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Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of…

The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in…

In order to enable high-quality decision making and motion planning of intelligent systems such as robotics and autonomous vehicles, accurate probabilistic predictions for surrounding interactive objects is a crucial prerequisite. Although…

The interaction between individuals in biological populations, dilute components of chemical systems, or particles transported by turbulent flows depends critically on their contact statistics. This work clarifies those statistics under the…

Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…

Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…

Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…

The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online…

Besides mimicking bio-chemical and multi-scale communication mechanisms, molecular communication forms a theoretical framework for virus infection processes. Towards this goal, aerosol and droplet transmission has recently been modeled as a…

Understanding how biological organisms make decisions is of fundamental importance in understanding behavior. Such an understanding within evolutionary game theory so far has been sought by appealing to bounded rationality. Here, we present…

We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…

Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired…

The boundaries between physical and social networks have narrowed with the advent of the Internet and its pervasive platforms. This has given rise to a complex adaptive information ecosystem where individuals and machines compete for…

For group-living animals, reaching consensus to stay cohesive is crucial for their fitness, particularly when collective motion starts and stops. Understanding the decision-making at individual and collective levels upon sudden disturbances…

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…

Collaboration plays a key role in knowledge production. Here, we show that patterns of interaction during conferences can be used to predict who will subsequently form a new collaboration, even when interaction is prescribed rather than…

Research over the past few decades has assumed the richness (number of species) to be the primary driver of the biodiversity and ecosystem function (BEF) relationship. However, biodiversity is multi-dimensional, and richness alone does not…

Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…

Large animal groups -- bird flocks, fish schools, insect swarms -- are often assumed to form by gradual aggregation of sparsely distributed individuals. Using a mathematically precise framework based on time-varying directed interaction…

The motion of pedestrian crowds (e.g. for simulation of an evacuation situation) can be modeled as a multi-body system of self driven particles with repulsive interaction. We use a few simple situations to determine the simplest allowed…