scholarly journals Neuroepithelial Organoid Patterning is Mediated by Wnt-Driven Turing Mechanism

2021 ◽  
Author(s):  
Abdel Rahman Abdel Fattah ◽  
Sergei Grebeniuk ◽  
Laura PMH de Rooij ◽  
Idris Salmon ◽  
Suresh Poovathingal ◽  
...  
Keyword(s):  
Turing Mechanism

scholarly journals Linguistic evolution driven by network heterogeneity and the Turing mechanism

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Sayat Mimar ◽  
Mariamo Mussa Juane ◽  
Jorge Mira ◽  
Juyong Park ◽  
Alberto P. Muñuzuri ◽  
...  
Keyword(s):  
Network Heterogeneity ◽  
Turing Mechanism ◽  
Linguistic Evolution

The Turing mechanism and geometric pattern

2017 ◽  
pp. 60-88
Author(s):  
John Vandermeer ◽  
Ivette Perfecto
Keyword(s):  
Geometric Pattern ◽  
Turing Mechanism

The spatial dimension in environmental and resource economics

2010 ◽  
Vol 15 (6) ◽  
pp. 747-758 ◽  
Author(s):  
ANASTASIOS XEPAPADEAS
Keyword(s):  
Optimal Control ◽  
Spatial Patterns ◽  
Spatial Dimension ◽  
New Economic Geography ◽  
Distributed Parameter ◽  
The Maximum Principle ◽  
Environmental And Resource Economics ◽  
Spatial Domains ◽  
Turing Mechanism ◽  
State Functions

ABSTRACTMechanisms generating patterns in spatial domains have been extensively studied in biology, but also in economics in the context of new economic geography. The Turing mechanism or Turing diffusion-induced instability has been central to the understanding of forces which endogenously generate spatial patterns, but in a context where agents do not explicitly optimize an objective. The present paper reviews tools to study, in the spirit of Turing's analysis, a mechanism generating optimal diffusion-induced instability where optimizing agents generate optimal agglomerations. By extending the maximum principle to the optimal control of partial differential equations, it is shown how under certain conditions it will be optimal to design controls so that the price-quantity system implied by the costate–state functions of the optimal control of distributed parameter systems induces optimal spatial patterns. These methods might be useful in studying pattern formation both in problems of resource management and of economic development.

Why Turing mechanism is an obstacle to stationary periodic patterns in bounded reaction-diffusion media with advection

2010 ◽  
Vol 12 (16) ◽  
pp. 3957 ◽  
Author(s):  
Arik Yochelis ◽  
Moshe Sheintuch
Keyword(s):  
Reaction Diffusion ◽  
Periodic Patterns ◽  
Diffusion Media ◽  
Turing Mechanism

scholarly journals Investigation of Clustering in Turing Patterns to Describe the Spatial Relations of Slums

2020 ◽  
Author(s):  
Jakob Hartig ◽  
John Friesen ◽  
Peter F. Pelz
Keyword(s):  
Boundary Conditions ◽  
Satellite Data ◽  
Empirical Data ◽  
Characteristic Length ◽  
Empirical Studies ◽  
Spatial Relations ◽  
Turing Patterns ◽  
Size Distributions ◽  
Numerical Studies ◽  
Turing Mechanism

Worldwide, about one in eight people live in a slum. Empirical studies based on satellite data have identified that the size distributions of this type of settlement are similar in different cities of the Global South. Based on this result, a model was developed that describes the formation of slums with a Turing mechanism, in which patterns are created by diffusion-driven instability and the inherent characteristic length of the system is independent of boundary conditions. It has not yet been taken into account that Turing patterns usually arrange themselves regularly, while slums are often found in clusters. Therefore, this study investigates to what extent a common reaction kinetics for Turing models can be adapted to represent a locally concentrated arrangement of objects and to adapt the size distribution of the objects to the empirical results. Based on a summary of the literature and two numerical studies, it can be shown that although it is possible to adapt the model to the empirical data, this also increases the complexity of the model.

scholarly journals Insights from chemical systems into Turing-type morphogenesis

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
C. Konow ◽  
M. Dolnik ◽  
I. R. Epstein
Keyword(s):  
Reaction Diffusion ◽  
Behavioural Science ◽  
Future Directions ◽  
Reaction Diffusion Systems ◽  
Chemical Systems ◽  
Alan Turing ◽  
Diffusion Systems ◽  
Chemical Studies ◽  
Historical Role ◽  
Turing Mechanism

In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction–diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237 , 37–72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction–diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

scholarly journals Noise–Seeded Developmental Pattern Formation in Filamentous Cyanobacteria

Life ◽  
2018 ◽  
Vol 8 (4) ◽  
pp. 58 ◽  
Author(s):  
Rinat Arbel-Goren ◽  
Francesca Di Patti ◽  
Duccio Fanelli ◽  
Joel Stavans
Keyword(s):  
Pattern Formation ◽  
Essential Role ◽  
Developmental Pattern ◽  
Turing Patterns ◽  
Filamentous Cyanobacteria ◽  
Developmental Patterns ◽  
Anabaena Sp ◽  
Turing Mechanism ◽  
Demographic Noise ◽  
Pcc 7120

Under nitrogen-poor conditions, multicellular cyanobacteria such as Anabaena sp. PCC 7120 undergo a process of differentiation, forming nearly regular, developmental patterns of individual nitrogen-fixing cells, called heterocysts, interspersed between intervals of vegetative cells that carry out photosynthesis. Developmental pattern formation is mediated by morphogen species that can act as activators and inhibitors, some of which can diffuse along filaments. We survey the limitations of the classical, deterministic Turing mechanism that has been often invoked to explain pattern formation in these systems, and then, focusing on a simpler system governed by birth-death processes, we illustrate pedagogically a recently proposed paradigm that provides a much more robust description of pattern formation: stochastic Turing patterns. We emphasize the essential role that cell-to-cell differences in molecular numbers—caused by inevitable fluctuations in gene expression—play, the so called demographic noise, in seeding the formation of stochastic Turing patterns over a much larger region of parameter space, compared to their deterministic counterparts.

Turing mechanism for homeostatic control of synaptic density during C. elegans growth

2017 ◽  
Vol 96 (1) ◽  
Author(s):  
Heather A. Brooks ◽  
Paul C. Bressloff
Keyword(s):  
Homeostatic Control ◽  
Synaptic Density ◽  
C Elegans ◽  
Turing Mechanism

Is pigment patterning in fish skin determined by the Turing mechanism?

2015 ◽  
Vol 31 (2) ◽  
pp. 88-96 ◽  
Author(s):  
Masakatsu Watanabe ◽  
Shigeru Kondo
Keyword(s):  
Fish Skin ◽  
Turing Mechanism

scholarly journals Kidney branching morphogenesis under the control of a ligand–receptor-based Turing mechanism

2013 ◽  
Vol 10 (4) ◽  
pp. 046003 ◽  
Author(s):  
Denis Menshykau ◽  
Dagmar Iber
Keyword(s):  
Branching Morphogenesis ◽  
Turing Mechanism
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