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 authorlink1 Gary Lane year 1993 title Winning with the Scotch publisher Henry Holt and Company, Inc. isbn 0 8050 2940 0 page 11 ref harv ... seen are the knight moves 5.Nb3 the Potter Variation , recently played with success by Magnus ... more details
www.chesscafe.com text kibitz01.pdf 1996 Tim 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 ...Infobox chess opening openingname Frankenstein Dracula Variation image Chess diagram rd nd bd qd kd bd rd pd pd pd pd pd pd pd pd bl nd nl pl pl pl pl pl pl pl rl bl ql kl nl rl moves 1.e4 e5 2.Nc3 Nf6 3.Bc4 Nxe4 ECO C27 birth nameorigin Frankenstein s monster Frankenstein monster br Count Dracula parentopening Vienna Game AKA chessgid 1932676&move 4&moves e4.e5.Nc3.Nf6.Bc4.Nxe4&nodes 21720.21721.24109.24913.26166.1932676 The Frankenstein Dracula Variation is a chess opening , usually considered a branch of the Vienna Game , but can also be reached from the Bishop s Opening . The opening involves many complications, however with accurate play the opening is very playable for both sides. The variation was given its name by Tim Harding chess Tim Harding in his 1975 book on the Vienna Game, in which he said that the bloodthirstiness of the character of play was such that a game between Count Dracula Dracula and the Frankenstein s monster Frankenstein Monster would not seem out of place. The line is seen extremely infrequently in top level play, mainly because the Vienna Game is seen so little at top level play. Vassily Ivanchuk Ivanchuk used the opening against Vishy Anand Anand in Roquebrune in 1992 in a game that ended as a draw. Alexei Shirov had also played this in a simultaneous ... Nf6 3. Bc4 The moves which bring about the variation. Another common way of reaching the same position ... Dracula Variation. White cannot of course win material immediately, since 4.Nxe4 brings 4...d5 ... 0 8.Nd5 Nxe5 9.Qxe5 Re8 10.0 0 Bf8 11.Qf4. 6. Nb5 g6 7. Qf3 f5 David Bronstein once won a game with 7 ... s 1998 column cited below. Notable game http www.chessgames.com perl chessgame?gid 1102845 Ost Hansen ... more details
wiktionary variation tocright 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 Andrew Lloyd Webber album Variations Andrew Lloyd Webber album Variations Eddie Rabbitt album Variations Eddie Rabbitt album Variations Cage , a series of works by American avant garde composer John Cage Variations Stravinsky , Igor Stravinsky s last orchestral composition, written in 1963 64 Variation on a theme , in art history Ballet Variation ballet , solo dance or dance figure Balanchine s 1947 Theme and Variations ballet Theme and Variations Balanchine s 1966 Variations ballet 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 disambiguation Variations on a Theme disambiguation disambiguation ca Variaci cs Variace de Variation es Variaci n gl Variaci n it Variazione disambigua ka lt Variacija ja no Variasjon pl Wariacja pt Varia o ru sk Vari cia fi Variaatio uk ... more details
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 of the French ... 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 s to denote a single thing. In A Dictionary of Modern English Usage 1926 he says It is the second rate writers, those intent rather on expressing themselves prettily than on conveying their meaning ... 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 recast the term as inelegant variation . Reference necessary Despite Fowler s arguments, elegant variation is still common among contemporary authors writing ... wondering what the significance of the change is, only to conclude that there is none. Elegant variation ... 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 ... sixteen years ... 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 party ... problems inherent to elegant variation. date April 2011 In poetry Elegant variation in poetry .... In other languages Whereas elegant variation in English prose is thought by some to be excessive ... International Publishing Group Continuum quote . . . the rule of elegant variation that is, using ... State University Press quote Elegant variation French tends to avoid repetition of proper names, with a description ... 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 Language varieties and styles ... more details
no footnotes 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, which is a change ... is a condition 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 ... . Genetic variation can also be identified by examining variation at the level of enzyme s using ... are less common in vertebrates. Ultimately, genetic variation is caused by variation in the order ... DNA which 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 ... sequence influence 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 ... of genetic variation because they alter the order of bases in the nucleotides of DNA. Mutations ... alleles can be favored by natural selection. Genetic variation can also be produced by the recombination ..., random fertilization also contributes to variation. Variation and recombination can be facilitated ..., SINEs, etc. Maintenance in populations A variety of factors maintain genetic variation in populations ... common zygosity homozygous individuals . Natural selection can also maintain genetic variation in balanced ... 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
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 terms Ballet Category Ballet terminology Variation ballet eo Variado baleto ja sv Variation balett ... 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
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
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 music 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 Category Baroque music Category Variations Suite Category Suites classical music 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
be described as a simple fault rather than bottle variation, even though the corked bottle would be clearly different from a non corked example. Sometimes, it is not clear what causes the variation. Bottles ... 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 Chromosomal translocation translocation s, deletion s, insertion s and duplication s 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 pathotoxin s, 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 .... Ways of reducing somaclonal 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 ... new explants might reduce variability over time. Another way of reducing somaclonal variation is to avoid ... 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 Century 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 VSOP planets 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 McFadden 1996 ref ... Press year 1996 isbn 0 12 49125 1 DEFAULTSORT Secular Variation Category Geomagnetism Category ... 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
Equivalent variation EV is a Measurement measure of how much more money a consumer would pay before a price increase to avert the price increase. Because the meaning of equivalent may be unclear, it is also called extortionary variation . John Hicks 1939 is attributed with introducing the concept of compensating variation compensating and equivalent variation. It is a useful tool when the present prices are the best place to make a comparison. The value of the equivalent variation is given in terms of the expenditure function math e cdot, cdot math as math EV e p 0, u 1 e p 0, u 0 math math e p 0, u 1 w math math e p 0, u 1 e p 1, u 1 math where math w math is the wealth level, math p 0 math and math p 1 math are the old and new prices respectively, and math u 0 math and math u 1 math are the old and new utility levels respectively. Value function form Equivalently, in terms of the value function math v cdot, cdot math , math v p 0,w EV u 1 math This can be shown to be equivalent to the above by taking the expenditure function of both sides at math p 0 math math e p 0,v p 0,w EV e p 0,u 1 math math w EV e p 0,u 1 math math EV e p 0,u 1 w math One of the three identical equations above. See also Compensating variation CV is a closely related measure of welfare change. References Mas Colell, A., Whinston, M and Green, J. 1995 Microeconomic Theory , Oxford University Press, New York. Category Welfare economics econ stub de quivalente Variation ru ... 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 ... index t ranging over the non negative real numbers. Its quadratic variation is the process, written ... variables convergence in probability . Note that a process may be of finite quadratic variation ... variation for every t 0 in the classical sense of taking the supremum of the sum over all partitions ... 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 ..., all continuously differentiable functions. The quadratic 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 equal to the sum of the squares ... X sub t sub X sub t sub . Then, the quadratic 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 ... t sub X is the variation of X over 0, t . math begin align sum k 1 n X t k X t k 1 2& le max k le ... The quadratic variation of a standard Wiener process Brownian motion B exists, and is given by B ... motion. Any such process has quadratic variation given by math X t int 0 t sigma s 2 ,ds. math ... Martingales All c dl g martingales, and local martingale s have well defined quadratic variation ... that the quadratic variation M of a general local martingale M is the unique right continuous and increasing ... variation. For a local martingale M starting at zero, with maximum denoted by M sub t sub sup sup ... positive value of p . An alternative process, the predictable quadratic variation is sometimes used ... more details
axis, shown as a red ball, is the total variation of the function. In mathematics , the total variation ... a , b , its total variation on the interval of definition is a measure of the one ... a , b . Historical note The concept of total variation for functions of one real variable ... series of discontinuous function discontinuous periodic function s whose variation is Bounded variation ... for various reasons. Definitions Total variation for functions of one real variable EquationRef 1 Definition 1.1. The total variation of a real number real valued or more generally complex number ... mathematics interval . Total variation for functions of n 1 real variables EquationRef 2 Definition ... to math L 1 Omega math , the total variation of math f math in is defined as math V f, Omega sup ... function is a bounded set . Total variation in measure theory Following Harvtxt Saks 1937 p ... scriptstyle underline mathrm W mu, cdot math , respectively called upper variation and lower variation , as follows math overline mathrm W mu,E sup left mu A A in Sigma text and A subset E right ... W mu,E qquad forall E in Sigma math EquationRef 3 Definition 1.3. The variation also called absolute variation of the signed measure math mu math is the set function math mu E overline mathrm W mu,E left underline mathrm W mu,E right qquad forall E in Sigma math and its total variation is defined ... decomposition according to his version of this theorem, the upper and lower variation are respectively ... variation measure . If the measure math mu math is Complex number complex valued i.e. is a complex measure , its upper and lower variation cannot be defined and the Hahn&ndash Jordan decomposition ... Rudin 1966 pp 137&ndash 139 and define 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 ... of disjoint measurable subsets. The variation so defined is a positive measure see Harvtxt Rudin ... more details
Facilitated variation is a new theory that has been presented by Marc W. Kirschner , a professor and chair at the Department of Systems Biology, Harvard Medical School , and John C. Gerhart , a professor at the Graduate School, University of California, Berkeley . ref name Charlesworth2005 Cite journal last Charlesworth first Brian year 2005 title EVOLUTION on the Origins of Novelty and Variation journal Science volume 310 issue 5754 pages 1619 1620 doi 10.1126 science.1119727 url http toriah.org articles charlesworth 2005.pdf ref The theory of facilitated variation addresses the nature and function of genetic variability variation in evolution . Recent advances in cell biology cellular and developmental biology in the light of evolutionary biology shed light on a number of mechanisms for generating novelty. While the concept and mechanism of natural selection is well understood, the variation component of the evolutionary theory remains under developed. Variation mechanisms such as mutations, genetic drift, and genetic flow have been studied and documented thoroughly. The theory of facilitated variation is an effort to illustrate that seemingly complex biological systems can arise with a limited number of genes, and a limited number of variation mechanisms. This is accomplished by exploring the relation between the genotype and phenotype, specifically How are changes in the genotype translated to changes in the phenotype? Can environmental conditions affecting the phenotype affect the genotype? Since selection operates on the phenotype, how can physiological adaptability affect selection? The theory can be summarized in the following points Organisms have constrained and deconstrained ..., limbs, or the brain. Alternatively, facilitated variation asserts that the physiological ... in 2005. cite journal author Gerhart J, Kirschner M title The theory of facilitated variation journal ... Variation Category Evolutionary biology de Erleichterte Variation ... more details
In economics , compensating variation CV is a measure of utility change introduced by John Hicks 1939 . Compensating variation refers to the amount of additional money an agent would need to reach its initial utility after a change in prices, or a change in product quality, or the introduction of new products. Compensating variation can be used to find the effect of a price change on an agent s net welfare. CV reflects new prices and the old utility level. It is often written using an expenditure function , e p,u math CV e p 1, u 1 e p 1, u 0 math math w e p 1, u 0 math math e p 0, u 0 e p 1, u 0 math where math w math is the wealth level, math p 0 math and math p 1 math are the old and new prices respectively, and math u 0 math and math u 1 math are the old and new utility levels respectively. The first equation can be interpreted as saying that, under the new price regime, the consumer would accept CV in exchange for allowing the change to occur. More intuitively, the equation can be written using the value function , v p,w math v p 1,w CV u 0 math math e p 1,v p1,w CV e p 1,u 0 math math w CV e p 1,u 0 math math CV w e p 1,u 0 math one of the equivalent definitions of the CV . Compensating variation is the metric behind Kaldor Hicks efficiency if the winners from a particular policy change can compensate the losers it is Kaldor Hicks efficient, even if the compensation is not made. Equivalent variation EV is a closely related measure that uses old prices and the new utility level. It measures the amount of money a consumer would pay to avoid a price change, before it happens. When the good is neither normal nor inferior, or when there are no income effects for the good, then EV Equivalent variation CV Compensating Variation CS Consumer Surplus See also Equivalent variation EV is a closely related measure of welfare change. References Hicks, J.R. Value and capital An inquiry .... Category Welfare economics de Kompensierende Variation es Variaci n Compensatoria ru ... more details
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