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Barnes G-function-Taylor series expansion-By Taylor's theorem, and considering the logarithmic derivatives of the Barnes function, the following series expansion can be obtained: log log 2π−(z+(1+γ)z22)+∑k=2∞(−1)kζ(k)k+1zk+1.
It is valid for 0<z<1 . Here, ζ(x) is the Riemann Zeta function: ζ(s)=∑n=1∞1ns.
Exponentiat... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Multiplication formula-Like the gamma function, the G-function also has a multiplication formula: G(nz)=K(n)nn2z2/2−nz(2π)−n2−n2z∏i=0n−1∏j=0n−1G(z+i+jn) where K(n) is a constant given by: 12 12 12 ⋅(2π)(n−1)/2.
Here ζ′ is the derivative of the Riemann zeta function and A is the Glaisher–Kinkelin co... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Absolute value-It holds true that G(z¯)=G(z)¯ , thus |G(z)|2=G(z)G(z¯) . From this relation and by the above presented Weierstrass product form one can show that exp exp (−y2k).
This relation is valid for arbitrary x∈R∖{0,−1,−2,…} , and y∈R . If x=0 , then the below formula is valid instead: exp... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Asymptotic expansion-The logarithm of G(z + 1) has the following asymptotic expansion, as established by Barnes: log log log 12 log 12 log A)+∑k=1NB2k+24k(k+1)z2k+O(1z2N+2).
Here the Bk are the Bernoulli numbers and A is the Glaisher–Kinkelin constant. (Note that somewhat confusingly at the time of... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Relation to the Loggamma integral-The parametric Loggamma can be evaluated in terms of the Barnes G-function (Ref: this result is found in Adamchik below, but stated without proof): log log log log G(1+z) The proof is somewhat indirect, and involves first considering the logarithmic difference of the... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Relation to the Loggamma integral-Taking the logarithm of the Weierstrass product forms of the Barnes function and gamma function gives: log log log log log log log log (1+zk)+z22k−z}] A little simplification and re-ordering of terms gives the series expansion: log log log log log G(1+z) Finally, ta... | milkshake721/2.1M-wiki-STEM |
Energy shot-Energy shot-Energy shots are a specialized kind of energy drink that contain a dose of the stimulant caffeine in a small amount of liquid. Whereas most energy drinks are sold in cans or bottles, energy shots are usually sold in 50ml bottles. Energy shots can contain the same total amount of caffeine, vitami... | milkshake721/2.1M-wiki-STEM |
Energy shot-Ingredients-Similar to energy drinks, energy shots contain caffeine, vitamins, and herbs such as guarana, ginseng or ginkgo biloba, taurine, maltodextrin, inositol, carnitine, creatine or glucuronolactone. Some energy shots contain sugar; however, many brands also offer artificially-sweetened 'diet' version... | milkshake721/2.1M-wiki-STEM |
Energy shot-Ingredients-The average 50ml energy shot has about 80 mg of caffeine. This is approximately equivalent to a cup of coffee. | milkshake721/2.1M-wiki-STEM |
Energy shot-Effects-The functional ingredients of energy shots are comparable to those of energy drinks, and their effects on improvement in mental and cognitive performances and subjective alertness are in line with the effects of traditional energy drinks. Vitamin based energy shots have variable benefits dependent o... | milkshake721/2.1M-wiki-STEM |
Energy shot-History-The idea of energy shots started decades ago in Japan, where small “tonics” became very popular among consumers, served highly concentrated and without carbonation. With the introduction of energy drinks as of the late 1980s, the efficacy of these energy shots started to travel the world as a new pr... | milkshake721/2.1M-wiki-STEM |
Energy shot-Products-As of June 2009, there were approximately 250 energy shot brands in the US. 5-Hour Energy owned 90% of the market share in 2011, according to research firm of Symphony IRI.Some of the manufacturers of energy shots also market energy drinks, however, crossover success has not been common for the lar... | milkshake721/2.1M-wiki-STEM |
Rigid bus-Rigid bus-A rigid bus (either a motor bus or trolleybus) is a vehicle used in public transportation services with a single, rigid chassis. A bus of this type is to be contrasted with an articulated or bi-articulated bus, which will have two or more rigid sections linked by a pivoting joint, also with a traile... | milkshake721/2.1M-wiki-STEM |
Rigid bus-Rigid bus-The term "rigid bus" is used mainly in British English and Australian English and usually only when distinguishing such buses from articulated buses, such as describing a fleet that includes both types. In the case of two-axle buses, which must be single-chassis, rigid vehicles, British English ofte... | milkshake721/2.1M-wiki-STEM |
Rigid bus-Rigid bus-The term "rigid bus" is not used in American English, where the distinction is commonly made using the term "non-articulated" bus or, when the context is clear, "standard bus". However, the term "standard bus" can be confusing, because it is sometimes used, in other English-speaking countries, refer... | milkshake721/2.1M-wiki-STEM |
Rigid bus-Rigid bus-Single-decker rigid buses are used mainly on bus lines with an average ridership (for example, as transit buses or regional buses on routes with normal levels of patronage), or as coaches. | milkshake721/2.1M-wiki-STEM |
Tisotumab vedotin-Tisotumab vedotin-Tisotumab vedotin, sold under the brand name Tivdak, is an antibody-drug conjugate used to treat cervical cancer. It is a combination of tisotumab, a monoclonal antibody against tissue factor, and monomethyl auristatin E (MMAE), a potent inhibitor of cell division. It is administered... | milkshake721/2.1M-wiki-STEM |
Tisotumab vedotin-Adverse effects-In the United States, Tivdak carries a black box warning for ocular toxicity, which occurs in up to 60% of treated patients. In clinical trials, the most common forms of ocular toxicity were dry eye, conjunctivitis, corneal damage, and blepharitis.Other common adverse effects include b... | milkshake721/2.1M-wiki-STEM |
Tisotumab vedotin-Mechanism of action-The antibody portion of tisotumab vedotin (tisotumab) binds to and forms a complex with tissue factor, a molecule expressed on the surface of cancer cells. This complex is then taken up into the cell, where tisotumab vedotin is broken down by proteolytic cleavage, releasing MMAE, w... | milkshake721/2.1M-wiki-STEM |
Tisotumab vedotin-History-Tisotumab vedotin was developed by Genmab in Utrecht, the Netherlands, and Copenhagen, Denmark, with the code name TF-011-MMAE. In September 2021, tisotumab vedotin was granted accelerated approval by United States Food and Drug Administration for the use of recurrent or metastatic cervical ca... | milkshake721/2.1M-wiki-STEM |
Tisotumab vedotin-Society and culture-Names Tisotumab vedotin is the international nonproprietary name. Tivdak is the brand name for tisotumab vedotin in the United States. | milkshake721/2.1M-wiki-STEM |
Bell triangle-Bell triangle-In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element is the largest singleton. It is named for its close connection to the Bell numbers, which may be found on both sides of the triangle, and... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Values-Different sources give the same triangle in different orientations, some flipped from each other. In a format similar to that of Pascal's triangle, and in the order listed in the Online Encyclopedia of Integer Sequences, its first few rows are: 1 1 2 2 3 5 5 7 10 15 15 20 27 37 52 52 67 87 114 151 ... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Construction-The Bell triangle may be constructed by placing the number 1 in its first position. After that placement, the leftmost value in each row of the triangle is filled by copying the rightmost value in the previous row. The remaining positions in each row are filled by a rule very similar to that ... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Construction-Thus, after the initial placement of the number 1 in the top row, it is the last position in its row and is copied to the leftmost position in the next row. The third value in the triangle, 2, is the sum of the two previous values above-left and left of it. As the last value in its row, the 2... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Combinatorial interpretation-The Bell numbers themselves, on the left and right sides of the triangle, count the number of ways of partitioning a finite set into subsets, or equivalently the number of equivalence relations on the set. | milkshake721/2.1M-wiki-STEM |
Bell triangle-Combinatorial interpretation-Sun & Wu (2011) provide the following combinatorial interpretation of each value in the triangle. Following Sun and Wu, let An,k denote the value that is k positions from the left in the nth row of the triangle, with the top of the triangle numbered as A1,1. Then An,k counts t... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Combinatorial interpretation-For instance, the number 3 in the middle of the third row of the triangle would be labeled, in their notation, as A3,2, and counts the number of partitions of {1, 2, 3, 4} in which 3 is the largest singleton element. There are three such partitions: {1}, {2, 4}, {3} {1, 4}, {2... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Combinatorial interpretation-In the same notation, Sun & Wu (2011) augment the triangle with another diagonal to the left of its other values, of the numbers An,0 = 1, 0, 1, 1, 4, 11, 41, 162, ...(sequence A000296 in the OEIS)counting partitions of the same set of n + 1 items in which only the first item ... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Combinatorial interpretation-An alternative but more technical interpretation of the numbers in the same augmented triangle is given by Quaintance & Kwong (2013). | milkshake721/2.1M-wiki-STEM |
Bell triangle-Diagonals and row sums-The leftmost and rightmost diagonals of the Bell triangle both contain the sequence 1, 1, 2, 5, 15, 52, ... of the Bell numbers (with the initial element missing in the case of the rightmost diagonal). The next diagonal parallel to the rightmost diagonal gives the sequence of differ... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Diagonals and row sums-In this way, as Aitken (1933) observed, this triangle can be interpreted as implementing the Gregory–Newton interpolation formula, which finds the coefficients of a polynomial from the sequence of its values at consecutive integers by using successive differences. This formula close... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Diagonals and row sums-The sums of each row of the triangle, 1, 3, 10, 37, ..., are the same sequence of first differences appearing in the second-from-right diagonal of the triangle. The nth number in this sequence also counts the number of partitions of n elements into subsets, where one of the subsets ... | milkshake721/2.1M-wiki-STEM |
Bell triangle-Related constructions-A different triangle of numbers, with the Bell numbers on only one side, and with each number determined as a weighted sum of nearby numbers in the previous row, was described by Aigner (1999). | milkshake721/2.1M-wiki-STEM |
Faith deconstruction-Faith deconstruction-Faith deconstruction, also known as deconstructing faith, evangelical deconstruction, the deconstruction movement, or simply deconstruction, is a phenomenon within American evangelicalism in which Christians rethink their faith and jettison previously held beliefs, sometimes to... | milkshake721/2.1M-wiki-STEM |
Faith deconstruction-Description-The term can have a range of meanings. Alisa Childers defines deconstruction as "the process of systematically dissecting and often rejecting the beliefs you grew up with." Tyler Huckabee, writing for Relevant magazine, defines it as "a process of re-examining the faith you grew up with... | milkshake721/2.1M-wiki-STEM |
Faith deconstruction-Responses-After preaching a sermon in which he equated deconstruction with leaving the faith, Matt Chandler clarified that it "doesn’t mean doubt or theological wrestle or struggling through church hurt." John Cooper has stated, "It is time that we declare war against this deconstruction Christian ... | milkshake721/2.1M-wiki-STEM |
Laughter-Laughter-Laughter is a pleasant physical reaction and emotion consisting usually of rhythmical, often audible contractions of the diaphragm and other parts of the respiratory system. It is a response to certain external or internal stimuli. Laughter can rise from such activities as being tickled, or from humor... | milkshake721/2.1M-wiki-STEM |
Laughter-Laughter-Laughter is a part of human behavior regulated by the brain, helping humans clarify their intentions in social interaction and providing an emotional context to conversations. Laughter is used as a signal for being part of a group—it signals acceptance and positive interactions with others. Laughter i... | milkshake721/2.1M-wiki-STEM |
Laughter-Nature-Laughter might be thought of as an audible expression or appearance of excitement, an inward feeling of joy and happiness. It may ensue from jokes, tickling, and other stimuli completely unrelated to psychological state, such as nitrous oxide. One group of researchers speculated that noises from infants... | milkshake721/2.1M-wiki-STEM |
Laughter-Nature-Laughter researcher Robert Provine said: "Laughter is a mechanism everyone has; laughter is part of universal human vocabulary. There are thousands of languages, hundreds of thousands of dialects, but everyone speaks laughter in pretty much the same way." Babies have the ability to laugh before they eve... | milkshake721/2.1M-wiki-STEM |
Laughter-Nature-A very rare neurological condition has been observed whereby the sufferer is unable to laugh out loud, a condition known as aphonogelia. | milkshake721/2.1M-wiki-STEM |
Laughter-Brain-Neurophysiology indicates that laughter is linked with the activation of the ventromedial prefrontal cortex, that produces endorphins. Scientists have shown that parts of the limbic system are involved in laughter. This system is involved in emotions and helps us with functions necessary for humans' surv... | milkshake721/2.1M-wiki-STEM |
Laughter-Health-A link between laughter and healthy function of blood vessels was first reported in 2005 by researchers at the University of Maryland Medical Center with the fact that laughter causes the dilatation of the inner lining of blood vessels, the endothelium, and increases blood flow. Drs. Michael Miller (Uni... | milkshake721/2.1M-wiki-STEM |
Laughter-Communication-A number of studies using methods of conversation analysis and discourse analysis have documented the systematic workings of laughter in a variety of interactions, from casual conversations to interviews, meetings, and therapy sessions. Working with recorded interactions, researchers have created... | milkshake721/2.1M-wiki-STEM |
Laughter-Communication-These studies challenge several widely held assumptions about the nature of laughter. Contrary to notions that it is spontaneous and involuntary, research documents that laughter is sequentially organized and precisely placed relative to surrounding talk. Far more than merely a response to humor,... | milkshake721/2.1M-wiki-STEM |
Laughter-Causes-Common causes for laughter are sensations of joy and humor; however, other situations may cause laughter as well. | milkshake721/2.1M-wiki-STEM |
Laughter-Causes-A general theory that explains laughter is called the relief theory. Sigmund Freud summarized it in his theory that laughter releases tension and "psychic energy". This theory is one of the justifications of the beliefs that laughter is beneficial for one's health. This theory explains why laughter can ... | milkshake721/2.1M-wiki-STEM |
Laughter-Causes-Philosopher John Morreall theorizes that human laughter may have its biological origins as a kind of shared expression of relief at the passing of danger. Friedrich Nietzsche, by contrast, suggested laughter to be a reaction to the sense of existential loneliness and mortality that only humans feel. | milkshake721/2.1M-wiki-STEM |
Laughter-Causes-For example: a joke creates an inconsistency and the audience automatically tries to understand what the inconsistency means; if they are successful in solving this 'cognitive riddle' and they realize that the surprise was not dangerous, they laugh with relief. Otherwise, if the inconsistency is not res... | milkshake721/2.1M-wiki-STEM |
Laughter-Causes-Laughter can also be brought on by tickling. Although most people find it unpleasant, being tickled often causes heavy laughter, thought to be an (often uncontrollable) reflex of the body. | milkshake721/2.1M-wiki-STEM |
Laughter-Structure and anatomy-A normal laugh has the structure of "ha-ha-ha" or "ho-ho-ho". It is unnatural, and one is physically unable, to have a laugh structure of "ha-ho-ha-ho". The usual variations of a laugh most often occur in the first or final note in a sequence- therefore, "ho-ha-ha" or "ha-ha-ho" laughs ar... | milkshake721/2.1M-wiki-STEM |
Laughter-Negative aspects-Laughter is not always a pleasant experience and is associated with several negative phenomena. Excessive laughter can lead to cataplexy, and unpleasant laughter spells, excessive elation, and fits of laughter can all be considered negative aspects of laughter. Unpleasant laughter spells, or "... | milkshake721/2.1M-wiki-STEM |
Laughter-Negative aspects-Excessive elation is a common symptom associated with bipolar disorder psychoses and mania/hypomania. Those with schizophrenic psychoses seem to experience the opposite—they do not understand humor or get any joy out of it. A fit describes an abnormal time when one cannot control the laughter ... | milkshake721/2.1M-wiki-STEM |
Laughter-Therapy-Laughter has been used as a therapeutic tool for many years because it is a natural form of medicine. Laughter is available to everyone and it provides benefits to a person's physical, emotional, and social well being. Some of the benefits of using laughter therapy are that it can relieve stress and re... | milkshake721/2.1M-wiki-STEM |
Laughter-Research and philosophy-Laughter in literature, although considered understudied by some, is a subject that has received attention in the written word for millennia. The use of humor and laughter in literary works has been studied and analyzed by many thinkers and writers, from the Ancient Greek philosophers o... | milkshake721/2.1M-wiki-STEM |
Laughter-Research and philosophy-Ancient Herodotus For Herodotus, laughers can be distinguished into three types: Those who are innocent of wrongdoing, but ignorant of their own vulnerability Those who are mad Those who are overconfidentAccording to Donald Lateiner, Herodotus reports about laughter for valid literary a... | milkshake721/2.1M-wiki-STEM |
Laughter-Research and philosophy-Hobbes Thomas Hobbes wrote, "The passion of laughter is nothing else but sudden glory arising from sudden conception of some eminency in ourselves, by comparison with the infirmity of others, or with our own formerly." Schopenhauer Philosopher Arthur Schopenhauer devotes the 13th chapte... | milkshake721/2.1M-wiki-STEM |
Laughter-Research and philosophy-Nietzsche Friedrich Nietzsche distinguishes two different purposes for the use of laughter. In a positive sense, "man uses the comical as a therapy against the restraining jacket of logic, morality and reason. He needs from time to time a harmless demotion from reason and hardship and i... | milkshake721/2.1M-wiki-STEM |
Laughter-Research and philosophy-Ludovici Anthony Ludovici developed the thoughts of Hobbes even further in The Secret of Laughter. His conviction is that there's something sinister in laughter, and that the modern omnipresence of humour and the idolatry of it are signs of societal weakness, as instinctive resort to hu... | milkshake721/2.1M-wiki-STEM |
Laughter-Research and philosophy-Bellieni Carlo Bellieni examined laughter in an essay published in New Ideas in Psychology. He wrote we can strip back laughter to a three-step process. First, it needs a situation that seems odd and induces a sense of incongruity (bewilderment or panic). Second, the worry or stress the... | milkshake721/2.1M-wiki-STEM |
Artisanal food-Artisanal food-Artisanal food encompasses breads, cheeses, fruit preserves, cured meats, beverages, oils, and vinegars that are made by hand using traditional methods by skilled craftworkers, known as food artisans. The foodstuff material from farmers and backyard growers can include fruit, grains and fl... | milkshake721/2.1M-wiki-STEM |
Artisanal food-Food artisans-Food artisans produce foods and edible foodstuffs that are not mass produced, but rather made by hand. These include cheeses, breads and baked goods, charcuterie and other foods that involve preservation or fermentation, home preservation or canning processes, and fruit preserves, cured mea... | milkshake721/2.1M-wiki-STEM |
Artisanal food-Legislation-In 2009, the Food Safety Enhancement Act was proposed and passed the House of Representatives, but did not pass. The measure was renegotiated and became known as the Food Safety Modernization Act (FSMA). On 4 January 2011, President Barack Obama signed the bill into law.
Tester-Hagan Amendmen... | milkshake721/2.1M-wiki-STEM |
Artisanal food-Controversy-As of 2016, there was not a published official standard or definition for artisan foods. A good working definition can be gleaned from the Tester-Hagen Amendment that stated artisanal food producers are constrained to: "make less than $500,000 a year and sell greater than 50% of their product... | milkshake721/2.1M-wiki-STEM |
Artisanal food-Points of distribution-Farmers' markets, either temporary or permanent, are a tremendous resource for consumers to procure artisanal foods. They exist in many communities in the United States, Canada, the United Kingdom, and throughout the European Union countries. | milkshake721/2.1M-wiki-STEM |
Minkowski content-Minkowski content-The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary meas... | milkshake721/2.1M-wiki-STEM |
Minkowski content-Minkowski content-It is related to, although different from, the Hausdorff measure. | milkshake721/2.1M-wiki-STEM |
Minkowski content-Definition-For A⊂Rn , and each integer m with 0≤m≤n , the m-dimensional upper Minkowski content is lim sup r→0+μ({x:d(x,A)<r})α(n−m)rn−m and the m-dimensional lower Minkowski content is defined as lim inf r→0+μ({x:d(x,A)<r})α(n−m)rn−m where α(n−m)rn−m is the volume of the (n−m)-ball of radius r and... | milkshake721/2.1M-wiki-STEM |
Minkowski content-Properties-The Minkowski content is (generally) not a measure. In particular, the m-dimensional Minkowski content in Rn is not a measure unless m = 0, in which case it is the counting measure. Indeed, clearly the Minkowski content assigns the same value to the set A as well as its closure.
If A is a c... | milkshake721/2.1M-wiki-STEM |
Orofaciodigital syndrome 1-Orofaciodigital syndrome 1-Orofaciodigital syndrome 1 (OFD1), also called Papillon-League and Psaume syndrome, is an X-linked congenital disorder characterized by malformations of the face, oral cavity, and digits with polycystic kidney disease and variable involvement of the central nervous ... | milkshake721/2.1M-wiki-STEM |
Orofaciodigital syndrome 1-Cause-Orofaciodigital syndrome type 1 is caused by mutations in the OFD1 gene. OFD1 localizes to both centrosomes and basal bodies within the human genetic cellular structure. This suggests that this syndrome may fall into a broad category of ciliary diseases. The ciliary organelles are prese... | milkshake721/2.1M-wiki-STEM |
Orofaciodigital syndrome 1-Diagnosis-Orofaciodigital syndrome type 1 is diagnosed through genetic testing. Some symptoms of Orofaciodigital syndrome type 1 are oral features such as, split tongue, benign tumors on the tongue, cleft palate, hypodontia and other dental abnormalities. Other symptoms of the face include hy... | milkshake721/2.1M-wiki-STEM |
Orofaciodigital syndrome 1-Management-Orofaciodigital syndrome type 1 can be treated with reconstructive surgery or the affected parts of the body. Surgery of cleft palate, tongue nodules, additional teeth, accessory frenulae, and orthodontia for malocclusion. Routine treatment for patients with renal disease and seizu... | milkshake721/2.1M-wiki-STEM |
CLDN22-CLDN22-Claudin-22 is a protein that in humans is encoded by the CLDN22 gene. It belongs to the group of claudins. | milkshake721/2.1M-wiki-STEM |
Thermal cycler-Thermal cycler-The thermal cycler (also known as a thermocycler, PCR machine or DNA amplifier) is a laboratory apparatus most commonly used to amplify segments of DNA via the polymerase chain reaction (PCR). Thermal cyclers may also be used in laboratories to facilitate other temperature-sensitive reacti... | milkshake721/2.1M-wiki-STEM |
Thermal cycler-History-The earliest thermal cyclers were designed for use with the Klenow fragment of DNA polymerase I. Since this enzyme is destroyed during each heating step of the amplification process, new enzyme had to be added every cycle. This led to a cumbersome machine based on an automated pipettor, with open... | milkshake721/2.1M-wiki-STEM |
Thermal cycler-Modern innovations-Modern thermal cyclers are equipped with a heated lid that presses against the lids of the reaction tubes. This prevents condensation of water from the reaction mixtures on the insides of the lids. Traditionally, a layer of mineral oil was used for this purpose. Some thermal cyclers ar... | milkshake721/2.1M-wiki-STEM |
Thermal cycler-Modern innovations-Some thermal cyclers are equipped with multiple blocks allowing several different PCRs to be carried out simultaneously. Some models also have a gradient function to allow for different temperatures in different parts of the block. This is particularly useful when testing suitable anne... | milkshake721/2.1M-wiki-STEM |
Correlation function-Correlation function-A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables representing the same quantity measur... | milkshake721/2.1M-wiki-STEM |
Correlation function-Correlation function-Correlation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for i... | milkshake721/2.1M-wiki-STEM |
Correlation function-Definition-For possibly distinct random variables X(s) and Y(t) at different points s and t of some space, the correlation function is corr (X(s),Y(t)), where corr is described in the article on correlation. In this definition, it has been assumed that the stochastic variables are scalar-valued. ... | milkshake721/2.1M-wiki-STEM |
Correlation function-Definition-When n=q, sometimes the trace of this matrix is focused on. If the probability distributions have any target space symmetries, i.e. symmetries in the value space of the stochastic variable (also called internal symmetries), then the correlation matrix will have induced symmetries. Simila... | milkshake721/2.1M-wiki-STEM |
Correlation function-Definition-If the random vector has only one component variable, then the indices i,j are redundant. If there are symmetries, then the correlation function can be broken up into irreducible representations of the symmetries — both internal and spacetime. | milkshake721/2.1M-wiki-STEM |
Correlation function-Properties of probability distributions-With these definitions, the study of correlation functions is similar to the study of probability distributions. Many stochastic processes can be completely characterized by their correlation functions; the most notable example is the class of Gaussian proces... | milkshake721/2.1M-wiki-STEM |
Correlation function-Properties of probability distributions-The Feynman path integral in Euclidean space generalizes this to other problems of interest to statistical mechanics. Any probability distribution which obeys a condition on correlation functions called reflection positivity leads to a local quantum field the... | milkshake721/2.1M-wiki-STEM |
4-Fluoropethidine-4-Fluoropethidine-4-Fluoropethidine is a drug that is a derivative of pethidine (meperidine), which combines pethidine's opioid analgesic effects with increased monoamine reuptake inhibition. It is around 50% less potent than pethidine as an opioid analgesic, but conversely is 50% more potent as a dop... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Stomach rumble-A stomach rumble, also known as a bowel sound, peristaltic sound, abdominal sound, bubble gut or borborygmus (pronounced ; plural borborygmi), is a rumbling, growling or gurgling noise produced by movement of the contents of the gastrointestinal tract as they are propelled through the smal... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Etymology-The scientific name borborygmus is related to the 16th-century French word borborygme, itself from Latin, ultimately from Ancient Greek βορβορυγμός (borborygmós). The Greek term is probably onomatopoetic in origin. | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Other causes-Other causes of stomach rumbles: Incomplete digestion of food can lead to excess gas in the intestine. In humans, this can be due to incomplete digestion of carbohydrate-containing foods, including milk and other dairy products (lactose intolerance or the use of α-glucosidase inhibitors by d... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Other causes-Louder rumbles may occur when one is hungry. The sound of air moving around the lumen of the stomach is amplified by the empty space. Around two hours after the stomach has been emptied, it sends signals to the brain, which tells the digestive muscles to restart peristalsis in a wave called ... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Other causes-Stomach rumbles can form further along the gastrointestinal system when air is swallowed while talking, eating, and drinking. This phenomenon occurs in most people and is typical. | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Diseases and conditions-Celiac disease is a condition that prevents the small intestine from absorbing parts of food that are needed to stay healthy. Consuming food containing gluten is dangerous for people with this disease: Intestinal villi help to absorb nutrients from food, but when gluten is consume... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Diseases and conditions-Colitis is swelling of the large intestine. The many different forms of colitis include cytomegalovirus or Cryptosporidium infection, and necrotizing and pseudomembranous colitis. The usual causes of colitis are infection and lack of blood flow. Symptoms may include bloody stools,... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Nonmedical usage-The word borborygmic has been used in literature to describe noisy plumbing. In Ada, Vladimir Nabokov wrote: "All the toilets and waterpipes in the house had been suddenly seized with borborygmic convulsions".
In A Long Way Down (New York: Harper, 1959, p. 54), Elizabeth Fenwick wrote: "... | milkshake721/2.1M-wiki-STEM |
Stomach rumble-Nonmedical usage-The word borborygmus has also been used in journalism to describe political turbulence. In an article in The Atlantic, Graeme Wood used the word to describe the effects of mass refugee migration into Europe: "Central Europe had to digest a massive refugee flow from Syria and Afghanistan,... | milkshake721/2.1M-wiki-STEM |
Slitherlink-Slitherlink-Slitherlink (also known as Fences, Takegaki, Loop the Loop, Loopy, Ouroboros, Suriza, Rundweg and Dotty Dilemma) is a logic puzzle developed by publisher Nikoli. | milkshake721/2.1M-wiki-STEM |
Slitherlink-Rules-Slitherlink is played on a rectangular lattice of dots. Some of the squares formed by the dots have numbers inside them. The objective is to connect horizontally and vertically adjacent dots so that the lines form a simple loop with no loose ends. In addition, the number inside a square represents how... | milkshake721/2.1M-wiki-STEM |
Slitherlink-Rules-Other types of planar graphs can be used in lieu of the standard grid, with varying numbers of edges per vertex or vertices per polygon. These patterns include snowflake, Penrose, Laves and Altair tilings. These add complexity by varying the number of possible paths from an intersection, and/or the nu... | milkshake721/2.1M-wiki-STEM |
Slitherlink-Solution methods-Notation Whenever the number of lines around a cell matches the number in the cell, the other potential lines must be eliminated. This is usually indicated by marking an X on lines known to be empty. | milkshake721/2.1M-wiki-STEM |
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