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Matrix Factorization and Stochastic State Representations

Proceedings of the 45th IEEE Conference on Decision and Control, 2006
Given a two-point finite valued process, we consider the problem of finding an underlying two-point state process such that the output at a certain time instant is a probabilistic function of the state at the same time instant. This problem is related to the hidden Markov realization problem for finite valued processes.
Bart Vanluyten   +2 more
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Stochastic Logic Realization of Matrix Operations

2014 17th Euromicro Conference on Digital System Design, 2014
Stochastic computing (SC) is a re-emerging technique to process probability data encoded in digital bit-streams. Its main advantage is that arithmetic operations can be implemented by extremely small and low-power logic circuits. This makes SC suitable for signal-processing applications involving matrix operations whose VLSI implementation is very ...
Pai-Shun Ting, John Patrick Hayes
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A Nontrivial Solution to a Stochastic Matrix Equation

East Asian Journal on Applied Mathematics, 2012
Summary: If \(A\) is a nonsingular matrix such that its inverse is a stochastic matrix, the classic Brouwer fixed point theorem implies that the matrix equation \(AXA = XAX\) has a nontrivial solution. An explicit expression of this nontrivial solution is found via the mean ergodic theorem, and fixed point iteration is considered to find a nontrivial ...
Ding, J., Rhee, N. H.
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Stochastic shape functions and stochastic strain–displacement matrix for a stochastic finite element stiffness matrix

Acta Mechanica, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Permanent of a Doubly Stochastic Matrix

Canadian Journal of Mathematics, 1966
If is an n X n matrix, the permanent of A, Per A, is defined by1where the sum is over all permutations. If A is doubly stochastic (i.e., nonnegative with row and column sums all equal to 1), then it has been conjectured that Per A ⩾ n!/nn. When confronted with a vaguely similar problem about determinants, M.
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Matrix-Geometric Methods for the General Stochastic Epidemic

Mathematical Medicine and Biology, 1984
This paper outlines a matrix-geometric formulation of the general stochastic epidemic for the case of a generalized infection mechanism. The forward Kolmogorov equations of the system are derived, and the Laplace transforms of the state probabilities obtained recursively. These lead to the probabilities of survivors of the epidemic.
Gani, J., Purdue, P.
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DECOMPOSITION OF STOCHASTIC FLOWS AND ROTATION MATRIX

Stochastics and Dynamics, 2002
We provide geometrical conditions on the manifold for the existence of the Liao's factorization of stochastic flows [10]. If M is simply connected and has constant curvature, then this decomposition holds for any stochastic flow, conversely, if every flow on M has this decomposition, then M has constant curvature.
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Targetted stochastic matrix inversion

Journal of Computational Physics, 1989
This paper introduces a new method for inverting stochastic matrices. The Pan-Reif algorithm is used to allow any non-singular matrix to be stochastically inverted. The original von Neumann-Ulam method is largely improved to overcome some of its efficiency problems. The method is tested on some physical problems.
Dreitlein, Joseph F., Sowers, George F.
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Concerning the Minimum Function of a Stochastic Matrix

Canadian Mathematical Bulletin, 1967
A square matrix is said to be stochastic if its elements are non-negative and if each of its row sums is equal to one. Thus λ = 1 is always an eigenvalue of a stochastic matrix.
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Stochastic Matrix Models

1997
This chapter, like Chapter 2, is about population models in which time and population structure are discrete, but here the models contain vital rates that vary randomly over time. Such random variation is ubiquitous and can strongly influence the dynamics and evolution of populations.
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