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Encyclopedia results for Fisher information metric

Fisher information metric





Encyclopedia results for Fisher information metric

  1. Fisher information metric

    Context date February 2010 In information geometry , the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measure s defined on a common probability space . It can be used to calculate the informational difference between measurements. It takes the form math g jk int frac partial log p x, theta partial theta j frac partial log p x, theta partial theta k p x, theta , dx. math Where j and k index local coordinate axes. Substituting math i ln p math from information theory , the formula becomes math g jk int frac partial i x, theta partial theta j frac partial i x, theta partial theta k p x, theta , dx. math Which can be thought of intuitively as The distance between two points on a statistical differential manifold is the amount of information between them, i.e. the informational difference between them. An equivalent form of the above equation is math g jk int frac partial 2 i x, theta partial theta j partial theta k p x, theta , dx mathrm E left frac partial 2 i x, theta partial theta j partial theta k right . math A Riemannian metric defines the local geometry of most Riemannian manifolds of interest. See also Information geometry Cram r Rao bound Fisher information Bures metric References Shun ichi Amari Differential geometrical methods in statistics , Lecture notes in statistics, Springer Verlag, Berlin, 1985. Shun ichi Amari, Hiroshi Nagaoka Methods of information geometry , Translations of mathematical monographs v. 191, American Mathematical Society, 2000. Category Differential geometry Category Statistical distance measures ...   more details



  1. Fisher information

    Fisher information to differential geometry . In that context, this metric is known as the Fisher ... under different parametrization. In general, the Fisher information matrix provides a Riemannian metric ... mathcal I theta 1 ,. math See also Observed information Fisher information metric Formation matrix ...In mathematical statistics and information theory , the Fisher information sometimes simply called information .... Edgeworth . The Fisher information is also used in the calculation of the Jeffreys prior , which is used in Bayesian statistics. The Fisher information matrix is used to calculate the covariance matrices ... statistics, such as the Wald test . History The Fisher information was discussed by several early statisticians ... ref Savage 1976 , page 156 ref says In it Fisher information , he Fisher was to some extent anticipated ... ref ref Hald 1998,1999 ref Definition The Fisher information is a way of measuring the amount ... mathematics moment of the score is 0. The second moment is called the Fisher information math mathcal ... 0 leq mathcal I theta infty math . A random variable carrying high Fisher information implies that the absolute value of the score is often high. The Fisher information is not a function of a particular ... of the score statistics score is zero, the Fisher information is also the variance of the score ... conditions, then the Fisher information may also be written as ref Lehmann and Casella, eq. 2.5.16 ... right theta right ,. math Thus, the Fisher information is the negative of the expectation of the second ... of Fisher information, and the independence of h X from . More generally, if nowrap T t X is a statistic ... of the Fisher information is a lower bound on the variance of any unbiased estimator of ... which describes use of the Fisher information, informally Consider an unbiased estimator math ... limited by the Fisher Information of the likelihood function. Single parameter Bernoulli experiment ... 1 defines Fisher information. 2 invokes the fact that the information in a sufficient statistic is the same ...   more details



  1. Minimum Fisher information

    In information theory , the principle of minimum Fisher information MFI is a variational principle which, when applied with the proper constraints needed to reproduce empirically known expectation values, determines the best probability distribution that characterizes the system. See also Fisher information . Measures of information Measurement Information theory Information measures IM are the most important tools of information theory . They measure either the amount of positive information or of missing information an observer possesses with regards to any system of interest. The most famous IM is the so called Entropy information theory Shannon entropy 1948 , which determines how much additional information the observer still requires in order to have all the available knowledge regarding ... values, maximizes otherwise Shannon s IM. Fisher s information measure Fisher information Fisher s information FIM , named after Ronald Fisher , 1925 is another kind of measure, in two respects, namely, 1 it reflects the amount of positive information of the observer, br 2 it depends no only ... and versatility. Applications of the MFI Thermodynamics Much effort has been devoted to Fisher s information measure, shedding much light upon the manifold physical applications ref B. R. Frieden, Science from Fisher Information , Cambridge University Press, Cambridge, England, 2004. ref ref ... elements of such system. This is then a missing information measure. The IM is a functional of the PD ... a global one . The corresponding counterpart of MaxEnt is now the FIM minimization, since Fisher ... form does not change under translational transformations. In this case, Fisher measure becomes shift invariant. Such minimizing of Fisher s measure leads to a Schr dinger equation Schr dinger like equation ... s ref Zipf s law from a Fisher variational principle A. Hernando, D. Puigdom nech, D. Villuendas, C ... Category Information theory ...   more details



  1. Metric

    Wiktionary metric Metric s may refer to the metric system of measurement International System of Units , or Syst me International SI , the modern form of the metric system Metric ton , a measurement of mass equal to 1,000  kg an analytical measurement intended to quantify the state of a system. For example population density is one metric which may be used to describe a city. Metric mathematics , an abstraction of the notion of distance in a metric space Metric tensor , in mathematics, a symmetric rank 2 tensor, used to measure length and angle Metric band , a Canadian indie rock band Metrics networking , set of properties of a communication path Font Metrics Font metrics , a group of properties describing a font Reuse metrics , a quantitative indicator of an attribute for software reuse and reusability Router metrics , used by a router to make routing decisions Software metric s, a measure of some property of a piece of software or its specifications Performance metric s, a measure of an organization s activities and performance. METRIC a computer model Mapping EvapoTranspiration at high Resolution with Internalized Calibration that uses Landsat satellite data to compute and map evapotranspiration ET . See also Meter disambiguation Units of measurement Metric expansion of space disambiguation cs Metrika da Metrik de Metrik el es M trica desambiguaci n eo Metriko fr M trique pl Metryka ru sk Metrika sr sv Metrik uk ...   more details



  1. METRIC

    Other uses Metric disambiguation Metric METRIC is a computer model Mapping EvapoTranspiration at high Resolution with Internalized Calibration that uses Landsat satellite data to compute and map evapotranspiration ET developed by Richard Allen et.al. at the University of Idaho . ref Idaho Department of Water Resources Mapping Evapotranspiration http www.idwr.idaho.gov GeographicInfo METRIC et.htm ref Climate Change is a world wide problem that affects every country on earth. Understanding the processes and factors that control or affect ecosystem response to climate change is essential to mitigate impacts. Studying the regional to global radiation balance, hydrologic energy, water and carbon dioxide fluxes is important to understand effects of climate change on ecosystem health and evolution, including impacts of invasive species such as cheatgrass bromus tectorum in the western US. The exchanges of water and carbon at the plant atmosphere interface are coupled through the active control of leaf and needle stomata on the exchange of gas into or out of leaves with the atmosphere and by effects of direct evaporation from soil. Given the importance of carbon uptake and vapor outputs, the ability to quantify the uptake is important, particularly in large areas with significant capability to assimilate carbon. In the upper Snake River system of Idaho, the most common ecosystems, besides farms, are alpine forest, sage brush, invasive cheatgrass and bunch grass. A primary goal of this research is to contribute toward a better understanding and methods of quantifying the magnitude, timing, distribution and coupling of carbon, energy and water fluxes in these three dominant natural ecosystems, including effects of burning, and improve the accuracy of modeling sensible heat flux H ..., hydrosphere, atmosphere, and biosphere. METRIC helps us estimate surface energy flux s on a large ... that why METRIC is so valuable because it can produce ET maps that have values across the entire landscape ...   more details



  1. Bures metric

    of the statistical distance ref statdist between the quantum states. Quantum Fisher Information The Bures metric can be seen as the quantum equivalent of the Fisher information metric and can be rewritten ... mu d theta nu math where the quantum Fisher metric tensor components is identified as math J mu nu tr rho frac L mu L nu L nu L mu 2 . math The definition of the SLD implies that the quantum Fisher metric is 4 times the Bures metric. In other words, given that math g mu nu math are components of the Bures metric tensor, one has math J mu nu 4 g mu nu math As it happens with the classical Fisher information metric, the quantum Fisher metric can be used to find the Cram r Rao bound of the covariance . Explicit Formulas The actual computation of the Bures metric is not evident from the definition ... x 1 2 x 2 2 x 3 2 frac pi 2 8 math See also Fidelity of quantum states Fisher information Fisher information metric References Uhlmann, A., http www.ma.utexas.edu mp arc c 92 92 44.ps.gz The Metric of Bures ... of quantum and classical Fisher information to two level complex and quaternionic and three level complex systems , J. Math. Phys. 37, 2682, 1996. Paul B Slater, Quantum Fisher Bures information of two ...Orphan date April 2011 The Bures metric defines the infinitesimal distance between density matrix operators ... of the Bures metric include that given a target error, it allows the calculation of the minimum ... form of the Bures metric, valid for 2x2 and 3x3 systems, respectively math d rho, rho d ... 2 2 x 3 2 le 1 math . The components of the Bures metric in this parametrization can be calculated as math ... Mixed States , Seminar Sophus Lie, 73 , 1993. Dittmann J., Explicit formulae for the Bures metric ..., M., Computation of Uhlmann s parallel transport for density matrices and the Bures metric on three ... and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000 ... mechanics Category Quantum information science ...   more details



  1. Metric Commission

    , 1984 1984 federal election . This followed the abolition of the United States Metric Board by President Ronald Reagan in 1982. The Metric Commission was replaced by a small metric office within Industry Canada. By October of that same year, the metric office became the Measurement Information Division ... Information Division was shut down. The Metric Commission Order remains in force under the Industry ...Image Canadian Metric Movement.svg right thumb Logo of the Metric Commission The Metric Commission , formally the Preparatory Commission for the Conversion to the Metric System was a Canada Canadian government agency established by the Government of Canada federal government in 1971 to facilitate Metrication in Canada Canada s conversion to the Metric system from the imperial system of weights and measures and to educate the public on the Metric system. The Commission was formed following the release of The White Paper on Metric Conversion , a January 1971 federal government document which noted most nations had adopted the metric system and anticipated that the Metrication in the United States ... 10612 science technology metric system clip1 accessdate 2007 11 11 date 4 February 1970 title The metric ... had been vocal in their opposition to the metric system during the previous Liberal Party ... technology metric system clip1 accessdate 2007 11 11 date 27 September 1977 title The great Canadian metric debate publisher CBC Television work 90 Minutes Live ref The agency was abolished on March ... accessdate 2007 11 11 date 2 February 2006 title Population Affiliation Report Metric Commission ... ca regu crc972 title Metric Commission Order, C.R.C., c. 972 accessdate 2007 11 11 date 1971? federal government order which created the Metric Commission See also Metrication in Canada Metrication ... External links cite web url http www.canlii.org ca regu crc972 title Metric Commission Order, C.R.C., c. 972 accessdate 2007 11 11 date 1971? federal government order which created the Metric Commission ...   more details



  1. Fisher

    Wiktionary fisher dablink Homonyms include Fischer and fissure Fisher is an archaic term for fisherman , revived as gender neutral. Fisher or Fishers may also refer to Fisher animal Martes pennanti , a North American mustelid Fisher band , a rock band featuring Kathy Fisher as lead singer Fisher yachts , famous British motorsailers Fisher comic strip Fisher comic strip , a Canadian comic strip by Philip Street The Fisher The Fisher A brand of high fidelity audio equipment marketed by Avery Fisher Sergey Golovkin 1959 1996 , a Russian serial killer known as The Fisher Places Australia Fisher, Australian Capital Territory Fisher Island Queensland Fisher Island Tasmania Fisher Island Reef , Tasmania Division of Fisher , an electoral district in the Australian House of Representatives, in Queensland Electoral district of Fisher , a state electoral district in South Australia United Kingdom Fisher Bank , a sea area of the UK shipping forecast United States Fisher, Arkansas Fisher, California disambiguation , multiple locations Fisher, Humboldt County, California Fisher, Shasta County, California Fisher, Illinois Fisher, Louisiana Fisher, Minnesota Fisher, Pennsylvania Fisher Island, Florida Fishers, Indiana Fishers, New York Fishers Island, New York People See Fisher surname Other the Fisher meteorite of 1894, which landed in Minnesota, United States see meteorite falls Max M. Fisher College of Business also known as Fisher College , a unit of The Ohio State University Fisher Athletic F.C. , defunct football club in England Fisher Electronics , a Sanyo subsidiary producing low cost hi fi equipment Fisher F.C. , football club based in England Fisher Site , archaeological site in the USA Fisher Farm Site , archaeological site in the USA Fisher s exact test , a statistical significance test Fisher s method , also known as Fisher s combined probability test Sam Fisher disambiguation , multiple people Elena Fisher , character from the Uncharted video game series Fisher equation ...   more details



  1. Metric conversion

    Metric conversion may refer to Converting a non metric quantity to the metric equivalent see Conversion of units Conversion of a country from non metric units to metric units see Metrication disambiguation ...   more details



  1. Metric tree

    title Satisfying General Proximity Similarity Queries with Metric Trees journal Information Processing ...About the data structure the type of metric space Real tree A metric tree is any tree data structure tree data structure specialized to index data in metric space s. Metric trees exploit properties of metric spaces such as the triangle inequality to make accesses to the data more efficient. Examples include the M tree , vp tree s, cover tree s, MVP Tree s, and bk tree s. ref name Samet cite book last Samet first Hanan title Foundations of multidimensional and metric data structures year 2006 publisher Morgan Kaufmann isbn 978 0 12 369446 1 url http books.google.dk books?id KrQdmLjTSaQC ref should have a list and summary of metric trees, with links to the main articles. Multidimensional search Most algorithms and data structures for searching a dataset are based on the classical binary search algorithm, and generalizations such as the k d tree or range tree work by interleaving the binary search algorithm over the separate coordinates and treating each spatial coordinate as an independent search constraint. These data structures are well suited for range query problems asking for every point math x,y math that satisfies math mbox min x leq x leq mbox max x math and math mbox min y leq y leq mbox max y math . A limitation of these multidimensional search structures is that they are only defined for searching over objects that can be treated as vectors. They aren t applicable for the more ... to a given query image. Metric data structures If there is no structure to the similarity measure .... The first article on metric trees, as well as the first use of the term metric tree , published ... data structures, and research on metric tree data structures blossomed in the late 1990s and included ... conference last Brin first Sergey title Near Neighbor Search in Large Metric Spaces booktitle 21st International Conference on Very Large Data Bases VLDB date 1995 ref The first textbook on metric ...   more details



  1. String metric

    In mathematics and computer science , a string metric also known as a string similarity metric or string distance function is a metric mathematics metric that measure similarity or dissimilarity distance between two string computer science text strings for approximate string matching or comparison and in fuzzy string searching . For example the strings Sam and Samuel can be considered to be similar. A string metric provides a number indicating an algorithm specific indication of similarity. The most widely known string metric is a rudimentary one called the Levenshtein distance Levenshtein Distance also known as Edit Distance . It operates between two input strings, returning a score equivalent to the number of substitutions and deletions needed in order to transform one input string into another. Simplistic string metrics such as Levenshtein distance have expanded to include phonetic, token parser token , grammatical and character based methods of statistical comparisons. A widespread example of a string metric is DNA sequence analysis and RNA analysis, which are performed by optimised string metrics to identify matching sequences. String metrics are used heavily in information integration and are currently used in areas including fraud detection , fingerprint analysis , plagiarism detection , ontology merging , DNA analysis , RNA analysis, image analysis , evidence based machine learning, database data deduplication , data mining , Web interfaces, e.g. Ajax programming Ajax ... Soundex distance metric Matching coefficient Dice s coefficient Jaccard similarity or Jaccard coefficient ... similarity Variational distance Hellinger distance or Bhattacharyya distance Information radius Jensen Shannon divergence Harmonic mean Skew divergence Confusion probability Tau metric , an approximation of the Kullback Leibler divergence Fellegi and Sunters metric SFS TFIDF or TF IDF Maximal ... http www.dcs.shef.ac.uk sam stringmetrics.html ukkonen DEFAULTSORT String Metric Category String ...   more details



  1. Metric gauge

    Metric gauge may refer to Metre gauge , a rail gauge Any Gauge engineering gauge or Pressure measurement pressure gauge that reads in Metric system metric measurements disambig ...   more details



  1. Acoustic metric

    In mathematical physics , a metric mathematics metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal carrying properties characteristic of a given particulate medium in acoustics , or in fluid dynamics . Other descriptive names such as sonic metric are also sometimes used, interchangeably. A simple fluid example For simplicity, we will assume that the underlying background geometry is Euclidean , and that this space is filled with an isotropic inviscid fluid at zero temperature e.g. a superfluid . This fluid is described by a density field and a velocity field math vec v math . The speed of sound at any given point depends upon the compressibility which in turn depends upon the density at that point. This can be specified by the speed of sound field c. Now, the combination of both isotropy and Galilean ... that sound is like light moving though a spacetime described by an effective metric tensor called the acoustic metric . The acoustic metric math mathbf g g 00 dt otimes dt 2g 0i dx i otimes dt g ij .... Acoustic horizons Main Sonic black holes An acoustic metric can give rise to acoustic horizons also known as sonic horizons , analogous to the event horizons in the spacetime metric of general relativity. However, unlike the spacetime metric, in which the invariant speed is the absolute upper limit on the propagation of all causal effects, the invariant speed in an acoustic metric is not the upper ... metric. It is possible for certain physical effects to propagate back across an acoustic ..., since a generic analog model depends upon BOTH the acoustic metric AND the underlying background ... geometry. See also Analog models of gravity Hawking radiation gravastar acoustics metric mathematics ... evaporation Phys. Rev. Lett. 46 1981 , 1351 1353. font considers information leakage through a transsonic ...   more details



  1. Metric map

    In the mathematics mathematical theory of metric space s, a metric map is a Function mathematics function between metric spaces that does not increase any distance such functions are always continuous function continuous . These maps are the morphism s in the category of metric spaces , Met Isbell 1964 . They are also called Lipschitz continuity Lipschitz functions with Lipschitz constant 1, nonexpansive maps , nonexpanding maps , weak contractions , or short maps . Specifically, suppose that X and Y are metric spaces and is a function mathematics function from X to Y . Thus we have a metric map when, for any points x and y in X , math d Y f x ,f y leq d X x,y . math Here d sub X sub and d sub Y sub denote the metrics on X and Y respectively. A map between metric spaces is an isometry if and only if 1 it is metric, 2 it is a bijection , and 3 its inverse functions inverse is also metric. The composite function composite of metric maps is also metric. Thus metric spaces and metric maps form a category theory category Category of metric spaces Met Met is a subcategory of the category of metric spaces and Lipschitz functions, and the isomorphism s in Met are the isometries. One can say that is strictly metric if the inequality mathematics inequality is strict for every two different points. Thus a contraction mapping is strictly metric, but not necessarily the other way around. Note that an isometry is never strictly metric, except in the degeneracy mathematics degenerate case of the empty set empty space or a single point space. References cite journal author Isbell, J. R. authorlink John R. Isbell title Six theorems about injective metric spaces journal Comment. Math. Helv. volume 39 year 1964 pages 65 76 url http www.digizeitschriften.de resolveppn GDZPPN002058340 doi 10.1007 BF02566944 Category Metric geometry Category Lipschitz maps Geometry stub es Funci n corta fr Application non expansive it Funzione non espansiva pl Odwzorowanie nierozszerzaj ce pt Fun o ...   more details



  1. Performance metric

    mergeto performance measurement discuss Talk Performance metric Merge of article date October 2011 A performance metric is a measure of an organization s activities and performance. Performance metrics should support a range of Stakeholder corporate stakeholder needs from customers , shareholders to employees ref Mark Graham Brown, Using the Right Metrics to Drive World class Performance ref . While traditionally many metrics are financed based, inwardly focusing on the performance of the organization, metrics may also focus on the performance against customer requirements and Value marketing value . ref http www.leanyourcompany.com methods Value based performance metrics.asp Value based performance metrics ref In project management , performance metrics are used to assess the health of the project and consist of the measuring of six criteria time, cost, resources, scope, quality, and actions. ref http www.pmhut.com measuring project health Measuring Project Health Neville Turbit, 2008 ref Developing performance metrics usually follows a process of Establishing critical processes customer requirements, Developing measures, Establishing targets which the results can be scored against. A criticism of performance metrics is that when the value of information is computed using mathematical methods, it shows that even performance metrics professionals choose measures that have little value. This is referred to as the measurement inversion . ref Douglas Hubbard, The IT Measurement Inversion , CIO Magazine , 1999 ref ref Douglas Hubbard, How to Measure Anything Finding the Value of Intangibles in Business . John Wiley & Sons, 2007 ref For example, metrics seem to emphasize what organizations ... inversion other methods, like applied information economics , introduce the value of information ... information. Often closely tied in with outputs, performance metrics should usually encourage improvement ... DEFAULTSORT Performance Metric Category Business terms ...   more details



  1. Metric dimension

    In mathematics , the term metric dimension has various meanings. The Metric dimension graph theory metric dimension of an undirected graph G is the minimum number of vertices in a subset S of G such that all other vertices are uniquely determined by their distances to the vertices in S . The Minkowski Bouligand dimension also called the metric dimension is a way of determining the dimension of a fractal set in a Euclidean space by counting the number of fixed size boxes needed to cover the set as a function of the box size. The equilateral dimension of a metric space also called the metric dimension is the maximum number of points at equal distances from each other. The Hausdorff dimension is an Extended real number line extended non negative real number associated with any metric space that generalizes the notion of the dimension of a real vector space. mathdab ...   more details



  1. Karlsruhe metric

    In metric geometry , the Karlsruhe metric the name alludes to the layout of the city of Karlsruhe is a measure of distance that assumes travel is only possible along radial streets and along circular avenues around the center. ref http www.personal.kent.edu rmuhamma Compgeometry MyCG CG Applets VoroKarlsruhe karlcli.htm Karlsruhe Metric Voronoi Diagram ref See also Metric mathematics Manhattan distance Hamming distance Notes Reflist External links http www.nirarebakun.com voro ekarl.html Karlsruhe metric Voronoi diagram , by Takashi Ohyama http www.personal.kent.edu rmuhamma Compgeometry MyCG CG Applets VoroKarlsruhe karlcli.htm Karlsruhe Metric Voronoi Diagram , by Rashid Bin Muhammad Category Digital geometry Category Metric geometry ...   more details



  1. Fisher & Fisher

    File Midland Savings Building.jpg thumb Midland Savings Building, downtown Denver Fisher & Fisher, 1926 File Railway Exchange Building.JPG thumb Railway Exchange New Building, downtown Denver Fisher, Fisher & Howell, 1937 and adjoining Railway Exchange Extension Fisher & Fisher, 1909 13 Fisher & Fisher was an architectural firm based in Denver, Colorado named for partners William Ellsworth Fisher 1871 1937 and Arthur Addison Fisher 1878 1965 . ref http eadsrv.denverlibrary.org sdx pl doc tdm.xsp?id WH932 d0e33&fmt text&base fa Historical Note, Fisher and Fisher Architectural Records, Western History ... The Fisher Legacy mdash William Ellsworth Fisher, Arthur Addison Fisher, Alan Berney Fisher date 11 July 2000 accessdate November 24, 2011 ref The firm was founded in 1892 by William Ellsworth Fisher as William Fisher, Architect. After ten years in practice alone, mainly designing starter homes, he partnered with Daniel Riggs Huntington from 1901 to 1905 as Fisher & Huntington, during which time ... more became William Fisher, Architect until 1907, when William was joined by his younger brother Arthur Addison Fisher they worked together as William Fisher Architect and Brother until 1910 and then as William E. Fisher and Arthur A. Fisher, Architects until William s death in 1937. William s son Alan B. Fisher , who had previously joined the firm, then became his uncle s partner and the firm was renamed Arthur A. Fisher and Alan B. Fisher, Architects. From 1956 to 1959 they were joined by Rodney S. Davis as Fisher, Fisher and Davis on Arthur s retirement the firm became Fisher and Davis. Finally beginning in 1967, Alan Fisher was in partnership with John D. Reece and Hilary M. Johnson as Fisher ... in Denver identifiable as being by Fisher & Fisher, 50 are either listed on the U.S. National Register .... ref name colorado Although most work by Fisher & Fisher was in Denver, buildings by them elsewhere ..., William and Arthur Fisher planned the town of Parco, Wyoming now Sinclair, Wyoming Sinclair and designed ...   more details



  1. Lévy metric

    In mathematics , the L vy metric is a metric mathematics metric on the space of cumulative distribution function s of one dimensional random variable s. It is a special case of the L vy Prokhorov metric , and is named after the France French mathematician Paul Pierre L vy . Definition Let math F, G mathbb R to 0, infty math be two cumulative distribution functions. Define the L vy distance between them to be math L F, G inf varepsilon 0 F x varepsilon varepsilon leq G x leq F x varepsilon varepsilon mathrm ,for ,all , x in mathbb R . math Intuitively, if between the graphs of F and G one inscribes squares with sides parallel to the coordinate axes at points of discontinuity of a graph vertical segments are added , then the side length of the largest such square is equal to  L F ,  G . See also C dl g L vy Prokhorov metric Wasserstein metric References springer author V.M. Zolotarev id l l058310 title L vy metric Category Measure theory Levy metric Category Metric geometry Levy metric Category Probability theory Levy metric ...   more details



  1. Peres metric

    Orphan date January 2010 The Peres metric tensor metric is defined by the proper time math d tau 2 dt 2 2f , t z, ,x, ,y dt dz 2 dx 2 dy 2 dz 2 math for any arbitrary function f . If f is a harmonic function with respect to x and y , then the corresponding Peres metric satisfies the Einstein field equations in vacuum . Such a metric is often studied in the context of gravitational waves . The metric is named for Israel i physicist Asher Peres , who first defined the metric in 1959. References Peres, A. Some Gravitational Waves. Phys. Rev. Lett. 3, 571 1959 Category Gravitation physics stub ...   more details



  1. Metric Martyrs

    The Metric Martyrs are a British advocacy group based in the United Kingdom who campaign for the freedom to choose what units of measurement are presented. The group states that it believes that vendors should have the freedom to mark their goods with any units they choose. This can be solely imperial units , solely metric units or both. Citation needed date August 2010 Background The advocacy group ... imperial measures, including not displaying metric signage, and for using unstamped weighing machines which had had their stamps removed by the authorities . Newspapers dubbed the group the metric martyrs ... Metric 20Culprits.htm title BMWA Metric Culprits accessdate 2009 02 06 ref Legal cases ... were not capable of weighing in the metric system as well as imperial, and hence were no longer ... law does not prohibit the use of imperial units when selling loose goods, but metric units must be displayed ... skynews article 0,,30100 13014828,00.html title Metric Martyr Is Dead publisher Sky News work ... en.pdf title 1999 No. 3042 PRICES The Price Marking Order 1999 publisher Office of Public Sector Information ... publisher Office of Public Sector Information date 9 July 1974 accessdate 2010 05 18 ref of delivering ..., required him to label his goods in metric quantities with imperial quantities allowed only as optional ... to EEC EU weights and measures directives had required the use of metric units for certain activities ... permitted the equivalent imperial unit to be displayed alongside the metric unit as a supplementary ... Commission announced that for the cases where metric units were required, it had extended the option ... url http news.bbc.co.uk 1 hi england wear 6918912.stm title MP calls for metric martyr pardon publisher ... title EU ends pointless battle to make UK metric publisher TimesOnline work timesonline.co.uk ... the provision of quantity information and the sale of goods by quantity. ref cite web url http ... Category History of the United Kingdom Category Anti metrication de Metric Martyrs ...   more details



  1. Metric prefix

    Use dmy dates date February 2012 common metric prefixes A metric prefix or SI prefix is a unit prefix that precedes a basic unit of measure to indicate a decimal decadic multiple mathematics multiple or fraction mathematics fraction of the unit. Each prefix has a unique symbol that is prepended to the unit ... have been a feature of all forms of the metric system with many dating back to the system s introduction in the 1790s. Metric prefixes have even been appended to non metric units. Today the prefixes ... of the metric system in the 1790s, long before the 1960 introduction of the SI. The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not e.g. millidynes and milligauss . Metric prefixes may also be used with non metric ... is occasionally used to disambiguate the metric tonne from the various non metric tons. An exception ... thousand gram calories. It is common to apply metric prefixes to the gram calorie but not the kilogram calorie. Non metric units Metric prefixes rarely appear with imperial units imperial or United ... XXXVI myriametres from Basel Former metric prefixes Some of the prefixes formerly used in the metric ... cite web url http lamar.colostate.edu hillger laws metric act bill.html title H.R. 596, An Act to authorize the use of the metric system of weights and measures author 29th Congress of the United ... date accessdate 1 March 2012 ref were parts of the original metric system adopted ... kg was the metric replacement for an avoirdupois unit, the quarter 25 pounds . see also myriogramme ... 1 March 2012 ref where MMbbl is the symbol for millions of barrels . In the information technology field a series of binary prefix es is used with the information units the bit and byte . Being based on 2 sup 10 sup gaps 1 024 , these are of comparable size to the metric prefixes and have traditionally ... units with limited char sets.pdf?func doc.Fetch&nodeid 4289384 International Standard ISO 2955 Information ...   more details



  1. Metric system

    about the metric system in general information about specific versions of the system, such as the International ..., suggest that this information is out of date ref cite web url http www.cl.cam.ac.uk mgk25 metric ... See introduction Introduction to the metric system Image FourMetricInstruments.JPG thumb 280px The metric ... that have metric calibrations are shown. Three of the objects, a tape measure calibrated in centimetre ... use by tradesmen . The metric system is an international decimal ised systems of measurement ... have been refined and the metric system extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries ... industrialized country that does not use the metric system as its official system of measurement, although the metric system has been officially sanctioned for use there since 1866. Although the United Kingdom committed to officially adopting the metric system for many measurement applications ... of these prototypes can be retired by 2014. From its beginning, the main feature of the metric system .... The uncoordinated use of the metric system by different scientific and engineering disciplines, particularly ... standard internationally recognised standard metric system. Features Although the metric system ... internationally recognised characters. The metric system was, in the words of the French philosopher ... of prefixes that have now been defined in SI. ref SI Brochure 3.1 SI prefixes p 103 ref The metric .... However, these overtures failed and the custody of the metric system remained in the hands of the French ... Decimal multiples The metric system is decimal, except where the non SI units for time and plane angle ... MacTutor Decimal prefixes are a characteristic of the metric system conversions between units of different ... to overcome this problem while retaining the other benefits of the metric system by replacing all ... of Great Britain accessdate 23 April 2012 ref Prefixes common metric prefixes Main metric prefix A common ...   more details



  1. The Fisher

    The Fisher was the brand name for high fidelity hi fi electronic equipment manufactured in New York by The Fisher ... founder, Avery Fisher . ref name Stereophile ref name Life cite book url http books.google.com books?id YVYEAAAAMBAJ&pg PA14&dq 22The Fisher 22 stereo&hl en&ei kpRBTNWaGYOcsQP5kZmrDA&sa X&oi book result&ct result&resnum 9&ved 0CFsQ6AEwCA v onepage&q 22The 20Fisher 22 20stereo&f false title Ad for The Fisher ...?id xV6tghvO0oMC&pg PA397&dq 22The Fisher 22 stereo&hl en&ei kpRBTNWaGYOcsQP5kZmrDA&sa X&oi book result&ct ... 1960s models were also available as kits. Fisher tube equipment is considered quite collectible today. Fisher s first receiver was the model 500, a mono AM FM receiver using two EL37 output tubes. It had ... Amplifier The Fisher was also used on Fisher s early US made solid state equipment, such as the model 210 receiver. Fisher FM tuners and receivers often used similar designs and components thus allowing ... module. ref name Stereophile cite web url http stereophile.com historical 605fisher title Fisher 500 ... Fairly Rare Fisher Allegro Model X19 Tube 20 Watt Stereo Amplifier and Matching FM Multiplex Tuner Circa 1962 Image Fisher Allegro 007.jpg Fisher Allegro A19 Tube Tuner and Model X19 Amplifier As removed from portable console Image 800BFacplateCrop.jpg Circa 1962 Fisher Model 800B AM FM Tube Stereo Receiver 32 Watts Per Channel 429.00 list price Image 800BRear.jpg The Business Side Fisher 800B Tube Stereo Receiver Image 800BbeamFMcrop.jpg Fisher often used the Tuning Eye or Stereo Beam as shown on the Model 800B Image Fisher64b.JPG 1964 Fisher Marketing Brochure and Price List Guide Image Fisher64c.JPG Typical Fisher Marketing Brochure From This Period Circa 1964 Image Realistic214Front.jpg Extremely Rare Model 214 FM Multiplex Tube Tuner made by Fisher and sold with Realistic badging through ... FM Multiplex Tube Tuner made by Fisher and sold with Realistic badging through Radio Shack Stores ... fisher.htm The Fisher, history and hifi classics hifi studio.de HiFi Classics. Private German project ...   more details



  1. Metric foot

    for the poetical term foot prosody A metric foot is a nickname occasionally used in the United Kingdom for a length of 300 millimetre s 30  cm . A metric foot can be divided into twelve metric inch es of 25 millimetre s 2.5  cm each. The metric foot and inch are therefore 4.8 and 0.4 millimetres or about frac 1 60 shorter than an Imperial unit imperial Foot length foot and inch respectively. The term metric foot does not appear in any British Standard . The practice of choosing multiples of 300  mm and 600  mm as preferred dimension s in the construction industry originated from the international standard on modular coordination ISO 2848 . These numbers were chosen because of their large number of divisors. Any multiple of 600 mm can be evenly divided into 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, etc. parts. While the term metric foot is still occasionally used in the United Kingdom , in particular in the timber trade, dimensions are most likely to be quoted exclusively in metric units today. The sizes of the studios at BBC BBC Television Centre Television Centre in London , which opened in 1960, are specified and measured in metric feet a contrast to film stages where imperial feet and inches prevail. Historically in France, under the mesures usuelles system intermediary between traditional French units of measurement French units and metric units , a metric foot was exactly a third of a metre frac 333 1 3   mm . See also Tonne metric ton Metric mile Decimal Dozen Further reading British Standard BS 6750 Modular coordination in building. Martin Kempton http www.tvstudiohistory.co.uk tv 20centre 20history.htm An unofficial history of Television Centre Category Units of length Category Non SI metric units Category Metrication Category Decimalisation ...   more details




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