Related papers: A Generalized Population Dynamics Model of a City …
A population protocol describes a set of state change rules for a population of $n$ indistinguishable finite-state agents (automata), undergoing random pairwise interactions. Within this very basic framework, it is possible to resolve a…
The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency…
Migration plays a crucial role in urban growth. Over time, individuals opting to relocate led to vast metropolises like London and Paris during the Industrial Revolution, Shanghai and Karachi during the last decades and thousands of smaller…
The interaction of all mobile species with their environment hinges on their movement patterns: the places they visit and how frequently they go there. In human society, where the prevalent form of cohabitation is in cities, the highly…
Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium…
We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random…
Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very…
Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others.…
We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at…
Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical-mechanical model of urban…
We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two…
Why are human societies unstable? Theories based on the observation of recurring patterns in historical data indicate that economic inequality, as well as social factors are key drivers. So far, models of this phenomenon are more…