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An Investigation of the Dynamical Transitions in Harmonically Driven Random Networks of Firing-Rate Neurons

Kyriacos Nikiforou, Pedro A. M. Mediano, Murray Shanahan
2017 Cognitive Computation  
Additionally, we propose a novel technique for exploring the stationary points and locally linear dynamics of these networks in order to understand the origin of input-dependent dynamical transitions.  ...  In this article, we study the response of stable and unstable networks to different harmonically oscillating stimuli by varying a parameter ρ, the ratio between the timescale of the network and the stimulus  ...  the European Union Future and Emerging Technologies grant (GA:641100) TIMESTORM-Mind and Time: Investigation of the Temporal Traits of Human-Machine Convergence.  ... 
doi:10.1007/s12559-017-9464-6 pmid:28680506 pmcid:PMC5487873 fatcat:up4rsq6fxbaf7fzeoyje5c7e2q

Complexity matching in neural networks

Javad Usefie Mafahim, David Lambert, Marzieh Zare, Paolo Grigolini
2015 New Journal of Physics  
We use an integrate-and-fire model where the randomness of each neuron is only due to the random choice of a new initial condition after firing.  ...  In the wide literature on the brain and neural network dynamics the notion of criticality is being adopted by an increasing number of researchers, with no general agreement on its theoretical definition  ...  In the earlier work of [20] this rate was expected to remain constant because after firing each neurons jumps back to x = 0, while here each neuron after firing moves to a random value > x 0, with a  ... 
doi:10.1088/1367-2630/17/1/015003 fatcat:accemajktja2zkat5z5jmf7c64

Emergent Oscillations in Networks of Stochastic Spiking Neurons

Edward Wallace, Marc Benayoun, Wim van Drongelen, Jack D. Cowan, Boris S. Gutkin
2011 PLoS ONE  
Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency.  ...  These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in  ...  Author Contributions Analyzed the data: EW MB. Wrote the paper: EW MB WvD JDC. Conceived and designed simulations: EW MB WvD JDC. Wrote and performed simulations: EW MB.  ... 
doi:10.1371/journal.pone.0014804 pmid:21573105 pmcid:PMC3089610 fatcat:rkh6e6caivdlhgohfn5txfk5nu

An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex

D. Cai, L. Tao, M. Shelley, D. W. McLaughlin
2004 Proceedings of the National Academy of Sciences of the United States of America  
This powerful kinetic theory captures the full dynamic range of neuronal networks, from the mean-driven limit (a limit such as the number of neurons N 3 ؕ, in which the fluctuations vanish) to the fluctuation-dominated  ...  dynamic phenomena, such as, transitions to bistability and hysteresis, even in the presence of large fluctuations.  ...  We thank Bob Shapley for many discussions throughout the entire course of this work, Dan Tranchina for introducing us to pdf representations of neuronal networks and his comments on this work, and Fernand  ... 
doi:10.1073/pnas.0401906101 pmid:15131268 pmcid:PMC419679 fatcat:y34i3t7srbhonnrplyo2sikdsa

Shaping Intrinsic Neural Oscillations with Periodic Stimulation

Christoph S. Herrmann, Micah M. Murray, Silvio Ionta, Axel Hutt, Jérémie Lefebvre
2016 Journal of Neuroscience  
Our results suggest that rhythmic stimulation can form the basis of a control paradigm in which one can manipulate the intrinsic oscillatory properties of driven networks via a plurality of input-driven  ...  Our results show that, in addition to resonance and entrainment, nonlinear acceleration is involved in shaping the rhythmic response of our modeled network.  ...  This is also reflected in the spiking activity of driven neurons: firing rates increase into tightly synchronized bursts of spike discharges.  ... 
doi:10.1523/jneurosci.0236-16.2016 pmid:27170129 fatcat:swzcplpbxzdf7nwf5bdc6y5sbe

Critical and resonance phenomena in neural networks [article]

A. V. Goltsev, M. A. Lopes, K.-E. Lee, J. F. F. Mendes
2012 arXiv   pre-print
Using an analytical approach and simulations of a cortical circuit model of neural networks with stochastic neurons in the presence of noise, we show that spontaneous appearance of network oscillations  ...  occurs as a dynamical (non-equilibrium) phase transition at a critical point determined by the noise level, network structure, the balance between excitatory and inhibitory neurons, and other parameters  ...  In the present paper, we study collective dynamics of neural networks composed by excitatory and inhibitory neurons in the presence of noise.  ... 
arXiv:1211.5686v1 fatcat:vrr6iuun4bdyvikm5irrzcjemm

Advances in Biologically Inspired Reservoir Computing

Simone Scardapane, John B. Butcher, Filippo M. Bianchi, Zeeshan K. Malik
2017 Cognitive Computation  
The interplay between randomness and optimization has always been a major theme in the design of neural networks [3] .  ...  As long as the recurrent part of the network possesses a form of fading memory of the input, the dynamics of the neurons are enough to efficiently process many spatio-temporal signals, provided that their  ...  We would like to thank the editor in chief of the journal, Amir Hussain, for the strong support given when organizing and publishing this special issue; all the authors who participated in the issue; and  ... 
doi:10.1007/s12559-017-9469-1 fatcat:pgdtsxvqvndr5ijsddht537fzm

Network mechanisms underlying the role of oscillations in cognitive tasks

Helmut Schmidt, Daniele Avitabile, Ernest Montbrió, Alex Roxin, Boris S. Gutkin
2018 PLoS Computational Biology  
Specifically, we investigate how the frequency of oscillatory input interacts with the intrinsic dynamics in networks of recurrently coupled spiking neurons to cause changes of state: the neuronal correlates  ...  We leverage a recently derived set of exact mean-field equations for networks of quadratic integrate-and-fire neurons to systematically study the bifurcation structure in the periodically forced spiking  ...  This type of spike synchrony is seen ubiquitously in networks of both heterogeneous and noise-driven spiking neurons operating in the mean-driven regime, in which neurons fire as oscillators [15, 22,  ... 
doi:10.1371/journal.pcbi.1006430 pmid:30188889 pmcid:PMC6143269 fatcat:zybx3u63u5fankgqpyrvmkebh4

Asynchronous and Coherent Dynamics in Balanced Excitatory-Inhibitory Spiking Networks

Hongjie Bi, Matteo di Volo, Alessandro Torcini
2021 Frontiers in Systems Neuroscience  
The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models.  ...  Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex.  ...  On the distribution of firing rates in networks of cortical neurons. J.  ... 
doi:10.3389/fnsys.2021.752261 pmid:34955768 pmcid:PMC8702645 fatcat:7tma4kbpf5ft3dwozqvldzh2na

Asynchronous and coherent dynamics in balanced excitatory-inhibitory spiking networks [article]

Hongjie Bi, Matteo Di Volo, Alessandro Torcini
2021 arXiv   pre-print
The analysis is performed by combining simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models.  ...  Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex.  ...  ACKNOWLEDGMENTS The authors acknowledge extremely useful discussions with D.G. Goldobin, G. Mongillo, E. Montbrió, S. Olmi, and A. Politi.  ... 
arXiv:2108.13666v2 fatcat:xpnftxv6ozcn3pid74hdqo2nbm

A large-scale simulation of the piriform cortex by a cell automaton-based network model

E.T. Claverol, A.D. Brown, J.E. Chad
2002 IEEE Transactions on Biomedical Engineering  
An event-driven framework is used to construct a physiologically motivated large-scale model of the piriform cortex containing in the order of 10 5 neuron-like computing units.  ...  The network model incorporates four neuron types, and glutamatergic excitatory and and inhibitory synapses.  ...  To investigate the dynamics of a large-scale cortical model, the cell types and the connectivity patterns in the network were constrained by piriform cortex anatomy.  ... 
doi:10.1109/tbme.2002.801986 pmid:12214882 fatcat:qbihejuwevc3vm2gw5w72riwvu

Dynamic Control of Synchronous Activity in Networks of Spiking Neurons

Axel Hutt, Andreas Mierau, Jérémie Lefebvre, Maurice J. Chacron
2016 PLoS ONE  
Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations.  ...  We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics.  ...  Fig 1 . 1 Frequency transitions in a random network of spiking neurons. A.  ... 
doi:10.1371/journal.pone.0161488 pmid:27669018 pmcid:PMC5036852 fatcat:lrf65rbrx5cg5ccrp75cohr32q

Neuronal Dynamics [chapter]

Nicolas Brunel, Vincent Hakim
2009 Encyclopedia of Complexity and Systems Science  
Presentation of an external stimulus (sample 1 in the figure) increases the firing rate of the relevant neurons (see red curve in bottom panel, average firing rate of neurons in population 1).  ...  Architectures in Rate Models Rate models are often used to investigate the dynamics of spatially extended networks, or systems which encode continuous stimuli.  ... 
doi:10.1007/978-0-387-30440-3_359 fatcat:lmiylxvqozdjhl44ydfuma35z4

How pattern formation in ring networks of excitatory and inhibitory spiking neurons depends on the input current regime

Birgit Kriener, Moritz Helias, Stefan Rotter, Markus Diesmann, Gaute T Einevoll
2013 BMC Neuroscience  
Pattern formation in networks of spiking neurons Frontiers in Computational Neuroscience www.frontiersin.org January 2014 | Volume 7 | Article 187 | 2 350 J = 1.1 mV J = 0.9 mV Rate [1/s] J = 0.6 mV J  ...  Frontiers in Computational Neuroscience www.frontiersin.org January 2014 | Volume 7 | Article 187 | 1 COMPUTATIONAL NEUROSCIENCE Kriener et al.  ...  We gratefully acknowledge funding by the eScience program of the Research Council of Norway under grant 178892/V30 (eNeuro), the Helmholtz Association: HASB and portfolio theme SMHB, the Next-Generation  ... 
doi:10.1186/1471-2202-14-s1-p123 pmcid:PMC3704539 fatcat:m6fngrzvezcwvbjqic4ft4rony

How pattern formation in ring networks of excitatory and inhibitory spiking neurons depends on the input current regime

Birgit Kriener, Moritz Helias, Stefan Rotter, Markus Diesmann, Gaute T. Einevoll
2014 Frontiers in Computational Neuroscience  
Pattern formation in networks of spiking neurons Frontiers in Computational Neuroscience www.frontiersin.org January 2014 | Volume 7 | Article 187 | 2 350 J = 1.1 mV J = 0.9 mV Rate [1/s] J = 0.6 mV J  ...  Frontiers in Computational Neuroscience www.frontiersin.org January 2014 | Volume 7 | Article 187 | 1 COMPUTATIONAL NEUROSCIENCE Kriener et al.  ...  We gratefully acknowledge funding by the eScience program of the Research Council of Norway under grant 178892/V30 (eNeuro), the Helmholtz Association: HASB and portfolio theme SMHB, the Next-Generation  ... 
doi:10.3389/fncom.2013.00187 pmid:24501591 pmcid:PMC3882721 fatcat:ixmls5rcmjbvtawawpbriady2u
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