Rapidly forming, slowly evolving, spatial patterns from quasi-cycle Mexican Hat coupling
A lattice-indexed family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family performs the reaction part of a discrete stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. Quasi-cycles are a proposed mechanism for the production of neural oscillations, and Mexican Hat coupling is ubiquitous in the brain. Thus this combination might provide insight into the function of neural oscillations in the brain. Importantly, we study this system only in the transient case, on time intervals before saturation occurs. In one dimension, for weak coupling, we find that the phases of the coupled quasi-cycles synchronize (establish a relatively constant relationship, or phase lock) rapidly at coupling strengths lower than those required to produce spatial patterns of their amplitudes. In two dimensions the amplitude patterns form more quickly, but there remain parameter regimes in which phase synchronization patterns form without being accompanied by clear amplitude patterns. At higher coupling strengths we find patterns both of phase synchronization and of amplitude (resembling Turing patterns) corresponding to the patterns of phase synchronization. Specific properties of these patterns are controlled by the parameters of the reaction and of the Mexican Hat coupling.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Adaptive foveated single-pixel imaging with dynamic super-sampling
As an alternative to conventional multi-pixel cameras, single-pixel cameras enable images to be recorded using a single detector that measures the correlations between the scene and a set of patterns. However, to fully s…
Compressive SensingMomentum-Anchored Multi-Scale Fusion Model for Long-Tailed Chest X-Ray Classification
Chest X-ray classification suffers from severe class imbalance where gradient updates bias toward majority classes, causing feature drift and poor performance on rare but critical pathologies. We propose a Momentum-Ancho…
Medical Image ClassificationA Time-aware tensor decomposition for tracking evolving patterns
Time-evolving data sets can often be arranged as a higher-order tensor with one of the modes being the time mode. While tensor factorizations have been successfully used to capture the underlying patterns in such higher-…
Tensor DecompositionEvolutionary and topological properties of gene modules and driver mutations in a leukemia gene regulatory network
The diverse, specialized genes in today's lifeforms evolved from a common core of ancient, elementary genes. However, these genes did not evolve individually: gene expression is controlled by a complex network of interac…
OBSR: Open Benchmark for Spatial Representations
GeoAI is evolving rapidly, fueled by diverse geospatial datasets like traffic patterns, environmental data, and crowdsourced OpenStreetMap (OSM) information. While sophisticated AI models are being developed, existing be…