Related papers: The strategy of survival for a competition between…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
In this work, the aim is to study the diffusion of innovation of two competing products. The main focus has been to understand the effects of the competitive dynamic market on the diffusion of innovation. The global smartphone operating…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
Understanding and identifying different types of single molecules' diffusion that occur in a broad range of systems (including living matter) is extremely important, as it can provide information on the physical and chemical characteristics…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…
In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…
The deviation from pure Brownian motion generally referred to as anomalous diffusion has received large attention in the scientific literature to describe many physical scenarios. Several methods, based on classical statistics and machine…
The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
The presence of adversarial examples poses a significant threat to deep learning models and their applications. Existing defense methods provide certain resilience against adversarial examples, but often suffer from decreased accuracy and…