Rapid synchronization through fast threshold modulation
TL;DR: The results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components.
Abstract: Synchronization properties of locally coupled neural oscillators were investigated analytically and by computer simulation. When coupled in a manner that mimics excitatory chemical synapses, oscillators having more than one time scale (relaxation oscillators) are shown to approach synchrony using mechanisms very different from that of oscillators with a more sinusoidal waveform. The relaxation oscillators make critical use of fast modulations of their thresholds, leading to a rate of synchronization relatively independent of coupling strength within some basin of attraction; this rate is faster for oscillators that have conductance-based features than for neural caricatures such as the FitzHugh-Nagumo equations that lack such features. Computer simulations of one-dimensional arrays show that oscillators in the relaxation regime synchronize much more rapidly than oscillators with the same equations whose parameters have been modulated to yield a more sinusoidal waveform. We present a heuristic explanation of this effect based on properties of the coupling mechanisms that can affect the way the synchronization scales with array length. These results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components. Possible implications for perceptual feature binding and attention are discussed.
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TL;DR: Recent findings indicate that network oscillations bias input selection, temporally link neurons into assemblies, and facilitate synaptic plasticity, mechanisms that cooperatively support temporal representation and long-term consolidation of information.
Abstract: Clocks tick, bridges and skyscrapers vibrate, neuronal networks oscillate. Are neuronal oscillations an inevitable by-product, similar to bridge vibrations, or an essential part of the brain’s design? Mammalian cortical neurons form behavior-dependent oscillating networks of various sizes, which span five orders of magnitude in frequency. These oscillations are phylogenetically preserved, suggesting that they are functionally relevant. Recent findings indicate that network oscillations bias input selection, temporally link neurons into assemblies, and facilitate synaptic plasticity, mechanisms that cooperatively support temporal representation and long-term consolidation of information.
5,512 citations
Book•
01 Oct 2006
TL;DR: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition, providing a link between the two disciplines.
Abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience
3,683 citations
Cites background from "Rapid synchronization through fast ..."
...Some of the bifurcations considered in this chapter, such as the bluesky catastrophe, are classified as “exotic” by Kuznetsov (1995), though the catastrophe was recently found in a model of a leech heart interneuron (Shilnikov and Cymbalyuk 2005)....
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TL;DR: The phenomenon of neural bursting is described, and geometric bifurcation theory is used to extend the existing classification of bursters, including many new types, and it is shown that different bursters can interact, synchronize and process information differently.
Abstract: Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here. We show how the type of bifurcation determines the neuro-computational properties of the cells. For example, when the rest state is near a saddle-node bifurcation, the cell can fire all-or-none spikes with an arbitrary low frequency, it has a well-defined threshold manifold, and it acts as an integrator; i.e. the higher the frequency of incoming pulses, the sooner it fires. In contrast, when the rest state is near an Andronov–Hopf bifurcation, the cell fires in a certain frequency range, its spikes are not all-or-none, it does not have a well-defined threshold manifold, it can fire in response to an inhibitory pulse, and it acts as a resonator; i.e. it responds preferentially to a certain (resonant) frequency of the input. Increasing the input frequency may actually delay or terminate its firing. We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types. We discuss how the type of burster defines its neuro-computational properties, and we show that different bursters can interact, synchronize and process information differently.
1,765 citations
TL;DR: This review summarizes the recent evidence that synchronous neural oscillations reveal much about the origin and nature of cognitive processes such as memory, attention and consciousness.
913 citations
TL;DR: Synthetic gene networks will lead to new logical forms of cellular control, which could have important applications in functional genomics, nanotechnology, and gene and cell therapy.
Abstract: A central focus of postgenomic research will be to understand how cellular phenomena arise from the connectivity of genes and proteins This connectivity generates molecular network diagrams that resemble complex electrical circuits, and a systematic understanding will require the development of a mathematical framework for describing the circuitry From an engineering perspective, the natural path towards such a framework is the construction and analysis of the underlying submodules that constitute the network Recent experimental advances in both sequencing and genetic engineering have made this approach feasible through the design and implementation of synthetic gene networks amenable to mathematical modelling and quantitative analysis These developments have signalled the emergence of a gene circuit discipline, which provides a framework for predicting and evaluating the dynamics of cellular processes Synthetic gene networks will also lead to new logical forms of cellular control, which could have important applications in functional genomics, nanotechnology, and gene and cell therapy
711 citations
Cites background from "Rapid synchronization through fast ..."
...Relaxation oscillators exhibit rapid transitions followed by periods of slow change, and previous theoretical wor...
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References
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TL;DR: A new hypothesis about the role of focused attention is proposed, which offers a new set of criteria for distinguishing separable from integral features and a new rationale for predicting which tasks will show attention limits and which will not.
11,452 citations
"Rapid synchronization through fast ..." refers methods in this paper
...In the context of this synchronized binding hypothesis, our findings suggest a new, possible mechanism for "attentional searchlight" processing (e.g., Treisman 1982; Treisman and Gelade 1980) in coherent perception....
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11,285 citations
"Rapid synchronization through fast ..." refers methods in this paper
...Numerical integration was performed with two fundamentally different algorithms, Runge-Kut t a and Bulirsch-Stoer (Press et al. 1988), and thus it is unlikely that numerical error had a significant effect on our results....
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TL;DR: Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle, which qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve.
5,430 citations
01 Jan 1989
TL;DR: This paper presents a list of recommended recipes for making CDRom decks and some examples of how these recipes can be modified to suit theommelier's needs.
Abstract: Keywords: informatique ; numerical recipes Note: contient un CDRom Reference Record created on 2004-09-07, modified on 2016-08-08
4,920 citations
4,036 citations