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Journal articles on the topic 'Exchangeable probability partition function'

Author: Grafiati

Published: 9 March 2023

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1

Bassetti, Federico, and Lucia Ladelli. "Mixture of Species Sampling Models." Mathematics 9, no. 23 (2021): 3127. http://dx.doi.org/10.3390/math9233127.

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We introduce mixtures of species sampling sequences (mSSS) and discuss how these sequences are related to various types of Bayesian models. As a particular case, we recover species sampling sequences with general (not necessarily diffuse) base measures. These models include some “spike-and-slab” non-parametric priors recently introduced to provide sparsity. Furthermore, we show how mSSS arise while considering hierarchical species sampling random probabilities (e.g., the hierarchical Dirichlet process). Extending previous results, we prove that mSSS are obtained by assigning the values of an e

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2

Kurt, Noemi, and Mathias Rafler. "Recursions for the exchangeable partition function of the seedbank coalescent." Theoretical Population Biology 114 (April 2017): 95–106. http://dx.doi.org/10.1016/j.tpb.2016.12.002.

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3

Crane, Harry, and Peter McCullagh. "Reversible Markov structures on divisible set partitions." Journal of Applied Probability 52, no. 03 (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&gt; 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

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4

Speed, T. P., and H. L. Silcock. "Cumulants and partition lattices VI. variances and covariances of mean squares." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 3 (1988): 362–88. http://dx.doi.org/10.1017/s1446788700032158.

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AbstractFormulae are given for the variances and covariances for mean squares in anova under the broadest possible assumptions. The results of ther authors are obtained by specializing appropriately: these include ones concerning randomization and/or random sampling models, as well as additive (linear) models consisting of mutually independent sets of exchangeable effects. Although the illustrations given refer only to doubly and triply-indexed arrays, the approach is quite general. Particular attention is drawn to the generalized cumulants (and their natural unbiased estimators) which vanish

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5

GNEDIN, ALEXANDER, and JIM PITMAN. "Poisson Representation of a Ewens Fragmentation Process." Combinatorics, Probability and Computing 16, no. 6 (2007): 819–27. http://dx.doi.org/10.1017/s0963548306008352.

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A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [n] = 1,. . .,nat time θ ≥ 0 is governed by the Ewens sampling formula with parameter θ. These partition-valued processes are exchangeable and consistent, asnvaries. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx−1dx on/mathbbR+, arranged to beintensifying as θ increases.

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6

Ono, Ken. "Distribution of the Partition Function Modulo m." Annals of Mathematics 151, no. 1 (2000): 293. http://dx.doi.org/10.2307/121118.

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7

de Tilière, Béeatrice. "Partition function of periodic isoradial dimer models." Probability Theory and Related Fields 138, no. 3-4 (2006): 451–62. http://dx.doi.org/10.1007/s00440-006-0041-2.

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8

Watson, G. S. "An ordering inequality for exchangeable random variables." Advances in Applied Probability 18, no. 1 (1986): 274–76. http://dx.doi.org/10.2307/1427246.

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Let X1, · ··, Xn be exchangeable random variables with finite variance and two sequences of constants satisfying a1≦···≦an, b1≦···≦bn. Suppose that a′1, ···, a′n is a rearrangement of a1, ···, an and that g(x) is a non-decreasing function. Then

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9

Hansen, Jennie C. "A functional central limit theorem for the Ewens sampling formula." Journal of Applied Probability 27, no. 1 (1990): 28–43. http://dx.doi.org/10.2307/3214593.

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For each n > 0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integer n. To determine the limiting distributions for the part sizes of a partition with respect to the measures given by this formula, we associate to each partition a step function on [0, 1]. Each jump in the function equals the number of parts in the partition of a certain size. We normalize these functions and show that the induced measures on D[0, 1] converge to Wiener measure. This result complements Kingman's frequency limit theorem [10] for the Ewens partition struct

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10

Hoyle, David C. "Replica analysis of the lattice-gas restricted Boltzmann machine partition function." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 1 (2023): 013301. http://dx.doi.org/10.1088/1742-5468/acaf83.

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Abstract We study the expectation value of the logarithm of the partition function of large binary-to-binary lattice-gas restricted Boltzmann machines (RBMs) within a replica-symmetric ansatz, averaging over the disorder represented by the parameters of the RBM Hamiltonian. Averaging over the Hamiltonian parameters is done with a diagonal covariance matrix. Due to the diagonal form of the parameter covariance matrix not being preserved under the isomorphism between the Ising and lattice-gas forms of the RBM, we find differences in the behaviour of the quenched log partition function of the lat

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11

Scarsini, Marco. "Lower bounds for the distribution function of a k-dimensionaln-extensible exchangeable process." Statistics & Probability Letters 3, no. 2 (1985): 57–62. http://dx.doi.org/10.1016/0167-7152(85)90024-0.

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12

Navarro, Jorge, and Moshe Shaked. "Hazard rate ordering of order statistics and systems." Journal of Applied Probability 43, no. 2 (2006): 391–408. http://dx.doi.org/10.1239/jap/1152413730.

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Let X = (X1, X2, …, Xn) be an exchangeable random vector, and write X(1:i) = min{X1, X2, …, Xi}, 1 ≤ i ≤ n. In this paper we obtain conditions under which X(1:i) decreases in i in the hazard rate order. A result involving more general (that is, not necessarily exchangeable) random vectors is also derived. These results are applied to obtain the limiting behaviour of the hazard rate function of the lifetimes of various coherent systems in reliability theory. The notions of the Samaniego signatures and the minimal signatures of such systems are extensively used in the paper. An interesting relat

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13

Ribeiro, G. A. P., A. Klümper, and P. A. Pearce. "On the partition function of the Sp(4) integrable vertex model." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 11 (2022): 113102. http://dx.doi.org/10.1088/1742-5468/ac99d5.

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Abstract In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp(4) symmetry. We establish a set of functional relations which include a transfer matrix inversion identity. The solution of these relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental Sp(4) representation of the vertex model. As a byproduct we also obtain the partition function per site of a vertex model mixing the four and five dimensional representations of the Sp(4) symmetry.

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14

Lu, Wentao T., and F. Y. Wu. "Partition function zeroes of a self-dual Ising model." Physica A: Statistical Mechanics and its Applications 258, no. 1-2 (1998): 157–70. http://dx.doi.org/10.1016/s0378-4371(98)00273-8.

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15

Abe, Takaaki. "Cartel Formation in Cournot Competition with Asymmetric Costs: A Partition Function Approach." Games 12, no. 1 (2021): 14. http://dx.doi.org/10.3390/g12010014.

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In this paper, we use a partition function form game to analyze cartel formation among firms in Cournot competition. We assume that a firm obtains a certain cost advantage that allows it to produce goods at a lower unit cost. We show that if the level of the cost advantage is “moderate”, then the firm with the cost advantage leads the cartel formation among the firms. Moreover, if the cost advantage is relatively high, then the formed cartel can also be stable in the sense of the core of a partition function form game. We also show that if the technology for the low-cost production can be copi

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16

Gardner, E., and B. Derrida. "The probability distribution of the partition function of the random energy model." Journal of Physics A: Mathematical and General 22, no. 12 (1989): 1975–81. http://dx.doi.org/10.1088/0305-4470/22/12/003.

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17

Hui, Zhi Xin. "The Practicability of Pluralistic Nr-E-V Distribution and a Comparison of it with Singular Statistical Distribution." Applied Mechanics and Materials 330 (June 2013): 1071–74. http://dx.doi.org/10.4028/www.scientific.net/amm.330.1071.

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This paper, based on the maximum entropy and conditional extremum, deals with the practicability of Nr-E-V distribution of the pluralistic single-phase system. Whats more, in the paper other kinds of distributions formulas of probability and partition function have been derived from Nr-E-V distribution. Finally, the thermodynamics function of partition function, internal energy, entropy and pressure of E distribution are derived from the example of pluralistic ideal gas composed of single-atomic molecule.

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18

Harata, Pipat, and Prathan Srivilai. "Grand canonical partition function of a serial metallic island system." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 013101. http://dx.doi.org/10.1088/1742-5468/ac3e6c.

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Abstract We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described using Grassmann numbers. The Coulomb charging energy of the system is represented in terms of phase fields conjugate to the island charges. By the large channel approximation, the tunneling action phase dependence can also be determined explicitly. Therefore, we represent the partition function as a path integral over phase fields with a path proba

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19

Zhou, Haijun, Chuang Wang, Jing-Qing Xiao, and Zedong Bi. "Partition function expansion on region graphs and message-passing equations." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 12 (2011): L12001. http://dx.doi.org/10.1088/1742-5468/2011/12/l12001.

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20

Janse van Rensburg, E. J. "Partition and generating function zeros in adsorbing self-avoiding walks." Journal of Statistical Mechanics: Theory and Experiment 2017, no. 3 (2017): 033208. http://dx.doi.org/10.1088/1742-5468/aa5ec9.

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21

Kogan, Yaakov. "Exact analysis for a class of simple, circuit-switched networks with blocking." Advances in Applied Probability 21, no. 4 (1989): 952–55. http://dx.doi.org/10.2307/1427782.

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We consider the same circuit switching problem as in Mitra [1]. The calculation of the blocking probabilities is reduced to finding the partition function for a closed exponential pseudo-network with L−1 customers. This pseudo-network differs from that in [1] in one respect only: service rates at nodes 1, 2, …, p depend on the queue length. The asymptotic expansion developed in [1] follows from our exact expression for the partition function.

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22

Sinclair, Christopher D. "The partition function of multicomponent log-gases." Journal of Physics A: Mathematical and Theoretical 45, no. 16 (2012): 165002. http://dx.doi.org/10.1088/1751-8113/45/16/165002.

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23

Jokela, Niko, Matti Järvinen, Esko Keski-Vakkuri, and Jaydeep Majumder. "Disk partition function and oscillatory rolling tachyons." Journal of Physics A: Mathematical and Theoretical 41, no. 1 (2007): 015402. http://dx.doi.org/10.1088/1751-8113/41/1/015402.

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24

Beaton, N. R., and E. J. Janse van Rensburg. "Partition function zeros of adsorbing Dyck paths." Journal of Physics A: Mathematical and Theoretical 51, no. 11 (2018): 114002. http://dx.doi.org/10.1088/1751-8121/aaabcf.

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25

DO, KIM HANG PHAM, and HENK NORDE. "THE SHAPLEY VALUE FOR PARTITION FUNCTION FORM GAMES." International Game Theory Review 09, no. 02 (2007): 353–60. http://dx.doi.org/10.1142/s021919890700145x.

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Different axiomatizations of the Shapley value for TU games can be found in the literature. The Shapley value has been generalized in several ways to the class of games in partition function form. In this paper we discuss another generalization of the Shapley value and provide a characterization.

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26

Mann, Ryan L., and Michael J. Bremner. "Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs." Quantum 3 (July 11, 2019): 162. http://dx.doi.org/10.22331/q-2019-07-11-162.

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We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computin

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27

Yang, Di, and Jian Zhou. "Grothendieck’s dessins d’enfants in a web of dualities. III." Journal of Physics A: Mathematical and Theoretical 56, no. 5 (2023): 055201. http://dx.doi.org/10.1088/1751-8121/acb744.

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Abstract We give a new proof of the equivalence between the dessin partition function and the partition function of the Laguerre unitary ensemble (LUE), originally found by Ambjørn and Chekhov. We also introduce a correction factor for the dessin/LUE partition function, and show that the corrected dessin/LUE partition function is a Dubrovin–Zhang type tau-function of the Toda lattice hierarchy. As an application, we use the approach of Dubrovin and Zhang for the computation of the dessin correlators. In physicists’ terminology, we establish dualities among dessin counting, generalized Penner m

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28

Majumdar, Debjyoti, and Somendra M. Bhattacharjee. "Zeros of partition function for continuous phase transitions using cumulants." Physica A: Statistical Mechanics and its Applications 553 (September 2020): 124263. http://dx.doi.org/10.1016/j.physa.2020.124263.

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29

Keshavarzi, Ezat, Mozhgan Sabzehzari, and Mehdi Eliasi. "Quantum vibrational partition function in the non-extensive Tsallis framework." Physica A: Statistical Mechanics and its Applications 389, no. 14 (2010): 2733–38. http://dx.doi.org/10.1016/j.physa.2010.03.026.

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30

Filali, G., and N. Kitanine. "Erratum: Partition function of the trigonometric SOS model with reflecting end." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 07 (2010): E07002. http://dx.doi.org/10.1088/1742-5468/2010/07/e07002.

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31

Pham, Anh Minh. "A Pfaffian formula for the Ising partition function of surface graphs." Journal of Statistical Mechanics: Theory and Experiment 2020, no. 8 (2020): 083103. http://dx.doi.org/10.1088/1742-5468/aba1e4.

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32

ALBIZURI, M. J., J. ARIN, and J. RUBIO. "AN AXIOM SYSTEM FOR A VALUE FOR GAMES IN PARTITION FUNCTION FORM." International Game Theory Review 07, no. 01 (2005): 63–72. http://dx.doi.org/10.1142/s0219198905000405.

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Lucas and Trall (1963) defined the games in partition function form as a generalization of the cooperative games with transferable utility. In our work we propose by means of an axiomatic characterization a solution for such games in partition function form. This solution will be a generalization of the Shapley value (1953).

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33

JU, YUAN. "THE CONSENSUS VALUE FOR GAMES IN PARTITION FUNCTION FORM." International Game Theory Review 09, no. 03 (2007): 437–52. http://dx.doi.org/10.1142/s0219198907001515.

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This paper studies a procedural and axiomatic extension of the consensus value [cf. Ju et al. (2007)] to the class of partition function form games. This value is characterized as the unique function that satisfies efficiency, complete symmetry, the quasi-null player property and additivity. By means of the transfer property, a second characterization is provided. Moreover, it is shown that the consensus value satisfies individual rationality under a superadditivity condition, and well balances the tradeoff between coalitional effects and externality effects. In this respect, explicit differen

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34

Assis, M., J. L. Jacobsen, I. Jensen, J.-M. Maillard, and B. M. McCoy. "The hard hexagon partition function for complex fugacity." Journal of Physics A: Mathematical and Theoretical 46, no. 44 (2013): 445202. http://dx.doi.org/10.1088/1751-8113/46/44/445202.

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35

Filali, G., and N. Kitanine. "The partition function of the trigonometric SOS model with a reflecting end." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 06 (2010): L06001. http://dx.doi.org/10.1088/1742-5468/2010/06/l06001.

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36

Viswanathan, G. M. "The hypergeometric series for the partition function of the 2D Ising model." Journal of Statistical Mechanics: Theory and Experiment 2015, no. 7 (2015): P07004. http://dx.doi.org/10.1088/1742-5468/2015/07/p07004.

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37

Knoll, Christian, and Franz Pernkopf. "Belief propagation: accurate marginals or accurate partition function—where is the difference?" Journal of Statistical Mechanics: Theory and Experiment 2020, no. 12 (2020): 124009. http://dx.doi.org/10.1088/1742-5468/abcaef.

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38

Heirwegh, K. P. M., J. A. T. P. Meuwissen, M. Vermeir, and H. De Smedt. "Liposomes as carriers of poorly water-soluble substrates: linear modelling of membrane systems with catalytic or binding sites of different facedness. Significance of experimental membrane partition coefficients and of kinetic and equilibrium parameters." Biochemical Journal 254, no. 1 (1988): 101–8. http://dx.doi.org/10.1042/bj2540101.

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1. A multiphasic modelling approach to systems containing membrane-bound receptors or catalytic sites and a liposomal preparation as a substrate carrier is described. Kinetic expressions are derived for a single-substrate enzymic reaction operating at constant liposome concentration or at a fixed substrate/liposome concentration ratio. 2. The assumption that accumulation of exchangeable components into the phospholipid bilayers can be described by linear bulk-phase partition leads to simple relationships between the initial reaction rate and (a) two kinetic coefficients (V and K'm), (b) the pa

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39

Kalbasi, Kamran, Thomas S. Mountford, and Frederi G. Viens. "Anderson Polymer in a Fractional Brownian Environment: Asymptotic Behavior of the Partition Function." Journal of Theoretical Probability 31, no. 3 (2017): 1429–68. http://dx.doi.org/10.1007/s10959-017-0756-2.

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40

Bolger, E. M. "A set of axioms for a value for partition function games." International Journal of Game Theory 18, no. 1 (1989): 37–44. http://dx.doi.org/10.1007/bf01248494.

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41

Sun, J. Q. "A Nonuniform Cell Partition for the Analysis of Nonlinear Stochastic Systems." Journal of Applied Mechanics 65, no. 4 (1998): 867–69. http://dx.doi.org/10.1115/1.2791924.

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This paper presents a study of nonuniform cell partition for analyzing the response of nonlinear stochastic systems by using the generalized cell mapping (GCM) method. The necessity of nonuniform cell partition for nonlinear systems is discussed first. An ad hoc scheme is then presented for determining optimal cell sizes based on the statistical analysis of the GCM method. The proposed nonuniform cell partition provides a roughly uniform accuracy for the estimate of the one-step transition probability density function over a large region in the state space where the system varies significantly

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42

GALANIS, ANDREAS, DANIEL ŠTEFANKOVIČ, and ERIC VIGODA. "Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models." Combinatorics, Probability and Computing 25, no. 4 (2016): 500–559. http://dx.doi.org/10.1017/s0963548315000401.

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Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006), establish a beautiful picture of the computational complexity of approximating the partition function of the hard-core model. Let λc($\mathbb{T}_{\Delta}$) denote the critical activity for the hard-model on the infinite Δ-regular tree. Weitz presented anFPTASfor the partition function when λ < λc($\mathbb{T}_{\Delta}$) for graphs with constant maximum degree Δ. In contrast, Sly showed that for all Δ ⩾ 3, there exists εΔ> 0 such that (unless RP = NP) there is noFPRASfor appr

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43

Izergin, A. G., E. Karjalainen, and N. A. Kitanin. "Integrable equations for the partition function of the six-vertex model." Journal of Mathematical Sciences 100, no. 2 (2000): 2141–46. http://dx.doi.org/10.1007/bf02675734.

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44

JÁJÁ, JOSEPH, and KWAN WOO RYU. "AN OPTIMAL RANDOMIZED PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM." Parallel Processing Letters 06, no. 02 (1996): 187–93. http://dx.doi.org/10.1142/s0129626496000182.

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We describe a randomized parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O( log n) time using O(n) operations with high probability on the Priority CRCW PRAM. The previous best known algorithms run in O( log 2 n) time using O(n log 2 n) operations on the CREW PRAM and O( log n) time using O(n log log n) operations on the Arbitrary CRCW PRAM. The technique presented can be used to generate the Euler tour of a rooted tree optimally from the parent representation.

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45

Speed, T. P. "Cumulants and partition lattices II: generalised k-statistics." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (1986): 34–53. http://dx.doi.org/10.1017/s1446788700026483.

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AbstractThe role played by the Möbius function of the lattice of all partitions of a set in the theory of k-statistics and their generalisations is pointer out and the main results conscerning these statistics are drived. The definitions and formulae for the expansion of products of generalished k-statistics are presented from this viewpoint and applied to arrays of random variables whos moments satisfy stitable symmentry constraints. Applications of the theory are given including the calculation of (joint) cumulants of k-statistics, the minimum variace estimation of (generalised) moments and

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46

GROTHAUS, MARTIN, LUDWIG STREIT, and IGOR V. VOLOVICH. "KNOTS, FEYNMAN DIAGRAMS AND MATRIX MODELS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 03 (1999): 359–80. http://dx.doi.org/10.1142/s0219025799000217.

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A U (N)-invariant matrix model with d matrix variables is studied. It was shown that in the limit N → ∞ and d→0 the model describes the knot diagrams. We realize the free partition function of the matrix model as the generalized expectation of a Hida distribution ΦN,d. This enables us to give a mathematically rigorous meaning to the partition function with interaction. For the generalized function ΦN,d, we prove a Wick theorem and we derive explicit formulas for the propagators.

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47

Sano, Takashi. "A noniterative solution to the inverse Ising problem using a convex upper bound on the partition function." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 2 (2022): 023406. http://dx.doi.org/10.1088/1742-5468/ac50b1.

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Abstract The inverse Ising problem, or the learning of Ising models, is notoriously difficult, as evaluating the partition function has a large computational cost. To quickly solve this problem, inverse formulas using approximation methods such as the Bethe approximation have been developed. In this paper, we employ the tree-reweighted (TRW) approximation to construct a new inverse formula. An advantage of using the TRW approximation is that it provides a rigorous upper bound on the partition function, allowing us to optimize a lower bound for the learning objective function. We show that the

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48

Khanjari Sadegh, Mohammad. "A note on the mean residual life function of a coherent system with exchangeable or nonidentical components." Journal of Statistical Planning and Inference 141, no. 9 (2011): 3267–75. http://dx.doi.org/10.1016/j.jspi.2011.04.013.

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49

Zimmerman, Donald W., Richard H. Williams, and Bruno D. Zumbo. "Correction of the Student T Statistic for Nonindependence of Sample Observations." Perceptual and Motor Skills 75, no. 3 (1992): 1011–20. http://dx.doi.org/10.2466/pms.1992.75.3.1011.

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A computer-simulation study examined the one-sample Student t test under violation of the assumption of independent sample observations. The probability of Type I errors increased, and the probability of Type II errors decreased, spuriously elevating the entire power function. The magnitude of the change depended on the correlation between pairs of sample values as well as the number of sample values that were pairwise correlated. A modified t statistic, derived from an unbiased estimate of the population variance that assumed only exchangeable random variables instead of independent, identica

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Chen, Chi-Ning, and Chai-Yu Lin. "Partition function zeros of the two-dimensional HP model for protein folding." Physica A: Statistical Mechanics and its Applications 350, no. 1 (2005): 45–51. http://dx.doi.org/10.1016/j.physa.2004.11.035.

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