Related papers: Logistic approximations and their consequences to …
We examine the feasibility of predicting and subsequently managing the future evolution of a Complex Adaptive System. Our archetypal system mimics a competitive population of mechanical, biological, informational or human objects. We show…
Mixing dependency lengths from sequences of different length is a common practice in language research. However, the empirical distribution of dependency lengths of sentences of the same length differs from that of sentences of varying…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
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…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
With the increasing capabilities of LLMs, recent studies focus on understanding whose opinions are represented by them and how to effectively extract aligned opinion distributions. We conducted an empirical analysis of three straightforward…
Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this…
We consider a parameter dependent periodic-logistic problem with a logistic term involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
The growth of world population, limitation of resources, economic problems and environmental issues force engineers to develop increasingly efficient solutions for logistic systems. Pure optimization for efficiency, however, has often led…
We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare…