Game Theory Cancer Models of Cancer Cell–Stromal Cell Dynamics Using Interacting Particle Systems

2020 ◽  
pp. 39-61
Author(s):  
Yinan Zheng ◽  
Yusha Sun ◽  
Gonzalo Torga ◽  
Kenneth Pienta ◽  
Robert Austin
Keyword(s):  
Game Theory ◽  
Cancer Cell ◽  
Stromal Cell ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Cell Dynamics ◽  
Interacting Particle ◽  
Cancer Models

Game Theory Cancer Models of Cancer Cell-Stromal Cell Dynamics using Interacting Particle Systems

2020 ◽  
Vol 15 (03) ◽  
pp. 171-193
Author(s):  
Yinan Zheng ◽  
Yusha Sun ◽  
Gonzalo Torga ◽  
Kenneth Pienta ◽  
Robert Austin
Keyword(s):  
Game Theory ◽  
Interacting Particle Systems ◽  
Evolutionary Game ◽  
Mean Field ◽  
Theory Model ◽  
Particle Systems ◽  
Cell Dynamics ◽  
Field Approach ◽  
Interacting Particle ◽  
The Mean

We describe an evolutionary game theory model that has been used to predict the population dynamics of interacting cancer and stromal cells. We first consider the mean field case assuming homogeneous and nondiscrete populations. Interacting Particle Systems (IPS) are then presented as a discrete and spatial alternative to the mean field approach. Finally, we discuss cases where IPS gives results different from the mean field approach.

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

scholarly journals Holomorphic Bogoliubov functionals for interacting particle systems in continuum

2006 ◽  
Vol 238 (2) ◽  
pp. 375-404 ◽  
Author(s):  
Yuri G. Kondratiev ◽  
Tobias Kuna ◽  
Maria João Oliveira
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle
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