scholarly journals Statistical mechanics of multistable perception

2014 ◽  
Author(s):  
Gurinder Singh Atwal
Keyword(s):  
Stochastic Dynamics ◽  
Dynamical Phase Transition ◽  
Scale Free ◽  
Dynamical Phase ◽  
Neural Signal Processing ◽  
Multistable Perception ◽  
Perception Bias ◽  
Spectrum Characteristic ◽  
Statistical Estimation Problem ◽  
The Brain

The stochastic dynamics of multistable perception poses an enduring challenge to our understanding of neural signal processing in the brain. We show that the emergence of perception switching and stability can be understood using principles of probabilistic Bayesian inference where the prior temporal expectations are matched to a scale-free power spectrum, characteristic of fluctuations in the natural environment. The optimal percept dynamics are inferred by an exact mapping of the statistical estimation problem to the motion of a dissipative quantum particle in a multi-well potential. In the bistable case the problem is further mapped to a long-ranged Ising model. Optimal inference in the presence of a 1/f noise prior leads to critical dynamics, exhibiting a dynamical phase transition from unstable perception to stable perception, as demonstrated in recent experiments. The effect of stimulus fluctuations and perception bias is also discussed.

scholarly journals Analytical investigation of self-organized criticality in neural networks

2013 ◽  
Vol 10 (78) ◽  
pp. 20120558 ◽  
Author(s):  
Felix Droste ◽  
Anne-Ly Do ◽  
Thilo Gross
Keyword(s):  
Neural Networks ◽  
Stochastic Dynamics ◽  
Analytical Investigation ◽  
Homeostatic Plasticity ◽  
Dynamical Phase Transition ◽  
Discrete State ◽  
Dynamical Phase ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Activity Dependent

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity-dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In a low-dimensional representation of the macroscopic dynamics, this corresponds to a transcritical bifurcation. We show analytically that adding activity-dependent rewiring rules, inspired by homeostatic plasticity, leads to the emergence of an attractive steady state at criticality and present numerical evidence for the system's evolution to such a state.

scholarly journals Scale-free channeling patterns near the onset of erosion of sheared granular beds

2016 ◽  
Vol 113 (42) ◽  
pp. 11788-11793 ◽  
Author(s):  
Pascale Aussillous ◽  
Zhenhai Zou ◽  
Élisabeth Guazzelli ◽  
Le Yan ◽  
Matthieu Wyart
Keyword(s):  
Spatial Organization ◽  
Laminar Flows ◽  
Microscopic Level ◽  
Strongly Correlated ◽  
Particle Interactions ◽  
Dynamical Phase Transition ◽  
Scale Free ◽  
Dynamical Phase ◽  
Depinning Transition ◽  
The Mean

Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we study, experimentally, the collective dynamics of the moving particles, using a setup where the system spontaneously evolves toward the erosion onset. We find that the spatial organization of the erosion flux is heterogeneous in space and occurs along channels of local flux σ whose distribution displays scaling near threshold and follows P(σ)≈J/σ, where J is the mean erosion flux. Channels are strongly correlated in the direction of forcing but not in the transverse direction. We show that these results quantitatively agree with a model where the dynamics is governed by the competition of disorder (which channels mobile particles) and particle interactions (which reduces channeling). These observations support that, for laminar flows, erosion is a dynamical phase transition that shares similarity with the plastic depinning transition occurring in dirty superconductors. The methodology we introduce here could be applied to probe these systems as well.

scholarly journals Nervous Activity of the Brain in Five Dimensions

Biophysica ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 38-47
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
Norbert Jausovec ◽  
Arjuna P. H. Don ◽  
Sheela Ramanna ◽  
...  
Keyword(s):  
Fourier Analysis ◽  
Nervous Activity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Sets ◽  
Spatial And Temporal Patterns ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Scale Free ◽  
The Brain

The nervous activity of the brain takes place in higher-dimensional functional spaces. It has been proposed that the brain might be equipped with phase spaces characterized by four spatial dimensions plus time, instead of the classical three plus time. This suggests that global visualization methods for exploiting four-dimensional maps of three-dimensional experimental data sets might be used in neuroscience. We asked whether it is feasible to describe the four-dimensional trajectories (plus time) of two-dimensional (plus time) electroencephalographic traces (EEG). We made use of quaternion orthographic projections to map to the surface of four-dimensional hyperspheres EEG signal patches treated with Fourier analysis. Once achieved the proper quaternion maps, we show that this multi-dimensional procedure brings undoubted benefits. The treatment of EEG traces with Fourier analysis allows the investigation the scale-free activity of the brain in terms of trajectories on hyperspheres and quaternionic networks. Repetitive spatial and temporal patterns undetectable in three dimensions (plus time) are easily enlightened in four dimensions (plus time). Further, a quaternionic approach makes it feasible to identify spatially far apart and temporally distant periodic trajectories with the same features, such as, e.g., the same oscillatory frequency or amplitude. This leads to an incisive operational assessment of global or broken symmetries, domains of attraction inside three-dimensional projections and matching descriptions between the apparently random paths hidden in the very structure of nervous fractal signals.

scholarly journals Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

2021 ◽  
Vol 11 ◽  
Author(s):  
Orestis Stylianou ◽  
Frigyes Samuel Racz ◽  
Andras Eke ◽  
Peter Mukli
Keyword(s):  
Resting State ◽  
Functional Coupling ◽  
Dependent Manner ◽  
Coupled Dynamics ◽  
Scale Free ◽  
Neural Processes ◽  
Eeg Recordings ◽  
Cortical Regions ◽  
The Brain

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

scholarly journals Pre-stimulus phase and amplitude regulation of phase-locked responses are maximized in the critical state

eLife ◽  
2020 ◽  
Vol 9 ◽  
Author(s):  
Arthur-Ervin Avramiea ◽  
Richard Hardstone ◽  
Jan-Matthis Lueckmann ◽  
Jan Bím ◽  
Huibert D Mansvelder ◽  
...  
Keyword(s):  
Computational Model ◽  
Critical State ◽  
Global Dynamics ◽  
Critical Dynamics ◽  
Neuronal Responses ◽  
Scale Free ◽  
Stimulus Response ◽  
Functional States ◽  
The Brain

Understanding why identical stimuli give differing neuronal responses and percepts is a central challenge in research on attention and consciousness. Ongoing oscillations reflect functional states that bias processing of incoming signals through amplitude and phase. It is not known, however, whether the effect of phase or amplitude on stimulus processing depends on the long-term global dynamics of the networks generating the oscillations. Here, we show, using a computational model, that the ability of networks to regulate stimulus response based on pre-stimulus activity requires near-critical dynamics—a dynamical state that emerges from networks with balanced excitation and inhibition, and that is characterized by scale-free fluctuations. We also find that networks exhibiting critical oscillations produce differing responses to the largest range of stimulus intensities. Thus, the brain may bring its dynamics close to the critical state whenever such network versatility is required.

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