Related papers: Point Mutations and Transitions Between Cellular A…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
The replicator-mutator dynamic was originally derived to model the evolution of language, and since the model was derived in such a general manner, it has been applied to the dynamics of social behavior and decision making in multi-agent…
Reinforcement learning algorithms are typically designed for generic Markov Decision Processes (MDPs), where any state-action pair can lead to an arbitrary transition distribution. In many practical systems, however, only a subset of the…
A toggle switch consists of two genes that mutually repress each other. This regulatory motif is active during cell differentiation and is thought to act as a memory device, being able to choose and maintain cell fate decisions. In this…
Binary-state models are those in which the constituent elements can only appear in two possible configurations. These models are fundamental in the mathematical treatment of a number of phenomena such as spin interactions in magnetism,…
A hybrid Potts model where a random concentration $p$ of the spins assume $q_0$ states and a random concentration $1-p$ of the spins assume $q>q_0$ states is introduced. It is known that when the system is homogeneous, with an integer spin…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in…
We propose an iterative algorithm to investigate the cooperative evolution dominated by information encoded within state spaces in a random quantum cellular automaton. Inspired by the 2-gram model in statistical linguistics, the updates of…
Attractor neural network models of cortical decision-making circuits represent them as dynamical systems in the state space of neural firing rates with the attractors of the network encoding possible decisions. While the attractors of these…
An introduction to cellular automata (both deterministic and probabilistic) with examples. Definition of deterministic automata, dynamical properties, damage spreading and Lyapunov exponents; probabilistic automata and Markov processes,…
A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to control pathwisely the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
We represent a filamentous actin molecule as a graph of finite-state machines (F-actin automaton). Each node in the graph takes three states --- resting, excited, refractory. All nodes update their states simultaneously and by the same…
A biological transition from a state N to a state T is characterized by a rearrangement of the gene expression profile in the system, quantitatively measured through the differential expression of genes. In contrast, changes in genetic…
Living cells inherently reorganize their intracellular structures in response to mechanical cues from their environment. Among these responses, the formation of actin-based stress fibers exhibits a series of structural transitions depending…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Regime-switching processes contain two components: continuous component and discrete component, which can be used to describe a continuous dynamical system in a random environment. Such processes have many different properties than general…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…