It is well known that visual cortical neurons respond vigorously to a limited range of stimulus orientations, while their primary afferent inputs, neurons in the lateral geniculate nucleus (LGN) respond well to all orientations. Mechanisms based on intracortical inhibition and/or converging thalamocortical afferents have previously been suggested to underlie the generation of cortical orientation selectivity; however, these models conflict with experimental data. Here, a 1:4 scale model of a 1700m by 200m region of layer IV of cat primary visual cortex (area 17) is presented in order to demonstrate that local intracortical excitation may provide the dominant source of orientation selective input. In agreement with experiment, model cortical cells exhibit sharp orientation selectivity despite receiving strong iso-- orientation inhibition, weak cross--orientation inhibition, no shunting inhibition, and weakly tuned thalamocortical excitation. Sharp tuning is provided by recurrent cortica...

Introduction The integrate-and-fire (IF) neuron has become popular as a simplified neural element in modeling the dynamics of large-scale networks of spiking neurons. A simple version of an IF neuron integrates the input current as an RC circuit (with a leakage current proportional to the depolarization) and emits a spike when the depolarization crosses a threshold. We will refer to it as the RC neuron. Networks of neurons schematized in this way exhibit a wide variety of characteristics observed in single and multiple neuron recordings in cortex in vivo. With biologically plausible time constants and synaptic efficacies, they can maintain spontaneous activity, and when the network is subjected to Hebbian learning (subsets of cells are repeatedly activated by the external stimuli), it shows many stable states of activation, each corresponding to a different attractor of the network dynamics, in coexistence with spontaneous activity (Amit & Brunel, 1997a). These s

To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky and Koch, 1993), it is critical to examine the dynamics of their neuronal integration as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick et al., 1985). After setting RC parameters, the post-spike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency vs. injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory "1= p N " and "random walk" pictures that have previously been proposed. When ISI's are dominated by post-spike recovery, 1= p N arguments hold and spiking is regular; after the "memory" of the last spike becomes ne...

Neurons in cortical slices emit spikes or bursts of spikes regularly in response to a suprathreshold current injection. This behavior is in marked contrast to the behavior of cortical neurons in vivo, whose response to electrical or sensory input displays a strong degree of irregularity. Correlation measurements show a significant degree of synchrony in the temporal fluctuations of neuronal activities in cortex. We explore the hypothesis that these phenomena are the result of the synchronized chaos generated by the deterministic dynamics of local cortical networks. A model of a "hypercolumn " in the visual cortex is studied. It consists of two populations of neurons, one inhibitory and one excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model of excitable voltage-clamped cells with several cellular and synaptic conductances. A slow potassium current is included in the dynamics of the excitatory population to reproduce the observed adaptation of the spike trains emitted by these neurons. The pattern of connectivity has a spatial structure which is correlated with the internal organization of hypercolumns in orientation columns. Numerical simulations of the model show that in an appropriate parameter range, the network settles in a synchronous chaotic state, characterized by a strong temporal variability ofthe neural activity which is correlated across the hypercolumn. Strong inhibitory feedback is essential for the stabilization of this state. These results show that the cooperative dynamics of large neuronal networks are capable of generating variability and synchrony similar to those observed in cortex. Auto-correlation and cross-correlation functions of

We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the θ-neuron. The θ-neuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude “kicks” to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the Morris-Lecar (M-L) neural model with random synaptic inputs: type I M-L yields high CVs. When this model is modified to have type II dynamics (periodicity arises via a Hopf bifurcation), however, it gives regular spike trains (CV below 0.3). Our results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by “random” inputs. In contrast, neural oscillators or neurons exhibiting type II excitability should produce regular spike trains.

The residual fluctuations that naturally arise in experimental inquiry are analyzed in terms of their time histories. Although these fluctuations are generally relegated to a statistical purgatory known as unexplained variance, this article shows that they may harbor a long-term memory process known as 1/f noise. This type of noise has been encountered in a number of biological and physical systems and is theorized to be a signature of dynamic complexity. Its presence in psychological data appears to be associated with the most elementary aspect of cognitive process, the formation of representations. The work described here concerns memory and the temporal evolution of cognitive activity. Although many of the ideas presented make little contact with current cognitive theories, almost all of the empirical work derives from the well-known observation that memory inevitably makes an appearance in repeated episodes of measurement. Explicit memory, for example, was a bedeviling factor in the early studies of magnitude estimation, signal detection, and absolute identification. People have a tendency to repeat themselves so that if they have just said "loud, " they are likely to

We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a one-dimensional network of neurons with long-range interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response. 1

Abstract: A naturalistic scheme of primitive conceptual representations is proposed using the statistical measure of mutual information. It is argued that a concept represents, not the class of objects that caused its tokening, but the class of objects that is most likely to have caused it (had it been tokened), as specified by the statistical measure of mutual information. This solves the problem of misrepresentation which plagues causal accounts, by taking the representation relation to be determined via ordinal relationships between conditional probabilities. The scheme can deal with statistical biases and does not rely on arbitrary criteria. Implications for the theory of meaning and semantic content are addressed. 1.

Introduction Spiking neurons are highly non-linear oscillators. As such they display collective behavior that may have important calculational manifestations. Synchronization between the firing of different neurons is the first topic to which we devote our attention. This behavior can be brought about in our integrate-and-fire model through excitatory synaptic couplings without delays, or inhibitory couplings with delays. Once the mechanism of synchronization is established, this phenomenon can be used for defining data clustering. The clusters correspond to neurons that fire synchronously, with different clusters firing at different times. This behavior can also be described as temporal segmentation, separating data through phase lags between excitations of different aggregates. This separation is characteristically limited to a small number of segments, a limitation that is inherent to the behavior of coupled non-linear oscillators. The importance of synchrony as s

Arrays of interacting identical neurons can develop coherent firing patterns, such as moving stripes that have been suggested as possible explanations of hallucinatory phenomena. Other known formations include rotating spirals and expanding concentric rings. We obtain all of them using a novel two variable description of integrate and fire neurons that allows for a continuum formulation of neural fields. One of these variables distinguishes between the two different states of refractoriness and depolarization and acquires topological meaning when it is turned into a field. Hence it leads to a topologic characterization of the ensuing solitary waves, or excitons. They are limited to point-like excitations on a line and linear excitations, including all the examples quoted above, on a two-dimensional surface. A moving patch of firing activity is not an allowed solitary wave on our neural surface. Only the presence of strong inhomogeneity that destroys the neural field continuity, allows ...