Related papers: Incorporating domain growth into hybrid methods fo…

This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime…

The performance of leaning-based perception algorithms suffer when deployed in out-of-distribution and underrepresented environments. Outdoor robots are particularly susceptible to rapid changes in visual scene appearance due to dynamic…

We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules…

Classical methods in robot motion planning, such as sampling-based and optimization-based methods, often struggle with scalability towards higher-dimensional state spaces and complex environments. Diffusion models, known for their…

Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…

Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…

Diffusion models arise as a powerful generative tool recently. Despite the great progress, existing diffusion models mainly focus on uni-modal control, i.e., the diffusion process is driven by only one modality of condition. To further…

Deep learning is widely applied in computer-aided pathological diagnosis, which alleviates the pathologist workload and provide timely clinical analysis. However, most models generally require large-scale annotated data for training, which…

Eosinophilic Esophagitis (EoE) represents a challenging condition for medical providers today. The cause is currently unknown, the impact on a patient's daily life is significant, and it is increasing in prevalence. Traditional approaches…

Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…

To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…

Generative models, such as GANs and diffusion models, have been used to augment training sets and boost performances in different tasks. We focus on generative models for cell detection instead, i.e., locating and classifying cells in given…

Detectors often suffer from performance drop due to domain gap between training and testing data. Recent methods explore diffusion models applied to domain generalization (DG) and adaptation (DA) tasks, but still struggle with large…

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…

We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…

Diffusion models have emerged as powerful tools for 3D medical image generation, yet bridging the gap between standard training objectives and clinical relevance remains a challenge. This paper presents a method to enhance 3D diffusion…

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…

The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…