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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. Exponentiating both sides of the Taylor expansion gives: exp log exp exp ⁡[∑k=2∞(−1)kζ(k)k+1zk+1]. Comparing this with the Weierstrass product form of the Barnes function gives the following relation: exp exp ⁡(z22k−z)}
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 constant.
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 exp ⁡(−y2k) for arbitrary real y.
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at the time of Barnes the Bernoulli number B2k would have been written as (−1)k+1Bk , but this convention is no longer current.) This expansion is valid for z in any sector not containing the negative real axis with \|z\| large.
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 gamma function and Barnes G-function: log log ⁡G(1+z) where 1Γ(z)=zeγz∏k=1∞{(1+zk)e−z/k} and γ is the Euler–Mascheroni constant.
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, take the logarithm of the Weierstrass product form of the gamma function, and integrate over the interval [0,z] to obtain: log log log log ⁡(1+zk)−z22k−z} Equating the two evaluations completes the proof: log log log log ⁡G(1+z) And since G(1+z)=Γ(z)G(z) then, log log log log ⁡G(z).
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, vitamins or other functional ingredients as their larger versions, and may be considered concentrated forms of energy drinks. "Micro shot" energy drinks also exist, containing only 1–5 teaspoonfuls (5–25 mL) of liquid.
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' versions. Some decaf varieties are also offered. The central ingredient in most energy shots is caffeine, the same stimulant found in coffee or tea. Vitamin based energy shots contain numerous additional vitamins and supplements for sustenance, sustainment, and overall health. 5-Hour contains vitamin levels sometimes hundreds of times higher than the recommended RDA, according to a 2010 test by ConsumerLab.com. Some energy shots include electrolytes, and others include a selection of vitamins.
Energy shot	Ingredients	The average 50ml energy shot has about 80 mg of caffeine. This is approximately equivalent to a cup of coffee.
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 on the additional ingredients.
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 product format. In 2003, the founder of 5-Hour Energy discovered an energy drink at a natural products trade show and formulated a similar product reducing the content from 16 to 2 ounces but keeping the energizing effects. Daily Finance credits them with largely creating the energy shot market. By 2008, there were over 25 brands offering energy shots in the US alone. In 2009, major energy drink producer Red Bull launched an energy shot. By 2011, energy shots became so popular that 5-Hour Energy sold $1 billion of their product at retail.Although originally marketed in the US, energy shots are also becoming popular in other parts of the world, such as Europe, The products are aimed at customers who seek high efficacy with little liquid intake, and include truck drivers and students.
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 larger brands such as Monster and Rockstar. Red Bull, the leader of the energy drink category, launched an energy shot of its own in April 2009.
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 trailer bus, which is formed out of a bus bodied semi-trailer pulled by a conventional tractor unit.
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 often refers to such vehicles as "two-axle" buses, only using the term "rigid" when referring to vehicles with three or more axles, which can be either rigid or articulated.
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, referring to a uniform bus design developed for and by a number of European bus manufacturers, in two model generations, between the 1960s and the end of the 20th century. The German VöV-Standard-Bus includes the Mercedes-Benz O305 and the Mercedes-Benz O405 types, each of which, in both rigid and articulated forms, was widely acquired and used by bus operators in English-speaking countries outside North America.Rigid buses may be of either single-deck or double-deck design, and may have either two axles or multi-axles. However, the expression "rigid bus" is seldom used to describe a double-decker bus, because very few double-decker buses have anything other than a rigid chassis.
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.
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 by infusion into a vein.Tisotumab vedotin was approved for medical use in the United States in September 2021. The U.S. Food and Drug Administration considers it to be a first-in-class medication.
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 bleeding (occurring in approximately 60% of patients, most often nosebleed) and peripheral neuropathy (42% of patients). Like all drugs containing MMAE, tisotumab vedotin can cause inflammation of the lungs.
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, which stops the cell cycle and kills the cell by apoptosis.
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 cancer with disease progression on or after chemotherapy.
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.
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 which are in turn named after Eric Temple Bell. The Bell triangle has been discovered independently by multiple authors, beginning with Charles Sanders Peirce (1880) and including also Alexander Aitken (1933) and Cohn et al. (1962), and for that reason has also been called Aitken's array or the Peirce triangle.
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 87 114 151 203 203 255 322 409 523 674 877
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 for Pascal's triangle: they are the sum of the two values to the left and upper left of the position.
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 is copied into the third row, and the process continues in the same way.
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.
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 the number of partitions of the set {1, 2, ..., n + 1} in which the element k + 1 is the only element of its set and each higher-numbered element is in a set of more than one element. That is, k + 1 must be the largest singleton of the partition.
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}, {3} {1, 2, 4}, {3}.The remaining partitions of these four elements either do not have 3 in a set by itself, or they have a larger singleton set {4}, and in either case are not counted in A3,2.
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 is a singleton. Their augmented triangle is 1 0 1 1 1 2 1 2 3 5 4 5 7 10 15 11 15 20 27 37 52 41 52 67 87 114 151 203 162 203 255 322 409 523 674 877 This triangle may be constructed similarly to the original version of Bell's triangle, but with a different rule for starting each row: the leftmost value in each row is the difference of the rightmost and leftmost values of the previous row.
Bell triangle	Combinatorial interpretation	An alternative but more technical interpretation of the numbers in the same augmented triangle is given by Quaintance & Kwong (2013).
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 differences of two consecutive Bell numbers, 1, 3, 10, 37, ..., and each subsequent parallel diagonal gives the sequence of differences of previous diagonals.
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 closely resembles a recurrence relation that can be used to define the Bell numbers.
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 is distinguished from the others; for instance, there are 10 ways of partitioning three items into subsets and then choosing one of the subsets.
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).
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 the point of no longer identifying as Christians. It is closely related to the exvangelical movement.
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." John Stonestreet and Timothy Padgett note that it is used both descriptively (covering everything from the deconversion of Kevin Max, through the soul searching of Derek Webb, to the theological revisions of Jen Hatmaker and Rob Bell), or prescriptively ("recommended, especially to those questioning what they’ve grown up with, as a courageous thing to do").There is broad agreement that the term is derived from Jacques Derrida's philosophical concept of deconstruction. David Hayward says that he "co-opted the term" from Derrida, whose work he was reading at the time his beliefs started to erode.Notable advocates of faith deconstruction include internet comedy duo Rhett McLaughlin and Link Neal (who published multiple podcast episodes detailing their spiritual deconstruction), John D. Caputo (who in 2007 wrote What Would Jesus Deconstruct?: The Good News of Postmodernism for the Church), and Richard Rohr. Prominent former Christians who underwent deconstruction include Joshua Harris (who briefly offered a course on deconstruction), Abraham Piper, and Marty Sampson.As of February 2022 there were 293,026 posts on Instagram using the hashtag #deconstruction.
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 movement... There is nothing Christian about it. It is a false religion."On the other hand, Tyler Huckabee argues that it can result in "deconversion", or "in your faith looking more or less the same it always did" but "most often, it's somewhere in between—rethinking the things you’ve always believed and coming to a new, different understanding of parts of it." Huckabee goes on to suggest that Martin Luther's own theological revolution "fits into the paradigm of what researchers would call deconstruction today."Carl Trueman argues that the "(mis)use of the Derridean d-word gives the whole a specious veneer of intellectualism and a certain superannuated postmodern chic."
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 humorous stories or thoughts. Most commonly, it is considered an auditory expression of a number of positive emotional states, such as joy, mirth, happiness, or relief. On some occasions, however, it may be caused by contrary emotional states such as embarrassment, surprise, or confusion such as nervous laughter or courtesy laugh. Age, gender, education, language, and culture are all indicators as to whether a person will experience laughter in a given situation. Other than humans, some other species of primate (chimpanzees, gorillas and orangutans) show laughter-like vocalizations in response to physical contact such as wrestling, play chasing or tickling.
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 is sometimes seen as contagious, and the laughter of one person can itself provoke laughter from others as a positive feedback.The study of humor and laughter, and its psychological and physiological effects on the human body, is called gelotology.
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 as early as 16 days old may be vocal laughing sounds or laughter. However, the weight of the evidence supports the appearance of such sounds at 15 weeks to four months of age.
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 ever speak. Children who are born blind and deaf still retain the ability to laugh.Provine argues that "Laughter is primitive, an unconscious vocalization." Provine argues that it probably is genetic. In a study of the "Giggle Twins", two happy twins who were separated at birth and only reunited 43 years later, Provine reports that "until they met each other, neither of these exceptionally happy ladies had known anyone who laughed as much as they did." They reported this even though they had been brought together by their adoptive parents, who they indicated were "undemonstrative and dour". He indicates that the twins "inherited some aspects of their laugh sound and pattern, readiness to laugh, and maybe even taste in humor".Scientists have noted the similarity in forms of laughter induced by tickling among various primates, which suggests that laughter derives from a common origin among primate species.The spotted hyena, another species of animal, was also known as the laughing hyena because of the way it sounds when it communicates.
Laughter	Nature	A very rare neurological condition has been observed whereby the sufferer is unable to laugh out loud, a condition known as aphonogelia.
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' survival. The structures in the limbic system that are involved in laughter are the hippocampus and the amygdala.The December 7, 1984, Journal of the American Medical Association describes the neurological causes of laughter as follows: "Although there is no known 'laugh center' in the brain, its neural mechanism has been the subject of much, albeit inconclusive, speculation. It is evident that its expression depends on neural paths arising in close association with the telencephalic and diencephalic centers concerned with respiration. Wilson considered the mechanism to be in the region of the mesial thalamus, hypothalamus, and subthalamus. Kelly and co-workers, in turn, postulated that the tegmentum near the periaqueductal grey contains the integrating mechanism for emotional expression. Thus, supranuclear pathways, including those from the limbic system that Papez hypothesised to mediate emotional expressions such as laughter, probably come into synaptic relation in the reticular core of the brain stem. So while purely emotional responses such as laughter are mediated by subcortical structures, especially the hypothalamus, and are stereotyped, the cerebral cortex can modulate or suppress them."Some drugs are well known for their laughter-facilitating properties (e. g. ethanol and cannabis), while the others, like salvinorin A (the active ingredient of Salvia divinorum), can even induce bursts of uncontrollable laughter.A research article was published December 1, 2000, on the psycho-evolution of laughter (Panksepp 2000).
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 (University of Maryland) and William Fry (Stanford) theorize that beta-endorphin-like compounds released by the hypothalamus activate receptors on the endothelial surface to release nitric oxide, thereby resulting in dilation of vessels. Other cardioprotective properties of nitric oxide include reduction of inflammation and decreased platelet aggregation.Laughter has various proven beneficial biochemical effects. It has been shown to lead to reductions in stress hormones such as cortisol and epinephrine. When laughing, the brain releases endorphins that can relieve some physical pain. Laughter also boosts the number of antibody-producing cells and enhances the effectiveness of T-cells, leading to a stronger immune system. A 2000 study found that people with heart disease were 40 percent less likely to laugh and be able to recognize humor in a variety of situations, compared to people of the same age without heart disease.Anecdotally, journalist and author Norman Cousins developed in 1964 a treatment program for his ankylosing spondylitis and collagen disease consisting of large doses of Vitamin C alongside laughter induced by comic films, including those of the Marx Brothers. "I made the joyous discovery that ten minutes of genuine belly laughter had an anesthetic effect and would give me at least two hours of pain-free sleep," he reported. "When the pain-killing effect of the laughter wore off, we would switch on the motion picture projector again and not infrequently, it would lead to another pain-free interval."
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 detailed transcripts that indicate not only the presence of laughter but also features of its production and placement.
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, laughter often works to manage delicate and serious moments. More than simply an external behavior "caused" by an inner state, laughter is highly communicative and helps accomplish actions and regulate relationships.
Laughter	Causes	Common causes for laughter are sensations of joy and humor; however, other situations may cause laughter as well.
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 be used as a coping mechanism when one is upset, angry or sad.
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.
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 resolved, there is no laugh, as Mack Sennett pointed out: "when the audience is confused, it doesn't laugh." This is one of the basic laws of a comedian, referred to as "exactness". It is important to note that sometimes the inconsistency may be resolved and there may still be no laugh. Because laughter is a social mechanism, an audience may not feel as if they are in danger, and the laugh may not occur. In addition, the extent of the inconsistency (and aspects of its timing and rhythm) has to do with the amount of danger the audience feels, and how hard or long they laugh.
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.
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 are possible. Normal note durations with unusually long or short "inter-note intervals" do not happen due to the result of the limitations of our vocal cords. This basic structure allows one to recognize a laugh despite individual variants.It has also been determined that eyes moisten during laughter as a reflex from the tear glands.
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 "sham mirth", usually occur in people who have a neurological condition, including patients with pseudobulbar palsy, multiple sclerosis and Parkinson's disease. These patients appear to be laughing out of amusement but report that they are feeling undesirable sensations "at the time of the punch line".
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 or one's body, sometimes leading to seizures or a brief period of unconsciousness. Some believe that fits of laughter represent a form of epilepsy.
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 relax the whole body. It can also boost the immune system and release endorphins to relieve pain. Additionally, laughter can help prevent heart disease by increasing blood flow and improving the function of blood vessels. Some of the emotional benefits include diminishing anxiety or fear, improving overall mood, and adding joy to one's life. Laughter is also known to reduce allergic reactions in a preliminary study related to dust mite allergy sufferers.Laughter therapy also has some social benefits, such as strengthening relationships, improving teamwork and reducing conflicts, and making oneself more attractive to others. Therefore, whether a person is trying to cope with a terminal illness or just trying to manage their stress or anxiety levels, laughter therapy can be a significant enhancement to their life.Ramon Mora-Ripoll in his study on The Therapeutic Value Of Laughter In Medicine, stated that laughter therapy is an inexpensive and simple tool that can be used in patient care. It is a tool that is only beneficial when experienced and shared. Care givers need to recognize the importance of laughter and possess the right attitude to pass it on. He went on to say that since this type of therapy is not widely practiced, health care providers will have to learn how to effectively use it. In another survey, researchers looked at how Occupational Therapists and other care givers viewed and used humor with patients as a means of therapy. Many agreed that while they believed it was beneficial to the patients, the proper training was lacking in order to effectively use It. Even though laughter and humor has been used therapeutically in medical conditions, according to Mora-Ripoll, there was not enough data to clearly establish that laughter could be used as an overall means of healing. It did suggest that additional research was still needed since "well-designed randomized controlled trials have not been conducted to date validating the therapeutic efficacy of laughter."In 2017, an institution in Japan conducted an open-label randomized controlled trial to evaluate the effects of laughter therapy on quality of life in patients with cancer. The study used laughter yoga, comedy, clown and jokes. The result showed that laughter therapy was helpful in improving quality of life and cancer symptoms in some areas for cancer survivors. Improvements were seen in the area of depression, anxiety and stress levels. There were limited harmful side effects. Laughter therapy should be used in conjunction with other cancer treatment.
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 onward. Henri Bergson's Laughter: An Essay on the Meaning of the Comic (Le rire, 1901) is a notable 20th-century contribution.
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 and historiological reasons. "Herodotus believes either that both nature (better, the gods' direction of it) and human nature coincide sufficiently, or that the latter is but an aspect or analogue of the former, so that to the recipient the outcome is suggested." When reporting laughter, Herodotus does so in the conviction that it tells the reader something about the future and/or the character of the person laughing. It is also in this sense that it is not coincidental that in about 80% of the times when Herodotus speaks about laughter it is followed by a retribution. "Men whose laughter deserves report are marked, because laughter connotes scornful disdain, disdain feeling of superiority, and this feeling and the actions which stem from it attract the wrath of the gods." Modern There is a wide range of experiences with laughter. A 1999 study by two humor researchers asked 80 people to keep a daily laughter record, and found they laughed an average of 18 times per day. However, their study also found a wide range, with some people laughing as many as 89 times per day, and others laughing as few as 0 times per day.
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 chapter of the first part of his major work, The World as Will and Representation, to laughter.
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 in this sense laughter has a positive character for Nietzsche." Laughter can, however, also have a negative connotation when it is used for the expression of social conflict. This is expressed, for instance, in The Gay Science: "Laughter -- Laughter means to be schadenfroh, but with clear conscience.""Possibly Nietzsche's works would have had a totally different effect, if the playful, ironical and joking in his writings would have been factored in better." Bergson In Laughter: An Essay on the Meaning of the Comic, French philosopher Henri Bergson, renowned for his philosophical studies on materiality, memory, life and consciousness, tries to determine the laws of the comic and to understand the fundamental causes of comic situations. His method consists in determining the causes of the comic instead of analyzing its effects. He also deals with laughter in relation to human life, collective imagination and art, to have a better knowledge of society. One of the theories of the essay is that laughter, as a collective activity, has a social and moral role, in forcing people to eliminate their vices. It is a factor of uniformity of behaviours, as it condemns ludicrous and eccentric behaviours.
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 humour became a sort of escapism from responsibility and action. Ludovici considered laughter to be an evolutionary trait and he offered many examples of different triggers for laughter with their own distinct explanations.
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 incongruous situation has provoked must be worked out and overcome (resolution). Third, the actual release of laughter acts as an all-clear siren to alert bystanders (relief) that they are safe.
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 flours, milks for cheese, cured meats, fish, beverages, oils, and vinegars. The movement is focused on providing farm to fork type foods with locally sourced products that benefit the consumer, small scale growers and producers, and the local economy.
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 meats, beverages, oils, and vinegars. Fermentation or otherwise controlling the preservation environment for beneficial microorganisms can be utilized for vinegars, cheeses, cured meats, wine, oolong tea, kimchi and other examples. An artisan food item is usually developed and produced over a long period of time and consumed relatively close to where the food is created.
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 Amendment Senator Jon Tester (D-MT) and Senator Kay Hagan (D-NC) introduced two amendments to the FSMA that removed local food growers and food processors from federal oversight. These growers and producers would remain under the jurisdiction of state and local health and sanitation laws, rules, and regulations.
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 products direct to consumers in the same state and within a 400-mile radius".The advertising and marketing industries have latched on to the trendy word "artisanal" and now have artisanal products on supermarket shelves and offerings from local fast food chains. Dunkin' Donuts came out with an "artisanal" bagel, Domino's Pizza dished out an "artisanal" pizza, Tostitos served up "artisanal" chips, McDonald's offered an "artisan" bun, Wendy's introduced an "artisan" egg sandwich, and Subway provided "sandwich artisans" to prepare lunch.In April 2012, Davidovich Bagels, an artisanal maker of hand rolled, bagels in NYC filed a Federal complaint, claiming false advertising against Dunkin' Donuts to have them cease and desist claiming their commercially manufactured bagels were "Artisan". This case brought international attention to the meaning of the word in commerce and the parameters of representations to the consuming public.
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.
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 measurable sets. It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces.
Minkowski content	Minkowski content	It is related to, although different from, the Hausdorff measure.
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 μ is an n -dimensional Lebesgue measure. If the upper and lower m-dimensional Minkowski content of A are equal, then their common value is called the Minkowski content Mm(A).
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 closed m-rectifiable set in Rn, given as the image of a bounded set from Rm under a Lipschitz function, then the m-dimensional Minkowski content of A exists, and is equal to the m-dimensional Hausdorff measure of A.
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 system.
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 present in many cellular types throughout the human body. Cilia defects adversely affect numerous critical developmental signaling pathways essential to cellular development.Other types include: OMIM: 252100 Mohr syndrome; Orofaciodigital syndrome 2 at NIH's Office of Rare Diseases OMIM: 258860 Orofaciodigital syndrome 4 at NIH's Office of Rare Diseases OMIM: 300238 Orofaciodigital syndrome, Shashi type at NIH's Office of Rare Diseases OMIM: 277170 Varadi Papp syndrome; OFD6 at NIH's Office of Rare Diseases Relation to other rare genetic disorders Recent findings in genetic research have suggested that a large number of genetic disorders, both genetic syndromes and genetic diseases, that were not previously identified in the medical literature as related, may be, in fact, highly related in the genotypical root cause of these widely varying, phenotypically-observed disorders. Orofaciodigital syndrome has been found to be a ciliopathy. Other known ciliopathies include primary ciliary dyskinesia, Bardet–Biedl syndrome, polycystic kidney disease and polycystic liver disease, nephronophthisis, Alström syndrome, Meckel–Gruber syndrome and some forms of retinal degeneration.
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 hypertelorism and micrognathia. Bodily abnormalities such as webbed, short, joined, or abnormally curved fingers and toes are also symptoms of Orofaciodigital syndrome type 1. The most frequent symptoms are accessory oral frenulum, broad alveolar ridges, frontal bossing, high palate, hypertelorism, lobulated tongue, median cleft lip, and wide nasal bridge. Genetic screening of the OFD1 gene is used to officially diagnose a patient who has the syndrome, this is detected in 85% of individuals who are suspected to have Orofaciodigital syndrome type 1.
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 seizures may also be necessary. Speech therapy and special education in the later development may also be used as management.
CLDN22	CLDN22	Claudin-22 is a protein that in humans is encoded by the CLDN22 gene. It belongs to the group of claudins.
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 reactions, including restriction enzyme digestion or rapid diagnostics. The device has a thermal block with holes where tubes holding the reaction mixtures can be inserted. The cycler then raises and lowers the temperature of the block in discrete, pre-programmed steps.
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 reaction tubes. Later, the PCR process was adapted to the use of thermostable DNA polymerase from Thermus aquaticus, which greatly simplified the design of the thermal cycler. While in some old machines the block is submerged in an oil bath to control temperature, in modern PCR machines a Peltier element is commonly used. Quality thermal cyclers often contain silver blocks to achieve fast temperature changes and uniform temperature throughout the block. Other cyclers have multiple blocks with high heat capacity, each of which is kept at a constant temperature, and the reaction tubes are moved between them by means of an automated process. Miniaturized thermal cyclers have been created in which the reaction mixture moves via channel through hot and cold zones on a microfluidic chip. Thermal cyclers designed for quantitative PCR have optical systems which enable fluorescence to be monitored during reaction cycling.
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 are equipped with a fully adjustable heated lid to allow for nonstandard or diverse types of PCR plasticware.
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 annealing temperatures for PCR primers.
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 measured at two different points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables are sometimes called cross-correlation functions to emphasize that different variables are being considered and because they are made up of cross-correlations.
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 interpolating values at points for which there are no observations. Correlation functions used in astronomy, financial analysis, econometrics, and statistical mechanics differ only in the particular stochastic processes they are applied to. In quantum field theory there are correlation functions over quantum distributions.
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. If they are not, then more complicated correlation functions can be defined. For example, if X(s) is a random vector with n elements and Y(t) is a vector with q elements, then an n×q matrix of correlation functions is defined with i,j element corr ⁡(Xi(s),Yj(t)).
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. Similarly, if there are symmetries of the space (or time) domain in which the random variables exist (also called spacetime symmetries), then the correlation function will have corresponding space or time symmetries. Examples of important spacetime symmetries are — translational symmetry yields C(s,s') = C(s − s') where s and s' are to be interpreted as vectors giving coordinates of the points rotational symmetry in addition to the above gives C(s, s') = C(\|s − s'\|) where \|x\| denotes the norm of the vector x (for actual rotations this is the Euclidean or 2-norm).Higher order correlation functions are often defined. A typical correlation function of order n is (the angle brackets represent the expectation value) Ci1i2⋯in(s1,s2,⋯,sn)=⟨Xi1(s1)Xi2(s2)⋯Xin(sn)⟩.
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.
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 processes. Probability distributions defined on a finite number of points can always be normalized, but when these are defined over continuous spaces, then extra care is called for. The study of such distributions started with the study of random walks and led to the notion of the Itō calculus.
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 theory after Wick rotation to Minkowski spacetime (see Osterwalder-Schrader axioms). The operation of renormalization is a specified set of mappings from the space of probability distributions to itself. A quantum field theory is called renormalizable if this mapping has a fixed point which gives a quantum field theory.
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 dopamine reuptake inhibitor, with other derivatives such as the 4-iodo and 3,4-dichloro analogues being even more potent dopamine reuptake inhibitors again. However none of these compounds substitute for cocaine or produce stimulant effects in animals, suggesting that they still act primarily as opioid analgesic drugs in practice. Its action and degree of relation to pethidine means that it may be controlled in those countries which have laws about controlled-substance analogues; it is not itself listed in the Controlled Substances Act 1970.
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 small intestine by a series of muscle contractions called peristalsis. A trained healthcare provider can listen to these intestinal noises with a stethoscope, but they may be audible enough to be heard with the naked ear as the fluid and gas move forward in the intestines (in the vicinity of, but not actually within the stomach). The lack of bowel sounds is indicative of ileus, intestinal obstruction, or some other serious pathology.
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.
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 diabetics), gluten (protein in wheat, barley, and rye) (coeliac disease), fruit, vegetables, beans, legumes, and high-fiber whole grains. In rare instances, excessive abdominal noise may be a sign of digestive disease, especially when accompanied by abdominal bloating, abdominal pain, diarrhea or constipation. Some examples of diseases that may be associated with this symptom include carcinoid neoplasm and coeliac sprue.
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 the migrating motor complex. Food left behind after the first cycle is swept up, and the vibrations of the empty stomach cause hunger. Appetite plays a big role in this situation. Peristalsis recurs about every hour, and one's appetite may cause 10- to 20-minute food cravings.
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.
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 consumed, the immune system attacks these villi as a result. Symptoms may include abdominal pain, nausea, and bulky or foul smelling stools.
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, chills, dehydration, diarrhea, and fever. Diverticulitis is a condition where small bulging sacs, usually found in the large intestine, become inflamed or infected. The most probable cause is a low-fiber diet, possibly a result of eating processed food. Diverticulitis is usually seen in about half the American population over the age of 60. Symptoms may include bloating, fever, and nausea. Irritable bowel syndrome, a disorder in the lower intestinal tract, is usually accompanied by other symptoms, such as abdominal pain and diarrhea. It is more common in women and it usually occurs during early adulthood. There are many risk factors such as emotional stress and a low-fiber diet. These can all cause stomach disorders.
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: "The room was very quiet, except for its borborygmic old radiator".Graham Greene's short story "Alas, Poor Maling" tells the tale of a luckless individual whose borborygmus takes the form of irritating noises that he has recently heard.
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, and the resulting borborygmus upended European politics and enabled a populist wave that has yet to crest."
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.
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 many of its four sides are segments in the loop.
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 number of sides to each polygon; but similar rules apply to their solution.
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.

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