Related papers: How nature discovers rare Turing islands: explorat…
Nature features a plethora of extraordinary photonic architectures that have been optimized through natural evolution. While numerical optimization is increasingly and successfully used in photonics, it has yet to replicate any of these…
The reproduction of a living cell requires a repeatable set of chemical events to be properly coordinated. Such events define a replication cycle, coupling the growth and shape change of the cell membrane with internal metabolic reactions.…
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…
Mounting evidence indicates that our planet might experience runaway effects associated to rising temperatures and ecosystem overexploitation, leading to catastrophic shifts on short time scales. Remediation scenarios capable of…
Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a…
Assembly theory predicts that a distinguishing signature of life is its ability to produce complex molecules in abundance, opening new possibilities for life detection. Experimental validation of this approach has so far relied on abiotic…
The central task in the study of self-organization is to explore the general mechanism of emergences. However, this is inhibited by the missing of a full knowledge of the microscopic dynamics of emergence. Here, in this study, the…
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic…
We study a discrete-time interacting particle system with continuous state space which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
This letter seeks to illuminate the profound connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy concepts that are foundational to understanding our universe. By examining these ideas through…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
Ecosystems are commonly organized into trophic levels -- organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby…
Microbial ecosystems exhibit a surprising amount of functionally relevant diversity at all levels of taxonomic resolution, presenting a significant challenge for most modeling frameworks. A long-standing hope of theoretical ecology is that…