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The Origin-Destination~(OD) networks provide an estimation of the flow of people from every region to others in the city, which is an important research topic in transportation, urban simulation, etc. Given structural regional urban…
Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited,…
Cancer cell populations often exhibit remarkably similar growth laws despite their heterogeneity. Explanations of universal cell population growth remain partly unresolved to this day. Here, we present a growth-law unification by…
The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
Droplets are essential for spatially controlling biomolecules in cells. To work properly, cells need to control the emergence and morphology of droplets. On the one hand, driven chemical reactions can affect droplets profoundly. For…
In harsh environments, organisms may self-organize into spatially patterned systems in various ways. So far, studies of ecosystem spatial self-organization have primarily focused on apparent orders reflected by regular patterns. However,…
Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
Notch signaling is an evolutionary conserved cell-cell communication pathway. Besides regulating cell-fate decisions at an individual cell level, Notch signaling coordinates the emergent spatiotemporal patterning in a tissue through…
This study presents a novel algorithm based on graph theory for the precise segmentation and measurement of detonation cells from 3D pressure traces, termed detonation lattices, addressing the limitations of manual and primitive 2D edge…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy…
In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance…
Vegetation patterns, a natural phenomenon observed worldwide, are typically driven by spatially distributed feedback. However, the spatial colonization mechanisms of clonal plants, driven by the growth of a rhizome, are usually not…
Despite the common misconception of nearly static organisms, plants do interact continuously with the environment and with each other. It is fair to assume that during their evolution they developed particular features to overcome problems…
In multi-cellular organisms, cells differentiate into multiple types as they divide. States of these cell types, as well as their numbers, are known to be robust to external perturbations; as conceptualized by Waddington's epigenetic…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…