Unreferenced stub auto yes date December 2009 Orphan date February 2009 In game design , variation is the process whereby the game community community of players, rather than any officiating authority, adapts the rules for informal play. If a variant becomes popular, it will often be published in a rules document like Edmund Hoyle Hoyle s Rules of Games . It may supplant the original game. For example, Hearts game Hearts is usually played with a variation whereby the Playing card Jack of Diamonds carries a 10 desired, since points are penalty point value, in a variant known as Omnibus hearts . DEFAULTSORT VariationGame Category Game terminology Game stub ... more details
A Variation can refer to a specific sequence of successive moves in a turn based game, often used to specify a hypothetical future state of a game that is being played. Although the term is most commonly used in the context of Chess analysis, it has been applied to other games. It also is a useful term used when describing computer game tree tree search algorithms for example minimax algorithm minimax for playing games such as Go board game Go ref cite web url http www.andromeda.com people ddyer go search.html title Searches, tree pruning and tree ordering in Go date 21 December 2007 ref or Chess . A variation can be any number of steps as long as each step would be legal if it were to be played. It is often as far ahead as a human or computer can calculate or however long is necessary to reach a particular position of interest. It may also lead to a terminal state in the game, in which case the term Winning Variation or Losing Variation is sometimes used. Principal variation Image Principle variation 16bit.PNG thumb right The principal variation of this minimax game tree is shown in blue The principal variation refers to the particular variation that is the most advantageous to the current player, assuming each other player will respond with the move that best improves their own position. In other words, it is the best or correct line of play. In the context of game tree tree searching game Artificial Intelligence in which this term is most common it may also refer to the sequence of moves which is currently believed to be the most advantageous, but is not guaranteed due to the technical limitations of the algorithm. See also Game tree Backtracking Minimax Negamax Alpha beta pruning Negascout References references http www.red bean.com sgf var.htm Variations Category Combinatorial game theory Category Game artificial intelligence Category Search algorithms Category Computer chess Category Trees graph theory ru ... more details
chess notation Infobox chess opening openingname Scotch Game, Classical Variation image Chess diagram rd bd qd kd nd rd pd pd pd pd pd pd pd nd bd nl pl pl pl pl pl pl pl rl nl bl ql kl bl rl moves 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Nxd4 Bc5 ECO C45 birth 1750 parentopening Scotch Game AKA chessgid 2360949&move 5&moves e4.e5.Nf3.Nc6.d4.exd4.Nxd4.Bc5&nodes 62546.1805596.2360949 The Classical Variation of the Scotch Game is a chess opening that begins with the moves 1. b Chess Opening Theory 1. e4 e4 b Chess Opening Theory 1. e4 1...e5 e5 2. b Chess Opening Theory 1. e4 1...e5 2. Nf3 Nf3 b Chess Opening Theory 1. e4 1...e5 2. Nf3 2...Nc6 Nc6 3. b Chess Opening Theory 1. e4 1...e5 2. Nf3 2...Nc6 3. d4 d4 b Chess Opening Theory 1. e4 1...e5 2. Nf3 2...Nc6 3. d4 3...exd4 exd4 4. b Chess Opening Theory 1. e4 1...e5 2. Nf3 2...Nc6 3. d4 3... exd4 4. Nxd4 Nxd4 b Chess Opening Theory 1. e4 1...e5 2. Nf3 2...Nc6 3. d4 3...exd4 4. Nxd4 4...Bc5 Bc5 White has several fifth move options Most common is 5.Be3 . Black then typically replies with 5...Qf6 , although 5...Bb6 and, less frequently, 5...Nxd4 or 5...Bxd4 are also played. After 5...Qf6 , play typically continues with 6.c3 Nge7 . Here white again has options, the most popular being 7.Bc4 and 7.g3. Black may reply to 7.Bc4 with 7...Ne5 8.Be2 Qg6 9.O O d6 9...Qxe4? 10.b4 is a risky venture for black 10.f3 O O and then 11.Nd2 or 11.Kh1 , 7...O O 8.O O Bb6 and then 9.Na3 or 9.Nc2, among others , or 7...b6 8.O O Bb7 and then 9.Nb5, 9.f4, or 9.Nb3 . It was claimed in an analysis by Alexey Sokolsky in the 1940s that 7...Ne5 followed by 8...Qg6 led to equality, and for this reason 7.Bc4 fell out of popularity until it was revived in the 1990s by Kasparov , among others. ref Cite book last1 Lane first1 Gary author 1 link Gary Lane year 1993 title Winning with the Scotch publisher Henry Holt and Company, Inc. isbn 0 8050 2940 0 page 11 ref harv ... . Also seen are the knight moves 5.Nb3 the Potter Variation , recently played with success by Magnus ... more details
Bf8 11.Qf4. 6. Nb5 g6 7. Qf3 f5 David Bronstein once won a game after with 7...f6 ? 8.Nxc7 Qxc7 9.Qxf6 ... from 14...Bh6, 14...Bg7, and 14...Bxa8. See Harding s 1998 column cited below. Notable game http ... Harding column about the variation PDF http www.chesscafe.com text kibitz21.txt 1998 Tim Harding column about the variation http www.chess.com opening eco C27 Vienna Game Stanley Variation Frankenstein Dracula Variation 167 Games at Chess.com Category Chess openings Category Frankenstein Category 1975 ... more details
Variation Biodiversity Genetic diversity , differences within a species Physics Magnetic variation , difference between magnetic north and true north, measured as an angle. Variation astronomy , any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon Mathematics Bounded variation Calculus of variations , a field of mathematics which deals with functions of functions. Coefficient of variation Permutation Arts Variation music , formal technique where material is altered during repetition Variations album , composed by Andrew Lloyd Webber Variation on a theme , in art history Ballet Variation ballet , solo dance or dance figure Balanchine s 1947 Theme and Variations ballet Balanchine s 1966 Variations ballet , an earlier version of Variations for Orchestra Balanchine s 1982 Variations for Orchestra , a subsequent revision of Variations Other Variationgame , modifications made to a game by a community of players as opposed to a central authority Variationgame tree , particular series of moves. Variation linguistics See also Variability Variations on a Theme disambiguation disambig ca Variaci cs Variace de Variation es Variaci n gl Variaci n lt Variacija ka ja no Variasjon pl Wariacja pt Varia o ru sk Vari cia fi Variaatio uk ... more details
. ref Watson 1986, p. 29. ref Not all exchange variations are quiet the Exchange Variation of the Grunfeld ... Variation of the Queen s Gambit Declined often involves attacks by one or both sides on the enemy .... In the Ruy Lopez, Exchange Variation pieces White s bishop and Black s knight rather than pawns are traded. In the Exchange Variation of the Grunfeld Defence Grunfeld Defense , both a pair of pawns and a pair of knights are traded. The diagram at right shows a position in the Exchange Variation ... Ruy Lopez, Exchange Variation 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 deferred exchange variations are also ... References reflist Category Chess openings Exchange variation Category Chess terminology de Abtauschvariante ... more details
Elegant variation is a phrase coined by Henry Watson Fowler referring to the unnecessary use of synonym ... open to the allurements of elegant variation. . . . The fatal influence . . . is the advice ... limit. In the 1920s, when Fowler coined the term elegant variation , the word elegant had a since ... and Style , Bryan Garner unambiguously renamed the term inelegant variation . Despite Fowler s arguments, elegant variation is an almost universally accepted norm among contemporary authors writing ... of the change is, only to conclude that there is none. Elegant variation is still common in modern ... of the potential negative effect of elegant variation is the use of elongated yellow fruit as an elegant variation of banana . Another bad example in a newspaper was the red headed non driver ... ... with mule and donkey used as elegant variation synonyms although they are different sorts of animals. Another elegant variation nuisance can happen with dates e.g. replacing 1947 ... 1963 by 1947 ... result in cases that look like elegant variation but are not, for example A newspaper sub editor accustomed to replacing game by match or bout to avoid word repeats may get into error with tennis where a game is not the same as a match likewise in cricket a draw game ran out of time is not the same as a tie game finished, same number of runs each . In a local election for councillor s, political ... illustrate problems inherent to elegant variation. In poetry Elegant variation in poetry occurs by the poet ... languages Whereas elegant variation in English prose is thought by some to be excessive, in other languages ... of elegant variation that is, using synonyms wherever possible , which purists consider ... 1984 isbn 0271003685 page 35 publisher Penn State University Press quote Elegant variation French tends ... See also Pleonasm Kenning References http www.bartleby.com 116 302.html Elegant Variation Fowler s discussion of elegant variation in The King s English 1908 reflist DEFAULTSORT Elegant Variation Category ... more details
Unreferenced date February 2007 Variation or Classical Variation sometimes referred to as a Pas seul , meaning to Dance Alone in ballet is a solo dance. As with an Aria in opera , which allows the singer to demonstrate his or her interpretive skills, the variation in ballet has the same function. Typically, variations in ballet have traditional choreography, with every dancer dancing the same steps as in opera, a singer singing the same words . Ballet Category Ballet terminology Variation ballet eo Variado baleto sv Variation balett ... more details
nofootnotes date August 2010 Image wheat.gif right thumb Genetic variation , variation in allele s of gene s, occurs both within and among population s. Genetic variation is important because it provides the raw material for natural selection . Genetic variation is brought about by mutation, a change ... wherein organisms have three or more sets of genetic variation 3n or more . Among individuals within a population Genetic variation among individuals within a population can be identified at a variety of levels. It is possible to identify genetic variation from observations of phenotype phenotypic variation in either quantitative traits traits that vary continuously and are coded for by many ... variation can also be identified by examining variation at the level of enzyme s using the process ... common in vertebrates. Ultimately, genetic variation is caused by variation in the order of bases ... has identified even more genetic variation than was previously detected by protein electrophoresis. Examination of DNA has shown genetic variation in both coding regions and in the non coding intron region of genes. Genetic variation will result in phenotypic variation if variation in the order of nucleotides ... the shape, and thus the function of the enzyme. Between populations Geographic variation in genes often occurs among populations living in different locations. Geographic variation may be due to differences in selective pressures or to genetic drift . Measurement Genetic variation within a population ... variation because they alter the order of bases in the nucleotides of DNA. Mutations are likely ... be favored by natural selection. Genetic variation can also be produced by the recombination of chromosome ... also contributes to variation. Variation and recombination can be fascilitated by transposable ... see variation inducing genetic element s. Maintenance in populations A variety of factors maintain genetic variation in populations. Potentially harmful recessive alleles can be hidden from selection ... more details
Typostrophic variation is a term used in population genetics to describe the type of variation found in peripherally isolated populations. Variation of this kind is wiktionary heterogeneous heterogeneous , due to factors such as geographic isolation and inbreeding . In 1954 Ernst Mayr wrote a landmark paper developing the idea that subspecies in typostophic populations lead to formation of species incipient species . ref Mayr, E. http www.blackwellpublishing.com ridley classictexts mayr.asp Change of genetic environment and evolution. In Julian Huxley et al., eds., Evolution as a Process . London Allen and Unwin, pp. 157 180. ref According to Mayr species formation rarely occurred in populations which were exemplified by ecotypic variation . Notes Reflist Category Population genetics Genetics stub ... more details
Antigenic variation is the process by which an Pathogen infectious organism alters its Protein surface proteins in order to evade a host biology host immune response . Antigenic variation not only enables immune evasion but also allows pathogens to cause reinfection as they are not recognised by the host s immune system. When an organism is exposed to a particular antigen i.e. a protein on the surface of a bacterium an immune response is stimulated and antibodies are generated to target that specific antigen. The immune system will then remember that particular antigen immunological memory and if the host is exposed to that same antigen again, those antibodies will act rapidly to destroy the pathogen ... antigen. Antigenic variation enables viruses to cross the species barrier e.g. H5N1 virus jumping ... antigenic variation have a selective advantage over their more mutation genetically stable counterparts. Antigenic variation occurs in bacteria , virus es and protozoa . Antigenic variation in bacteria ... host immune response and the Streptococci variate their M protein. Antigenic variation in viruses ... from chimpanzees to humans, to give HIV, due to antigenic variation. This antigenic variation enabled ..., perhaps the master of viral antigenic variation is the influenza virus. This highly adaptable virus ... to give antigenically distinct variants. Due to this regular antigenic variation, lifelong immunity to the influenza virus is impossible. Antigenic variation in protozoa is best demonstrated by species ... variation can occur through three broadly defined genetic processes gene mutation , genetic recombination recombination , and Regulation of gene expression switching . In all cases, antigenic variation ... escape from host immunity by a genome program for antigenic variation , Proc Natl Acad Sci U S A. 2006 Nov 13 Barbour AG, Restrepo BI., Antigenic variation in vector borne pathogens. Emerg Infect Dis. 2000 Sep Oct 6 5 449 57. Review. refend DEFAULTSORT Antigenic Variation Category Immune system ... more details
Variation suite is a music al genre most popular during the early Baroque era. The variation suite consists of two or more movements where the first movement presents a theme and the remaining movements present variations on that theme. Movements in the variation suite are typically dance or dance like forms, and are all in the same main key area. This cyclic form was predominantly used by German composers. ref name buk Paul Peuerl is credited with composing the first true variation suites, which were included in his Neue Paduan 1611 . The form was codified by Johann Schein in his 1617 Banchetto musicale . ref name buk cite book last Bukofzer first Manfred F. title Music in the Baroque Era From Monteverdi to Bach year 2008 publisher Von Elterlein Press isbn 1443726192 pages 109 114 ref Both based their compositional technique in the variation suite on the earlier varied couples form. ref name buk The form is generally considered a hybrid of the variation music theme and variations and the suite . ref cite book last Gillespie first John title Five Centuries of Keyboard Music year 1972 publisher Dover Publications isbn 048622855X pages 44 ref References reflist music stub Category Baroque music Category Variations ... more details
Somaclonal variation It is the term used to describe the variation seen in plants that have been produced by plant tissue culture . Chromosome Chromosomal rearrangements are an important source of this variation. Somaclonal variation is not restricted to, but is particularly common in plants regenerated from callus cell biology callus . The variations can be genotypic or phenotypic , which in the latter case can be either genetic or epigenetic in origin. Typical genetic alterations are changes in chromosome numbers polyploidy and aneuploidy , chromosome structure translocations, deletions, insertions and duplications and DNA sequence base mutations . Typical epigenetic related events are gene amplification and gene methylation. If no visual, morphogenic changes are apparent, other plant screening procedures must be applied. There are both benefits and disadvantages to somaclonal variation. The phenomenon of high variability in individuals from plant cell cultures or adventitious shoots has been named somaclonal variation. Benefits The major likely benefit of somaclonal variation in plant is improvement. Somaclonal variation leads to the creation of additional genetic variability. Characteristics for which somaclonal mutants can be enriched during in vitro culture includes resistance to disease pathotoxins, herbicides and tolerance to environmental or chemical stress, as well as for increased production of secondary metabolites. Micropropagation can be carried out throughout the year independent of the seasons. Disadvantages A serious disadvantage of somaclonal variation occurs in operations which require clonal uniformity, as in the horticulture and forestry industries where ... variation Different steps can be used. It is well known that increasing numbers of subculture increases the likelihood of somaclonal variation, so the number of subcultures in micropropagation protocols ... over time. Another way of reducing somaclonal variation is to avoid 2,4 Dichlorophenoxyacetic ... more details
The Taimanov Variation can refer to variations of four different chess opening s, all List of chess openings named after people named after Mark Taimanov In the Sicilian Defense Taimanov Variation 4...Nc6 Sicilian Defense , 1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 Nc6 In the Nimzo Indian Defense , 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.e3 Nc6 In the Benoni Defense , 1.d4 Nf6 2.c4 c5 3.d5 e6 4.Nc3 exd5 5.cxd5 d6 6.e4 g6 7.f4 Bg7 8.Bb5 , the moves 7.f4 and 8.Bb5 defining the variation In the Gr nfeld Defence 1.d4 Nf6 2.c4 g6 3.Nc3 d5 4.Bg5 disambig ... more details
The secular variation of a time series is its long term non periodic variation see Decomposition of time series . Whether something is perceived as a secular variation or not depends on the available timescale a secular variation over a time scale of centuries may be part of a periodic variation over a time scale of millions of years. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long term trend. Examples The term secular variation is used wherever time series are applicable in economics , operations research , biological anthropology , astronomy particularly celestial mechanics such as secular variations of the planetary orbits etc. Astronomy In astronomy , secular phenomena refers to long term perturbations in the motion of planets. The Axial precession astronomy precession of the Earth s axis has a period of 25,771.5 years, so on a much shorter time frame it appears to be a drift of the position of the equinox in the plane of the ecliptic of approximately one degree every 71.6 years. ref harvnb Lowrie 2004 ref Market trends Market trends are classified as secular , primary and secondary for long, medium and short time frames. ref harvnb Edwards McGee Bessetti 2007 p 17 ref Traders identify market trends using technical analysis . Geomagnetic secular variation Geomagnetic secular variation refers to changes in the Earth s magnetic field . The field has variations on time scales from milliseconds to millions of years, but rapid changes mostly come from currents in the ionosphere and magnetosphere . The secular variation is the changes over periods of a year or more, reflecting changes in the Earth s core . Phenomena associated with this secular variation include geomagnetic jerk , westward drift and geomagnetic reversals . ref harvnb Merrill McElhinny ... volume 63 publisher Academic Press year 1996 isbn 0 12 49125 1 DEFAULTSORT Secular Variation Category ... more details
The variation ratio is a simple measure of statistical dispersion in nominal distribution s it is the simplest measure of qualitative variation . It is defined as the proportion of cases which are not the mode statistics mode math mathbf v 1 frac f m N . math While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by Harv Freeman 1965 . Just as with the range statistics range or standard deviation , the larger the variation ratio, the more differentiated or dispersed the data are and the smaller the variation ratio, the more concentrated and similar the data are. For example, a group which is 55 female and 45 male has a proportion of 0.55 females and therefore variation ratio of 1.0 0.55 0.45 and is more dispersed in terms of gender than a group which is 95 female and has a variation ratio of only 0.05. Similarly, a group which is 25 Catholic where Catholic is the modal religious preference has a variation ratio of 0.75 and is much more dispersed religiously than a group which is 85 Catholic and has a variation ratio of only 0.15. See also Qualitative variation , for a number of other measures of dispersion in nominal variables References Citation last Freeman first Linton C. title Elementary Applied Statistics publisher John Wiley and Sons location New York year 1965 pages 40 43 Category Statistical deviation and dispersion Category Statistical ratios Category Summary statistics for categorical data ... more details
Ecotypic variation is a term used in population genetics to describe the type of variation found in a large continuous geographic populations. Variation of this kind is wiktionary homogeneous homogeneous , due to factors such as gene flow . In 1954 Ernst Mayr wrote a landmark paper attacking the idea that subspecies in ecotypic populations lead to formation of incipient species. ref Mayr, E. http www.blackwellpublishing.com ridley classictexts mayr.asp Change of genetic environment and evolution. In Julian Huxley et al., eds., Evolution as a Process . London Allen and Unwin, pp. 157 180. ref According to Mayr species formation occurred in populations which were small and isolated, that is, populations which exemplified typostrophic variation . Notes reflist Category Population genetics genetics stub ... more details
In advertising , repetition variation is an advertising technique in which repeated Advertisement ads contain slight variations in order to optimize their effectiveness and prevent advertising wearout . ref cite journal coauthors David W. Schumann, D. Scott Clemons year 1989 title THE REPETITION VARIATION HYPOTHESES CONCEPTUAL AND METHOLOGICAL ISSUES journal Advances in Consumer Research volume Volume 16 pages 529 534 url http www.acrwebsite.org volumes display.asp?id 6958 ref References Reflist advertising stub Category Advertising techniques ... more details
In general relativity and gravitation the Palatini variation is nowadays thought of as variation of a Lagrangian with respect to the connection. For general relativity Palatini variation gives that the connection is the Christoffel connection. The reason that Palatini variation is considered important is that it means that the use of the Christoffel connection in general relativity does not have to be added as a separate assumption, the information is already in the Lagrangian. For theories of gravitation which have more complex lagrangians than the Einstein Hilbert Lagrangian of general relativity Palatini variation sometimes gives more complex connections and sometimes tensorial equations. Attilio Palatini 1889 1949 was an Italian mathematician who received his doctorate from the University of Padova, where he studied under Levi Civita and Ricci Curbastro. The history of the subject, and Palatini s connection with it, is not straightfoward, see the references. References A. Palatini 1919 Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton , Rend. Circ. Mat. Palermo 43, 203 English translation by R.Hojman and C. Mukku in P.G. Bergmann and V. De Sabbata eds. Cosmology and Gravitation, Plenum Press, New York 1980 M. Ferraris, M. Francaviglia, C. Reina, Variational Formulation of General Relativity from 1915 to 1925 Palatini s Method Discovered by Einstein in 1925 , Gen. Rel. Grav. 14 1982 243 254. Category Lagrangian mechanics ... more details
variation of the function. In mathematics , the total variation identifies several slightly different ... , defined on an interval mathematics interval a , b , its total variation on the interval ... variation for functions of one real variable was first introduced by Camille Jordan in the paper ... function s whose variation is Bounded variation bounded . The extension of the concept to functions of more than one variable however is not simple for some reasons. Definitions Total variation for functions of one real variable EquationRef 1 Definition 1.1. The total variation of a real number ... of a,b right math of the given interval mathematics interval . Total variation for functions ... n sup . Given a function math f math belonging to math L 1 Omega math , the total variation of math ... domain math Omega math sup n sup of the given function is a bounded set . Total variation in measure ... called upper variation and lower variation , as follows math overline mathrm W mu,E sup left ... 1.3. The variation also called absolute variation of the signed measure math mu math is the set ... math and its total variation is defined as the value of this measure on the whole space of definition ... and lower variation are respectively a non negative and a non positive Measure mathematics measure ... the last one sometimes being called, by abuse of notation , total variation measure . When the measure math mu math is Complex number complex valued i.e. is a complex measure , its upper and lower variation ... the total variation of the complex valued measure math mu math as follows EquationRef 4 Definition 1.4. The variation of the complex valued measure math mu math is the set function math mu E sup ... math pi math of a measurable set math E math into a finite number of disjoint measurable subsets. The variation ... defined by EquationNote 3 1.3 when math mu math is a signed measure its total variation is defined as above. This definition works also if math mu math is a vector measure the variation is then defined ... more details
Free variation in linguistics is the phenomenon of two or more sounds or forms appearing in the same environment without a change in meaning and without being considered incorrect by native speaker s. ref name Clark cite book last1 Clark first1 John Ellery last2 Yallop first2 Colin last3 Fletcher first3 Janet year 2007 title Introduction to Phonetics and Phonology pages 110, 116 18 location Oxford publisher Blackwell isbn 1405130830 url http books.google.de books?id dX5P5mxtYYIC&pg PA116 v onepage&q&f false ref ref SIL International, 2004 01 05. http www.sil.org linguistics GlossaryOfLinguisticTerms WhatIsFreeVariation.htm What is free variation? . Retrieved 2011 01 26. ref Examples from English language English include glottalization of voiceless consonant voiceless stop consonant stops in word final position for example, the word stop may be pronounced with a plain unaspirated IPA p , IPA st p , or with a glottalized IPA p , IPA st p the word economics may be pronounced with IPA i or IPA in the first syllable although individual speakers may prefer one or the other, and although one may be more common in some dialect s than others, both forms are encountered within a single dialect and sometimes even within a single idiolect the comparative of many disyllabic adjective s can be formed either with the word more or with the Affix suffix er , for example more stupid or stupider . When phoneme s are in free variation, speakers are sometimes strongly aware of the fact especially where such variation is only visible across a dialectal or sociolectal divide , and will note, for example ... words show such variations. In the case of allophones , however, free variation is exceedingly common, and, along with differing intonation patterns, variation in allophony is the most important ... analysis References reflist Category Phonology als Freie Variation ar de Freie Variation Linguistik fr Variante libre ko it Variazione libera ru sv Fri variation ... more details
In musical composition music composition , developing variation is a musical form formal technique in which the concepts of musical development development and variation music variation are united in that variations are produced through the development of existing material. Though the term was coined by Arnold Schoenberg , inventor of the twelve tone technique , he felt it was one of the most important compositional principles since around 1750 ref name Haimo Haimo, Ethan. 1990. Schoenberg s Serial Odyssey The Evolution of his Twelve Tone Method, 1914 1928 , p.73n8. Oxford England Clarendon Press New York Oxford University Press ISBN 0 19 3152 60 6. ref quote Music of the homophony homophonic melody melodic style of composition, that is, music with a main theme music theme , accompaniment accompanied by and based on harmony , produces its material by, as I call it, developing variation . This means that variation of the features of a basic unit produces all the thematic formulations which provide for fluency, contrasts, variety, logic and unity, on the one hand, and character, mood, expression, and every needed differentiation, on the other hand thus elaborating the idea of the piece. Schoenberg distinguished this from the unravelling procedures of counterpoint contrapuntal tonality tonal music but developing variation may be related to other textures and to Schoenberg s own freely atonality atonal pieces which employ a method of atonal developing variation each chord music chord , line, and harmony results from the subtle alteration and recombination of musical idea musical ideas from earlier in the piece and Schoenberg describes its importance to his developmental of serialism. ref name Haimo quote Similarly, as in the case of Die Jakobsleiter , here also all main themes ... that Schoenberg reconciled serial organization and developing variation in the twelve tone technique. Further reading Frisch, Walter 1984 . Brahms and the Principle of Developing Variation , p.1 ... more details
In mathematics , quadratic variation is used in the analysis of stochastic process es such as Wiener process Brownian motion and Martingale probability theory martingale s. Quadratic variation is just one kind of Total variationvariation of a process. Definition Suppose that X sub t sub is a real valued stochastic process defined on a probability space &Omega ,F,P and with time index t ranging over the non negative real numbers. Its quadratic variation is the process, written as X sub t sub , defined ... covariation may be written in terms of the quadratic variation by the polarization identity math X,Y t frac 1 2 X Y t X t Y t . math Finite variation processes A process X is said to have finite variation if it has bounded variation over every finite time interval with probability 1 . Such processes ... variation exists for all continuous finite variation processes, and is zero. This statement can be generalized to non continuous processes. Any c dl g finite variation process X has quadratic variation ... variation is given by math X t sum 0 s le t Delta X s 2. math The proof that continuous finite variation processes have zero quadratic variation follows from the following inequality. Here, P is a partition of the interval 0, t , and V sub t sub X is the variation of X over 0, t . math begin align sum ... P Vert math goes to zero. It processes The quadratic variation of a standard Wiener process Brownian ... 0 t mu s ,ds, math where B is a Brownian motion. Any such process has quadratic variation given by math ... well defined quadratic variation, which follows from the fact that such processes are examples of semimartingales. It can be shown that the quadratic variation M of a general local martingale M is the unique ... of a martingale in terms of the quadratic variation. For a local martingale M starting ..., the predictable quadratic variation is sometimes used for locally square integrable martingales. This is written ..., it is the same as the quadratic variation. See also Total variation Bounded variation References Citation ... more details
Phase variation is a method for dealing with rapidly varying environments without requiring random mutation employed by various types of bacteria, including Salmonella species. It involves the variation of protein expression, frequently in an on off fashion, within different parts of a bacterial population. Although it has been most commonly studied in the context of immune evasion, it is observed in many other areas as well. Phase variation is defined as the random switching of phenotype at frequencies that are much higher sometimes 1 than classical mutation rates. Phase variation contributes to virulence by generating heterogeneity certain environmental or host pressures select those bacteria that express the best adapted phenotype Salmonella use this technique to switch between different types of the protein flagellin . As a result, flagella with different structures are assembled. Once an adaptive response has been mounted against one type of flagellin, or if a previous encounter has left the adaptive immune system ready to deal with one type of flagellin, switching types renders previously high affinity antibodies, TCRs and BCRs ineffective against the flagella. Category Microbiology bacteria stub ja ... more details
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