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Food allergy

A food allergy is an abnormal immune response to food. The symptoms of the allergic reaction may range from mild to severe. They may include itchiness, swelling of the tongue, vomiting, diarrhea, hives, trouble breathing, or low blood pressure. This typically occurs within minutes to several hours of exposure. When the symptoms are severe, it is known as anaphylaxis. A food intolerance and food poisoning are separate conditions, not due to an immune response.

Common foods involved include cow's milk, peanuts, eggs, shellfish, fish, tree nuts, soy, wheat, and sesame. The common allergies vary depending on the country. Risk factors include a family history of allergies, vitamin D deficiency, obesity, and high levels of cleanliness. Allergies occur when immunoglobulin E (IgE), part of the body's immune system, binds to food molecules. A protein in the food is usually the problem. This triggers the release of inflammatory chemicals such as histamine. Diagnosis is usually based on a medical history, elimination diet, skin prick test, blood tests for food-specific IgE antibodies, or oral food challenge.

Management involves avoiding the food in question and having a plan if exposure occurs. This plan may include giving adrenaline (epinephrine) and wearing medical alert jewelry. Early childhood exposure to potential allergens may be protective against later development of a food allergy. The benefits of allergen immunotherapy for treating food allergies are not proven, thus not recommended. Some types of food allergies among children resolve with age, including those to milk, eggs, and soy; while others such as to nuts and shellfish typically do not.

In the developed world, about 4% to 8% of people have at least one food allergy. They are more common in children than adults and appear to be increasing in frequency. Male children appear to be more commonly affected than females. Some allergies more commonly develop early in life, while others typically develop in later life. In developed countries, more people believe they have food allergies when they actually do not have them.

Signs and symptoms
Food allergy symptoms occur within minutes to hours after exposure and may include:
 * Rash
 * Hives
 * Itching of mouth, lips, tongue, throat, eyes, skin, or other areas
 * Swelling (angioedema) of lips, tongue, eyelids, or the whole face
 * Difficulty swallowing
 * Runny or congested nose
 * Hoarse voice
 * Wheezing and/or shortness of breath
 * Diarrhea, abdominal pain, and/or stomach cramps
 * Lightheadedness
 * Fainting
 * Nausea
 * Vomiting

In some cases, however, onset of symptoms may be delayed for hours.

Symptoms can vary. The amount of food needed to trigger a reaction also varies.

Serious danger regarding allergies can begin when the respiratory tract or blood circulation is affected. The former can be indicated through wheezing and cyanosis. Poor blood circulation leads to a weak pulse, pale skin and fainting.

A severe case of an allergic reaction, caused by symptoms affecting the respiratory tract and blood circulation, is called anaphylaxis. When symptoms are related to a drop in blood pressure, the person is said to be in anaphylactic shock. Anaphylaxis occurs when IgE antibodies are involved, and areas of the body that are not in direct contact with the food become affected and show symptoms. Those with asthma or an allergy to peanuts, tree nuts, or seafood are at greater risk for anaphylaxis.

Common food allergies
Allergic reactions are abnormal immune responses that develop after exposure to a given food allergen. Food allergens account for about 90% of all allergic reactions. The most common food allergens include milk, eggs, peanuts, tree nuts, fish, shellfish, soy, and wheat, which are referred to as "the big eight", and are required by US law to be on labels of foods that contain those foods. In April 2021, President Biden signed the FASTER Act into law. This recognized sesame as the ninth US mandatory food label allergen.

Peanuts, a member of the legume family, are one of the most common food allergens that induce reactions in both children and adults. Affecting about 2% of the Western population, peanut allergies tend to cause more severe reactions and anaphylaxis than other food allergies. Tree nuts, including almonds, brazil nuts, cashews, coconuts, hazelnuts, macadamia nuts, pecans, pistachios, pine nuts, and walnuts, are also common allergens. Affected individuals may be sensitive to one particular tree nut or many different ones. Peanuts and seeds, including sesame seeds and poppy seeds, can be processed to extract oils, but trace amounts of protein may also elicit an allergic reaction. Peanut and tree nut allergies are lifelong conditions for the majority of those affected, although evidence shows that ~20% of those with peanut allergies and 9% of those with tree nut allergies may outgrow them.

Egg allergies affect about one in 50 children but are frequently outgrown when children reach age five. Affected individuals can be sensitive to proteins both in the egg white and egg yolk, but most children are allergic to those in the white while most adults are allergic to those in the yolk.

Cow's milk is the most common food allergen in infants and young children, yet many adults are also sensitized to cow's milk. Many affected individuals cannot tolerate dairy products such as cheese and yogurt. A small portion of children with milk allergy, roughly 10%, have a reaction to beef because it contains small amounts of protein that are also present in cow's milk.

Shellfish, which are divided into crustaceans (shrimp, crab, lobster, etc.) and mollusks (mussel, oyster, scallop, squid, octopus, snail, etc.), are the most common food allergy in adults. People may be allergic to other types of seafood, such as fish. Fish allergies were found to be more common in countries that have high fish consumption compared to those with lower consumption.

Other common food allergens include soy and wheat. Those allergic to wheat may be sensitized to any protein in the wheat kernel. To a lesser frequency, people may be mildly allergic to raw fruits and vegetables, a disease known as oral allergy syndrome. Less common allergens include maize, spices, synthetic and natural colors, and chemical additives.

Balsam of Peru, which is in various foods, is in the "top five" allergens most commonly causing patch test reactions in people referred to dermatology clinics.

Routes of exposure
Exposure to certain food proteins triggers the production of antigen-specific immunoglobulin E (IgE) antibodies, which, if unaccompanied by allergic symptoms, is known as allergic sensitization. Oral ingestion is the main sensitization route for most food allergy cases, yet other routes of exposure include inhalation and skin contact.

For example, inhaling airborne particles in a farm-scale or factory-scale peanut shelling/crushing environment, or from cooking, can induce respiratory effects in allergic individuals. Furthermore, peanut allergies are much more common in adults who had oozing and crusted skin rashes as infants, suggesting that impaired skin may be a risk factor for sensitization. An estimated 28.5 million people worldwide are engaged in the seafood industry, which includes fishing, aquaculture, processing and industrial cooking. In these occupational settings, individuals with fish and shellfish allergies are at high risk of exposure to allergenic proteins via aerosolization. Respiratory symptoms may be induced by inhalation of wet aerosols from fresh fish handling, inhalation of dry aerosols from fishmeal processing, and dermal contact through skin breaks and cuts. Another occupational food allergy that involves respiratory symptoms is "baker's asthma," which commonly develops in food service workers who work with baked goods. Previous studies detected 40 allergens from wheat, some cross-reacted with rye proteins and a few cross-reacted with grass pollens.

Allergic sensitization can occur via skin antigen exposure, which usually manifests as hives. The skin has been suggested to be a critical sensitization route for peanut-allergic individuals. Peanut allergies are much more common in adults who had oozing and crusted skin rashes as infants, reinforcing that those with disrupted epithelial barriers, notably the skin barrier, are more prone to skin sensitization. Environmental factors, such as exposure to food, microorganisms, creams, and detergents, may lead to skin barrier dysfunction. Several studies reveal that children exposed to skin creams containing peanut oil are reported to have a higher risk of peanut allergy, suggesting that impaired skin may be a risk factor for sensitization.

Atopy
Food allergies develop more easily in people with the atopic syndrome, a very common combination of diseases: allergic rhinitis and conjunctivitis, eczema, and asthma. The syndrome has a strong inherited component; a family history of allergic diseases can be indicative of the atopic syndrome.

Cross-reactivity
Some children who are allergic to cow's milk protein also show a cross-sensitivity to soy-based products. Some infant formulas have their milk and soy proteins hydrolyzed, so when taken by infants, their immune systems do not recognize the allergen and they can safely consume the product. Hypoallergenic infant formulas can be based on proteins partially predigested to a less antigenic form. Other formulas, based on free amino acids, are the least antigenic and provide complete nutritional support in severe forms of milk allergy.

Crustaceans (shrimp, crab, lobster, etc.) and molluscs (mussel, oyster, scallop, squid, octopus, snail, etc.) are different invertebrate classes, but the allergenic protein tropomyosin is present and responsible for cross-reactivity.

People with latex allergy often also develop allergies to bananas, kiwifruit, avocados, and some other foods.

Pathophysiology

Conditions caused by food allergies are classified into three groups according to the mechanism of the allergic response:

 * 1) IgE-mediated (classic) – the most common type, occurs shortly after eating and may involve anaphylaxis.
 * 2) Non-IgE mediated – characterized by an immune response not involving immunoglobulin E; may occur some hours after eating, complicating diagnosis
 * 3) IgE and/or non-IgE-mediated – a hybrid of the above two types

Allergic reactions are abnormal immune responses to certain substances that are normally harmless. When immune cells encounter the allergenic protein, IgE antibodies are produced; this is similar to the immune system's reaction to foreign pathogens. The IgE antibodies identify the allergenic proteins as harmful and initiate the allergic reaction. The harmful proteins are those that do not break down due to the strong bonds of the protein. IgE antibodies bind to a receptor on the surface of the protein, creating a tag, just as a virus or parasite becomes tagged. Why some proteins do not denature and subsequently trigger allergic reactions and hypersensitivity while others do is not entirely clear.

Hypersensitivities are categorized according to the parts of the immune system that are attacked and the amount of time it takes for the response to occur. The four types of hypersensitivity reaction are: type 1, immediate IgE-mediated; type 2, cytotoxic; type 3, immune complex-mediated; and type 4, delayed cell-mediated. The pathophysiology of allergic responses can be divided into two phases. The first is an acute response that occurs immediately after exposure to an allergen. This phase can either subside or progress into a "late-phase reaction" which can substantially prolong the symptoms of a response, and result in tissue damage.

Many food allergies are caused by hypersensitivities to particular proteins in different foods. Proteins have unique properties that allow them to become allergens, such as stabilizing forces in their tertiary and quaternary structures which prevent degradation during digestion. Many theoretically allergenic proteins cannot survive the destructive environment of the digestive tract, thus do not trigger hypersensitive reactions.

Acute response
In the early stages of allergy, a type I hypersensitivity reaction against an allergen, encountered for the first time, causes a response in a type of immune cell called a TH2 lymphocyte, which belongs to a subset of T cells that produce a cytokine called interleukin-4 (IL-4). These TH2 cells interact with other lymphocytes called B cells, whose role is the production of antibodies. Coupled with signals provided by IL-4, this interaction stimulates the B cell to begin production of a large amount of a particular type of antibody known as IgE. Secreted IgE circulates in the blood and binds to an IgE-specific receptor (a kind of Fc receptor called FcεRI) on the surface of other kinds of immune cells called mast cells and basophils, which are both involved in the acute inflammatory response. The IgE-coated cells, at this stage, are sensitized to the allergen.

If later exposure to the same allergen occurs, the allergen can bind to the IgE molecules held on the surface of the mast cells or basophils. Cross-linking of the IgE and Fc receptors occurs when more than one IgE-receptor complex interacts with the same allergenic molecule and activates the sensitized cell. Activated mast cells and basophils undergo a process called degranulation, during which they release histamine and other inflammatory chemical mediators (cytokines, interleukins, leukotrienes, and prostaglandins) from their granules into the surrounding tissue causing several systemic effects, such as vasodilation, mucous secretion, nerve stimulation, and smooth-muscle contraction. This results in rhinorrhea, itchiness, dyspnea, and anaphylaxis. Depending on the individual, the allergen, and the mode of introduction, the symptoms can be system-wide (classical anaphylaxis), or localized to particular body systems.

Late-phase response
After the chemical mediators of the acute response subside, late-phase responses can often occur due to the migration of other leukocytes such as neutrophils, lymphocytes, eosinophils, and macrophages to the initial site. The reaction is usually seen 2–24 hours after the original reaction. Cytokines from mast cells may also play a role in the persistence of long-term effects.

Diagnosis
Diagnosis is usually based on a medical history, elimination diet, skin prick test, blood tests for food-specific IgE antibodies, or oral food challenge.
 * For skin-prick tests, a tiny board with protruding needles is used. The allergens are placed either on the board or directly on the skin.  The board is then placed on the skin, to puncture the skin and for the allergens to enter the body. If a hive appears, the person is considered positive for the allergy. This test only works for IgE antibodies.  Allergic reactions caused by other antibodies cannot be detected through skin-prick tests.

Skin-prick testing is easy to do and results are available in minutes. Different allergists may use different devices for testing. Some use a "bifurcated needle", which looks like a fork with two prongs. Others use a "multitest", which may look like a small board with several pins sticking out of it. In these tests, a tiny amount of the suspected allergen is put onto the skin or into a testing device, and the device is placed on the skin to prick, or break through, the top layer of skin. This puts a small amount of the allergen under the skin. A hive will form at any spot where the person is allergic. This test generally yields a positive or negative result. It is good for quickly learning if a person is allergic to a particular food or not because it detects IgE. Skin tests cannot predict if a reaction would occur or what kind of reaction might occur if a person ingests that particular allergen. They can, however, confirm an allergy in light of a patient's history of reactions to a particular food. Non-IgE-mediated allergies cannot be detected by this method.
 * Patch testing is used to determine if a specific substance causes allergic inflammation of the skin. It tests for delayed food reactions.
 * Blood testing is another way to test for allergies; however, it poses the same disadvantage and only detects IgE allergens and does not work for every possible allergen. Radioallergosorbent testing (RAST) is used to detect IgE antibodies present to a certain allergen. The score taken from the RAST is compared to predictive values, taken from a specific type of RAST. If the score is higher than the predictive values, a great chance the allergy is present in the person exists. One advantage of this test is that it can test many allergens at one time.

A CAP-RAST has greater specificity than RAST; it can show the amount of IgE present to each allergen. Researchers have been able to determine "predictive values" for certain foods, which can be compared to the RAST results. If a person's RAST score is higher than the predictive value for that food, over a 95% chance exists that patients will have an allergic reaction (limited to rash and anaphylaxis reactions) if they ingest that food. Currently, predictive values are available for milk, egg, peanut, fish, soy, and wheat. Blood tests allow for hundreds of allergens to be screened from a single sample, and cover food allergies as well as inhalants. However, non-IgE-mediated allergies cannot be detected by this method. Other widely promoted tests such as the antigen leukocyte cellular antibody test and the food allergy profile are considered unproven methods, the use of which is not advised.
 * Food challenges test for allergens other than those caused by IgE allergens. The allergen is given to the person in the form of a pill, so the person can ingest the allergen directly. The person is watched for signs and symptoms. The problem with food challenges is that they must be performed in the hospital under careful watch, due to the possibility of anaphylaxis.

Food challenges, especially double-blind, placebo-controlled food challenges, are the gold standard for diagnosis of food allergies, including most non-IgE-mediated reactions, but is rarely done. Blind food challenges involve packaging the suspected allergen into a capsule, giving it to the patient, and observing the patient for signs or symptoms of an allergic reaction.

The recommended method for diagnosing food allergy is to be assessed by an allergist. The allergist will review the patient's history and the symptoms or reactions that have been noted after food ingestion. If the allergist feels the symptoms or reactions are consistent with food allergy, he/she will perform allergy tests. Additional diagnostic tools for evaluation of eosinophilic or non-IgE mediated reactions include endoscopy, colonoscopy, and biopsy.

Differential diagnosis
Important differential diagnoses are:
 * Lactose intolerance generally develops later in life, but can present in young patients in severe cases. It is not an immune reaction and is due to an enzyme deficiency (lactase). It is more common in many non-Western people.
 * Celiac disease. While it is caused by a permanent intolerance to gluten (present in wheat, rye, barley and oats), is not an allergy nor simply an intolerance, but a chronic, multiple-organ autoimmune disorder primarily affecting the small intestine.
 * Irritable bowel syndrome
 * C1 Esterase inhibitor deficiency (hereditary angioedema), a rare disease, generally causes attacks of angioedema, but can present solely with abdominal pain and occasional diarrhea, and thus may be confused with allergy-triggered angioedema.

Prevention
Breastfeeding for more than four months may prevent atopic dermatitis, cow's milk allergy, and wheezing in early childhood. Early exposure to potential allergens may be protective. Specifically, early exposure to eggs and peanuts reduces the risk of allergies to these. Guidelines suggest introducing peanuts as early as 4–6 months and include precautionary measures for high-risk infants. The former guidelines, advising delaying the introduction of peanuts, are now thought to have contributed to the increase in peanut allergy seen recently.

To avoid an allergic reaction, a strict diet can be followed. It is difficult to determine the amount of allergenic food required to elicit a reaction, so complete avoidance should be attempted. In some cases, hypersensitive reactions can be triggered by exposures to allergens through skin contact, inhalation, kissing, participation in sports, blood transfusions, cosmetics, and alcohol.

Early introduction of peanut and egg alongside other solids, or by one year of age, may help prevent development of food allergy. Introduction of these allergenic foods within the first year of life appears to be safe. A window of opportunity for the introduction of different food allergens may exist, such as egg introduction ahead of peanut.

Inhalation exposure
Allergic reactions to airborne particles or vapors of known food allergens have been reported as an occupational consequence of people working in the food industry, but can also take place in home situations, restaurants, or confined spaces such as airplanes. According to two reviews, respiratory symptoms are common, but in some cases there has been progression to anaphylaxis. The most frequent reported cases of reactions by inhalation of allergenic foods were due to peanut, seafood, legumes, tree nut, and cow's milk. Steam rising from cooking of lentils, green beans, chickpeas and fish has been well documented as triggering reactions, including anaphylactic reactions. One review mentioned case study examples of allergic responses to inhalation of other foods, including examples in which oral consumption of the food is tolerated.

Treatment
The mainstay of treatment for food allergy is total avoidance of the foods identified as allergens. An allergen can enter the body by consuming a portion of food containing the allergen, and can also be ingested by touching any surfaces that may have come into contact with the allergen, then touching the eyes or nose. For people who are extremely sensitive, avoidance includes avoiding touching or inhaling problematic food. Total avoidance is complicated because the declaration of the presence of trace amounts of allergens in foods is not mandatory (see regulation of labelling).

If the food is accidentally ingested and a systemic reaction (anaphylaxis) occurs, then epinephrine should be used. A second dose of epinephrine may be required for severe reactions. The person should then be transported to the emergency room, where additional treatment can be given. Other treatments include antihistamines and steroids.

Epinephrine
Epinephrine (adrenaline) is the first-line treatment for severe allergic reactions (anaphylaxis). If administered in a timely manner, epinephrine can reverse its effects. Epinephrine relieves airway swelling and obstruction, and improves blood circulation; blood vessels are tightened and heart rate is increased, improving circulation to body organs. Epinephrine is available by prescription in an autoinjector.

Antihistamines
Antihistamines can alleviate some of the milder symptoms of an allergic reaction, but do not treat all symptoms of anaphylaxis. Antihistamines block the action of histamine, which causes blood vessels to dilate and become leaky to plasma proteins. Histamine also causes itchiness by acting on sensory nerve terminals. The most common antihistamine given for food allergies is diphenhydramine.

Steroids
Glucocorticoid steroids are used to calm down the immune system cells that are attacked by the chemicals released during an allergic reaction. This treatment in the form of a nasal spray should not be used to treat anaphylaxis, for it only relieves symptoms in the area in which the steroid is in contact. Another reason steroids should not be used is the delay in reducing inflammation. Steroids can also be taken orally or through injection, by which every part of the body can be reached and treated, but a long time is usually needed for these to take effect.

Immunotherapy
Immunotherapies seek to condition the immune system to elicit or suppress a specific immune response. In the treatment of allergies, common immunotherapies seek to desensitize the immune system by gradually exposing the body to allergens in increasing amounts. These forms of immunotherapy have had varying and limited success and have generally been used to treat peanut and environmental allergies.

Omalizumab
Omalizumab, an injectable asthma treatment drug sold under the brand name Xolair, was approved in the United States in February 2024 to reduce severe reactions to accidental exposure to food allergens. It is a genetically engineered monoclonal antibody which specifically binds to immunoglobulin E (IgE) to reduce the severity of an immune response. Successful results were reported for wheat, eggs, milk and baked products containing wheat and milk.

Epidemiology
Food allergies affect up to 10% of the worldwide population, and they are currently more prevalent in children (~8%) than adults (~5) in western nations. In several industrialized countries, food allergies affect up to 10% of children. Children are most commonly allergic to cow's milk, chicken eggs, peanuts, and tree nuts. While studies on adults with food allergy are not as abundant, surveys suggest that the most common food allergens for adults include fish, shellfish, peanuts, and tree nuts.

Food allergies have become increasingly prevalent in industrialized/westernized nations over the last 2-3 decades. An estimated 15 million people currently have food allergies in the United States. In 1997, 0.4% children in the United States were reported to have peanut allergy, yet this number markedly rose to 1.4% in 2008. In Australia, hospital admission rates for food-induced anaphylaxis increased by an average of 13.2% from 1994-2005. One possible explanation for the rise in food allergy is the "old friends" hypothesis, which suggests that non disease causing organisms, such as helminths, could protect against allergy. Therefore, reduced exposure to these organisms, particularly in developed countries, could have contributed towards the increase.

Children of East Asian or African descent who live in westernized countries were reported to be at significantly higher risk of food allergy compared to Caucasian children. Several studies predict that Asia and Africa may experience a growth in food allergy prevalence as the lifestyles there become more westernized.

The prevalence of certain food allergies is suggested to depend partly on the geographical area and country. For instance, allergy to buckwheat flour, used for soba noodles, is more common in Japan than peanuts, tree nuts or foods made from soy beans. Also, shellfish allergy is the most common cause of anaphylaxis in adults and adolescents particularly in East Asian countries like Hong Kong, Taiwan, Singapore, and Thailand. Individuals in East Asia have further developed an allergy to rice, which forms a large part of their diet. Another example is that, out of 9 European countries, egg allergy was found to be most prevalent in the UK and least prevalent in Greece.

Special population: children
About 75% of children who have allergies to milk protein are able to tolerate baked-in milk products, i.e., muffins, cookies, cake, and hydrolyzed formulas. About 50% of children with allergies to milk, egg, soy, peanuts, tree nuts, and wheat will outgrow their allergy by the age of 6. Those who are still allergic by the age of 12 or so have less than an 8% chance of outgrowing the allergy.

United States
In the United States, food allergy affects as many as 5% of infants less than three years of age and 3% to 4% of adults. The prevalence of food allergies is rising. Food allergies cause roughly 30,000 emergency room visits and 150 deaths per year.

Regulation
Whether rates of food allergy are increasing or not, food allergy awareness has definitely increased, with impacts on the quality of life for children, their parents and their caregivers. In the United States, the Food Allergen Labeling and Consumer Protection Act of 2004 causes people to be reminded of allergy problems every time they handle a food package, and restaurants have added allergen warnings to menus. The Culinary Institute of America, a premier school for chef training, has courses in allergen-free cooking and a separate teaching kitchen. School systems have protocols about what foods can be brought into the school. Despite all these precautions, people with serious allergies are aware that accidental exposure can easily occur at other peoples' houses, at school or in restaurants.

Regulation of labelling
In response to the risk that certain foods pose to those with food allergies, some countries have responded by instituting labeling laws that require food products to clearly inform consumers if their products contain priority allergens or byproducts of major allergens among the ingredients intentionally added to foods.

The priority allergens vary by country. There are no labeling laws mandating declaration of the presence of trace amounts in the final product as a consequence of cross-contamination, except in Brazil.

Ingredients intentionally added
In the United States, the Food Allergen Labeling and Consumer Protection Act of 2004 requires companies to disclose on the label whether a packaged food product contains any of these eight major food allergens, added intentionally: cow's milk, peanuts, eggs, shellfish, fish, tree nuts, soy and wheat. The eight-ingredient list originated in 1999 from the World Health Organisation Codex Alimentarius Commission. To meet labeling requirements, if an ingredient is derived from one of the required-label allergens, then it must either have its "food sourced name" in parentheses, for example, "Casein (milk)," or as an alternative, there must be a statement separate but adjacent to the ingredients list: "Contains milk" (and any other of the allergens with mandatory labeling). The European Union requires listing for those eight major allergens plus molluscs, celery, mustard, lupin, sesame and sulfites.

In 2018, the US FDA issued a request for information for the consideration of labeling for sesame to help protect people who have sesame allergies. A decision was reached in November 2020 that food manufacturers voluntarily declare that when powdered sesame seeds are used as a previously unspecified spice or flavor, the label be changed to "spice (sesame)" or "flavor (sesame)."

Congress and the President passed a law in April 2021, the "FASTER Act", stipulating that labeling be mandatory, to be effect January 1, 2023, making it the ninth required food ingredient label.

The Food Allergen Labeling and Consumer Protection Act of 2004 applies to packaged foods regulated by the FDA, which does not include poultry, most meats, certain egg products, and most alcoholic beverages. However, some meat, poultry, and egg processed products may contain allergenic ingredients. These products are regulated by the Food Safety and Inspection Service, which requires that any ingredient be declared in the labeling only by its common or usual name. Neither the identification of the source of a specific ingredient in a parenthetical statement nor the use of statements to alert for the presence of specific ingredients, like "Contains: milk", are mandatory. The act also does not apply to food prepared in restaurants. The EU Food Information for Consumers Regulation 1169/2011 – requires food businesses to provide allergy information on food sold unpackaged, for example, in catering outlets, deli counters, bakeries and sandwich bars.

In the United States, there is no federal mandate to address the presence of allergens in drug products, medicines, or cosmetics.

Trace amounts as a result of cross-contamination
The value of allergen labeling other than for intentional ingredients is controversial. This concerns labeling for ingredients present unintentionally as a consequence of cross-contact or cross-contamination at any point along the food chain (during raw material transportation, storage or handling, due to shared equipment for processing and packaging, etc.). Experts in this field propose that if allergen labeling is to be useful to consumers, and healthcare professionals who advise and treat those consumers, ideally there should be agreement on which foods require labeling, threshold quantities below which labeling may be of no purpose, and validation of allergen detection methods to test and potentially recall foods that were deliberately or inadvertently contaminated.

Labeling regulations have been modified to provide for mandatory labeling of ingredients plus voluntary labeling, termed precautionary allergen labeling, also known as "may contain" statements, for possible, inadvertent, trace amount, cross-contamination during production. Precautionary allergen labeling can be confusing to consumers, especially as there can be many variations on the wording of the warning. Precautionary allergen labeling is optional in the United States. , precautionary allergen labeling is regulated only in Switzerland, Japan, Argentina, and South Africa. Argentina decided to prohibit precautionary allergen labeling since 2010 and instead puts the onus on the manufacturer to control the manufacturing process and label only those allergenic ingredients known to be in the products. South Africa does not permit the use of precautionary allergen labeling, except when manufacturers demonstrate the potential presence of allergen due to cross-contamination through a documented risk assessment and despite adherence to Good Manufacturing Practice. In Australia and New Zealand there is a recommendation that precautionary allergen labeling be replaced by guidance from VITAL 2.0 (Vital Incidental Trace Allergen Labeling). A review identified "the eliciting dose for an allergic reaction in 1% of the population" as the threshold reference dose for certain foods (such as cow's milk, egg, peanut and other proteins) to provide food manufacturers with guidance for developing precautionary labeling and give consumers a better idea of what might be accidentally in a food product beyond "may contain." VITAL 2.0 was developed by the Allergen Bureau, a food industry sponsored, non-government organization. The European Union has initiated a process to create labeling regulations for unintentional contamination but is not expected to publish such before 2024.

In Brazil, since April 2016, the declaration of the possibility of cross-contamination is mandatory when the product does not intentionally add any allergenic food or its derivatives, but the Good Manufacturing Practices and allergen control measures adopted are not sufficient to prevent the presence of accidental trace amounts. These allergens include wheat, rye, barley, oats and their hybrids, crustaceans, eggs, fish, peanuts, soybean, milk of all species of mammalians, almonds, hazelnuts, cashew nuts, Brazil nuts, macadamia nuts, walnuts, pecan nuts, pistachios, pine nuts, and chestnuts.

Genetically modified food
There is a scientific consensus that available food derived from genetically modified crops poses no greater risk to human health than conventional food,  and a 2016 U.S. National Academy of Sciences report concluded that there is no relationship between consumption of genetically modified foods and the increase in prevalence of food allergies. However, there are concerns that genetically modified foods, also described as foods sourced from genetically modified organisms, could be responsible for allergic reactions, and that the widespread acceptance of these types of foods may be responsible for what is a real or perceived increase in the percentage of people with allergies.

One concern is that genetic engineering could make an allergy-provoking food more allergic, meaning that smaller portions would suffice to set off a reaction. Of the food currently in widespread use of genetically modified organisms, only soybeans are identified as a common allergen. However, for the soybean proteins known to trigger allergic reactions, there is more variation from strain to strain than between those and the genetically modified varieties. Another concern is that genes transferred from one species to another could introduce an allergen in a food not thought of as particularly allergenic. Research on an attempt to enhance the quality of soybean protein by adding genes from Brazil nuts was terminated when human volunteers known to have tree nut allergy reacted to the modified soybeans.

Prior to a new genetically modified food receiving government approval, certain criteria need to be met. These include: Is the donor species known to be allergenic? Does the amino acid sequence of the transferred proteins resemble the sequence of known allergenic proteins? Are the transferred proteins resistant to digestion - a trait shared by many allergenic proteins? Genes approved for animal use can be restricted from human consumption due to potential for allergic reactions. In 1998 Starlink brand corn restricted to animals was detected in the human food supply, leading to first a voluntary and then a FDA mandated recall. There are requirements in some countries and recommendations in others that all foods containing genetically modified ingredients be so labeled, and that there be a post-launch monitoring system to report adverse effects (similar to the requirements in some countries for drug and dietary supplement reporting).

Restaurants
In the US, the FDA Food Code states that the person in charge in restaurants should have knowledge about major food allergens, cross-contacts, and symptoms of food allergy reactions. Restaurant staff, including wait staff and kitchen staff, may not be adequately informed about allergenic ingredients, or the risk of cross-contact when kitchen utensils used to prepare food may have been in previous contact with an allergenic food. The problem may be compounded when customers have a hard time describing their food allergies or when wait staff have a hard time understanding those with food allergies when taking an order.

Diagnosing issues
There exists both over-reporting and under-reporting of the prevalence of food allergies. Self-diagnosed perceptions of food allergy are greater than the rates of true food allergy because people confuse non-allergic intolerance with allergy, and also attribute non-allergy symptoms to an allergic response. Conversely, healthcare professionals treating allergic reactions on an out-patient or even hospitalized basis may not report all cases. Recent increases in reported cases may reflect a real change in incidence or an increased awareness on the part of healthcare professionals.

Social impact
Food fear has a significant impact on quality of life. For children with allergies, their quality of life is also affected by the actions of their peers. An increased occurrence of bullying has been observed, which can include threats or deliberate acts of forcing allergic children to contact foods that they must avoid or intentional contamination of allergen-free food. The social impacts of food allergies can carry over into adulthood.

Portrayal in media
Media portrayals of food allergy in television and film are not accurate, often used for comedic effect or underplaying the potential severity of an allergic reaction. These tropes misinform the public and also contribute to how entertainment media will continue to wrongly portray food allergies in the future. Types of tropes: 1) characters have food allergies, providing a weakness that can be used to sabotage them. In the movie Parasite a housekeeper is displaced by taking advantage of her peach allergy. In the animated film Peter Rabbit, the farm owner is attacked by being pelted with blackberries, causing an anaphylactic reaction requiring emergency treatment with epinephrine. After many public protests, Sony Pictures and the Peter Rabbit director apologized for making light of food allergies. 2) Food allergy is used for comedic effect, such as in the movies Hitch and in television, Kelso's egg allergy in That '70s Show 3) Food allergies may be incorporated into characters who are also portrayed as annoying, weak and oversensitive, which can be taken as implying that their allergies are either not real or not potentially severe. In season 1, episode 16 of The Big Bang Theory Howard Wolowitz deliberately consumes a peanut-containing food bar (and has a serious reaction) just to delay Leonard from returning to his apartment where a surprise birthday party is being arranged. 4) Any of these portrayals may underplay the potential severity of food allergy, some showing that Benadryl treatment is sufficient. Viewing of humorous portrayals of food allergies has been shown to have a negative effect on related health policy support due to low perceived seriousness.

Research
Several theories have been suggested to explain why certain individuals develop allergic sensitization instead of oral tolerance to food allergens. One such theory is the dual allergen hypothesis, which states that ingesting food allergens early on promotes oral tolerance while skin exposure leads to sensitization. Instead of oral ingestion, skin barrier disruption in conditions like eczema, for instance, was suggested to cause allergic sensitization in animal and human infants. Inhalation was recently proposed to be an additional sensitization route in the dual allergen hypothesis. Another theory is the barrier regulation hypothesis, describing the role of commensal bacteria in preventing the development of food allergy by maintaining integrity of the intestinal epithelial barrier. Environmental and lifestyle factors, such as early life nutrition and antibiotic treatment, may contribute to food allergy prevalence by affecting gut microbial composition, and thus, intestinal immune homeostasis in infants and young children.

A number of desensitization techniques are being studied. Areas of research include specific oral tolerance induction (also known as oral immunotherapy), and sublingual immunotherapy. The benefits of allergen immunotherapy for food allergies is unclear, thus is not recommended.

There is research on the effects of increasing intake of polyunsaturated fatty acids during pregnancy, lactation, via infant formula and in early childhood on the subsequent risk of developing food allergies during infancy and childhood. From two reviews, maternal intake of omega-3, long-chain fatty acids during pregnancy appeared to reduce the risks of medically diagnosed IgE-mediated allergy, eczema and food allergy per parental reporting in the first 12 months of life, but the effects were not all sustained past 12 months. The reviews characterized the literature's evidence as inconsistent and limited. Results when breastfeeding mothers were consuming a diet high in polyunsaturated fatty acids were inconclusive. For infants, supplementing their diet with oils high in polyunsaturated fatty acids did not affect the risks of food allergies, eczema or asthma either as infants or into childhood.

There is research on probiotics, prebiotics and the combination of the two (synbiotics) as a means of treating or preventing infant and child allergies. From reviews, there appears to be a treatment benefit for eczema, but not asthma, wheezing or rhinoconjunctivitis. The evidence was not consistent for preventing food allergies and this approach cannot yet be recommended.

The Food Standards Agency, in the United Kingdom, are in charge of funding research into food allergies and intolerance. Since their founding in 1994 they have funded over 45 studies. In 2005 Europe created EuroPrevall, a multi-country project dedicated to research involving allergies.

title: Food allergy


text:
Deformation (mathematics)

In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or a vector of small quantities. The infinitesimal conditions are the result of applying the approach of differential calculus to solving a problem with constraints. The name is an analogy to non-rigid structures that deform slightly to accommodate external forces.

Some characteristic phenomena are: the derivation of first-order equations by treating the ε quantities as having negligible squares; the possibility of isolated solutions, in that varying a solution may not be possible, or does not bring anything new; and the question of whether the infinitesimal constraints actually 'integrate', so that their solution does provide small variations. In some form these considerations have a history of centuries in mathematics, but also in physics and engineering. For example, in the geometry of numbers a class of results called isolation theorems was recognised, with the topological interpretation of an open orbit (of a group action) around a given solution. Perturbation theory also looks at deformations, in general of operators.

Deformations of complex manifolds
The most salient deformation theory in mathematics has been that of complex manifolds and algebraic varieties. This was put on a firm basis by foundational work of Kunihiko Kodaira and Donald C. Spencer, after deformation techniques had received a great deal of more tentative application in the Italian school of algebraic geometry. One expects, intuitively, that deformation theory of the first order should equate the Zariski tangent space with a moduli space. The phenomena turn out to be rather subtle, though, in the general case.

In the case of Riemann surfaces, one can explain that the complex structure on the Riemann sphere is isolated (no moduli). For genus 1, an elliptic curve has a one-parameter family of complex structures, as shown in elliptic function theory. The general Kodaira–Spencer theory identifies as the key to the deformation theory the sheaf cohomology group

 * $$ H^1(\Theta) \, $$

where Θ is (the sheaf of germs of sections of) the holomorphic tangent bundle. There is an obstruction in the H2 of the same sheaf; which is always zero in case of a curve, for general reasons of dimension. In the case of genus 0 the H1 vanishes, also. For genus 1 the dimension is the Hodge number h1,0 which is therefore 1. It is known that all curves of genus one have equations of form y2 = x3 + ax + b. These obviously depend on two parameters, a and b, whereas the isomorphism classes of such curves have only one parameter. Hence there must be an equation relating those a and b which describe isomorphic elliptic curves. It turns out that curves for which b2a−3 has the same value, describe isomorphic curves. I.e. varying a and b is one way to deform the structure of the curve y2 = x3 + ax + b, but not all variations of a,b actually change the isomorphism class of the curve.

One can go further with the case of genus g > 1, using Serre duality to relate the H1 to

 * $$ H^0(\Omega^{[2]}) $$

where Ω is the holomorphic cotangent bundle and the notation Ω[2] means the tensor square (not the second exterior power). In other words, deformations are regulated by holomorphic quadratic differentials on a Riemann surface, again something known classically. The dimension of the moduli space, called Teichmüller space in this case, is computed as 3g − 3, by the Riemann–Roch theorem.

These examples are the beginning of a theory applying to holomorphic families of complex manifolds, of any dimension. Further developments included: the extension by Spencer of the techniques to other structures of differential geometry; the assimilation of the Kodaira–Spencer theory into the abstract algebraic geometry of Grothendieck, with a consequent substantive clarification of earlier work; and deformation theory of other structures, such as algebras.

Deformations and flat maps
The most general form of a deformation is a flat map $$f:X \to S$$ of complex-analytic spaces, schemes, or germs of functions on a space. Grothendieck was the first to find this far-reaching generalization for deformations and developed the theory in that context. The general idea is there should exist a universal family $$\mathfrak{X} \to B$$ such that any deformation can be found as a unique pullback square $$\begin{matrix} X & \to & \mathfrak{X} \\ \downarrow & & \downarrow \\ S & \to & B \end{matrix}$$ In many cases, this universal family is either a Hilbert scheme or Quot scheme, or a quotient of one of them. For example, in the construction of the moduli of curves, it is constructed as a quotient of the smooth curves in the Hilbert scheme. If the pullback square is not unique, then the family is only versal.

Deformations of germs of analytic algebras
One of the useful and readily computable areas of deformation theory comes from the deformation theory of germs of complex spaces, such as Stein manifolds, complex manifolds, or complex analytic varieties. Note that this theory can be globalized to complex manifolds and complex analytic spaces by considering the sheaves of germs of holomorphic functions, tangent spaces, etc. Such algebras are of the form"$A \cong \frac{\mathbb{C}\{z_1,\ldots, z_n\}}{I}$ |undefined"where $$\mathbb{C}\{z_1,\ldots,z_n \}$$ is the ring of convergent power-series and $$I$$ is an ideal. For example, many authors study the germs of functions of a singularity, such as the algebra"$A \cong \frac{\mathbb{C}\{z_1,\ldots,z_n\}}{(y^2 - x^n)}$|undefined"representing a plane-curve singularity. A germ of analytic algebras is then an object in the opposite category of such algebras. Then, a deformation of a germ of analytic algebras $$X_0$$ is given by a flat map of germs of analytic algebras $$f:X \to S$$ where $$S$$ has a distinguished point $$0$$ such that the $$X_0$$ fits into the pullback square $$\begin{matrix} X_0 & \to & X \\ \downarrow & & \downarrow \\ \end{matrix}$$ These deformations have an equivalence relation given by commutative squares $$\begin{matrix} X'& \to & X \\ \downarrow & & \downarrow \\ S' & \to & S \end{matrix}$$ where the horizontal arrows are isomorphisms. For example, there is a deformation of the plane curve singularity given by the opposite diagram of the commutative diagram of analytic algebras $$\begin{matrix} \frac{\mathbb {C} \{x,y\}}{(y^{2}-x^{n})} & \leftarrow & \frac{\mathbb {C} \{x,y, s\}}{(y^{2}-x^{n} + s)} \\ \uparrow & & \uparrow \\ \mathbb{C} & \leftarrow & \mathbb{C}\{s\} \end{matrix}$$ In fact, Milnor studied such deformations, where a singularity is deformed by a constant, hence the fiber over a non-zero $$s$$ is called the Milnor fiber.
 * & \xrightarrow[0]{} & S

Cohomological Interpretation of deformations
It should be clear there could be many deformations of a single germ of analytic functions. Because of this, there are some book-keeping devices required to organize all of this information. These organizational devices are constructed using tangent cohomology. This is formed by using the Koszul–Tate resolution, and potentially modifying it by adding additional generators for non-regular algebras $$A$$. In the case of analytic algebras these resolutions are called the Tjurina resolution for the mathematician who first studied such objects, Galina Tyurina. This is a graded-commutative differential graded algebra $$(R_\bullet, s)$$ such that $$R_0 \to A$$ is a surjective map of analytic algebras, and this map fits into an exact sequence"$\cdots \xrightarrow{s} R_{-2} \xrightarrow{s} R_{-1} \xrightarrow{s} R_0 \xrightarrow{p} A \to 0$"Then, by taking the differential graded module of derivations $$(\text{Der}(R_\bullet), d)$$, its cohomology forms the tangent cohomology of the germ of analytic algebras $$A$$. These cohomology groups are denoted $$T^k(A)$$. The $$T^1(A)$$ contains information about all of the deformations of $$A$$ and can be readily computed using the exact sequence"$0 \to T^0(A) \to \text{Der}(R_0) \xrightarrow{d} \text{Hom}_{R_0}(I,A) \to T^1(A) \to 0$"If $$A$$ is isomorphic to the algebra"$\frac{\mathbb{C}\{z_1,\ldots,z_n\}}{(f_1,\ldots, f_m)}$|undefined"then its deformations are equal to"$T^1(A) \cong \frac{A^m}{df \cdot A^n}$"were $$df$$ is the jacobian matrix of $$f = (f_1,\ldots, f_m): \mathbb{C}^n \to \mathbb{C}^m$$. For example, the deformations of a hypersurface given by $$f$$ has the deformations"$T^1(A) \cong \frac{A^n}{\left( \frac{\partial f}{\partial z_1}, \ldots, \frac{\partial f}{\partial z_n} \right)}$"For the singularity $$y^2 - x^3$$ this is the module"$\frac{A^2}{(y, x^2)}$"hence the only deformations are given by adding constants or linear factors, so a general deformation of $$f(x,y) = y^2 - x^3$$ is $$F(x,y,a_1,a_2) = y^2 - x^3 + a_1 + a_2x $$ where the $$a_i$$ are deformation parameters.

Functorial description
Another method for formalizing deformation theory is using functors on the category $$\text{Art}_k$$ of local Artin algebras over a field. A pre-deformation functor is defined as a functor
 * $$F: \text{Art}_k \to \text{Sets}$$

such that $$F(k)$$ is a point. The idea is that we want to study the infinitesimal structure of some moduli space around a point where lying above that point is the space of interest. It is typically the case that it is easier to describe the functor for a moduli problem instead of finding an actual space. For example, if we want to consider the moduli-space of hypersurfaces of degree $$d$$ in $$\mathbb{P}^n$$, then we could consider the functor
 * $$F: \text{Sch} \to \text{Sets}$$

where

F(S) = \left\{ \begin{matrix} X \\ \downarrow \\ S \end{matrix}
 * \text{ each fiber is a degree } d \text{ hypersurface in }\mathbb{P}^n\right\}

$$

Although in general, it is more convenient/required to work with functors of groupoids instead of sets. This is true for moduli of curves.

Technical remarks about infinitesimals
Infinitesimals have long been in use by mathematicians for non-rigorous arguments in calculus. The idea is that if we consider polynomials $$F(x,\varepsilon)$$ with an infinitesimal $$\varepsilon$$, then only the first order terms really matter; that is, we can consider
 * $$ F(x,\varepsilon) \equiv f(x) + \varepsilon g(x) + O(\varepsilon^2)$$

A simple application of this is that we can find the derivatives of monomials using infinitesimals:
 * $$ (x+\varepsilon)^3 = x^3 + 3x^2\varepsilon + O(\varepsilon^2)$$

the $$\varepsilon$$ term contains the derivative of the monomial, demonstrating its use in calculus. We could also interpret this equation as the first two terms of the Taylor expansion of the monomial. Infinitesimals can be made rigorous using nilpotent elements in local artin algebras. In the ring $$k[y]/(y^2)$$ we see that arguments with infinitesimals can work. This motivates the notation $$k[\varepsilon] = k[y]/(y^2)$$, which is called the ring of dual numbers.

Moreover, if we want to consider higher-order terms of a Taylor approximation then we could consider the artin algebras $$k[y]/(y^k)$$. For our monomial, suppose we want to write out the second order expansion, then
 * $$(x+\varepsilon)^3 = x^3 + 3x^2\varepsilon + 3x\varepsilon^2 + \varepsilon^3$$

Recall that a Taylor expansion (at zero) can be written out as
 * $$f(x) = f(0) + \frac{f^{(1)}(0)}{1!}x + \frac{f^{(2)}(0)}{2!}x^2 + \frac{f^{(3)}(0)}{3!}x^3 + \cdots $$

hence the previous two equations show that the second derivative of $$x^3$$ is $$6x$$.

In general, since we want to consider arbitrary order Taylor expansions in any number of variables, we will consider the category of all local artin algebras over a field.

Motivation
To motivate the definition of a pre-deformation functor, consider the projective hypersurface over a field

\begin{matrix} \operatorname{Proj}\left( \dfrac{\mathbb{C}[x_0,x_1,x_2,x_3]}{(x_0^4 + x_1^4 + x_2^4 + x_3^4)} \right) \\ \downarrow \\ \operatorname{Spec}(k) \end{matrix} $$ If we want to consider an infinitesimal deformation of this space, then we could write down a Cartesian square

\begin{matrix} \operatorname{Proj}\left( \dfrac{\mathbb{C}[x_0,x_1,x_2,x_3]}{(x_0^4 + x_1^4 + x_2^4 + x_3^4)} \right) & \to & \operatorname{Proj}\left( \dfrac{ \mathbb{C}[x_0,x_1,x_2,x_3][\varepsilon]}{(x_0^4 + x_1^4 + x_2^4 + x_3^4 + \varepsilon x_0^{a_0} x_1^{a_1} x_2^{a_2} x_3^{a_3}) } \right) \\ \downarrow & & \downarrow\\ \operatorname{Spec}(k) & \to & \operatorname{Spec}(k[\varepsilon]) \end{matrix} $$ where $$a_0 + a_1 + a_2 + a_3 = 4$$. Then, the space on the right hand corner is one example of an infinitesimal deformation: the extra scheme theoretic structure of the nilpotent elements in $$\operatorname{Spec}(k[\varepsilon])$$ (which is topologically a point) allows us to organize this infinitesimal data. Since we want to consider all possible expansions, we will let our predeformation functor be defined on objects as

F(A) = \left\{ \begin{matrix} \operatorname{Proj}\left( \dfrac{\mathbb{C}[x_0,x_1,x_2,x_3]}{(x_0^4 + x_1^4 + x_2^4 + x_3^4)} \right) & \to & \mathfrak{X} \\ \downarrow & & \downarrow \\ \operatorname{Spec}(k) & \to & \operatorname{Spec}(A) \end{matrix} \right\} $$ where $$A$$ is a local Artin $$k$$-algebra.

Smooth pre-deformation functors
A pre-deformation functor is called smooth if for any surjection $$A' \to A$$ such that the square of any element in the kernel is zero, there is a surjection
 * $$F(A') \to F(A)$$

This is motivated by the following question: given a deformation

\begin{matrix} X & \to & \mathfrak{X} \\ \downarrow & & \downarrow \\ \operatorname{Spec}(k) & \to & \operatorname{Spec}(A) \end{matrix} $$ does there exist an extension of this cartesian diagram to the cartesian diagrams

\begin{matrix} X & \to & \mathfrak{X} & \to & \mathfrak{X}' \\ \downarrow & & \downarrow & & \downarrow \\ \operatorname{Spec}(k) & \to & \operatorname{Spec}(A) & \to & \operatorname{Spec}(A') \end{matrix} $$ the name smooth comes from the lifting criterion of a smooth morphism of schemes.

Tangent space
Recall that the tangent space of a scheme $$X$$ can be described as the $$\operatorname{Hom}$$-set
 * $$TX := \operatorname{Hom}_{\text{Sch}/k}(\operatorname{Spec}(k[\varepsilon]),X)$$

where the source is the ring of dual numbers. Since we are considering the tangent space of a point of some moduli space, we can define the tangent space of our (pre-)deformation functor as
 * $$T_F := F(k[\varepsilon]).$$

Dimension of moduli of curves
One of the first properties of the moduli of algebraic curves $$\mathcal{M}_g$$ can be deduced using elementary deformation theory. Its dimension can be computed as"$\dim(\mathcal{M}_g) = \dim H^1(C,T_C)$"for an arbitrary smooth curve of genus $$g$$ because the deformation space is the tangent space of the moduli space. Using Serre duality the tangent space is isomorphic to $$\begin{align} H^1(C,T_C) &\cong H^0(C,T_C^* \otimes \omega_C)^\vee \\ &\cong H^0(C,\omega_C^{\otimes 2})^\vee \end{align}$$ Hence the Riemann–Roch theorem gives $$\begin{align} h^0(C,\omega_C^{\otimes 2}) - h^1(C,\omega_C^{\otimes 2}) &= 2(2g - 2) - g + 1 \\ &= 3g - 3 \end{align}$$ For curves of genus $$g \geq 2$$ the $$h^1(C,\omega_C^{\otimes 2}) = 0$$ because $$h^1(C,\omega_C^{\otimes 2}) = h^0(C, (\omega_C^{\otimes 2})^{\vee}\otimes \omega_C) $$ the degree is $$\begin{align} \text{deg}((\omega_C^{\otimes 2})^\vee \otimes \omega_C) &= 4 - 4g + 2g - 2 \\ &= 2 - 2g \end{align}$$ and $$h^0(L) = 0$$ for line bundles of negative degree. Therefore the dimension of the moduli space is $$3g - 3$$.

Bend-and-break
Deformation theory was famously applied in birational geometry by Shigefumi Mori to study the existence of rational curves on varieties. For a Fano variety of positive dimension Mori showed that there is a rational curve passing through every point. The method of the proof later became known as Mori's bend-and-break. The rough idea is to start with some curve C through a chosen point and keep deforming it until it breaks into several components. Replacing C by one of the components has the effect of decreasing either the  genus or the degree of C. So after several repetitions of the procedure, eventually we'll obtain a curve of genus 0, i.e. a rational curve. The existence and the properties of deformations of C require arguments from deformation theory and a reduction to positive characteristic.

Arithmetic deformations
One of the major applications of deformation theory is in arithmetic. It can be used to answer the following question: if we have a variety $$X/\mathbb{F}_p$$, what are the possible extensions $$\mathfrak{X}/\mathbb{Z}_p$$? If our variety is a curve, then the vanishing $$H^2$$ implies that every deformation induces a variety over $$\mathbb{Z}_p$$; that is, if we have a smooth curve

\begin{matrix} X \\ \downarrow \\ \operatorname{Spec}(\mathbb{F}_p) \end{matrix} $$ and a deformation

\begin{matrix} X & \to & \mathfrak{X}_2 \\ \downarrow & & \downarrow \\ \operatorname{Spec}(\mathbb{F}_p) & \to & \operatorname{Spec}(\mathbb{Z}/(p^2)) \end{matrix} $$ then we can always extend it to a diagram of the form

\begin{matrix} X & \to & \mathfrak{X}_2 & \to & \mathfrak{X}_3 & \to \cdots \\ \downarrow & & \downarrow & & \downarrow & \\ \operatorname{Spec}(\mathbb{F}_p) & \to & \operatorname{Spec}(\mathbb{Z}/(p^2)) & \to & \operatorname{Spec}(\mathbb{Z}/(p^3)) & \to \cdots \end{matrix} $$

This implies that we can construct a formal scheme $$\mathfrak{X} = \operatorname{Spet}(\mathfrak{X}_\bullet)$$ giving a curve over $$\mathbb{Z}_p$$.

Deformations of abelian schemes
The Serre–Tate theorem asserts, roughly speaking, that the deformations of abelian scheme A is controlled by deformations of the p-divisible group $$A[p^\infty]$$ consisting of its p-power torsion points.

Galois deformations
Another application of deformation theory is with Galois deformations. It allows us to answer the question: If we have a Galois representation
 * $$G \to \operatorname{GL}_n(\mathbb{F}_p)$$

how can we extend it to a representation
 * $$G \to \operatorname{GL}_n(\mathbb{Z}_p) \text{?}$$

Relationship to string theory
The so-called Deligne conjecture arising in the context of algebras (and Hochschild cohomology) stimulated much interest in deformation theory in relation to string theory (roughly speaking, to formalise the idea that a string theory can be regarded as a deformation of a point-particle theory). This is now accepted as proved, after some hitches with early announcements. Maxim Kontsevich is among those who have offered a generally accepted proof of this.

Pedagogical

 * Palamodov, V. P., III. Deformations of complex spaces. Complex Variables IV (very down to earth intro)
 * Course Notes on Deformation Theory (Artin)
 * Studying Deformation Theory of Schemes
 * Notes from Hartshorne's Course on Deformation Theory
 * MSRI – Deformation Theory and Moduli in Algebraic Geometry
 * Notes from Hartshorne's Course on Deformation Theory
 * MSRI – Deformation Theory and Moduli in Algebraic Geometry

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Deformation (mathematics)


text:
Talk:West Lake

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 4 October 2021 and 9 December 2021. Further details are available on the course page. Student editor(s): Jjjjdddd199704.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 12:51, 17 January 2022 (UTC)

Untitled
My Lonely Planet (China, 2002, p360) says "There are 36 lakes in China called Xī Hú, but this one is the most famous." However, the article says "800 West Lakes in China (according to the Lonely Planet)." Which figure is correct, and where exactly did the 800 come from? Ralmin

The 800 figure is definite incorrect. In the Cihai encyclopedia, only three Xihu was listed.

The text says the average depth is 0.8 m (less than 3 ft) but the info box says otherwise. What is the correct value?59.93.91.70 (talk) 09:37, 31 August 2011 (UTC)

 * Does anyone have a source for some geographical features of the lake? It's at least partially a geographical article in my mind, so i expect some measurements like circumference and average diameter or something.  Doviende 08:38, 11 March 2007 (UTC)

 * The article also needs information on surface elevation. I could find one source showing it is between 9-13 metres above sea level. Also the Chinese Wikipedia has info on its width dimensions. ~ AH1 (discuss!) 23:15, 5 September 2011 (UTC)

FYI....
http://zh.wikipedia.org/w/index.php?title=%E7%99%BD%E5%A0%A4&variant=zh-cn

http://scholar.google.com/scholar?hl=en&q=West%20Lake%20Baidi&um=1&ie=UTF-8&sa=N&tab=ws --222.67.212.168 (talk) 11:11, 18 July 2009 (UTC)

http://scholar.google.com/scholar?hl=en&q=%22West+Lake%22+Baidi&btnG=Search --222.67.212.168 (talk) 11:18, 18 July 2009 (UTC)

Water Quality?
In the section Ecology there is missing a paragraphe about "water quality". During my last visit in 2015 the water was stinky and dark, and everywhere swimming was forbidden. Could sb. helb with the data for water quality? Thanks. ++--84.75.181.98 (talk) 15:38, 10 September 2016 (UTC)--++

Wiki Education assignment: Research Process and Methodology - FA22 - Sect 201 - Thu
— Assignment last updated by BartonRei (talk) 00:45, 6 December 2022 (UTC)

title: Talk:West Lake


text:
Leave (U.S. military)

In the United States's military, leave is permission to be away from one's unit for a specific period of time. This includes all six service branches of the military and the National Oceanic and Atmospheric Administration (NOAA).

Entitlement
Under normal circumstances, all personnel are granted 30 days of leave per year. This time is usually used for vacations and other extended time periods away from the service that are longer than three days or need to be taken in the middle of the week. Leave is accumulated at the rate of 2.5 days per month. A member's leave is annotated in the monthly Leave and Earnings Statement.

Under, civilian federal employees who are reservists are allowed “15 days” of annual paid leave for reserve or National Guard training. Prior to 2000, the Justice Department, as had other federal agencies, included days employees were not scheduled to work but would be at reserve training when calculating how much leave an employee used. This miscalculation resulted in the federal appeal of Butterbaugh v. Department of Justice, 336 F.3d 1332 (Fed. Cir. 2003). The Butterbaugh Decision changed things for these reservists and would result in many more federal employees finding their reservist time wrongly charged.

Leave and passes
Leave and passes are terms to describe days off work. A typical weekend day off is also known as a regular pass. Up to four consecutive days off can be either leave days or pass days. Leave days are deducted from the Service Member's 30 annual days off. Pass days are not deducted. Five or more days off must be deducted as leave. Leave and pass days can now be taken consecutively, as long as the Service Member is in the local area to sign back in from or on leave; for example, a Service Member may put in for a 4-day pass over the 4th of July weekend, and utilize leave starting the day after the 4-day weekend, as long as the service member personally signs in or out on leave.

If leave is taken through a weekend, Saturday and Sunday are also deducted as leave days. For example, a Service Member who takes leave from Thursday to the following Tuesday will be deducted six days of leave for Thursday, Friday, Saturday, Sunday, Monday, and Tuesday.

Passes can also be awarded to Service Members for particular achievements. Although passes may be taken for up to 4 days, 3 day passes are granted on most occasions. When 3 day passes are awarded, they are most commonly taken over a weekend giving the Service Member one duty day off. There is a process in getting a leave pass for the Service Member which will be charged by the Department.

One or 2 day passes can also be granted for exceptional circumstances during the duty week; for example, a Service Member can be given a pass for a Wednesday in order to accompany their several children for school physicals, or a Wednesday-Thursday if the Service Member is having to travel overnight for an appointment or event.

Absent without leave
Absent without leave (AWOL) is considered employee misconduct and an attendance issue. This means a Service Member is absent from his/her assigned duty and the absences was not authorized and/or was denied.

Types of leave
The four most common types of leave are:
 * Ordinary leave which is regular chargeable leave time.
 * Emergency leave which is processed more quickly due to an emergency situation but still treated as chargeable leave.
 * Convalescent leave which is non-chargeable and only allowed with a doctor's signature that states the servicemember cannot return to duty for an extended period of time.
 * Excess Leave (see AR 600-8-10)
 * Permissive TDY (Temporary Duty), which is non-chargeable and is only used while traveling between stations while using their leave for government related purposes. Servicemembers using PTDY (Permissive TDY) are not charged while on leave but are also not granted travel pay. Permissive TDY is typically used when PCSing (Permanent Change of Station) and can be granted to a service member when looking for a place to live. Typically for only 10 days.

Rollover
Leave time will "rollover" from year to year. A servicemember may carry up to 60 days of leave before he or she must take it. Leave in excess of 60 days is known as "Use or Lose": if the servicemember does not use the excess leave by October 1 (the beginning of the new fiscal and training year), he or she will lose it (this was extended from 60 days to 75 from June 27, 2008 until 30 September 2015 ). Under certain circumstances, the use or lose threshold may be extended to 80 days, if the member is unable to take leave due to duty requirements, usually because of a deployment. If a servicemember leaves the military without having used all his or her leave time, the unused days are paid for at the member's regular rate of pay upon separation. Conversely, though the situation is less common, pay will be deducted as excess leave on separation if too many days were taken.

Block leave
Block leave refers to time when most or all of the unit takes leave at the same time (as a "block"). Commonly, block leave time is allowed during the summer and Christmas holidays, and before and after deployments.

Terminal leave
Prior to separation or retirement from the military, a member may take the remainder of the leave accumulated. For instance, if a member's separation/retirement date is June 30, and the member has 30 days of leave accrued, the member may go on "terminal leave" beginning June 1. All outprocessing from the service would need to be accomplished prior to June 1. Once entering "terminal leave", he/she would have no further military duties, but would still collect a paycheck and other entitlements such as basic allowance for housing, basic allowance for subsistence, and medical coverage, through the official separation/retirement date of June 30.

title: Leave (U.S. military)


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Prince Hoare (younger)

Prince Hoare (1755 – 22 December 1834) was an English painter, art critic, dramatist and librettist. ('Prince' is a given name, not a royal title.) Among many interventions in Britain's art scene around 1800, Hoare was active in the Royal Academy as its Secretary for Foreign Correspondence.

Life
Prince Hoare was born in Bath, the son of painter William Hoare and his wife. He was named 'Prince' after his father's brother, a sculptor. He studied art from an early age, and became well known as a painter of portraits and historical scenes. His sister Mary Hoare was also a noted painter. He also became a leading facilitator of art criticism and controversy, beginning with Inquiry into the Requisite Cultivation and Present State of the Arts of Design in England (1806).

Later in his life, Hoare wrote 20 plays. He also compiled the Memoirs of Granville Sharp (1820), based on the British abolitionist's manuscripts, family documents and material from the African Institution, London.

Selected works

 * The Three and the Deuce (1795)
 * Indiscretion (1800)

title: Prince Hoare (younger)


text: User talk:80.132.126.176

title: User talk:80.132.126.176


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Varietal

A varietal wine is a wine made primarily from a single named grape variety, and which typically displays the name of that variety on the wine label. Examples of grape varieties commonly used in varietal wines are Cabernet Sauvignon, Chardonnay and Merlot. Wines that display the name of two or more varieties on their label, such as a Chardonnay-Viognier, are blends and not varietal wines. The term is frequently misused in place of vine variety; the term variety refers to the vine or grape, while varietal refers to the wine produced by a variety.

The term was popularized in the US by Maynard Amerine at the University of California, Davis after Prohibition seeking to encourage growers to choose optimal vine varieties, and later promoted by Frank Schoonmaker in the 1950s and 1960s, ultimately becoming widespread during the California wine boom of the 1970s. Varietal wines are commonly associated with New World wines in general, but there is also a long-standing tradition of varietal labelling in Germany and other German-influenced wine regions including Austria, Alsace, and the Czech Republic.

Marketing relevance
The alternatives to the marketing differentiation of wines by grape variety are branded wine, such as Hearty Burgundy, or geographical appellations, such as Champagne or Bordeaux. The poor quality and unknown provenance of many branded wines and the multitude of potentially confusing appellations leaves varietal labeling as perhaps the most popular for quality wines in many markets. This is much less the case in places where appellations have a long and strong tradition, as for instance in France. In the past, the grape variety was very uncommonly mentioned on the labels of French wine bottles, and was forbidden for almost all AOC wines. New World varietal wines from newcomers like Australia and Chile have made a significant dent in traditional French export markets like the UK, and so the French are adopting varietal labeling in some cases, particularly for vin de pays.

Australia
Australia has virtually completed a three decade long transition from labelling by style, e.g. "claret", "burgundy", "hock", "chablis" to a varietal system. While this has been done in response to pressure from the EU, particularly France, it has paved the way for growing interest among Australian consumers for so called alternative varietals, such as Pinot grigio / (Pinot gris), Sangiovese and Tempranillo.

Europe

Within the European Union, a wine using a varietal label must contain at least 85% of that variety. 85% is a common minimum standard; national regulations may set the limit higher in certain cases, but not lower.

France
In most regions of France, terroir is thought to surpass the impact of variety, so almost all French wines traditionally have no variety listed at all, and would in many cases not be allowed for AOC wines. Champagne, for instance, is typically a blend of Chardonnay, Pinot noir and Pinot Meunier, but this is not indicated anywhere on the label. In Alsace, winemakers adopt the German custom of varietal labeling.

In recent years, varietal labels have become more common for French wines. Most of these wines are Vin de pays rather than AOC wines, but varietal names are also seen on some regional AOCs.

United States
In the United States, the Alcohol and Tobacco Tax and Trade Bureau regulations specify a minimum variety content of 75% of the labeled grape, for Vitis vinifera wines, and 51% for Vitis labrusca wines. There is no restriction on the identity of the balance. Many states in the United States require specific compositions to qualify for sale under a particular varietal labels. For example, in Oregon, wines subject to its regulation must be identified by the grape variety from which it was made, and certain varietals must contain at least 95% of that variety, although the new "Southern Oregon" sub-AVA allows for the minimum 75% figure.

title: Varietal


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Kingsbury Water Park

Kingsbury Water Park is a country park in north Warwickshire, England, not far from Birmingham and lying on the River Tame. It is owned and managed by Warwickshire County Council. It has fifteen lakes situated in over 600 acre of country park. It is renowned for its birdlife, and is popular with birdwatchers. It is bordered on the western edge by the Birmingham and Fazeley Canal.

History
The area which is now Kingsbury Water Park was previously the site of gravel extraction pits that were operated by the Midland Gravel Company. The lakes were created from the craters left behind after the gravel had been taken out. The Water Park was opened on 24 May 1975 with two lakes and 123 acres. It has been expanded over the years and as of 2011 has fifteen lakes in an area covering over 600 acres. The Park welcomed 50,000 visitors in its first year, a number which had expanded to 350,000 in 2007. The Water Park was briefly closed to the public in June 2007 after the area was hit by the worst flooding since the 1930s. At the time it was estimated the floods had caused tens of thousands of pounds' worth of damage. The Park was opened again once the flooding had subsided.

Features
Throughout the park are a number of bridleways, marked cycle routes and footpaths. There are a variety of opportunities available for water sports, including water skiing, jetskis, power boats, sailing and model boat racing.

There is also a 7¼" gauge ridable miniature railway known as Echills Wood Railway. It is run by enthusiasts, who eventually hope to provide a 2 km loop, running a selection of steam, diesel and electric trains.

In November 2011 a new bird hide was erected by Warwickshire County Council allowing birdwatchers to observe birds in their natural habitat. A previous bird hide had been burnt down in December 2010.

Twelve of the lakes provide the opportunity for angling, offering a variety of coarse angling.

Events
Every Saturday at 9am, the park hosts a free 5-kilometre run, organised by Parkrun. The first Kingsbury Water Parkrun was held on 20 July 2013, with 143 runners. The biggest attendance was 792 runners on 1 January 2019 for the New Year's Day Parkrun.

Children's facilities
Broomey Croft Children's Farm is home to many animals and a play park and is suitable for children of all ages. Situated around the park are a number of play areas, picnic areas and cafés. The park is also home to a bicycle hire centre and has a well established visitor centre and shop.

title: Kingsbury Water Park


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William Hoare

William Hoare of Bath (c. 1707 – 12 December 1792) was a British portraitist, painter and printmaker. From c. 1740 to 1759, he was the leading oil portraitist at Bath, Somerset, until Thomas Gainsborough arrived in the town. Noted for his pastels, he was a foundation member of the Royal Academy.

Life
Born near Eye, Suffolk, Hoare received a gentleman's education in Faringdon and he may be the William Hoare baptised on 9 October 1707 in nearby Little Coxwell. He showed an aptitude for drawing and was sent to London to study under Giuseppe Grisoni, who had left Florence for London in 1715. When Grisoni returned to Italy in 1728, Hoare went with him, travelling to Rome and continuing his studies under the direction of Francesco Imperiali. He remained in Rome for nine years, returning to London in 1737/8.

Failing to establish himself in London, Hoare settled in Bath, an expanding spa town popular with the wealthier classes. He obtained numerous commissions, the most important being for official portraits of social leaders of the day (including George Frideric Handel) and political men (e.g., Prime Ministers Robert Walpole and William Pitt, 1st Earl of Chatham, c.1754). There are several versions of most of these, suggesting that he had a studio, and they were further publicised by the production of mezzotints by leading engravers of the day. Hoare himself was a delicate etcher and published a number of private plates, mostly of family and friends, including a Miss Hoare (probably Mary), Christopher Anstey and the 3rd Duke of Beaufort. His pastels were influenced by Rosalba Carriera.

William Hoare was the first fashionable portraitist to settle in Bath, and he was the leading portraitist there until the arrival of Thomas Gainsborough in 1759. He remained the favourite of his powerful patron the Duke of Newcastle, his family, followers and political associates. Included amongst his other important patrons were the Earls of Pembroke and Chesterfield, and the Duke of Beaufort. With Gainsborough and Joshua Reynolds, he was a founding member of the Royal Academy.

Hoare was closely involved with the running of the Royal Mineral Water Hospital in Bath from 1742. He served as a governor of the hospital, his aim was to develop specialist treatments for rheumatic disorders. Where he became acquainted with Bath's notable visitors and the neighbouring landed families. Chalmers described him as 'an ingenious and amiable English painter'. He died at Bath on 10 December 1792. Interred at the vault of St Swithins Church, Bath.

His son, Prince Hoare, achieved fame as a painter and dramatist. His daughter Mary Hoare was also a noted painter.

Works
Hoare's oil painting Dr Oliver and Mr Pierce examining patients with Paralysis, Rheumatism and Leprosy hung prominently at the Royal Mineral Water Hospital until 2019, when it was transferred to a new building at Bath's Royal United Hospital site.

Portrait of Ayuba Suleiman Diallo by William Hoare, was first seen by the public in December 2009 when it came up for auction and sold for over £500,000. The new owner unnamed wished to take it out the country but was stopped due to its national importance.

title: William Hoare


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List of Puerto Rican slang words and phrases

This article is a summary of common slang words and phrases used in Puerto Rico. Idiomatic expressions may be difficult to translate fully and may have multiple meanings, so the English translations below may not reflect the full meaning of the expression they intend to translate. This is a short list and more may be found on the Academia Puertorriqueña de la Lengua Española website.

List

 * ataque de nervios
 * a sudden nervous reaction, similar to hysterics, or losing control, experienced in response to something

 * ¡Bendito!
 * variants are ¡Ay bendito! and dito - “aww poor you” or “oh my god”; “ay” meaning lament, and “bendito” meaning blessed.

 * abombao / abombá
 * Referring to food; rotten or damaged.

 * al garete
 * Wild, off the rails, disastrous. Doing something rash. Comes from the Arabic phrase meaning "adrift" (Arabic: على غير هدى (/ʕa.'laː.ɣajr.'hu.dan/), romanized: ealaa ghayr hudaa).

 * asicalao
 * flawless, clean, immaculate. From standard Spanish acicalado

 * bembé
 * a big party.

 * bichote
 * Important person. From English big shot.

 * birras
 * Beer.

 * bochinche
 * gossip

 * boricua
 * The name given to Puerto Rico people by Puerto Ricans.

 * bregar
 * To work on a task, to do something with effort and dedication.

 * broki
 * brother or friend.

 * cafre
 * a lowlife. Comes from Arabic (Arabic: كافر (/kafir), romanized: Kafir).

 * cangri
 * A badass, hunk or hottie. An influential person. From English congressman.

 * cariduro
 * person who should be ashamed of their actions but isn't; a stubborn person

 * chacho
 * short for muchacho - Guy, male,

in mexico this can mean dude or guy relating to someone younger but in puerto rican slang, it is used in replacement of dinero/money
 * chavo
 * chulería
 * While in other countries this word means "insolence", in Puerto Rico it has an entirely different meaning and is used to describe that something is good, fun, funny, great or beautiful.

 * corillo
 * Friend, or group of friends.

 * dura
 * Normally means “hard”, but in Puerto Rican slang means that someone is really good at what they do.

 * embustería
 * series of lies, something that is completely false, a "pack of lies"

 * ¡Fo!
 * literally translates to "eww!" or "yuck!" it is often used as an exclamation in reaction to a bad smell.

 * fregao, fregá
 * shameless person

 * guajana
 * The flower of the sugarcane.

 * guinda
 * steep slope

 * gufear
 * to act goofy.

 * janguear
 * “to hang out”. Comes from the American expression “hang out”.

 * jartera
 * to be full.

 * jevo/a
 * boyfriend / girlfriend

 * jíbaro
 * A person who lives in the countryside, mountain people, the agricultural worker, who cuts sugarcane, for example. From a Taino compound word ("Jiba" meaning mountain or forest, and "iro" meaning man or men) though commonly mistaken for originating from the Arabic (Mofarite Arabic: جبري (Jabre), romanized: Jabre), in the Mofarite related Ethiopian Semitic languages ገበሬ(Gabre), romanized: Gabre).

 * jumeta
 * Drunk

 * lambeojo
 * Lackey,brownoser;toady,sycophant.

 * ligar
 * to peep

 * ligón
 * Peeping Tom

 * limber
 * Also, "limbel". A home-made flavored frozen treat usually made from natural fruits or sweet milk mixtures and often served on a small piece of water-resistant paper, a plastic or paper cup, or a popsicle stick. The name is said to have originated from the last name of Charles Lindbergh after the islanders noticed how "awfully cold as ice" he was as compared to the warmth of the locals during Lindbergh's visit to the Island in 1928.

 * mamey
 * Used when referring to something that is easy to do.

 * mami, papi
 * Terms of endearment; mami when referring to a cute woman, papi when referring to a handsome man, or to address a lover

 * nene, nena
 * Boy/girl In standard Spanish it means "baby".

 * panna, pana
 * Friend / Buddy ("pana" is also a name for breadfruit in Puerto Rico)  From partner.

 * pasárselas con la cuchara ancha
 * to get away with murder or to get away with it

 * perreo, perrear
 * A way of dancing ("grinding") or a danceable song.

 * pichea
 * “forget about that”, Disregard.

 * por encima de los gandules
 * Expression of admiration, to say that something is outstanding or beyond good.

 * revolú
 * Used to describe chaotic situations.

 * servirse con la cuchara grande
 * to get away with murder or to get away with it

 * soplapote
 * a nobody, or a worker low on the hierarchy, or an enabler

 * tapón
 * traffic jam. In standard Spanish, "a bottle top" or "a clog".

 * tráfala
 * a lowlife.

Typically used at parties, dances, or general hype events to express of joy or excitement, hence the direct translation "That's awesome!"
 * wepa


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List of mathematical theories

This is a list of mathematical theories.

• Almgren–Pitts min-max theory

• Approximation theory

• Arakelov theory

• Artin–Schreier theory

• Asymptotic theory

• Automata theory

• Bass–Serre theory

• Bifurcation theory

• Braid theory

• Brill–Noether theory

• Catastrophe theory

• Category theory

• Chaos theory

• Character theory

• Choquet theory

• Class field theory

• Cobordism theory

• Coding theory

• Cohomology theory

• Complex function theory

• Complexity theory

• Computation theory

• Continuum theory

• Control theory

• Deformation theory

• Dempster-Shafer theory

• Dimension theory

• Distribution theory

• Dynamical systems theory

• Elimination theory

• Ergodic theory

• Extremal graph theory

• Field theory

• Formal language theory

• Fourier theory

• Galois theory

• Game theory

• Graph theory

• Grothendieck's Galois theory

• Group theory

• Hodge theory

• Homology theory

• Homotopy theory

• Ideal theory

• Index theory

• Information theory

• Invariant theory

• Iwasawa theory

• K-theory

• Knot theory

• L-theory

• Lattice theory

• Lie theory

• M-theory

• Measure theory

• Model theory

• Morse theory

• Module theory

• Network theory

• Nevanlinna theory

• Number theory

• Obstruction theory

• Operator theory

• Optimization theory

• Order theory

• Percolation theory

• Perturbation theory

• Probability theory

• Proof theory

• Quantum theory

• Queue theory

• Ramsey theory

• Random matrix theory

• Recursion theory

• Relational theory

• Representation theory

• Ring theory

• Scheme theory

• Seiberg–Witten theory

• Semigroup theory

• Set theory

• Shape theory

• Sheaf theory

• Singularity theory

• Soliton theory

• Spectral theory

• String theory

• Sturm-Liouville theory

• Surgery theory

• Teichmüller theory

• Theory of equations

• Theory of statistics

• Topos theory

• Transcendental number theory

• Twistor theory

• Type theory

• Universal theory

• Wheel theory

title: List of mathematical theories


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User talk:Marijne

Hello, welcome to Wikipedia. If you have any questions, you can ask at the help desk or on my talk page. I hope you enjoy editing here. 172 10:34, 25 May 2004 (UTC)
 * BTW, good job editing the Cold War articles. 172 10:37, 25 May 2004 (UTC)

Talk pages
Wikipedia's talk pages are not forums. They are not for general chatter. I have once again removed the unnecessary and useless discussion at Talk:George Lazenby. Please take the time to read Wikipedia's polcies and guidelines on discussion pages, specifically found at WP:NOT and WP:TPG. Thank you. K1Bond007 21:09, 4 March 2006 (UTC)

title: User talk:Marijne


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Pat Dobson

Patrick Edward Dobson, Jr. (February 12, 1942 – November 22, 2006) was an American right-handed starting pitcher in Major League Baseball who played for the Detroit Tigers (1967–69), San Diego Padres (1970), Baltimore Orioles (1971–72), Atlanta Braves (1973), New York Yankees (1973–75) and Cleveland Indians (1976–77). He was best known for being one of four Orioles pitchers to win 20 games in their season.

Baseball career
Dobson was born in Depew, New York. He signed with Detroit in. After spending seven years in the minor leagues and winter ball, pitching both in relief and starting, he made his debut with the big team in the season after starting the season 4–1 with a 1.47 ERA in six starts for the AAA Toledo Mud Hens. Dobson would spend the next $2 1/2$ years as a reliever and spot starter for the Tigers including pitching $4 2/3$ innings of relief in the team's 1968 World Series victory over the St. Louis Cardinals. Unable to claim a spot in the Tigers' rotation of Mickey Lolich, Denny McLain, Earl Wilson, and Joe Sparma, Dobson was traded to San Diego in along with Dave Campbell for a young Joe Niekro. After going 14–15 with 185 strikeouts and a 3.76 earned run average as the staff ace for the last-place Padres, he was traded along with Tom Dukes to Baltimore for Enzo Hernández, Tom Phoebus, Fred Beene and Al Severinsen on December 1, 1970.

In 1971 Dobson had a winning streak of 12 games (including nine consecutive complete games) and a scoreless inning streak of 23. On September 24, he recorded his 20th win, a 7–0 shutout against the Indians. Dobson posted a 20–8, 187, 2.90 season record, and was part of the Orioles' "Big Four" pitching staff along with Dave McNally (21–5), Mike Cuellar (20–9), and Jim Palmer (20–10). Baltimore went on to win 101 games, with the distinction of having four 20-game winners in a season; only one other team in MLB history, the Chicago White Sox, have had four 20-game winners. On November 2, 1971, Dobson threw a 2–0 no-hitter against the Yomiuri Giants in Tokyo. It was the first no-hit game in the Japanese-American baseball exhibition history. Dobson was an All-Star in. His 2.65 ERA was a major improvement from his 20-win season, but he went 16–18, tying for the AL lead in losses with Yankee Mel Stottlemyre.

In a transaction primarily driven by the Orioles' need for a power-hitting catcher, he was dealt along with Davey Johnson, Johnny Oates and Roric Harrison to the Atlanta Braves for Earl Williams and Taylor Duncan on the last day of the Winter Meetings on December 1, 1972. After starting the 1973 season 3–7, Dobson was sent to the Yankees on June 7 for four minor league players (none of whom panned out). Escaping Atlanta, he again blossomed and finished the season with a 9–8 record for the Yankees. Dobson started the 1974 campaign weakly, achieving only a 6–11 record by mid–season. However, Dobson anchored the Yankees' pitching staff in the second half of the season, finishing with a 19–15 record and a 3.07 ERA, the best numbers that year for a Yankee pitcher. After a slumping 11–14, 4.07 in, Dobson was traded to the Indians, and recovered in with a 16–12, 3.48 record. The season proved to be his last, as Dobson compiled a 3–12, 6.16 record. He was released by the Indians during spring training of 1978.

In his 11-season career Dobson had a record of 122–129, with 1,301 strikeouts, a 3.54 earned run average, 74 complete games, 14 shutouts, 19 saves, and $2,120 1/3$ innings pitched in 414 games.

Later life
After his playing days, Dobson became a pitching coach for the Brewers, Padres, Royals and Orioles. From 1989 to 1990, he was the manager of the Fort Myers Sun Sox of the Senior Professional Baseball Association, leading the team to a 37–35 record and a playoff berth in his first season and an 11–14 record at the time of the league's demise on December 26, 1990. In 1997, Dobson joined the San Francisco Giants organization and worked as an advance major league scout and assistant to general manager Brian Sabean.

In 2006 Dobson died from leukemia in San Diego at the age of 64, one day after being diagnosed with the disease.

title: Pat Dobson


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Talk:Termagant

[Untitled]
Could it not be a corrupted form of al-Rahman? Zsigri 23:35, 4 January 2007 (UTC)

 * Who knows? Paul B 00:08, 5 January 2007 (UTC)

 * That doesn't seem likely. Considering that the Christians also thought that "Allahu Akbar" referred to Muslim worship of twin goddesses Allat and Akbar, I suppose anything is possible. The question is, what can be established as true (and then reported in a secondary source, so I can be added here uncontroversially), and the answer is, probably, nothing. --75.36.136.207 (talk) 19:51, 22 February 2008 (UTC)

I didn't know that! --Bluejay Young 10:38, 25 May 2004 (UTC)

-

Should this article mention that in Games Workshop's game, Warhammer 40k, the Tyranids  have an unit called Termagant ? --Acolyte of Discord 22:14, 6 May 2006 (UTC)

 * Since the're NOT called that...probably not, no. So, I changed it.213.113.252.16 (talk) 16:43, 2 July 2008 (UTC)

Walter W. Skeat
In the article: "W. W. Skeat in the 19th century, speculated that the name was originally "Trivagante", meaning 'thrice wandering'" I think this refers to Skeat's notes to Chaucer's Tale of Sir Thopas. If anyone can find the note, and improve the reference, that would be a useful tweak.--Wetman (talk) 10:09, 11 May 2009 (UTC)

A mystery
Yes, Mahound is mentioned in the English mystery plays. But I challenge anybody to provide evidence of the use of Termagant. I have done some searches of the texts listed here and can find nothing. — RHaworth (talk · contribs) 20:40, 21 November 2017 (UTC)

title: Talk:Termagant


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Duchsustus

Duchsustus (דוכסוסטוס, from Greek δυσχιστός dyschistos) is the name of a type of parchment used for religious writings in Judaism. It is originally a Greek word and one of three Talmudic names for animal skin. The other two are klaf and gevil. The meanings of these terms, however, are the subject of controversy in Jewish law.

According to the Talmud, a sefer Torah should, ideally, be written on gevil, but may also be on klaf; tefillin must be written on klaf; and mezuzot may be written on duchsustus, klaf, or gevil. Duchsustus is the animal's dermis, klaf is the epidermis, and gevil is both layers tanned and unseparated.

This instruction is dated to Moses at Mount Sinai.

Maimonides' prescriptions
There are halachic rules for the use of each of the three types of tanned skin. According to Maimonides, Torah scrolls must be written on g'vil only on the side on which the hair had grown, and never on duchsustos (understood as the half-skin from the flesh side). Phylacteries, if written on k'laf, must be written on the flesh side. A mezuzah, when written on duchsustos, must be written on the hair side. It is unacceptable to write on the hair side of k'laf or on the flesh side of g'vil and duchsustos.

title: Duchsustus