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Low-discrepancy point sets for non-uniform measures

Christoph Aistleitner, Josef Dick (2014)

Acta Arithmetica

We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on [ 0 , 1 ] d there exists a point set x 1 , . . . , x N ∈ [ 0 , 1 ] d whose star-discrepancy with respect to μ is of order D N * ( x 1 , . . . , x N ; μ ) ≪ ( ( l o g N ) ( 3 d + 1 ) / 2 ) / N . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...

Marginalization in models generated by compositional expressions

Francesco M. Malvestuto (2015)

Kybernetika

In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.

Marginalization in multidimensional compositional models

Vladislav Bína, Radim Jiroušek (2006)

Kybernetika

Efficient computational algorithms are what made graphical Markov models so popular and successful. Similar algorithms can also be developed for computation with compositional models, which form an alternative to graphical Markov models. In this paper we present a theoretical basis as well as a scheme of an algorithm enabling computation of marginals for multidimensional distributions represented in the form of compositional models.

Mathematical and Computational Models in Tumor Immunology

F. Pappalardo, A. Palladini, M. Pennisi, F. Castiglione, S. Motta (2012)

Mathematical Modelling of Natural Phenomena

The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...

Mathematical and numerical modeling of early atherosclerotic lesions***

Vincent Calvez, Jean Gabriel Houot, Nicolas Meunier, Annie Raoult, Gabriela Rusnakova (2010)

ESAIM: Proceedings

This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work [5] that was mainly restricted to a one-dimensional setting, we couple...

Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics

T. Stiehl, A. Marciniak-Czochra (2012)

Mathematical Modelling of Natural Phenomena

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts....

Mean field limit for the one dimensional Vlasov-Poisson equation

Maxime Hauray (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

We consider systems of N particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the Vlasov-Poisson equation. Actually a rigorous proof of that convergence was given by Trocheris in [Tro86]. Here we shall give a simpler proof of this result, and explain why it implies the so-called “Propagation of molecular chaos”. More precisely, both results will...

Measuring the Irreversibility of Numerical Schemes for Reversible Stochastic Differential Equations

Markos Katsoulakis, Yannis Pantazis, Luc Rey-Bellet (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility...

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