Faculty Bibliography

Using a large-scale model of the Macaque Primary Visual Cortex (V1), we offer an explanation for observed and systematic differences in orientation selectivity of Simple and Complex cells. Our network model represents the activity of 4 adjoining orientation hypercolumns in layer 4Calpha. This model reproduces experimentally observed distributions of spatial summation properties, from both extra-and intra-cellular measurements, with Simple cell behavior observed in neurons dominated by geniculate excitation and Complex cell behavior in neurons dominated by cortical excitation (Tao et al 2003). The two neuronal mechanisms behind these differences underlay two different mechanisms of orientation selectivity. In our model, convergent feedforward input from the lateral geniculate nucleus sets up the orientation preference of an individual Simple neuron. Recurrent cortical connections, isotropic and non-specific, then sharpens its selectivity. The most selective Simple cells are found near orientation pinwheel singularities where the cortical inhibition comes from neurons at different orientation preference and thus is "global" in orientation. In contrast, the most selective Complex cells are found in iso-orientation domains away from the pinwheel center, where the cortical excitation comes from neurons preferring similar orientations. This correlation of selectivity with distance to pinwheel centers can be attributed to differing length-scales of coupling within cortex

This paper reports on the consequences of large, activity dependent, synaptic conductances for neurons in a large-scale neuronal network model of the input layer 4Calpha of the Macaque primary visual cortex (Area V1). This high conductance state accounts for experimental observations about orientation selectivity, dynamics, and response magnitude (D. McLaughlin et al. (2000) Proc. Natl. Acad. Sci. USA 97: 8087-8092), and the linear dependence of Simple cells on visual stimuli (J. Wielaard et al. (2001) J. Neuroscience 21: 5203-5211). The source of large conductances in the model can be traced to inhibitory corticocortical synapses, and the model's predictions of large conductance changes are consistent with recent intracellular measurements (L. Borg-Graham et al. (1998) Nature 393: 369-373; J. Hirsch et al. (1998) J. Neuroscience 15: 9517-9528; J.S. Anderson et al. (2000) J. Neurophysiol. 84: 909-926). During visual stimulation, these conductances are large enough that their associated time-scales become the shortest in the model cortex, even below that of synaptic interactions. One consequence of this activity driven separation of time-scales is that a neuron responds very quickly to temporal changes in its synaptic drive, with its intracellular membrane potential tracking closely an effective reversal potential composed of the instantaneous synaptic inputs. From the effective potential and large synaptic conductance, the spiking activity of a cell can be expressed in an interesting and simplified manner, with the result suggesting how accurate and smoothly graded responses are achieved in the model network. Further, since neurons in this high-conductance state respond quickly, they are also good candidates as coincidence detectors and burst transmitters

We present a reduction of a large-scale network model of visual cortex developed by McLaughlin, Shapley, Shelley, and Wielaard. The reduction is from many integrate-and-fire neurons to a spatially coarse-grained system for firing rates of neuronal subpopulations. It accounts explicitly for spatially varying architecture, ordered cortical maps (such as orientation preference) that vary regularly across the cortical layer, and disordered cortical maps (such as spatial phase preference or stochastic input conductances) that may vary widely from cortical neuron to cortical neuron. The result of the reduction is a set of nonlinear spatiotemporal integral equations for 'phase-averaged' firing rates of neuronal subpopulations across the model cortex, derived asymptotically from the full model without the addition of any extra phenomological constants. This reduced system is used to study the response of the model to drifting grating stimuli-where it is shown to be useful for numerical investigations that reproduce, at far less computational cost, the salient features of the point-neuron network and for analytical investigations that unveil cortical mechanisms behind the responses observed in the simulations of the large-scale computational model. For example, the reduced equations clearly show (1) phase averaging as the source of the time-invariance of cortico-cortical conductances, (2) the mechanisms in the model for higher firing rates and better orientation selectivity of simple cells which are near pinwheel centers, (3) the effects of the length-scales of cortico-cortical coupling, and (4) the role of noise in improving the contrast invariance of orientation selectivity

Downstream development is a term encompassinga variety of effects relating to the propagation of storm systems at midlatitude. We investigate a mechanism behind downstream development and study how wave propagation is affected by varying several physical parameters. We then develop a multiple scales modulation theory based on processes in the leading edge of propagating fronts to examine the effect of nonlinearity and weak variation in the background flow. Detailed comparisons are made with numerical experiments for a simple model system

Simple cells in the striate cortex respond to visual stimuli in an approximately linear manner, although the LGN input to the striate cortex, and the cortical network itself, are highly nonlinear. Although simple cells are vital for visual perception, there has been no satisfactory explanation of how they are produced in the cortex. To examine this question, we have developed a large-scale neuronal network model of layer 4Calpha in V1 of the macaque cortex that is based on, and constrained by, realistic cortical anatomy and physiology. This paper has two aims: (1) to show that neurons in the model respond like simple cells. (2) To identify how the model generates this linearized response in a nonlinear network. Each neuron in the model receives nonlinear excitation from the lateral geniculate nucleus (LGN). The cells of the model receive strong (nonlinear) lateral inhibition from other neurons in the model cortex. Mathematical analysis of the dependence of membrane potential on synaptic conductances, and computer simulations, reveal that the nonlinearity of corticocortical inhibition cancels the nonlinear excitatory input from the LGN. This interaction produces linearized responses that agree with both extracellular and intracellular measurements. The model correctly accounts for experimental results about the time course of simple cell responses and also generates testable predictions about variation in linearity with position in the cortex, and the effect on the linearity of signal summation, caused by unbalancing the relative strengths of excitation and inhibition pharmacologically or with extrinsic current.

In this article, we study numerically a one-dimensional model of dispersive wave turbulence. The article begins with a description of the model which we introduced earlier, followed by a concise summary of our previous results about it. In those previous studies, in addition to the spectra of weak turbulence (WT) theory, we also observed another distinct spectrum (the "MMT spectrum"). Our new results, presented here, include: (i) A detailed description of coexistence of spectra at distinct spatial scales, and the transitions between them at different temporal scales; (ii) The existence of a stable MMT front in k-space which separates the WT cascades from the dissipation range, for various forms of strong damping including "selective dissipation"; (iii) The existence of turbulent cycles in the one-dimensional model with focusing nonlinearity, induced by the interaction of spatially localized coherent structures with the resonant quartets of dispersive wave radiation; (iv) The detailed composition of these turbulent cycles - including the self-similar formation of focusing events (distinct in the forced and freely decaying cases), and the transport by the WT direct and inverse cascades of excitations between spatial scales. This one-dimensional model admits a very precise and detailed realization of these turbulent cycles and their components. Our numerical experiments demonstrate that a complete theory of dispersive wave turbulence will require a full description of the turbulent field over all spatial scales (including those of the forcing and dissipation), and over extremely long times (as the nonlinear turnover time becomes very long in the weakly nonlinear limit). And, in the focusing case, a complete theory must also incorporate the interaction of localized coherent structures with resonant radiation. (C) 2001 Elsevier Science B.V. All rights reserved

To address finite-size effects in the use of the decay mutual information to characterize spatiotemporal chaotic dynamics, we modify the dispersion of the nonlinear Schrodinger equation to obtain a model system for which the number of unstable modes remains fired while the domain size increases. Our numerical study of the model system clearly establishes that spatiotemporal chaos arises in the presence of only two unstable modes. In this spatially extended system, the spatiotemporal chaos is characterized by chaotic dynamics in time and by an exponential decay in space of mutual information, with the decay rate becoming system-size independent in the large system-size limit. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved