Related papers: Griffiths phases and localization in hierarchical …
Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this community structure from data. The question of why modular hierarchical organizations are so…
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled…
In this paper, we develop an approach to modeling high-dimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multi-scale factor analysis (MSFA) model which partitions the…
Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based…
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…
Balanced neural networks -- in which excitatory and inhibitory inputs compensate each other on average -- give rise to a dynamical phase dominated by fluctuations called asynchronous state, crucial for brain functioning. However, structural…
We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (non-topological) sources of quenched disorder. The slow…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an…
The Griffiths phase in systems with quenched disorder occurs below the ordering transition of the pure system down to the ordering transition of the actual disordered system. While it does not exhibit long-range order, large fluctuations in…
Reckoning of pairwise dynamical correlations significantly improves the accuracy of mean-field theories and plays an important role in the investigation of dynamical processes on complex networks. In this work, we perform a nonperturbative…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
A simple model to study cooperation is the two-species symbiotic contact process (2SCP), in which two different species spread on a graph and interact by a reduced death rate if both occupy the same vertex, representing a symbiotic…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D $q$-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
Griffiths phases are typically associated with quenched disorder, while frustration gives rise to multistability and spin-glass behavior. Whether extended criticality can arise in other contexts remains an open question. Here, we show that…
Functional magnetic resonance imaging recordings in the resting-state (RS) from the human brain are characterized by spontaneous low-frequency fluctuations in the blood oxygenation level dependent signal that reveal functional connectivity…
We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the integers that is assumed to be invariant under index shifts…
A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…