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The classic differential evolution algorithm and its convergence properties

Roman Knobloch, Jaroslav Mlýnek, Radek Srb (2017)

Applications of Mathematics

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the...

The compositional construction of Markov processes II

L. de Francesco Albasini, N. Sabadini, R. F. C. Walters (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, 
arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput. 37 (2007) 977–1013].

The compositional construction of Markov processes II

L. de Francesco Albasini, N. Sabadini, R. F.C. Walters (2011)

RAIRO - Theoretical Informatics and Applications

We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, 
arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].

The continuum reaction-diffusion limit of a stochastic cellular growth model

Stephan Luckhaus, Livio Triolo (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered....

The critical barrier for the survival of branching random walk with absorption

Bruno Jaffuel (2012)

Annales de l'I.H.P. Probabilités et statistiques

We study a branching random walk on ℝ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law, Biggins et al. [Ann. Appl. Probab.1(1991) 573–581] determined whether a linear barrier allows the process to survive. In this paper, we refine their result: in the boundary case in which the speed of the barrier matches the speed of the minimal position of a particle...

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