Wiktionary metricMetric 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
Other uses Metric disambiguation MetricMETRIC 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
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
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
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
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
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
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
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
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 ..., 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 ... 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
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
In mathematics , the product metric is a definition of metric mathematics metric on the Cartesian product of two metric spaces . As described below, the p product metric of the Cartesian product of n metric spaces is the Lp space p norm of the n vector of the norms of the n subspaces math d p mathbf x 1, dots, mathbf x n d 1 mathbf x 1 , dots, d n mathbf x n p math Definition Let math X, d X math and math Y, d Y math be metric spaces and let math 1 leq p leq infty math . Define the math p math product metric math d p math on math X times Y math by math d p left x 1 , y 1 , x 2 , y 2 right left d X x 1 , x 2 p d Y y 1 , y 2 p right 1 p math for math 1 leq p infty math math d infty left x 1 , y 1 , x 2 , y 2 right max left d X x 1 , x 2 , d Y y 1 , y 2 right . math for math x 1 , x 2 in X math , math y 1 , y 2 in Y math . Choice of norm For Euclidean space s, using the L sub 2 sub norm gives rise to the Euclidean metric in the product space however, any other choice of p will lead to a topologically equivalent metric space. In the category of metric spaces , the sup norm is used. References citation last1 Deza first1 Michel Marie author1 link Michel Deza last2 Deza first2 Elena page 83 publisher Springer Verlag title Encyclopedia of Distances url http books.google.com books?id LXEezzccwcoC&pg PA83 year 2009 . DEFAULTSORT Product Metric Category Metric geometry ... more details
In the mathematics mathematical study of metric spaces , one can consider the arclength of paths in the space ... to that distance. The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the length of all paths from one point to the other. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space. Definitions Let math M, d , math be a metric space . We define a new metric math d I , math on math M , math , known as the induced intrinsic metric , as follows math d I x,y , math is the infimum of the lengths ... M, d , math is a length space or a path metric space and the metric math d , math is intrinsic . We say that the metric math d , math has approximate midpoints if for any math varepsilon 0 math ... 2 varepsilon math . Examples Euclidean space R sup n sup with the ordinary Euclidean metric is a path metric space. R sup n sup 0 is as well. The unit circle S sup 1 sup with the metric inherited from the Euclidean metric of R sup 2 sup the chordal metric is not a path metric space. The induced intrinsic metric on S sup 1 sup measures distances as angle s in radian s, and the resulting length metric space is called the Riemannian circle . In two dimensions, the chordal metric on the sphere is not intrinsic, and the induced intrinsic metric is given by the great circle distance . Every Riemannian manifold can be turned into a path metric space by defining the distance of two points as the infimum ... is defined included Finsler manifold s and sub Riemannian manifold s. Any complete metric space complete and convex metric space is a length metric space harv Khamsi Kirk 2001 loc Theorem 2.16 , a result of Karl Menger . The converse does not hold in general, however there are length metric spaces ... by d . The space M , d sub l sub is always a path metric space with the caveat, as mentioned above, that d sub l sub can be infinite . The metric of a length space has approximate midpoints. Conversely ... more details
A spill metric is a Heuristic computer science heuristic metric used by Register allocation register allocators to decide which registers to spill. Popular spill metrics are cost degree introduced in Chaitin s algorithm cost degree sup 2 sup emphasizes the spill s effect on neighbours cost emphasizes Run time program lifecycle phase run time minimising number of spill operations Where cost is the estimated cost of spilling a value from registers into memory. DEFAULTSORT Spill Metric Category Digital registers compu stub ... more details
Notability date July 2010 Metric Today is the newsletter of the U.S. Metric Association . It features the latest developments in US metrication efforts. In the spirit of international standardization, it is dimensioned to the A4 paper size . External links http lamar.colostate.edu hillger mtoday.htm Official site Category Metrication ... more details
Image Metric Marvels.png thumb right The Metric Marvels, from left to right Meter Man, Liter Leader, Wonder Gram and Super Celsius The Metric Marvels is a series of seven animation animated educational short film shorts featuring songs about metre meters , litre liters , Celsius , and gram s, designed to teach United States American children how to use the metric system . They were produced by George Newall Newall & Thomas G. Yohe Yohe , the same advertising agency which produced American Broadcasting Company ABC s popular Schoolhouse Rock series, and first aired on the NBC television network in September 1978. Voices for the Metric Marvels shorts included Lynn Ahrens , Bob Dorough , Bob Kaliban , and Paul Winchell . Origins On December 23, 1975, President Gerald Ford signed the Metric Conversion Act into law this act gave official sanction for the United States to convert to the metric system of measurement. Traditionally, the United States has used and continues to prefer the United States customary units U.S. Customary system over metric measurements. Ford s presidential successor, Jimmy Carter , began to implement this law in earnest, helping to set up the U.S. Metric Board as a task force to determine when and how the U.S. would Metrication in the United States convert to metrics ... service announcement s on radio and television. The Metric Marvels was one such television PSA, aired during NBC s Saturday morning cartoons. The shorts featured four animated metric superheroes Liter ... children the difference between the old English system and the new metric system. Episodes 1 1 Meet Meter Man superhero Meter Man helps people convert length and distance to metric terms 1 2 Mara Mara ... Baby a young Wonder Gram converts pounds to kilograms Effectiveness Ultimately, The Metric Marvels failed to convince Americans to convert to the metric system. Although it shared the animation style ... 0320888 The Metric Marvels tv.com 19791 The Metric Marvels DEFAULTSORT Metric Marvels, The Category ... more details
This article is about the concept in Riemannian geometry . For the typographic concept, see Typeface Font metrics . Merge to metric connection discuss Talk metric connection merge metric compatibility here? date September 2011 In mathematics, given a metric tensor math g ab math , a covariant derivative is said to be compatible with the metric if the following condition is satisfied math nabla c , g ab 0. math Although other covariant derivatives may be supported within the metric, usually one only ever considers the metric compatible one. This is because given two covariant derivatives, math nabla math and math nabla math , there exists a tensor for transforming from one to the other math nabla a x b nabla a x b C ab c x c. math If the space is also torsion tensor torsion free , then the tensor math C ab c math is symmetric in its first two indices. References cite arxiv last Rodrigues first W. A. last2 Fern ndez first2 V. V. last3 Moya first3 A. M. year 2005 title Metric compatible covariant derivatives eprint math 0501561 Citation last Wald first Robert M. title General Relativity book General Relativity publisher University of Chicago Press year 1984 isbn 0 226 87033 2 Category Differential geometry Category Riemannian geometry Relativity stub ... more details
In mathematics , a metric connection is a connection vector bundle connection in a vector bundle E equipped with a metric vector bundle metric Red link until someone wants to write an appropriate article. metric tensor isn t right. for which the inner product of any two vectors will remain the same when those vectors are parallel transport ed along any curve. Other common equivalent formulations of a metric connection include A connection for which the connection vector bundle covariant derivative s of the metric on E vanish. A connection principal bundle principal connection on the bundle of orthonormal frame s of E . A special case of a metric connection is the Levi Civita connection . Here the bundle E is the tangent bundle of a manifold. In addition to being a metric connection, the Levi Civita connection is required to be torsion tensor torsion free . Riemannian connections An important special case of a metric connection is a Riemannian connection . This is a connection math nabla math on the tangent bundle of a pseudo Riemannian manifold M , g such that math nabla X g 0 math for all vector fields X on M . Equivalently, math nabla math is Riemannian if the parallel transport it defines preserves the metric g . A given connection math nabla math is Riemannian if and only if math Xg Y,Z g nabla XY,Z g Y, nabla XZ math for all vector fields X , Y and Z on M , where math Xg Y,Z math denotes the derivative of the function math g Y,Z math along this vector field math X math . The Levi Civita connection is the torsion tensor torsion free Riemannian connection on a manifold. It is unique by the fundamental theorem of Riemannian geometry . External links http projecteuclid.org Dienst UI 1.0 Summarize euclid.cmp 1103858479 a pdf about this Category Connection mathematics Category Riemannian geometry differential geometry stub de Metrischer Zusammenhang ru ... more details
In mathematics , the metric derivative is a notion of derivative appropriate to Parametric equation parametrized path topology paths in metric space s. It generalizes the notion of speed or absolute velocity to spaces which have a notion of distance i.e. metric spaces but not direction such as vector space s . Definition Let math M, d math be a metric space. Let math E subseteq mathbb R math have a limit point at math t in mathbb R math . Let math gamma E to M math be a path. Then the metric derivative of math gamma math at math t math , denoted math gamma t math , is defined by math gamma t lim s to 0 frac d gamma t s , gamma t s , math if this Limit mathematics limit exists. Properties Recall that absolute continuity AC sup p sup I X is the space of curves I X such that math d left gamma s , gamma t right leq int s t m tau , mathrm d tau mbox for all s, t subseteq I math for some m in the Lp space L sup p sup space L sup p sup I R . For AC sup p sup I X , the metric derivative of exists for Lebesgue measure Lebesgue almost all times in I , and the metric derivative is the smallest m L sup p sup I R such that the above inequality holds. If Euclidean space math mathbb R n math is equipped with its usual Euclidean norm math math , and math dot gamma E to V math is the usual Fr chet derivative with respect to time, then math gamma t dot gamma t , math where math d x, y x y math is the Euclidean metric. References cite book author Ambrosio, L., Gigli, N. & Savar , G. title Gradient Flows in Metric Spaces and in the Space of Probability Measures publisher ETH Z rich, Birkh user Verlag, Basel year 2005 isbn 3 7643 2428 7 Category Differential calculus Category Metric geometry ... more details
In mathematics , a metric space is a Set mathematics set where a notion of distance called a metric mathematics metric between elements of the set is defined. The metric space which most closely corresponds ... of metric is a generalization of the Euclidean metric arising from the four long known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length ... depend on the metric chosen, and by using a different metric we can construct interesting non Euclidean geometries such as those used in the theory of general relativity . A metric space also induces ... abstract topological space s. History Expand section Reasons for generalizing the Euclidean metric, first ... metric spaces in his work Sur quelques points du calcul fonctionnel , Rendic. Circ. Mat. Palermo 22 1906 1 74. Definition A metric space is an ordered pair math M,d math where math M math is a set and math d math is a metric mathematics metric on math M math , i.e., a function math d colon ... writes math M math for a metric space if it is clear from the context what metric is used. Examples of metric spaces Finite Metric space redirects here Ignoring mathematical details, for any system of roads ... route connecting those locations. To be a metric there shouldn t be any one way roads. The triangle ... n math space with the Euclidean distance , are complete space complete metric spaces. The rational number s with the same distance also form a metric space, but are not complete. The positive real numbers with distance function math d x,y vert log y x vert math is a complete metric space. Any normed vector space is a metric space by defining math d x,y lVert y x rVert math , see also Metric 28mathematics ... metric space complete , we call it a Banach space . Examples The Norm mathematics Taxicab norm or Manhattan ... chess chess king would take to travel from math x math to math y math . The British Rail metric also called the Post Office metric or the SNCF metric on a normed vector space is given by math d x ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name Alex Metric background non performing personnel alias Alex Drury origin London , England genre House music House , techno , funk years active 2008 present associated acts The Infadels br Charli XCX website URL alexmetric.com Alex Metric born Alex Drury is a British musician, DJ and producer. He has released numerous EPs, remixed artists ... for acts such as The Infadels , Charli XCX and Adam Freeland . Career Alex Metric started ... http www.marineparade.net artists alex metric ref In 2009, Metric joined Radio 1 s In New DJs We Trust with his first show on June 12, 2009. Metric quit the station at the end of 2010 to concentrate ... alex metric brodinski ref 2011 saw the release of his collaboration with Steve Angello open Your Eyes on Virgin Positive which stayed on the BBC Radio 1 A list for 4 weeks. A compilation of Alex Metric ... Boys. In 2010, Metric completed his rock n rave production work for the Infadel s forthcoming ... . Gravity Boy is expected to be released sometime in the fall of 2011. More recently, Alex Metric & Steve ... for their vocal version of the electro house centric track, Open Your Eyes . Metric also collaborated ... Bush. Alex Metric is a regular at clubs and festivals around the world with his DJ sets and Live shows ... 4 , as intro and gameplay music. Discography ref http www.discogs.com artist Alex Metric ref Singles ... Alex Metric Bootleg Metric Monster Hospital Alex Metric Bootleg Stress Thriller Alex Metric Mash Up Cassius Sound of Violence Alex Metric Re Edit Blur Song 2 Alex Metric Festival Edit Eurythmics Sweet Dreams Alex Metric Bootleg Cheryl Cole Parachute Alex Metric Bootleg References reflist colwidth ... alexmetric youtube u alexmetric Persondata Metadata see Wikipedia Persondata . NAME Metric, Alex ... Metric, Alex Category British electronic musicians Category British radio presenters Category Remixers Category Living people it Alex Metric ru Alex Metric ... more details
A risk metric is the abstract concept in financial risk management quantified by risk measure s. When choosing a risk metric, an agent is picking an aspect of perceived risk to investigate, such as volatility finance volatility or mean return. ref name Holton cite journal last Holton first Glyn A. year 2004 title Defining risk journal Financial Analysts Journal volume 60 issue 6 pages 19 25 url http www.riskexpertise.com papers risk.pdf format pdf accessdate March 11, 2012 ref Risk measure and risk metric In a general sense, a measure is an algorithm for quantifying something. A metric is our interpretation of the number. ref name glossary cite web author Glyn A. Holton year 2002 title Risk Measure and Risk Metric url http www.riskglossary.com link risk metric and risk measure.htm accessdate March 11, 2012 ref In other words, the method or formula to calculate a risk metric is called a risk measure. Value at risk metric The VaR risk metric summarizes the Probability distribution distribution of possible losses by a Quantile function quantile , a point with a specified probability of greater losses. ref name Jorion cite book last Jorion first Philippe title Value at Risk The New Benchmark for Managing Financial Risk edition 3rd publisher McGraw Hill year 2006 isbn 978 0071464956 ref Examples Standard deviation or volatility finance Volatility Mean Absolute deviation Expected shortfall Sharpe ratio Sortino ratio Value at risk See also Risk measure Coherent risk measure Deviation risk measure Spectral risk measure Distortion risk measure References Reflist Finance stub Category Financial risk ... more details
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 ... title Satisfying General Proximity Similarity Queries with Metric Trees journal Information Processing ... 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
Unit of length m 1600 accuracy 4 number of significant figures Metric mile is a distance which approximates one statute mile 1609.344 m at a round figure of metre s the SI or metric unit of length . The term is most commonly used in track running and swimming sport swimming . In track running, the 1500 metres 1500 m race became the standard middle distance track event middle distance race in Europe in the late 19th century, ref name nelsonpluquercetania cite book last Nelson first Cordner coauthors Quercetani, Roberto title The Milers url date 1985 isbn 0 911521 15 1 unused data p.14 ref and has been the standard distance in the Olympic Games since 1896. The distance of the race is sometimes referred to as a metric mile. ref cite web url http www.britannica.com eb article 9052542 middle distance running title Middle distance running accessdate 2008 01 13 ref However, even in countries which do not embrace the metric system, most running tracks have a lap distance of 400 metres in the innermost lane. The standard middle distance in many United States high school competitions, for instance, is four times around the track, and this 1600 m distance is sometimes referred to as a metric mile as well. See also Metric foot Metrication Scandinavian mile References reflist Category Units of length Category Athletics track and field terminology Category Middle distance running Track running Category Decimalisation ... more details
In mathematics , the Wasserstein or Vasershtein metric is a metric mathematics distance function defined between probability measure probability distribution s on a given metric space M . Intuitively, if each distribution is viewed as a unit amount of dirt piled on M , the metric is the minimum cost of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the distance it has to be moved. Because of this analogy, the metric is known in computer science ... Germanic origin . Definition Let M , d be a metric space for which every probability measure on M ... of all probability measures on M with Moment mathematics Moments in metric spaces finite ... sub p sub notation. The Wasserstein metric may be equivalently defined by math W p mu, nu p inf ... and respectively. Applications The Wasserstein metric is a natural way to compare the probability ... uniform perturbations random or deterministic . In computer science, for example, the metric W sub ... images . Properties Metric structure It can be shown that W sub p sub satisfies all the axiom s of a metric mathematics metric on P sub p sub M . Furthermore, convergence with respect to W sub p sub ... Radon metric math rho mu, nu sup left left. int M f x , mathrm d mu nu x right mbox continuous f M to 1, 1 right . math If the metric d is bounded by some constant C , then math 2 W 1 mu, nu leq C rho mu, nu , math and so convergence in the Radon metric also known as strong convergence implies convergence in the Wasserstein metric, but not vice versa. Separability and completeness For any p 1, the metric space P sub p sub M , W sub p sub is Separable space separable , and is Complete space complete if M , d is separable and complete. See also L vy metric L vy Prokhorov metric Transportation theory References cite book author Ambrosio, L., Gigli, N. & Savar , G. title Gradient Flows in Metric ... metric title Wasserstein metric Category Measure theory Category Metric geometry Category Probability ... more details
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