Related papers: Diffusion vs. direct transport in the precision of…
Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between…
A large variety of real systems are composed by entities in relationships which can be represented by networks. In many of these systems, elements are embedded in the space and location information impacts properties and evolution. Local…
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
Channel-mediated transport is ubiquitous in biology. A series of works by different theoreticians have sought to determine how the diffusive flux through a channel depends on (a) stochastic gating, (b) channel geometry, and (c)…
The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…
Intracellular transport is essential for maintaining proper cellular function in most eukaryotic cells, with perturbations in active transport resulting in several types of disease. Efficient delivery of critical cargos to specific…
The migratory dynamics of cells can be influenced by the complex micro-environment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their micro-environment. Here, we propose a…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Turing patterns are fundamental in biophysics, emerging from short-range activation and long-range inhibition processes. However, their paradigm is based on diffusive transport processes, which yields Turing patters that are less sharp than…
Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by incorporating a guidance term that steers the generative…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…
In this work, we consider diffusion-based molecular communication with and without drift between two static nano-machines. We employ type-based information encoding, releasing a single molecule per information bit. At the receiver, we…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {\em sticky} environments. Therefore, diffusing particles experience both…
Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to \textit{compositionally generalize}. Nonetheless, the precise…
Within the domain of molecular communications, researchers mimic the techniques in nature to come up with alternative communication methods for collaborating nanomachines. This work investigates the channel transfer function for molecular…