Related papers: Estimation of Parameter Distributions for Reaction…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
In many applications concerning statistical graphical models the data originate from several subpopulations that share similarities but have also significant differences. This raises the question of how to estimate several graphical models…
We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…
Spatio-temporal biochemical signaling in a large class of protein-protein interaction networks is well modeled by a reaction-diffusion system. The global existence of the solution to the reaction-diffusion system is determined by the…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt…
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…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…