Extreme-value statistics of networks with inhibitory and excitatory couplings

Dwivedi

2014

Phys. Rev. E

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-The importance of the balance in inhibitory and excitatory couplings in the brain has increasingly been realized. Despite the key role played by inhibitory-excitatory couplings in the functioning of brain networks, the impact of a balanced condition on the stability properties of underlying networks remains largely unknown. We investigate properties of the largest eigenvalues of networks having such couplings, and find that they follow completely different statistics when in the balanced situation. Based on numerical simulations, we demonstrate that the transition from Weibull to Fréchet via the Gumbel distribution can be controlled by the variance of the column sum of the adjacency matrix, which depends monotonically on the denseness of the underlying network. As a balanced condition is imposed, the largest real part of the eigenvalue emulates a transition to the generalized extreme value statistics, independent of the inhibitory connection probability. Furthermore, the transition to the Weibull statistics and the small-world transition occur at the same rewiring probability, reflecting a more stable system.

contrasting

confidence: 59%

mentioning

confidence: 99%

Extreme-value statistics of brain networks: Importance of balanced condition

Dwivedi

2014

Phys. Rev. E

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“…They also help in unraveling the evolutionary rules behind the existence of local motif structures having cliques of order three. While importance of inhibition has already been emphasized for functioning and evolution (see for example [19,35]), this paper demonstrates that inhibition is crucial for the evolution of clustering, with an additional essential parameter which is randomness. Even in the case of systems with only inhibitory couplings, clustering exists in absence of randomness in coupling strength.…”

mentioning

confidence: 66%

“…This notion has further been propagated for neural networks where eigenvalues with larger real part destabilize the silent state of the system [18]. Recent work has demonstrated that the fluctuations of R max leads to transition to the extreme value statistics at particular ratio of inhibitory couplings further emphasizing the importance of inhibitory connections in networks [19].Genetic algorithm (GA) is a randomized technique motivated from the natural selection process encountered in a species in course of its evolution, that has been successfully applied to computational problems dealing with exponentially large search space [20] as well to model evolutionary systems [21]. Evolution of hierarchical modularity in random directed networks has been proposed [22].…”

mentioning

confidence: 96%

Emergence of clustering: Role of inhibition

Dwivedi

2014

Phys. Rev. E

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Though biological and artificial complex systems having inhibitory connections exhibit high degree of clustering in their interaction pattern, the evolutionary origin of clustering in such systems remains a challenging problem. Using genetic algorithm we demonstrate that inhibition is required in the evolution of clique structure from primary random architecture, in which the fitness function is assigned based on the largest eigenvalue. Further, the distribution of triads over nodes of the network evolved from mixed connections reveals a negative correlation with its degree providing insight into origin of this trend observed in real networks. PACS numbers: 89.75.Fb,02.10.Yn,89.75.Hc,87.23.Kg Structural features of interaction patterns in complex systems are not completely random, they possess some non-random part, possibly dynamical response dependent local or global structures [1]. Several models as well as statistical measures have been proposed to quantify specific features of networks like degree distribution, small world property, community structure, assortative or disassortative mixing etc. Abundance of cliques of order three, indicated by high clustering coefficient (C), plays a crucial role in organizing local motif structures that enhance the robustness of the underlying system [9,10] are rich in the clique structure. Moreover, the local C of nodes have been found to be negatively correlated with their degree in metabolic networks [4]. This paper presents a novel method to understand the evolution of clustering and distribution pattern of cliques over nodes which are known to lead hierarchical organization of modularity in network. Here we use stability criteria for genetic algorithm to choose from the population which leads to the evolution of clustering in the final network. We find that presence of inhibitory links during evolution is very crucial for evolution of clustering.Previous attempts to provide evolutionary understanding of emergence of cooperation [11] as well as to use clustering based constraints for the evolution of other structural properties [12] fail to incorporate effect of inhibition in the connection. Coexistence of inhibitory and excitatory couplings have been implicated in various systems. For instance, in ecosystems, competitive, predatorprey and mutualistic interactions exist among communities of species [13]. Excitatory (friendly) and inhibitory (antagonistic) interactions are also evident in social systems [14]. In neural networks, excitatory and inhibitory synapses regulate the potential variations in neural populations [15]. In context of ecological systems, a celebrated * sarika@iiti.ac.in work by Robert May demonstrates that largest real part of eigenvalues (R max ) of corresponding adjacency matrix, determined by equal contribution from connectivity and disorder in coupling strength contains information about stability of the underlying system [13]. Spectral properties for matrices of ecological and metabolic systems have been further shown to be useful for determi...

“…Furthermore, inhibition has also been considered in ecological networks to interpret complex predator-prey interactions among various species 29 . We introduce inhibition (repulsive couplings) in one layer 30 and investigate its impact on the emergence of chimera state in another layer.…”

Section: Introductionmentioning

confidence: 99%

Is repulsion good for the health of chimeras?

Chaos: An Interdisciplinary Journal of Nonlinear Science

Ghosh

Patra

2017

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Yes! Very much so.A chimera state refers to the coexistence of a coherent-incoherent dynamical evolution of identically coupled oscillators. We investigate the impact of multiplexing of a lyer having repulsively coupled oscillators on occurrence of chimeras in the layer having attractively coupled identical oscillators. We report that there exists an enhancement in the appearance of chimera state in one layer of multiplex network in the presence of repulsive coupling in the other layer. Furthermore, we show that a small amount of inhibition or repulsive coupling in one layer is sufficient to yield chimera state in another layer by destroying its synchronized behavior. These results can be used to get insight into dynamical behaviors of those systems where both attractive and repulsive coupling exist among their constituents. In 1975, Kuramoto had introduced a mathematical model for nonidentical, nonlinear phase oscillators which exhibits a convergence to a global synchrony at a critical coupling value. In 2002, Kuramoto demonstrated that identical phase oscillators can show coexistence of coherent and incoherent dynamics under certain special conditions. Later, Abrams and Strogatz, christened this dynamical state as chimera state and provided a detailed description about special conditions required for its emergence. Since then, chimera remains an exotic phenomenon with ambiguities. Initially, non-local, non-global topology was stated to be a prerequisite for the emergence of the chimera state. However, subsequent investigations presented an appearance of the chimera state for both local and global couplings. Furthermore, multiplex framework which incorporate various types of interactions between the same pair of nodes as different layers, provide a better portrayal of complex natural networks. Here we consider a multiplex network with each layer having identical coupling architecture but not necessarily identical nature of the couplings. Particularly, we consider attractive and repulsive coupling among dynamical units and show that by keeping network architecture same, coupling in one layer have profound impact on the occurrence of chimera in another layer in multiplex networks. This investigation is crucial for many different complex systems possessing different types of coupling, particularly attractive and repulsive coupling among the same units. For instance, the a) Electronic mail: sarikajalan9@gmail.com b) Electronic mail: sapta15@gmail.com brain has inhibitory and excitatory neurons representing repulsive and attractive couplings, respectively. Studies on the impact of inhibition on the emergence of chimera state in the multiplex framework will be useful for a better understanding of such complex systems in different conditions.