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1

Extremal particles in branching processes

Meller R.

Mathematica Applicanda

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2017

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Vol. 45, No. 1

3--20

EN

The purpose of this study is to investigate the behavior of extremal particles in a spatial branching process on R with the heavy-tailed compound Poisson process motion and inhomogeneous potential.

PL

W pracy rozważane są dwa modele procesów gałązkowych, pierwszy bazujący na procesie Galtona-Watsona, drugi na złożonym procesie Poissona. Oba procesy posiadają nieograniczony potencjał rozmnażania. Badana jest najwyższa cząstka w modelu poprzez określenie jej asymptotyki prawie na pewno z dokładnością do stałej. Oszacowanie z dołu polega na odgadnięciu prawie optymalnej strategii poruszania się cząstek. Oszacowanie z góry polega na badaniu innych modeli, prostszych w analizie, które stochastycznie szybciej się przemieszczają.

2

Reachability in Contextual Nets

Winkowski J.

Fundamenta Informaticae

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2002

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Vol. 51, nr 1,2

235-250

EN

Contextual nets, or Petri nets with read arcs, are models of concurrent systems with context dependent actions. The problem of reachability in such nets consists in finding a sequence of transitions that leads from the initial marking of a given contextual net to a given goal marking. The solution to this problem that is presented in this paper consists in constructing a finite complete prefix of the unfolding of the given contextual net, that is a finite prefix in which all the markings that are reachable from the initial marking are present, and in searching in each branch of this prefix for the goal marking by solving an appropriate linear programming problem.

3

An Application of General Branching Processes to a Cell Cycle model With Two Uncoupled Subcycles and Unequal Cell Division

Alexandersson M.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 1

131-145

EN

A cell population model is constructed and analysed in the frameworkof general branching process theory. The model uses the idea that the DNA division cycle and the cell growth cycle are loosely coupled. The cell division is assumed to be unequal and the structure variables of the modelare size and growth, where the growth is regulated by supramitotic growth control. An explicit expression for the stable birth type distributionis given and asymptotics, such as the alpha- and beta_1-curve and various size distributions, are derived. We also prove that the microheterogeneity ingrowth causes the mother-daughter life length correlation to be non-negative.

4

Mathematical modeling of telomere shortening: an overview

Olofsson P.

Archives of Control Sciences

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1999

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Vol. 9, no. 1/2

133-141

EN

Shortening of telomeres is one of the supposed mechanisms of aging and death. This paper reviews the attempts to model and analyze this process with mathematical methods. The emphasis is put on branching process models where the main features are irreducibility and polynomial growth.