnik V COVID-19 vaccine and started using a vaccine produced by the Chinese company Sinopharm. It aimed to vaccinate 70 percent of the population by the end of 2021.
March In March 2021, Juan Guaidó and the opposition National Assembly approved 30 million dollars to import Oxford–AstraZeneca vaccines. Delcy Rodríguez announced that permits for its use would not be conceded. Venezuela decided not to approve use of the Oxford–AstraZeneca vaccine when several European countries suspended their vaccination programmes due to concerns over possible side-effects.
October School children and university students started going back to their classes in October 2021. The government claimed that 56% of the population had been vaccinated but Johns Hopkins University reported that less than 22% of the population had been fully vaccinated. Venezuelans could get vaccinated from the age of 11.
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COVID-19 pandemic in Venezuela
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Measures
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Executive response On 12 March, Nicolás Maduro declared a public health emergency in the country and suspended all inbound flights from Europe and Colombia for 30 days. He also announced that public gatherings were to be suspended and that the government would be evaluating whether or not to suspend flights from other regions in the coming weeks. According to Maduro, there had been 30 suspected cases in Venezuela, but these had all tested negative.After the first cases in the country were confirmed, Vice-president Delcy Rodríguez instructed all passengers of the 5 March and 8 March flights of Iberia 6673 to immediately enter into a mandatory preventive quarantine because two passengers tested positive.Rodríguez announced that all classes would be suspended at public and private schools from Monday 16 March until further notice, while Néstor Reverol announced that the government would provide border control authorities with face masks, gloves and thermometers, without mentioning supplies for citizens and hospitals. Reverol also announced that the operational control of all the police forces would be transferred to the Armed Forces in order to coordinate the action and contingency plan.On 14 March, authorities arrested two people for spreading false information about the virus, recording a video about fake cases in Los Teques. SUDEBAN, the government's department related to banks and financial institutions, announced the suspension of banking activities, effective from 16 March.Defense Minister Vladimir Padrino López announced that, effective from 16 March, the Armed Forces would control access to the six states and the Capital District declared by Nicolás Maduro to be in quarantine.On 16 March, Maduro reversed the country's official position against the International Monetary Fund (IMF), asking the institution for US$5 billion to combat the pandemic, a first during Maduro's presidency; he has been a critic of the institution. The IMF also has had conflicts with the Venezuelan government in the past, as Maduro's predecessor Hugo Chávez had pledged to cut ties with the fund in 2007, and the IMF suspended US$400 million in special drawing rights during the Venezuelan presidential crisis in 2019. The IMF rejected the deal as it was not clear, among its member states, on who it recognizes as Venezuela's president, Nicolás Maduro or Juan Guaidó. According to a report by Bloomberg, the Maduro administration also tried to request aid of $1 billion from the IMF after the first request was denied.On 19 March, Rodríguez announced that 4,000 diagnosis kits were delivered from China to test for coronavirus disease. The government said that the Chinese diagnosis kits would benefit 300,000 Venezuelans and thanked the Chinese government and President Xi Jinping for their generosity. In a separate measure, Venezuela's INEA maritime authority has prohibited crews aboard ships docking in the country's ports from disembarking. The same day, Maduro announced that he had received a letter from the United Nations (UN) Resident Coordinator and United Nations Development Programme (UNDP) Resident Representative Peter Grohmann, confirming that the organization "is ready to support the Venezuelan government in its fight against COVID-19." Maduro stressed that the UN has taken concrete actions, particularly in the areas of health and water, sanitation and hygiene, and "will support the Ministry of Health in the care and containment of the coronavirus." Likewise, they will offer support in the disclosure of reliable and updated information. China provided a further one million rapid antigen test kits in March 2020.On 20 March, Maduro said that Russia was considering "a significant donation of special humanitarian aid" to the country, such as medical equipment and kits for the diagnosis of COVID-19, which were expected to arrive by the following week. On 23 March, Foreign Minister Jorge Arreaza and Russian ambassador Sergei Melik-Bagdasarov announced that 10,000 diagnosis kits had been delivered from Russia, with more to be supplied in future shipments. In a tweet, Maduro thanked the Russian government and President Vladimir Putin for their generosity and for standing in solidarity with the Venezuelan people.Maduro announced several economic measures on 23 March to deal with unemployment, the assumption of wage payment by the state, the suspension of rent and credit interests payments, the assignment of new bonds, the flexibility of new loans and credit, the prohibition of the cutting of telecommunication services and the guarantee of CLAP (Local Committees for Supply and Production) supplies.
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COVID-19 pandemic in Venezuela
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Measures
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Russian Sputnik V vaccine In September 2020, Maduro suggested administering the Russian Sputnik V COVID-19 vaccine to the candidates in the upcoming legislative elections so that they could campaign safely. In October 2020, the Venezuelan government received a shipment of the Sputnik V vaccine. Venezuela was the first country in Latin America to participate in the Sputnik V trial, which involved around 2000 Venezuelan participants. In December 2020, the Venezuelan government signed a contract to acquire enough doses of the Sputnik V vaccine for 10 million people.
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COVID-19 pandemic in Venezuela
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Measures
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Doctors without Borders The international aid group Doctors without Borders (MSF) stopped operations in Caracas in November 2020 due to government restrictions. About 150 doctors, that worked in Petare, a poor neighborhood, risk to lose their jobs. Maribelsi Mancera, head nurse for MSF, stated that they do not understand the government decision. Miguel Pizarro, Venezuela's representative in the United Nations, regretted the decision and criticized the government behavior against non governmental organizations trying to help with the crisis.
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COVID-19 pandemic in Venezuela
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Measures
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National Assembly response In March 2020, Juan Guaidó said that the country is experiencing one of the most serious health crises in its history, caused by the inaction of the Maduro government, and announced a series of measures in order to take "responsible measures against the pandemic." These include the postponement of opposition protests and the creation of the Special Health Commission. Guaidó also called for the entry of humanitarian aid from the United Nations, and said that health services are not impacted by international sanctions.The Committee of Electoral Candidacies, in charge of appointing a new National Electoral Council (CNE), announced that it would suspend its meetings because of the pandemic.Julio Castro, head of the Special Health Commission appointed by Juan Guaidó, said on 16 March that face masks are a prevention measure useful only for one day, and that once used the mask loses its effectiveness and can become a source of infection; he also said that Venezuelans have to take additional measures to deal with the pandemic.In March 2020, National Assembly deputy Jesús Yánez announced that the government of Taiwan donated 1,000 surgical masks as a measure to prevent the coronavirus pandemic. The masks were distributed in five stations of the Caracas Metro (Plaza Sucre, Pérez Bonalde, Plaza Venezuela, Chacao and Petare). Yánez highlighted that the metro is a means of transportation used by a large part of the population and is a breeding ground for the pandemic due to the crowding of people in closed spaces, should any one of them be carrying the virus.In March 2020, Guaidó's Special Health Commission collected 3,500 protection kits for caregivers at five hospitals on 16 March.On 21 March, Guaidó announced that he delivered medical kits to protect the health sector from the coronavirus pandemic. On his official Twitter account, he shared a video expressing that "We are protecting a sector that today is giving everything: the health sector, our doctors and nurses. To support them is to support us all. We must bring this help to hundreds who need it", and concluded "We can contain this emergency. Venezuela is in our hands." Guaidó also announced the creation of the Human Rights Observatory as a response to the increase of human rights violations in the country during the social isolation orders.Guaidó called for the creation of a "national emergency government", not led by Maduro, on 28 March. According to Guaidó, a loan of US$1.2 billion was ready to be given in support of a power-sharing coalition between pro-Maduro officials, the military and the opposition in order to fight the pandemic in Venezuela. If accepted, the money would go to assist families affected by the disease and its economic consequences.Juan Guaidó announced a financial help to health workers during the pandemic supported by Venezuelan funds frozen in the Federal Reserve Bank of New York. In August 2020, opposition parties announced that the request had been granted by the United States Department of the Treasury. In the statement, an amount of 300 USD would be granted to 62,000 health workers, with US$100 a month starting 23 August 2020 for those registered. The resources were planned to be distributed through AirTM, a digital payment platform, but after the announcement the access to the platform was blocked in Venezuela. A manual to circumvent the internet block using a virtual private network (VPN) was published afterwards. An amount of US$4.5 million to support Venezuelans at risk of death, was also announced.The "Health heroes" program of Guaidó is the first time that frozen funds in United States, as part of sanctions on Venezuela, were directly transferred to Venezuelan health workers. By November 2020, the second wave of payments were granted.
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COVID-19 pandemic in Venezuela
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Measures
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Joint response In June 2020, Carlos Alvarado, Maduro's health minister and Julio Castro, representing Juan Guaidó and the National Assembly, signed an unprecedent joint agreement with the World Health Organization and the Pan American Health Organization. The accord seeks cooperation between Maduro's government and the opposition deputies of the National Assembly to handle the pandemic and seek funds.According to opposition lawmakers, Maduro administration violated the agreement in January 2021, as resources and equipment to handle the pandemic were transferred to facilities controlled by Maduro administration.
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COVID-19 pandemic in Venezuela
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Measures
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Other responses Baltazar Porras, Apostolic Administrator of Caracas, announced the suspension of ecclesiastic activities on 15 March, while assuring that temples would remain open, asking Venezuelans to avoid crowded places and to remain calm.The Health Ministry certified the microbiology laboratory of the University of the Andes, in Mérida state, to start carrying out tests to detect the presence of SARS-CoV-2, the coronavirus responsible for the COVID-19 disease, on 18 March. Once the necessary supplies are received, the laboratory will be able to perform up to 20 tests per day and would be the second laboratory in the country to perform detection tests after the National Hygiene Institute in Caracas; it would be expected to carry out tests for the states of Mérida, Táchira, Trujillo and Barinas, and possibly other states in the west, as it is closer than the Hygiene Institute in Caracas.Three men that were playing dominoes outdoors during the quarantine were murdered on 21 March in the 23 de Enero parish, in Caracas, and two more were injured. According to neighbors and relatives, a dozen members of the colectivo Tres Raíces arrived while they were playing and were responsible for their deaths; the witnesses accused the colectivo members of being linked with Iris Varela, Minister of Popular Power for the Prison Service, being linked to a CICPC officer, and of wearing FAES and National Police uniforms, announcing that they would protest as a response to the killings, in defiance of the quarantine. The colectivo denied the accusations of being related to the government or police, saying that the murders were instead motivated by revenge.On late March 2020, the colectivos Tres Raíces and La Piedrita started imposing a paramilitary-enforced curfew in the 23 de Enero parish, increasing repression and imposing closure times to businesses.
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COVID-19 pandemic in Venezuela
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Reactions
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Government reactions Maduro asked people to not politicize the pandemic, while also expressing concern as to how the country could control the pandemic with the United States-imposed sanctions. Maduro called on US President Donald Trump to lift the sanctions so the country could acquire necessary medical supplies.Juan Guaidó said that since the start of the pandemic, human rights violations by Maduro's administration had increased, citing the murders in the 23 de Enero parish, the arrest of Darvinson Rojas, and human rights abuses against political prisoners, who are held in prisons with a high infection risk. Guaidó announced the creation of a Human Rights Observatory as a response.
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COVID-19 pandemic in Venezuela
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Reactions
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Other reactions The Venezuelan Medical Federation expressed condemnation at how a medic in Zulia was forced to leave for Colombia after denouncing the inability of Venezuela to cope if the disease arrived; it also asked for the release of the political prisoners in the country, who are vulnerable to the virus, specifically Roberto Marrero, Juan Requesens, and other lawmakers.In the Anzoátegui state, nurses denounced the lack of face masks, gloves and disposable gowns.Transparencia Venezuela asked for transparency and access to public information regarding the handling of the emergency.Media outlets, such as El Nacional, denounced the price increase of face masks. Outlets have also reported on the violation of the quarantine for reasons such as buying food, medicines, and both cleaning and hygiene products, as well as the public services crisis, including the lack of drinking water, electric power, cooking gas, telephone signal and waste collection.
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COVID-19 pandemic in Venezuela
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Reactions
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International sanctions The Virtual United States Embassy in Venezuela rejected claims from Nicolás Maduro and Jorge Arreaza that sanctions are preventing the government from purchasing medical supplies, saying that "medicines, medical supplies, spare parts and components for medical devices in Venezuela, or to people from third countries who buy specifically for resale from Venezuela are excluded from the sanctions." Days later, Foreign Minister Jorge Arreaza called the statements "the height of impudence and falsehood." He declared that Venezuelan government assets worth more than US$5 billion were blocked overseas, in addition to "Venezuela's ban on access to the international banking system."Former Attorney General Luisa Ortega Díaz declared that Maduro "lied" when saying that there were no medicines in the country because of the sanctions, saying that the reasons were incompetence and corruption. The US Acting Assistant Secretary for Western Hemisphere Affairs Michael Kozak also accused Maduro of lying, saying that U.S. sanctions never block food or medicine purchases. He emphasized that shortages in Venezuela resulted from "the regime's theft of the nation's wealth."On 24 March, UN High Commissioner for Human Rights Michelle Bachelet called for any sanctions imposed on Venezuela and other countries facing the pandemic such as Cuba, Iran, and Zimbabwe to be "urgently reevaluated" in order to avoid pushing strained medical systems into collapse. In a statement, Bachelet said: "At this crucial time, both for global public health reasons, and to support the rights and lives of millions of people in these countries, sectoral sanctions should be eased or suspended." Bachelet also accentuated the need to protect health workers in these countries as authorities should not punish professionals that point out the deficiencies in the state response to the crisis.On 10 June 2021, Venezuelan officials announced they have been unable to complete payments for available vaccines from the COVAX program. Initially the transaction of $120 million was to be paid per agreement with Juan Guaidó using funds frozen in the United States via Washington's sanctions against Maduro, but later Venezuelan officials said they would use their own funds. Subsequently, Swiss bank UBS confirmed that four operations, totaling $4.6 million, "were blocked and under investigation." Vice President Delcy Rodríguez remarked the remaining payment of $10 million could not be completed. UBS would not specify further due to legal and regulatory reasons. The Maduro government said for months that it was unable to pay for the COVAX program because of U.S. sanctions. Venezuela expressed interest in the Janssen and Novavax vaccines after the requested shipment of AstraZeneca/Oxford vaccines was never approved by national authorities. In August 2021, those payments were reportedly unblocked, and Venezuela will receive 6.2 million doses of the Sinopharm BIBP vaccine and CoronaVac through the program.
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COVID-19 pandemic in Venezuela
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Reactions
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International concern International concern was raised before the first cases were reported, as Venezuela's health care system has completely collapsed due to the ongoing crisis, meaning its already suffering population is especially vulnerable to the spread of a pandemic.Per the Global Health Security Index, Venezuela's health system is ranked among the worst in the world in its ability to detect, quickly respond, and mitigate a pandemic. Hospitals are plagued by chronic shortages of supplies, including eye protectors, gloves, masks, and soap. Due to ongoing shortages of resources, hospitals must also constantly deal with chronic lack of staff, thus making the response to treating a large number of infected patients significantly more challenging. Patients are also often turned away at hospitals due to overcrowding, or asked to bring in their own gauze, IV solution, or syringes, while there are often no hygiene facilities like toilets, and power outages are a regular occurrence.The Pan American Health Organization (PAHO) said that it would be prioritizing Venezuela alongside Haiti and other Central and South American countries because of "challenges to their health systems."Associated Press reported that experts are worried that the Venezuelan refugee crisis could worsen the spread of the virus.
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COVID-19 pandemic in Venezuela
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Reactions
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Prison system Reuters reported that Venezuela's notoriously overcrowded and unsanitary prisons could spread the coronavirus "like a fast-moving fire." Venezuelan prisons frequently lack bathrooms, people sleep on floors, and many inmates spend their days without shirts or shoes on, in part to combat the infernal heat of windowless facilities. This has caused US Secretary of State Mike Pompeo to demand the Maduro government release six Citgo executives, held in prison since 2017, on humanitarian grounds. Pompeo said that all six men have weakened immune systems and "face a grave health risk if they become infected" with the coronavirus pandemic.On 18 March, 84 out of 518 inmates escaped from a prison in San Carlos, Zulia, after restrictions against the pandemic were announced, including jail visits. Mayor Bladimir Labrador declared that ten prisoners were killed during the prison break and that two policemen were detained for complicity. According to Carlos Nieto Palma from the NGO Ventana a la Libertad, the suspension of visits directly affects the prisoner's nutrition, given that there was no state-sponsored program to feed them. The NGO PROVEA denounced "grave human rights violations" after a military spokesperson announced the "neutralization" of 35 escapees. State authorities later declared that there were eight deaths.
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COVID-19 pandemic in Venezuela
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Reactions
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Hearing over the Esequibo The International Court of Justice (ICJ) planned to discuss Guyana and Venezuela border dispute over Guayana Esequiba in March 2020. The hearing was postponed due to the pandemic. In April, Guyana reported cases of COVID-19 in the disputed territory.The first hearing was finally carried out on 30 June 2020, but Venezuela did not participate saying that the ICJ lacked jurisdiction. The hearing was held by video conference due to the pandemic.
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COVID-19 pandemic in Venezuela
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Economic impact
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As a result of the pandemic's economic impact, some businesses have sought to supplement lost business with deliveries, though exact figures remain obscure and the services are prohibitively costly for average Venezuelans. Some have started to make deliveries to support their families using bicycles instead of motorcycles due to gasoline shortages.
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COVID-19 pandemic in Venezuela
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Misinformation by authorities
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In a national broadcast on 27 February 2020, Nicolás Maduro warned that COVID-19 may have been a US-made biological weapon aimed against China, without providing any evidence.Maduro has supported in social media the use of infusions as a cure to COVID-19. Twitter deleted a tweet of Maduro in March that cited the works of Sergio Quintero, a Venezuelan doctor that claims to have found an herbal antidote against COVID-19. Quintero also claims that the virus was created by the United States as a biological weapon. The works were also posted in Facebook and government webpages and shared by thousands of users. The Venezuelan Institute for Scientific Research refuted Quintero's claims. Agence France Presse has fact checked this information and has cataloged Quintero's works as misleading and false, no natural cure has either been approved by other specialists nor by the World Health Organization.Maduro's administration has authorized and supported the use of chloroquine and interferon alfa-2b at large scale as treatments for COVID-19. Interferon alfa-2b is an antiviral that has been used in China and has been promoted by Cuba, sometimes as a "vaccine". Both chloroquine and interferon have not been proven to be effective against the disease. Chloroquine is an antimalarial drug that can cause cardiac problems if abused.Throughout March and July 2020, Maduro and his administration have accused Colombia of promoting the "intentional infection" of Venezuelan migrants that returned to their country, saying they were "biological weapon" and threatening them with quarantine. Local authorities have repeated the accusations since. Maduro administration has given the hypothesis of a "Colombian virus", that would be a more aggressive strain of the virus, to explain the increase in numbers in neighboring Zulia state, but no medical evidence has been provided.Maduro notified the Pan American Health Organization in October 2020, that a molecule that nullifies the replication capacity of the new coronavirus had been discovered, yet no proof was ever disclosed.In early 2021, Nicolás Maduro started promoting Carvativir, a thyme-based oral medication that he said was tested on patients in Caracas and neutralizes COVID-19 with no side effect. He described the drug as "tears of José Gregorio Hernández", a 19th-century Venezuelan doctor beatified in 2020. Francisco Marty, an infectious diseases expert at Brigham and Women's Hospital said that the claims about the efficiency of drug effects were unsubstantiated. David Boulware, professor of medicine and an infectious diseases physician at the University of Minnesota Medical School, noted the lack of scientific data. Venezuela's National Academy of Medicine stated that Carvativir had therapeutic potential against coronavirus but warned that, according to international protocols, more data was needed to consider it an anti-COVID-19 medication.In March 2021, Nicolás Maduro Facebook page was frozen for violating policies against spreading misinformation about the coronavirus of the website.
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COVID-19 pandemic in Venezuela
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Concerns with government estimates
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The official reports have not always been consistent, presenting errors such as missing states, numbers that do not match and inconsistencies with the published estimates. The government keeps a centralized system and does not authorize private clinics and universities to access the tests processing.The government receives many tests kits from China. Early May, the Maduro administration reported to have performed over 400,000 tests, the largest number of tests in South America at the time. Many of these tests are unreliable rapid tests, raising the possibility of a large number of false positives and negatives.As of 17 April, only the laboratory of the National Institute of Hygiene (INH) was certified to analyze COVID-19 tests. It is estimated that the INH only has the capacity to analyze 100 samples per day. The current virology team consists of three technicians, working on aging equipment. In comparison, Colombia has 38 certified labs. The government does not allow universities or private clinics to test, even if they have the capacity to do so. Due to lack of transparency, even some top health officials do not know how fast the epidemic is spreading. According to health workers that disclosed information to Reuters, the government is prioritizing sectors that are allied with the United Socialist Party of Venezuela.The Maduro administration was reporting an average of less than a dozen cases daily until the last weeks of May, a very low number compared to other countries in South America. Human Rights Watch and Johns Hopkins University published that Venezuela's hospitals were "grossly unprepared" and most hospitals lack running water. The American director from Human Rights Watch indicated that "Maduro's statistics are absolutely absurd," in a country "where doctors do not even have water to wash their hands." Kathleen Page from the Johns Hopkins University School of Medicine involved in the report said that some of the health official interviewed stated "that even when they see confirmed cases of Covid-19 they are not being reported in the epidemiological reports".Many Venezuelans are skeptical of the government statistics due to the Maduro administration's history of hiding numbers.Juan Guaidó has questioned the veracity of the official number of cases, stating that there are inconsistencies in the estimates given. In an interview with El Nuevo Herald on 22 March, Guaidó declared that the number of confirmed cases in Venezuela could be more than two hundred, according to opposition estimates, contrary to the 70 cases that Maduro's administration recognized at the moment. El Nuevo Herald reported that internal sources extraofficially confirmed that estimate, that according to said sources there were 181 confirmed cases on the morning of 21 March and a total of 298 in observation.The United Nations High Commissioner for Human Rights Michelle Bachelet, when discussing Cuba, North Korea, Venezuela and Zimbabwe, called for the easing of sanctions to enable their medical systems to combat COVID-19. These countries should provide transparent information and accept offers of humanitarian help when needed, according to Bachelet. She also said that Venezuela suffers from many kind of supply and technical shortages, that pre-date the sanctions. She also called Venezuelan government to protect health workers saying that they "should never be punished by the authorities for pointing out deficiencies in the response to the crisis." Non-government estimates Four cases were extraofficially reported in El Helicoide on 18 March 2020, three women and a male officer of the motorized brigade of the National Police.A person self-identified as a member of the Tupamaro colectivo in the 23 de Enero parish of Caracas declared to his community with a megaphone that a case was confirmed on 19 March 2020, specifically in Block 39, asking his neighbors to stay home and to prevent other blocks from being infected.Venezuelan newspaper El Nacional, reported a total of 65 cases for 20 March, according to undisclosed sources from the Health Ministry. On that day the ministry did not report any official numbers, the toll was officially updated the next day going from 42 to 70. Similarly, before the official report on 23 March, El Nacional reported 84 cases according undisclosed source from the Health Ministry.The Academy of Physical, Mathematical and Natural Science (Spanish: Academia de Ciencias Físicas, Matemáticas y Naturales) warned that on 2 April the epidemiological curves of Venezuela were unusual, saying that there was just a linear increase of accumulated confirmed cases, a pattern that is atypical for the initial phase of COVID-19 outbreaks.Physician and opposition deputy, Jose Manuel Olivares, said Maduro's administration has concealed at least four COVID-19 deaths from the 10 it has made public up to 27 May 2020. Two of these extra cases had received PCR tests that resulted positive after their death, but were not counted in the official reports.
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COVID-19 pandemic in Venezuela
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Authorities' actions on reporting
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On 13 March, Delta Amacuro indigenous leader and journalist Melquiades Ávila, who has criticized health infrastructure in the country, questioned publicly through Facebook "will our hospital be ready for coronavirus?" and ridiculed Maduro's claim that 46 hospitals were prepared for COVID-19. The Governor of Delta Amacuro Lizeta Hernández and member of the United Socialist Party of Venezuela, sent the state army to detain Ávila. When asked why by Reuters on the matter, she said that it was to "orient" Ávila and ensure he was being "serious and responsible".An opposition lawmaker, Tony Geara, was arrested on 14 March in a roadblock after declaring that there was no running water in one of the hospitals listed as prepared by the Bolivarian government. A court charged Geara with illegal possession of explosives and weapons. Geara denies the charges.According to twelve medical workers interviewed by Reuters, security forces use roadblocks and checkpoints to shakedown medical staff.Julio Molinos, a medical union leader and retired technician, published a video asking the government to be transparent about hospital conditions on 15 March. Special Action Forces (FAES) arrested Molinos, who was sentenced to house arrest on charges of conspiracy and inciting hatred.The National Assembly released a webpage to provide information and health recommendations on COVID-19 but the access to the website was restricted by CANTV, the state internet provider. The censorship was denounced by Guaidó.Iván Virgüez, a 65-year-old human rights lawyer was arrested in April for criticizing the conditions of quarantine centers for migrants returning to Venezuela. He reports to the Human Rights Watch to have been handcuffed for two hours under the sun to a metal tube 2 feet off the ground and was denied a bathroom for 26 hours. Virgüez was later held under house arrest, charged with public disturbance, contempt, defamation of authorities and instigation of rebellion.According to a Human Rights Watch report, healthcare worker Andrea Sayago was coerced to resign after the photos she shared of their first coronavirus cases through WhatsApp, a private messaging service, were leaked through social media in April. Her photos were described as "terrorism" and she was charged with misuse of privileged information.
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COVID-19 pandemic in Venezuela
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Authorities' actions on reporting
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Arrest of Darvinson Rojas On the night of 21 March 2020, journalist Darvinson Rojas was arrested at his home in Caracas by officials of the Bolivarian National Police (PNB) and around fifteen armed personnel from the Special Actions Force (FAES). According to the National Union of Press Workers (SNTP), the arrest was related to the coverage of Rojas with his recent publications on the COVID-19 situation in Venezuela.The Committee to Protect Journalists (CPJ) called for the immediate release of Rojas. Nathalie Southwick, CPJ coordinator, stated that "Violently detaining a journalist and interrogating him about his sources on a vital public health issue like the COVID-19 outbreak has an undeniable chilling effect that will only discourage other journalists from reporting on the pandemic." Amnesty International demanded Rojas immediate and unconditional release.The SNTP, on 24 March, denounced that Darvinson was presented in the tribunals "illegally" and "clandestinely".After 12 days incarcerated, Darvinson Rojas was set free on 3 April 2020 under precautionary measures.
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COVID-19 pandemic in Venezuela
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Authorities' actions on reporting
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Backlash on Venezuelan scientific report Venezuela's Academy of Physical, Mathematical and Natural Science published an estimate of the future cases in Venezuela in May 2020. The report predicts that the number of infected in Venezuela could reach 4000 cases sometime in June. The report also states that the number of deaths reported so far were inconsistent with the epidemic. The academy called for an increase in the number of PCR tests and raised concerns of the difficulty of flattening the curve under the current conditions.Diosdado Cabello, vice-president of the United Socialist Party of Venezuela and president of pro-government Constituent National Assembly, criticized the academy for provoking "terror" in the population, discredited the academy report and demanded security forces to investigate its researchers. The academy answered by saying "it worries us as scientists, that we are harassed and marked for a technical report intended to improve management of the pandemic." The National Assembly defended the academy and answered that "Providing scientific facts in an unbiased way for the well-being of our people who are suffering the worst crisis in our history, is a heroic act that deserves to be recognized by all Venezuelans." Human Rights Watch report In an August 2020 report, Human Rights Watch described how the Venezuelan government had used the pandemic to control and crackdown on journalists, healthcare workers, human rights lawyers and political opponents that are critical to the government response. The report listed 162 alleged cases of physical abuse and torture committed by the authorities between March and June, corroborated through interviews with the victims, media reports and human rights advocate groups.
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COVID-19 pandemic in Venezuela
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Statistics
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Cumulative number of cases and recoveries Notes: There was no official report on 20 March 2020, Worldometer and the Center for Systems Science and Engineering (CSSE) of the Johns Hopkins University reported 65 cases, numbers coming from an article of El Nacional from undisclosed sources from the Venezuelan Ministry of Health.
The recoveries from 21 March to 25 March indicate people without symptoms for at least 5 days, considered as recovered in the official reports.
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COVID-19 pandemic in Venezuela
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Statistics
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Daily new cases Cumulative number of deaths Daily deaths Regional distribution Cases per federal entity touched by the pandemic, as of 29 September 2021: Various Venezuelan newspapers have pointed out that there have been some inconsistencies with the government reports by federal states. For example, 24 March report differs from 23 report, as Táchira and Portuguesa that reported cases before, were no longer included. On 26 March, while the official report indicated 107 total cases, the number of cases per dependency amounted to 108.In April, the Ministry of Public Health of Guyana confirmed patients with coronavirus in Barima-Waini, located in Guayana Esequiba and a territory disputed with Venezuela. These cases are not included in the statistics provided by the Bolivarian Government of Venezuela.
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COVID-19 pandemic in Venezuela
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Statistics
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Per origin As of 16 March, there were 33 confirmed cases in Venezuela. According to official estimates, among these, 28 came from Europe and 5 from Cúcuta, Colombia. Two of the cases consisted of foreign citizens, one of a diplomatic official, while the rest consisted of Venezuelan residents.By 22 March, Maduro announced out of all the 77 cases were imported. According to him, 43 had traveled recently, the distribution was as follows: On 24 March, Maduro first mentioned the existence of cases transmitted locally in the country.Jorge Rodríguez announced on 15 May that between 70 and 80% of the cases reported in May were from foreign origin.
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2CB-Ind
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2CB-Ind
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2CB-Ind is a conformationally-restricted derivative of the phenethylamine hallucinogen 2C-B, discovered in 1974 by Alexander Shulgin. It acts as a moderately potent and selective agonist for the 5-HT2A and 5-HT2C receptors, but unlike the corresponding benzocyclobutene derivative TCB-2 which is considerably more potent than the parent compound 2C-B, 2CB-Ind is several times weaker, with racemic 2CB-Ind having a Ki of 47nM at the human 5-HT2A receptor, only slightly more potent than the mescaline analogue (R)-jimscaline.
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Glycoside hydrolase family 66
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Glycoside hydrolase family 66
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In molecular biology, glycoside hydrolase family 66 is a family of glycoside hydrolases.
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Glycoside hydrolase family 66
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Glycoside hydrolase family 66
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Glycoside hydrolases EC 3.2.1. are a widespread group of enzymes that hydrolyse the glycosidic bond between two or more carbohydrates, or between a carbohydrate and a non-carbohydrate moiety. A classification system for glycoside hydrolases, based on sequence similarity, has led to the definition of >100 different families. This classification is available on the CAZy web site, and also discussed at CAZypedia, an online encyclopedia of carbohydrate active enzymes.Glycoside hydrolase family 66 CAZY GH_66 includes enzymes with cycloisomaltooligosaccharide glucanotransferase EC 2.4.1.248 and dextranase EC 3.2.1.11 activities.
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Periodontal abscess
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Periodontal abscess
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A periodontal abscess (also termed lateral abscess, or parietal abscess), is a localized collection of pus (i.e. an abscess) within the tissues of the periodontium. It is a type of dental abscess. A periodontal abscess occurs alongside a tooth, and is different from the more common periapical abscess, which represents the spread of infection from a dead tooth (i.e. which has undergone pulpal necrosis). To reflect this, sometimes the term "lateral (periodontal) abscess" is used. In contrast to a periapical abscess, periodontal abscesses are usually associated with a vital (living) tooth. Abscesses of the periodontium are acute bacterial infections classified primarily by location.
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Periodontal abscess
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Signs and symptoms
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The main symptom is pain, which often suddenly appears, and is made worse by biting on the involved tooth, which may feel raised and prominent in the bite. The tooth may be mobile, and the lesion may contribute to destruction of the periodontal ligament and alveolar bone. The pain is deep and throbbing. The oral mucosa covering an early periodontal abscess appears erythematous (red), swollen and painful to touch. The surface may be shiny due to stretching of the mucosa over the abscess. Before pus has formed, the lesion will not be fluctuant, and there will be no purulent discharge. There may be regional lymphadenitis.
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Periodontal abscess
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Signs and symptoms
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When pus forms, the pressure increases, with increasing pain, until it spontaneously drains and relieves the pain. When pus drains into the mouth, a bad taste and smell are perceived. Usually drainage occurs via the periodontal pocket, or else the infection may spread as a cellulitis or a purulent odontogenic infection. Local anatomic factors determine the direction of spread (see fascial spaces of the head and neck). There may be systemic upset, with an onset of pain and fever.
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Periodontal abscess
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Causes
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A periodontal abscess most commonly occurs as a complication of advanced periodontal disease (which is normally painless). A periodontal pocket contains dental plaque, bacteria and subgingival calculus. Periodontal pathogens continually find their way into the soft tissues, but normally they are held in check by the immune system. A periodontal abscess represents a change in this balance, related to decreased local or systemic resistance of the host. An inflammatory response occurs when bacteria invade and multiply within the soft tissue of the gingival crevice/periodontal pocket. A pus-filled abscess forms when the immune system responds and attempts to isolate the infection from spreading.
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Periodontal abscess
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Causes
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Communication with the oral environment is maintained via the opening of the periodontal pocket. However, if the opening of a periodontal pocket becomes obstructed, as may occur if the pocket has become very deep (e.g. with furcation involvement), then plaque and calculus are trapped inside. Food packing may also obstruct a periodontal pocket. Food packing is usually caused by failure to accurately reproduce the contact points when dental restorations are placed on the interproximal surfaces of teeth. Another potential cause occurs when a periodontal pocket is scaled incompletely. Following this procedure, the gingival cuff tightens around the tooth, which may be enough to trap the bacteria left in the pocket. A gingival retraction cord which is accidentally left in situ is an occasional cause of a periodontal abscess.
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Periodontal abscess
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Causes
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Penetrating injury to the gingiva--for example, with a toothbrush bristle, fishbone, toothpick or periodontal instrument--may inoculate bacteria into the tissues. Trauma to the tissues, such as serious impact on a tooth or excessive pressure exerted on teeth during orthodontic treatment, can be a possible cause as well. Occlusal overload may also be involved in the development of a periodontal abscess, but this is rare and usually occurs in combination with other factors. Bruxism is a common cause of excessive occlusal forces.
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Periodontal abscess
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Causes
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Systemic immune factors such as diabetes can predispose a person to the formation of periodontal abscesses.
Perforation of a root canal during endodontic therapy can also lead to a periodontal abscess which if left untreated could become "prolonged" ultimately rupture then enter the blood stream and could lead to serious situations such as endocarditis.
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Periodontal abscess
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Diagnosis
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Periodontal abscesses may be difficult to distinguish from periapical abscesses. Since the management of a periodontal abscess is different from a periapical abscess, this differentiation is important to make (see Dental abscess#Diagnostic approach) For example, root canal therapy is unnecessary and has no impact on pain in a periodontal abscess.
Classification There are four types of abscesses that can involve the periodontal tissues: Gingival abscess—a localized, purulent infection involves only the soft gum tissue near the marginal gingiva or the interdental papilla.
Periodontal abscess—a localized, purulent infection involving a greater dimension of the gum tissue, extending apically and adjacent to a periodontal pocket.
Pericoronal abscess—a localized, purulent infection within the gum tissue surrounding the crown of a partially or fully erupted tooth. Usually associated with an acute episode of pericoronitis around a partially erupted and impacted mandibular third molar (lower wisdom tooth).
combined periodontal/endodontic abscess
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Periodontal abscess
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Treatment
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An important factor is whether the involved tooth is to be extracted or retained. Although the pulp is usually still vital, a history of recurrent periodontal abscesses and significantly compromised periodontal support indicate that the prognosis for the tooth is poor and it should be removed.
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Periodontal abscess
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Treatment
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The initial management of a periodontal abscess involves pain relief and control of the infection. The pus needs to be drained, which helps both of these aims. If the tooth is to be removed, drainage will occur via the socket. Otherwise, if pus is already discharging from the periodontal pocket, this can be encouraged by gentle irrigation and scaling of the pocket whilst massaging the soft tissues. If this does not work, incision and drainage is required, as described in Dental abscess#Treatment.
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Periodontal abscess
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Treatment
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Antibiotics are of secondary importance to drainage, which if satisfactory renders antibiotics unnecessary. Antibiotics are generally reserved for severe infections, in which there is facial swelling, systemic upset and elevated temperature. Since periodontal abscesses frequently involve anaerobic bacteria, oral antibiotics such as amoxicillin, clindamycin (in penicillin allergy or pregnancy) and/or metronidazole are given (although metronidazole should be used in conjunction with a penicillin given its lack of aerobic gram positive coverage).. Ideally, the choice of antibiotic is dictated by the results of microbiological culture and sensitivity testing of a sample of the pus aspirated at the start of any treatment, but this rarely occurs outside the hospital setting.
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Periodontal abscess
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Treatment
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Other measures that are taken during management of the acute phase might include reducing the height of the tooth with a dental drill, so it no longer contacts the opposing tooth when biting down; and regular use of hot salt water mouth washes (antiseptic) that encourages further drainage of the infection.
The management following the acute phase involves removing any residual infection, and correcting the factors that lead to the formation of the periodontal abscess. Usually, this will be therapy for periodontal disease, such as oral hygiene instruction and periodontal scaling.
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Single-machine scheduling
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Single-machine scheduling
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Single-machine scheduling or single-resource scheduling is an optimization problem in computer science and operations research. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on a single machine, in a way that optimizes a certain objective, such as the throughput.
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Single-machine scheduling
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Single-machine scheduling
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Single-machine scheduling is a special case of identical-machines scheduling, which is itself a special case of optimal job scheduling. Many problems, which are NP-hard in general, can be solved in polynomial time in the single-machine case.: 10–20 In the standard three-field notation for optimal job scheduling problems, the single-machine variant is denoted by 1 in the first field. For example, " 1|| ∑Cj " is an single-machine scheduling problem with no constraints, where the goal is to minimize the sum of completion times.
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Single-machine scheduling
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Single-machine scheduling
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The makespan-minimization problem 1|| max , which is a common objective with multiple machines, is trivial with a single machine, since the makespan is always identical. Therefore, other objectives have been studied.
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Single-machine scheduling
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Minimizing the sum of completion times
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The problem 1|| ∑Cj aims to minimize the sum of completion times. It can be solved optimally by the Shortest Processing Time First rule (SPT): the jobs are scheduled by ascending order of their processing time pj The problem 1|| ∑wjCj aims to minimize the weighted sum of completion times. It can be solved optimally by the Weighted Shortest Processing Time First rule (WSPT): the jobs are scheduled by ascending order of the ratio pj/wj .: lecture 1, part 2 The problem 1|chains| ∑wjCj is a generalization of the above problem for jobs with dependencies in the form of chains. It can also be solved optimally by a suitable generalization of WSPT.: lecture 1, part 3
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Single-machine scheduling
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Minimizing the cost of lateness
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The problem 1|| max aims to minimize the maximum lateness. For each job j, there is a due date dj . If it is completed after its due date, it suffers lateness defined as := Cj−dj . 1|| max can be solved optimally by the Earliest Due Date First rule (EDD): the jobs are scheduled by ascending order of their deadline dj .: lecture 2, part 2 The problem 1|prec| max generalizes the 1|| max in two ways: first, it allows arbitrary precedence constraints on the jobs; second, it allows each job to have an arbitrary cost function hj, which is a function of its completion time (lateness is a special case of a cost function). The maximum cost can be minimized by a greedy algorithm known as Lawler's algorithm.: lecture 2, part 1 The problem 1| rj max generalizes 1|| max by allowing each job to have a different release time by which it becomes available for processing. The presence of release times means that, in some cases, it may be optimal to leave the machine idle, in order to wait for an important job that is not released yet. Minimizing maximum lateness in this setting is NP-hard. But in practice, it can be solved using a branch-and-bound algorithm.: lecture 2, part 3
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Single-machine scheduling
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Maximizing the profit of earliness
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In settings with deadlines, it is possible that, if the job is completed by the deadline, there is a profit pj. Otherwise, there is no profit. The goal is to maximize the profit. Single-machine scheduling with deadlines is NP-hard; Sahni presents both exact exponential-time algorithms and a polynomial-time approximation algorithm.
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Single-machine scheduling
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Maximizing the throughput
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The problem 1|| ∑Uj aims to minimize the number of late jobs, regardless of the amount of lateness. It can be solved optimally by the Hodgson-Moore algorithm.: lecture 3, part 1 It can also be interpreted as maximizing the number of jobs that complete on time; this number is called the throughput.
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Single-machine scheduling
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Maximizing the throughput
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The problem 1|| ∑wjUj aims to minimize the weight of late jobs. It is NP-hard, since the special case in which all jobs have the same deadline (denoted by 1| dj=d |∑wjUj ) is equivalent to the Knapsack problem.: lecture 3, part 2 The problem 1| rj |∑Uj generalizes 1|| ∑Uj by allowing different jobs to have different release times. The problem is NP-hard. However, when all job lengths are equal, the problem can be solved in polynomial time. It has several variants: The weighted optimization variant, 1| rj,pj=p |∑wjUj , can be solved in time O(n7) The unweighted optimization variant, maximizing the number of jobs that finish on time,denoted 1| rj,pj=p |∑Uj , can be solved in time O(n5) using dynamic programming, when all release times and deadlines are integers.
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Single-machine scheduling
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Maximizing the throughput
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The decision variant - deciding whether it is possible that all given jobs complete on time - can be solved by several algorithms, the fastest of them runs in time log n) .Jobs can have execution intervals. For each job j, there is a processing time tj and a start-time sj, so it must be executed in the interval [sj, sj+tj]. Since some of the intervals overlap, not all jobs can be completed. The goal is to maximize the number of completed jobs, that is, the throughput. More generally, each job may have several possible intervals, and each interval may be associated with a different profit. The goal is to choose at most one interval for each job, such that the total profit is maximized. For more details, see the page on interval scheduling.
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Single-machine scheduling
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Maximizing the throughput
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More generally, jobs can have time-windows, with both start-times and deadlines, which may be larger than the job length. Each job can be scheduled anywhere within its time-window. Bar-Noy, Bar-Yehuda, Freund, Naor and Schieber present a (1-ε)/2 approximation.
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Cloroqualone
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Cloroqualone
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Cloroqualone is a quinazolinone-class GABAergic and is an analogue of methaqualone developed in the 1980s and marketed mainly in France and some other European countries. It has sedative and antitussive properties resulting from its agonist activity at the β subtype of the GABAa receptor and sigma-1 receptor, and was sold either alone or in combination with other ingredients as a cough medicine. Cloroqualone has weaker sedative properties than methaqualone and was sold for its useful cough-suppressing effects, but was withdrawn from the French market in 1994 because of concerns about its potential for abuse and overdose.
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Pedagogical relation
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Pedagogical relation
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The pedagogical relation refers to special kind of personal relationship between adult and child or adult or student for the sake of the child or student. The pedagogical relation is described by Hermann Nohl, Klaus Mollenhauer, and others in the Northern European human science pedagogical tradition. It has been discussed more recently in English by Max van Manen, Norm Friesen, Tone Saevi and others..
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Pedagogical relation
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Pedagogical relation
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In the pedagogical relation, adult and child encounter each other in ways that are different from other relationships (e.g., friendship) In the pedagogical relation the adult is directed toward the child. The relation is asymmetrical.. The adult is "there" for the child in a way that the child is not "there" for the adult.
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Pedagogical relation
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Pedagogical relation
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In the pedagogical relation the adult wants or intends both what is good for the child in the present and in the future. This relationship is oriented to what the child or young person may become (without trying to predetermine it), but without ignoring what is important for the child in the present. These two, present needs and the likely requirements of the future, exist in constant tension this relation.
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Pedagogical relation
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Pedagogical relation
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The pedagogical relation comes to an end. The child grows up and the asymmetry of the relation dissolves. As Klaus Mollenhauer explains, "upbringing comes to an end when the child no longer needs to be "called" to self-activity, but instead has the wherewithal to educate himself." In the pedagogical relation the adult is tactful. It is not about following rules and guidelines, but rather, about acting and also not acting according to what is appropriate for both the present and the future of a specific child in question.
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Pedagogical relation
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Pedagogical relation
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In the pedagogical relation, the adult mediates the relationship of the child with the world. This can happen by protecting the child from certain aspects of the world; it often happens by simplifying certain aspects of the world for the child, by directing the child's attention through gestures of pointing and guiding.In a text from 1933, educationist Herman Nohl describes the pedagogical relation as a relationship between a particular stance of the educator in relationship to the one being educated (educand): This basic stance … is decisively characterized by the fact that its perspective is unconditionally that of the educand. This means that its task is not to draw the child towards … specific, predetermined, objective goals that it might see … [in] the state, the church, the law, the economy, and also not of a [political] party or worldview. Instead, it sees its goal in the subject and his/her physical and personal realization or unfolding (körperlich-geistige Entfaltung). That this child here comes to his life’s purpose (Lebensziel), that is [its] … autonomous and inalienable task. (p. 152) The pedagogical relation, finally, has as its interest not necessarily the "success" of the student, but rather their "subjectivation"--their becoming a subject, a person, something that is to be pursued as an end in itself.
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Ro20-8552
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Ro20-8552
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Ro20-8552 is a benzodiazepine derivative with sedative and anxiolytic effects, which has been sold as a designer drug.
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Polar amplification
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Polar amplification
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Polar amplification is the phenomenon that any change in the net radiation balance (for example greenhouse intensification) tends to produce a larger change in temperature near the poles than in the planetary average. This is commonly referred to as the ratio of polar warming to tropical warming. On a planet with an atmosphere that can restrict emission of longwave radiation to space (a greenhouse effect), surface temperatures will be warmer than a simple planetary equilibrium temperature calculation would predict. Where the atmosphere or an extensive ocean is able to transport heat polewards, the poles will be warmer and equatorial regions cooler than their local net radiation balances would predict. The poles will experience the most cooling when the global-mean temperature is lower relative to a reference climate; alternatively, the poles will experience the greatest warming when the global-mean temperature is higher.In the extreme, the planet Venus is thought to have experienced a very large increase in greenhouse effect over its lifetime, so much so that its poles have warmed sufficiently to render its surface temperature effectively isothermal (no difference between poles and equator). On Earth, water vapor and trace gasses provide a lesser greenhouse effect, and the atmosphere and extensive oceans provide efficient poleward heat transport. Both palaeoclimate changes and recent global warming changes have exhibited strong polar amplification, as described below.
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Polar amplification
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Polar amplification
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Arctic amplification is polar amplification of the Earth's North Pole only; Antarctic amplification is that of the South Pole.
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Polar amplification
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History
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An observation-based study related to Arctic amplification was published in 1969 by Mikhail Budyko, and the study conclusion has been summarized as "Sea ice loss affects Arctic temperatures through the surface albedo feedback." The same year, a similar model was published by William D. Sellers. Both studies attracted significant attention since they hinted at the possibility for a runaway positive feedback within the global climate system. In 1975, Manabe and Wetherald published the first somewhat plausible general circulation model that looked at the effects of an increase of greenhouse gas. Although confined to less than one-third of the globe, with a "swamp" ocean and only land surface at high latitudes, it showed an Arctic warming faster than the tropics (as have all subsequent models).
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Polar amplification
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Amplification
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Amplifying mechanisms Feedbacks associated with sea ice and snow cover are widely cited as one of the principal causes of terrestrial polar amplification. These feedbacks are particularly noted in local polar amplification, although recent work has shown that the lapse rate feedback is likely equally important to the ice-albedo feedback for Arctic amplification. Supporting this idea, large-scale amplification is also observed in model worlds with no ice or snow. It appears to arise both from a (possibly transient) intensification of poleward heat transport and more directly from changes in the local net radiation balance. Local radiation balance is crucial because an overall decrease in outgoing longwave radiation will produce a larger relative increase in net radiation near the poles than near the equator. Thus, between the lapse rate feedback and changes in the local radiation balance, much of polar amplification can be attributed to changes in outgoing longwave radiation. This is especially true for the Arctic, whereas the elevated terrain in Antarctica limits the influence of the lapse rate feedback.Some examples of climate system feedbacks thought to contribute to recent polar amplification include the reduction of snow cover and sea ice, changes in atmospheric and ocean circulation, the presence of anthropogenic soot in the Arctic environment, and increases in cloud cover and water vapor. CO2 forcing has also been attributed to polar amplification. Most studies connect sea ice changes to polar amplification. Both ice extent and thickness impact polar amplification. Climate models with smaller baseline sea ice extent and thinner sea ice coverage exhibit stronger polar amplification. Some models of modern climate exhibit Arctic amplification without changes in snow and ice cover.The individual processes contributing to polar warming are critical to understanding climate sensitivity. Polar warming also affects many ecosystems, including marine and terrestrial ecosystems, climate systems, and human populations. Polar amplification is largely driven by local polar processes with hardly any remote forcing, whereas polar warming is regulated by tropical and midlatitude forcing. These impacts of polar amplification have led to continuous research in the face of global warming.
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Polar amplification
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Amplification
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Ocean circulation It has been estimated that 70% of global wind energy is transferred to the ocean and takes place within the Antarctic Circumpolar Current (ACC). Eventually, upwelling due to wind-stress transports cold Antarctic waters through the Atlantic surface current, while warming them over the equator, and into the Arctic environment. This is especially noticed in high latitudes. Thus, warming in the Arctic depends on the efficiency of the global ocean transport and plays a role in the polar see-saw effect.Decreased oxygen and low-pH during La Niña are processes that correlate with decreased primary production and a more pronounced poleward flow of ocean currents. It has been proposed that the mechanism of increased Arctic surface air temperature anomalies during La Niña periods of ENSO may be attributed to the Tropically Excited Arctic Warming Mechanism (TEAM), when Rossby waves propagate more poleward, leading to wave dynamics and an increase in downward infrared radiation.
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Polar amplification
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Amplification
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Amplification factor Polar amplification is quantified in terms of a polar amplification factor, generally defined as the ratio of some change in a polar temperature to a corresponding change in a broader average temperature: PAF=ΔTpΔT¯ ,where ΔTp is a change in polar temperature and ΔT¯ is, for example, a corresponding change in a global mean temperature.
Common implementations define the temperature changes directly as the anomalies in surface air temperature relative to a recent reference interval (typically 30 years). Others have used the ratio of the variances of surface air temperature over an extended interval.
Amplification phase It is observed that Arctic and Antarctic warming commonly proceed out of phase because of orbital forcing, resulting in the so-called polar see-saw effect.
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Polar amplification
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Paleoclimate polar amplification
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The glacial / interglacial cycles of the Pleistocene provide extensive palaeoclimate evidence of polar amplification, both from the Arctic and the Antarctic. In particular, the temperature rise since the last glacial maximum 20,000 years ago provides a clear picture. Proxy temperature records from the Arctic (Greenland) and from the Antarctic indicate polar amplification factors on the order of 2.0.
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Polar amplification
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Recent Arctic amplification
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Suggested mechanisms leading to the observed Arctic amplification include Arctic sea ice decline (open water reflects less sunlight than sea ice), atmospheric heat transport from the equator to the Arctic, and the lapse rate feedback.The Arctic was historically described as warming twice as fast as the global average, but this estimate was based on older observations which missed the more recent acceleration. By 2021, enough data was available to show that the Arctic had warmed three times faster than the globe - 3.1 °C between 1971 and 2019, as opposed to the global warming of 1 °C over the same period. Moreover, this estimate defines the Arctic as everything above 60th parallel north, or a full third of the Northern Hemisphere: in 2021–2022, it was found that since 1979, the warming within the Arctic Circle itself (above the 66th parallel) has been nearly four times faster than the global average. Within the Arctic Circle itself, even greater Arctic amplification occurs in the Barents Sea area, with hotspots around West Spitsbergen Current: weather stations located on its path record decadal warming up to seven times faster than the global average. This has fuelled concerns that unlike the rest of the Arctic sea ice, ice cover in the Barents Sea may permanently disappear even around 1.5 degrees of global warming.The acceleration of Arctic amplification has not been linear: a 2022 analysis found that it occurred in two sharp steps, with the former around 1986, and the latter after 2000. The first acceleration is attributed to the increase in anthropogenic radiative forcing in the region, which is in turn likely connected to the reductions in stratospheric sulfur aerosols pollution in Europe in the 1980s in order to combat acid rain. Since sulphate aerosols have a cooling effect, their absence is likely to have increased Arctic temperatures by up to 0.5 degrees Celsius. The second acceleration has no known cause, which is why it did not show up in any climate models. It is likely to an example of multi-decadal natural variability, like the suggested link between Arctic temperatures and Atlantic Multi-decadal Oscillation (AMO), in which case it can be expected to reverse in the future. However, even the first increase in Arctic amplification was only accurately simulated by a fraction of the current CMIP6 models.
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Chi distribution
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Chi distribution
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In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. It is thus related to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution.
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Chi distribution
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Chi distribution
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If Z1,…,Zk are k independent, normally distributed random variables with mean 0 and standard deviation 1, then the statistic Y=∑i=1kZi2 is distributed according to the chi distribution. The chi distribution has one positive integer parameter k , which specifies the degrees of freedom (i.e. the number of random variables Zi ).
The most familiar examples are the Rayleigh distribution (chi distribution with two degrees of freedom) and the Maxwell–Boltzmann distribution of the molecular speeds in an ideal gas (chi distribution with three degrees of freedom).
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Chi distribution
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Definitions
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Probability density function The probability density function (pdf) of the chi-distribution is otherwise .
where Γ(z) is the gamma function.
Cumulative distribution function The cumulative distribution function is given by: F(x;k)=P(k/2,x2/2) where P(k,x) is the regularized gamma function.
Generating functions The moment-generating function is given by: M(t)=M(k2,12,t22)+t2Γ((k+1)/2)Γ(k/2)M(k+12,32,t22), where M(a,b,z) is Kummer's confluent hypergeometric function. The characteristic function is given by: φ(t;k)=M(k2,12,−t22)+it2Γ((k+1)/2)Γ(k/2)M(k+12,32,−t22).
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Chi distribution
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Properties
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Moments The raw moments are then given by: μj=∫0∞f(x;k)xjdx=2j/2Γ(12(k+j))Γ(12k) where Γ(z) is the gamma function. Thus the first few raw moments are: μ1=2Γ(12(k+1))Γ(12k) μ2=k, μ3=22Γ(12(k+3))Γ(12k)=(k+1)μ1, μ4=(k)(k+2), μ5=42Γ(12(k+5))Γ(12k)=(k+1)(k+3)μ1, μ6=(k)(k+2)(k+4), where the rightmost expressions are derived using the recurrence relationship for the gamma function: Γ(x+1)=xΓ(x).
From these expressions we may derive the following relationships: Mean: μ=2Γ(12(k+1))Γ(12k), which is close to k−12 for large k.
Variance: V=k−μ2, which approaches 12 as k increases.
Skewness: γ1=μσ3(1−2σ2).
Kurtosis excess: γ2=2σ2(1−μσγ1−σ2).
Entropy The entropy is given by: ln ln (2)−(k−1)ψ0(k/2)) where ψ0(z) is the polygamma function.
Large n approximation We find the large n=k+1 approximation of the mean and variance of chi distribution. This has application e.g. in finding the distribution of standard deviation of a sample of normally distributed population, where n is the sample size.
The mean is then: μ=2Γ(n/2)Γ((n−1)/2) We use the Legendre duplication formula to write: 2n−2Γ((n−1)/2)⋅Γ(n/2)=πΓ(n−1) ,so that: μ=2/π2n−2(Γ(n/2))2Γ(n−1) Using Stirling's approximation for Gamma function, we get the following expression for the mean: 12 12 (n−2)+O(1n2)] =(n−2)1/2⋅[1+14n+O(1n2)]=n−1(1−1n−1)1/2⋅[1+14n+O(1n2)] =n−1⋅[1−12n+O(1n2)]⋅[1+14n+O(1n2)] =n−1⋅[1−14n+O(1n2)] And thus the variance is: V=(n−1)−μ2=(n−1)⋅12n⋅[1+O(1n)]
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Chi distribution
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Related distributions
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If X∼χk then X2∼χk2 (chi-squared distribution) lim k→∞χk−μkσk→dN(0,1) (Normal distribution) If X∼N(0,1) then |X|∼χ1 If X∼χ1 then σX∼HN(σ) (half-normal distribution) for any σ>0 χ2∼Rayleigh(1) (Rayleigh distribution) χ3∼Maxwell(1) (Maxwell distribution) ‖Ni=1,…,k(0,1)‖2∼χk , the Euclidean norm of a standard normal random vector of with k dimensions, is distributed according to a chi distribution with k degrees of freedom chi distribution is a special case of the generalized gamma distribution or the Nakagami distribution or the noncentral chi distribution The mean of the chi distribution (scaled by the square root of n−1 ) yields the correction factor in the unbiased estimation of the standard deviation of the normal distribution.
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Lattice model (finance)
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Lattice model (finance)
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In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise, though methods now exist for solving this problem.
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Lattice model (finance)
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Equity and commodity derivatives
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In general the approach is to divide time between now and the option's expiration into N discrete periods. At the specific time n, the model has a finite number of outcomes at time n + 1 such that every possible change in the state of the world between n and n + 1 is captured in a branch. This process is iterated until every possible path between n = 0 and n = N is mapped. Probabilities are then estimated for every n to n + 1 path. The outcomes and probabilities flow backwards through the tree until a fair value of the option today is calculated. For equity and commodities the application is as follows. The first step is to trace the evolution of the option's key underlying variable(s), starting with today's spot price, such that this process is consistent with its volatility; log-normal Brownian motion with constant volatility is usually assumed. The next step is to value the option recursively: stepping backwards from the final time-step, where we have exercise value at each node; and applying risk neutral valuation at each earlier node, where option value is the probability-weighted present value of the up- and down-nodes in the later time-step. See Binomial options pricing model § Method for more detail, as well as Rational pricing § Risk neutral valuation for logic and formulae derivation.
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Lattice model (finance)
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Equity and commodity derivatives
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As stated above, the lattice approach is particularly useful in valuing American options, where the choice whether to exercise the option early, or to hold the option, may be modeled at each discrete time/price combination; this is also true for Bermudan options. For similar reasons, real options and employee stock options are often modeled using a lattice framework, though with modified assumptions. In each of these cases, a third step is to determine whether the option is to be exercised or held, and to then apply this value at the node in question. Some exotic options, such as barrier options, are also easily modeled here; for other Path-Dependent Options, simulation would be preferred. (Although, tree-based methods have been developed.
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Lattice model (finance)
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Equity and commodity derivatives
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) The simplest lattice model is the binomial options pricing model; the standard ("canonical") method is that proposed by Cox, Ross and Rubinstein (CRR) in 1979; see diagram for formulae. Over 20 other methods have been developed, with each "derived under a variety of assumptions" as regards the development of the underlying's price. In the limit, as the number of time-steps increases, these converge to the Log-normal distribution, and hence produce the "same" option price as Black-Scholes: to achieve this, these will variously seek to agree with the underlying's central moments, raw moments and / or log-moments at each time-step, as measured discretely. Further enhancements are designed to achieve stability relative to Black-Scholes as the number of time-steps changes. More recent models, in fact, are designed around direct convergence to Black-Scholes.A variant on the Binomial, is the Trinomial tree, developed by Phelim Boyle in 1986. Here, the share price may remain unchanged over the time-step, and option valuation is then based on the value of the share at the up-, down- and middle-nodes in the later time-step.
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Lattice model (finance)
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Equity and commodity derivatives
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As for the binomial, a similar (although smaller) range of methods exist. The trinomial model is considered to produce more accurate results than the binomial model when fewer time steps are modelled, and is therefore used when computational speed or resources may be an issue. For vanilla options, as the number of steps increases, the results rapidly converge, and the binomial model is then preferred due to its simpler implementation. For exotic options the trinomial model (or adaptations) is sometimes more stable and accurate, regardless of step-size.
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Lattice model (finance)
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Equity and commodity derivatives
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Various of the Greeks can be estimated directly on the lattice, where the sensitivities are calculated using finite differences. Delta and gamma, being sensitivities of option value w.r.t. price, are approximated given differences between option prices - with their related spot - in the same time step. Theta, sensitivity to time, is likewise estimated given the option price at the first node in the tree and the option price for the same spot in a later time step. (Second time step for trinomial, third for binomial. Depending on method, if the "down factor" is not the inverse of the "up factor", this method will not be precise.) For rho, sensitivity to interest rates, and vega, sensitivity to input volatility, the measurement is indirect, as the value must be calculated a second time on a new lattice built with these inputs slightly altered - and the sensitivity here is likewise returned via finite difference. See also Fugit, the estimated time to exercise, which is typically calculated using a lattice.
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Lattice model (finance)
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Equity and commodity derivatives
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When it is important to incorporate the volatility smile, or surface, implied trees can be constructed. Here, the tree is solved such that it successfully reproduces selected (all) market prices, across various strikes and expirations. These trees thus "ensure that all European standard options (with strikes and maturities coinciding with the tree nodes) will have theoretical values which match their market prices". Using the calibrated lattice one can then price options with strike / maturity combinations not quoted in the market, such that these prices are consistent with observed volatility patterns. There exist both implied binomial trees, often Rubinstein IBTs (R-IBT), and implied trinomial trees, often Derman-Kani-Chriss (DKC; superseding the DK-IBT). The former is easier built, but is consistent with one maturity only; the latter will be consistent with, but at the same time requires, known (or interpolated) prices at all time-steps and nodes. (DKC is effectively a discretized local volatility model.) As regards the construction, for an R-IBT the first step is to recover the "Implied Ending Risk-Neutral Probabilities" of spot prices. Then by the assumption that all paths which lead to the same ending node have the same risk-neutral probability, a "path probability" is attached to each ending node. Thereafter "it's as simple as One-Two-Three", and a three step backwards recursion allows for the node probabilities to be recovered for each time step. Option valuation then proceeds as standard, with these substituted for p. For DKC, the first step is to recover the state prices corresponding to each node in the tree, such that these are consistent with observed option prices (i.e. with the volatility surface). Thereafter the up-, down- and middle-probabilities are found for each node such that: these sum to 1; spot prices adjacent time-step-wise evolve risk neutrally, incorporating dividend yield; state prices similarly "grow" at the risk free rate. (The solution here is iterative per time step as opposed to simultaneous.) As for R-IBTs, option valuation is then by standard backward recursion.
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Lattice model (finance)
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Equity and commodity derivatives
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As an alternative, Edgeworth binomial trees allow for an analyst-specified skew and kurtosis in spot price returns; see Edgeworth series. This approach is useful when the underlying's behavior departs (markedly) from normality. A related use is to calibrate the tree to the volatility smile (or surface), by a "judicious choice" of parameter values—priced here, options with differing strikes will return differing implied volatilities. For pricing American options, an Edgeworth-generated ending distribution may be combined with an R-IBT. This approach is limited as to the set of skewness and kurtosis pairs for which valid distributions are available. The more recent Johnson binomial trees use the Johnson "family" of distributions, as this is capable of accommodating all possible pairs.
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Lattice model (finance)
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Equity and commodity derivatives
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For multiple underlyers, multinomial lattices can be built, although the number of nodes increases exponentially with the number of underlyers. As an alternative, Basket options, for example, can be priced using an "approximating distribution" via an Edgeworth (or Johnson) tree.
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Lattice model (finance)
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Interest rate derivatives
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Lattices are commonly used in valuing bond options, Swaptions, and other interest rate derivatives In these cases the valuation is largely as above, but requires an additional, zeroeth, step of constructing an interest rate tree, on which the price of the underlying is then based. The next step also differs: the underlying price here is built via "backward induction" i.e. flows backwards from maturity, accumulating the present value of scheduled cash flows at each node, as opposed to flowing forwards from valuation date as above. The final step, option valuation, then proceeds as standard. See top for graphic, and aside for description.
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Lattice model (finance)
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Interest rate derivatives
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The initial lattice is built by discretizing either a short-rate model, such as Hull–White or Black Derman Toy, or a forward rate-based model, such as the LIBOR market model or HJM. As for equity, trinomial trees may also be employed for these models; this is usually the case for Hull-White trees.
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Lattice model (finance)
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Interest rate derivatives
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Under HJM, the condition of no arbitrage implies that there exists a martingale probability measure, as well as a corresponding restriction on the "drift coefficients" of the forward rates. These, in turn, are functions of the volatility(s) of the forward rates. A "simple" discretized expression for the drift then allows for forward rates to be expressed in a binomial lattice. For these forward rate-based models, dependent on volatility assumptions, the lattice might not recombine. (This means that an "up-move" followed by a "down-move" will not give the same result as a "down-move" followed by an "up-move".) In this case, the Lattice is sometimes referred to as a "bush", and the number of nodes grows exponentially as a function of number of time-steps. A recombining binomial tree methodology is also available for the Libor Market Model.As regards the short-rate models, these are, in turn, further categorized: these will be either equilibrium-based (Vasicek and CIR) or arbitrage-free (Ho–Lee and subsequent). This distinction: for equilibrium-based models the yield curve is an output from the model, while for arbitrage-free models the yield curve is an input to the model. In the former case, the approach is to "calibrate" the model parameters, such that bond prices produced by the model, in its continuous form, best fit observed market prices. The tree is then built as a function of these parameters.
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Lattice model (finance)
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Interest rate derivatives
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In the latter case, the calibration is directly on the lattice: the fit is to both the current term structure of interest rates (i.e. the yield curve), and the corresponding volatility structure.
Here, calibration means that the interest-rate-tree reproduces the prices of the zero-coupon bonds—and any other interest-rate sensitive securities—used in constructing the yield curve; note the parallel to the implied trees for equity above, and compare Bootstrapping (finance).
For models assuming a normal distribution (such as Ho-Lee), calibration may be performed analytically, while for log-normal models the calibration is via a root-finding algorithm; see for example, the boxed-description under Black–Derman–Toy model.
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Lattice model (finance)
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Interest rate derivatives
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The volatility structure—i.e. vertical node-spacing—here reflects the volatility of rates during the quarter, or other period, corresponding to the lattice time-step. (Some analysts use "realized volatility", i.e. of the rates applicable historically for the time-step; to be market-consistent, analysts generally prefer to use current interest rate cap prices, and the implied volatility for the Black-76-prices of each component caplet; see Interest rate cap § Implied Volatilities.) Given this functional link to volatility, note now the resultant difference in the construction relative to equity implied trees: for interest rates, the volatility is known for each time-step, and the node-values (i.e. interest rates) must be solved for specified risk neutral probabilities; for equity, on the other hand, a single volatility cannot be specified per time-step, i.e. we have a "smile", and the tree is built by solving for the probabilities corresponding to specified values of the underlying at each node.
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