Related papers: Labyrinthine Turing Pattern Formation in the Cereb…
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…
For long it has been known that specific patterns of folding are necessary for an optimally functioning brain. For instance, lissencephaly and polymicrogyria can lead to severe mental retardation, short life expectancy, epileptic seizures,…
Despite differences in brain sizes and cognitive niches among mammals, their cerebral cortices posses many common features and regularities. These regularities have been a subject of experimental investigation in neuroanatomy for the last…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
The phenomenon of pattern formation in nonlinear optical resonators is commonly related to an off-resonance excitation mechanism, where patterns occur due to mismatch between the excitation and resonance frequency. In this paper we show…
While our understanding of the way single neurons process chromatic stimuli in the early visual pathway has advanced significantly in recent years, we do not yet know how these cells interact to form stable representations of hue. Drawing…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor--that of the cascade. The…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the…
Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the…
Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a…
The exterior of the mammalian brain - the cerebral cortex - has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large…
Space is represented in the mammalian brain by the activity of hippocampal place cells as well as in their spike-timing correlations. Here we propose a theory how this temporal code is transformed to spatial firing rate patterns via…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Dynamical coherent structure (pattern) formation in the Klein-Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that besides spatial patterns discovered recently (V.M.Burlakov,…