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A novel robust principal component analysis method for image and video processing

Guoqiang Huan, Ying Li, Zhanjie Song (2016)

Applications of Mathematics

The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the ℓ 1 -norm. However, the sparse noise has clustering effect in practice so using a certain ℓ p -norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery...

A stochastic extension of R. Thomas regulatory network modelling

Bartek Wilczyński (2008)

Banach Center Publications

In this paper we present the extension of the kinetic logic proposed by René Thomas for analysis of genetic regulatory gene networks. We consider the case with a Gaussian noise added to the regulation function and propose a method of analyzing the resulting model with a discrete time Markov model.

Approximate Aggregation Methods in Discrete Time Stochastic Population Models

L. Sanz, J. A. Alonso (2010)

Mathematical Modelling of Natural Phenomena

Approximate aggregation techniques consist of introducing certain approximations that allow one to reduce a complex system involving many coupled variables obtaining a simpler ʽʽaggregated systemʼʼ governed by a few variables. Moreover, they give results that allow one to extract information about the complex original system in terms of the behavior of the reduced one. Often, the feature that allows one to carry out such a reduction is the presence...

Bottom-up modeling of domestic appliances with Markov chains and semi-Markov processes

Rajmund Drenyovszki, Lóránt Kovács, Kálmán Tornai, András Oláh, István Pintér (2017)

Kybernetika

In our paper we investigate the applicability of independent and identically distributed random sequences, first order Markov and higher order Markov chains as well as semi-Markov processes for bottom-up electricity load modeling. We use appliance time series from publicly available data sets containing fine grained power measurements. The comparison of models are based on metrics which are supposed to be important in power systems like Load Factor, Loss of Load Probability. Furthermore, we characterize...

Comparación numérica de algoritmos para calcular distribuciones estacionarias de cadenas de Markov finitas.

Antonio López Quílez, Enriqueta Vercher (1992)

Trabajos de Investigación Operativa

En este trabajo se estudia la eficiencia de un conjunto de algoritmos, exactos e iterativos, para el problema de obtener la distribución estacionaria de una cadena de Markov homogénea, irreducible y finita. Se presentan los resultados computacionales obtenidos al resolver problemas de diferentes tipos y tamaños, aleatoriamente generados, así como el tratamiento estadístico realizado sobre los mismos. Se ha comparado la estabilidad de estos algoritmos frente a la pérdida de irreducibilidad y la existencia...

Compound Poisson approximation of word counts in DNA sequences

Sophie Schbath (2010)

ESAIM: Probability and Statistics

Identifying words with unexpected frequencies is an important problem in the analysis of long DNA sequences. To solve it, we need an approximation of the distribution of the number of occurrences N(W) of a word W. Modeling DNA sequences with m-order Markov chains, we use the Chen-Stein method to obtain Poisson approximations for two different counts. We approximate the “declumped” count of W by a Poisson variable and the number of occurrences N(W) by a compound Poisson variable. Combinatorial...

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