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The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts

A. Szabó, A. Czirók (2010)

Mathematical Modelling of Natural Phenomena

Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...

The role of Mechanics in Tumor growth : Modelling and Simulation

D. Ambrosi (2011)

ESAIM: Proceedings

A number of biological phenomena are interlaced with classical mechanics. In this review are illustrated two examples from tumor growth, namely the formation of primordial networks of vessels (vasculogenesis) and the avascular phase of solid tumors. In both cases the formalism of continuum mechanics, accompanied by accurate numerical simulations, are able to shed light on biological controversies. The converse is also true: non-standard mechanical problems suggest new challenging mathematical questions....

The Rothe method for the McKendrick-von Foerster equation

Henryk Leszczyński, Piotr Zwierkowski (2013)

Czechoslovak Mathematical Journal

We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in L ∞ and...

The Second Half-With a Quarter of a Century Delay

O. Diekmann, M. Gyllenberg (2008)

Mathematical Modelling of Natural Phenomena

We show how results by Diekmann et al. (2007) on the qualitative behaviour of solutions of delay equations apply directly to a resource-consumer model with age-structured consumer population.

The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below

Tomasz Cieślak (2006)

Banach Center Publications

In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.

The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

Igor Sazonov, Mark Kelbert, Michael B. Gravenor (2008)

Mathematical Modelling of Natural Phenomena

A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres is considered numerically and analytically. The limiting solutions describing the behaviour of the standard SIR model with a small number of initially infected individuals are derived, and expressions found for the duration of an outbreak. We study a model for a weakly mixed population distributed between the interacting centres. The centres are modelled as SIR nodes with interaction between sites determined by a diffusion-type...

The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification

Hans-Joachim Böckenhauer, Michal Forišek, Ján Oravec, Björn Steffen, Kathleen Steinhöfel, Monika Steinová (2010)

RAIRO - Theoretical Informatics and Applications

Analyzing genomic data for finding those gene variations which are responsible for hereditary diseases is one of the great challenges in modern bioinformatics. In many living beings (including the human), every gene is present in two copies, inherited from the two parents, the so-called haplotypes. In this paper, we propose a simple combinatorial model for classifying the set of haplotypes in a population according to their responsibility for a certain genetic disease. This model is based...

The Use of CFSE-like Dyes for Measuring Lymphocyte Proliferation : Experimental Considerations and Biological Variables

B.J.C. Quah, A.B. Lyons, C.R. Parish (2012)

Mathematical Modelling of Natural Phenomena

The measurement of CFSE dilution by flow cytometry is a powerful experimental tool to measure lymphocyte proliferation. CFSE fluorescence precisely halves after each cell division in a highly predictable manner and is thus highly amenable to mathematical modelling. However, there are several biological and experimental conditions that can affect the quality of the proliferation data generated, which may be important to consider when modelling dye...

The Wiener number of Kneser graphs

Rangaswami Balakrishnan, S. Francis Raj (2008)

Discussiones Mathematicae Graph Theory

The Wiener number of a graph G is defined as 1/2∑d(u,v), where u,v ∈ V(G), and d is the distance function on G. The Wiener number has important applications in chemistry. We determine the Wiener number of an important family of graphs, namely, the Kneser graphs.

The Wiener number of powers of the Mycielskian

Rangaswami Balakrishnan, S. Francis Raj (2010)

Discussiones Mathematicae Graph Theory

The Wiener number of a graph G is defined as 1 / 2 ∑ u , v ∈ V ( G ) d ( u , v ) , d the distance function on G. The Wiener number has important applications in chemistry. We determine a formula for the Wiener number of an important graph family, namely, the Mycielskians μ(G) of graphs G. Using this, we show that for k ≥ 1, W ( μ ( S ₙ k ) ) ≤ W ( μ ( T ₙ k ) ) ≤ W ( μ ( P ₙ k ) ) , where Sₙ, Tₙ and Pₙ denote a star, a general tree and a path on n vertices respectively. We also obtain Nordhaus-Gaddum type inequality for the Wiener number of μ ( G k ) .

Theorem on signatures

Władysław Kulpa, Andrzej Szymański (2007)

Acta Universitatis Carolinae. Mathematica et Physica

Thermal ablation modeling via the bioheat equation and its numerical treatment

Agnieszka Bartłomiejczyk, Henryk Leszczyński, Artur Poliński (2015)

Applicationes Mathematicae

The phenomenon of thermal ablation is described by Pennes' bioheat equation. This model is based on Newton's law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.

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