Related papers: Self-Organized Criticality from Protected Mean-Fie…
Unlike digital computers, the brain exhibits spontaneous activity even during complete rest, despite the evolutionary pressure for energy efficiency. Inspired by the critical brain hypothesis, which proposes that the brain operates…
Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…
Superintelligence is commonly envisioned as a quantitative extrapolation of human cognitive abilities driven by scale and computational power. Here we show that qualitative transitions in intelligence instead arise as dynamical phase…
Understanding the relationship between large-scale structural and functional brain networks remains a crucial issue in modern neuroscience. Recently, there has been growing interest in investigating the role of homeostatic plasticity…
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…
Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover,…
This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)) where the tools of the field theoretical renormalization group were employed to explain…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task related neural dynamics we study trained Recurrent Neural Networks. We develop a Mean Field Theory for Reservoir Computing…
Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that…
Recent studies on the complex systems have shown that the synchronization of oscillators including neuronal ones is faster, stronger, and more efficient in the small-world networks than in the regular or the random networks, and many…
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…
It has long been argued that neural networks have to establish and maintain a certain intermediate level of activity in order to keep away from the regimes of chaos and silence. Strong evidence for criticality has been observed in terms of…
Using a matched asymptotic expansion we analyze the two-dimensional, near- critical reflection of a weakly nonlinear, internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar…
Criticality describes a regime between order and chaos that supports flexible yet stable information processing. Here we examine whether neural dynamics can be volitionally shifted toward criticality through the self-regulation of…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
In this article, we propose a very efficient technique to enhance the dynamical robustness for a network of mean-field coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed…
We study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional…