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During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially or simultaneously. These growth patterns are manifested in all types of bacteria and yeasts. The ubiquity of these growth…

Discovering causal relations from observational data becomes possible with additional assumptions such as considering the functional relations to be constrained as nonlinear with additive noise (ANM). Even with strong assumptions, causal…

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…

Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to…

Active loop extrusion - the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes - is firmly established mechanism responsible for chromatin spatial organization at different…

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…

Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…

Actin growth is a fundamental biophysical process and it is, at the same time, a prototypical example of diffusion-mediated surface growth. We formulate a coupled chemo-mechanical, one-dimensional growth model encompassing both material…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…

Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure.…

Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…

Vascular and non-vascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear…

We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…

Granular materials segregate spontaneously due to differences in particle size, shape, density and flow behaviour. In this paper we experimentally investigate density-difference-driven segregation for a range of density ratios and a range…

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…

In densely-packed two-dimensional systems of growing cells, such as rod-shaped bacteria, a number of experimental and numerical studies report distinct patterns of nematic orientational order in the presence of confinement. So far, these…