Related papers: The lingering phenomenon and pattern formation in …

Dynamics of the imbalance in occupations on even and odd sites of a lattice serves as one of the key characteristics for identification of the many-body localization transition. In this work, we investigate the long-time behaviour of the…

We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…

Despite remarkable successes achieved by modern neural networks in a wide range of applications, these networks perform best in domain-specific stationary environments where they are trained only once on large-scale controlled data…

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…

While cognitive representations of an environment can last for days and even months, the synaptic architecture of the neuronal networks that underlie these representations constantly changes due to various forms of synaptic and structural…

The recent proliferation of research into transformer based natural language processing has led to a number of studies which attempt to detect the presence of human-like cognitive behavior in the models. We contend that, as is true of human…

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…

Human close-range proximity interactions are the key determinant for spreading processes like knowledge diffusion, norm adoption, and infectious disease transmission. These dynamical processes can be modeled with time-respecting paths on…

We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which…

Continual learning -- the ability to acquire knowledge incrementally without forgetting previous skills -- is fundamental to natural intelligence. While the human brain excels at this, artificial neural networks struggle with "catastrophic…

Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances,…

Despite recent efforts, neural networks still struggle to learn in non-stationary environments, and our understanding of catastrophic forgetting (CF) is far from complete. In this work, we perform a systematic study on the impact of model…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…

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…

Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity…

Hysteresis and bet-hedging (random choice of phenotypes) are two different observations typically linked with multiplicity of phenotypes in biological systems. Hysteresis can be viewed as form of the system's persistent memory of past…

We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…

Lifelong language learning seeks to have models continuously learn multiple tasks in a sequential order without suffering from catastrophic forgetting. State-of-the-art approaches rely on sparse experience replay as the primary approach to…

Spatial awareness in mammals is based on internalized representations of the environment---cognitive maps---encoded by networks of spiking neurons. Although behavioral studies suggest that these maps can remain stable for long periods, it…

The dynamics of populations is rich, taking into account that both, the individual's actions and the population's fitness are coupled. The way in which an individual chooses a strategy depends off course on the interaction with other…