Related papers: Linear competition processes and generalized Polya…
We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…
We consider a system of $N$ individuals consisting of $S$ species that interact pairwise: $x_m+x_\ell \rightarrow 2x_m\,\,$ with arbitrary probabilities $p_m^\ell $. With no spatial structure, the master equation yields a simple set of rate…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process,…
The global asymptotic behavior of the classical diffusive Lotka-Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under…
We study systems of three interacting particles, in which drifts and variances are assigned by rank. These systems are "degenerate": the variances corresponding to one or two ranks can vanish, so the corresponding ranked motions become…
The Thoma cone is an infinite-dimensional locally compact space, which is closely related to the space of extremal characters of the infinite symmetric group. In another context, the Thoma cone appears as the set of parameters for totally…
The resources in a cell are finite, which implies that the various components of the cell must compete for resources. One such resource is the ribosomes used during translation to create proteins. Motivated by this example, we explore this…
Competing risk models are survival models with several events of interest acting in competition and whose occurrence is only observed for the event that occurs first in time. This paper presents a Bayesian approach to these models in which…
The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and…
We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $\lambda>0$. With probability $p \in [0,1]$ an offspring is fertile…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
A competitive resource-consumer dynamical model is analyzed based on an integrated model of a competitive Lotka-Volterra model and a prey-predator Rosenzweig-MacArthur model that we call that LV-RM model throughout this paper. Resource…
We construct a Markov process model to describe the evolution of labor division and its dynamical behavior is investigated by numerical simulations in detail. We have shown that under the mechanism of increasing returns, the division of…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…
Linear Fisher market is one of the most fundamental economic models. The market is traditionally examined on the basis of individual's price-taking behavior. However, this assumption breaks in markets such as online advertising and…