Much experimental study of real neural networks relies on the proper classification of extracellulary sampled neural signals (i.e.

ABSTRACT A computer model of the hippocampal pyramidal cell (HPC) is described which integrates data from a variety of sources in order to develop a consistent description for this cell type. The model presently includes descriptions of eleven nonlinear somatic currents of the HPC, and the electrotonic structure of the neuron is modelled with a soma/short-cable approximation. Model simulations qualitatively or quantitatively reproduce a wide range of somatic electrical behavior i HPCs, and demonstrate possible roles for the various currents in information processing. There are several substrates for neuronal computation, including connectivity, synapses, morphometries of dendritic trees, linear parameters of cell membrane, as well as nonlinear, time-varying membrane conductances, also referred to as currents or channels. In the classical description of neuronal function, the contribution of membrane channels is constrained to that of generating the action potential, setting firing threshold, and establishing the relationship between (steady-state) stimulus intensity and firing frequency.

Centric Models of the Orientation Map in Primary Visual Cortex William Baxter Department of Computer Science, S.U.N.Y. at Buffalo, NY 14620 Bruce Dow Department of Physiology, S.U.N.Y. at Buffalo, NY 14620 Abstract In the visual cortex of the monkey the horizontal organization of the preferred orientations of orientation-selective cells follows two opposing rules: 1) neighbors tend to have similar orientation preferences, and 2) many different orientations are observed in a local region. Several orientation models which satisfy these constraints are found to differ in the spacing and the topological index of their singularities. Using the rate of orientation change as a measure, the models are compared to published experimental results. Introduction It has been known for some years that there exist orientation-sensitive neurons in the visual cortex of cats and mOnkeysl,2. These cells react to highly specific patterns of light occurring in narrowly circumscribed regiOns of the visual field, i.e., the cell's receptive field. The best patterns for such cells are typically not diffuse levels of illumination, but elongated bars or edges oriented at specific angles.

In this article we consider two aspects of computation with neural networks. Firstly we consider the problem of the complexity of the network required to compute classes of specified (structured) functions. We give a brief overview of basic known complexity theorems for readers familiar with neural network models but less familiar with circuit complexity theories. We argue that there is considerable computational and physiological justification for the thesis that shallow circuits (Le., networks with relatively few layers) are computationally more efficient. We hence concentrate on structured (as opposed to random) problems that can be computed in shallow (constant depth) circuits with a relatively few number (polynomial) of elements, and demonstrate classes of structured problems that are amenable to such low cost solutions. We discuss an allied problem-the complexity of learning-and close with some open problems and a discussion of the observed limitations of the theoretical approach. We next turn to a rigourous classification of how much a network of given structure can do; i.e., the computational capacity of a given construct.

American Institute of Physics 1988 716 Asynthetic neural network simulation of cerebral neocortex was developed based on detailed anatomy and physiology. Processing elements possess temporal nonlinearities and connection patterns similar to those of cortical neurons. The network was able to replicate spatial and temporal integration properties found experimentally in neocortex. A certain level of randomness was found to be crucial for the robustness of at least some of the network's computational capabilities. Emphasis was placed on how synthetic simulations can be of use to the study of both artificial and biological neural networks.

Asa means of probing these cerebellar mechanisms, my colleagues and I have been conducting microelectrode studies of the neural messages that flow through the intermediate divisionof the cerebellum and onward to limb muscles via the rubrospinal tract. We regard this cerebellorubrospinal pathwayas a useful model system for studying general problems of sensorimotor integration and adaptive brain function.

Much experimental study of real neural networks relies on the proper classification of extracellulary sampled neural signals (i.e.

ABSTRACT A single cell theory for the development of selectivity and ocular dominance in visual cortex has been presented previously by Bienenstock, Cooper and Munrol. This has been extended to a network applicable to layer IV of visual cortex2 . In this paper we present a mean field approximation that captures in a fairly transparent manner the qualitative, and many of the quantitative, results of the network theory. Finally, we consider the application of this theory to artificial neural networks and show that a significant reduction in architectural complexity is possible. ASINGLE LAYER NETWORK AND THE MEAN FIELD APPROXIMATION We consider a receive signals from the layer (Figure 1).

Centric Models of the Orientation Map in Primary Visual Cortex William Baxter of Computer Science, S.U.N.Y. at Buffalo, NY 14620Department Bruce Dow Department of Physiology, S.U.N.Y. at Buffalo, NY 14620 Abstract the visual cortex of the monkey the horizontal organization of the preferredIn of orientation-selective cells follows two opposing rules: 1) neighbors tendorientations Several orientation models which satisfy these constraints are found in the spacing and the topological index of their singularities. Using the rateto differ of orientation change as a measure, the models are compared to published experimental results. Introduction It has been known for some years that there exist orientation-sensitive neurons in the visual cortex of cats and mOnkeysl,2. These cells react to highly specific patterns of light occurring in narrowly circumscribed regiOns of the visual field, i.e., the cell's receptive field. The best patterns for such cells are typically not diffuse levels of but elongated bars or edges oriented at specific angles.

Lyle J. Borg-Graham Harvard-MIT Division of Health Sciences and Technology and Center for Biological Information Processing, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ABSTRACT A computer model of the hippocampal pyramidal cell (HPC) is described which integrates data from a variety of sources in order to develop a consistent descriptionfor this cell type. The model presently includes descriptions of eleven nonlinear somatic currents of the HPC, and the electrotonic structure of the neuron is modelled with a soma/short-cable approximation. Model simulations qualitatively or quantitatively reproduce a wide range of somatic electrical behavior i HPCs, and demonstrate possible roles for the various currents in information processing. There are several substrates for neuronal computation, including connectivity, synapses,morphometries of dendritic trees, linear parameters of cell membrane, as well as nonlinear, time-varying membrane conductances, also referred to as currents or channels. In the classical description of neuronal function, the contribution of membrane channels is constrained to that of generating the action potential, setting firing threshold, and establishing the relationship between (steady-state) stimulus intensity and firing frequency.