Related papers: The Kinetic Basis of Self-Organized Pattern Format…

Populations can become spatially organised through chemotaxis autoattraction, wherein population members release their own chemoattractant. Standard models of this process usually assume phenotypic homogeneity, but recent studies have shed…

The last decades witnessed the emergence of the field of correlated disordered media, a great challenge offering a large panel of new perspectives for applications in theoretical modelling and material fabrication. The efficient design of…

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently,…

Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions…

A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…

In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal…

Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebra and giraffe, the patterns of our interest are {\it transient} although…

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…

We demonstrate that active rotations in chemically signalling particles, such as autochemotactic {\it E. coli} close to walls, create a route for pattern formation based on a nonlinear yet deterministic instability mechanism. For slow…

We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…

We revisit human motion synthesis, a task useful in various real world applications, in this paper. Whereas a number of methods have been developed previously for this task, they are often limited in two aspects: focusing on the poses while…

What networks can form and persist when agents are self-interested? Can such networks be efficient? A substantial theoretical literature predicts that the only networks that can form and persist must have very special shapes and that such…

The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…

MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…

The biopolymers actin and microtubules are often in an ongoing assembling/disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a…

In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson…

We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a…

Bayesian mechanics provides a framework that addresses dynamical systems that can be conceptualised as Bayesian inference. However, elucidating the requisite generative models is essential for empirical applications to realistic…

Biological functions rely on ordered structures and intricately controlled collective dynamics. In contrast to systems in thermodynamic equilibrium, order is typically established and sustained in stationary states by continuous dissipation…