A model for neural representation of temporal duration

To address how temporal duration is encoded in neural systems, we put forward a simple model for recurrent neural networks. Particular assumptions are only the following two: (1) neuronal bistability and; (2) environmental effects described by a heat bath. The results of Monte Carlo simulation show that population activity triggered at an initial time continues for a prolonged duration, followed by an abrupt self-termination. This time course seems highly suitable for neural representation of temporal duration. The time scale of this prolonged duration is much longer than the time scale of neuronal firing which is of the order of ms. The former time scale implies that of interval timing in cognition and behaviour. Thus, the model provides a possible explanation for a link between these two separated time scales. The Weber law, a hallmark of humans and animals' interval timing, can also be reproduced in our model.     

A model for the coordinated development of columnar systems in primate striate cortex

The existence of patchy regions in primate striate cortex in which orientation selectivity is reduced, and which lie in the centers of ocular dominance stripes is well established (Hubel and Livingstone 1981). Analysis of functional maps obtained with voltage sensitive dyes (Blasdel and Salama 1986) has suggested that regions where the spatial rate of change of orientation preference is high, tend to be aligned either along the centers of ocular dominance stripes, or to intersect stripe borders at right angles. In this paper I present results from a developmental model which show that a tendency for orientation selectivity to develop more slowly in the centers of ocular dominance stripes would lead to the observed relationships between the layout of ocular dominance and the map of orientation gradient. This occurs despite the fact that there is no direct connection between the measures of preferred orientation (from which the gradient map is derived) and orientation selectivity (which is independent of preferred orientation). I also show that in both the monkey and the model, orientation singularities have an irregular distribution, but tend to be concentrated in the centers of the ocular dominance stripes. The average density of singularities is about 3/ ², where is the period of the orientation columns. The results are based on an elaboration of previous models (Swindale 1980, 1982) which show how, given initially disordered starting conditions, lateral interactions that are short-range excitatory and long-range inhibitory can lead to the development of patterns of orientation or ocular dominance that resemble those found in monkey striate cortex. To explain the coordinated development of the two kinds of column, it is proposed that there is an additional tendency in development for the rate of increase in orientation selectivity to be reduced in the centers of emerging ocular dominance stripes. This might come about if a single factor modulates plasticity in each cell, or column of cells. Thus plasticity may be turned off first in regions in the centers of ocular dominance stripes where relatively extreme and therefore stable ocular dominance values are achieved early in development. Consequently it will be hard for cells in these columns to modify other properties such as orientation preference or selectivity.     

A model of neural network extracting binocular parallax

A model of neural network extracting binocular parallax is proposed. It is a multilayered network composed of analog threshold elements. Three types of binocular neurons are included in this model. They are binocular simple neurons, binocular gate neurons and binocular depth neurons. The final layers of this model consist of elements which correspond to the binocular depth neurons. The performance of the model has been simulated on a digital computer. The results of the computer simulation show that every element of this model acts like neurons found in cat's and monkey's visual system and this model extracts binocular parallax caused by simple line components satisfactorily.     

Evidence for surface-based processing of binocular disparity

It is convenient to think of an object's location as a point within a Cartesian framework; the x axis corresponds to right and left, the y axis to up and down, and the z axis to forward or backward. When an observer is looking straight ahead, binocular disparities provide information about distance along the z axis from the fixation plane. In this coordinate system, changes in disparity are treated as independent of changes in location along the orthogonal x and y axes. Does the human visual system use this three-dimensional coordinate system, or does it specify feature location in a coordinate frame determined by other nearby visible features? Here we show that the sensitivity of the human stereo system is determined by the distance of points with respect to a local reference plane, rather than by the distance along the z axis with respect to the fixation plane. There is a distinct advantage to using a local frame of reference for specifying location. It obviates the need to construct a complex three-dimensional space in either eye-centered or head-centered coordinates that must be updated with every shift of the eyes and head.     

A reaction-diffusion model to capture disparity selectivity in primary visual cortex

Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.     

A precise and adaptive neural mechanism for predictive temporal processing in the frontal cortex

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A neural network model for the mechanism of feature-extraction

We propose a new multilayered neural network model which has the ability of rapid self-organization. This model is a modified version of the cognitron (Fukushima, 1975). It has modifiable inhibitory feedback connections, as well as conventional modifiable excitatory feedforward connections, between the cells of adjoining layers. If a feature-extracting cell in the network is excited by a stimulus which is already familiar to the network, the cell immediately feeds back inhibitory signals to its presynaptic cells in the preceding layer, which suppresses their response. On the other hand, the feature-extracting cell does not respond to an unfamiliar feature, and the responses from its presynaptic cells are therefore not suppressed because they do not receive any feedback inhibition. Modifiable synapses in the new network are reinforced in a way similar to those in the cognitron, and synaptic connections from cells yielding a large sustained output are reinforced. Since familiar stimulus features do not elicit a sustained response from the cells of the network, only circuits which detect novel stimulus features develop. The network therefore quickly acquires favorable pattern-selectivity by the mere repetitive presentation of set of learning patterns.     

A neural network model for kindling of focal epilepsy: basic mechanism

A simple neural network model is proposed for kindling — the phenomenon of generating epilepsy by means of repeated electrical stimulation. The model satisfies Dale's hypothesis, incorporates a Hebb-like learning rule and has low periodic activity in absence of shocks. Many of the experimental observations are reproduced and some new experiments are suggested. It is proposed that the main reason for kindling is the formation of a large number of excitatory synaptic connections due to learning.     

Interpolation coding: A representation for numbers in neural models

A central task of perception can be defined as one of computing hierarchies of invariants. One way of representing such invariants in intermediate levels of abstraction in this hierarchy is to use discrete units. These have been termed value units. A problem with such an encoding is that there has not been a good way to represent accurate numerical quantities using these units. This paper remedies the deficiency by describing a scheme that interpolates values between units representing fixed numerical quantities. The scheme has nice properties: it extends across functional mappings and it allows different sources of evidence to be combined.This work was supported in part by the National Science Foundation under Grant DCR-8405720 and the National Institutes of Health under Public Health Service Grant 1R01NS22407-01     

Coverage and the design of striate cortex

Hubel and Wiesel (1977) suggested that ocular dominance and orientation columns in the macaque monkey striate cortex might be bands of uniform width that intersected orthogonally. They pointed out that if this were the case, there would be an equal allocation of cells of different orientation preference to each eye and to each point in visual space. However, orientation and ocular dominance columns have a more complex structural organization than is implied by this model: for example, iso-orientation domains do not intersect ocular dominance stripes at right angles and the two columnar systems have different periodicities. This raises the question as to how well the striate cortex manages to allocate equal numbers of neurons of different orientation preference to each eye and to each region of visual space, a factor referred to here as coverage. This paper defines a measure of uniformity of coverage, c, and investigates its dependence on several different parameters of columnar organisation. Calculations were done first using a simplified one-dimensional model of orientation and ocular dominance columns and were then repeated using more realistic two-dimensional models, generated with the algorithms described in the preceding paper (Swindale 1991). Factors investigated include the relative periodicities of the two columnar systems, the size of the cortical point image, the width of orientation tuning curves, whether columns are spatially anisotropic or not, and the role of the structural relationships between columns described by Blasdel and Salama (1986). The results demonstrate that coverage is most uniform when orientation hypercolumns are about half the size of ocular dominance hypercolumns. Coverage is most uneven when the hypercolumns are the same size, unless they are related in the way described by Blasdel and Salama, in which case coverage gets only slightly worse as the size ratio (ori/od) increases above 0.5. The minimum diameter of cortical point image that ensures reasonably uniform coverage is about twice the size of an ocular dominance hypercolumn i.e. about 1.5–2.0 mm.     

A hybrid model for the neural representation of complex mental processing in the human brain

In the present conceptual review several theoretical and empirical sources of information were integrated, and a hybrid model of the neural representation of complex mental processing in the human brain was proposed. Based on empirical evidence for strategy-related and inter-individually different task-related brain activation networks, and further based on empirical evidence for a remarkable overlap of fronto-parietal activation networks across different complex mental processes, it was concluded by the author that there might be innate and modular organized neuro-developmental starting regions, for example, in intra-parietal, and both medial and middle frontal brain regions, from which the neural organization of different kinds of complex mental processes emerge differently during individually shaped learning histories. Thus, the here proposed model provides a hybrid of both massive modular and holistic concepts of idiosyncratic brain physiological elaboration of complex mental processing. It is further concluded that 3-D information, obtained by respective methodological approaches, are not appropriate to identify the non-linear spatio-temporal dynamics of complex mental process-related brain activity in a sufficient way. How different participating network parts communicate with each other seems to be an indispensable aspect, which has to be considered in particular to improve our understanding of the neural organization of complex cognition.     

A binocular model for the simple cell

We authors propose a mathematical model for simple cell binocular response. It comprises two Gabor-type receptive fields (RF) having the same RF center, preferred spatial frequency, and preferred orientation. The model integrates the equally weighted signals from both eyes and performs a threshold operation. Poggio and Fischer (1977) classified binocular disparity cells in the striate cortex into four groups: tuned excitatory (TE), tuned inhibitory (TI), near, and far cells. They also found that most of the TE cells are ocularly balanced and that the other three types are usually unbalanced. This model can imitate these four types of disparity sensitivities and their ocular dominance tendency. We perform model fittings to Poggio's data using the “simulated annealing” method and discuss parameter dependence of the model's response. The model can also respond with exceptional disparity sensitivity: i.e., flat type, alternating type, and intermediate type.     

A neural network model for the development of direction selectivity in the visual cortex

A neural network model is proposed to explain the development of direction selectivity of cortical cells. The model is constructed under the following three hypotheses that are very plausible from recent neurophysiological findings. (1) Direction selectivity is developed by modifiable inhibitory synapses. (2) It results not from the direct convergence of many excitatory inputs from LGN cells but from cortical neural networks. (3) Direction-selective mechanism is independent of orientation-selective mechanism.—The model was simulated on a computer for a few kinds of inhibitory connections and initial conditions. The results were consistent with neurophysiological facts not only for normal cats but for cats reared in an abnormal visual environment.     

Parallel processing of binocular disparity in the cat's retinogeniculocortical pathways

In the cat, parallel streams of information processing have been traced from X-, Y- and W-type retinal ganglion cells to visual cortical areas 17 (X-, Y- and W-type), 18 (Y-type) and 19 (W-type). In the present study we have examined, in the anaesthetized and paralysed adult cat, the role played by X-, Y- and W-subsystems, projecting to areas 17 and 19, in the processing of binocular retinal disparity. The tapetal reflection technique was used to monitor residual eye movements and to provide a map, for each eye, of the retinal blood vessels which could later be compared with retinal wholemounts stained with cresyl violet to reveal the area centralis. The receptive-field disparities of cells recorded from areas 17 and 19 were compared with each other and with reference to the visual axes defined by the area centralis of each eye. Cells of area 19 (receiving W-type input) had horizontal receptive-field disparities that were significantly more divergent than those of the cells in area 17 and 17-18 'border region'. Referred to the area centralis, the mean horizontal receptive-field disparity in area 19 was -0.5 degrees (+/- 0.8 degrees). The mean horizontal receptive-field disparity of area 17 (receiving X-, Y- and W-type input) was convergent with respect to the visual axis at +2 degrees (+/- 0.5 degrees). Finally, the mean horizontal receptive-field disparity of the cells in the 17-18 border region (which receive mainly Y-type input) was even more convergent (2.6 degrees +/- 1.5 degrees) than that of area 17. Binocular interactions of cortical neurons were tested with the Risley biprism technique. Area 19 cells had maximal responses to binocular stimulation when the receptive-field disparities were either close to zero or slightly divergent. In contrast, area 17 cells tended to respond optimally to disparities that were either slightly or strongly convergent. At the level of the lateral geniculate nucleus there were significant differences between the receptive-field disparities inferred from the comparison of receptive-field positions of adjacent neurons recorded on either side of the border between the A and A1 geniculate laminae and those inferred from a similar comparison at the C1-C2 border. The mean horizontal disparities inferred from the interlaminar comparison at the A-A1 border were +2.1 degrees (+/- 0.3 degrees); those inferred from the interlaminar comparison at the C1-C2 border -0.2 (+/- 0.2 degrees) were more divergent.(ABSTRACT TRUNCATED AT 400 WORDS)     

A neural network model of semantic memory linking feature-based object representation and words

Recent theories in cognitive neuroscience suggest that semantic memory is a distributed process, which involves many cortical areas and is based on a multimodal representation of objects. The aim of this work is to extend a previous model of object representation to realize a semantic memory, in which sensory-motor representations of objects are linked with words. The model assumes that each object is described as a collection of features, coded in different cortical areas via a topological organization. Features in different objects are segmented via γ-band synchronization of neural oscillators. The feature areas are further connected with a lexical area, devoted to the representation of words. Synapses among the feature areas, and among the lexical area and the feature areas are trained via a time-dependent Hebbian rule, during a period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from acoustic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits).     

A neural model of predictive recognition in form pathway of visual cortex

We present a functional model of form pathway in visual cortex based on predictive coding scheme, in which the prediction is compared with feedforward signals filtered by two kinds of spatial resolution maps, broad and fine resolution map. We propose here the functional role of the prediction and of the two kinds of resolution maps in perception of object form in visual system. The prediction is represented based on memory of dynamical attractors in temporal cortex, categorized by an elemental figure in posterior temporal cortex. The prediction is generated by the feedforward signals of main neurons in broad resolution maps of V(1) and V(4), and then is compared with the feedforward signals of main neurons in fine resolution map of V(1) and V(4).     

Organization of space perception: neural representation of three-dimensional space in the posterior parietal cortex.

The representation of perceptual space in the posterior parietal cortex can be divided into at least two categories: far space, beyond arm's reach, and peripersonal space, within arm's reach. These are encoded by different groups of neurons that are closely related to the control of gaze and the guidance of arm and hand movement, respectively.     

Physiologically realistic modelling of a mechanism for neural representation of intervals of time

A model for a recurrent network of bistable spiking neurons is examined. Each neuron is described by a leaky-integrate-and-fire formulation with biophysically realistic currents and noise. Specially, neuronal bistability is equipped by after-depolarisation current. Results obtained by computer simulation show that spiking of each neuron starting at an initial time continues for an extended period and then suddenly ceases at around a certain time. We hypothesise that activation of neurons that starts at t = 0 and voluntarily ceases at t = T is a neural underpinning of internal representation of an interval of time T. The above results theoretically support this hypothesis by demonstrating one possible mechanism to generate such time course of neuronal activation.