Related papers: Square Root Laws in Structured Fisheries
Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the…
We consider the Fisher-Snedecor diffusion; that is, the Kolmogorov-Pearson diffusion with the Fisher-Snedecor invariant distribution. In the nonstationary setting, we give explicit quantitative rates for the convergence rate of respective…
Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough…
Superstatistics is a general method from nonequilibrium statistical physics which has been applied to a variety of complex systems, ranging from hydrodynamic turbulence to traffic delays and air pollution dynamics. Here, we investigate…
Wetlands are important to communities, offering benefits ranging from water purification, and flood protection to recreation and tourism. Therefore, identifying and prioritizing potential wetland areas is a critical decision problem. While…
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…
A generalised one-dimensional Fisher-Wright diffusion process with mutations is considered. This is a well-known model in population genetics. An exponential recurrence is established for the process, which also implies an exponential rate…
We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
Rapoport's rule claims that latitudinal ranges of plant and animal species are generally smaller at low than at high latitudes. However, doubts as to the generality of the rule have been expressed, because studies providing evidence against…
Statistical learning under distributional drift remains poorly characterized, especially in closed-loop settings where learning alters the data-generating law. We introduce an intrinsic drift budget $C_T$ that quantifies cumulative…
While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability…
The goal of this paper is to disentangle the roles of volume and of participation rate in the price response of the market to a sequence of transactions. To do so, we are inspired the methodology introduced in arXiv:1402.1288,…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
We consider a dynamical system obtained by the random switching between $N$ Lotka-Volterra food chains. Our key assumption will be that at least two vector fields only differ on the resources allocated to the growth rate of the first…
We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [23], and is mathematically equivalent to an endemic variation of the Reed-Frost epidemic model introduced in [27].…
Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
Seed banks are a common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with…