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Опубліковано: 7 липня 2024

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Статті в журналах з теми "Partitions de Markov":

Crane, Harry, and Peter McCullagh. "Reversible Markov structures on divisible set partitions." Journal of Applied Probability 52, no. 03 (September 2015): 622–35. http://dx.doi.org/10.1017/s0021900200113336.

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We studyk-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integerk= 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, fork> 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeablek-divisible partitions that are consistent under random deletion. We further introduce the notion ofMarkovian partition structures, which are ensembles of exchangeable Markov chains onk-divisible partitions that are consistent under a random process ofMarkovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).

Crane, Harry, and Peter McCullagh. "Reversible Markov structures on divisible set partitions." Journal of Applied Probability 52, no. 3 (September 2015): 622–35. http://dx.doi.org/10.1239/jap/1445543836.

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We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeable k-divisible partitions that are consistent under random deletion. We further introduce the notion of Markovian partition structures, which are ensembles of exchangeable Markov chains on k-divisible partitions that are consistent under a random process of Markovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).

Infante, Guillermo, Anders Jonsson, and Vicenç Gómez. "Globally Optimal Hierarchical Reinforcement Learning for Linearly-Solvable Markov Decision Processes." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6970–77. http://dx.doi.org/10.1609/aaai.v36i6.20655.

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We present a novel approach to hierarchical reinforcement learning for linearly-solvable Markov decision processes. Our approach assumes that the state space is partitioned, and defines subtasks for moving between the partitions. We represent value functions on several levels of abstraction, and use the compositionality of subtasks to estimate the optimal values of the states in each partition. The policy is implicitly defined on these optimal value estimates, rather than being decomposed among the subtasks. As a consequence, our approach can learn the globally optimal policy, and does not suffer from non-stationarities induced by high-level decisions. If several partitions have equivalent dynamics, the subtasks of those partitions can be shared. We show that our approach is significantly more sample efficient than that of a flat learner and similar hierarchical approaches when the set of boundary states is smaller than the entire state space.

Cawley, Elise. "Smooth Markov partitions and toral automorphisms." Ergodic Theory and Dynamical Systems 11, no. 4 (December 1991): 633–51. http://dx.doi.org/10.1017/s0143385700006404.

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AbstractWe show that the only hyperbolic toral automorphisms f for which there exist Markov partitions with piecewise smooth boundary are those for which a power fk is linearly covered by a direct product of automorphisms of the 2-torus. Only a finite number of shapes occur in a certain natural set of cross-sections of the partition boundary. The behavior of the stratified structure of a piecewise smooth boundary under the mapping forces these shapes to be self-similar. This, together with expanding properties of the mapping, means that a piecewise smooth partition is in fact piecewise linear. Orbits of affine disks in the boundary are used to construct a basis of 2-dimensional invariant toral subgroups, and then the product decomposition of a covering follows easily.

Jung, Ho Yub, and Kyoung Mu Lee. "Image Segmentation by Edge Partitioning over a Nonsubmodular Markov Random Field." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/683176.

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Edge weight-based segmentation methods, such as normalized cut or minimum cut, require a partition number specification for their energy formulation. The number of partitions plays an important role in the segmentation overall quality. However, finding a suitable partition number is a nontrivial problem, and the numbers are ordinarily manually assigned. This is an aspect of the general partition problem, where finding the partition number is an important and difficult issue. In this paper, the edge weights instead of the pixels are partitioned to segment the images. By partitioning the edge weights into two disjoints sets, that is, cut and connect, an image can be partitioned into all possible disjointed segments. The proposed energy function is independent of the number of segments. The energy is minimized by iterating the QPBO-α-expansion algorithm over the pairwise Markov random field and the mean estimation of the cut and connected edges. Experiments using the Berkeley database show that the proposed segmentation method can obtain equivalently accurate segmentation results without designating the segmentation numbers.

Ashley, Jonathan, Bruce Kitchens, and Matthew Stafford. "Boundaries of Markov partitions." Transactions of the American Mathematical Society 333, no. 1 (January 1, 1992): 177–201. http://dx.doi.org/10.1090/s0002-9947-1992-1073772-3.

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Wagoner, J. B. "Markov partitions and K2." Publications mathématiques de l'IHÉS 65, no. 1 (December 1987): 91–129. http://dx.doi.org/10.1007/bf02698936.

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Borodin, Alexei, and Grigori Olshanski. "Markov processes on partitions." Probability Theory and Related Fields 135, no. 1 (August 17, 2005): 84–152. http://dx.doi.org/10.1007/s00440-005-0458-z.

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NEKRASHEVYCH, VOLODYMYR. "SELF-SIMILAR INVERSE SEMIGROUPS AND SMALE SPACES." International Journal of Algebra and Computation 16, no. 05 (October 2006): 849–74. http://dx.doi.org/10.1142/s0218196706003153.

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Self-similar inverse semigroups are defined using automata theory. Adjacency semigroups of s-resolved Markov partitions of Smale spaces are introduced. It is proved that a Smale space can be reconstructed from the adjacency semigroup of its Markov partition, using the notion of the limit solenoid of a contracting self-similar semigroup. The notions of the limit solenoid and a contracting semigroup is described.

Friston, Karl, Conor Heins, Kai Ueltzhöffer, Lancelot Da Costa, and Thomas Parr. "Stochastic Chaos and Markov Blankets." Entropy 23, no. 9 (September 17, 2021): 1220. http://dx.doi.org/10.3390/e23091220.

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In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology.

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Дисертації з теми "Partitions de Markov":

Kenny, Robert. "Orbit complexity and computable Markov partitions." University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0231.

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Markov partitions provide a 'good' mechanism of symbolic dynamics for uniformly hyperbolic systems, forming the classical foundation for the thermodynamic formalism in this setting, and remaining useful in the modern theory. Usually, however, one takes Bowen's 1970's general construction for granted, or restricts to cases with simpler geometry (as on surfaces) or more algebraic structure. This thesis examines several questions on the algorithmic content of (topological) Markov partitions, starting with the pointwise, entropy-like, topological conjugacy invariant known as orbit complexity. The relation between orbit complexity de nitions of Brudno and Galatolo is examined in general compact spaces, and used in Theorem 2.0.9 to bound the decrease in some of these quantities under semiconjugacy. A corollary, and a pointwise analogue of facts about metric entropy, is that any Markov partition produces symbolic dynamics matching the original orbit complexity at each point. A Lebesgue-typical value for orbit complexity near a hyperbolic attractor is also established (with some use of Brin-Katok local entropy), and is technically distinct from typicality statements discussed by Galatolo, Bonanno and their co-authors. Both our results are proved adapting classical arguments of Bowen for entropy. Chapters 3 and onwards consider the axiomatisation and computable construction of Markov partitions. We propose a framework of 'abstract local product structures'

Praggastis, Brenda L. "Markov partitions for hyperbolic toral automorphisms /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5773.

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Jeandenans, Emmanuelle. "Difféomorphismes hyperboliques des surfaces et combinatoires des partitions de Markov." Dijon, 1996. http://www.theses.fr/1996DIJOS032.

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Cette thèse traite des difféomorphismes des surfaces qui préservent l'orientation et qui vérifient l'axiome A et la transversalité forte. Une première partie étudie les plus simples d'entre eux: ceux dont les variétés invariantes ne dessinent pas de bouclette. Dans cette partie, on donne explicitement la semi-conjugaison topologique entre un tel difféomorphisme et le représentant pseudo-Anosov de sa classe d'isotopie. Une seconde partie s'intéresse à la combinatoire des partitions de Markov géométrisées (on se soucie du sens de passage de l'image des rectangles dans les rectangles). On établit une condition nécessaire et suffisante pour que le genre d'une telle partition (i. E. Le genre d'une surface compacte contenant la partition et tous ses itères) soit fini, en analysant finement le comportement des itères des rectangles, en particulier au voisinage des points périodiques situes sur le bord des rectangles initiaux. La troisième partie complète la deuxième: étant donnée une partition de Markov géométrisée de genre fini, on montre qu'il n'y a pas d'obstruction topologique à la construction d'une surface compacte munie d'un difféomorphisme vérifiant l'axiome A et la transversalité forte, admettant comme partition de Markov géométrisée celle que l'on s'est fixée. Pour ce faire, on plonge les rectangles de la partition et leurs premiers itères dans une surface compacte que l'on construit à cet effet puis on prolonge le difféomorphisme défini par la partition géométrisée en un homéomorphisme de cette surface.

Cruz, Diaz Inti. "An Algorithmic Classification of Generalized Pseudo-Anosov Homeomorphisms via Geometric Markov Partitions." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCK083.

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Cette thèse vise à fournir une classification des homéomorphismes pseudo-Anosov généralisés jusqu'à la conjugaison topologique en utilisant une approche algorithmique. Cela implique l'obtention d'invariants finis et calculables pour chaque classe de conjugaison.Une partition de Markov d'un homéomorphisme pseudo-Anosov généralisé est une décomposition de la surface en un nombre fini de rectangles avec des intérieurs disjoints, de telle manière que leurs images interagissent avec n'importe quel autre rectangle de la partition de Markov le long d'un nombre fini de sous-rectangles horizontaux. Chaque homéomorphisme pseudo-Anosov généralisé a une partition de Markov, et en utilisant l'orientation de la surface, nous pouvons doter toute partition de Markov d'une géométrisation. Ce processus implique d'étiqueter les rectangles et de choisir une orientation sur les feuilles stables et instables de chacun de ces rectangles.Le type géométrique d'une partition de Markov géométrique a été défini par Bonatti et Langevin dans leur livre "Difféomorphismes de Smale des surfaces" pour classer les pièces de base de type selle des difféomorphismes structurellement stables sur les surfaces. Un type géométrique est un objet combinatoire abstrait qui généralise la matrice d'incidence d'une partition de Markov. Il prend en compte non seulement le nombre de fois où l'image d'un rectangle interagit avec un autre rectangle de la famille, mais aussi l'ordre et le changement d'orientation induit par les homéomorphismes.Cette thèse utilise le type géométrique d'une partition de Markov géométrique pour classer les classes de conjugaison des homéomorphismes pseudo-Anosov. Nos principaux résultats peuvent être résumés comme suit :Le type géométrique est un invariant complet de la conjugaison : Une paire d'homéomorphismes pseudo-Anosov généralisés est topologiquement conjuguée l'un à l'autre à travers un homéomorphisme préservant l'orientation si et seulement si ils ont des partitions de Markov géométriques avec le même type géométrique.La réalisation : Les types géométriques sont définis de manière large, et chaque type géométrique abstrait ne correspond pas nécessairement à un homéomorphisme pseudo-Anosov. Un type géométrique T est considéré comme faisant partie de la classe pseudo-Anosov s'il existe un homéomorphisme pseudo-Anosov généralisé avec une partition de Markov géométrique de type T. Notre deuxième résultat fournit un critère calculable et combinatoire pour déterminer si un type géométrique abstrait appartient à la classe pseudo-Anosov.Représentations équivalentes : Chaque homéomorphisme pseudo-Anosov généralisé a un nombre infini de partitions de Markov géométriques avec différents types géométriques. Notre troisième résultat est un algorithme permettant de déterminer si deux types géométriques dans la classe pseudo-Anosov sont réalisés par des homéomorphismes pseudo-Anosov généralisés qui sont topologiquement conjugués ou non
This thesis aims to provide a classification of generalized pseudo-Anosov homeomorphisms up to topological conjugacy using an algorithmic approach. This entails obtaining finite and computable invariants for each conjugacy class.A Markov partition of a generalized pseudo-Anosov homeomorphism is a decomposition of the surface into a finite number of rectangles with disjoint interiors and such that their images intersect with any other rectangle in the Markov partition along a finite number of horizontal sub-rectangles. Every generalized pseudo-Anosov homeomorphism has a Markov partition, and, using the surface's orientation, we can endow any Markov partition with a geometrization. This process involves labeling the rectangles and choosing an orientation on the stable and unstable leaves of each of these rectangles.The geometric type of a geometric Markov partition was defined by Bonatti and Langevin in their book, "Difféomorphismes de Smale des surfaces," to classify saddle-type basic pieces for structurally stable diffeomorphisms on surfaces. A geometric type is an abstract combinatorial object that generalizes the incidence matrix of a Markov partition. It takes into account not only the number of times the image of a rectangle intersects with any other rectangle in the family but also the order and change of orientation induced by the homeomorphisms.This thesis employs the geometric type of a geometric Markov partition to classify the conjugacy classes of pseudo-Anosov homeomorphisms. Our main results can be summarized as follows:The geometric type is a complete invariant of conjugation: A pair of generalized pseudo-Anosov homeomorphisms is topologically conjugate to each other through an orientation-preserving homeomorphism if and only if they have geometric Markov partitions with the same geometric type.The realization: Geometric types are defined broadly, and not every abstract geometric type corresponds to a pseudo-Anosov homeomorphism. A geometric type T is considered part of the pseudo-Anosov class if there exists a generalized pseudo-Anosov homeomorphism with a geometric Markov partition of geometric type T. Our second result provides a computable and combinatorial criterion for determining whether an abstract geometric type belongs to the pseudo-Anosov class.Equivalent representations: Every generalized pseudo-Anosov homeomorphism has an infinite number of geometric Markov partitions with different geometric types. Our third result is an algorithm for determining whether two geometric types in the pseudo-Anosov class are realized by generalized pseudo-Anosov homeomorphisms that are topologically conjugated or not

Wong, Chi-hung, and 黃志雄. "Hand-written Chinese character recognition by hidden Markov models andradical partition." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31220058.

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Wingate, David. "Solving Large MDPs Quickly with Partitioned Value Iteration." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd437.pdf.

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Wong, Chi-hung. "Hand-written Chinese character recognition by hidden Markov models and radical partition /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19669380.

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Smith, Adam Nicholas. "Bayesian Analysis of Partitioned Demand Models." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497895561381294.

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Hadriche, Abir. "Caractérisation du répertoire dynamique macroscopique de l'activité électrique cérébrale humaine au repos." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4724/document.

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Nous proposons un algorithme basé sur une approche orientée d'ensemble de système dynamique pour extraire une organisation grossière de l'espace d'état de cerveau sur la base des signaux de l'EEG. Nous l'utilisons pour comparer l'organisation de l'espace d'état des données simulées à grande échelle avec la dynamique cérébrale réelle au repos chez des sujets sains et pathologiques (SEP)
We propose an algorithme based on set oriented approach of dynamical system to extract a coarse grained organization of brain state space on the basis of EEG signals. We use it for comparing the organization of the state space of large scale simulation of brain dynamics with actual brain dynamics of resting activity in healthy and SEP subjects

Joder, Cyril. "Alignement temporel musique-sur-partition par modèles graphiques discriminatifs." Phd thesis, Télécom ParisTech, 2011. http://pastel.archives-ouvertes.fr/pastel-00664260.

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Cette thèse étudie le problème de l'alignement temporel d'un enregistrement musical et de la partition correspondante. Cette tâche peut trouver de nombreuses applications dans le domaine de l'indexation automatique de documents musicaux. Nous adoptons une approche probabiliste et nous proposons l'utilisation de modèles graphiques discriminatifs de type champs aléatoires conditionnels pour l'alignement, en l'exprimant comme un problème d'étiquetage de séquence. Cette classe de modèles permet d'exprimer des modèles plus flexibles que les modèles de Markov cachés ou les modèles semi-markoviens cachés, couramment utilisés dans ce domaine. En particulier, elle rend possible l'utilisation d'attributs (ou descripteurs acoustiques) extraits de séquences de trames audio qui se recouvrent, au lieu d'observations disjointes. Nous tirons parti de cette propriété pour introduire des attributs qui réalisent une modélisation implicite du tempo au plus bas niveau du modèle. Nous proposons trois structures de modèles différentes de complexité croissant, correspondant à différents niveaux de précision dans la modélisation de la durées des évènements musicaux. Trois types de descripteurs acoustiques sont utilisés, pour caractériser localement l'harmonie, les attaques de notes et le tempo de l'enregistrement. Une série d'expériences réalisées sur une base de données de piano classique et de musique pop permet de valider la grande précision de nos modèles. En effet, avec le meilleur des systèmes proposés, plus de 95 % des attaques de notes sont détectées à moins de 100 ms de leur position réelle. Plusieurs attributs acoustiques classiques, calculés à partir de différentes représentation de l'audio, sont utiliser pour mesurer la correspondance instantanée entre un point de la partition et une trame de l'enregistrement. Une comparaison de ces descripteurs est alors menée sur la base de leurs performances d'alignement. Nous abordons ensuite la conception de nouveaux attributs, grâce à l'apprentissage d'une transformation linéaire de la représentation symbolique vers une représentation temps-fréquence quelconque de l'audio. Nous explorons deux stratégies différentes, par minimum de divergence et maximum de vraisemblance, pour l'apprentissage de la transformation optimale. Les expériences effectuées montrent qu'une telle approche peut améliorer la précision des alignements, quelle que soit la représentation de l'audio utilisée. Puis, nous étudions différents ajustements à effectuer afin de confronter les systèmes à des cas d'utilisation réalistes. En particulier, une réduction de la complexité est obtenue grâce à une stratégie originale d'élagage hiérarchique. Cette méthode tire parti de la structure hiérarchique de la musique en vue d'un décodage approché en plusieurs passes. Une diminution de complexité plus importante que celle de la méthode classique de recherche par faisceaux est observée dans nos expériences. Nous examinons en outre une modification des modèles proposés afin de les rendre robustes à d'éventuelles différences structurelles entre la partition et l'enregistrement. Enfin, les propriétés de scalabilité des modèles utilisés sont étudiées.

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Книги з теми "Partitions de Markov":

Field, Mike. Ergodic theory of equivariant diffeomorphisms: Markov partitions and stable ergodicity. Providence, R.I: American Mathematical Society, 2004.

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Csenki, Attila. Dependability for systems with a partitioned state space: Markov and semi-Markov theory and computational implementation. New York: Springer-Verlag, 1994.

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Babington, Mary F., and Christine M. Shearer. Private companies in prebuilt housing components: Trusses, walls & partitions, pre-hung windows & doors, millwork and other prebuilt housing components. Cleveland, Ohio: Freedonia Group, 1998.

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Parametric state space structuring. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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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.

Csenki, Attila. Dependability for Systems with a Partitioned State Space: Markov and Semi-Markov Theory and Computational Implementation. Springer, 2014.

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Csenki, Attila. Dependability for Systems with a Partitioned State Space: Markov and Semi-Markov Theory and Computational Implementation. Springer London, Limited, 2012.

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Misri, Deepti. Introduction. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038853.003.0001.

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This introductory chapter describes a cultural history of violence associated with widely divergent ideas of India after 1947—an India post-British Raj, post-Partition, post-Independence, and postcolonial. Communal violence, ethnonationalist insurgencies, terrorism, and counterinsurgent state violence have marked the postcolonial Indian nation-state since its very inception, often intersecting with prevailing forms of gendered violence within communities. These forms of violence have frequently indexed a serious disjoint between communally and regionally specific ideas of nationhood on the one hand, and the politically bounded, militarily enforced entity known as “India” on the other. In addition, the book is part of a wider feminist undertaking to critically examine how violence is conceptualized in the many discourses that shape public consciousness in the Indian subcontinent and its diasporic extensions.

Makatjane, Katleho, and Roscoe van Wyk. Identifying structural changes in the exchange rates of South Africa as a regime-switching process. UNU-WIDER, 2020. http://dx.doi.org/10.35188/unu-wider/2020/919-8.

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Exchange rate volatility is said to exemplify the economic health of a country. Exchange rate break points (known as structural breaks) have a momentous impact on the macroeconomy of a country. Nonetheless, this country study makes use of both unsupervised and supervised machine learning algorithms to classify structural changes as regime shifts in real exchange rates in South Africa. Weekly data for the period January 2003–June 2020 are used. To these data we apply both non-linear principal component analysis and Markov-switching generalized autoregressive conditional heteroscedasticity. The former approach is used to reduce the dimensionality of the data using an orthogonal linear transformation by preserving the statistical variance of the data, with the proviso that a new trait is non-linearly independent, and it identifies the number of regime switches that are to be used in the Markov-switching model. The latter is used to partition the variance in each regime by allowing an estimation of multiple break transitions. The transition breakpoints estimates derived from this machine learning approach produce results that are comparable to other methods on similar system sizes. Application of these methods shows that the machine learning approach can also be employed to identify structural changes as a regime-switching process. During times of financial crisis, the growing concern over exchange rate volatility, including its adverse effects on employment and growth, broadens the debates on exchange rate policies. Our results should help the South African monetary policy committee to anticipate when exchange rates will pick up and be prepared for the effects of periods of high exchange rates.

Частини книг з теми "Partitions de Markov":

Shub, Michael. "Markov Partitions." In Global Stability of Dynamical Systems, 122–46. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-1947-5_10.

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Barreira, Luis. "Invariant Manifolds and Markov Partitions." In Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, 201–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28090-0_7.

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Sinai, Ya G. "Markov Partitions and C-Diffeomorphisms." In Selecta, 257–79. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-87870-6_11.

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Blanchard, Philippe, and Dimitri Volchenkov. "Introduction to Permutations, Markov Chains, and Partitions." In Springer Series in Synergetics, 1–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19592-1_1.

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Kitchens, Bruce. "Symbolic Dynamics, Group Automorphisms and Markov Partitions." In Real and Complex Dynamical Systems, 133–63. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8439-5_6.

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Pesin, Yakov. "Sinai’s Work on Markov Partitions and SRB Measures." In The Abel Prize, 257–85. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-99028-6_11.

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Kalpazidou, S. "Cycle Representations of Markov Processes: An Application to Rotational Partitions." In Stochastic Processes and Related Topics, 253–73. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-2030-5_14.

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Katsikas, Anastassis A., and John S. Nicolis. "Chaotic dynamics of generating Markov partitions, and linguistic sequences mimicking Zipf's law." In Parallelism, Learning, Evolution, 335–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-55027-5_20.

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Csenki, Attila. "Sojourn times for Discrete-Parameter Markov Chains." In Dependability for Systems with a Partitioned State Space, 14–52. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2674-1_2.

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Csenki, Attila. "Sojourn Times for Continuous-Parameter Markov Chains." In Dependability for Systems with a Partitioned State Space, 69–105. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2674-1_4.

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Тези доповідей конференцій з теми "Partitions de Markov":

Gerontidis, Ioannis I., and Stavros P. Kontakos. "Markov Chain Lumpability on Fuzzy Partitions." In 2007 IEEE International Fuzzy Systems Conference. IEEE, 2007. http://dx.doi.org/10.1109/fuzzy.2007.4295387.

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Gerontidis, Ioannis I., and Ioannis E. Petasakis. "Lumpability of absorbing Markov chains and replacement chains on fuzzy partitions." In 2010 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2010. http://dx.doi.org/10.1109/fuzzy.2010.5584241.

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Arruda, Edilson F., Marcelo D. Fragoso, and Fabricio O. Ourique. "Multi-partition time aggregation for Markov Chains." In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. http://dx.doi.org/10.1109/cdc.2017.8264387.

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Lu, Youwei, Shogo Okada, and Katsumi Nitta. "Weibull partition models with applications to hidden semi-Markov models." In 2017 International Joint Conference on Neural Networks (IJCNN). IEEE, 2017. http://dx.doi.org/10.1109/ijcnn.2017.7965850.

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Chatterjee, Shankar, and Rama Chellappa. "Texture Segmentation Using Gaussian Markov Random Field Models." In Machine Vision. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/mv.1985.fb3.

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Segmentation of imagery data has received much attention because of its potential application in several disciplines, e.g., medicine, remote-sensing, robot vision etc.. The image segmentation problem can be specified in the following way: let A be the index set for the pixel values for the whole image; we assume that there exists a partition on A, A = A1 ⋃ A2 ⋃…⋃ Aq such that Ai ≠ ϕ and Ai ∩ Aj = ϕ ∀ i ≠ j, where each Ai is homogeneous in some sense. Thus the problem is to find A1, A2,...,Aq. The segmentation problem has been approached using both structural and statistical procedures.

Hu, He, Shuping Yao, and Peng Wu. "Security Decision Making Based on Domain Partitional Markov Decision Process." In 2009 International Conference on Information Engineering and Computer Science. ICIECS 2009. IEEE, 2009. http://dx.doi.org/10.1109/iciecs.2009.5365272.

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Wu, Jue, and Albert C. S. Chung. "Markov Random Field Energy Minimization via Iterated Cross Entropy with Partition Strategy." In 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07. IEEE, 2007. http://dx.doi.org/10.1109/icassp.2007.366715.

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Viola, M. L. Lanfredi, and Jesús E. García. "Independence’s partition of the set of coordinates of a multivariate Markov chain." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0211060.

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Lv, Hai Rong, Wen Jun Yin, and Jin Dong. "Off-line signature verification based on deformable grid partition and Hidden Markov Models." In 2009 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2009. http://dx.doi.org/10.1109/icme.2009.5202512.

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Krause, Oswin, Asja Fischer, and Christian Igel. "Algorithms for Estimating the Partition Function of Restricted Boltzmann Machines (Extended Abstract)." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/704.

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Estimating the normalization constants (partition functions) of energy-based probabilistic models (Markov random fields) with a high accuracy is required for measuring performance, monitoring the training progress of adaptive models, and conducting likelihood ratio tests. We devised a unifying theoretical framework for algorithms for estimating the partition function, including Annealed Importance Sampling (AIS) and Bennett's Acceptance Ratio method (BAR). The unification reveals conceptual similarities of and differences between different approaches and suggests new algorithms. The framework is based on a generalized form of Crooks' equality, which links the expectation over a distribution of samples generated by a transition operator to the expectation over the distribution induced by the reversed operator. Different ways of sampling, such as parallel tempering and path sampling, are covered by the framework. We performed experiments in which we estimated the partition function of restricted Boltzmann machines (RBMs) and Ising models. We found that BAR using parallel tempering worked well with a small number of bridging distributions, while path sampling based AIS performed best with many bridging distributions. The normalization constant is measured w.r.t.~a reference distribution, and the choice of this distribution turned out to be very important in our experiments. Overall, BAR gave the best empirical results, outperforming AIS.