this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 3000--10,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 1987; Braitenberg and Schuz, 1991). More than half of these contacts are thought to arise from neurons within a 100--200 #m radius of the target cell, reflecting the stereotypical columnar organization of neocortex. Because neurons within a cortical column typically share similar physiological properties, the conditions that excite one neuron are likely to excite a considerable fraction of its afferent input as well (Mountcastle, 1978; Peters and Sethares, 1991), creating a scenario in which saturation of the neuron's firing rate could easily occur. This problem is exacerbated by the fact that EPSPs from individual axons appear to exert substantial impact on the membrane potential (Mason et al., 1991; Otmakhov Received Sept. 15, 1997; revised Feb. 25, 1998; accepted March 3, 1998.

temporal relations requires the joint evaluation of responses from more than one neuron, only experiments that permit simultaneous measurements of responses 60528 Frankfurt from multiple units are considered. These include multi-Federal Republic of Germany electrode recordings from multiple individual cells, but also measurements of local field potentials (LFPs) and electroencephalographic (EEG) or magnetoencephalo-Most of our knowledge about the functional organization of neuronal systems is based on the analysis of the firing patterns of individual neurons that have been recorded one by one in succession. This approach permits as-sessment of event-related variations in discharge rate, but it precludes detection of any covariations in the amplitude or timing of distributed responses if these graphic (MEG) recordings. The signals of these latter

The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more powerful than these other neural network models. A concrete biologically relevant function is exhibited which can be computed by a single spiking neuron (for biologically reasonable values of its parameters), but which requires hundreds of hidden units on a sigmoidal neural net. This article does not assume prior knowledge about spiking neurons, and it contains an extensive list of references to the currently available literature on computations in networks of spiking neurons and relevant results from neurobiology. 1 Definitions and Motivations If one classifies neural network models according to their computational units, one can distinguish three different generations. The first generation i...

In the classical feed-forward, modular view of visual processing, the primary visual cortex (area V1) is a module that serves to extract local features such as edges and bars. Representation and recognition of objects are thought to be functions of higher extrastriate cortical areas. This paper presents neurophysiological data that show the later part of V1 neurons' responses reflecting higher order perceptual computations related to Ullman's (Cognition 1984;18:97 -- 159) visual routines and Marr's (Vision NJ: Freeman 1982) full primal sketch, 2 1 2 D sketch and 3D model. Based on theoretical reasoning and the experimental evidence, we propose a possible reinterpretation of the functional role of V1. In this framework, because of V1 neurons' precise encoding of orientation and spatial information, higher level perceptual computations and representations that involve high resolution details, fine geometry and spatial precision would necessarily involve V1 and be reflected in the later...

We study image segmentation on the basis of locally excitatory globally inhibitory oscillator networks (LEGION), whereby the phases of oscillators encode the binding of pixels. We introduce a potential for each oscillator so that only those oscillators with strong connections from their neighborhood can develop high potentials. Based on the concept of potential, a solution to remove noisy regions in an image is proposed for LEGION, so that it suppresses the oscillators corresponding to noisy regions, without affecting those corresponding to major regions. We show analytically that the resulting oscillator network separates an image into several major regions, plus a background consisting of all noisy regions, and illustrate network properties by computer simulation. The network exhibits a natural capacity in segmenting images. The oscillatory dynamics leads to a computer algorithm, which is applied successfully to segmenting real graylevel images. A number of issues regarding biological plausibility and perceptual organization are discussed. We argue that LEGION provides a novel and effective framework for image segmentation and figure-ground segregation. DeLiang Wang and David Terman Image Segmentation 1.

The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are still not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model with excitatory and inhibitory populations of simple binary units. The internal feedback is mediated by relatively large synaptic strengths, so that the magnitude of the total excitatory as well as inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is large but small compared to the total number of cells in the network. The network also receives a large, temporally regular input from external sources. An analytical solution of the mean-field theory of this model which is exact in the limit of large network size is presented. This theory reveals a new cooperative stationary state of large networks, which we term a balanced state. In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations are of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses to the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes 1 the system's state and enables it to track a time-dependent input on time scales much shorter than the time constant of a single cell. The spatio-temporal statistics of the balanced state is calculated. It is shown that the auto-correlations decay on a short time scale yielding an approximate Poissonian temporal s...

We investigate the computational power of a formal model for networks of spiking neurons. It is shown that simple operations on phasedifferences between spike-trains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a small network of spiking neurons. We construct networks of spiking neurons that simulate arbitrary threshold circuits, Turing machines, and a certain type of random access machines with real valued inputs. We also show that relatively weak basic assumptions about the response- and threshold-functions of the spiking neurons are sufficient in order to employ them for such computations. 1 Introduction and Basic Definitions There exists substantial evidence that timing phenomena such as temporal differences between spikes and frequencies of oscillating subsystems are integral parts of various information processing mechanisms in biological neural systems (for a survey and references see e.g. Kandel et al., ...

may be the preferred variable for describing the response of a spiking neuron. Key words: neural coding; retinal ganglion cell; spike generator; refractory period; reproducibility; Poisson process There has been considerable speculation about the code used by spiking neurons to transmit information (Ferster and Spruston, 1995; Sejnowski, 1995; Stevens and Zador, 1995). The spectrum of proposed theories ranges from the "rate code," in which the firing rates of many neurons are averaged to obtain a reliable signal (Shadlen and Newsome, 1994), to "time codes," in which the precise time relations of spikes from many neurons are meaningful (Abeles, 1991; Singer and Gray, 1995; Softky, 1995; Meister, 1996). A key factor in distinguishing among these theories is the temporal precision of individual action potentials. Thus, it is important both to measure this precision experimentally and to describe neuronal spike trains by a formalism consistent with such measurements. Th

We describe an approach to analyzing single- and multi-unit (ensemble) discharge patterns based on information-theoretic distance measures and on empirical theories derived from work in universal signal processing. In this approach, we quantify the difference between response patterns, be they time-varying or not, using information-theoretic distance measures. We apply these techniques to single and multiple unit processing of sound amplitude and sound location. These examples illustrate that neurons can simultaneously represent at least two kinds of information with different levels of fidelity. The fidelity can persist through a transient and a subsequent steady-state response, indicating that it is possible for an evolving neural code to represent information with constant fidelity. 1 Johnson et al. Analysis of Neural Coding 1 Introduction Neural coding has been classified into two broadly defined types: rate codes the average rate of spike discharge and timing codes the t...

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...