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Collective motion in animal groups emerges from the interplay between individual variability and social coordination, yet connecting these scales quantitatively has remained a major challenge.Using high-resolution trajectories of schooling…
Random walks on the circle group $\mathbb{R}/\mathbb{Z}$ whose elementary steps are lattice variables with span $\alpha \not\in \mathbb{Q}$ or $p/q \in \mathbb{Q}$ taken mod $\mathbb{Z}$ exhibit delicate behavior. In the rational case we…
We report on the asymptotic behaviour of a new model of random walk, we term the bindweed model, evolving in a random environment on an infinite multiplexed tree. The term \textit{multiplexed} means that the model can be viewed as a nearest…
Walking animals, like stick insects, cockroaches or ants, demonstrate a fascinating range of locomotive abilities and complex behaviors. The locomotive behaviors can consist of a variety of walking patterns along with adaptation that allow…
Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active…
Collective animal movement fascinates children and scientists alike. One of the most commonly given explanations for collective animal movement is improved foraging. Animals are hypothesized to gain from searching for food in groups. Here,…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
Better machine understanding of pedestrian behaviors enables faster progress in modeling interactions between agents such as autonomous vehicles and humans. Pedestrian trajectories are not only influenced by the pedestrian itself but also…
Active particles such as swimming bacteria or self-propelled colloids are known to spontaneously organize into fascinating large-scale dynamic structures. The emergence of these collective states from the motility pattern of the individual…
Moving groups are routinely faced with a choice of different routes as part of their daily lives, such as choosing between exits from a building. Differences in moving speeds and environmental constraints often lead to individuals being…
Understanding factors affecting social interactions among animals is important for applied animal behavior research. Thus, there is a need to elicit statistical models to analyze data collected from pairwise behavioral interactions. In this…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
In collective motion, perceptually-limited individuals move in an ordered manner, without centralized control. The perception of each individual is highly localized, as is its ability to interact with others. While natural collective motion…
Motivated by the study of social insects, we introduce a stochastic model based on interacting particle systems in order to understand the effect of communication on the division of labor. Members of the colony are located on the vertex set…
We use immobility as an origin and reference for the measurement of locomotor behavior; speed, the direction of walking and the direction of facing as the three degrees of freedom shaping fly locomotor behavior, and cocaine as the parameter…
The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the…
The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model…
In this paper, we present a model describing the collective motion of birds. The model introduces spontaneous changes in direction which are initialized by few agents, here referred as leaders, whose influence act on their nearest…
We study a random walk driven by a particle system from a generic class, and establish a law of large numbers for the walk for almost all densities of the environment. To do so, we exploit the finite-ranged approximations of the environment…