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The S-matrix invariant is known to be complete for translation invariant topological stabilizer models in two spatial dimensions, as such models are phase equivalent to some number of copies of toric code. In three dimensions, much less is…

Quantum Physics · Physics 2019-10-25 Arpit Dua , Isaac H. Kim , Meng Cheng , Dominic J. Williamson

The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at…

Probability · Mathematics 2014-10-16 Nicolas Lanchier , Yuan Zhang

The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and…

Cell Behavior · Quantitative Biology 2017-12-05 Da Zhou , Shanjun Mao , Kaiyi Chen , Xiaofang Cao , Jie Hu

We consider the Moran process with two populations competing under an iterated Prisoners' Dilemma in the presence of mutation, and concentrate on the case where there are multiple Evolutionarily Stable Strategies. We perform a complete…

Dynamical Systems · Mathematics 2015-12-23 Lee DeVille , Meghan Galiardi

Ensemble averages of a stochastic model show that, after a formation stage, the tips of active blood vessels in an angiogenic network form a moving two dimensional stable diffusive soliton, which advances toward sources of growth factor.…

Statistical Mechanics · Physics 2020-08-26 L. L. Bonilla , M. Carretero , F. Terragni

We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent…

Statistical Mechanics · Physics 2015-06-25 Peter F. Arndt , Thomas Heinzel , Vladimir Rittenberg

A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…

Numerical Analysis · Mathematics 2019-02-19 Gopikrishnan C. Remesan

In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance, in the case of a bone tumor in a femur) initial colony. In…

Analysis of PDEs · Mathematics 2026-01-15 Rafael Granero-Belinchón , Martina Magliocca

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along…

Chaotic Dynamics · Physics 2009-11-10 Dominique Delande , Jakub Zakrzewski

Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful…

Tissues and Organs · Quantitative Biology 2007-05-23 Steve P. Lee , Ji-Rong Sun , Hong Qian , William H. McBride , H. Rodney Withers

Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the…

Cell Behavior · Quantitative Biology 2007-05-23 Sabrina L. Spencer , Matthew J. Berryman , Jose A. Garcia , Derek Abbott

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to…

Dynamical Systems · Mathematics 2024-05-31 Erik Blom , Stefan Engblom

We study a simple 2-d model representing two fields with different mass and a 3-point coupling term. The phase shift in the resonating 2-particle channel is determined from the energy spectrum obtained in Monte Carlo simulations on finite…

High Energy Physics - Lattice · Physics 2009-10-22 C. R. Gattringer , C. B. Lang

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…

Populations and Evolution · Quantitative Biology 2018-11-02 Alex McAvoy , Ben Adlam , Benjamin Allen , Martin A. Nowak

A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…

Cellular Automata and Lattice Gases · Physics 2007-05-23 J. R. Sanchez , R. Lopez-Ruiz

We introduce a superstatistical model for the progression statistics of malignant cancer cells. The metastatic cascade is modeled as a complex nonequilibrium system with several macroscopic pathways and inverse-chi-square distributed…

Medical Physics · Physics 2007-11-30 L. Leon Chen , Christian Beck

The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we…

Tissues and Organs · Quantitative Biology 2010-12-13 Roberto Chignola , Alessio Del Fabbro , Marcello Farina , Edoardo Milotti

A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…

Probability · Mathematics 2017-11-06 Christian Deuß , Julia Hörrmann , Christoph Thaele

We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…

Analysis of PDEs · Mathematics 2020-06-24 Andrea Genovese de Oliveira , John R. King

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…

Dynamical Systems · Mathematics 2023-03-21 Marvin Fritz