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Dynamics of a Recurrent Network of Spiking Neurons Before and Following Learning
, 1998
"... Extensive simulations of large recurrent networks of integrateandfire excitatory and inhibitory neurons in realistic cortical conditions (before and after Hebbian unsupervised learning of uncorrelated stimuli) exhibit a rich phenomenology of stochastic neural spike dynamics, and in particular, coe ..."
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Cited by 60 (12 self)
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Extensive simulations of large recurrent networks of integrateandfire excitatory and inhibitory neurons in realistic cortical conditions (before and after Hebbian unsupervised learning of uncorrelated stimuli) exhibit a rich phenomenology of stochastic neural spike dynamics, and in particular, coexistence between two types of stable states: spontaneous activity, upon stimulation by an unlearned stimulus; and `working memory' states strongly correlated with learned stimuli. Firing rates have very wide distributions, due to the variability in the connectivity from neuron to neuron. ISI histograms are exponential, except for small intervals. Thus the spike emission processes are well approximated by a Poisson process. The variability of the spike emission process is effectively controlled by the magnitude of the postspike reset potential relative to the mean depolarization of the cell. Crosscorrelations (CC) exhibit a central peak near zero delay, flanked by damped oscillations. The m...
A neurobiological theory of meaning in perception. Part 1. Information and meaning in nonconvergent and nonlocal brain dynamics
 Int. J. Bifurc. Chaos
, 2003
"... Synchrony among multicortical EEGs 2 Freeman, Gaál & Jörnsten Information transfer and integration among functionally distinct areas of cerebral cortex of oscillatory activity requires some degree of phase synchrony of the trains of action potentials that carry the information prior to the integ ..."
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Cited by 31 (14 self)
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Synchrony among multicortical EEGs 2 Freeman, Gaál & Jörnsten Information transfer and integration among functionally distinct areas of cerebral cortex of oscillatory activity requires some degree of phase synchrony of the trains of action potentials that carry the information prior to the integration. However, propagation delays are obligatory. Delays vary with the lengths and conduction velocities of the axons carrying the information, causing phase dispersion. In order to determine how synchrony is achieved despite dispersion, we recorded EEG signals from multiple electrode arrays on five cortical areas in cats and rabbits, that had been trained to discriminate visual or auditory conditioned stimuli. Analysis by timelagged correlation, multiple correlation and PCA, showed that maximal correlation was at zero lag and averaged.7, indicating that 50 % of the power in the gamma range among the five areas was at zero lag irrespective of phase or frequency. There were no stimulusrelated episodes of transiently increased phase locking among the areas, nor EEG &quot;bursts &quot; of transiently increased amplitude above the sustained level of synchrony. Three operations were identified to account for the sustained correlation. Cortices broadcast their outputs over divergentconvergent axonal
The Wave Packet: An Action Potential For The 21st Century
, 2003
"... prediction is made for clinical testing that wave packets are precursor to states of awareness. They are not by themselves accessible to experience, as may be the macroscopic states initiated by global state transitions. Keywords: EEG; meaning; mesoscopic neurodynamics; phase cone; state transiti ..."
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Cited by 16 (0 self)
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prediction is made for clinical testing that wave packets are precursor to states of awareness. They are not by themselves accessible to experience, as may be the macroscopic states initiated by global state transitions. Keywords: EEG; meaning; mesoscopic neurodynamics; phase cone; state transition; wave packet. 1. Introduction Brain systems operate on many levels of organization, each with its own scales of time and space. Dynamics applies to every level from the atomic to the molecular, and from macromolecular organelles to the neurons that incorporate them. In turn neurons form populations, these form the subassemblies in brains, and so on to embodied brains interacting intentionally with material, interpersonal, and social environments. Each level is macroscopic to that below it and microscopic to that above it. Among the most di#cult tasks scientists face are those of conceiving and describing the exchanges between levels, seeing that the measures of time 3 and distance ar
Controlling the Speed of Synfire Chains
 Proceedings of the International Conference on Artificial Neural Networks ICANN96
, 1996
"... . This paper deals with the propagation velocity of synfire chain activation in locally connected networks of artificial spiking neurons. Analytical expressions for the propagation speed are derived taking into account form and range of local connectivity, explicitly modelled synaptic potentials, tr ..."
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Cited by 11 (4 self)
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. This paper deals with the propagation velocity of synfire chain activation in locally connected networks of artificial spiking neurons. Analytical expressions for the propagation speed are derived taking into account form and range of local connectivity, explicitly modelled synaptic potentials, transmission delays and axonal conduction velocities. Wave velocities particularly depend on the level of external input to the network indicating that synfire chain propagation in real networks should also be controllable by appropriate inputs. The results are numerically tested for a network consisting of `integrateandfire' neurons. 1 Introduction The concept of synfire chains has been introduced by Abeles [1] in order to explain precisely correlated spike events observable in the cortex on surprisingly large timescales of up to hundreds of milliseconds. The main idea is that highly specific spatiotemporal firing patterns occur in the brain in such a way that synchronously firing pools ...
Another Neural Code?
, 1997
"... This paper presents the conjecture that functional integration may be mediated by the mutual induction and maintenance of stereotyped spatiotemporal patterns of activity (i.e., transients) in different neuronal populations. In contradistinction to temporal and rate coding models of neuronal interact ..."
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Cited by 8 (4 self)
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This paper presents the conjecture that functional integration may be mediated by the mutual induction and maintenance of stereotyped spatiotemporal patterns of activity (i.e., transients) in different neuronal populations. In contradistinction to temporal and rate coding models of neuronal interactions, transient coding considers that transactions among neuronal systems use transient dynamics that are distributed in a structured way over both space and time. In contrast to synchronization models, transient coding does not depend on interactions at the same frequencies, in different parts of the brain, but involves covariations among different frequencies and can therefore be considered a more general form of coding. Using an analysis of the correlations among the spectral density of neuromagnetic signals, measured at different cortical regions, this hypothesis was confirmed. For example high (gamma)frequency oscillations in the prefrontal cortex are associated with low (20 Hz)frequency oscillations in the parietal cortex. The results are consistent with transient coding and suggest that transient dynamics endure for at least 40–200 ms. Transient coding means that correlations (rate coding) and coherence (synchrony) are neither complete nor sufficient characterizations of neuronal interactions. Although temporal coding, rate coding, and synchrony are important aspects of neuronal interactions, the results speak to further integrative neuronal mechanisms of a more general nature.
Using Helmholtz Machines to analyze multichannel neuronal recordings
, 1998
"... One of the current challenges to understanding neural information processing in biological systems is to decipher the "code" carried by large populations of neurons acting in parallel. We present an algorithm for automated discovery of stochastic firing patterns in large ensembles of neuro ..."
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Cited by 3 (0 self)
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One of the current challenges to understanding neural information processing in biological systems is to decipher the "code" carried by large populations of neurons acting in parallel. We present an algorithm for automated discovery of stochastic firing patterns in large ensembles of neurons. The algorithm, from the "Helmholtz Machine" family, attempts to predict the observed spike patterns in the data. The model consists of an observable layer which is directly activated by the input spike patterns, and hidden units that are activated through ascending connections from the input layer. The hidden unit activity can be propagated down to the observable layer to create a prediction of the data pattern that produced it. Hidden units are added incrementally and their weights are adjusted to improve the fit between the predictions and data, that is, to increase a bound on the probability of the data given the model. This greedy strategy is not globally optimal but is computationally tractab...
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation
, 2009
"... Abstract. We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possi ..."
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Cited by 2 (2 self)
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Abstract. We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focusing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations ” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells.
2010b). Dynamical principles of emotioncognition interaction: mathematical images of mental disorders
 Biol. Cybern
, 2006
"... The key contribution of this work is to introduce a mathematical framework to understand selforganized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized LotkaVolterra systems. This coupling is bas ..."
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Cited by 1 (1 self)
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The key contribution of this work is to introduce a mathematical framework to understand selforganized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized LotkaVolterra systems. This coupling is based upon competition for common resources. The system can be regarded as a normal or canonical form for any distributed system that shows selforganized dynamics that entail winnerless competition. Crucially, we will show that some of the fundamental instabilities that arise in these coupled systems are remarkably similar to endogenous activity seen in the brain (using EEG and fMRI). Furthermore, by changing a small subset of the system’s parameters we can produce bifurcations and metastable sequential dynamics changing, which bear a remarkable similarity to pathological brain states seen in psychiatry. In what follows, we will consider the coupling of two macroscopic modes of brain activity, which, in a purely descriptive fashion, we will label as cognitive and emotional modes. Our aim is to examine the dynamical structures that emerge when coupling these two modes and relate them tentatively to