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37
Path integration and cognitive mapping in a continuous attractor neural network model
 Journal of Neuroscience
, 1997
"... A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of selflocation from the current representation and from the perceived velocity of motion. In the model, a placecell assembly called a “chart ” contains a twod ..."
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Cited by 169 (5 self)
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A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of selflocation from the current representation and from the perceived velocity of motion. In the model, a placecell assembly called a “chart ” contains a twodimensional attractor set called an “attractor map ” that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its
Synaptic Basis of Cortical Persistent Activity: the Importance of NMDA Receptors to Working Memory
 J. Neurosci
, 1999
"... this paper I present a network model of spiking neurons in which synapses are endowed with realistic gating kinetics, based on experimentally measured dynamical properties of cortical synapses. I will focus on how delayperiod activity could be generated by neuronally plausible mechanisms; the issue ..."
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Cited by 111 (16 self)
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this paper I present a network model of spiking neurons in which synapses are endowed with realistic gating kinetics, based on experimentally measured dynamical properties of cortical synapses. I will focus on how delayperiod activity could be generated by neuronally plausible mechanisms; the issue of memory field formation will be addressed in a separate study. A main problem to be investigated is that of "rate control" for a persistent state: if a robust persistent activity necessitates strong recurrent excitatory connections, how can the network be prevented from runaway excitation in spite of the powerful positive feedback, so that neuronal firing rates are low and comparable to those of PFC cells (10 50 Hz)? Moreover, a persistent state may be destabilized because of network dynamics. For example, fast recurrent excitation followed by a slower negative feedback may lead to network instability and a collapse of the persistent state. It is shown that persistent states at low firing rates are usually stable only in the presence of sufficiently slow excitatory synapses of the NMDA type. Functional implications of these results for the role of Received April 14, 1999; revised Aug. 12, 1999; accepted Aug. 12, 1999
Evolution and Analysis of Model CPGs for Walking I. Dynamical Modules
"... Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract des ..."
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Cited by 31 (13 self)
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Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on the concept of a dynamical module, a set of neurons that simultaneously make their transitions from one quasistable state to another while the synaptic inputs that they receive remain essentially constant, thus temporarily reducing the dimensionality of the circuit dynamics. Using the mathematical tools of dynamical systems theory, we describe a method for identifying dynamical modules, and demonstrate that this concept can be used to quantitatively characterize constraints on neural architecture, account for phase durations, and predict the effects of parameter changes. Moreover, this abstract description reveals coordinated parameter changes that leave the overall circuit...
Action potential onset dynamics and the response speed of neuronal populations
 J. Computational Neuroscience
, 2005
"... Abstract. The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to unde ..."
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Cited by 9 (0 self)
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Abstract. The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here, we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generalization of the θneuron, the normal form of the dynamics of TypeI excitable membranes. Using a novel sparse matrix representation of the FokkerPlanck equation, which describes the ensemble dynamics, we calculate the transmission functions for small modulations of the mean current and noise noise amplitude. In the highfrequency limit the transmission function decays as ω −γ, where γ surprisingly depends on the phase θs at which APs are emitted. If at θs the dynamics is insensitive to external inputs, the transmission function decays as (i) ω −3 for the case of a modulation of a white noise input and as (ii) ω −2 for a modulation of the mean input current in the presence of a correlated and uncorrelated noise as well as (iii) in the case of a modulated amplitude of a correlated noise input. If the insensitivity condition is lifted, the transmission function always decays as ω −1,asinconductance based neuron models. In a physiologically plausible regime up to 1 kHz the typical response speed is, however, independent of the highfrequency limit and is set by the rapidness of the
Dynamical Basis of Irregular Spiking in NMDADriven Prefrontal Cortex Neurons
 CEREBRAL CORTEX
, 2006
"... Slow NMethylDaspartic acid (NMDA) synaptic currents are assumed to strongly contribute to the persistently elevated firing rates observed in prefrontal cortex (PFC) during working memory. During persistent activity, spiking of many neurons is highly irregular. Here we report that highly irregular ..."
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Cited by 8 (0 self)
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Slow NMethylDaspartic acid (NMDA) synaptic currents are assumed to strongly contribute to the persistently elevated firing rates observed in prefrontal cortex (PFC) during working memory. During persistent activity, spiking of many neurons is highly irregular. Here we report that highly irregular firing can be induced through a combination of NMDA and dopamine D1 receptor agonists applied to adult PFC neurons in vitro. The highest interspikeinterval (ISI) variability occurred in a transition regime where the subthreshold membrane potential distribution shifts from mono to bimodality, while neurons with clearly mono or bimodal distributions fired much more regularly. Predictability within irregular ISI series was significantly higher than expected from a noisedriven linear process, indicating that it might best be described through complex (potentially chaotic) nonlinear deterministic processes. Accordingly, the phenomena observed in vitro could be reproduced in purely deterministic biophysical model neurons. High spiking irregularity in these models emerged within a chaotic, closetobifurcation regime characterized by a shift of the membrane potential distribution from mono to bimodality and by similar ISI return maps as observed in vitro. The nonlinearity of NMDA conductances was crucial for inducing this regime. NMDAinduced irregular dynamics may have important implications for computational processes during working memory and neural coding.
An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems
, 2003
"... A procedure to calculate the Lyapunov characteristic exponent of the response of structural continuous systems, discretized using finite element methods, is proposed. The Lyapunov characteristic exponent can be used to characterize the asymptotic stability of the system dynamic response, and it is f ..."
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Cited by 5 (2 self)
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A procedure to calculate the Lyapunov characteristic exponent of the response of structural continuous systems, discretized using finite element methods, is proposed. The Lyapunov characteristic exponent can be used to characterize the asymptotic stability of the system dynamic response, and it is frequently employed to identify a chaotic behaviour. The proposed procedure can also be used in the stability characterization of fluid–structure interaction systems in which the focus of the analysis is on the
Propagating waves in visual cortex: A largescale model of turtle visual cortex
 J. of Computational Neuroscience
, 2003
"... Abstract. This article describes a largescale model of turtle visual cortex that simulates the propagating waves of activity seen in real turtle cortex. The cortex model contains 744 multicompartment models of pyramidal cells, stellate cells, and horizontal cells. Input is provided by an array of 2 ..."
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Cited by 4 (1 self)
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Abstract. This article describes a largescale model of turtle visual cortex that simulates the propagating waves of activity seen in real turtle cortex. The cortex model contains 744 multicompartment models of pyramidal cells, stellate cells, and horizontal cells. Input is provided by an array of 201 geniculate neurons modeled as single compartments with spikegenerating mechanisms and axons modeled as delay lines. Diffuse retinal flashes or presentation of spots of light to the retina are simulated by activating groups of geniculate neurons. The model is limited in that it does not have a retina to provide realistic input to the geniculate, and the cortex and does not incorporate all of the biophysical details of real cortical neurons. However, the model does reproduce the fundamental features of planar propagating waves. Activation of geniculate neurons produces a wave of activity that originates at the rostrolateral pole of the cortex at the point where a high density of geniculate afferents enter the cortex. Waves propagate across the cortex with velocities of 4 µm/ms to 70 µm/ms and occasionally reflect from the caudolateral border of the cortex. Keywords: visual cortex, largescale model, cortical waves, KarhunenLoéve decomposition 1.
Reproductive phase locking of mosquito populations in response to rainfall frequency
 PLoS ONE
, 2007
"... The frequency of moderate to heavy rainfall events is projected to change in response to global warming. Here we show that these hydrologic changes may have a profound effect on mosquito population dynamics and rates of mosquitoborne disease transmission. We develop a simple model, which treats the ..."
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Cited by 4 (0 self)
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The frequency of moderate to heavy rainfall events is projected to change in response to global warming. Here we show that these hydrologic changes may have a profound effect on mosquito population dynamics and rates of mosquitoborne disease transmission. We develop a simple model, which treats the mosquito reproductive cycle as a phase oscillator that responds to rainfall frequency forcing. This model reproduces observed mosquito population dynamics and indicates that mosquitoborne disease transmission can be sensitive to rainfall frequency. These findings indicate that changes to the hydrologic cycle, in particular the frequency of moderate to heavy rainfall events, could have a profound effect on the transmission rates of some mosquitoborne diseases.
Feigenbaum Graphs: A Complex Network Perspective of Chaos
, 2011
"... The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graphtheoretical description of nonlinear systems with ..."
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Cited by 1 (1 self)
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The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graphtheoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the perioddoubling and bandsplitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesinlike relation equally valid out of chaos.