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54
Distributed representations of structure: A Theory of Analogical Access and Mapping
 Psychological Review
, 1997
"... This article describes an integrated theory of analogical access and mapping, instantiated in a ..."
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Cited by 247 (19 self)
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This article describes an integrated theory of analogical access and mapping, instantiated in a
Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons
, 1999
"... The dynamics of networks of sparsely connected excitatory and inhibitory integrateand re neurons is studied analytically. The analysis reveals a very rich repertoire of states, including: Synchronous states in which neurons re regularly; Asynchronous states with stationary global activity and very ..."
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Cited by 147 (11 self)
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The dynamics of networks of sparsely connected excitatory and inhibitory integrateand re neurons is studied analytically. The analysis reveals a very rich repertoire of states, including: Synchronous states in which neurons re regularly; Asynchronous states with stationary global activity and very irregular individual cell activity; States in which the global activity oscillates but individual cells re irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed: In the `fast' oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the `slow' oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size eects in the asynchronous state are also discussed.
A symbolicconnectionist theory of relational inference and generalization
 Psychological Review
, 2003
"... The authors present a theory of how relational inference and generalization can be accomplished within a cognitive architecture that is psychologically and neurally realistic. Their proposal is a form of symbolic connectionism: a connectionist system based on distributed representations of concept m ..."
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Cited by 68 (11 self)
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The authors present a theory of how relational inference and generalization can be accomplished within a cognitive architecture that is psychologically and neurally realistic. Their proposal is a form of symbolic connectionism: a connectionist system based on distributed representations of concept meanings, using temporal synchrony to bind fillers and roles into relational structures. The authors present a specific instantiation of their theory in the form of a computer simulation model, Learning and Inference with Schemas and Analogies (LISA). By using a kind of selfsupervised learning, LISA can make specific inferences and form new relational generalizations and can hence acquire new schemas by induction from examples. The authors demonstrate the sufficiency of the model by using it to simulate a body of empirical phenomena concerning analogical inference and relational generalization. A fundamental aspect of human intelligence is the ability to form and manipulate relational representations. Examples of relational thinking include the ability to appreciate analogies between seemingly different objects or events (Gentner, 1983; Holyoak & Thagard, 1995), the ability to apply abstract rules in novel situations (e.g., Smith, Langston, & Nisbett, 1992), the ability to understand and learn language (e.g., Kim, Pinker, Prince, & Prasada, 1991), and even the ability to appreciate perceptual similarities
What Matters in Neuronal Locking?
"... Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessa ..."
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Cited by 46 (10 self)
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Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1
The Number of Synaptic Inputs and the Synchrony of Large Sparse Neuronal Networks
, 1999
"... The prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons. We study synchronization in models of large networks of spiking neurons with random sparse connectivity. Synchrony oc ..."
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Cited by 35 (1 self)
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The prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons. We study synchronization in models of large networks of spiking neurons with random sparse connectivity. Synchrony occurs only when the average number of synapses, M , that a cell receives is larger than a critical value, M c . Below M c , the system is in an asynchronous state. In the limit of weak coupling, assuming identical neurons, we reduce the model to a system of phase oscillators which are coupled via an effective interaction, \Gamma. In this framework, we develop an approximate theory for sparse networks of identical neurons to estimate M c analytically from the Fourier coefficients of \Gamma. Our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it. We apply this theory to compute M c for a model of inhibitory networks of integrateandfire (I&F) neurons as a function of the intrinsic neuronal properties (e.g., the refractory period T r ), the synaptic time constants and the strength of the external stimulus, I ext . The number M c is found to be nonmonotonous with the strength of I ext . For T r = 0, we estimate the minimum value of M c over all the parameters of the model to be 363:8. Above M c , the neurons tend to fire in: 1) smeared one cluster states at high firing rates and 2) smeared two or more cluster states at low firing rates. Refractoriness decreases M c at intermediate and high firing rates. These results are compared against numerical simulations. We show numerically that systems with different sizes, N , behave in the same way provided the connectivity, M , is such a way that 1=M eff = 1=...
Spectral Properties and Synchronization in Coupled Map Lattices
 Rev. E
, 2001
"... Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The q ..."
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Cited by 35 (13 self)
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Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbour coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling. PACS Numbers: 05.45.Ra, 05.45.Xt, 89.75.Hc
Waves and bumps in neuronal networks with axodendritic synaptic interactions
 Physica D
, 2003
"... synaptic interactions ..."
Spatiotemporal Analysis of Prepyriform, Visual, Auditory, and Somesthetic Surface EEGs in Trained Rabbits
 J. Neurophysiol
, 1996
"... inst log frequency, revealed 1/f spectra in both pre and poststimulus segments for CS and CS+ stimuli. The yintercepts and slopes for average PSDs were significantly different between pre and poststimulus segments, owing to the evoked potentials, but not between CS and CS+ stimulus segments. ..."
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Cited by 28 (10 self)
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inst log frequency, revealed 1/f spectra in both pre and poststimulus segments for CS and CS+ stimuli. The yintercepts and slopes for average PSDs were significantly different between pre and poststimulus segments, owing to the evoked potentials, but not between CS and CS+ stimulus segments. 6.##### Spatiotemporal patterns were invariant over all frequency bins from 20100 Hz in the 1/ f domain. Spatiotemporal patterns in the 220 Hz domain progressively differed from the invariant patterns with decreasing frequency. 7.##### In the spatial frequency domain, the logarithm of the average spatial FFT power spectra from pre and poststimulus neocortical EEG segments, when plotted against the log spatial frequency, fell monotonically from the maximum at the lowest spatial frequency, concavely curving to a linear 1/f spectral domain. This curve in the 1/f spectral domain extended from 0.133  0.880 cycles/mm in the PPC and from 0.095  0.624 cycles/mm in the neocortices. 8.#####
Geometric Singular Perturbation Analysis of Neuronal Dynamics
 in Handbook of Dynamical Systems
, 2000
"... : In this chapter, we consider recent models for neuronal activity. We review the sorts of oscillatory behavior which may arise from the models and then discuss how geometric singular perturbation methods have been used to analyze these rhythms. We begin by discussing models for single cells which d ..."
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Cited by 23 (13 self)
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: In this chapter, we consider recent models for neuronal activity. We review the sorts of oscillatory behavior which may arise from the models and then discuss how geometric singular perturbation methods have been used to analyze these rhythms. We begin by discussing models for single cells which display bursting oscillations. There are, in fact, several dierent classes of bursting solutions; these have been classied by the geometric properties of how solutions evolve in phase space. We describe several of the bursting classes and then review related rigorous mathematical analysis. We then discuss the dynamics of small networks of neurons. We are primarily interested in whether excitatory or inhibitory synaptic coupling leads to either synchronous or desynchronous rhythms. We demonstrate that all four combinations are possible, depending on the details of the intrinsic and synaptic properties of the cells. Finally, we discuss larger networks of neuronal oscillators involving two dis...