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Reduction of absorbing Markov chain

Mariusz Górajski (2009)

Annales UMCS, Mathematica

In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on the initial...

Reinforced walk on graphs and neural networks

Józef Myjak, Ryszard Rudnicki (2008)

Studia Mathematica

A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.

Stability and throughput improvement for multichannel CSMA and CSMA/CD protocols with optimal bandwidth allocation

Ioannis E. Pountourakis (2000)

Kybernetika

This paper examines appropriate protocols for high speed multiple access communication systems where the bandwidth is divided into two separate asymmetric channels. Both channels operate using slotted non-persistent CSMA or CSMA/CD techniques. Free stations access the first channel while all retransmissions occur in the second channel. We define the stability regions and the rules for optimal bandwidth allocation among the two channels for improvement of the system performance in case of infinite...

Statistical Modelling: Application to the financial sector

Cláudia Roçadas, Teresa A. Oliveira, João T. Mexia (2011)

Discussiones Mathematicae Probability and Statistics

Our research is centred on the stochastic structure of matched open populations, subjected to periodical reclassifications. These populations are divided into sub-populations. In our application we considered two populations of customers of a bank: with and without account manager. Two or more of such population are matched when there is a 1-1 correspondence between their sub-populations and the elements of one of them can go to another, if and only if the same occurs with elements from the...

The Kendall theorem and its application to the geometric ergodicity of Markov chains

Witold Bednorz (2013)

Applicationes Mathematicae

We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of...

Theoretical analysis of steady state genetic algorithms

Alexandru Agapie, Alden H. Wright (2014)

Applications of Mathematics

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are...

Two algorithms based on Markov chains and their application to recognition of protein coding genes in prokaryotic genomes

Małgorzata Grabińska, Paweł Błażej, Paweł Mackiewicz (2013)

Applicationes Mathematicae

Methods based on the theory of Markov chains are most commonly used in the recognition of protein coding sequences. However, they require big learning sets to fill up all elements in transition probability matrices describing dependence between nucleotides in the analyzed sequences. Moreover, gene prediction is strongly influenced by the nucleotide bias measured by e.g. G+C content. In this paper we compare two methods: (i) the classical GeneMark algorithm, which uses a three-periodic non-homogeneous...

Un modelo de aprendizaje discriminado en tiempo continuo.

Juan Ignacio Domínguez Martínez (1983)

Trabajos de Estadística e Investigación Operativa

Se introduce, basándonos en el aprendizaje de identificación, un proceso de aprendizaje discriminado en tiempo continuo a partir del modelo discreto propuesto por Restle (1955), ampliado por Bourne y Restle (1959) y generalizado por Domínguez (1980), aplicándolo al aprendizaje "pareja-asociada" al considerar sólo dos tipos de respuestas. La contrucción teórica del modelo se basa en la teoría general de los procesos estocásticos de aprendizaje en tiempo continuo (Domínguez, 1979). La introducción...

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