Related papers: Triangulation sensing: how cells recover a source …

In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

The physical limit with which a cell senses external ligand concentration corresponds to the perfect absorber, where all ligand particles are absorbed and overcounting of same ligand particles does not occur. Here we analyze how the lateral…

Metastatic cancer cells detect the direction of lymphatic flow by self-communication: they secrete and detect a chemical which, due to the flow, returns to the cell surface anisotropically. The secretion rate is low, meaning detection noise…

Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal…

Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…

A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…

We study the effects of introducing a feedback channel in the erasure source-broadcast problem for the case of three receivers. In our problem formulation, we wish to transmit a binary source to three users over the erasure broadcast…

Cellular decision-making based on information received from the external environment is frequently initiated by transmembrane receptors. These receptors are known to propagate such information by triggering a series of irreversible,…

In the reconstruction process of sound waves in a 3D stratified waveguide, a key technique is to effectively reduce the huge computational demand. In this work, we propose an efficient and simple multilevel reconstruction method to help…

Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…

Generating molecules that bind to specific proteins is an important but challenging task in drug discovery. Previous works usually generate atoms in an auto-regressive way, where element types and 3D coordinates of atoms are generated one…

Molecular communication (MC), one of the emerging techniques in the field of communication, is entering a new phase following several decades of foundational research. Recently, attention has shifted toward MC in liquid media, particularly…

We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate $r$. We consider several generalisations of the model of…

The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…

From nutrient uptake, to chemoreception, to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors…

Accurate modeling of ultrasound wave propagation is essential for high-fidelity simulation and imaging in ultrasonic testing. A primary challenge lies in characterizing the excitation source, particularly for transducers with large…

We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The…