arXiv subjects

S. Amin Moosavi

Publications and source records attributed to S. Amin Moosavi.

5 recordsLinked to original sources

arXiv2021

A unifying framework for mean-field theories of asymmetric kinetic Ising systems

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system's temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system's correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes.

cond-mat.dis-nn↗

arXiv2018

Coexistence of scale invariant and rhythmic behavior in self-organized criticality

Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic oscillations as well as critical (scale-free) dynamics are thought to be important, but theoretically incompatible, features of a healthy brain. Motivated by the above, we study the possibility of coexistence of scale-free avalanches along with rhythmic behavior within the framework of self-organized criticality. In particular, we add an oscillatory perturbation to local threshold condition of the continuous Zhang model and characterize the subsequent activity of the system. We observe regular oscillations embedded in well-defined avalanches which exhibit scale-free size and duration in line with observed neuronal avalanches. The average amplitude of such oscillations are shown to decrease with increasing frequency consistent with real brain oscillations. Furthermore, it is shown that optimal amplification of oscillations occur at the critical point, further providing evidence for functional advantages of criticality.

cond-mat.dis-nn↗

arXiv2017

Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior

Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point ($λ=1$), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with $λ<1.0$, a standard critical behavior with exponents close to critical branching process for $λ=1$, a regime with $1<λ<2$ that exhibits an interesting scaling behavior, and an oscillating regime with $λ>2.0$. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.

cond-mat.dis-nn↗

arXiv2015

Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches

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 critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms which can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high average connectivity, random long range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionaly accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

cond-mat.stat-mech↗

arXiv2014

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

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 critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibit true criticality for a wide range of noise in various dimensions, given that conservation is respected \textit{on the average}. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, addition of noise does not affect the exponents at the upper critical dimension ($D=4$). In addition to extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method in order to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for general phenomena of criticality in non-equilibrium systems.

cond-mat.stat-mech↗