Context date February 2010 In information geometry , the Fisherinformationmetric 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 Fisherinformation 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
metric on the N dimension al parameter space , thus connecting Fisherinformation to differential geometry . In that context, this metric is known as the Fisherinformationmetric , and the topic ..., we have math mathcal I theta 1 ,. math See also Fisherinformationmetric Formation matrix ...Merge from Observed information discuss Talk Fisherinformation Merge Observed information date January 2010 In mathematical statistics and information theory , the Fisherinformation sometimes simply ... statistics mode depends on the Fisherinformation and not on the prior distribution prior according ... Pages 336 and 618 621 von Mises and Bernstein . ref The role of the Fisherinformation in the asymptotic ... Fisher following some initial results by Francis Ysidro Edgeworth F. Y. Edgeworth . The Fisherinformation .... The Fisherinformation matrix is used to calculate the covariance matrices associated with maximum ... test . History The Fisherinformation was discussed by several early statisticians, notably Francis ... ref says In it Fisherinformation , he Fisher was to some extent anticipated Edgeworth 1908 9 esp ... ref Definition The Fisherinformation is a way of measuring the amount of information that an observable ... is 0. The second moment is called the Fisherinformation math mathcal I theta operatorname ... theta infty math . A random variable carrying high Fisherinformation implies that the absolute value of the score is often high.The Fisherinformation is not a function of a particular observation, as the random ... score is zero, the Fisherinformation is also the variance of the score. If nowrap ln&thinsp ... Thus, the Fisherinformation is the negative of the expectation of the second derivative with respect ... theta ln left g T X theta right math which follows from the definition of Fisherinformation, and the independence ... of the Fisherinformation, informally Consider an unbiased estimator math hat theta X math . Mathematically ... right geq 1. math The right most factor is defined to be the FisherInformation math mathcal I left ... more details
In information theory , the principle of minimum Fisherinformation MFI is a variational principle which ..., determines the best probability distribution that characterizes the system. See also Fisherinformation . 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 FisherinformationFisher 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 FisherInformation , Cambridge University Press, Cambridge, England, 2004. ref ref ... invariant equivalent of the Ideal Gas ref Fisherinformation and the thermodynamics of scale invariant ... 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 ... 0908.0504 ref . References references Category Information theory ... more details
Wiktionarypar 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 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 ton , a measurement of mass equal to 1,000 kg 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 . Meter music , of or relating to an even note pattern or rhythmic unit which coincides with a measurement of beats in music Meter poetry , the linguistic sound patterns of a verse See also Units of measurement Metric expansion of space disambig 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
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 the University of Idaho . ref Idaho Department of Water Resources Mapping Evapotranspiration http www.idwr.idaho.gov GeographicInfo METRIC et.htm ref reflist climate stub Category Hydrology Category Meteorology Category Remote sensing Category Computer aided engineering software Category Hydrology models Category Environmental soil science ... more details
of the statistical distance ref statdist between the quantum states. Quantum FisherInformation The Bures metric can be seen as the quantum equivalent of the Fisherinformationmetric and can ... mu d theta nu math where the quantum Fishermetric 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 Fishermetric 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 Fisherinformationmetric, the quantum Fishermetric 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 ... 1 x 1 2 x 2 2 x 3 2 frac pi 2 8 math See also Fidelity of quantum states FisherinformationFisherinformationmetric References Uhlmann, A., http www.ma.utexas.edu mp arc c 92 92 44.ps.gz The Metric ... of quantum and classical Fisherinformation to two level complex and quaternionic and three level complex systems , J. Math. Phys. 37, 2682, 1996. Paul B Slater, Quantum Fisher Bures information ...The Bures metric defines the infinitesimal distance between density matrix operators defining quantum ... metric include that given a target error, it allows the calculation of the minimum number of measurements ... form of the Bures metric, valid for 2x2 and 3x3 systems, respectively math d rho, rho ... 2 x 2 2 x 3 2 le 1 math . The components of the Bures metric in this parametrization can be calculated ... 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 ... Quantum mechanics Category Quantum information science ... more details
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 Sergey Golovkin 1959 1996 , a Russian serial killer 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 , an equation in financial mathematics and economics Fisher transformation , a transformation in statistics ... 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 20th century United States would do likewise. ref cite web url http archives.cbc.ca IDC 1 75 1572 10612 science technology metric system clip1 accessdate 2007 11 11 date 4 February 1970 title The metric housewife publisher CBC Radio work Matinee ref A number of Progressive Conservative Members of Parliament had been vocal in their opposition to the metric system during the previous Liberal Party of Canada Liberal government of Pierre Trudeau . Dennis Braithwaite of the Toronto Star was a prominent ... 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 . It was replaced by a small metric office within Industry Canada. By October of that same year, the metric office became the Measurement Information Division of Industry Canada, and staff numbers were significantly decreased. In April 1988, the Measurement Information ... 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 Category Former Canadian federal departments ... more details
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 ... Integrated Amplifier X 200 Series Integrated Amplifier X 100 Series Integrated Amplifier The Fisher was also used on Fisher s early US made solid state equipment, such as the model 210 receiver. Fisher ... cite web url http stereophile.com historical 605fisher title Fisher 500 C vintage stereo receiver ... 16 July 2010 ref Photo gallery center gallery Image FisherAllegroX19.JPG 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 ... FM Multiplex Tube Tuner made by Fisher and sold with Realistic badging through Radio Shack Stores Circa ... made by Fisher and sold with Realistic badging through Radio Shack Stores Circa 1962 gallery center References Reflist External links http www.hifi studio.de hifi klassiker fisher.htm The Fisher, history ... more details
Metric conversion can 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 disambig ... more details
In mathematics , string metrics also known as similarity metrics are a class of textual based metric mathematics metric s resulting in a similarity or dissimilarity distance score between two string computer science text strings for approximate 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 floating point 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 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 style suggestions as you type, data ... distance or L1 distance or City block distance Jaro Winkler distance Soundex distance metric Matching ... 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 matches See also String matching ... String Metric Category Algorithms on strings Category String similarity measures ... 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 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 Galilean , and that this Galilean spacetime 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 ... if we imagine 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 ..., for example. 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 ... with the spacetime metric. It is possible for certain physical effects to propagate back across ... for this to hold, since a generic analog model depends upon BOTH the acoustic metric AND the underlying ... geometry. See also Analog models of gravity Hawking radiation gravastar acoustics metric ... black hole evaporation Phys. Rev. Lett. 46 1981 , 1351 1353. font considers information leakage ... 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, and bk tree s. should have a list and summary of metric trees, with links to the main articles. CS Trees Category Trees structure datastructure stub ... 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
npov date November 2010 The Metric Martyrs are a British advocacy group based in the United Kingdom who ... imperial units , solely metric units or both. Citation needed date August 2010 Newspapers dubbed the group the metric martyrs after Chris Howell, then weights and measures spokesman for the Institute ... to. ref cite web url http www.bwmaonline.com Metric 20Culprits.htm title BMWA Metric Culprits accessdate ... not displaying metric signage as well as imperial, and for using illegal uncalibrated weighing ... selling loose goods, but metric units must be displayed simultaneously. Defendants In 2001 Steve Thoburn ... of weighing in the metric system as well as imperial, and hence were no longer permitted for commercial ... web url http news.sky.com skynews article 0,,30100 13014828,00.html title Metric Martyr Is Dead publisher ... of Public Sector Information date 10 November 1999 accessdate 2010 05 18 ref for failing to display ... The Prices Act 1974 publisher Office of Public Sector Information date 9 July 1974 accessdate 2010 ... traders are subject, required him to label his goods in metric quantities with imperial quantities ... campaign Since 2001 EU weights and measures legislation has required the use of metric units for grocery goods, while permitting the use of dual labelling of goods in both metric and non metric units ... ref the EU s announcement as an end to the existing requirement for metric labelling of grocery goods, the Metric Martyrs asked for a posthumous pardon for Steve Thoburn, who died after having his last ... ref cite news url http news.bbc.co.uk 1 hi england wear 6918912.stm title MP calls for metric martyr ... article2431521.ece title EU ends pointless battle to make UK metric publisher TimesOnline work timesonline.co.uk ... and measuring equipment the provision of quantity information and the sale of goods by quantity ... colwidth 30em External links http www.metricmartyrs.co.uk Metric Martyrs defence fund http news.bbc.co.uk ... 0,3604,422250,00.html Article about the Metric Martyrs case http www.liberty human rights.org.uk ... 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 . Then 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. Then 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 it Funzione non espansiva pl Odwzorowanie nierozszerzaj ce ru ... 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
This article is about the metric system in general. Information that pertains to specific versions of the system ... were kept as working copies or as spares. The metric system is an international decimal ised ... des poids et mesures CGPM . At the outset, the main feature of the metric system is the use of a standard ... becoming an equally important feature. The uncoordinated use of the metric system by different ... standard internationally recognised standard metric system. Overview File Metric system adoption map.svg thumb right upright 1.5 Countries which have officially adopted the metric system font color ... http www.nist.gov ts wmd metric upload 1136a.pdf ref br The United States is the only industrialised ... us labelling rules ref One goal of the metric system is to have a single unit for every physical ... , produced the metric system, which was then adopted by the revolutionary government of France ... by Congress. In the early metric system, there were several fundamental or base units, the grad ... and nanofarads are more often encountered. Most everyday users of the metric system measure temperature ... the metric system as the primary measurement system. White identifies countries that already used the metric system at the time they gained their independence. See also Metrication Adoption of the metric .... The idea of a metric system has been attributed to John Wilkins , first secretary of the Royal ... newsid 6898200 6898274.stm?bw nb&mp wm&news 1&ms3 10 Metric system was British from the BBC video ... acre s , and is still in use. The early metric system included only a few SI prefix prefixes from ... adopted the metric system on 10 December 1799. ref cite book author National Industrial Conference Board title The metric versus the English system of weights and measures ... url http books.google.com ... inherited the metric system. In 1812, Napoleon introduced a system known as mesures usuelles which used the names of pre metric units of measure, but defined then in terms of metric units for example ... 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
Orphan date January 2010 The Peres 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
In the mathematics mathematical study of metric spaces , one can consider the arclength of paths in the space .... 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 and any ... 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
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
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 , first opened in 1960, are all specified and measured up 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 Metrication ... more details
A spill metric is a Heuristic computer science heuristic metric used by Register allocation register allocators to decide with 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 computing runtime 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
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