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Along with Jacobsohn, Flatau wrote a well-known textbook of comparative anatomy of the nervous system of mammals (1899). In 1906, he visited the Munich psychiatric clinic of Emil Kraepelin.In 1910 and 1911, he wrote three chapters on tumors of the brain and spinal cord for the two volumes of the handbook edited by the Berlin neurologist Max Lewandowsky.Together with the Warsaw surgeon Bronislaw Sawicki, he published a work on surgery of the spinal-cord cysts and treatment of tumors of the spine, in which he pointed out histopathological issues important for the surgical procedure. This publication was the culmination of several years of cooperation between the two doctors.Flatau was the first in Poland to describe the cases of encephalitis lethargica and on occasion the name "Economo-Flatau disease" was used to identify this disease in Polish medical literature.
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https://en.wikipedia.org/wiki/Edward_Flatau
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In 1911, Flatau and Wladyslaw Sterling published an article on progressive torsion spasm in children. The authors pointed out that the disease was associated with genetic factors. In the same year, Theodor Ziehen and Hermann Oppenheim published a paper claiming that dystonia is related to a disease of the muscles. However, Flatau and Sterling noted that the intellectual capacity of these patients was higher than average.
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In 1976, Eldridge suggested that the publication of Flatau and Sterling was one of the first to describe the genetic factors of neurological diseases.In 1927, Flatau, independently of Emil Redlich in Vienna, described the first cases of encephalomyelitis epidemica disseminata (Flatau-Redlich disease). Flatau was convinced that this illness is caused by a virus which was later confirmed by Mergulis. In 1925, Flatau described in detail Schilder disease and suggested new name "encephaloleukopathia scleroticans progressive". Between 1921 and 1923, he described the meningeal symptoms characteristic during tuberculosis-related inflammation of meningitis: namely, the pupil extension when bending head and erection of the penis during repeated bending of the torso forward.
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In 1912, he published in German and Polish one of the first modern monographs in the 20th century about migraine headaches which is still referenced in scientific literature. It was the first Polish textbook devoted to migraine. In a review of the historical background of general aspects of the headaches, Isler and Rose say, "His unique monograph of 1912, Die Migrane, contains a thoroughly structured survey of most earlier authors, precise clinical observations, a critical evaluation of pathophysiology, and uncritical opinions on treatment, including arsenic cures." In his monograph, Flatau presented the full clinical picture of migraine and described the disease as an innate disposition to pathological metabolic processes in the nervous system and described its distinguished characters – ocular, epileptic, mental and facial.
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The book was based on observations of himself and about 500 cases from his own practice.In the introduction to the monograph, he wrote,"Migraine, as such, is not an independent or autonomous disease; it is just one set of symptoms in the great chain of changed neurometabolism, whose crucial aspect are chemical changes and endocrine glands. Migraine attack is the expression of brain disorders; however, an exact mechanism which may be responsible is currently just a matter of conjecture and supposition. Today we cannot describe mechanisms that come to play and express them in well defined anatomical and physiological aspects.
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The forces that govern such mechanisms are also not known to us. We can only guess and make assumptions as to their operation. Nevertheless, great progress characterizing the development of neurology in the second half of the nineteenth century is visible in the field of research into migraine as well. As a result, one can describe some of the ideas on more reliable anatomical and physiological grounds."
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In addition to neurology, Flatau was a psychiatrist.Irena Solska, famous Polish actress, describes in her memoirs that playing Maria, a mad wife in nondivine comedy of Zygmunt Krasinski around 1920, she visited the psychiatric hospital (ward) of Edward Flatau. Another of his patients was well-known Polish poet Jan Lechoń. In the story of Isaac Bashevis Singer, "The Power of Darkness", Flatau is even called to cure the demons.
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Excerpt from Singer's story reads: "The word soon spread through Krochmalna Street and the surrounding streets that a dybbuk had settled in Tzeitel's ear, and that it chanted Torah ... A Warsaw nerve specialist became interested in the case – Dr. Flatau, who was famous not only in Poland, but in all Europe and maybe in America, too. And an article about the case appeared in a Yiddish newspaper. The author borrowed its title from Tolstoy's play The power of darkness."
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In addition to his scientific work, he had a private practice in Warsaw. In 1904, he became head of the Department of Neurology at the Szpital Starozakonnych w Warszawie, which he led for 28 years. There, many of the Polish neurologists were making their first steps. His pupil Eufemiusz Herman recalls: "Traditionally on Mondays, patient cases were reviewed.
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At the bedside of each patient, Flatau discussed their cases, he listened to the voice of everyone, even the youngest doctor ... As a teacher and a boss, he was deeply attached to each and every one who worked with him. They could draw richly from his great experience and extensive knowledge. He was patient, forgiving, always cheerful, treating students as their beloved family.
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Thinking forehead, deep dark eyes with a keen, yet warm gaze, low voice with a wide range of modulation – these are the features which, apart from the deep knowledge and great experience, attracted and charmed anyone who was in the circle of his indefatigable activity." In 1908, he lived on the Marszałkowska 150 Street in Warsaw on the first floor of the House of Fashion of Boguslaw Herse. He also lived for some time in the apartment on Chmielna Street 60. Other stories associated with Flatau and his Warsaw traces can be found in the articles of Jerzy Kasprzycki
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By 1899, Flatau had established a name for himself both in Germany and abroad, and returned to Poland during that year. Flatau was closely associated with attempts to re-establish Polish science during and after Russian occupation. After his return, he formed a private microscopy laboratory at his apartments in Warsaw, and worked in Warsaw hospitals as a consultant.
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In 1911, he established a neurological laboratory in the Warsaw Psychologic Society, and he became in 1913 the first head of the Department of Neurobiology of the Warsaw Scientific Society (Warszawskie Towarzystwo Naukowe) and from 1911 to 1923, head of the Department of Neurobiology at the Nencki Institute of Experimental Biology. For many years, he shared his responsibilities as experimentator and neurologist between the laboratory and the hospital. He was influential in establishing Polish medical periodicals Neurologia Polska and Warszawskie Czasopismo Lekarskie.
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Especially at the beginning of his career, he was involved in popular science activities in Poland. He published in popular medicine journals such as Zdrowie, Gazeta Lekarska, and Nowiny Lekarskie. Flatau's law, originally published in German, was reprinted in Polish in the journal Nowiny Lekarskie together with the basic introduction.
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His brain atlas and a book about migraine were translated into Polish, as well. He was interested in history of Polish medicine. In 1899, he notes: "Quite important for the history of Polish medicine is the fact that Robert Remak, one of the greatest histologists and neuropathologists, was born in Poznań in 1815 and published his fundamental work in the Polish language.
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This historical information was communicated to me by his son – Professor Ernst Remak in Berlin. He was also kind enough to give me a copy of this epic work in the Polish language.
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"He was co-editor of the German journal Jahresbericht Leistungen und über die Fortschritte auf dem Gebiete der Neurologie und Psychiatrie. Since its inception in 1897 until 1900, and afterwards as a collaborator, he contributed to the journal and was summarizing Polish neurological and psychiatric literature.According to the comments of Henryk Higier in 1932, "Flatau being convicted of the shameful behavior of the German occupying forces during the World War I stopped his friendly relations with Germany, to which scientist he felt deep affection, and moved entirely his scientific affinity towards medical sciences in France ..." . Analysis of his publications in that period indicates that he indeed increased significantly, after the World War I, publications in French journals, but still on occasion published in German.
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In the same article, Higier writes "In social life, Flatau ... a sense of responsibility for the state of Polish intellectual culture and the level and extent of Polish research ideas." In the early 20th century, the world neurology was beginning to be organized in international structures. In 1929, Flatau wrote to Henry Riley - secretary of the organizing committee of the I International Congress of Neurology which was to be held in 1931 - "as a representative of the Polish Committee, I express astonishment and grief that none of the vice-presidents of the Congress nor any of the honorary members ... are from Poland. Polish neurologists were relentless in their efforts during all the years of political dependence and their work has intensified since gaining independence."
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Flatau has played an important role in the development of the Nencki Institute of Experimental Biology in Warsaw (it exists to this day), and he created the first experimental neurobiological laboratory in Poland, and was member and contributed to development of the Warsaw Scientific Society (he was a member since 19 January 1908). As Poland was under occupation in that time, this society played an important role in re-establishing Polish science in the years to come. The neurological laboratory at the Nencki Institute had rather humble origin. In the early 20th century, after settling in Warsaw, Flatau established in his private apartment, microscopy laboratory in the building where the fashion house of Herse was located on Marszałkowska 150 street.
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The anecdote about this laboratory is: " carriage would take us to building on Marszalkowska Street, the same building where were mannequin ladies stood in shopping windows of House of Fashion of Boguslaw Herse (...) In this house lived, on the first floor, my uncle Edward Flatau, who – just like my father – was a neurologist and psychiatrist (...) There was a St. Bernard dog that had its idiosyncrasies. In the long, narrow room of the apartment stood, preserved in alcohol and covered, brains of animals and humans that uncle studied.
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At night, the St. Bernard used his paws to remove the cover and ate a brain, always just one. He was taking off the cover gently and quietly placed it on the table.
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Flatau would not detect it for several days because he did not work in the laboratory every day. Then he announced that St. Bernard would be thrown out (...).
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St. Bernard looked at my uncle with reproach and would leave the room in protest against these threats..."Subsequently, this laboratory moved on Jerozolimska Avenue 85 under auspices of the Psychological Society. In October 1911, Flatau donated to the Warsaw Scientific Society his neurological laboratory, along with the entire inventory and allowance of 2,000 rubles.
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In that time (1911), the Warsaw Scientific Society received as a gift from Józef Potocki, a house on Śniadeckich 8, where the laboratory was located. This is the same building where in 1913, Maria Skłodowska-Curie funded a radiology laboratory and was its honorary director. For many years, Flatau was the director of the neurological laboratory and was assisted by Teofil Simchowicz.
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According to Herman "Every day at 9 am, Flatau showed up in the neurobiological laboratory on Śniadecki 8 Street. Here, he was performing experiments on animals, reviewed the histology specimens, collaborated with his colleagues. At 11 am, he would go for coffee at a nearby Ostrowski cafe at the intersection of Koszykowa and Marszałkowska Streets, and after 15 minutes, he would go to the hospital on Czyste on Dworska 15 street."
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The laboratory conducted research in the fields of comparative anatomy, general and nervous system, physiology, pathological anatomy, experimental pathology, and experimental therapy of the nervous system. He collaborated with an assistant of Maria Skłodowska-Curie, Ludwik Wertenstein, on experimental oncology (use of radioactivity). The Institute of Experimental Biology of Marcel Nencki was established in Warsaw at the initiative of students and colleagues of Marceli Nencki.
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At the end of 1918, Kazimierz Białaszewicz, along with Edward Flatau and Romuald Minkiewicz, head of just created Department of General Biology (Zakład Biologii Ogólnej) applied to the board of the Warsaw Scientific Society with an initiative to separate these three laboratories and create an organization under the name of "Institute of Experimental Biology. Marcel Nencki". Flatau headed the Laboratory of Neurobiology, between 1911 and 1923.
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In January 1932, he diagnosed himself with a brain tumor. He kept notes about his illness, but they were lost during the war. He died five months later, and he is buried at the Jewish Cemetery in Warsaw (section 10, row 2).At his grave, Dr. A. Goldman said: "reticent in colloquial conversations, strong in resolving professional and academic difficulties, Edward Flatau died as a result of the suffering that he recognized himself and during the course of his illness he carefully and stoically made notes about its progress (...). His friend Samuel Goldflam mentioned: (...) I have to speak over the grave of my late friend ... He was a fanatic of work and he worked relentlessly, since January he knew perfectly well that he was afflicted with an incurable disease, but he did not confide it to anyone, he did not let anyone know."
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Several thousand people came to his funeral. His headstone was done by sculptor Mieczysław Lubelski. He died in 1932, the same year as two other notable Polish neurologists and friends, Samuel Goldflam and Joseph Jules François Félix Babinski (Polish-French neurologist).
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https://en.wikipedia.org/wiki/Edward_Flatau
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In a few universities in the United Kingdom, an advanced postgraduate (APG) is student enrolled in the first year (full-time) or first two years (part-time) of a PhD program. During this period, students usually research their particular research area for unanswered or unclear research questions or topics. The University also assesses whether the student is suitable to complete a PhD.
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https://en.wikipedia.org/wiki/Advanced_postgraduate
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At the end of this period, students are required to submit a report regarding the direction of their research during the remainder of their PhD. They usually present the report at a panel interview, called the APG interview. == References ==
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https://en.wikipedia.org/wiki/Advanced_postgraduate
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Louchébem or loucherbem (French pronunciation: ) is Parisian and Lyonnaise butchers' (French boucher) slang, similar to Pig Latin and Verlan. It originated in the mid-19th century and was in common use until the 1950s.
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The louchébem word-creation process resembles that of largonji, verlan, and javanais, in that existing words are camouflaged according to a set of rules. Strictly speaking, louchébem is a more rigid variety of largonji in which the ending -èm is obligatory. Largonji substitutes ⟨l⟩ for the consonant or consonant cluster at the beginning of the word, or, if the word begins with an ⟨l⟩ or a vowel, the second syllable; the initial consonant is then reattached to the end of the word along with a suffix particular to the argot: -ji , -oc , -ic , -uche , -ès , or in the case of louchébem, -em/ème . Note that louchébem is first and foremost an oral language, and spelling is usually phoneticized.
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Despite the name, louchébem seems to have been created not by butchers, but by inmates at Brest Prison, with records dating back to 1821.Edmund Clerihew Bentley used the language as a plot point in his 1937 short story "The Old-Fashioned Apache". During the Nazi occupation louchébem was used by Parisian members of the Resistance. Even today, louchébem is still well-known and used among those working at point-of-sale in the meat retail industry. Some words have even leaked into common, everyday use by the masses; an example is the word loufoque, meaning "eccentric".
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https://en.wikipedia.org/wiki/Louchébem
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Here are a few example Louchébem words. There is another French argot called largonji, which differs from louchébem only in the suffix that is added (-i instead of -em); the term is derived from jargon.
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https://en.wikipedia.org/wiki/Louchébem
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A dominance signal is used in a dominance hierarchy or pecking order to indicate an animal's dominance. Dominance signals are a type of internal environment signal that demonstrate the signalers attributes . Dominance signals are necessary for several species for mating, maintaining social hierarchies and defending territories Dominance signals also provide information about an animals fitness.
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https://en.wikipedia.org/wiki/Dominance_signal
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Animals have developed conflict management strategies to reduce frequency of aggressive incidents in competitive matters. This evolution is the basis of dominance signals. Dominance signals can be operationally defined by (1) acts or displays produced by signalers, (2) which conveys meaning messages to recipients such that (3) the signal is met with a response and (4) the response results in dominance being displayed.
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For example, (1) hermit claws raise their claws performing a threat signal, (2) which expresses intent to attack to challenger (3) and the challenger makes a decision to retreat which (4) reinforces signaller's dominance.The earliest study of animal signals can be attributed to Charles Darwin's "The Expressions of the Emotions in Man and Animals", which introduced the comparative study of signals across all animals. Expressive abilities of the face are the basis of nonverbal expression. These facial signals help maintain dominance or "status" relationships by allowing species to predict the outcome of their encounter, and calculate the cost of their own fitness.
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https://en.wikipedia.org/wiki/Dominance_signal
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Nikolaas Tinbergen furthered the essential framework for studying animal signals with his 'four questions' about the phylogeny, function, development and mechanism of signals or any other behaviour.Dominance signals are the basis of animal hierarchies and are triggered by stress environments. These signals are used to maintain courtship dominance, social dominance and territorial and resource dominance both within and between different species. Dominance signals are prominent far beyond the ethology literature, as humans express them in several forms.
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https://en.wikipedia.org/wiki/Dominance_signal
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Animals use several modalities of communication to express dominance. Aggressive encounters between competing individuals can result in significant costs for animals. To minimize fighting costs and increase fitness, many species have evolved specialized signalling systems to assert dominance by electing specific cues or signals. These signals allow individuals to gauge the status of conspecifics and not engage in combat with individuals of higher rank or strength. Such signals are found in several species and can present themselves in many different ways.
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https://en.wikipedia.org/wiki/Dominance_signal
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Visual communication is a common dominance signal among animals. They are an effective modality as they come at a low cost to the animal and minimize risk. The Gila Monster (Heloderma suspectum) for example, express bright orange splotches during territorial conflict to warn competitors that they are poisonous, and thus assert their dominance over a territory.
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Acoustic communication is often used by animals to express dominance. Acoustic sounds can vary substantially in amplitude, duration, and frequency structure which can influence how the signal is received. Vocalizations can be effective for a species as it may decrease physical interaction, which may decrease injury costs. Northern elephant seals (Mirounga angustirostris), for example, have a polygynous breeding system in which adult males establish dominance hierarchies that facilitates copulation with females. Acoustic signalling is detrimental in resolving competition between males for mates. Elephant seals express unique acoustic signals that allow males to remember the violations of past rivals and recall which seals are dominant.
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https://en.wikipedia.org/wiki/Dominance_signal
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Tactile signals occur when physical contact is made between two competing animals and can only be transmitted over very short distances. Tactile communication is often very important in building and maintaining relationship among social animals as it can establish hierarchies. Snakes (Serpentes) engage in tactile communication to compete for dominance. This communication is often referred to as a combat ritual.
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It involves interaction sequences between two male snakes and has been recorded in four groups of snakes including colubrids, elapids, viperines and crotalines. During competition, the male snakes will exert pressures through pushing, flipping or entwining, which will result in one physically subduing the other. The dominant male will then proceed to copulate with the females.
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Electric signalling is a mode of communication often used by aquatic animals living in murky water. Electric signalling can minimize fighting costs and allow dominance to be exerted in low visibility conditions. In Electric Fish (Sternarchorhynchus), the frequency of electric organ discharge signals the dominance status of individuals.
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Dominance signals, like other animal behaviours, have internal underlying mechanisms that allow for the external display to occur. Underlying mechanisms may include hormones, sensory organs, cognitive maps, spatial memory, associative learning, brain structure, mental representations and neural morphology. Dominance signalling in animals is often a result of hormone changes. Hormones can work in either positive feedback loops or negative feedback loops and can alter the phenotypes of behaviour.
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In Australasian swamphen (Porphyrio porphyrio melanotus), for example, badge display is an indicator of dominance. It has been found that altering a bird's badge can actually change androgen circulation and can cause feedback effects on the individuals physiology. In a field study by Cody Dey, researchers found that birds which had the apparent size of their frontal shield decreased, received more aggression and also decreased their true shield relative to individuals who did not have their apparent shield size altered.
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Dominance signals used during courtship are driven by interactions between a male's fitness and a female's preference. Dominance signals influence a female's choice of mate because the power of a signal may be a reflection of the male's genetic success.
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Dominance signals are elicited in wild turkeys during courtship. Wild turkeys fundamentally follow a dominant hierarchy as a way to increase their inclusive fitness. The dominant subordinate relationship occurs between two brothers. One brother, the dominant, copulates while the other male, the subordinate, helps.After birth, the physical appearance of the male turkeys is used to indicate dominance. Physical characters such as height, bulk, and density are evaluated.
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Electric fish express dominance signals during courtship by exerting electric organ discharge "chirps". The "chirps" are an indicator of a male's aggressiveness and size. The more "chirps" a male electric fish produces, increases his likelihood of reproductive success. Continual bouts of chirping can last hours on evenings prior to courting.
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The electric chirps stimulate females to spawn. The chirp involves a slight increase in frequency followed by a cessation of the male dominant frequency. Chirps are normally short and abrupt during aggressive encounters when courting females, however, become softer during actual copulation.
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Social dominance is formed through dominance hierarchies. Such hierarchies arise when a member of social group elicits a dominance signal to initiate competitive interaction.
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Gorilla's chest-drumming is a signal used to demonstrate social dominance. This non-verbal, rapid chest-drumming creates a sound because gorillas have air sacks on both sides of their throat. The drumming is often accompanied by screaming and non-specified sounds.
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This signal is used as a warning signal to young gorilla to back-down if they are trying to join their tribe. This signal will only cease if the young male backs-down or if they engage in battle. The young males are not challenging the dominant for courtship behaviour alone, but rather are trying for group-wide control.
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Chest-drumming is also used a sign of victory after a battle and demonstrates who is the male dominant. As gorillas are male dominant, females do not produce these dominance signals. Silverback gorillas also use chest-drumming to command their family to follow them, reinforcing familial dominance.Dominance signals that reinforce hierarchy are crucial for survival for animals like gorillas who are extremely aggressive. A Gorilla's chest drumming, for example, reduces intra-species aggression by making the dominant-subordinate relationship clear. For social animals like gorillas, having and maintaining a dominant male is crucial to maintain their way of life.
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Dominance signals are often elicited over competition for territory. Dominance over a territory can be highly beneficial as it would provide abundant recourse. However, the cost of holding a territory can also be quite high. Dominance signals allow signalers to convey the dominant-subordinate relationship to a receiver avoiding physical contact.
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Dominance signals used by Atlantic Salmon allow for territory to be defended. When an Atlantic salmon is challenged by another salmon for territory and resources, a physical change in colour display occurs. When a subordinate male enters the territory of a dominant male, it will become darker after assessment of the dominant male, while the dominant male remains his original colour. This change in colour has been recorded in the sclera of the eye and the overall body coloration. The darkening is a sign of submission and is beneficial for both males as it minimizes the risk of potential injury during prolonged fights.
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Dominance signals are typically associated with ethology. However, humans display such signals as it is an innate characteristic. Fundamentally, all social species must have expressions of dominance and engage in hierarchy systems to function. Men exhibiting greater dominance signals often have higher success mating with women.
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Human voice pitch is one of the most prevalent dominance signal and has evolutionary ties to non-human primates. Physically, men's vocal folds and vocal tracts are longer than those of women, which produces a lower fundamental frequency and closer spacing of formant frequencies in men. These differences are not fully clear from an evolutionary perspective; However, it has been suggested that voice pitch is linked to male dominance competition.
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Current research on male voice pitch suggests that lower pitch is perceived as increasing dominance. Lower pitch voices also tend to be indicators of physical and social dominance. Other vocalization signals include loud rapid speaking tempo and clear articulation. Empirical evidence shows that women perceive deep-voiced men to be more dominant and desirable for mating.
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Physical size is one of the most prevalent dominance signals a human can elicit. Height, weight, bulk, and muscularity send signals of strength and can hold power over subordinate males. Other non-verbal signals that are perceived as signs of dominance are rapid gait, straight postures, firm and strong stances, animated gesturing, and clothing or hair styles that create a bulkier appearance. Women generally view men who display great muscularity and strength to be more attractive. When observing the male wrestling competitions of the indigenous Mehinaku tribe of the Amazon rainforest, anthropologist Thomas Gregor noted that males who are "heavily muscled" and "imposingly built" have higher mating access to females, while small men, who are derogatorily referred to as peristsi, "fare badly". He reports that powerful male wrestlers are both frightening to villagers and the most sexually desirable to females.
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Facial expression is used as a dominance signal in humans. Derived from our primate ancestors, faces of mature members have broader faces with a more defined jaw, smaller ratio of eye size to face size and larger noses. Younger members are perceived as having baby-faced features which includes rounder, softer faces, larger eyes when compared to face ratio, and smaller noses. These facial features can be used as dominance signals as baby-faced individuals are perceived as weak and submissive compared to mature faces which can indicate physical and social dominance. In a study where women viewed mixed-martial arts fights, male winners whose faces indicated victory and dominance were perceived to be more attractive, stronger, aggressive, and masculine compared to the male losers.
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More subtle dominance signals have also been suggested such as head nods, less arm wrap, increasing gestures, and more left leg lean. These subtle differences are associated with perception of dominance among males. Little research has been conducted regarding how or if, women elicit subtle dominance signals to express dominance. == References ==
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https://en.wikipedia.org/wiki/Dominance_signal
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In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable. This sort of function usually comes in linear regression, where the coefficients are called regression coefficients. However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis), as well as in various other models, such as principal component analysis and factor analysis. In many of these models, the coefficients are referred to as "weights".
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https://en.wikipedia.org/wiki/Linear_predictor_function
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The basic form of a linear predictor function f ( i ) {\displaystyle f(i)} for data point i (consisting of p explanatory variables), for i = 1, ..., n, is f ( i ) = β 0 + β 1 x i 1 + ⋯ + β p x i p , {\displaystyle f(i)=\beta _{0}+\beta _{1}x_{i1}+\cdots +\beta _{p}x_{ip},} where x i k {\displaystyle x_{ik}} , for k = 1, ..., p, is the value of the k-th explanatory variable for data point i, and β 0 , … , β p {\displaystyle \beta _{0},\ldots ,\beta _{p}} are the coefficients (regression coefficients, weights, etc.) indicating the relative effect of a particular explanatory variable on the outcome.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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It is common to write the predictor function in a more compact form as follows: The coefficients β0, β1, ..., βp are grouped into a single vector β of size p + 1. For each data point i, an additional explanatory pseudo-variable xi0 is added, with a fixed value of 1, corresponding to the intercept coefficient β0. The resulting explanatory variables xi0(= 1), xi1, ..., xip are then grouped into a single vector xi of size p + 1.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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This makes it possible to write the linear predictor function as follows: f ( i ) = β ⋅ x i {\displaystyle f(i)={\boldsymbol {\beta }}\cdot \mathbf {x} _{i}} using the notation for a dot product between two vectors.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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An equivalent form using matrix notation is as follows: f ( i ) = β T x i = x i T β {\displaystyle f(i)={\boldsymbol {\beta }}^{\mathrm {T} }\mathbf {x} _{i}=\mathbf {x} _{i}^{\mathrm {T} }{\boldsymbol {\beta }}} where β {\displaystyle {\boldsymbol {\beta }}} and x i {\displaystyle \mathbf {x} _{i}} are assumed to be a (p+1)-by-1 column vectors, β T {\displaystyle {\boldsymbol {\beta }}^{\mathrm {T} }} is the matrix transpose of β {\displaystyle {\boldsymbol {\beta }}} (so β T {\displaystyle {\boldsymbol {\beta }}^{\mathrm {T} }} is a 1-by-(p+1) row vector), and β T x i {\displaystyle {\boldsymbol {\beta }}^{\mathrm {T} }\mathbf {x} _{i}} indicates matrix multiplication between the 1-by-(p+1) row vector and the (p+1)-by-1 column vector, producing a 1-by-1 matrix that is taken to be a scalar.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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An example of the usage of a linear predictor function is in linear regression, where each data point is associated with a continuous outcome yi, and the relationship written y i = f ( i ) + ε i = β T x i + ε i , {\displaystyle y_{i}=f(i)+\varepsilon _{i}={\boldsymbol {\beta }}^{\mathrm {T} }\mathbf {x} _{i}\ +\varepsilon _{i},} where ε i {\displaystyle \varepsilon _{i}} is a disturbance term or error variable — an unobserved random variable that adds noise to the linear relationship between the dependent variable and predictor function.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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In some models (standard linear regression, in particular), the equations for each of the data points i = 1, ..., n are stacked together and written in vector form as y = X β + ε , {\displaystyle \mathbf {y} =\mathbf {X} {\boldsymbol {\beta }}+{\boldsymbol {\varepsilon }},\,} where y = ( y 1 y 2 ⋮ y n ) , X = ( x 1 ′ x 2 ′ ⋮ x n ′ ) = ( x 11 ⋯ x 1 p x 21 ⋯ x 2 p ⋮ ⋱ ⋮ x n 1 ⋯ x n p ) , β = ( β 1 ⋮ β p ) , ε = ( ε 1 ε 2 ⋮ ε n ) . {\displaystyle \mathbf {y} ={\begin{pmatrix}y_{1}\\y_{2}\\\vdots \\y_{n}\end{pmatrix}},\quad \mathbf {X} ={\begin{pmatrix}\mathbf {x} '_{1}\\\mathbf {x} '_{2}\\\vdots \\\mathbf {x} '_{n}\end{pmatrix}}={\begin{pmatrix}x_{11}&\cdots &x_{1p}\\x_{21}&\cdots &x_{2p}\\\vdots &\ddots &\vdots \\x_{n1}&\cdots &x_{np}\end{pmatrix}},\quad {\boldsymbol {\beta }}={\begin{pmatrix}\beta _{1}\\\vdots \\\beta _{p}\end{pmatrix}},\quad {\boldsymbol {\varepsilon }}={\begin{pmatrix}\varepsilon _{1}\\\varepsilon _{2}\\\vdots \\\varepsilon _{n}\end{pmatrix}}.} The matrix X is known as the design matrix and encodes all known information about the independent variables.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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The variables ε i {\displaystyle \varepsilon _{i}} are random variables, which in standard linear regression are distributed according to a standard normal distribution; they express the influence of any unknown factors on the outcome. This makes it possible to find optimal coefficients through the method of least squares using simple matrix operations. In particular, the optimal coefficients β ^ {\displaystyle {\boldsymbol {\hat {\beta }}}} as estimated by least squares can be written as follows: β ^ = ( X T X ) − 1 X T y .
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https://en.wikipedia.org/wiki/Linear_predictor_function
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{\displaystyle {\boldsymbol {\hat {\beta }}}=(X^{\mathrm {T} }X)^{-1}X^{\mathrm {T} }\mathbf {y} .} The matrix ( X T X ) − 1 X T {\displaystyle (X^{\mathrm {T} }X)^{-1}X^{\mathrm {T} }} is known as the Moore–Penrose pseudoinverse of X. The use of the matrix inverse in this formula requires that X is of full rank, i.e. there is not perfect multicollinearity among different explanatory variables (i.e. no explanatory variable can be perfectly predicted from the others). In such cases, the singular value decomposition can be used to compute the pseudoinverse.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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Although the outcomes (dependent variables) to be predicted are assumed to be random variables, the explanatory variables themselves are usually not assumed to be random. Instead, they are assumed to be fixed values, and any random variables (e.g. the outcomes) are assumed to be conditional on them. As a result, the data analyst is free to transform the explanatory variables in arbitrary ways, including creating multiple copies of a given explanatory variable, each transformed using a different function. Other common techniques are to create new explanatory variables in the form of interaction variables by taking products of two (or sometimes more) existing explanatory variables.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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When a fixed set of nonlinear functions are used to transform the value(s) of a data point, these functions are known as basis functions. An example is polynomial regression, which uses a linear predictor function to fit an arbitrary degree polynomial relationship (up to a given order) between two sets of data points (i.e. a single real-valued explanatory variable and a related real-valued dependent variable), by adding multiple explanatory variables corresponding to various powers of the existing explanatory variable.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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Mathematically, the form looks like this: y i = β 0 + β 1 x i + β 2 x i 2 + ⋯ + β p x i p . {\displaystyle y_{i}=\beta _{0}+\beta _{1}x_{i}+\beta _{2}x_{i}^{2}+\cdots +\beta _{p}x_{i}^{p}.}
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https://en.wikipedia.org/wiki/Linear_predictor_function
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In this case, for each data point i, a set of explanatory variables is created as follows: ( x i 1 = x i , x i 2 = x i 2 , … , x i p = x i p ) {\displaystyle (x_{i1}=x_{i},\quad x_{i2}=x_{i}^{2},\quad \ldots ,\quad x_{ip}=x_{i}^{p})} and then standard linear regression is run. The basis functions in this example would be ϕ ( x ) = ( ϕ 1 ( x ) , ϕ 2 ( x ) , … , ϕ p ( x ) ) = ( x , x 2 , … , x p ) . {\displaystyle {\boldsymbol {\phi }}(x)=(\phi _{1}(x),\phi _{2}(x),\ldots ,\phi _{p}(x))=(x,x^{2},\ldots ,x^{p}).}
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https://en.wikipedia.org/wiki/Linear_predictor_function
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This example shows that a linear predictor function can actually be much more powerful than it first appears: It only really needs to be linear in the coefficients. All sorts of non-linear functions of the explanatory variables can be fit by the model. There is no particular need for the inputs to basis functions to be univariate or single-dimensional (or their outputs, for that matter, although in such a case, a K-dimensional output value is likely to be treated as K separate scalar-output basis functions).
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https://en.wikipedia.org/wiki/Linear_predictor_function
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An example of this is radial basis functions (RBF's), which compute some transformed version of the distance to some fixed point: ϕ ( x ; c ) = ϕ ( | | x − c | | ) = ϕ ( ( x 1 − c 1 ) 2 + … + ( x K − c K ) 2 ) {\displaystyle \phi (\mathbf {x} ;\mathbf {c} )=\phi (||\mathbf {x} -\mathbf {c} ||)=\phi ({\sqrt {(x_{1}-c_{1})^{2}+\ldots +(x_{K}-c_{K})^{2}}})} An example is the Gaussian RBF, which has the same functional form as the normal distribution: ϕ ( x ; c ) = e − b | | x − c | | 2 {\displaystyle \phi (\mathbf {x} ;\mathbf {c} )=e^{-b||\mathbf {x} -\mathbf {c} ||^{2}}} which drops off rapidly as the distance from c increases. A possible usage of RBF's is to create one for every observed data point. This means that the result of an RBF applied to a new data point will be close to 0 unless the new point is near to the point around which the RBF was applied.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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That is, the application of the radial basis functions will pick out the nearest point, and its regression coefficient will dominate. The result will be a form of nearest neighbor interpolation, where predictions are made by simply using the prediction of the nearest observed data point, possibly interpolating between multiple nearby data points when they are all similar distances away. This type of nearest neighbor method for prediction is often considered diametrically opposed to the type of prediction used in standard linear regression: But in fact, the transformations that can be applied to the explanatory variables in a linear predictor function are so powerful that even the nearest neighbor method can be implemented as a type of linear regression.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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It is even possible to fit some functions that appear non-linear in the coefficients by transforming the coefficients into new coefficients that do appear linear. For example, a function of the form a + b 2 x i 1 + c x i 2 {\displaystyle a+b^{2}x_{i1}+{\sqrt {c}}x_{i2}} for coefficients a , b , c {\displaystyle a,b,c} could be transformed into the appropriate linear function by applying the substitutions b ′ = b 2 , c ′ = c , {\displaystyle b'=b^{2},c'={\sqrt {c}},} leading to a + b ′ x i 1 + c ′ x i 2 , {\displaystyle a+b'x_{i1}+c'x_{i2},} which is linear. Linear regression and similar techniques could be applied and will often still find the optimal coefficients, but their error estimates and such will be wrong.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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The explanatory variables may be of any type: real-valued, binary, categorical, etc. The main distinction is between continuous variables (e.g. income, age, blood pressure, etc.) and discrete variables (e.g. sex, race, political party, etc.). Discrete variables referring to more than two possible choices are typically coded using dummy variables (or indicator variables), i.e. separate explanatory variables taking the value 0 or 1 are created for each possible value of the discrete variable, with a 1 meaning "variable does have the given value" and a 0 meaning "variable does not have the given value". For example, a four-way discrete variable of blood type with the possible values "A, B, AB, O" would be converted to separate two-way dummy variables, "is-A, is-B, is-AB, is-O", where only one of them has the value 1 and all the rest have the value 0.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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This allows for separate regression coefficients to be matched for each possible value of the discrete variable. Note that, for K categories, not all K dummy variables are independent of each other. For example, in the above blood type example, only three of the four dummy variables are independent, in the sense that once the values of three of the variables are known, the fourth is automatically determined.
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https://en.wikipedia.org/wiki/Linear_predictor_function
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Thus, it's really only necessary to encode three of the four possibilities as dummy variables, and in fact if all four possibilities are encoded, the overall model becomes non-identifiable. This causes problems for a number of methods, such as the simple closed-form solution used in linear regression. The solution is either to avoid such cases by eliminating one of the dummy variables, and/or introduce a regularization constraint (which necessitates a more powerful, typically iterative, method for finding the optimal coefficients).
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https://en.wikipedia.org/wiki/Linear_predictor_function
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Zeppelin University (German: Zeppelin Universität, ZU) is a small and highly selective private research university on the shores of Lake Constance in Friedrichshafen, Germany. The university is accredited by the Ministry of Science, Research and the Arts of Baden-Württemberg. The university was established in 2003 and is known for its avant-garde character as well as for its sophisticated method of selecting students. It is named after the German general and airship constructor Ferdinand Graf von Zeppelin, whose foundation is a prominent financier of the university.
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https://en.wikipedia.org/wiki/Zeppelin_University
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Zeppelin University has two campuses in Friedrichshafen: the Lake Campus at the shores of Lake Constance, and the nearby ZF Campus, which was completed in 2015. The ZF Campus was funded by a donation of 20 million Euro from ZF Friedrichshafen. Both campuses are modern, designed by well-known architects, and contain classrooms, lecture halls, offices, cafeterias, a library, a fitness studio and a co-working wing for students. In 2018 the ZF Campus was named one of four new exceptional constructions in Germany by the German Architecture Museum. The university was also awarded with the "Deutscher Hochschulbaupreis 2018" by the Deutsche Universitätsstiftung.
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https://en.wikipedia.org/wiki/Zeppelin_University
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Zeppelin University is a small and exclusive private university and offers fewer programs than traditional universities in Germany. Because it is relatively new and small, it typically goes unranked in international comparisons. In the most reputable German ranking, the CHE, the Zeppelin University achieved the best result of all German universities in the political science/social sciences for its teaching offerings and general study situation in 2021/22.In the previous year, the bachelor's and master's degree programs of the ZU in economics ranked first among all German universities in the CHE ranking, together with Johann Wolfgang Goethe University Frankfurt am Main. In the CHE Ranking 2018/2019, the Bachelor's and Master's programs of the ZU in Politics, Administration & International Relations were among the best-ranked in Germany.
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https://en.wikipedia.org/wiki/Zeppelin_University
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In the CHE Ranking 2017/2018, ZU was ranked among the top 3 German universities for the Bachelor's and Master's programs in Economics.In 2015/2016, the Center for Higher Education Development ranked Zeppelin University's Master's program in Political Science as the third-best among all German universities. In the CHE Ranking 2014/15, the ZU's bachelor's degree programs in Economics, Cultural and Communication Studies, and Political and Administrative Science occupied positions in the top group among German universities. The ranking particularly lauds the supervision ratio, study situation, subject selection, and students' intellectual freedom.In 2014/15 CHE Master's University Ranking, Zeppelin University's Master's program in Economics and Johannes Gutenberg University Mainz formed the top group among Germany's universities.In the Handelsblatt Karriere magazine, in edition 07/08 dated 27 April 2007, Zeppelin University appeared in a university ranking for the first time. Its economics program reached eighth place in the german-speaking area back then.
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https://en.wikipedia.org/wiki/Zeppelin_University
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The university offers 16 Bachelor's and Master's tracks, including executive Master's education. Students can graduate with the academic degree of Bachelor of Arts and a consecutive or non-consecutive Master of Arts or Master of Science. Zeppelin University only offers four years undergraduate study programs. One year is intended to be used as a "Humboldt year", a one-year research project at a partner university. To enable this, the university's academic calendar closely mirrors international academic calendars.
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https://en.wikipedia.org/wiki/Zeppelin_University
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Zeppelin University has partnerships with around 85 universities, some of which are: University of California, Berkeley Sciences Po Copenhagen Business School University of Twente Goldsmiths College Maastricht University
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https://en.wikipedia.org/wiki/Zeppelin_University
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Tuition for undergraduate programs in the nominal study period of four years cost between 36,720 to 42,000 euro. For postgraduate programs, the tuition costs between 13,320 and 23,160 euros for the two-year program. Students not in receipt of a scholarship are offered low-interest loans by Sparkasse Bodensee. More than two-thirds of students avail of such loans. Alternatively, students can apply for grants from ZU-Bildungsfonds.
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https://en.wikipedia.org/wiki/Zeppelin_University
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Applicants are selected by the university in a two-step selection process: after a detailed written application, in which the first round of selection is made, candidates are invited to an assessment day (Pioneers Wanted). Candidates go through several interviews with professors, students, alumni, and external reviewers. Written tests are also featured.
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https://en.wikipedia.org/wiki/Zeppelin_University
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Candidates have to complete a group project which is presented to the assessment committee.The university's selection procedure is considered sophisticated, and not just because its methods differ from those of other universities. It does not just use numerus clausus (which is widely used in Germany), but instead tries to find students who—beyond having the required academic qualifications— also fit the university's character. The university's undergraduate acceptance rate is lower than 10%, and its graduate acceptance rate is about 16%.
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https://en.wikipedia.org/wiki/Zeppelin_University
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There are some 59 student groups and projects, such as groups affiliated with political parties (LHG, Jusos, RCDS), a debating club (Soapbox), the Club of International Politics (CIP), a Model United Nations group (MUN), which also organizes LakeMun, entrepreneurial groups, a cultural club which also organizes a music festival at the university (SeeKult), a student medical service (ZUFA), a film group, several bands and many more – some of them are even known nationally (RockYourLife, for example). A student radio station Welle20 went on air in 2008. In the last few years new initiatives have emerged for example the "ZUtaten" career fair, or the student consulting group "Whyknot". There is also an ERASMUS group named "International Student Group" and the "Hochschulsport" club which organises several sport activities such as volleyball, cheerleading, lacrosse, rowing, etc.
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https://en.wikipedia.org/wiki/Zeppelin_University
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The Zeppelin University has various integrated interdisciplinary research institutes, which are partly funded by donations. These include the Leadership Excellence Institute Zeppelin (LEIZ), which is supported by the Karl Schlecht Stiftung, the Friedrichshafener Institut für Familienunternehmen (Institute for family business), the Forschungszentrum für Verbraucher, Markt und Politik (a research institute for consumers, markets and politics), and the European Center for Sustainability Research supported by Audi and Rolls-Royce Power Systems.
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https://en.wikipedia.org/wiki/Zeppelin_University
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A prime meridian is an arbitrary meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great circle. This great circle divides a spheroid, like Earth, into two hemispheres: the Eastern Hemisphere and the Western Hemisphere (for an east-west notational system). For Earth's prime meridian, various conventions have been used or advocated in different regions throughout history.
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https://en.wikipedia.org/wiki/Prime_meridian
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Earth's current international standard prime meridian is the IERS Reference Meridian. It is derived, but differs slightly, from the Greenwich Meridian, the previous standard. A prime meridian for a planetary body not tidally locked (or at least not in synchronous rotation) is entirely arbitrary, unlike an equator, which is determined by the axis of rotation.
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https://en.wikipedia.org/wiki/Prime_meridian
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However, for celestial objects that are tidally locked (more specifically, synchronous), their prime meridians are determined by the face always inward of the orbit (a planet facing its star, or a moon facing its planet), just as equators are determined by rotation. Longitudes for the Earth and Moon are measured from their prime meridian (at 0°) to 180° east and west. For all other Solar System bodies, longitude is measured from 0° (their prime meridian) to 360°. West longitudes are used if the rotation of the body is prograde (or 'direct', like Earth), meaning that its direction of rotation is the same as that of its orbit. East longitudes are used if the rotation is retrograde.
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https://en.wikipedia.org/wiki/Prime_meridian
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The notion of longitude for Greeks was developed by the Greek Eratosthenes (c. 276 – 195 BCE) in Alexandria, and Hipparchus (c. 190 – 120 BCE) in Rhodes, and applied to a large number of cities by the geographer Strabo (64/63 BCE – c.
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https://en.wikipedia.org/wiki/Prime_meridian
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24 CE). But it was Ptolemy (c. 90 – 168 CE) who first used a consistent meridian for a world map in his Geographia.
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https://en.wikipedia.org/wiki/Prime_meridian
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Ptolemy used as his basis the "Fortunate Isles", a group of islands in the Atlantic, which are usually associated with the Canary Islands (13° to 18°W), although his maps correspond more closely to the Cape Verde islands (22° to 25° W). The main point is to be comfortably west of the western tip of Africa (17.5° W) as negative numbers were not yet in use. His prime meridian corresponds to 18° 40' west of Winchester (about 20°W) today.
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https://en.wikipedia.org/wiki/Prime_meridian
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