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Journal articles on the topic 'Canonical Representation'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

YAMASHITA, HIDEYASU, and MASANAO OZAWA. "NONSTANDARD REPRESENTATIONS OF THE CANONICAL COMMUTATION RELATIONS." Reviews in Mathematical Physics 12, no. 11 (2000): 1407–27. http://dx.doi.org/10.1142/s0129055x00000617.

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Kelemen and Robinson reconstructed the [Formula: see text] model of Glimm and Jaffe with methods of nonstandard analysis. In order to apply nonstandard analysis to other constructions of field models systematically, this paper generalizes their nonstandard analytical methods of representing the canonical commutation relations in the framework of the theory of nonstandard unitary representations. For this purpose, such notions are introduced and examined in detail as nonstandard hulls of representations, approximate representations, and their standardizations. As applications, the following rep

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2

Chua, L. O., and A. C. Deng. "Canonical piecewise-linear representation." IEEE Transactions on Circuits and Systems 35, no. 1 (1988): 101–11. http://dx.doi.org/10.1109/31.1705.

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3

ACCARDI, LUIGI, and YUJI HIBINO. "CANONICAL REPRESENTATION OF STATIONARY QUANTUM GAUSSIAN PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 03 (2002): 421–28. http://dx.doi.org/10.1142/s0219025702000869.

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Stimulated by the quantum generalization of the canonical representation theory for Gaussian processes in Ref. 1, we first give the representations (not necessarily canonical) of two stationary Gaussian processes X and Y by means of white noises qt and pt with no assumptions on their commutator. We then assume that qt + ipt annihilates the vacuum state and prove that the representations are the joint Boson–Fock ones if and only if X and Y have a scalar commutator.

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4

Arai, Asao. "Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations." Reviews in Mathematical Physics 31, no. 08 (2019): 1950026. http://dx.doi.org/10.1142/s0129055x19500260.

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We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

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5

KEEVER, R. D. "MINIMAL 3-BRAID REPRESENTATIONS." Journal of Knot Theory and Its Ramifications 03, no. 02 (1994): 163–77. http://dx.doi.org/10.1142/s0218216594000125.

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This paper provides necessary and sufficient conditions for a representation of any 3-braid to be minimal (with regard to the number of crossings) and includes an algorithm to obtain such a representation, the number of distinct minimal representations of a given 3-braid, as well as a unique canonical form for each braid in B3. Also presented are necessary and sufficient conditions for any 3-string braid word to be a minimal representation of its conjugacy class. A canonical form for each conjugacy class in B3 is given.

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6

Gilboa, Itzhak, and David Schmeidler. "Canonical Representation of Set Functions." Mathematics of Operations Research 20, no. 1 (1995): 197–212. http://dx.doi.org/10.1287/moor.20.1.197.

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7

Vemuri, M. K. "Realizations of the canonical representation." Proceedings Mathematical Sciences 118, no. 1 (2008): 115–31. http://dx.doi.org/10.1007/s12044-008-0007-7.

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8

Htay, Win Win. "Optimalities for random functions Lee-Wiener’s network and non-canonical representation of stationary Gaussian processes." Nagoya Mathematical Journal 149 (March 1998): 9–17. http://dx.doi.org/10.1017/s0027763000006528.

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Abstract.Representation of a Gaussian process in terms of a Brownian motion is a powerful tool in the investigation of its structure. Among various representations is the canonical representation which is viewed as the best one from the viewpoint of the prediction theory. We have discovered some significance of non-canonical representations and discuss their optimality in an information theoretical approach.

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9

GAGU, Cristian. "THE CANONICAL REPRESENTATION OF THE HOLY TRINITY IN ORTHODOX ICONOGRAPHY." Icoana Credintei 9, no. 17 (2023): 5–30. http://dx.doi.org/10.26520/icoana.2023.17.9.5-30.

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The iconography of the Holy Trinity represents an extremely important issue, considering that the icon must fully express the truth of the Churchʼs faith, and current at the same time, since in church painting we can easily observe deviations from the canon of orthodoxy. That is precisely why, appealing to both the Orthodox and the Catholic bibliography, the present study aims to bring to the attention of theologians, clergy, iconographers and, why not, the laity alike, in a succinct presentation, the question of iconography and, implicitly, of the iconology of the Holy Trinity, to understand

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10

GRUNDLING, HENDRIK, and KARL-HERMANN NEEB. "FULL REGULARITY FOR A C*-ALGEBRA OF THE CANONICAL COMMUTATION RELATIONS." Reviews in Mathematical Physics 21, no. 05 (2009): 587–613. http://dx.doi.org/10.1142/s0129055x09003670.

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The Weyl algebra — the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect, in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S, B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a

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11

Bauer, Dietmar, and Martin Wagner. "A STATE SPACE CANONICAL FORM FOR UNIT ROOT PROCESSES." Econometric Theory 28, no. 6 (2012): 1313–49. http://dx.doi.org/10.1017/s026646661200014x.

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In this paper we develop a canonical state space representation of autoregressive moving average (ARMA) processes with unit roots with integer integration orders at arbitrary unit root frequencies. The developed representation utilizes a state process with a particularly simple dynamic structure, which in turn renders this representation highly suitable for unit root, cointegration, and polynomial cointegration analysis. We also propose a new definition of polynomial cointegration that overcomes limitations of existing definitions and extends the definition of multicointegration for I(2) proce

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12

Larget, Bret. "A canonical representation for aggregated Markov processes." Journal of Applied Probability 35, no. 2 (1998): 313–24. http://dx.doi.org/10.1239/jap/1032192850.

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A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete- and continuous-time, we show that any aggregated Markov process which satisfies mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization of all that can be identified about the underlying Markov process. Hidden Markov models on finite state spaces may be fra

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13

Larget, Bret. "A canonical representation for aggregated Markov processes." Journal of Applied Probability 35, no. 02 (1998): 313–24. http://dx.doi.org/10.1017/s0021900200014972.

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A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete- and continuous-time, we show that any aggregated Markov process which satisfies mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization of all that can be identified about the underlying Markov process. Hidden Markov models on finite state spaces may be fra

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14

Painsky, Amichai, Meir Feder, and Naftali Tishby. "Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach." Entropy 22, no. 2 (2020): 208. http://dx.doi.org/10.3390/e22020208.

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Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Nonlinear CCA extends this notion to a broader family of transformations, which are more powerful in many real-world applications. Given the joint probability, the Alternating Conditional Expectation (ACE) algorithm provides an optimal solution to the nonlinear CCA problem. However, it suffers from limited performance and an increasing computational burden when only a finite number of samples is available. In this work, we introduce an information-theore

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15

Kober, Martin. "Canonical quantum gravity on noncommutative space–time." International Journal of Modern Physics A 30, no. 17 (2015): 1550085. http://dx.doi.org/10.1142/s0217751x15500852.

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In this paper canonical quantum gravity on noncommutative space–time is considered. The corresponding generalized classical theory is formulated by using the Moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression

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16

Kahlert, C., and L. O. Chua. "A generalized canonical piecewise-linear representation." IEEE Transactions on Circuits and Systems 37, no. 3 (1990): 373–83. http://dx.doi.org/10.1109/31.52731.

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17

Webster, Ben. "Canonical bases and higher representation theory." Compositio Mathematica 151, no. 1 (2014): 121–66. http://dx.doi.org/10.1112/s0010437x1400760x.

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AbstractThis paper develops a general theory of canonical bases and how they arise naturally in the context of categorification. As an application, we show that Lusztig’s canonical basis in the whole quantized universal enveloping algebra is given by the classes of the indecomposable 1-morphisms in a categorification when the associated Lie algebra is of finite type and simply laced. We also introduce natural categories whose Grothendieck groups correspond to the tensor products of lowest- and highest-weight integrable representations. This generalizes past work of the author’s in the highest-

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18

Valdes-Perez, Raul E. "A canonical representation of multistep reactions." Journal of Chemical Information and Modeling 31, no. 4 (1991): 554–56. http://dx.doi.org/10.1021/ci00004a021.

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19

Rudas, Tamás. "CANONICAL REPRESENTATION OF LOG-LINEAR MODELS." Communications in Statistics - Theory and Methods 31, no. 12 (2002): 2311–23. http://dx.doi.org/10.1081/sta-120017227.

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20

Bihui, Hou, and Yang Hongbo. "A group representation of canonical transformation." Applied Mathematics and Mechanics 19, no. 4 (1998): 345–50. http://dx.doi.org/10.1007/bf02457538.

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21

Chen, Zirui, and Michael Bonner. "Canonical Dimensions of Neural Visual Representation." Journal of Vision 23, no. 9 (2023): 4937. http://dx.doi.org/10.1167/jov.23.9.4937.

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22

Nagamochi, Hiroshi, and Tiko Kameda. "Canonical cactus representation for minimum cuts." Japan Journal of Industrial and Applied Mathematics 11, no. 3 (1994): 343–61. http://dx.doi.org/10.1007/bf03167227.

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23

Cotaescu, Ion I. "Canonical quantization of the covariant fields on de Sitter space–times." International Journal of Modern Physics A 33, no. 08 (2018): 1830007. http://dx.doi.org/10.1142/s0217751x18300077.

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The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators

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24

Meszáros, András, János Papp, and Miklós Telek. "Fitting traffic traces with discrete canonical phase type distributions and Markov arrival processes." International Journal of Applied Mathematics and Computer Science 24, no. 3 (2014): 453–70. http://dx.doi.org/10.2478/amcs-2014-0034.

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Abstract Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to

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25

Martínez, Servet. "Entropy of killed-resurrected stationary Markov chains." Journal of Applied Probability 58, no. 1 (2021): 177–96. http://dx.doi.org/10.1017/jpr.2020.81.

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AbstractWe consider a strictly substochastic matrix or a stochastic matrix with absorbing states. By using quasi-stationary distributions we show that there is an associated canonical Markov chain that is built from the resurrected chain, the absorbing states, and the hitting times, together with a random walk on the absorbing states, which is necessary for achieving time stationarity. Based upon the 2-stringing representation of the resurrected chain, we supply a stationary representation of the killed and the absorbed chains. The entropies of these representations have a clear meaning when o

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26

Miković, Aleksandar, and Branislav Sazdović. "W-Strings on Curved Backgrounds." Modern Physics Letters A 12, no. 07 (1997): 501–9. http://dx.doi.org/10.1142/s0217732397000522.

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We discuss a canonical formalism method for constructing actions describing propagation of W-strings on curved backgrounds. The method is based on the construction of a representation of the W-algebra in terms of currents made from the string coordinates and the canonically conjugate momenta. We construct such a representation for a W3-string propagating in the background metric with one flat direction by using a simple ansatz for the W-generators where each generator is a polynomial of the canonical currents and the vierbeins. In the case of a general background, we show that the simple polyn

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27

HARPER, ROBERT, and DANIEL R. LICATA. "Mechanizing metatheory in a logical framework." Journal of Functional Programming 17, no. 4-5 (2007): 613–73. http://dx.doi.org/10.1017/s0956796807006430.

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AbstractThe LF logical framework codifies a methodology for representing deductive systems, such as programming languages and logics, within a dependently typed λ-calculus. In this methodology, the syntactic and deductive apparatus of a system is encoded as the canonical forms of associated LF types; an encoding is correct (adequate) if and only if it defines acompositional bijectionbetween the apparatus of the deductive system and the associated canonical forms. Given an adequate encoding, one may establish metatheoretic properties of a deductive system by reasoning about the associated LF re

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28

Karami, Mahdi, and Dale Schuurmans. "Deep Probabilistic Canonical Correlation Analysis." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (2021): 8055–63. http://dx.doi.org/10.1609/aaai.v35i9.16982.

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We propose a deep generative framework for multi-view learning based on a probabilistic interpretation of canonical correlation analysis (CCA). The model combines a linear multi-view layer in the latent space with deep generative networks as observation models, to decompose the variability in multiple views into a shared latent representation that describes the common underlying sources of variation and a set of viewspecific components. To approximate the posterior distribution of the latent multi-view layer, an efficient variational inference procedure is developed based on the solution of pr

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29

Krzyśko, Mirosław, and Łukasz Waszak. "Methods of representation for kernel canonical correlation analysis." Statistics in Transition new series 13, no. 2 (2013): 301–10. http://dx.doi.org/10.59170/stattrans-2012-024.

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Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation. This problem is equivalent to solving the generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we construct nonlinear canonical correlation analysis in reproducing kernel Hilbert spaces. The new kernel generalized eigenvalue problem always has the solution equal t

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30

Yushchenko, Olga V., and Anna Yu Badalyan. "Canonical Representation of the Active Nanoparticles Kinetics." Universal Journal of Materials Science 2, no. 2 (2014): 42–48. http://dx.doi.org/10.13189/ujms.2014.020204.

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31

Shpiz, G., and A. Kryukov. "Canonical Representation of Polynomial Expressions with Indices." Programming and Computer Software 45, no. 2 (2019): 81–87. http://dx.doi.org/10.1134/s0361768819020105.

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32

Bertot, Yves. "A simple canonical representation of rational numbers." Electronic Notes in Theoretical Computer Science 85, no. 7 (2003): 1–16. http://dx.doi.org/10.1016/s1571-0661(04)80754-0.

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33

Delgado, M., M. A. Vila, and W. Voxman. "On a canonical representation of fuzzy numbers." Fuzzy Sets and Systems 93, no. 1 (1998): 125–35. http://dx.doi.org/10.1016/s0165-0114(96)00144-3.

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34

Nikanorova, M. Yu. "Canonical representation of tangent vectors of Grassmannians." Journal of Mathematical Sciences 140, no. 4 (2007): 582–88. http://dx.doi.org/10.1007/s10958-007-0440-7.

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35

Gustavsen, Trond Stølen, and Runar Ile. "Representation theory for log-canonical surface singularities." Annales de l’institut Fourier 60, no. 2 (2010): 389–416. http://dx.doi.org/10.5802/aif.2526.

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36

KURATSUJI, HIROSHI, and KEN-ICHI TAKADA. "CANONICAL PHASE, TOPOLOGICAL INVARIANT AND REPRESENTATION THEORY." Modern Physics Letters A 05, no. 12 (1990): 917–25. http://dx.doi.org/10.1142/s0217732390001013.

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We show that the non-integrable phase defined over the generalized phase space, which is called the canonical phase, yields the topological quantization that reveals the connection with the irreducible representation of a certain class of compact Lie groups. Although this consequence by itself is already known in mathematics under the general scheme named geometric quantization, it has not yet been fully appreciated in physics except for some specific problems. The descriptive technique adopted here seems fresh enough to commit itself to the topological aspect of quantum mechanics even includi

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37

Brunat, Josep M., and Antonio Montes. "Computing the Canonical Representation of Constructible Sets." Mathematics in Computer Science 10, no. 1 (2016): 165–78. http://dx.doi.org/10.1007/s11786-016-0248-2.

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38

Pollack, Randy, Masahiko Sato, and Wilmer Ricciotti. "A Canonical Locally Named Representation of Binding." Journal of Automated Reasoning 49, no. 2 (2011): 185–207. http://dx.doi.org/10.1007/s10817-011-9229-y.

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39

Cutzu, Florin, and Shimon Edelman. "Canonical views in object representation and recognition." Vision Research 34, no. 22 (1994): 3037–56. http://dx.doi.org/10.1016/0042-6989(94)90277-1.

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40

Wen, Chengtao, and Xiaoyan Ma. "A Canonical Piecewise-Linear Representation Theorem: Geometrical Structures Determine Representation Capability." IEEE Transactions on Circuits and Systems II: Express Briefs 58, no. 12 (2011): 936–40. http://dx.doi.org/10.1109/tcsii.2011.2172715.

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41

BRZOZOWSKI, JANUSZ, and HELMUT JÜRGENSEN. "REPRESENTATION OF SEMIAUTOMATA BY CANONICAL WORDS AND EQUIVALENCES." International Journal of Foundations of Computer Science 16, no. 05 (2005): 831–50. http://dx.doi.org/10.1142/s0129054105003327.

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We study a novel representation of semiautomata, which is motivated by the method of trace-assertion specifications of software modules. Each state of the semiautomaton is represented by an arbitrary word leading to that state, the canonical word. The transitions of the semiautomaton give rise to a right congruence, the state-equivalence, on the set of input words of the semiautomaton: two words are state-equivalent if and only if they lead to the same state. We present a simple algorithm for finding a set of generators for state-equivalence. Directly from this set of generators, we construct

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42

Coşkun, Kemal Çağlar, Muhammad Hassan, and Rolf Drechsler. "Equivalence Checking of System-Level and SPICE-Level Models of Linear Circuits." Chips 1, no. 1 (2022): 54–71. http://dx.doi.org/10.3390/chips1010006.

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Due to the increasing complexity of analog circuits and their integration into System-on-Chips (SoC), the analog design and verification industry would greatly benefit from an expansion of system-level methodologies using SystemC AMS. These can provide a speed increase of over 100,000× in comparison to SPICE-level simulations and allow interoperability with digital tools at the system-level. However, a key barrier to the expansion of system-level tools for analog circuits is the lack of confidence in system-level models implemented in SystemC AMS. Functional equivalence of single Laplace Trans

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43

Srivastava, H. M., Firdous A. Shah, and Aajaz A. Teali. "On Quantum Representation of the Linear Canonical Wavelet Transform." Universe 8, no. 9 (2022): 477. http://dx.doi.org/10.3390/universe8090477.

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For the efficient identification of quantum states, we propose the notion of linear canonical wavelet transform in the framework of quantum mechanics. Using the machinery of Dirac representation theory and integration within an ordered product of operators, we recast the linear canonical wavelet transform to a matrix element of the squeezing–displacing operator U(μ,s)KM between analyzing vector ⟨ψ| and two-mode quantum state vector |f⟩ to be transformed. We also derive the inner product relation and inversion formula for the linear canonical wavelet transform in the realm of quantum mechanics.

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44

Kupsch, Joachim. "Canonical transformations for fermions in superanalysis." Reviews in Mathematical Physics 26, no. 06 (2014): 1450009. http://dx.doi.org/10.1142/s0129055x14500093.

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Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

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45

Wang, Minghui, Lingling Yue, Situo Xu, and Rufeng Chen. "The Real Representation of Canonical Hyperbolic Quaternion Matrices and Its Applications." Academic Journal of Applied Mathematical Sciences, no. 56 (June 15, 2019): 62–68. http://dx.doi.org/10.32861/ajams.56.62.68.

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In this paper, we construct the real representation matrix of canonical hyperbolic quaternion matrices and give some properties in detail. Then, by means of the real representation, we study linear equations, the inverse and the generalized inverse of the canonical hyperbolic quaternion matrix and get some interesting results.

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46

Benedetti, Vladimiro, Sara Angela Filippini, Laurent Manivel, and Fabio Tanturri. "Orbital Degeneracy Loci II: Gorenstein Orbits." International Mathematics Research Notices 2020, no. 24 (2018): 9887–932. http://dx.doi.org/10.1093/imrn/rny272.

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Abstract In [3] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In this paper we show that their canonical bundles can be conveniently controlled in the case where the affine coordinate ring of the subvariety is Gorenstein. We then study in a systematic way the subvarieties obtained as orbit closures in representations with finitely many orbits, and we determine the canonical bundles of the corresponding orbital degene

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47

Perez-Garcia, D., F. Verstraete, M. M. Wolf, and J. I. Cirac. "Matrix product state representations." Quantum Information and Computation 7, no. 5&6 (2007): 401–30. http://dx.doi.org/10.26421/qic7.5-6-1.

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This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.

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48

Lusztig, George. "The canonical basis of the quantum adjoint representation." Journal of Combinatorial Algebra 1, no. 1 (2017): 45–57. http://dx.doi.org/10.4171/jca/1-1-2.

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49

Quinton, Patrice, Sanjay Rajopadhye, and Tanguy Risset. "On Manipulating Z-Polyhedra Using a Canonical Representation." Parallel Processing Letters 07, no. 02 (1997): 181–94. http://dx.doi.org/10.1142/s012962649700019x.

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Z-polyhedra are intersections of polyhedra and integral lattices. They arise in the domain of automatic parallelization and VLSI array synthesis. In this paper, we address the problem of computation on Z-polyhedra. We introduce a canonical representation for Z-polyhedra which allows one to perform comparisons and transformations of Z-polyhedra with the help of a computational kernel on polyhedra.

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50

Tesu, I. C., and F. Dartu. "A comment on 'A generalized canonical PWL representation'." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 39, no. 12 (1992): 885–87. http://dx.doi.org/10.1109/82.208588.

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