scholarly journals The New Inclusion Region of Eigenvalue Different from 1 for a Stochastic Matrix

2016 ◽  
Vol 06 (04) ◽  
pp. 361-367
Author(s):  
宝星 周
Keyword(s):  
Stochastic Matrix ◽  
Inclusion Region

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

scholarly journals G7H, a New Soybean mosaic virus Strain: Its Virulence and Nucleotide Sequence of CI Gene

Plant Disease ◽  
2003 ◽  
Vol 87 (11) ◽  
pp. 1372-1375 ◽  
Author(s):  
Yul-Ho Kim ◽  
Ok-Sun Kim ◽  
Bong-Choon Lee ◽  
Jung-Kyung Moon ◽  
Sang-Chul Lee ◽  
...  
Keyword(s):  
Nucleotide Sequence ◽  
Mosaic Virus ◽  
Virus Strain ◽  
Soybean Mosaic Virus ◽  
Mosaic Symptom ◽  
Inclusion Region ◽  
Soybean Cultivars ◽  
Soybean Mosaic Virus Strain ◽  
Local Lesions ◽  
Differential Cultivars

A new Soybean mosaic virus (SMV) strain was isolated in Korea and designated as G7H. Its virulence on eight differentials and 42 Korean soybean cultivars was compared with existing SMV strains. G7H caused the same symptoms as G7 did on the eight differential cultivars. However, it caused different symptoms on the G7-immune Korean soybean cultivars; G7H caused necrosis in Suwon 97 (Hwangkeumkong) and Suwon 181 (Daewonkong), and a mosaic symptom in Miryang 41 (Duyoukong), while G7 caused only local lesions on those varieties. The nucleotide sequence of the cylindrical inclusion region of G7H was determined and compared with other SMV strains. G7H shared 96.3 and 91.3% nucleotide similarities with G2 and G7, respectively; whereas G7 shared 95.6% nucleotide similarity with G5H.

scholarly journals Markov Stochastic Processes in Biology and Mathematics -- the Same, and yet Different

2018 ◽  
Vol 14 (1) ◽  
pp. 7540-7559
Author(s):  
MI lOS lAWA SOKO
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Stochastic Matrix ◽  
Random Number Generator ◽  
Point Of View ◽  
State Transitions ◽  
Similar Principle ◽  
Probabilistic Space ◽  
And Mathematics

Virtually every biological model utilising a random number generator is a Markov stochastic process. Numerical simulations of such processes are performed using stochastic or intensity matrices or kernels. Biologists, however, define stochastic processes in a slightly different way to how mathematicians typically do. A discrete-time discrete-value stochastic process may be defined by a function p : X0 × X → {f : Î¥ → [0, 1]}, where X is a set of states, X0 is a bounded subset of X, Î¥ is a subset of integers (here associated with discrete time), where the function p satisfies 0 < p(x, y)(t) < 1 and  EY p(x, y)(t) = 1. This definition generalizes a stochastic matrix. Although X0 is bounded, X may include every possible state and is often infinite. By interrupting the process whenever the state transitions into the X −X0 set, Markov stochastic processes defined this way may have non-quadratic stochastic matrices. Similar principle applies to intensity matrices, stochastic and intensity kernels resulting from considering many biological models as Markov stochastic processes. Class of such processes has important properties when considered from a point of view of theoretical mathematics. In particular, every process from this class may be simulated (hence they all exist in a physical sense) and has a well-defined probabilistic space associated with it.

Computer Modelling of Non-Equilibrium Multiple-Trapping and Hopping Transport in Amorphous Semiconductors

2005 ◽  
Vol 862 ◽  
Author(s):  
C. Main ◽  
J. M. Marshall ◽  
S. Reynolds ◽  
M.J. Rose ◽  
R. Brüggemann
Keyword(s):  
Computer Modelling ◽  
Stochastic Matrix ◽  
Computational Procedure ◽  
Amorphous Semiconductors ◽  
Extended State ◽  
Hopping Transport ◽  
Multiple Trapping ◽  
Extended States ◽  
Localised States ◽  
Gap States

AbstractIn this paper we demonstrate a simple computational procedure for the simulation of transport in a disordered semiconductor in which both multi-trapping and hopping processes are occurring simultaneously. We base the simulation on earlier work on hopping transport, which used a Monte-Carlo method. Using the same model concepts, we now employ a stochastic matrix approach to speed computation, and include also multi-trapping transitions between localised and extended states. We use the simulation to study the relative contributions of extended state conduction (with multi-trapping) and hopping conduction (via localised states) to transient photocurrents, for various distributions of localised gap states, and as a function of temperature. The implications of our findings for the interpretation of transient photocurrents are examined.

Permanents of Random Doubly Stochastic Matrices

1974 ◽  
Vol 26 (3) ◽  
pp. 600-607 ◽  
Author(s):  
R. C. Griffiths
Keyword(s):  
Symmetric Group ◽  
Stochastic Matrix ◽  
Stochastic Matrices ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic ◽  
Survey Article ◽  
Doubly Stochastic Matrices ◽  
Image Position

The permanent of an n × n matrix A = (aij) is defined aswhere Sn is the symmetric group of order n. For a survey article on permanents the reader is referred to [2]. An unresolved conjecture due to van der Waerden states that if A is an n × n doubly stochastic matrix; then per (A) ≧ n!/nn, with equality if and only if A = Jn = (1/n).

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