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Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban development, such models influence decisions that affect…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
The present work proposes the concept of induced percolation over multiple-object systems, so that features such as the number of merged clusters can be used as a relevant measurement. The suggested approach involves the expansion of the…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
To determine an optimal plan for complex tasks, one often deals with dynamic and hierarchical relationships between several entities. Traditionally, such problems are tackled with optimal control, which relies on the optimization of cost…
Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies)…
As the frontiers of biology become increasingly interdisciplinary, the physics education community has engaged in ongoing efforts to make physics classes more relevant to life sciences majors. These efforts are complicated by the many…
One of the greatest research challenges of this century is to understand the neural basis for how behavior emerges in brain-body-environment systems. To this end, research has flourished along several directions but have predominantly…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
This paper deals with the micro-macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in in…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
All aspects of our society, including the life sciences, need a mechanism for people working within them to represent the concepts they employ to carry out their research. For the information systems being designed and developed to support…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…
Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform…