P P n 1 math , called the n canonical map. The size of R is a basic invariant of V , and is called ... Proof of the Finite Generation of the Canonical Ring last1 Siu first1 Yum Tong year 2006 ... of the Canonical Ring last1 Siu first1 Yum Tong year 2007 Category Algebraic geometry Category ... more details
Unreferenced stub auto yes date December 2009 A canonic election is a legal valid election based on the jurisdiction of a canon law canonic legal system . Canonic legal systems are of democratic structure, but more complicated than ordinary state structures. One example for a canonic election would be the election of a pope by the cardinals in the Papal conclave conclave . DEFAULTSORT Canonical Election Category Canon law Election stub ... more details
orphan date November 2007 In astrodynamics , A canonical unit is a unit of measurement defined in terms of an object s reference orbit . In this system, a reference mass, for example the sun, is assumed to be 1 mass unit and the mean distance from the orbiting object to the reference object is considered the distance unit . Canonical units are useful when the precise distances and masses of objects in space are not available. However, by setting the mass of a given object to be 1 mass unit and the mean distance of the reference object to another object in question, many calculations can be simplified. Overview The distance unit math DU math is defined to be the mean radius of the reference orbit. The time unit math TU math is defined by the gravitational parameter math mu math math mu G M , math math G math is the gravitational constant math M math is the mass of the central reference body For Canonical Units, the gravitational parameter is defined as math mu 1 frac DU 3 TU 2 math The quantity of the time unit TU can be solved in another unit system eg. the metric system if the mass and radius of the central body has been determined. Using the above equation and applying dimensional analysis , set the two equations expressing math mu math equal to each other math mu G M 1 frac DU 3 TU 2 math The Time unit TU can be converted to another unit system for a more useful qualitative solution using the following equation math TU sqrt frac DU 3 G M math Approximate unit conversions are as follows 1 DU 6378.1 Km 20,925,524.97 ft 1 DU TU 7.90538 Km sec 25,936.29 ft sec 1 TU 806.80415 sec Astronomical Units An Astronomical units is canonical unit based on the orbit of the Earth around the Sun See also Astronomical unit Conversion of units References Roger R. Bate, Donald D. Mueller, Jerry E. White. Fundamentals of Astrodynamics . Category Astrodynamics Category Celestial mechanics ... more details
In statistics , canonical correlation analysis , introduced by Harold Hotelling , is a way of making sense of cross covariance matrix cross covariance matrices . If we have two sets of variables, math x 1, dots, x n math and math y 1, dots, y m math , and there are correlations among the variables, then canonical correlation analysis will enable us to find linear combinations of the math x math s and the math ... matrix based on sampled data from math X math and math Y math i.e. from a pair of data matrices . Canonical ... . The random variables math U a X math and math V b Y math are the first pair of canonical variables ... with the first pair of canonical variables this gives the second pair of canonical ... math is proportional to math Sigma YY 1 2 Sigma YX a math The canonical variables are defined by math ... this point is irrelevant. Practical uses A typical use for canonical correlation in the experimental ... accounted for a substantial amount of shared variance between the two tests. One can also use canonical ... 8 1999 . ref Visualization of the results of canonical correlation is usually through bar plots of the coefficients of the two sets of variables for the pairs of canonical variates showing significant ... book chapter Canonical correlation analysis Use of composite heliographs for representing multiple patterns ... of math X math and math Y math , correspondingly. The definition of the canonical variables ... product . The canonical correlations math operatorname cor U,V math is equal to the cosine of principal angles . See also Regularized canonical correlation analysis Generalized Canonical Correlation ... language R http www.qmrg.org.uk files 2008 12 3 understanding canonical correlation analysis1.pdf Understanding canonical correlation analysis Concepts and Techniques in Modern Geography Canonical ... A note on the ordinal canonical correlation analysis of two sets of ranking scores Also provides ... Representation Constrained Canonical Correlation Analysis A Hybridization of Canonical Correlation ... more details
In Hamiltonian mechanics , a canonical transformation is a change of canonical coordinates q , p , t ... Hamiltonian itself. This is sometimes known as form invariance . Canonical transformations are useful ... are a type of canonical transformation. However, the class of canonical transformations is much broader ... coordinates and momenta. Canonical transformations that do not include the time explicitly are called restricted canonical transformations many textbooks consider only this type . For clarity ... read the related symplectomorphism article. Canonical transformations are a special case of a symplectomorphism ... between q , p and Q , P we may check if the transformation is restricted canonical, as follows ... p cdot frac partial mathbf p partial P m math If the transformation is canonical, these two must ... a given transformation is canonical. Liouville s theorem The direct conditions allow us to prove ... is conserved under canonical transformations, i.e., math int d mathbf q d mathbf p int d mathbf Q ..., the scaling factor math lambda math is set equal to one canonical transformations for which math lambda neq 1 math are called extended canonical transformations . math frac dG dt math is kept, otherwise the problem would be rendered trivial and there would be not much freedom for the new canonical ... function of one old canonical coordinates canonical coordinate math mathbf q math or math mathbf p math , one new canonical coordinates canonical coordinate math mathbf Q math or math mathbf P math ... from old to new canonical coordinates , and any such transformation math mathbf q , mathbf p rightarrow mathbf Q , mathbf P math is guaranteed to be canonical. Type 1 generating function The type ... and the old canonical coordinates math mathbf q , mathbf p math . Ideally, one can invert these relations to obtain formulae for each math Q k math as a function of the old canonical coordinates. Substitution ... generalized momenta math mathbf P math in terms of the old canonical coordinates math mathbf q ... more details
Statistical mechanics cTopic Statistical ensemble mathematical physics Ensembles The canonical ensemble ... mechanics partition function of the canonical ensemble. Specifying this dependence of math Z math ... p i math above. The canonical ensemble and its partition function is widely used as a tool to calculate ... elements of the canonical ensemble. Other related thermodynamic formulas are given in the partition ..., the canonical ensemble is known as the Gibbs measure , where, because it has the Markov property of statistical ... E i , math . This distribution is called the canonical distribution. To determine math alpha , math ... function for the canonical ensemble. Note on derivation As mentioned above, the derivation hinges ... multiplicities of the reservoir the same can be said for the grand canonical ensemble ... this approach is employed. The canonical ensemble is also called the Gibbs ensemble , in honor of Willard ...... the phase space density in modern language ... is called canonical... if the index of probability ... math P e frac E A kT , math is taken to define the canonical ensemble and to be the fundamental ... the canonical ensemble, but this is part of his demonstration Gibbs, pp 169 183 that the principle of equal a priori probabilities, therefore the microcanonical ensemble, are inferior to the canonical ... mechanics, where the canonical ensemble is defined as the probability measure math e E A over kT dp , dq math with p and q being the canonical coordinates. Characteristic state function The characteristic state function of the canonical ensemble is the Helmholtz free energy function, as the following ... the canonical partition function, one can easily obtain the corresponding results for a canonical ensemble ... Q is the quantum mechanical version of the canonical partition function. Putting C back into the equation ... counterpart of the canonical partition function, being the normalization factor for the mixed state of interest. The density operator obtained above therefore describes the mixed state of a canonical ... more details
A canonical cover F sub c sub for F a set of functional dependencies on a relation scheme is a set of dependencies such that F logically implies all dependencies in F sub c sub , and F sub c sub logically implies all dependencies in F. The set F sub c sub has two important properties No functional dependency in F c contains an extraneous attribute. Each left side of a functional dependency in F c is unique. That is, there are no two dependencies a b and c d in F sub c sub such that a c. Algorithm for computing a canonical cover nowiki F sub c sub F Repeat Use the union rule to replace any dependencies in F sub c sub of the from a b and a d with a bd. Find a functional dependency in F sub c sub with an extraneous attribute and delete it from F sub c sub until F c does not change nowiki ref Database system concepts by Abraham Silberschatz et al ref References reflist Category Database theory Category Mathematical concepts Category Algorithms and data structures ... more details
A canonical territory is a geographical area seen as belonging to a particular patriarchate or autocephalous Church as its own. The concept is found both in the Eastern Orthodox Church and in the Roman Catholic Church , and is mentioned extensively in the Code of Canons of the Eastern Churches . ref Examples of canons of this code that speak of the canonical territory of an autonomous Church are 57, 78, 86, 102, 132, 133, 138 140, 143, 146 150, ... ref Historical background Canons of the Apostles See Canons of the Apostles Bishop Hilarion Alfeyev asserts that blockquote t he model of church organization that was formed during the first three centuries of Christianity was based on the principle of one city one bishop one Church , which foresaw the assignment of a certain ecclesiastical territory to one concrete bishop. In accordance with this principle, the Canons of the Apostles and other canonical decrees of the ancient Church point to the inadmissibility of violating the boundaries of ecclesiastical territories by bishops or clergy. blockquote ref name Alfeyev cite web title One City, One Bishop, One Church work The Principle of Canonical Territory and the Appearance of Parallel Hierarchies url http www.orthodoxytoday.org articles6 HilarionOneBishop.php ref The Canons ref name Alfeyev .... Present situation The issue of canonical territory has proven to be a significant point of dispute ... church unity r c t e.htm title Canonical Territory in the Russian Orthodox Tradition ref Eastern ... synod elects bishops for the patriarchate s canonical territory, while bishops who head eparchy ... www.intratext.com IXT LAT0758 PM.HTM Code of Canons of the Eastern Churches, canon 181 ref Canonical ... with canonical territory have often given rise to the problem of phyletism , which is defined ... of Canonical Territory and the Appearance of Parallel Hierarchies url http www.orthodoxytoday.org ... DEFAULTSORT Canonical Territory Category Canon law Catholic Church Category Christian terms ... more details
Orphan date February 2009 Cleanup date April 2007 Canonical admonitions are a preliminary means used by the Roman Catholic Church towards a suspected person, as a preventive of harm or a remedy of evil. History The 1880 instruction, by direction of Pope Leo XIII , from the Congregation of Bishops and Regulars to the bishop s of Italy , gave them the privilege to use a summary procedure in trials of the clergy for criminal or disciplinary transgressions. Article IV decrees Among the preservative measures are chiefly to be reckoned the spiritual retreat, admonitions, and injunctions. Article VI The canonical admonitions may be made in a paternal and private manner even by letter or by an intermediary person , or in legal form, but always in such a way that proof of their having been made shall remain on record. Usage These admonitions are to be founded upon a suspicion of guilt that is excited by public rumor and investigated by a proper authority, with the result establishing a reasonable basis for the suspicion. If little foundation for the suspicion is discovered, the superior should not even admonish the person, unless the suspected person has given, on previous occasions, serious motive for faultfinding. Admonitions may be either paternal or legal canonical . If the grounds are such as to produce a serious likelihood, or half proof , they will suffice for a paternal admonition, which is administered after the following steps The prelate either personally or through a confidential delegate informs the suspected person of what has been said about him or her, without mentioning the source of information, and without threat, but urges amendment. If the suspected party can at once show that there is no basis for suspicion, nothing further is to be done in the matter. If his ... for the above mentioned canonical or legal admonition. The assumed half proof is strengthened .... http www.newadvent.org cathen 01144b.htm Canonical Admonitions at Catholic Encyclopedia Category ... more details
Quantum field theory In physics , canonical quantization is a procedure for quantization physics quantizing a classical theory while attempting to preserve the formal structure of the classical theory, to the extent possible. Historically, this was Werner Heisenberg s route to obtaining quantum mechanics . The word canonical arises from the Hamiltonian mechanics Hamiltonian approach to classical mechanics, in which a system s dynamics is generated via canonical Poisson bracket s, a structure that is preserved to the extent possible in canonical quantization. This method was used in the context ... date May 2010 whose quantum mechanics was first investigated by Paul Dirac Dirac . The name canonical ... and momenta math p math . These specify the state of a classical system. The canonical structure also ... as canonical transformation s in classical mechanics. In quantum mechanics , observables are represented ... may be considered a quantum analog of the canonical structure of classical mechanics. Second quantization ... mechanics, so that all particles are now described relativistically by quantum field s. When the canonical ... is different. One drawback to canonical quantization for a relativistic field is that by relying on the Hamiltonian ... . The details of the canonical quantization depend on the field being quantized, and whether it is free or interacting. Real scalar field A Scalar field theory provides a good example of the canonical ... dt math . The canonical momentum obtained via the Legendre transform using the action math L math ... left frac 1 2 pi 2 frac 1 2 partial x phi 2 frac 1 2 m 2 phi 2 V phi right . math Canonical quantization treats the variables math phi x math and math pi x math as operators with canonical commutation ... math in one of these vacua may be considered a condensate of the field math phi math . Canonical quantization ... Canonical Quantization ? http www.quantumfieldtheory.info Pedagogic Aides to Quantum Field Theory .... DEFAULTSORT Canonical Quantization Category Quantum field theory Category Mathematical quantization ... more details
Orphan date April 2012 A canonical account or built in account , in the context of computer software and systems, is an account that is included by default with a program or firmware . Such accounts usually also have a default password and may have certain access rights by default. As such accounts and their password and permissions are usually common knowledge, given that anyone possessing a copy of the software, the device or their documentation will likely know of the account, a common security measure is to change the account s password and to double check or modify the groups if any it is included in, or simply disable or delete it if it is not required. Examples Zyxel routers typically have admin as their default firmware administration account and 1234 as the default password . The password can and should be changed as soon as possible. Microsoft Windows 2000 and Windows XP XP , and possibly other versions, have an account named Guest by default, which has no password and grants a very basic access to the operating system. Even though it is disabled by default, some administrators may choose to activate it, change the password and disable it once more for good measure. This account cannot be deleted. If not blank, canonical passwords are usually simple and may often be A simple sequence 1234 , 4321 , abcd The same as the account if the account is bob , the password will also be bob A word relating to the account or software support , finance , windows Simply password , pass External links http www.phenoelit.de dpl dpl.html Default Router Password List http www.helith.net projects alecto Alecto Default Password List Project Category Windows software Category Password authentication Windows software stub ... more details
A Canonical S expression or csexp is a binary encoding form of a subset of general S expression . It was designed for use in SPKI to retain the power of S expressions and ensure canonical form for applications such as digital signatures while achieving the compactness of a binary form and maximizing the speed of parsing. The particular subset of general S expressions applicable here is composed of atoms , which are byte strings, and parentheses used to delimit lists or sub lists. These S expressions are fully recursive. While S expressions are typically encoded as text, with spaces delimiting atoms and quotation marks used to surround atoms that contain spaces, when using the canonical encoding each atom is encoded as a length prefixed byte string. No whitespace separating adjacent elements in a list is permitted. The length of an atom is expressed as an ASCII decimal number followed by a . Example The sexp this Canonical S expression has 5 atoms becomes the csexp 4 this22 Canonical S expression3 has1 55 atoms Note that no quotation marks are required to escape the space character internal to the atom Canonical S expression , because the length prefix clearly points to the end of the atom. Note also that there is no whitespace separating an atom from the next element in the list. Properties Uniqueness of canonical encoding Forbidding whitespace between list elements and providing just one way of encoding atoms ensures that every S expression has exactly one encoded form. Since the unique encoded form is itself a sequence of bytes, by hashing it we can provide every S expression with a unique hash value. Furthermore, we can decide whether two S expressions are equivalent by comparing their encodings. Support for binary data Atoms can be any binary string. So, a cryptographic hash value or a public key modulus that would otherwise have to be encoded in base64 or some other printable encoding can be expressed in csexp as its binary bytes. Support for type tagging encoded ... more details
Canonical institution from the Latin institutio , from instituere , to establish is a technical term of the canon law of the Roman Catholic Church , meaning in practice an institution having full recognition and status within the Church. Benefices In its widest signification, canonical institution denotes any manner, in accordance with canon law, of acquiring an ecclesiastical benefice ref Regula prima juris, in VIto ref . In its strictest sense, the word denotes the collation of an ecclesiastical benefice by a legitimate authority, on the presentation of a candidate by a third person institutio tituli collativa . The term is used also for the actual putting in possession of a benefice institutio corporalis , and for the approbation requisite for the exercising of the ecclesiastical ministry when an authority inferior to the bishop has power to confer an ecclesiastical benefice institutio auctorisabilis . ref Cf. gloss on Regula prima juris , in VIto, s. v. Beneficium . ref Institutio tituli collativa The institutio tituli collativa that which gives the title , sometimes also called verbalis which may be by word of mouth or by writing, as distinguished from the institutio corporalis , or realis , is the act by which an ecclesiastical authority confers a benefice on a candidate presented by a third person enjoying the right of presentation. This occurs in the case of benefices subject to the right of patronage jus patronatus , one of the principal prerogatives of which is the right of presenting to the bishop a titular for a vacant benefice. It also occurs when, in virtue of a privilege or of a concordat , a chapter, a sovereign, or a government has the right to present to the pope ... see canonical provision , in the case of minor benefices it requires an actual installation by a competent ... by a special act. Notes references References Attribution Catholic wstitle Canonical Institution ... Canonical Institution Category Canon law ... more details
A canonical visitation is the act of an ecclesiastical superior who in the discharge of his office visits persons or places with a view of maintaining faith and discipline, and of correcting abuses by the application of proper remedies. Catholic usage The practice was re established in the Catholic Church by the Council of Trent in these words Patriarchs, primates, metropolitans and bishops shall not fail to visit their respective dioceses either personally, or if they be lawfully impeded, by their vicar general or visitor if unable on account of its extent to make the visitation of the whole diocese annually, they shall visit at least the greater part thereof, so that the whole shall be completed within two years, either by themselves or their visitors. Of the purpose of visitation the Council says But the principal object of all the visitations shall be to lead men to sound and orthodox doctrine by banishing heresies, to maintain good morals, and to correct such as are evil by admonition and exhortation to animate the people to religion, peace, and innocence, and to put in vogue whatever else may be dictated by the prudence of the visitors for the benefit of the faithful, as time, place and opportunity shall permit. Rights of visitation The right of visitation belongs to all prelates who have ordinary jurisdiction over persons in the external forum. The pope through his delegates may institute a visitation throughout the world, patriarch s, primate religion primate s, Metropolitan bishop Catholic metropolitan s, bishop s, a vicar apostolic and a vicar capitular or administrator of a vacant diocese, all in their respective territories, religious superiors within their own jurisdiction. A prelate nullius enjoys this right in conjunction with the neighbouring bishop, whose ..., and then only after the visitation of his own diocese has been completed. The canonical visitation ... minor breaches of rule, since they are devoid of canonical jurisdiction. Difficulties beyond ... more details
Canonical hours are divisions of time which serve as increments between the prescribed prayer s of the daily ... . In western Roman Catholic Church Catholicism , canonical hours may also be called offices , since ... note and among likewise Byzantine Rite Eastern Catholic Churches Catholics ref the canonical hours ... the Hours. With the Cluniac reforms of the 11th century there was a new emphasis on liturgy and the canonical .... Already well established by the ninth century in the West, these canonical offices consisted .... Development Judaism and the Early Church As is noted above, the canonical hours stemmed from Jewish ... 4 23 30 , which has remained a part of the canonical hours and all Christian prayer since. By 60 AD ... s Prayer three times a day this practice found its way into the canonical hours as well. Pliny ... A sundial showing the four Tide time Tides and five Canonical hours, based on the example on the Bewcastle ... in daily life in monastery monasteries . By the fourth century, the characteristics of the canonical ..., the breviary contained the entire text of the canonical hours. Roman Rite since the Council of Trent ... of the canonical hours and sought to make them more suited to the needs of today s apostolate ... four week cycle of praying nearly the entire set of Psalms with each of the canonical hours ... are said by the Bishop for the Canonical Hours, this differs little from what is in the Priest s Service ... and special occasions. In the Slavic usage, the Evang lion contains the four gospels in canonical ... the tomb and carried to the altar. Aggregates Aggregate liturgy redirects here The sundry Canonical .... Oriental Orthodox usage Coptic usage The Coptic Orthodox Church of Alexandria Coptic cycle of canonical ... Horologion is the Agpeya . Seven canonical hours exist, corresponding largely to the Byzantine ... the Shhimo , simple prayer. The shhimo has offices for the canonical hours for each day of the week. Each canonical office begins and ends with a qawmo , a set of prayers that includes the Lord s Prayer ... more details
disambig Canonical Book of the Tang Dynasty may refer to one of the two canonical history books about the Tang Dynasty First Canonical Book of the Tang Dynasty , compiled under Liu Xu in 945 Second Canonical Book of the Tang Dynasty , compiled under Ouyang Xiu and Song Qi in 1060 ChineseText Twenty Four Canonical Histories ... more details
In algebraic geometry and differential geometry , the canonical line bundle may refer to either The canonical bundle the top exterior power of the bundle of differential forms on a manifold or variety The tautological line bundle the total space of lines represented by a projective space. This is not the canonical bundle of the projective space as defined above. mathdab ... more details
Context date January 2010 In mathematics , the relative canonical model of a singular variety math X math is a particular canonical form canonical variety that maps to math X math , which simplifies the structure. The precise definition is If math f Y to X math is a Resolution of singularities resolution define the adjunction sequence to be the sequence of subsheaves math f omega Y otimes n math if math omega X math is invertible math f omega Y otimes n I n omega X otimes n math where math I n math is the higher adjunction ideal. Problem. Is math oplus n f omega Y otimes n math finitely generated? If this is true then math Proj oplus n f omega Y otimes n to X math is called the relative canonical model em of Y, or the em canonical blow up of X. ref name R Some basic properties were as follows The relative canonical model was independent of the choice of resolution. Some integer multiple math r math of the canonical divisor of the relative canonical model was Cartier and the number of exceptional components where this agrees with the same multiple of the canonical divisor of Y is also independent of the choice of Y. When it equals the number of components of Y it was called crepant resolution crepant . em ref name R M. Reid, http www.uni due.de mat903 sem ws0708 C3f.pdf Canonical 3 folds courtesy copy , proceedings of the Angiers Journees de Geometrie Algebrique 1979 ref It was not known whether relative canonical models were Cohen Macaulay . Because the relative canonical model is independent of math Y math , most authors simplify the terminology, referring to it as the relative canonical model of math X math rather than either the relative canonical model of math Y math or the canonical blow up of math X math . The class of varieties that are relative canonical models have canonical singularities . Since that time in the 1970s other mathematicians solved affirmatively ... canonical models always exist. References reflist Category Algebraic geometry Category Birational ... more details
A canonical link element is an HTML element that helps webmasters prevent duplicate content issues by specifying the canonical , or preferred , version of a web page ref name googleblog http googlewebmastercentral.blogspot.com 2009 02 specify your canonical.html ref ref http www.mattcutts.com blog canonical link tag ref ref http www.seomoz.org blog canonical url tag the most important advancement in seo practices since sitemaps ref as part of search engine optimization . Duplicate content issues occur when the same content is accessible from multiple URLs. ref http www.google.com support webmasters bin answer.py?answer 66359 ref For example, tt nowiki http www.example.com page.html nowiki tt would be considered by search engines to be an entirely different page to tt nowiki http www.example.com page.html?parameter 1 nowiki tt , even though both URLs return the same content. Another example is essentially the same tabular content, but sorted differently. In February 2009, Google, Yahoo and Microsoft announced support for the canonical link element, which can be inserted into the HTML element .... ref http searchengineland.com canonical tag 16537 ref The canonical link element helps webmasters ..., the canonical link element is not considered to be a directive, but a hint that the web crawler will honor strongly . ref name googleblog While the canonical link element has its benefits, Matt ... is because Google s Web crawler spiders can choose to ignore a canonical link element if they feel ... tags ref Examples of the code canonical code link element source lang html4strict link rel canonical href http www.example.com source source lang html4strict link rel canonical href http www.example.com page.html source source lang html4strict link rel canonical href http www.example.com directory page.html source References Reflist DEFAULTSORT Canonical link element Category Search engine optimization Category HTML de Canonical Link ... more details
Georg Philipp Telemann s 6 Canonical Sonatas is a set of six canonical sonatas written for two recorders or two violins. Each sonata is written as a Canon music canon at the unison, meaning the second player plays the same melody as the first but several bars later. music publication stub External links http imslp.org wiki 6 Sonatas for 2 Flutes or Violins 28Telemann, Georg Philipp 29 Arrangement for 2 violas or 2 cellos at IMSLP free . Category Compositions by Georg Philipp Telemann ... more details
refimprove date July 2011 Regularized canonical correlation analysis is a way of using ridge regression to solve the singularity problem in the cross covariance matrix cross covariance matrices of canonical correlation analysis . By converting math operatorname cov X, X math and math operatorname cov Y, Y math into math operatorname cov X, X lambda I X math and math operatorname cov Y, Y lambda I Y math , it ensures that the above matrices will have reliable inverses. The idea probably dates back to Hrishikesh D. Vinod s publication in 1976 where he called it Canonical ridge . ref Cite journal author Hrishikesh D. Vinod title Canonical ridge and econometrics of joint production journal Journal of Econometrics volume 4 issue 2 month May pages 147 166 doi 10.1016 0304 4076 76 90010 5 ref ref Cite book author Kanti Mardia et al. title Multivariate Analysis ref It has been suggested for use in the analysis of functional neuroimaging data as such data are often singular. ref Cite journal author Finn rup Nielsen, Lars Kai Hansen, Stephen C. Strother title Canonical ridge analysis with ridge parameter optimization year 1998 journal NeuroImage volume 7 pages S758 month May url http www2.imm.dtu.dk pubdb views edoc download.php 4981 pdf imm4981.pdf ref It is possible to compute the regularized canonical vectors in the lower dimensional space. ref Cite thesis author Finn rup Nielsen year 2001 title Neuroinformatics in Functional Neuroimaging url http www2.imm.dtu.dk pubdb views edoc download.php 201 pdf imm201.pdf publisher Technical University of Denmark Section 3.18.5 ref References Reflist cite journal last1 Leurgans first1 S.E. last2 Moyeed first2 R.A. last3 Silverman first3 B.W. title Canonical correlation analysis when the data are curves journal Journal of the Royal Statistical Society series Series B Methodological year 1993 volume 55 number 3 pages 725 740 jstor 2345883 Category Mathematical analysis Category Calculus of variations ... more details
A Post canonical system , as created by Emil Post , is a string manipulation system that starts with finitely many strings and repeatedly transforms them by applying a finite set of specified rules of a certain form, thus generating a formal language . Today they are mainly of historical relevance because every Post canonical system can be reduced to a string rewriting system semi Thue system , which is simpler a formulation. Both formalisms are Turing complete . Definition A Post canonical system is a triplet A , I , R , where A is a finite alphabet, and finite possibly empty strings on A are called words . I is a finite set of initial words . R is a finite set of string transforming rules called production rules , each rule being of the following form math begin matrix g 10 11 g 11 12 g 12 dots 1m 1 g 1m 1 g 20 21 g 21 22 g 22 dots 2m 2 g 2m 2 dots dots dots dots dots dots dots dots g k0 k1 g k1 k2 g k2 dots km k g km k downarrow h 0 1 h 1 2 h 2 dots n h n end matrix math where each g and h is a specified u fixed u word, and each and is a u variable u standing for an arbitrary word. The strings before and after the arrow in a production rule are called the rule s antecedents and consequent , respectively. It is required that each in the consequent be one of the s in the antecedents ... 2 dots m g m rightarrow h 0 1 h 1 2 h 2 dots n h n math The formal language generated by a Post canonical ... A Post canonical system is said to be in normal form if it has only one initial word and every production ... form Theorem , which applies to the most general type of Post canonical system Given any Post canonical system on an alphabet A , a Post canonical system in normal form can be constructed from it, possibly ..., being also monogenic . A canonical system is said to be monogenic if, given any string, at most ... rewriting systems, Type 0 formal grammars A string rewriting system is a special type of Post canonical ... g &rarr h . It has been proved that any Post canonical system is reducible to such a substitution ... more details
In computing canonical signed digit CSD is a number system for encoding a floating point value in a two s complement representation. This encoding contains 33 fewer non zeros than the two s complement form, leading to efficient implementations of add subtract networks in hardwired Digital signal processing . The representation uses a sequence of one or more of the symbols, 1, 0, 1 alternatively , 0 or with each position possibly representing the addition or subtraction of a power of 2. For instance 23 is represented as 0 00 , which expands to math 2 5 2 3 2 0 math or math 32 8 1 23 math External links http citeseerx.ist.psu.edu viewdoc download?doi 10.1.1.126.5477&rep rep1&type pdf Fractions in the Canonical Signed Digit Number System Category Computing terminology ... more details
Unreferenced date February 2010 In statistics , the generalized canonical correlation analysis gCCA , is a way of making sense of cross correlation matrices between the sets of random variables when there are more than two sets. While a conventional CCA generalizes Principal component analysis PCA to two sets of random variables, a gCCA generalizes PCA to more than two sets of random variables. The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA. Applications The Helmert Wolf blocking HWB method of estimating linear regression parameters can find an optimal solution only if all cross correlations between the data blocks are zero. They can always be made to vanish by introducing a new regression parameter for each common factor. The gCCA method can be used for finding those harmful common factors that create cross correlation between the blocks. However, no optimal HWB solution exists if the random variables do not contain enough information on all of the new regression parameters. External links http factominer.free.fr FactoMineR free exploratory multivariate data analysis software linked to R programming language R Category Covariance and correlation Category Estimation theory Sun, Q.S., Liu, Z.D., Heng, P.A., Xia, D.S. A Theorem on the Generalized Canonical Projective Vectors. Pattern Recognition 38 3 2005 449 fr Analyse canonique g n ralis e ... more details
Multiple issues unreferenced December 2009 technical June 2011 context June 2011 A canonical Huffman code is a particular type of Huffman code with unique properties which allow it to be described in a very compact manner. Data compression Data compressor s generally work in one of two ways. Either the decompressor can infer what codebook the compressor has used from previous context, or the compressor must tell the decompressor what the codebook is. Since a canonical Huffman codebook can be stored especially efficiently, most compressors start by generating a normal Huffman codebook, and then convert it to canonical Huffman before using it. Algorithm The normal Huffman coding algorithm assigns a variable length code to every symbol in the alphabet. More frequently used symbols will be assigned a shorter code. For example, suppose we have the following non canonical codebook A 11 B 0 C 101 D 100 Here the letter A has been assigned 2 bit s, B has 1 bit, and C and D both have 3 bits. To make the code a canonical Huffman code, the codes are renumbered. The bit lengths stay the same with the code book being sorted first by codeword length and secondly by alphabetical Value computer science value B 0 A 11 C 101 D 100 Each of the existing codes are replaced with a new one of the same length .... This can be thought of as a Logical shift left shift . By following these three rules, the canonical ... advantage of a canonical Huffman tree is that one can encode the description the codebook in fewer ... of bits and code 2,11 , 1,0 , 3,101 , 3,100 With our canonical version we have the knowledge that the symbols .... Note that our canonical Huffman tree always has higher values for longer bit lengths and that any ... symbol need be transmitted 2, 1, 3, 3 With knowledge of the canonical Huffman algorithm, it is then possible ... by bit length, the following pseudo code will print a canonical Huffman code book code 0 while more ... DEFAULTSORT Canonical Huffman Code Category Lossless compression algorithms Category Coding theory ca ... more details
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