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Updated: Jun 5, 2026

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
Published on: June 26, 2013
Spatial pattern formation induced by Gaussian white noise
Stefania Scarsoglio1, Francesco Laio, Paolo D'Odorico
1Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Turin, Italy. stefania.scarsoglio@polito.it
Abstract:
The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable environmental disturbances, and (iii) a linear spatial coupling component, which provides spatial coherence and takes into account diffusion mechanisms. We investigate these dynamics using analytical tools, such as mean-field theory, linear stability analysis and structure function analysis, and use numerical simulations to confirm these analytical results.
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