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Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…
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…
Inter and intra-cellular signaling are essential for individual cells to execute various physiological tasks and accurately respond to changes in their environment. Signaling is carried out via diffusible molecules, the transport of which…
We study a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in Ref. [15] and explore this new model numerically in terms of…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…
This work proposes a novel method for estimating the influence that unknown static objects might have over mobile agents. Since the motion of agents can be affected by the presence of fixed objects, it is possible use the information about…
Exchange of biochemical substances is essential way in establishing communication between bacterial cells. It is noticeable that all phases of the process are heavily influenced by perturbations of either internal or external parameters.…
We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform an evolutionary self-preservation…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…
Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these…
This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…
Modeling how human moves in the space is useful for policy-making in transportation, public safety, and public health. Human movements can be viewed as a dynamic process that human transits between states (\eg, locations) over time. In the…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Polymorphism in the peripheral sensory system (e.g., congenital individual differences in photopigment configuration) is important in diverse research fields, ranging from evolutionary biology to engineering, because of its potential…
Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely…
Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian…
Prediction of human motions is key for safe navigation of autonomous robots among humans. In cluttered environments, several motion hypotheses may exist for a pedestrian, due to its interactions with the environment and other pedestrians.…
The strategic behaviour of pedestrians is largely determined by how they perceive and react to neighbouring people. This issue is addressed in this paper by a model which combines, in a time and space-dependent way, discrete and continuous…