title: Hyperkalemia

text: Hyperkalemic periodic paralysis is an autosomal dominant clinical condition where there is a mutation in gene located at 17q23 that regulates the production of protein SCN4A. SCN4A is an important component of sodium channels in skeletal muscles. During exercise, sodium channels would open to allow influx of sodium into the muscle cells for depolarization to occur. But in hyperkalemic periodic paralysis, sodium channels are slow to close after exercise, causing excessive influx of sodium and displacement of potassium out of the cells.


title: Hyperkalemia

text: Rare causes of hyperkalemia are discussed as follows. Acute digitalis overdose such as digoxin toxicity may cause hyperkalemia through the inhibition of sodium-potassium-ATPase pump. Massive blood transfusion can cause hyperkalemia in infants due to leakage of potassium out of the red blood cells during storage. Giving succinylcholine to people with conditions such as burns, trauma, infection, prolonged immobilisation can cause hyperkalemia due to widespread activation of acetylcholine receptors rather than a specific group of muscles. Arginine hydrochloride is used to treat refractory metabolic alkalosis. The arginine ions can enter cells and displace potassium out of the cells, causing hyperkalemia. Calcineurin inhibitors such as cyclosporine, tacrolimus, diazoxide, and minoxidil can cause hyperkalemia. Box jellyfish venom can also cause hyperkalemia.


title: Hyperkalemia

text: Excessive intake of potassium is not a primary cause of hyperkalemia because the human body usually can adapt to the rise in the potassium levels by increasing the excretion of potassium into urine through aldosterone hormone secretion and increasing the number of potassium secreting channels in kidney tubules. Acute hyperkalemia in infants is also rare even though their body volume is small, with accidental ingestion of potassium salts or potassium medications. Hyperkalemia usually develops when there are other co-morbidities such as hypoaldosteronism and chronic kidney disease.


title: Hyperkalemia

text: Pseudohyperkalemia occurs when the measured potassium level is falsely elevated. This condition is usually suspected when the patient is clinically well without any ECG changes. Mechanical trauma during blood drawing can cause potassium leakage out of the red blood cells due to haemolysis of the blood sample. Repeated fist clenching during the blood draw can cause a transient rise in potassium levels. Prolonged length of blood storage can also increase serum potassium levels. Hyperkalemia may become apparent when a person's platelet concentration is more than 500,000/microL in a clotted blood sample (serum blood sample). Potassium leaks out of platelets after clotting has occurred. A high white cell count (greater than 120,000/microL) in people with chronic lymphocytic leukemia increases the fragility of red blood cells, thus causing pseudohyperkalemia during blood processing. This problem can be avoided by processing serum samples, because clot formation protects the cells from haemolysis during processing. A familial form of pseudohyperkalemia, a benign condition characterised by increased serum potassium in whole blood stored at cold temperatures, also exists. This is due to increased potassium permeability in red blood cells.


title: Hyperkalemia

text: Potassium is the most abundant intracellular cation and about 98% of the body's potassium is found inside cells, with the remainder in the extracellular fluid including the blood. Membrane potential is maintained principally by the concentration gradient and membrane permeability to potassium with some contribution from the Na+/K+ pump. The potassium gradient is critically important for many physiological processes, including maintenance of cellular membrane potential, homeostasis of cell volume, and transmission of action potentials in nerve cells.


title: Hyperkalemia

text: Potassium is eliminated from the body through the gastrointestinal tract, kidney and sweat glands. In the kidneys, elimination of potassium is passive (through the glomeruli), and reabsorption is active in the proximal tubule and the ascending limb of the loop of Henle. There is active excretion of potassium in the distal tubule and the collecting duct; both are controlled by aldosterone. In sweat glands potassium elimination is quite similar to the kidney, its excretion is also controlled by aldosterone.


title: Hyperkalemia

text: Regulation of serum potassium is a function of intake, appropriate distribution between intracellular and extracellular compartments, and effective bodily excretion. In healthy individuals, homeostasis is maintained when cellular uptake and kidney excretion naturally counterbalance a patient's dietary intake of potassium. When kidney function becomes compromised, the ability of the body to effectively regulate serum potassium via the kidney declines. To compensate for this deficit in function, the colon increases its potassium secretion as part of an adaptive response. However, serum potassium remains elevated as the colonic compensating mechanism reaches its limits.


title: Hyperkalemia

text: Hyperkalemia develops when there is excess production (oral intake, tissue breakdown) or ineffective elimination of potassium. Ineffective elimination can be hormonal (in aldosterone deficiency) or due to causes in the kidney that impair excretion.


title: Hyperkalemia

text: Increased extracellular potassium levels result in depolarization of the membrane potentials of cells due to the increase in the equilibrium potential of potassium. This depolarization opens some voltage-gated sodium channels, but also increases the inactivation at the same time. Since depolarization due to concentration change is slow, it never generates an action potential by itself; instead, it results in accommodation. Above a certain level of potassium the depolarization inactivates sodium channels, opens potassium channels, thus the cells become refractory. This leads to the impairment of neuromuscular, cardiac, and gastrointestinal organ systems. Of most concern is the impairment of cardiac conduction, which can cause ventricular fibrillation and/or abnormally slow heart rhythms.


title: Hyperkalemia

text: To gather enough information for diagnosis, the measurement of potassium must be repeated, as the elevation can be due to hemolysis in the first sample. The normal serum level of potassium is 3.5 to 5mmol/L. Generally, blood tests for kidney function (creatinine, blood urea nitrogen), glucose and occasionally creatine kinase and cortisol are performed. Calculating the trans-tubular potassium gradient can sometimes help in distinguishing the cause of the hyperkalemia.


title: Hyperkalemia

text: Also, electrocardiography (ECG) may be performed to determine if there is a significant risk of abnormal heart rhythms. Physicians taking a medical history may focus on kidney disease and medication use (e.g. potassium-sparing diuretics), both of which are known causes of hyperkalemia.


title: Hyperkalemia

text: Normal serum potassium levels are generally considered to be between 3.5 and 5.3 mmol/L. Levels above 5.5mmol/L generally indicate hyperkalemia, and those below 3.5mmol/L indicate hypokalemia.


title: Hyperkalemia

text: With mild to moderate hyperkalemia, there is prolongation of the PR interval and development of peaked T waves. Severe hyperkalemia results in a widening of the QRS complex, and the ECG complex can evolve to a sinusoidal shape. There appears to be a direct effect of elevated potassium on some of the potassium channels that increases their activity and speeds membrane repolarisation. Also, (as noted above), hyperkalemia causes an overall membrane depolarization that inactivates many sodium channels. The faster repolarisation of the cardiac action potential causes the tenting of the T waves, and the inactivation of sodium channels causes a sluggish conduction of the electrical wave around the heart, which leads to smaller P waves and widening of the QRS complex. Some of potassium currents are sensitive to extracellular potassium levels, for reasons that are not well understood. As the extracellular potassium levels increase, potassium conductance is increased so that more potassium leaves the myocyte in any given time period. To summarize, classic ECG changes associated with hyperkalemia are seen in the following progression: peaked T wave, shortened QT interval, lengthened PR interval, increased QRS duration, and eventually absence of the P wave with the QRS complex becoming a sine wave. Bradycardia, junctional rhythms and QRS widening are particularly associated with increased risk of adverse outcomes


title: Hyperkalemia

text: The serum potassium concentration at which electrocardiographic changes develop is somewhat variable. Although the factors influencing the effect of serum potassium levels on cardiac electrophysiology are not entirely understood, the concentrations of other electrolytes, as well as levels of catecholamines, play a major role.


title: Hyperkalemia

text: ECG findings are not a reliable finding in hyperkalemia. In a retrospective review, blinded cardiologists documented peaked T-waves in only 3 of 90 ECGs with hyperkalemia. Sensitivity of peaked-Ts for hyperkalemia ranged from 0.18 to 0.52 depending on the criteria for peak-T waves.


title: Hyperkalemia

text: Preventing recurrence of hyperkalemia typically involves reduction of dietary potassium, removal of an offending medication, and/or the addition of a diuretic (such as furosemide or hydrochlorothiazide). Sodium polystyrene sulfonate and sorbitol (combined as Kayexalate) are occasionally used on an ongoing basis to maintain lower serum levels of potassium though the safety of long-term use of sodium polystyrene sulfonate for this purpose is not well understood.


title: Hyperkalemia

text: High dietary sources include vegetables such as avocados, tomatoes and potatoes, fruits such as bananas, oranges and nuts.


title: Hyperkalemia

text: Emergency lowering of potassium levels is needed when new arrhythmias occur at any level of potassium in the blood, or when potassium levels exceed 6.5mmol/L. Several agents are used to temporarily lower K levels. The choice depends on the degree and cause of the hyperkalemia, and other aspects of the person's condition.


title: Hyperkalemia

text: Calcium (calcium chloride or calcium gluconate) increases threshold potential through a mechanism that is still unclear, thus restoring normal gradient between threshold potential and resting membrane potential, which is elevated abnormally in hyperkalemia. A standard ampule of 10% calcium chloride is 10 mL and contains 6.8mmol of calcium. A standard ampule of 10% calcium gluconate is also 10 mL but has only 2.26mmol of calcium. Clinical practice guidelines recommend giving 6.8mmol for typical EKG findings of hyperkalemia. This is 10 mL of 10% calcium chloride or 30 mL of 10% calcium gluconate. Though calcium chloride is more concentrated, it is caustic to the veins and should only be given through a central line. Onset of action is less than one to three minutes and lasts about 30–60 minutes. The goal of treatment is to normalise the EKG and doses can be repeated if the EKG does not improve within a few minutes.


title: Hyperkalemia

text: Some textbooks suggest that calcium should not be given in digoxin toxicity as it has been linked to cardiovascular collapse in humans and increased digoxin toxicity in animal models. Recent literature questions the validity of this concern.


title: Hyperkalemia

text: Several medical treatments shift potassium ions from the bloodstream into the cellular compartment, thereby reducing the risk of complications. The effect of these measures tends to be short-lived, but may temporise the problem until potassium can be removed from the body.


title: Hyperkalemia

text: Severe cases require hemodialysis, which are the most rapid methods of removing potassium from the body. These are typically used if the underlying cause cannot be corrected swiftly while temporising measures are instituted or there is no response to these measures.


title: Hyperkalemia

text: Loop diuretics (furosemide, bumetanide, torasemide) and thiazide diuretics (e.g., chlortalidone, hydrochlorothiazide, or chlorothiazide) can increase kidney potassium excretion in people with intact kidney function.


title: Hyperkalemia

text: Potassium can bind to a number of agents in the gastrointestinal tract. Sodium polystyrene sulfonate with sorbitol (Kayexalate) has been approved for this use and can be given by mouth or rectally. However, high quality evidence to demonstrate the effectiveness of sodium polystyrene are lacking, and use of sodium polystyrene sulfonate, particularly with high sorbitol content, is uncommonly but convincingly associated with colonic necrosis. There are no systematic studies (>6 months) looking at the long-term safety of this medication.


title: Hyperkalemia

text: Patiromer is taken by mouth and works by binding free potassium ions in the gastrointestinal tract and releasing calcium ions for exchange, thus lowering the amount of potassium available for absorption into the bloodstream and increasing the amount lost via the feces. The net effect is a reduction of potassium levels in the blood serum.


title: Hyperkalemia

text: Sodium zirconium cyclosilicate is a medication that binds potassium in the gastrointestinal tract in exchange for sodium and hydrogen ions. Onset of effects occurs in one to six hours. It is taken by mouth.


title: Hyperkalemia

text: Hyperkalemia is rare among those who are otherwise healthy. Among those who are in hospital, rates are between 1% and 2.5%.


title: Hyperkalemia

text: In the United States, hyperkalemia is induced by lethal injection in capital punishment cases. Potassium chloride is the last of the three drugs administered and actually causes death. Injecting potassium chloride into the heart muscle disrupts the signal that causes the heart to beat. This same amount of potassium chloride would do no harm if taken orally and not injected directly into the blood.


title: Minority group

text: The term 'minority group' has different usages depending on the context. According to its common usage, a minority group can simply be understood in terms of demographic sizes within a population: i.e. a group in society with the least number of individuals is therefore the 'minority'. However, in terms of sociology, economics, and politics; a demographic which takes up the smallest fraction of the population is not necessarily the 'minority'. In the academic context, 'minority' and 'majority' groups are more appropriately understood in terms of hierarchical power structures. For example, in South Africa during Apartheid, white Europeans held virtually all social, economic, and political power over black Africans. For this reason, black Africans are the 'minority group', despite the fact that they outnumber white Europeans in South Africa. This is why academics more frequently use the term 'minority group' to refer to a category of people who experience relative disadvantage as compared to members of a dominant social group.


title: Minority group

text: Minority group membership is typically based on differences in observable characteristics or practices, such as: ethnicity (ethnic minority), race (racial minority), religion (religious minority), sexual orientation (sexual minority), or disability. The framework of intersectionality can be used to recognize that an individual may simultaneously hold membership in multiple minority groups (e.g. both a racial and religious minority). Likewise, individuals may also be part of a minority group in regard to some characteristics, but part of a dominant group in regard to others.


title: Minority group

text: The term "minority group" often occurs within the discourse of civil rights and collective rights, as members of minority groups are prone to differential treatment in the countries and societies in which they live. Minority group members often face discrimination in multiple areas of social life, including housing, employment, healthcare, and education, among others. While discrimination may be committed by individuals, it may also occur through structural inequalities, in which rights and opportunities are not equally accessible to all. The language of minority rights is often used to discuss laws designed to protect minority groups from discrimination and afford them equal social status to the dominant group.


title: Minority group

text: Prior to the Paris Peace Conference (1919–1920), the term "minority" primarily referred to political parties in national legislatures, not ethnic, national, linguistic or religious groups. The Paris Conference has been attributed with coining the concept of minority rights and bringing prominence to it. The League of Nations Minorities Commission defined minority in 1919 as "nationals belonging to racial, religious, or linguistic minorities."


title: Minority group

text: Louis Wirth defined a minority group as "a group of people who, because of their physical or cultural characteristics, are singled out from the others in the society in which they live for differential and unequal treatment, and who therefore regard themselves as objects of collective discrimination". The definition includes both objective and subjective criteria: membership of a minority group is objectively ascribed by society, based on an individual's physical or behavioral characteristics; it is also subjectively applied by its members, who may use their status as the basis of group identity or solidarity. Thus, minority group status is categorical: an individual who exhibits the physical or behavioral characteristics of a given minority group is accorded the status of that group and is subject to the same treatment as other members of that group.


title: Minority group

text: Joe Feagin, states that a minority group has five characteristics: (1) suffering discrimination and subordination, (2) physical and/or cultural traits that set them apart, and which are disapproved by the dominant group, (3) a shared sense of collective identity and common burdens, (4) socially shared rules about who belongs and who does not determine minority status, and (5) tendency to marry within the group.


title: Minority group

text: There is a controversy with the use of the word minority, as it has a generic and an academic usage. Common usage of the term indicates a statistical minority; however, academics refer to power differences among groups rather than differences in population size among groups.


title: Minority group

text: The above criticism is based on the idea that a group can be considered a minority even if it includes such a large number of people that it is numerically not a minority in society.


title: Minority group

text: Some sociologists have criticized the concept of "minority/majority", arguing this language excludes or neglects changing or unstable cultural identities, as well as cultural affiliations across national boundaries. As such, the term historically excluded groups (HEGs) is often similarly used to highlight the role of historical oppression and domination, and how this results in the under-representation of particular groups in various areas of social life.


title: Minority group

text: The term national minority is often used to discuss minority groups in international and national politics. All countries contain some degree of racial, ethnic, or linguistic diversity. In addition, minorities may also be immigrant, indigenous or landless nomadic communities. This often results in variations in language, culture, beliefs, practices, that set some groups apart from the dominant group. As these differences are usually perceived negatively, this results in loss of social and political power for members of minority groups.


title: Minority group

text: There is no legal definition of national minorities in international law, though protection of minority groups is outlined by the United Nations Declaration on the Rights of Persons Belonging to National or Ethnic, Religious and Linguistic Minorities. International criminal law can protect the rights of racial or ethnic minorities in several ways. The right to self-determination is a key issue. The Council of Europe regulates minority rights in the European Charter for Regional or Minority Languages and the Framework Convention for the Protection of National Minorities.


title: Minority group

text: In some places, subordinate ethnic groups may constitute a numerical majority, such as Blacks in South Africa under apartheid. In the United States, for example, non-Hispanic Whites constitute the majority (63.4%) and all other racial and ethnic groups (Mexican, African Americans, Asian Americans, American Indian, and Native Hawaiians) are classified as "minorities". If the non-Hispanic White population falls below 50% the group will only be the "plurality", not the majority.


title: Minority group

text: There is inadequate evidence whether mass media targeting ethnic minorities are more effective in changing health behaviors such as smoking cessation, weight reduction, and food habits when compared to mass media intended for the general population. For example, Romani people are considered an ethnic minority in Europe. Romani people are Europe's largest ethnic minority.


title: Minority group

text: A national minority is a social group within a state that differs from the majority and/or dominant population in terms of ethnicity, language, culture, or religion, but also it also tends to have a close link with a specific territory from which the minority social group originates.


title: Minority group

text: Also known as "castelike minorities", involuntary minorities are a term for people who were originally brought into any society against their will. In the United States, for instance, it includes but is not limited to Native Americans, Native Hawaiians, Puerto Ricans, African Americans, and in the 1800s, native-born Mexican Americans.


title: Minority group

text: Immigrants take on minority status in their new country, usually in hopes of a better future economically, educationally, and politically than in their homeland. Because of their focus on success, voluntary minorities are more likely to do better in school than other migrating minorities. Adapting to a very different culture and language makes difficulties in the early stages of life in the new country. Voluntary immigrants do not experience a sense of divided identity as much as involuntary minorities and are often rich in social capital because of their educational ambitions. Major immigrant groups in the United States include Mexicans, Central and South Americans, Cubans, Africans, East Asians, and South Asians.


title: Minority group

text: The term sexual minority is frequently used by public health researchers to recognize a wide variety of individuals who engage in same-sex sexual behavior, including those who do not identify under the LGBTQ+ umbrella. For example, men who have sex with men (MSM), but do not identify as gay. In addition, the term gender minorities can include many types of gender variant people, such as intersex people, transgender people, or non-binary individuals. However, the terms sexual and gender minority are often not preferred by LGBTQ+ people, as they represent clinical categories rather than individual identity.


title: Minority group

text: Though lesbian, gay, bisexual, transgender, and queer (LGBTQ+) people have existed throughout human history, LGBTQ+ rights movements across many western countries led to the recognition of LGBTQ+ people as members of a minority group. LGBTQ+ people represent a numerical and social minority. They experience numerous social inequalities stemming from their group membership as LGBTQ+ people. These inequalities include social discrimination and isolation, unequal access to healthcare, employment, and housing, and experience negative mental and physical health outcomes due to these experiences.


title: Minority group

text: Leading up to the Human Rights Act 1998 in the UK, a rise in the awareness relating to how disabled people were being treated began. Many started to believe that they were being denied basic human rights. This act had a section that stated if authorities did not protect people with learning disabilities from others' actions, such as harm or neglect, then they could be prosecuted.


title: Minority group

text: The disability rights movement has contributed to an understanding of disabled people as a minority or a coalition of minorities who are disadvantaged by society, not just as people who are disadvantaged by their impairments. Advocates of disability rights emphasize the difference in physical or psychological functioning rather than inferiority. For example, some autistic people argue for acceptance of neurodiversity, much as opponents of racism argue for acceptance of ethnic diversity. The deaf community is often regarded as a linguistic and cultural minority rather than a group with disabilities, and some deaf people do not see themselves as having a disability at all. Rather, they are disadvantaged by technologies and social institutions designed to cater to the dominant group. ("See the Convention on the Rights of Persons with Disabilities".)


title: Minority group

text: People belonging to religious minorities have a faith that is different from that held by the majority. Most countries of the world have religious minorities. It is now widely accepted in the west that people should have the freedom to choose their religion, including not having any religion (atheism and/or agnosticism), and including the right to convert from one religion to another. However, in many countries, this freedom is constricted. In Egypt, a new system of identity cards requires all citizens to state their religion—and the only choices are Islam, Christianity, or Judaism (See Egyptian identification card controversy). Another example is the case of decreasing population of minorities in Pakistan, where they are being forcefully converted or killed.


title: Minority group

text: In most societies, numbers of men and women are roughly equal. Though women are not considered to be a minority, the status of women as a subordinate group has led to many social scientists to study them as disadvantaged group. Though women's legal rights and status vary widely across countries, women can experience social inequalities relative to men in various societies. Women are sometimes denied access to education and access to the same opportunities as men.


title: Minority group

text: In the politics of some countries, a "minority" is an ethnic group recognized by law, and having specified rights. Speakers of a legally recognized minority language, for instance, might have the right to education or communication with the government in their mother tongue. Countries with special provisions for minorities include Canada, China, Ethiopia, Germany, India, the Netherlands, Poland, Romania, Russia, Croatia, and the United Kingdom.


title: Minority group

text: The various minority groups in a country are often not given equal treatment. Some groups are too small or indistinct to obtain minority protections. For example, a member of a particularly small ethnic group might be forced to check "Other" on a checklist of different backgrounds and so might receive fewer privileges than a member of a more defined group.


title: Minority group

text: Many contemporary governments prefer to assume the people they rule all belong to the same nationality rather than separate ones based on ethnicity. The United States asks for race and ethnicity on its official census forms, which thus breaks up and organizes its population into sub-groups, primarily racial rather than national. Spain does not divide its nationals by ethnic group or national minorities, although it does maintain an official notion of minority languages, that is one of the criteria for to determine a national minority, upon the Framework Convention for the Protection of National Minorities.


title: Minority group

text: Some especially significant or powerful minorities receive comprehensive protection and political representation. For example, the former Yugoslav Republic of Bosnia and Herzegovina recognizes the three constitutive nations, none of which constitutes a numerical majority (see nations of Bosnia and Herzegovina). However, other minorities such as Romani and Jews, are officially labelled "foreign" and are excluded from many of these protections. For example, they may be excluded from political positions, including the presidency.


title: Minority group

text: There is debate over recognizing minority groups and their privileges. One view is that the application of special rights to minority groups may harm some countries, such as new states in Africa or Latin America not founded on the European nation-state model, since minority recognition may interfere with establishing a national identity. It may hamper the integration of the minority into mainstream society, perhaps leading to separatism or supremacism. In Canada, some feel that the failure of the dominant English-speaking majority to integrate French Canadians has provoked Quebec separatism.


title: Minority group

text: Others assert that minorities require specific protections to ensure that they are not marginalized: for example, bilingual education may be needed to allow linguistic minorities to fully integrate into the school system and compete equally in society. In this view, rights for minorities strengthen the nation-building project, as members of minorities see their interests well served, and willingly accept the legitimacy of the nation and their integration (not assimilation) within it.


title: Fairchild Aircraft

text: Fairchild was an American aircraft and aerospace manufacturing company based at various times in Farmingdale, New York; Hagerstown, Maryland; and San Antonio, Texas.


title: Fairchild Aircraft

text: The company was founded by Sherman Fairchild in 1924 as Fairchild Aviation Corporation, based in Farmingdale, and East Farmingdale, New York. It was established as the parent company for Fairchild's many aviation interests. The company produced the first US aircraft to include a fully enclosed cockpit and hydraulic landing gear, the Fairchild FC-1. At some point, it was also known as the Fairchild Aircraft Manufacturing Company. The Fairchild Aircraft Ltd. of Longueuil, Quebec, Canada was an aircraft manufacturer during the period of 1920 to 1950, which served as a subsidiary of the Fairchild company of the United States. The Fairchild Engine Company was formed with the purchase of the Caminez Engine Company in 1925. In 1929, Sherman Fairchild purchased a majority stock interest in Kreider-Reisner Aircraft Company of Hagerstown, Maryland. The company moved to Hagerstown in 1931.


title: Fairchild Aircraft

text: A series of related designs beginning with the Fairchild FC-1 and continuing to the Fairchild 71 were designed for aerial photography as a result of dissatisfaction towards available aircraft which were incapable of flying steadily enough at a sufficient altitude. In 1935, Fairchild was hired by the US government to do aerial photograph surveys of the United States to track soil erosion and its effects. Their performance and carrying ability led to them becoming one of the most popular bushplanes of the era. A Fairchild 71 monoplane, the "Virginia", was taken as one of three aircraft by Richard E. Byrd on his 1928–1929 expedition to the South Pole. It was used for test flights and reconnaissance.


title: Fairchild Aircraft

text: During World War II, Fairchild produced PT-19/PT-23/PT-26 (Cornell) and AT-21 Gunner trainers, C-82 Packet transports and drones. The Fairchild AT-21 Gunner, a twin-engine trainer, was manufactured at a former rayon mill in Burlington, North Carolina. Also large numbers of the Fairchild 24 (C-61/Argus) were produced for the military (principally as the Argus for the Royal Air Force), and continued production after the war for the civilian market. Fairchild ranked 73rd among United States corporations in the value of World War II military production contracts.


title: Fairchild Aircraft

text: The C-82 Packet led to the C-119 Flying Boxcar, another U.S. military transport aircraft. The C-119 could carry cargo, personnel, stretcher patients and mechanized equipment with the ability to make "paradrops" of cargo and troops. The first C-119 made its initial flight in November 1947, and by the time production ceased in 1955, more than 1,100 C-119s had been built for use in the USAF, the Royal Canadian Air Force and others. Many were converted into waterbombers after being retired from military service.


title: Fairchild Aircraft

text: In 1949, the Hagerstown, Maryland, Fairchild Engine and Airplane Corporation developed the Chase XCG-20 glider into the C-123 Provider transport which entered service in 1955. In 1954 Fairchild purchased the American Helicopter Company, incorporating it and the XH-26 Jet Jeep as a division. In 1956, the company acquired rights to the Fokker Friendship, producing 206 of the aircraft as the Fairchild F-27 and Fairchild Hiller FH-227. During the 1950s, Fairchild was a large subcontractor to Boeing for B-52 fuselage sections and wing panels. Later, the company built McDonnell-Douglas F-4 Phantom II tail sections, Grumman F-14 Tomcat tails, and Space Shuttle orbiter stabilizers.


title: Fairchild Aircraft

text: In 1964, the company purchased Hiller Aircraft, changing its name to Fairchild Hiller and producing the FH-1100, until 1973 when the helicopter division was sold back to Stanley Hiller. In 1965, the company acquired the Republic Aviation Company.


title: Fairchild Aircraft

text: Following the death of its founder, Fairchild changed its name to Fairchild Industries in 1971. This was a merge of Fairchild-Hiller Corporation, division and subsidiaries: Fairchild Aircraft Marketing Company, Fairchild Aircraft Services Division, Fairchild Republic Division, Fairchild Space and Electronics Division, Fairchild Stratos Division, Burns Aero Seat Company, Inc., Fairchild Arms International, Ltd., Fairchild Aviation (Asia) Ltd., Fairchild Aviation (Holland) N.V., Fairchild-Germantown Development Company, Inc. and S.J. Industries, Inc. Before 1971, Fairchild Industries was a term used to include many of the companies of its founder Sherman Mills Fairchild.


title: Fairchild Aircraft

text: After the name change, the company purchased Swearingen and manufactured the Fairchild Swearingen Metroliner, a successful commuter aircraft that gained orders from the U.S. military as the C-26 Metroliner. In 1971, the company began developing the Fairchild Republic A-10 Thunderbolt II, which prevailed over the rival Northrop YA-9 in the A-X competition for an eventual production run of 716 aircraft.


title: Fairchild Aircraft

text: The company developed the T-46 jet trainer to replace the elderly Cessna T-37 Tweet trainer, but it was not accepted by the Air Force because of performance problems.


title: Fairchild Aircraft

text: Their association with Boeing continued into the 1980s as they built wing control surfaces for 747s and 757s.


title: Fairchild Aircraft

text: After the company took over Dornier's civil assets in 1996, the company was renamed Fairchild Dornier. The company commenced production of the Dornier 328 in 1998 under license from Deutsche Aerospace AG (DASA).


title: Fairchild Aircraft

text: In December 1999, Fairchild Aerospace Corporation was acquired by German insurer Allianz A.G. and the United States investment group Clayton, Dubilier & Rice Inc. for $1.2 billion.


title: Fairchild Aircraft

text: In 2003, the assets of Fairchild were purchased by M7 Aerospace and the new company was moved to San Antonio.


title: Fairchild Aircraft

text: On December 15, 2010, M7 was purchased by the United States subsidiary of the Israeli defense contractor Elbit Systems. M7 Aerospace does not manufacture aircraft, with focus on aerospace parts and support services.


title: Corpse Party

text: The PSP game was followed by a sequel, "Corpse Party: Book of Shadows", which was released for the PSP on September 1, 2011, in Japan, and on January 15, 2013, in North America. A spin-off game, "Corpse Party: Sweet Sachiko's Hysteric Birthday Bash", was released for the PSP in Japan on August 2, 2012, and was released for Windows worldwide on April 10, 2019. A direct sequel of "Corpse Party: Book of Shadows", called "Corpse Party: Blood Drive", was released in Japan on July 24, 2014, on PlayStation Vita, and was released in North America by XSeed Games on October 13, 2015, and on October 20, 2015, in Europe.


title: Corpse Party

text: Another sequel titled "Corpse Party 2: Dead Patient" was created for the PC by GrindHouse, a dōjin circle founded by members affiliated with Team GrisGris. It is planned to be released episodically, with the first chapter released on May 29, 2013.


title: Corpse Party

text: The series has spawned several manga works, an anime OVA series, drama CDs, theme park attractions, and two live action films.


title: Corpse Party

text: The plot of the original "Corpse Party" game concerns a group of Japanese high school students, celebrating their school's culture festival. The group are telling ghost stories when a sudden earthquake transports them to a dilapidated schoolhouse in an alternate dimension. The school is haunted by the ghosts of people who have been trapped there. The main playable character is Satoshi Mochida, a kind-hearted high school student who is teased by his classmates for his cowardly nature. Three of the other characters are students from Satoshi's class: Naomi Nakashima, Satoshi's childhood friend; Yoshiki Kishinuma, an intimidating yet good-natured student; and Ayumi Shinozaki, the class representative. Rounding out the group is Yuka Mochida, Satoshi's younger sister. The game's antagonist is the ghost of a former student, a girl in a red dress who seeks vengeance for her death at the hands of a teacher many years prior.


title: Corpse Party

text: "Corpse Party: NewChapter" remake was released for mobile phones in four chapters from October 3, 2006 to December 26, 2007. It was discontinued before Chapter 5 was released. It contained the same plot additions as the later "Blood Covered", but had much smaller maps.


title: Corpse Party

text: "Blood Covered", released in five chapters (first two released together) from March 8, 2008 to July 28, 2011, is an enhanced remake and port of the 1996 "Corpse Party". It includes more characters, larger maps, updated graphics, and a cast of amateur voice actors. It was followed on August 12, 2010 by another enhanced remake, "Blood Covered: Repeated Fear", which was released internationally as "Corpse Party", which features updated art and the addition of professional voice actors.


title: Corpse Party

text: The remake thoroughly expands the plot and setting of the original game. Here, the haunted schoolhouse is named , a fictional Fujisawa elementary school that was torn down following the murders and disappearances of several of its staff and students. In modern-day Japan, the main characters' high school, , has been built over the elementary school site. The students are transported to Heavenly Host after performing a charm called , which would supposedly allow them to remain friends for eternity.


title: Corpse Party

text: In addition to the five protagonists of the original game, "Blood Covered" introduces four characters to the playable cast: Seiko Shinohara, Naomi's best friend; Mayu Suzumoto, a popular student due to transfer out of Kisaragi; Sakutaro Morishige, Mayu's best friend; and Yui Shishido, the class's homeroom teacher. "Blood Covered" also includes several characters from other schools who are also trapped inside Heavenly Host and affect the story. Two notable characters are Naho Saenoki, a selfish but helpful paranormalist from who discovered the Sachiko Ever After charm and came to investigate Heavenly Host; and Yuuya Kizami, a sadistic student from who accompanies Yuka as she is separated from her brother. The red ghost is re-envisioned as a little girl named Sachiko Shinozaki who kills the students of Heavenly Host in anger over her and her mother's murder.


title: Corpse Party

text: "Corpse Party: Another Child" is a spin-off manga that takes place during the events of "Corpse Party". With their school, , shutting down for good, the students of a small town were heading for different directions in life, not until they decide to perform the "Sachiko Ever After" charm swallowing the entire class to Heavenly Host Elementary, along with a mysterious girl's spirit. In order to get out, they must track and get rid of the spirit.


title: Corpse Party

text: A sequel to "Blood Covered", "Book of Shadows" features a series of nonlinear chapters that add new twists and backgrounds for various characters and details important to the storyline. The game mostly takes place during the same time the first game did, continuing from one of the "wrong ends" in "Corpse Party", where Sachiko sends the Kisaragi Academy students back in time. For this purpose, she erases their memories except for Satoshi's. He fails to dissuade his classmates from performing the charm, but he joins them, not wanting to let them go alone, sending them on alternative course of actions and encountering several supporting victims in Heavenly Host.


title: Corpse Party

text: The game's epilogue, "Blood Drive", serves as the set up to the eponymous sequel. Two weeks after escaping Heavenly Host, Ayumi and Naomi go to investigate the Shinozaki estate, Sachiko's birthplace, believing there is hope in reviving their dead friends since Naho and Kou Kibiki's existences were not erased like the other victims. At the estate, Ayumi discovers that she is of the same lineage as Sachiko. Hearing an eerie voice, Ayumi uncovers a magical tome known as the Book of Shadows. Ayumi and Naomi perform a resurrection spell for Mayu, but fail. As compensation for using black magic, the book unleashes its rage upon Ayumi until her older sister Hinoe Shinozaki rushes in and saves Ayumi, at the cost of her own life.


title: Corpse Party

text: On the day of Sachiko's birth and death, the curse on her weakens and she gets 24 hours to celebrate her birthday as someone closer to the girl she was before her death. She uses the timeloops as established in "Corpse Party: Book of Shadows" to force all survivors at that point to participate in activities she has set up. Given it is either that or die horribly again, something all are aware that they have already experienced but cannot remember in full, they go along with her demands. The game features almost all characters from the previous games and some new ones. While a pseudo-horror spin-off at best, it is part of the storyline, setting up a few details to prepare for "Corpse Party: Blood Drive".


title: Corpse Party

text: As with "Corpse Party: Book of Shadows", there is only one extra chapter. This extra chapter takes place during the previous game and is more conventional horror. It tells of Yoshiki's and Ayumi's encounter with four students from Sugatani Senior High School, notably Azusa Takai.


title: Corpse Party

text: "Corpse Party: Blood Drive" is the direct sequel to "Corpse Party: Book of Shadows", and is the first game featuring settings and characters rendered in 3D. The game was released for the Sony PlayStation Vita in Japan in July 2014 by 5pb. The characters are depicted in 3D chibi style, however traditional CG artwork appears during cutscenes, illustrated by Sakuya Kamishiro.


title: Corpse Party

text: Continuing from the prologue included in "Book of Shadows", Naomi manages to save Ayumi and takes her to a hospital. The Shinozaki estate and tome subsequently vanish without a trace. Ayumi had been severely ill for her misuse of the Book of Shadows' black magic. In the hospital, a woman claiming to be a spiritual associate of Hinoe's visits Ayumi. This woman belongs to the Wiccan Institute, an organization that worships spirits. She tells her Hinoe's last wish, which is to regain the Book of Shadows or the world will fall into the abyss. This is partially a lie, as the woman is under threat of other organizations to get Ayumi to find the book, which they wish to use for their own gain.


title: Corpse Party

text: After being discharged from the hospital two months later, Ayumi returns to Kisaragi Academy where Satoshi and friends give her a warm welcome. However, the absence of their dead friends is a constant reminder of their inevitable reality. A new teacher's assistant, Kuon Niwa, supervises their homeroom. Later, on her way home, a black hooded boy approaches Ayumi and tells her, "If you reclaim the Book of Shadows and use it at Heavenly Host, those who have died there will be revived." Ayumi pledges that she will once more take back the Book of Shadows. The trail leads into the previous residence of Makina Shinozaki. To make matters worse, Heavenly Host's curse is expanded by the "new Sachiko", later named Sachi.


title: Corpse Party

text: The game "Corpse Party 2: Dead Patient" takes place five years after the events of "Corpse Party" Heavenly Host Arc, implied to be the consequences of the Book of Shadows' powers starting to bring about the end of the world by allowing the spirit realm and real world to start to converge together. The setting takes place at fallen into a dark abyss. Patient records and clinical charts are scattered all over the hospital, with zombies and a bizarre SWAT team roaming through the hallways. An amnesiac girl, Ayame Itou, wakes up on an operating table and encounters the dark happenings around her.


title: Corpse Party

text: On August 11, 2020, MAGES YouTube channel released a "10 Years of Corpse Party Repeated Fear" video celebrating the Heavenly Host Saga, at the end of the Timeline they show off "202X" with then the words "Darkness Distortion" followed by the last words of "More Corpse...", which seems to tease a direct sequel to "Corpse Party: Blood Drive", which was called "The End of the Heavenly Host Saga".


title: Corpse Party

text: The first game in the series was developed using the RPG Maker version RPG Tsukūru Dante 98 software and released in 1996 for the PC-9801.


title: Corpse Party

text: Dummy head mics were utilized for "Blood Covered", "Book of Shadows", and "Blood Drive" to provide perceived three dimensional sound.


title: Corpse Party

text: The opening for "Corpse Party Blood Covered: ...Repeated Fear" is "Shangri-La" by Asami Imai, and the ending for "Blood Covered" is "Confutatis no Inori" by Artery Vein (Imai & Eri Kitamura). An insert song, "Yami ni Nureta Catastrophe", also sung by Artery Vein, plays at the end of the game.


title: Corpse Party

text: The opening theme for "Corpse Party: Book of Shadows" is "Hana no Saku Basho" by Imai, and the ending is "Pandora no Yoru", by Artery Vein.


title: Corpse Party

text: The opening theme for "Corpse Party: Sweet Sachiko's Hysteric Birthday Bash" is called "Limited Love" by Imai, and the ending theme is "Tsukigen" by ARTERY VEIN. An insert song, "Hanabi", sung by Yumi Hara, plays at the final scene where Sachiko's birthday has ended and she seemed to have only a brief memory of it, before screaming in agony and reverting to her malicious self.


title: Corpse Party

text: In "Corpse Party: Blood Drive", there are two openings; the first one being "In the Rain", by Hara, and the second being "Keshin" by Imai, which plays at Chapter 7 after Ayumi's retrieval of the Book of Shadows. The ending is "Translucent Days" by ARTERY VEIN.


title: Corpse Party

text: Although the series has received mixed to positive reviews as a whole, it is regarded as a "cult favorite" in Japan with a dedicated fan following. "Famitsu" gave "Corpse Party: Blood Drive" a score of 29/40.


title: Corpse Party

text: The video game series has been adapted into four manga series: "Corpse Party: Blood Covered", published by Square Enix; "Corpse Party: Musume" and "Corpse Party: Book of Shadows", published by Media Factory; and "Corpse Party: Another Child", published by Mag Garden. The manga series has sold over 1million copies, as of May 2015.


title: Corpse Party

text: One original video animation (OVA), "Corpse Party: Missing Footage", was released on August 2, 2012. Another OVA consisting of four episodes titled "", was released on July 24, 2013, and later licensed by Section23 Films.


title: Corpse Party

text: A movie adaptation was also made, which was released on August 1, 2015, while a film adaptation of "Corpse Party: Book of Shadows" was released on June 30, 2016.


title: Corpse Party

text: On June 12, 2015, the Chinese Ministry of Culture listed "Corpse Party" among 38 anime and manga titles banned in Mainland China.


title: Angelique Boyer

text: Angelique Monique-Paulette Boyer Rousseau (born 4 July 1988), simply known as Angelique Boyer, is an actress. Born in France, she has spent most of her life and her entire professional career in Mexico, becoming a dual French and Mexican citizen.


title: Angelique Boyer

text: Boyer was born in Saint-Claude, Jura, France. Boyer and her family moved to Mexico when she was two years old.


title: Angelique Boyer

text: While filming "Rebelde", she and two other co-stars – the actors who portray the characters of Celina (Estefanía Villareal) and José Luján (Zoraida Gómez) - formed the band Citricus or C3Q'S. After "Rebelde", Boyer auditioned for "Bailando por la Boda de mis Sueños" (Dancing for my Dream Wedding).


title: Angelique Boyer

text: In 2009, she was cast in the high crime drama television series "Mujeres Asesinas 2". These controversial roles marked a significant change in Boyer's acting career, for this was the first time fans had seen the actress in more mature roles.


title: Angelique Boyer

text: Not long after she was the protagonist-antagonist in "Teresa", she participated in a theatre role, "Ausencia de Dios" (God's Absence) she went from "la hembra mala" (femme fatale) to a "monja" (a nun in catholic religion), where she worked with Raquel Olmedo once again, and Jacqueline Andere.


title: Angelique Boyer

text: On June 26, 2013, it was confirmed that Boyer (along with Sebastián Rulli and Luis Roberto Guzmán) would star in Angelli Nesma's "Lo que la vida me robó", a remake of Ernesto Alonso's "Bodas de odio" produced in 1983. In late 2015, she was cast in Angelli Nesma Medina's telenovela "Tres veces Ana".


title: Angelique Boyer

text: She first appeared on television in the soap opera produced by Nicandro Díaz and Roberto Hernández Vázquez, Corazones al limite, where she debuted playing the character "Anette", the best friend of the protagonist played by Sara Maldonado, before she moved to another city.


title: Angelique Boyer

text: That same year, she participated in the soap opera Rebelde, a version of the Argentine soap opera Rebelde Way, and was produced by Pedro Damián. She was "Vico", a very liberal girl who had some boyfriends during the plot.


title: Angelique Boyer

text: In 2007, she returned to television with the novel by Emilio Larrosa, Muchachitas como tú, based on Muchachitas, where she shared credits with Ariadne Díaz. In the plot she was "Margarita", engaged to the villain who also had the role of antagonist, until he was redeemed.


title: Angelique Boyer

text: In 2008, she joined the soap opera Alma de Hierro, playing Sandra "Sandy" Hierro Jiménez, a girl who hid from her parents that she had the dream of being dancer, while they wanted the girl to study medicine.


title: Angelique Boyer

text: In 2009, she participated in the second season of the television series "Mujeres Asesinas", in the episode "Soledad Cautiva", playing Soledad Oropeza "Cindy" a girl who ends up getting involved with a man she met on the road, but what she didn't expect is that he would take her into the life of prostitution.


title: Angelique Boyer

text: Later, in the same year, she participated in the novel produced by Salvador Mejía and created by Caridad Bravo Adams, Corazón salvaje. She was "Jimena", a gypsy who hid her condition from the noble "Gabriel", character of Sebastián Zurita.


title: Angelique Boyer

text: In 2010, Boyer got her first starring role in the telenovela "Teresa" produced by José Alberto Castro. Boyer played protagonist Teresa Chávez Aguirre, alongside Aarón Díaz and Sebastián Rulli.


title: Angelique Boyer

text: In 2012, she starred in the telenovela "Abismo de Pasión", adapted from the 1996 soap opera "Cañaveral de pasiones", and shared credits with David Zepeda.


title: Angelique Boyer

text: In 2013, she was chosen by Angelli Nesma Medina to star in the telenovela "Lo que la vida me robó", an adaptation of the novels "Amor Real" and "Bodas de odio", starring alongside Sebastián Rulli and Luis Roberto Guzmán. She portrayed Montserrat, a socialite who was dominated by her mother Graziela.


title: Angelique Boyer

text: In 2016, Boyer was selected by producer Angelli Nesma Medina to star in "Tres veces Ana", an adaptation of "Lazos de amor", in which she tarred alongside Sebastián Rulli, David Zepeda and Pedro Moreno. She played three roles as the triplets Ana Lucía, Ana Laura, and Ana Letícia.


title: Angelique Boyer

text: In 2020, producer Giselle González chose Boyer to star in the soap opera "Imperio de mentiras", a remake of the Turkish soap opera "Kara Para Aşk". In this series she shared credits with Andrés Palacios, Leticia Calderón, Susana González and Alejandro Camacho. She played Elisa Cantú, a woman trying to solve the mystery of her father's death.


title: Angelique Boyer

text: In 2021, she was chosen by the production company Rosy Ocampo to star in "Vencer el pasado", playing molecular biologist Renata who is in a love triangle with Sebastián Rulli and Horacio Pancheri.


title: Angelique Boyer

text: In 2001, she belonged to the Rabanitos Verdes group, along with five boys. The band sang the opening theme of the children's telenovela "María Belén".


title: Angelique Boyer

text: In 2005, she was part of C3Q'S, a pop group within the soap opera "Rebelde" with Zoraida Gómez and Estefanía Villarreal, releasing only a single entitled "No Me Importa".


title: Coat of arms of Russia

text: The coat of arms of Russia derives from the earlier coat of arms of the Russian Empire which was abolished with the Russian Revolution in 1917. Though modified more than once since the reign of Ivan III (1462–1505), the current coat of arms is directly derived from its medieval original, with the double-headed eagle having Byzantine and earlier antecedents. The general tincture corresponds to the early fifteenth-century standard.


title: Coat of arms of Russia

text: The two main elements of Russian state symbols (the two-headed eagle and the mounted figure slaying the dragon) predate Peter the Great. According to the Kremlin's website:


title: Coat of arms of Russia

text: «...четырёхугольный, с закруглёнными нижними углами, заострённый в оконечности красный геральдический щит с золотым двуглавым орлом, поднявшим вверх распущенные крылья. Орел увенчан двумя малыми коронами и — над ними — одной большой короной, соединенными лентой. В правой лапе орла — скипетр, в левой — держава. На груди орла, в красном щите, — серебряный всадник в синем плаще на серебряном коне, поражающий серебряным копьём черного опрокинутого навзничь и попранного конём дракона.»


title: Coat of arms of Russia

text: "… a gold two-headed eagle with raised extended wings set against a four-cornered red heraldic shield with rounded lower corners. Two small crowns top the eagle's heads, with one large crown above them. The three crowns are linked by a ribbon. The eagle holds a sceptre in its right claw and an orb in its left claw. The eagle bears a red shield on its breast depicting a silver horseman in a blue cape, mounted upon a silver horse and slaying a black dragon with a silver spear."


title: Coat of arms of Russia

text: The current coat of arms was designed by artist Yevgeny Ukhnalyov; it was adopted on 30 November 1993 by a presidential decree, and then by a federal law signed by President Vladimir Putin on December 20, 2000.


title: Coat of arms of Russia

text: Today, the imperial crowns on each head stand for the unity and sovereignty of Russia, both as a whole and in its constituent republics and regions. The orb and scepter grasped in the eagle's talons are traditional heraldic symbols of sovereign power and authority. Of note is that the scepter shows the Droste effect, as it is topped by a miniature image of the coat-of-arms itself. They have been retained in the modern Russian arms despite the fact that the Russian Federation is not a monarchy, which led to objections by the Communists even though both the blue ribbon and the collar of the Order of St. Andrew (which in the imperial arms supported the three crowns and surrounded the central shield) have been removed from the current coat of arms.


title: Coat of arms of Russia

text: is a squared Russian tricolour defaced with the coat of arms of Russia, the banner of the Russian Armed Forces also has the coat of arms centered on the obverse side. Some state awards of Russia are also designed based on the coat of arms, including the State Prize. Russian ruble coins depict the coat of arms on the obverse side since 2016.


title: Coat of arms of Russia

text: The heraldic device of Russia has gone through three major periods in its history, undergoing major changes in the transitions between the Russian Empire, the Soviet Union, and the Russian Federation. The use of the double-headed eagle as a Russian coat of arms goes back to the 15th century. With the fall of Constantinople and the end of the Byzantine Empire in 1453, the Grand Dukes of Muscovy came to see themselves as the successors of the Byzantine heritage, a notion reinforced by the marriage of Ivan III to Sophia Paleologue (hence the expression "Third Rome" for Moscow and, by extension, for the whole of Imperial Russia). Ivan adopted the golden Byzantine double-headed eagle in his seal, first documented in 1472, marking his direct claim to the Roman imperial heritage and posing as a sovereign equal and rival to the Holy Roman Empire. In 1497, it was stamped on a charter of share and allotment of independent princes' possessions. At about the same time, the image of a gilt, double-headed eagle on a red background appeared on the walls of the Palace of Facets in the Moscow Kremlin.


title: Coat of arms of Russia

text: The other main Russian coat of arms, the image of St George slaying the dragon, is contemporaneous. In its first form, as a rider armed with a spear, it is found in the seal of Vasili I of Moscow in 1390. At the time of Ivan III, the dragon was added, but the final association with Saint George was not made until 1730, when it was described as such in an Imperial decree. Eventually, St George became the patron saint of Moscow (and, by extension, of Russia).


title: Coat of arms of Russia

text: After the assumption of the title of "Tsar" by Ivan IV, the two coats are found combined, with the eagle bearing an escutcheon depicting St George on the breast. With the establishment of the Moscow Patriarchate in 1589, a patriarchal cross was added for a time between the heads of the eagle.


title: Coat of arms of Russia

text: The Russian Empire had a coat of arms, displayed in either its greater, middle and lesser version. Its escutcheon was golden with a black two-headed eagle crowned with two imperial crowns, over which the same third crown, enlarged, with two flying ends of the ribbon of the Order of Saint Andrew. The State Eagle held a golden scepter and golden globus cruciger. On the chest of the eagle there was an escutcheon with the arms of Moscow, depicting Saint George, mounted and defeating the dragon. After approval by Alexander III on 24 July 1882, the greater coat of arms was adopted on 3 November, replacing the previous 1857 version.


title: Coat of arms of Russia

text: Its central element is the coat of arms, crowned with the helmet of Alexander Nevsky, with black and golden mantling, and flanked by the archangels Michael and Gabriel. The collar of the Order of Saint Andrew is suspended from the coat of arms. The whole lies within a golden ermine mantle, crowned by the Imperial Crown of Russia and decorated with black double-headed eagles. The inscription on the canopy reads: Съ Нами Богъ ("God is with us"). Above the canopy stands the state khorugv, of gold cloth, on which is depicted the Medium State Seal. The banner is topped by the State Eagle.


title: Coat of arms of Russia

text: Around the central composition are placed fifteen coats of arms of the various territories of the Russian Empire. Nine of these are crowned and placed on a laurel and oak wreath. Proceeding from the left in a counter-clockwise direction, these represent, as they are included in the full imperial title: the Khanate of Kazan, the Congress Kingdom of Poland, Tauric Chersonesos, the unified coat of arms of the Grand Principalities of Kiev, Vladimir and Novgorod, the dynastic arms of the House of Holstein-Gottorp-Romanov, the Grand Principality of Finland, the Georgian principalities, and the Khanates of Siberia and Astrakhan.


title: Coat of arms of Russia

text: The six upper escutcheons are joint depictions of various smaller principalities and "oblasts". From the left in a clockwise fashion, these are: the combined arms of the northeastern regions (Perm, Volga Bulgaria, Vyatka, Kondinsky, Obdorsk), of Belorussia and Lithuania (Lithuania, Białystok, Samogitia, Polatsk, Vitebsk, Mstislavl), the provinces of Great Russia proper (Pskov, Smolensk, Tver, Nizhniy-Novgorod, Ryazan, Rostov, Yaroslavl, Belozersk, Udorsky), the arms of the southwestern regions (Volhyn, Podolsk, Chernigov), the Baltic provinces (Estonia, Courland and Semigalia, Karelia, Livonia) and Turkestan.


title: Coat of arms of Russia

text: The Middle Coat of Arms (Средний государственный герб Российской Империи) is similar to the Great Coat of Arms, excluding the khorugv and the six upper escutcheons. The Abbreviated Imperial Title is inscribed over the perimeter of the Seal. The Lesser Coat of Arms (Малый государственный герб Российской Империи) depicts the imperial double-headed eagle, as used in the coat of arms, with the addition of the collar of the Order of Saint Andrew around the escutcheon of St. George, and the Arms of Astrakhan, Siberia, Georgia, Finland, Kiev-Vladimir-Novgorod, Taurica, Poland and Kazan on the wings (seen clockwise).


title: Coat of arms of Russia

text: In the beginning of the 17th century, with the ascension of the Romanov dynasty and its contacts with Western Europe, the image of the eagle changed. In 1625, for the first time the double-headed eagle appeared with three crowns. Traditionally, the latter have alternatively been interpreted as representing the conquered kingdoms of Kazan, Astrakhan and Siberia, as stated in the first edict concerning the state seal, on 14 December 1667, or as standing for the unity of Great Russia (Russia), Little Russia (the Ukraine) and White Russia (Belarus). Probably under influence from its German equivalent, the eagle, from 1654 onwards, was designed with spread wings and holding a scepter and orb in its claws.


title: Coat of arms of Russia

text: During the reign of Peter the Great, further changes were made. The collar of the newly established Order of Saint Andrew was added around the central escutcheon, and the crowns were changed to the imperial pattern after his assumption of the imperial title in 1721. At about this time, the eagle's color was changed from golden to black, which would be retained until the fall of the Russian monarchy in 1917. A final form for the eagle was adopted by imperial decree in 1729, and remained virtually unchanged until 1853.


title: Coat of arms of Russia

text: During the early 19th century, the eagle designs diversified, and two different variants were adopted by Emperor Nicholas I. The first type represented the eagle with spread wings, one crown, with an image of St.George on the breast and with a wreath and a thunderbolt in its claws. The second type followed the 1730 pattern, with the addition of the arms of Kazan, Astrakhan and Siberia on its left wing and those of Poland, the Taurica and Finland on the right one.


title: Coat of arms of Russia

text: In 1855–57, in the course of a general heraldic reform, the eagle's appearance was changed, mirroring German patterns, while St George was made to look to the left, in accordance with the rules of Western heraldry. At the same time, the full set of coat of arms of Great, Medium and Minor Arms, was laid down and approved. The final revisions and changes were made in 1882–83, and are those described above.


title: Coat of arms of Russia

text: The coat of arms of the Russian Soviet Federative Socialist Republic (RSFSR) was adopted on 10 July 1918 by the government of the Russian Soviet Federative Socialist Republic (Soviet Union), and modified several times afterwards. It shows wheat as the symbol of agriculture, a rising sun for the "future of the Russian nation", the red star (the RSFSR was the last Soviet Republic to include the star in its state emblem, in 1978) as well as the hammer and sickle for the victory of Communism and the "world-wide socialist community of states".


title: Coat of arms of Russia

text: The Soviet Union state motto ("Workers of the world, unite!") in Russian (" — ) is also a part of the coat of arms.


title: Coat of arms of Russia

text: Similar emblems were used by the Autonomous Socialist Soviet Republics (ASSR) within the Russian SFSR; the main differences were generally the use of the republic's acronym and the presence of the motto in the language(s) of the titular nations (with the exception of the state emblem of the Dagestan ASSR, which had the motto in eleven languages as there is no single Dagestani language).


title: Coat of arms of Russia

text: The Soviet Union as a whole adopted its emblem in 1923, which remained in use until the dissolution of the Soviet Union in 1991. Although it is technically an emblem rather than a coat of arms, since it does not follow traditional heraldic rules, in Russian it is called (), the word used for a traditional coat of arms. It was the first state insignia created in the style known as socialist heraldry, a style also seen in e.g. the Chinese national emblem.


title: Coat of arms of Russia

text: The emblem shows the Soviet emblems of the Hammer and Sickle and the Red Star over a globe, in the center of a wreath wrapped in ribbons emblazoned with the Soviet motto ("Workers of the world, unite!") in the official languages of the Soviet Republics, in the reverse order they were mentioned in the Soviet Constitution. Each Soviet Republic (SSR) and Autonomous Soviet Republic (ASSR) had its own coat of arms, largely inspired by the state emblem of the Union.


title: Coat of arms of Russia

text: Four versions were used: 6 ribbons were used in 1923, which were written on in Russian, Ukrainian, Belarusian, Georgian, Armenian, and Azerbaijani; 11 ribbons with the addition of Turkmen, Uzbek, Tajik, Kazakh, Kyrgyz; 16 with the addition of Estonian, Latvian, Lithuanian, Moldavian, and Finnish. Finally, the inscriptions in Azerbaijani, Turkmen, Uzbek, Tajik, Kazakh and Kyrgyz were updated to reflect their transition from the Latin to the Cyrillic script. The final version of the emblem was adopted in 1956 with the removal of the Finnish inscription from the insignia, reflecting the 1956 transformation of the Karelo-Finnish SSR into the Karelian ASSR.


title: Coat of arms of Russia

text: In 1992, the inscription was changed from RSFSR (") to the Russian Federation (") in connection with the change of the name of the state. In 1993, president Boris Yeltsin signed a decree to replace the Communist design by the present coat of arms.


title: Munmun Dutta

text: Munmun Dutta (born 28 September 1987) is an Indian television actress and model. She is best known for her portrayal of Babita Iyer in the popular Hindi sitcom "Taarak Mehta Ka Ooltah Chashmah".


title: Munmun Dutta

text: Dutta was born on 28 September 1987 in Durgapur, West Bengal. She completed a master's degree in English. In Kolkata, she used to perform as a child singer for Akashvani and Doordarshan. While living in Pune, Dutta participated in fashion shows. She came to Mumbai and had her acting debut in Zee TV's 2004 serial "Hum Sab Baraati". Her first film role was in Kamal Haasan's "Mumbai Xpress". In 2006, she appeared in the film "Holiday".


title: Munmun Dutta

text: On 9 May 2021, a case was registered, in Hansi, against her due to discriminatory slur (seemingly violating "Scheduled Caste and Scheduled Tribe (Prevention of Atrocities) Act, 1989") made by her on her Youtube video that went viral. The actress, however, apologized for the comment after hashtags demanding her arrest, on social media, after which she stated- "She did not know that language and didn't intend to hurt anyone's sentiments." She was arrested in 2022 and her anticipatory bail was rejected.


title: Munmun Dutta

text: In mid-September 2021, Dutta came in public interest due to her relationship with co-star Raj Anadkat. However, after some days both the actors denied all rumours and stated them "fake and false".


title: Weighted arithmetic mean

text: The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.


title: Weighted arithmetic mean

text: If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.


title: Weighted arithmetic mean

text: The mean for the morning class is 80 and the mean of the afternoon class is 90. The unweighted mean of the two means is 85. However, this does not account for the difference in number of students in each class (20 versus 30); hence the value of 85 does not reflect the average student grade (independent of class). The average student grade can be obtained by averaging all the grades, without regard to classes (add all the grades up and divide by the total number of students):


title: Weighted arithmetic mean

text: Or, this can be accomplished by weighting the class means by the number of students in each class. The larger class is given more "weight":


title: Weighted arithmetic mean

text: Thus, the weighted mean makes it possible to find the mean average student grade without knowing each student's score. Only the class means and the number of students in each class are needed.


title: Weighted arithmetic mean

text: Since only the "relative" weights are relevant, any weighted mean can be expressed using coefficients that sum to one. Such a linear combination is called a convex combination.


title: Weighted arithmetic mean

text: Therefore, data elements with a high weight contribute more to the weighted mean than do elements with a low weight. The weights cannot be negative. Some may be zero, but not all of them (since division by zero is not allowed).


title: Weighted arithmetic mean

text: The formulas are simplified when the weights are normalized such that they sum up to 1, i.e., formula_10.


title: Weighted arithmetic mean

text: Note that one can always normalize the weights by making the following transformation on the original weights:


title: Weighted arithmetic mean

text: The ordinary mean formula_13 is a special case of the weighted mean where all data have equal weights.


title: Weighted arithmetic mean

text: If the data elements are independent and identically distributed random variables with variance formula_14, the "standard error of the weighted mean", formula_15, can be shown via uncertainty propagation to be:


title: Weighted arithmetic mean

text: For the weighted mean of a list of data for which each element formula_17 potentially comes from a different probability distribution with known variance formula_18, all having the same mean, one possible choice for the weights is given by the reciprocal of variance:


title: Weighted arithmetic mean

text: The significance of this choice is that this weighted mean is the maximum likelihood estimator of the mean of the probability distributions under the assumption that they are independent and normally distributed with the same mean.


title: Weighted arithmetic mean

text: The weighted sample mean, formula_26, is itself a random variable. Its expected value and standard deviation are related to the expected values and standard deviations of the observations, as follows. For simplicity, we assume normalized weights (weights summing to one).


title: Weighted arithmetic mean

text: In particular, if the means are equal, formula_29, then the expectation of the weighted sample mean will be that value,


title: Weighted arithmetic mean

text: When treating the weights as constants, and having a sample of "n" observations from uncorrelated random variables, all with the same variance and expectation (as is the case for i.i.d random variables), then the variance of the weighted mean can be estimated as the multiplication of the variance by Kish's design effect (see proof):


title: Weighted arithmetic mean

text: However, this estimation is rather limited due to the strong assumption about the "y" observations. This has led to the development of alternative, more general, estimators.


title: Weighted arithmetic mean

text: From a "model based" perspective, we are interested in estimating the variance of the weighted mean when the different formula_35 are not i.i.d random variables. An alternative perspective for this problem is that of some arbitrary sampling design of the data in which units are selected with unequal probabilities (with replacement).


title: Weighted arithmetic mean

text: In Survey methodology, the population mean, of some quantity of interest "y", is calculated by taking an estimation of the total of "y" over all elements in the population ("Y" or sometimes "T") and dividing it by the population size – either known (formula_36) or estimated (formula_37). In this context, each value of "y" is considered constant, and the variability comes from the selection procedure. This in contrast to "model based" approaches in which the randomness is often described in the y values. The survey sampling procedure yields a series of Bernoulli indicator values (formula_38) that get 1 if some observation "i" is in the sample and 0 if it was not selected. This can occur with fixed sample size, or varied sample size sampling (e.g.: Poisson sampling). The probability of some element to be chosen, given a sample, is denoted as formula_39, and the one-draw probability of selection is formula_40 (If N is very large and each formula_41 is very small). For the following derivation we'll assume that the probability of selecting each element is fully represented by these probabilities. I.e.: selecting some element will not influence the probability of drawing another element (this doesn't apply for things such as cluster sampling design).


title: Weighted arithmetic mean

text: Since each element (formula_35) is fixed, and the randomness comes from it being included in the sample or not (formula_38), we often talk about the multiplication of the two, which is a random variable. To avoid confusion in the following section, let's call this term: formula_44. With the following expectancy: formula_45; and variance: formula_46.


title: Weighted arithmetic mean

text: When each element of the sample is inflated by the inverse of its selection probability, it is termed the formula_47-expanded "y" values, i.e.: formula_48. A related quantity is formula_49-expanded "y" values: formula_50. As above, we can add a tick mark if multiplying by the indicator function. I.e.: formula_51


title: Weighted arithmetic mean

text: In this "design based" perspective, the weights, used in the numerator of the weighted mean, are obtained from taking the inverse of the selection probability (i.e.: the inflation factor). I.e.: formula_52.


title: Weighted arithmetic mean

text: If the sampling design is one that results in a fixed sample size "n" (such as in pps sampling), then the variance of this estimator is:


title: Weighted arithmetic mean

text: The population total is denoted as formula_55 and it may be estimated by the (unbiased) Horvitz–Thompson estimator, also called the "formula_47"-estimator. This estimator can be itself estimated using the "pwr"-estimator (i.e.: formula_49-expanded with replacement estimator, or "probability with replacement" estimator). With the above notation, it is: formula_58.


title: Weighted arithmetic mean

text: The above formula was taken from Sarndal et al. (1992) (also presented in Cochran 1977), but was written differently. The left side is how the variance was written and the right side is how we've developed the weighted version:


title: Weighted arithmetic mean

text: An alternative term, for when the sampling has a random sample size (as in Poisson sampling), is presented in Sarndal et al. (1992) as:


title: Weighted arithmetic mean

text: With formula_63. Also, formula_64 where formula_65 is the probability of selecting both i and j. And formula_66, and for i=j: formula_67.


title: Weighted arithmetic mean

text: If the selection probability are uncorrelated (i.e.: formula_68), and when assuming the probability of each element is very small, then:


title: Weighted arithmetic mean

text: ) & = \frac{1}{N^2} \sum_{i=1}^n \sum_{j=1}^n \left( \check{\Delta}_{ij} \check{y}_i \check{y}_j \right) \\


title: Weighted arithmetic mean

text: The previous section dealt with estimating the population mean as a ratio of an estimated population total (formula_70) with a known population size (formula_36), and the variance was estimated in that context. Another common case is that the population size itself (formula_36) is unknown and is estimated using the sample (i.e.: formula_37). The estimation of formula_36 can be described as the sum of weights. So when formula_75 we get formula_76. When using notation from previous sections, the ratio we care about is the sum of formula_35s, and 1s. I.e.: formula_78. We can estimate it using our sample with: formula_79. As we moved from using N to using n, we actually know that all the indicator variables get 1, so we could simply write: formula_80. This will be the estimand for specific values of y and w, but the statistical properties comes when including the indicator variable formula_81.


title: Weighted arithmetic mean

text: In this case, the variability of the ratio depends on the variability of the random variables both in the numerator and the denominator - as well as their correlation. Since there is no closed analytical form to compute this variance, various methods are used for approximate estimation. Primarily Taylor series first-order linearization, asymptotics, and bootstrap/jackknife. The Taylor linearization method could lead to under-estimation of the variance for small sample sizes in general, but that depends on the complexity of the statistic. For the weighted mean, the approximate variance is supposed to be relatively accurate even for medium sample sizes. For when the sampling has a random sample size (as in Poisson sampling), it is as follows:


title: Weighted arithmetic mean

text: We note that if formula_83, then either using formula_84 or formula_85 would give the same estimator, since multiplying formula_86 by some factor would lead to the same estimator. It also means that if we scale the sum of weights to be equal to a known-from-before population size "N", the variance calculation would look the same. When all weights are equal to one another, this formula is reduced to the standard unbiased variance estimator.


title: Weighted arithmetic mean

text: The term formula_89 is the estimated covariance between the estimated sum of Y and estimated sum of Z. Since this is the covariance of two sums of random variables, it would include many combinations of covariances that will depend on the indicator variables. If the selection probability are uncorrelated (i.e.: formula_90), this term would still include a summation of "n" covariances for each element "i" between formula_91 and formula_92. This helps illustrate that this formula incorporates the effect of correlation between y and z on the variance of the ratio estimators.


title: Weighted arithmetic mean

text: If the selection probability are uncorrelated (i.e.: formula_90), and when assuming the probability of each element is very small (i.e.: formula_96), then the above reduced to the following:


title: Weighted arithmetic mean

text: A similar re-creation of the proof (up to some mistakes at the end) was provided by Thomas Lumley in crossvalidated.


title: Weighted arithmetic mean

text: We have (at least) two versions of variance for the weighted mean: one with known and one with unknown population size estimation. There is no uniformly better approach, but the literature presents several arguments to prefer using the population estimation version (even when the population size is known). For example: if all y values are constant, the estimator with unknown population size will give the correct result, while the one with known population size will have some variability. Also, when the sample size itself is random (e.g.: in Poisson sampling), the version with unknown population mean is considered more stable. Lastly, if the proportion of sampling is negatively correlated with the values (i.e.: smaller chance to sample an observation that is large), then the un-known population size version slightly compensates for that.


title: Weighted arithmetic mean

text: It has been shown, by Gatz et al. (1995), that in comparison to bootstrapping methods, the following (variance estimation of ratio-mean using Taylor series linearization) is a reasonable estimation for the square of the standard error of the mean (when used in the context of measuring chemical constituents):


title: Weighted arithmetic mean

text: Gatz et al. mention that the above formulation was published by Endlich et al. (1988) when treating the weighted mean as a combination of a weighted total estimator divided by an estimator of the population size, based on the formulation published by Cochran (1977), as an approximation to the ratio mean. However, Endlich et al. didn't seem to publish this derivation in their paper (even though they mention they used it), and Cochran's book includes a slightly different formulation. Still, it's almost identical to the formulations described in previous sections.


title: Weighted arithmetic mean

text: Because there is no closed analytical form for the variance of the weighted mean, it was proposed in the literature to rely on replication methods such as the Jackknife and Bootstrapping.


title: Weighted arithmetic mean

text: For uncorrelated observations with variances formula_101, the variance of the weighted sample mean is


title: Weighted arithmetic mean

text: whose square root formula_103 can be called the "standard error of the weighted mean (general case)".


title: Weighted arithmetic mean

text: Consequently, if all the observations have equal variance, formula_104, the weighted sample mean will have variance


title: Weighted arithmetic mean

text: where formula_106. The variance attains its maximum value, formula_107, when all weights except one are zero. Its minimum value is found when all weights are equal (i.e., unweighted mean), in which case we have formula_108, i.e., it degenerates into the standard error of the mean, squared.


title: Weighted arithmetic mean

text: Note that because one can always transform non-normalized weights to normalized weights all formula in this section can be adapted to non-normalized weights by replacing all formula_109.


title: Weighted arithmetic mean

text: Typically when a mean is calculated it is important to know the variance and standard deviation about that mean. When a weighted mean formula_110 is used, the variance of the weighted sample is different from the variance of the unweighted sample.


title: Weighted arithmetic mean

text: The "biased" weighted sample variance formula_111 is defined similarly to the normal "biased" sample variance formula_112:


title: Weighted arithmetic mean

text: where formula_114 for normalized weights. If the weights are "frequency weights" (and thus are random variables), it can be shown that formula_111 is the maximum likelihood estimator of formula_14 for iid Gaussian observations.


title: Weighted arithmetic mean

text: For small samples, it is customary to use an unbiased estimator for the population variance. In normal unweighted samples, the "N" in the denominator (corresponding to the sample size) is changed to "N" − 1 (see Bessel's correction). In the weighted setting, there are actually two different unbiased estimators, one for the case of "frequency weights" and another for the case of "reliability weights".


title: Weighted arithmetic mean

text: If the weights are "frequency weights" (where a weight equals the number of occurrences), then the unbiased estimator is:


title: Weighted arithmetic mean

text: For example, if values formula_118 are drawn from the same distribution, then we can treat this set as an unweighted sample, or we can treat it as the weighted sample formula_119 with corresponding weights formula_120, and we get the same result either way.


title: Weighted arithmetic mean

text: If the frequency weights formula_121 are normalized to 1, then the correct expression after Bessel's correction becomes


title: Weighted arithmetic mean

text: where the total number of samples is formula_123 (not formula_36). In any case, the information on total number of samples is necessary in order to obtain an unbiased correction, even if formula_86 has a different meaning other than frequency weight.


title: Weighted arithmetic mean

text: Note that the estimator can be unbiased only if the weights are not standardized nor normalized, these processes changing the data's mean and variance and thus leading to a loss of the base rate (the population count, which is a requirement for Bessel's correction).


title: Weighted arithmetic mean

text: If the weights are instead non-random ("reliability weights"), we can determine a correction factor to yield an unbiased estimator. Assuming each random variable is sampled from the same distribution with mean formula_126 and actual variance formula_127, taking expectations we have,


title: Weighted arithmetic mean

text: where formula_129 and formula_130. Therefore, the bias in our estimator is formula_131, analogous to the formula_132 bias in the unweighted estimator (also notice that formula_133 is the effective sample size). This means that to unbias our estimator we need to pre-divide by formula_134, ensuring that the expected value of the estimated variance equals the actual variance of the sampling distribution.


title: Weighted arithmetic mean

text: The degrees of freedom of the weighted, unbiased sample variance vary accordingly from "N" − 1 down to 0.


title: Weighted arithmetic mean

text: In a weighted sample, each row vector formula_137 (each set of single observations on each of the "K" random variables) is assigned a weight formula_138.


title: Weighted arithmetic mean

text: Similarly to weighted sample variance, there are two different unbiased estimators depending on the type of the weights.


title: Weighted arithmetic mean

text: If the weights are "frequency weights", the "unbiased" weighted estimate of the covariance matrix formula_142, with Bessel's correction, is given by:


title: Weighted arithmetic mean

text: Note that this estimator can be unbiased only if the weights are not standardized nor normalized, these processes changing the data's mean and variance and thus leading to a loss of the base rate (the population count, which is a requirement for Bessel's correction).


title: Weighted arithmetic mean

text: If all weights are the same, i.e. formula_153, then the weighted mean and covariance reduce to the unweighted sample mean and covariance above.


title: Weighted arithmetic mean

text: The above generalizes easily to the case of taking the mean of vector-valued estimates. For example, estimates of position on a plane may have less certainty in one direction than another. As in the scalar case, the weighted mean of multiple estimates can provide a maximum likelihood estimate. We simply replace the variance formula_14 by the covariance matrix formula_155 and the arithmetic inverse by the matrix inverse (both denoted in the same way, via superscripts); the weight matrix then reads:


title: Weighted arithmetic mean

text: (where the order of the matrix–vector product is not commutative), in terms of the covariance of the weighted mean:


title: Weighted arithmetic mean

text: For example, consider the weighted mean of the point [1 0] with high variance in the second component and [0 1] with high variance in the first component. Then


title: Weighted arithmetic mean

text: which makes sense: the [1 0] estimate is "compliant" in the second component and the [0 1] estimate is compliant in the first component, so the weighted mean is nearly [1 1].


title: Weighted arithmetic mean

text: In the general case, suppose that formula_162, formula_155 is the covariance matrix relating the quantities formula_17, formula_26 is the common mean to be estimated, and formula_166 is a design matrix equal to a vector of ones formula_167 (of length formula_168). The Gauss–Markov theorem states that the estimate of the mean having minimum variance is given by:


title: Weighted arithmetic mean

text: Consider the time series of an independent variable formula_172 and a dependent variable formula_173, with formula_168 observations sampled at discrete times formula_175. In many common situations, the value of formula_173 at time formula_175 depends not only on formula_17 but also on its past values. Commonly, the strength of this dependence decreases as the separation of observations in time increases. To model this situation, one may replace the independent variable by its sliding mean formula_179 for a window size formula_180.


title: Weighted arithmetic mean

text: In the scenario described in the previous section, most frequently the decrease in interaction strength obeys a negative exponential law. If the observations are sampled at equidistant times, then exponential decrease is equivalent to decrease by a constant fraction formula_182 at each time step. Setting formula_183 we can define formula_180 normalized weights by


title: Weighted arithmetic mean

text: The damping constant formula_191 must correspond to the actual decrease of interaction strength. If this cannot be determined from theoretical considerations, then the following properties of exponentially decreasing weights are useful in making a suitable choice: at step formula_192, the weight approximately equals formula_193, the tail area the value formula_194, the head area formula_195. The tail area at step formula_168 is formula_197. Where primarily the closest formula_168 observations matter and the effect of the remaining observations can be ignored safely, then choose formula_191 such that the tail area is sufficiently small.


title: Weighted arithmetic mean

text: The concept of weighted average can be extended to functions. Weighted averages of functions play an important role in the systems of weighted differential and integral calculus.


title: Weighted arithmetic mean

text: Weighted means are typically used to find the weighted mean of historical data, rather than theoretically generated data. In this case, there will be some error in the variance of each data point. Typically experimental errors may be underestimated due to the experimenter not taking into account all sources of error in calculating the variance of each data point. In this event, the variance in the weighted mean must be corrected to account for the fact that formula_200 is too large. The correction that must be made is


title: Weighted arithmetic mean

text: The square root formula_204 can be called the "standard error of the weighted mean (variance weights, scale corrected)".


title: Weighted arithmetic mean

text: When all data variances are equal, formula_23, they cancel out in the weighted mean variance, formula_206, which again reduces to the standard error of the mean (squared), formula_207, formulated in terms of the sample standard deviation (squared),


title: Pranayama

text: Pranayama is the yogic practice of focusing on breath. In Sanskrit, "prana" means "vital life force", and "yama" means to gain control. In yoga, breath is associated with "prana", thus, pranayama is a means to elevate the "prana" "shakti", or life energies. Pranayama is described in Hindu texts such as the "Bhagavad Gita" and the "Yoga Sutras of Patanjali". Later in Hatha yoga texts, it meant the complete suspension of breathing.


title: Pranayama

text: Macdonell gives the etymology as prana ("), breath, + "āyāma" and defines it as the suspension of breath.


title: Pranayama

text: Monier-Williams defines the compound ' as "of the three 'breath-exercises' performed during ("See" ', ', '". This technical definition refers to a particular system of breath control with three processes as explained by Bhattacharyya: ' (to take the breath inside), ' (to retain it), and " (to discharge it). There are other processes of prāṇāyāma besides this three-step model.


title: Pranayama

text: V. S. Apte's definition of ' derives it from ' + ' and provides several variant meanings for it when used in compounds. The first three meanings have to do with "length", "expansion, extension", and "stretching, extending", but in the specific case of use in the compound ' he defines " as meaning "restrain, control, stopping".


title: Pranayama

text: Pranayama is mentioned in verse 4.29 of the "Bhagavad Gītā", which states "Still others, who are inclined to the process of breath restraint to remain in trance, practice by offering the movement of the outgoing breath into the incoming, and the incoming breath into the outgoing, and thus at last remain in trance, stopping all breathing. Others, curtailing the eating process, offer the outgoing breath into itself as a sacrifice."


title: Pranayama

text: Pranayama is the fourth "limb" of the eight limbs of Ashtanga Yoga mentioned in verse 2.29 in the "Yoga Sutras of Patanjali". Patanjali, a Hindu Rishi, discusses his specific approach to pranayama in verses 2.49 through 2.51, and devotes verses 2.52 and 2.53 to explaining the benefits of the practice. Patanjali does not fully elucidate the nature of prana, and the theory and practice of pranayama seem to have undergone significant development after him. He presents pranayama as essentially an exercise that is preliminary to concentration.


title: Pranayama

text: Yoga teachers including B. K. S. Iyengar have advised that pranayama should be part of an overall practice that includes the other limbs of Patanjali's Raja Yoga teachings, especially Yama, Niyama, and Asana.


title: Pranayama

text: The Indian tradition of Hatha Yoga makes use of various pranayama techniques. The 15th century "Hatha Yoga Pradipika" is a key text of this tradition and includes various forms of pranayama such as Kumbhaka breath retention and various body locks (Bandhas). Other forms of pranayama breathing include Ujjayi breath ("Victorious Breath"), Sitali (breathing through the rolled tongue), Bhastrika ("Bellows Breath"), Kapalabhati ("Skull-shining Breath", a Shatkarma purification), Surya Bhedana ("Sun-piercing Breath"), and the soothing Bhramari (buzzing like a bee).


title: Pranayama

text: B. K. S. Iyengar cautions that pranayama should only be undertaken when one has a firmly established yoga practice and then only under the guidance of an experienced Guru.


title: Pranayama

text: According to the scholar-practitioner of yoga Theos Bernard, the ultimate aim of pranayama is the suspension of breathing (kevala kumbhaka), "causing the mind to swoon". Paramahansa Yogananda writes, "The real meaning of Pranayama, according to Patanjali, the founder of Yoga philosophy, is the gradual cessation of breathing, the discontinuance of inhalation and exhalation".


title: Pranayama

text: The yoga scholar Andrea Jain states that pranayama was "marginal to the most widely cited sources" before the 20th century, and that the breathing practices were "dramatically" unlike the modern ones; she writes that while pranayama in modern yoga as exercise consists of synchronising the breath with movements (between asanas), in texts like the "Bhagavad Gita" and the "Yoga Sutras of Patanjali", pranayama meant "complete cessation of breathing", for which she cites Bronkhorst 2007.


title: Pranayama

text: According to the Pali Buddhist Canon, the Buddha prior to his enlightenment practiced a meditative technique which involved pressing the palate with the tongue and forcibly attempting to restrain the breath. This is described as both extremely painful and not conducive to enlightenment. In some Buddhist teachings or metaphors, breathing is said to stop with the fourth jhana, though this is a side-effect of the technique and does not come about as the result of purposeful effort.


title: Pranayama

text: The Buddha did incorporate moderate modulation of the length of breath as part of the preliminary tetrad in the Anapanasati Sutta. Its use there is preparation for concentration. According to commentarial literature, this is appropriate for beginners.


title: Pranayama

text: Later Indo-Tibetan developments in Buddhist pranayama which are similar to Hindu forms can be seen as early as the 11th century, in the Buddhist text titled the "Amṛtasiddhi", which teaches three bandhas in connection with yogic breathing (kumbakha).


title: Pranayama

text: Tibetan Buddhist breathing exercises such as the "nine breathings of purification" or the "Ninefold Expulsion of Stale Vital Energy" ("rlung ro dgu shrugs"), a form of alternate nostril breathing, commonly include visualizations. In the Nyingma tradition of Dzogchen these practices are collected in the textual cycle known as "The Oral Transmission of Vairotsana" ("Vai ro snyan brgyud").