Synchronization in time-varying networks

Kohar, Vivek; Ji, Peng; Choudhary, Anshul; Sinha, Sudeshna; Kurths, Jüergen

doi:10.1103/physreve.90.022812

Cited by 92 publications

(46 citation statements)

References 38 publications

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“…Advances in network theory are now showing that features of the neural circuitry between these two length scales – i.e. , the distribution of neuronal connections in a network, and the clustering of these connections to form functional modules or microcircuits – are key variables that affect information flow through the network, the synchronization of activity across neuronal clusters, and the network activity patterns that can emerge from the network (Kohar et al, 2014; Liu et al, 2011; Pandit and Amritkar, 1999; Watts and Strogatz, 1998). However, developing more precise, circuit-based understanding of task performance at this intermediate scale remains elusive, partly because we have limited ability to characterize the functional connections of neurons within a microcircuit and how these connections are modified during cognition.…”

Section: Introductionmentioning

confidence: 99%

Automated quantification of neuronal networks and single-cell calcium dynamics using calcium imaging

Patel

Man

Firestein

et al. 2015

Journal of Neuroscience Methods

157

189

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Background Recent advances in genetically engineered calcium and membrane potential indicators provide the potential to estimate the activation dynamics of individual neurons within larger, mesoscale networks (100s–1000 +neurons). However, a fully integrated automated workflow for the analysis and visualization of neural microcircuits from high speed fluorescence imaging data is lacking. New method Here we introduce FluoroSNNAP, Fluorescence Single Neuron and Network Analysis Package. FluoroSNNAP is an open-source, interactive software developed in MATLAB for automated quantification of numerous biologically relevant features of both the calcium dynamics of single-cells and network activity patterns. FluoroSNNAP integrates and improves upon existing tools for spike detection, synchronization analysis, and inference of functional connectivity, making it most useful to experimentalists with little or no programming knowledge. Results We apply FluoroSNNAP to characterize the activity patterns of neuronal microcircuits undergoing developmental maturation in vitro. Separately, we highlight the utility of single-cell analysis for phenotyping a mixed population of neurons expressing a human mutant variant of the microtubule associated protein tau and wild-type tau. Comparison with existing method(s) We show the performance of semi-automated cell segmentation using spatiotemporal independent component analysis and significant improvement in detecting calcium transients using a template-based algorithm in comparison to peak-based or wavelet-based detection methods. Our software further enables automated analysis of microcircuits, which is an improvement over existing methods. Conclusions We expect the dissemination of this software will facilitate a comprehensive analysis of neuronal networks, promoting the rapid interrogation of circuits in health and disease.

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Section: Introductionmentioning

confidence: 99%

Automated quantification of neuronal networks and single-cell calcium dynamics using calcium imaging

Patel

Man

Firestein

et al. 2015

Journal of Neuroscience Methods

157

189

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“…robots [19], ordered motion in a group of animals [20] and even in the process of chemotaxis [21], this framework has a significant resemblance. Emergence of complete synchronization from different aspects in temporal networks [22][23][24][25][26][27][28][29][30][31][32], particularly among interacting moving oscillators has been investigated previously [19,[33][34][35][36][37][38][39][40][41] and most of these articles considered the framework in which each and every agent always carries a vision shape based on which they create neighbors and interact. In this paper, we consider a planar space in which some identical moving chaotic oscillators interact with each other only when they visit the same restricted regions pre-defined in the planar zone.…”

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confidence: 99%

Synchronization to extreme events in moving agents

et al. 2019

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Interactions amongst agents frequently exist only at particular moments in time, depending on their closeness in space and movement parameters. Here we propose a minimal model of moving agents where the network of contacts changes over time due to their motion. In particular, agents interact based on their proximity in a two-dimensional space, but only if they belong to the same fixed interaction zones. Our research reveals the emergence of global synchronization if all the interaction zones are attractive. However, if some of the interaction zones are repulsive, they deflect synchrony and lead to short-lasting but recurrent deviations that constitute extreme events in the network. We use two paradigmatic oscillators for the description of the agent dynamics to demonstrate our findings numerically, and we also provide an analytical formulation to describe the emergence of complete synchrony and the thresholds that distinguish extreme events from other intermittent states based on the peak-over-threshold approach. IntroductionResearch to understand the interplay between complex networks and the dynamical properties of coupled oscillators has been a hotspot for the last few decades and the developing phenomenon of synchronization [1-4] is one of the most important dynamical processes that has been in the center of these researches. Cooperation [5,6] and time series analysis [7,8] in complex network have been studied in the past few years. From the perspective of synchronization among coupled oscillators placed into a complex network [9,10], the correlation between the network's topology and local dynamics is quite decisive. Here, synchronization signifies a process of adaptation to a common collective behavior of oscillators due to their interaction. In most of the previous studies of such systems, the network topology is assumed to be invariant over time and thus the system is controlled by a deterministic static formation for all the course of time. But such a crude assumption regarding the network connectivity inhibits one to model and study most of the practical instances.Recently, time-varying networks have grabbed the attention of the researchers due to their enormous applications in various fields like functional brain network [11], epidemic modeling [12], communication systems [13,14] and many more. Time-varying networks, also known as temporal networks [15] indicate those networks in which links get activated for a certain course of time. On the assumption of time-invariant nodes which are static over time, many network architecture is studied, e.g. power transmission elements are considered as such nodes among which haphazard links are treated as the coupling between elements of the power transmission system [16]. Even for functional brain networks [11], these types of nodes are considered to characterize the dynamical evolution. Particularly, the scenario of time-varying networks owing to the mobility in the nodes is really a significant platform to study several dynamical processes over them in which no...

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“…Even though studied intensively under various aspects567891011, yet a full clarification is needed on the effects of time-dependent coupling structures1213141516, particularly for those circumstances for which the coupling strengths (or connection topologies) may switch in time. For the specific condition (termed as the blinking network case) for which the graph structure changes much more rapidly than the units’ dynamics, a comprehensive theoretical framework was established, and applications were developed accordingly171819.…”

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confidence: 99%

Synchronization in slowly switching networks of coupled oscillators

Zhou

Zou

Guan

et al. 2016

Sci Rep

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Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units’ dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure and coupling strength, which is of evident relevance for broad applications in real world systems.

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Synchronization in time-varying networks

Cited by 92 publications

References 38 publications

Automated quantification of neuronal networks and single-cell calcium dynamics using calcium imaging

Automated quantification of neuronal networks and single-cell calcium dynamics using calcium imaging

Synchronization to extreme events in moving agents

Synchronization in slowly switching networks of coupled oscillators

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