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Pollen grains are known for their impressive variety of species-specific, microscale surface patterning. Despite having similar biological developmental steps, pollen grain surface features are remarkably geometrically varied. Previous work…
We consider the subdiffusion--absorption process in a system which consists of two different media separated by a thin membrane. The process is described by subdiffusion--absorption equations with fractional Riemann--Liouville time…
Solvent-based techniques usually involve preparing dilute blends of electron-donor and electron-acceptor materials dissolved in a volatile solvent. After some form of coating onto a substrate, the solvent evaporates. An initially…
Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods. We propose torsional diffusion, a…
Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
Cell fate decisions in multicellular organisms are precisely coordinated, leading to highly reproducible macroscopic outcomes of developmental processes. The origins of this reproducibility can be found at the molecular level during the…
The compartmentalization of distinct templates in protocells and the exchange of templates between them (migration) are key elements of a modern scenario for prebiotic evolution. Here we use the diffusion approximation of population…
It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion…
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost…
An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive…
Here we address a fundamental issue in surface physics: the dynamics of adsorbed molecules. We study this problem when the particle's desorption is characterized by a non Markovian process, while the particle's adsorption and its motion in…
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…
The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organization. Many of these transitions are achieved…
Structure of monolayers built during adsorption process is strongly related to the properties of adsorbed particles. The most important factor is their shape. For example, adsorption of elongated molecules on patterned surfaces may produce…
Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…
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…