Related papers: Pattern reconstruction through generalized eigenve…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
Transitions from turbulence to order are studied experimentally in thin fluid layers and magnetically confined toroidal plasma. It is shown that turbulence self-organizes through the mechanism of spectral condensation. The spectral…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Patterns are ubiquitous in nature, but how they form is often unclear. Turing developed a seminal theory to explain patterns based on reactions that counteract the equalizing tendency of diffusion. These reactions require continuous energy…
We consider problems in which a system receives external \emph{perturbations} from time to time. For instance, the system can be a train network in which particular lines are repeatedly disrupted without warning, having an effect on…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors…
We analyze the ordering efficiency and the structure of disordered configurations for the zero-temperature Glauber model on Watts-Strogatz networks obtained by rewiring 2D regular square lattices. In the small-world regime, the dynamics…
Behavioral changes in animals and humans, as a consequence of an error or a verbal instruction, can be extremely rapid. Improvement in behavioral performances are usually associated in machine learning and reinforcement learning to synaptic…
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…
Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…
Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution although these are often experimentally inaccessible. Here we propose a theory for revealing…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
Many real-world networks such as social networks consist of strategic agents. The topology of these networks often plays a crucial role in determining the ease and speed with which certain information driven tasks can be accomplished.…