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Books on the topic 'Markov algebras'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

1946-, Demuth Michael, ed. Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras. Berlin: Akademie Verlag, 1996.

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2

Evolution algebras and their applications. Berlin: Springer, 2008.

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3

Conference Board of the Mathematical Sciences., ed. Algebraic ideas in ergodic theory. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1990.

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4

Hisayuki, Hara, Takemura Akimichi, and SpringerLink (Online service), eds. Markov Bases in Algebraic Statistics. New York, NY: Springer New York, 2012.

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5

Aoki, Satoshi, Hisayuki Hara, and Akimichi Takemura. Markov Bases in Algebraic Statistics. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3719-2.

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6

Shapiro, Helene. Linear Algebra And Matrices: Topics For A Second Course. Rhode Island, USA: American Mathematical Society, 2015.

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7

Noncommutative stationary processes. Berlin: Springer, 2004.

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8

Meyer, Carl D., and Robert J. Plemmons, eds. Linear Algebra, Markov Chains, and Queueing Models. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-8351-2.

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9

Cycle representations of Markov processes. New York: Springer-Verlag, 1995.

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10

Kalpazidou, Sophia L. Cycle representations of Markov processes. 2nd ed. New York: Springer, 2011.

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11

Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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12

Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. Providence, Rhode Island: American Mathematical Society, 2016.

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13

Vladas, Sidoravicius, and Smirnov S. (Stanislav) 1970-, eds. Probability and statistical physics in St. Petersburg: St. Petersburg School in Probability and Statistical Physics : June 18-29, 2012 : St. Petersburg State University, St. Petersburg, Russia. Providence, Rhode Island: American Mathematical Society, 2015.

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14

Schrodinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras. Vch Pub, 1996.

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15

Schrohe, Elmar, B. W. Schulze, and Johannes Sjostrand. Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras. John Wiley & Sons, 1996.

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16

Carl D. Meyer Robert J. Plemmons. Linear Algebra, Markov Chains, and Queueing Models. Springer, 2011.

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17

D, Meyer C., and Plemmons Robert J, eds. Linear algebra, Markov chains, and queueing models. New York: Springer-Verlag, 1993.

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18

Meyer, Carl D., and Robert J. Plemmons. Linear Algebra, Markov Chains, and Queueing Models. Springer, 2012.

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19

Tian, Jianjun Paul. Evolution Algebras and their Applications (Lecture Notes in Mathematics Book 1921). Springer, 2007.

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20

Tian, Jianjun Paul. Evolution Algebras and Their Applications. Springer, 2008.

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21

Hara, Hisayuki, Akimichi Takemura, and Satoshi Aoki. Markov Bases in Algebraic Statistics. Springer New York, 2014.

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22

Markov Bases In Algebraic Statistics. Springer, 2012.

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23

Gohm, Rolf. Noncommutative Stationary Processes. Springer London, Limited, 2004.

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24

Kalpazidou, Sophia L. Cycle Representations of Markov Processes. Springer London, Limited, 2013.

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25

Cycle Representations of Markov Processes (Stochastic Modelling and Applied Probability). Springer, 2006.

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26

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomial. Elsevier, 2022. http://dx.doi.org/10.1016/c2016-0-01793-x.

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27

El Karoui, Noureddine. Algebraic geometry and matrix models. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.29.

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This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first describes the moduli space of algebraic curves and its parameterization via the Jenkins-Strebel differentials before analysing the relation between the so-called formal matrix models (solutions of the loop equation) and algebraic hierarchies of Dijkgraaf-Witten-Whitham-Krichever type. It also presents the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations, along with higher expansion terms and symplectic invariants.

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28

Farb, Benson, and Dan Margalit. Thurston's Proof. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0016.

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This chapter describes Thurston's original path of discovery to the Nielsen–Thurston classification theorem. It first provides an example that illustrates much of the general theory, focusing on Thurston's iteration of homeomorphisms on simple closed curves as well as the linear algebra of train tracks. It then explains how the general theory works and presents Thurston's original proof of the Nielsen–Thurston classification. In particular, it considers the Teichmüller space and the measured foliation space. The chapter also discusses measured foliations on a pair of pants, global coordinates for measured foliation space, the Brouwer fixed point theorem, the Thurston compactification for the torus, and Markov partitions. Finally, it evaluates other approaches to proving the Nielsen–Thurston classification, including the use of geodesic laminations.

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29

van Moerbeke, Pierre. Determinantal point processes. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.11.

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This article presents a list of algebraic, combinatorial, and analytic mechanisms that give rise to determinantal point processes. Determinantal point processes have been used in random matrix theory (RMT) since the early 1960s. As a separate class, determinantal processes were first used to model fermions in thermal equilibrium and the term ‘fermion’ point processes were adopted. The article first provides an overview of the generalities associated with determinantal point processes before discussing loop-free Markov chains, that is, the trajectories of the Markov chain do not pass through the same point twice almost surely. It then considers the measures given by products of determinants, namely, biorthogonal ensembles. An especially important subclass of biorthogonal ensembles consists of orthogonal polynomial ensembles. The article also describes L-ensembles, a general construction of determinantal point processes via the Fock space formalism, dimer models, uniform spanning trees, Hermitian correlation kernels, and Pfaffian point processes.

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30

Farb, Benson, and Dan Margalit. Braid Groups. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0010.

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This chapter introduces the reader to Artin's classical braid groups Bₙ. The group Bₙ is isomorphic to the mapping class group of a disk with n marked points. Since disks are planar, the braid groups lend themselves to special pictorial representations. This gives the theory of braid groups its own special flavor within the theory of mapping class groups. The chapter begins with a discussion of three equivalent ways of thinking about the braid group, focusing on Artin's classical definition, fundamental groups of configuration spaces, and the mapping class group of a punctured disk. It then presents some classical facts about the algebraic structure of the braid group, after which a new proof of the Birman–Hilden theorem is given to relate the braid groups to the mapping class groups of closed surfaces.

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31

Haesemeyer, Christian, and Charles A. Weibel. The Norm Residue Theorem in Motivic Cohomology. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691191041.001.0001.

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This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The book draws on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduces the key figures behind its development. It proceeds to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. It then addresses symmetric powers of motives and motivic cohomology operations. The book unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.

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32

Little, Max A. Machine Learning for Signal Processing. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198714934.001.0001.

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Digital signal processing (DSP) is one of the ‘foundational’ engineering topics of the modern world, without which technologies such the mobile phone, television, CD and MP3 players, WiFi and radar, would not be possible. A relative newcomer by comparison, statistical machine learning is the theoretical backbone of exciting technologies such as automatic techniques for car registration plate recognition, speech recognition, stock market prediction, defect detection on assembly lines, robot guidance and autonomous car navigation. Statistical machine learning exploits the analogy between intelligent information processing in biological brains and sophisticated statistical modelling and inference. DSP and statistical machine learning are of such wide importance to the knowledge economy that both have undergone rapid changes and seen radical improvements in scope and applicability. Both make use of key topics in applied mathematics such as probability and statistics, algebra, calculus, graphs and networks. Intimate formal links between the two subjects exist and because of this many overlaps exist between the two subjects that can be exploited to produce new DSP tools of surprising utility, highly suited to the contemporary world of pervasive digital sensors and high-powered and yet cheap, computing hardware. This book gives a solid mathematical foundation to, and details the key concepts and algorithms in, this important topic.

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