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Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Legged locomotion demands controllers that are both robust and adaptable, while remaining compatible with task and safety considerations. However, model-free reinforcement learning (RL) methods often yield a fixed policy that can be…
Animals often exhibit changes in their behavior during migration. Telemetry data provide a way to observe geographic position of animals over time, but not necessarily changes in the dynamics of the movement process. Continuous-time models…
Natural and expressive human motion generation is the holy grail of computer animation. It is a challenging task, due to the diversity of possible motion, human perceptual sensitivity to it, and the difficulty of accurately describing it.…
Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Diffusion-based models, such as the Stable Diffusion model, have revolutionized text-to-image synthesis with their ability to produce high-quality, high-resolution images. These advancements have prompted significant progress in image…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Earth System Models (ESMs) are essential tools for understanding the impact of human actions on Earth's climate. One key application of these models is studying extreme weather events, such as heat waves or dry spells, which have…
We present a Master Equation formulation based on a Markovian random walk model that exhibits sub-diffusion, classical diffusion and super-diffusion as a function of a single parameter. The non-classical diffusive behavior is generated by…
Subdiffusion is a hallmark of complex systems, ranging from protein folding to transport in viscoelastic media. However, despite its pervasiveness, the mechanistic origins of subdiffusion remain contested. Here, we analyze both Markovian…
We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
Earth System Models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations…