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Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Predicting human mobility between locations has practical applications in transportation science, spatial economics, sociology and many other fields. For more than 100 years, many human mobility prediction models have been proposed, among…
After Anderson's prediction of disorder-induced insulating behavior, extensive work found no singularities in the density of states of localized systems. However, Johri and Bhatt recently uncovered the existence of a non-analyticity in the…
Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and…
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
It is highly believed that the individuals' mobility plays an important role in phase transition in animal collective motion. Here, we propose a model to study the effects of individuals' mobility in a distributed animal collective…
In stochastic population dynamics, stochastic wandering can produce transition to an absorbing state. In particular, under Allee effects, low densities amplify the possibility of population collapse. We investigate this in an…
Population boundary is a classic indicator of climatic response in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental…
Being determined by human social behaviour, pedestrian group dynamics depends on "intrinsic properties" of the group such as the purpose of the pedestrians, their personal relation, their gender, age, and body size. In this work we…
We study a model of $ N $ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from…
Let $\{U^N_t\}_{t\ge 0}$ be a standard Brownian motion on $\mathbb{U}(N)$. For fixed $N\in\mathbb{N}$ and $t>0$, we give explicit bounds on the $L_1$-Wasserstein distance of the empirical spectral measure of $U^N_t$ to both the…
There is quickly growing literature on machine-learned models that predict human driving trajectories in road traffic. These models focus their learning on low-dimensional error metrics, for example average distance between model-generated…
Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behavior consider only interactions among isolated individuals, it turns out that up to 70% of people…
Distance control in many-particle systems is a fundamental problem in nature. This becomes particularly relevant in systems of active agents, which can sense their environment and react by adjusting their direction of motion. We employ…
When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
We explore how physical scale and population size shape the emergence of complex behaviors in open-ended ecological environments. In our setting, agents are unsupervised and have no explicit rewards or learning objectives but instead evolve…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…