92 research outputs found
Design principles of columnar organization in visual cortex
Visual space is represented by cortical cells in an orderly manner. Only little variation in the cell behavior is found with changing depth below the cortical surface, that is, all cells in a column with axis perpendicular to the cortical plane have approximately the same properties (Hubel and Wiesel 1962, 1963, 1968). Therefore, the multiple features of the visual space (e.g., position in visual space, preferred orientation, and orientation tuning strength) are mapped on a two-dimensional space, the cortical plane. Such a dimension reduction leads to complex maps (Durbin and Mitchison 1990) that so far have evaded an intuitive understanding. Analyzing optical imaging data (Blasdel 1992a, b; Blasdel and Salama 1986; Grinvald et al. 1986) using a theoretical approach we will show that the most salient features of these maps can be understood from a few basic design principles: local correlation, modularity, isotropy, and homogeneity. These principles can be defined in a mathematically exact sense in the Fourier domain by a rather simple annulus-like spectral structure. Many of the models that have been developed to explain the mapping of the preferred orientations (Cooper et al. 1979; Legendy 1978; Linsker 1986a, b; Miller 1992; Nass and Cooper 1975; Obermayer et al. 1990, 1992; Soodak 1987; Swindale 1982, 1985, 1992; von der Malsburg 1973; von der Malsburg and Cowan 1982) are quite successful in generating maps that are close to experimental maps. We suggest that this success is due to these principles, which are common properties of the models and of biological maps
Bose-Einstein Condensation in Competitive Processes
We introduce an irreversible discrete multiplicative process that undergoes
Bose-Einstein condensation as a generic model of competition. New players with
different abilities successively join the game and compete for limited
resources. A player's future gain is proportional to its ability and its
current gain. The theory provides three principles for this type of
competition: competitive exclusion, punctuated equilibria, and a critical
condition for the distribution of the players' abilities necessary for the
dominance and the evolution. We apply this theory to genetics, ecology and
economy.Comment: 4 pages, 3 figures, submitted to PR
Generation of Direction Selectivity by Isotropic Intracortical Connections
To what extent do the mechanisms generating different receptive field properties of neurons depend on each other? We investigated this question theoretically within the context of orientation and direction tuning of simple cells in the mammalian visual cortex. In our model a cortical cell of the "simple" type receives its orientation tuning by afferent convergence of aligned receptive fields of the lateral geniculate nucleus (Hubel and Wiesel 1962). We sharpen this orientation bias by postulating a special type of radially symmetric long-range lateral inhibition called circular inhibition. Surprisingly, this isotropic mechanism leads to the emergence of a strong bias for the direction of motion of a bar. We show that this directional anisotropy is neither caused by the probabilistic nature of the connections nor is it a consequence of the specific columnar structure chosen but that it is an inherent feature of the architecture of visual cortex
Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?
We demonstrate that the map of the preferred orientations and the corresponding map of the orientation tuning strengths as measured with optical imaging are not independent, but that band-pass filtering of the preferred orientation map at each location yields a good approximation of the orientation tuning strength. Band-pass filtering is performed by convolving the map of orientation preference with its own autocorrelation function. We suggest an interpretation of the autocorrelation function of the preferred orientations as synaptic coupling function, i.e., synaptic strength as a function of intracortical distance between cortical cells. In developmental models it has been shown previously that a âMexican hatâ-shaped synaptic coupling function (with a shape similar to that of the autocorrelation function) can produce a realistical-looking pattern of preferred orientations. Since optical imaging performs surface averaging, we discuss the possibility that the connection between the two maps is a measurement artifact of optical imaging. Whether this is the case can only be decided by combining electrode penetrations with optical imaging techniques for which we suggest experiments. We present a model for the generation of both maps from a single computational concept. The model is based on inverse Fourier transform of rather simple two-dimensional annulus-shaped spectra which will produce a column structure very similar to real data. Thus, our approach shows that the complex appearance of cortical orientation columns has a rather simple description in the Fourier domain. Our theoretical analysis explains why singularities in the cortex do not have vorticities other than ±1/2, a result which corresponds to recent experimental findings. This study combines the results from several modeling approaches with recently available optical imaging data to construct a model of both aspects (angle and strength) of the cortical orientation column system. This could alter ideas about cortical development if the link between the two maps can be established as a physiological result
Efficient Simulation of Biological Neural Networks on Massively Parallel Supercomputers with Hypercube Architecture
We present a neural network simulation which we implemented
on the massively parallel Connection Machine 2. In contrast to previous work, this simulator is based on biologically realistic neurons with nontrivial single-cell dynamics, high connectivity with a structure modelled in agreement with biological data, and preservation
of the temporal dynamics of spike interactions. We simulate
neural networks of 16,384 neurons coupled by about 1000 synapses per neuron, and estimate the performance for much larger systems. Communication between neurons is identified as the computationally most demanding task and we present a novel method to overcome this bottleneck. The simulator has already been used to study the primary visual system of the cat
Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics
We propose a hierarchically modular, dynamical neural network model whose
architecture minimizes a specifically designed energy function and defines its
temporal characteristics. The model has an internal and an external space that
are connected with a layered internetwork that consists of a pair of forward
and backward subnets composed of static neurons (with an instantaneous
time-course). Dynamical neurons with large time constants in the internal space
determine the overall time-course. The model offers a framework in which state
variables in the network relax in a warped space, due to the cooperation
between dynamic and static neurons. We assume that the system operates in
either a learning or an association mode, depending on the presence or absence
of feedback paths and input ports. In the learning mode, synaptic weights in
the internetwork are modified by strong inputs corresponding to repetitive
neuronal bursting, which represents sinusoidal or quasi-sinusoidal waves in the
short-term average density of nerve impulses or in the membrane potential. A
two-dimensional mapping relationship can be formed by employing signals with
different frequencies based on the same mechanism as Lissajous curves. In the
association mode, the speed of convergence to a goal point greatly varies with
the mapping relationship of the previously trained internetwork, and owing to
this property, the convergence trajectory in the two-dimensional model with the
non-linear mapping internetwork cannot go straight but instead must curve. We
further introduce a constrained association mode with a given target trajectory
and elucidate that in the internal space, an output trajectory is generated,
which is mapped from the external space according to the inverse of the mapping
relationship of the forward subnet.Comment: 44 pages, 22 EPS figure
Control of Selective Visual Attention: Modeling the "Where" Pathway
Intermediate and higher vision processes require selection of a subset of the available sensory information before further processing. Usually, this selection is implemented in the form of a spatially circumscribed region of the visual field, the so-called "focus of attention"
which scans the visual scene dependent on the input and
on the attentional state of the subject. We here present a model for the control of the focus of attention in primates, based on a saliency map. This mechanism is not only expected to model the functionality of biological vision but also to be essential for the understanding
of complex scenes in machine vision
Neurobiology, Psychophysics, and Computational Models of Visual Attention
The purpose of this workshop was to discuss both recent experimental findings and
computational models of the neurobiological implementation of selective attention.
Recent experimental results were presented in two of the four presentations given
(C.E. Connor, Washington University and B.C. Motter, SUNY and V.A. Medical
Center, Syracuse), while the other two talks were devoted to computational models
(E. Niebur, Caltech, and B. Olshausen, Washington University)
An oscillation-based model for the neuronal basis of attention
We propose a model for the neuronal implementation of selective visual attention based on the temporal structure of neuronal activity. In particular, we set out to explain the electrophysiological data from areas V4 and IT in monkey cortex of Moran and Desimone [(1985)Science, 229, 782â784] using the âtemporal taggingâ hypothesis of Crick and Koch, 1990a and Crick and Koch, 1990bSeminars in the neurosciences (pp. 1â36)]. Neurons in primary visual cortex respond to visual stimuli with a Poisson distributed spike train with an appropriate, stimulus-dependent mean firing rate. The firing rate of neurons whose receptive fields overlap with the âfocus of attentionâ is modulated with a periodic function in the 40 Hz range, such that their mean firing rate is identical to the mean firing rate of neurons in ânon-attendedâ areas. This modulation is detected by inhibitory interneurons in V4 and is used to suppress the response of V4 cells associated with non-attended visual stimuli. Using very simple single-cell models, we obtain quantitative agreement with Moran and Desimone's (1985) experiments
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