A neural model of figure-ground organization

Psychophysical studies suggest that figure-ground organization is a largely autonomous process that guides--and thus precedes--allocation of attention and object recognition. The discovery of border-ownership representation in single neurons of early visual cortex has confirmed this view. Recent theoretical studies have demonstrated that border-ownership assignment can be modeled as a process of self-organization by lateral interactions within V2 cortex. However, the mechanism proposed relies on propagation of signals through horizontal fibers, which would result in increasing delays of the border-ownership signal with increasing size of the visual stimulus, in contradiction with experimental findings. It also remains unclear how the resulting border-ownership representation would interact with attention mechanisms to guide further processing. Here we present a model of border-ownership coding based on dedicated neural circuits for contour grouping that produce border-ownership assignment and also provide handles for mechanisms of selective attention. The results are consistent with neurophysiological and psychophysical findings. The model makes predictions about the hypothetical grouping circuits and the role of feedback between cortical areas.

A novel method for visualizing functional connectivity using principal component analysis

Functional connectivity is a useful measure of voxel-wise functional magnetic resonance imaging signals that allows for the identification of functionally related brain areas and distributed networks. However, the high dimensionality of functional connectivity makes it difficult to visualize. In most studies, a small percentage of the total functional connectivity is visualized through diagrams that are constructed using individual seed voxels. In the present study describes a new method for visualizing most of the functional connectivity through a single diagram. This method does not rely on seed voxels, but rather employs a reduction of the high-dimensionality of the functional connectivity via a projection onto a three-dimensional color space using principal components analysis. With this new method, most of the information contained in a functional connectivity matrix can be represented through a single color-coded functional connectivity map, thereby facilitating a greater visual appreciation of functional connectivity.

Rate and synchrony in feedforward networks of coincidence detectors: analytical solution

We provide an analytical recurrent solution for the firing rates and cross-correlations of feedforward networks with arbitrary connectivity, excitatory or inhibitory, in response to steady-state spiking input to all neurons in the first network layer. Connections can go between any two layers as long as no loops are produced. Mean firing rates and pairwise cross-correlations of all input neurons can be chosen individually. We apply this method to study the propagation of rate and synchrony information through sample networks to address the current debate regarding the efficacy of rate codes versus temporal codes. Our results from applying the network solution to several examples support the following conclusions: (1) differential propagation efficacy of rate and synchrony to higher layers of a feedforward network is dependent on both network and input parameters, and (2) previous modeling and simulation studies exclusively supporting either rate or temporal coding must be reconsidered within the limited range of network and input parameters used. Our exact, analytical solution for feedforward networks of coincidence detectors should prove useful for further elucidating the efficacy and differential roles of rate and temporal codes in terms of different network and input parameter ranges.

Phase transitions in multiplicative competitive processes

We introduce a discrete multiplicative process as a generic model of competition. Players with different abilities successively join the game and compete for finite resources. Emergence of dominant players and evolutionary development occur as a phase transition. The competitive dynamics underlying this transition is understood from a formal analogy to statistical mechanics. The theory is applicable to bacterial competition, predicting novel population dynamics near criticality.

Correlated inhibitory and excitatory inputs to the coincidence detector: analytical solution

We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of excitatory and inhibitory inputspike trains. All excitatory spike trains have identical binomial count distributions (which includes Poisson statistics as a special case) and arbitrary pairwise cross correlations between them. The same applies to the inhibitory inputs, and the rates and correlation functions of excitatory and inhibitory populations may be the same or different from each other. Thus, for each population independently, the correlation may range from complete independence to perfect correlation (identical processes). We find that inhibition, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rates for the case of identical inhibitory and excitory input rates. This leads to the prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate, and shows some qualitative similarities to the case of purely excitatory inputs with synaptic depression. In general, we find that including inhibition invariably and significantly increases the behavioral repertoire of the coincidence detector over the case of pure excitatory input.

Texture contrast attracts overt visual attention in natural scenes

In natural vision, the central nervous system actively selects information for detailed processing through mechanisms of visual attention. It is widely held that simple stimulus features such as color, orientation and intensity contribute to the determination of visual salience and thus can act to guide the selection process in a bottom-up fashion. Contrary to this view, Einhäuser, W. & König, P. [(2003) Eur. J. Neurosci., 17, 1089-1097] conclude from their study of human eye movements that luminance contrast does not contribute to the calculation of stimulus salience and that top-down, rather than bottom-up, factors therefore determine attentional allocation in natural scenes. In this article, we dispute their conclusion and argue that the Einhäuser and König study has a number of methodological problems, the most prominent of which is the unintentional introduction of changes in texture contrast. We hypothesize that texture contrast, like luminance contrast, can contribute to the guidance of attention in a bottom-up fashion, and that an appeal to top-down factors is not necessary. To test this hypothesis, we implement a purely bottom-up model of visual selective attention where salience is derived from both luminance and texture contrast. We find that the model can quantitatively account for Einhäuser and König's results and that texture contrast strongly influences attentional guidance in this particular paradigm. The significance of this result for attentional guidance in other paradigms is discussed.

Synaptic depression leads to nonmonotonic frequency dependence in the coincidence detector

In this letter, we extend our previous analytical results (Mikula & Niebur, 2003) for the coincidence detector by taking into account probabilistic frequency-dependent synaptic depression. We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of input spike trains with identical binomial count distributions (which includes Poisson statistics as a special case) and identical arbitrary pairwise cross-correlations, from zero correlation (independent processes) to perfect correlation (identical processes). Synapses vary their efficacy probabilistically according to the observed depression mechanisms. Our results show that synaptic depression, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rate. This leads to the counterintuitive prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate.

Scene content selected by active vision

The primate visual system actively selects visual information from the environment for detailed processing through mechanisms of visual attention and saccadic eye movements. This study examines the statistical properties of the scene content selected by active vision. Eye movements were recorded while participants free-viewed digitized images of natural and artificial scenes. Fixation locations were determined for each image and image patches were extracted around the observed fixation locations. Measures of local contrast, local spatial correlation and spatial frequency content were calculated on the extracted image patches. Replicating previous results, local contrast was found to be greater at the points of fixation when compared to either the contrast for image patches extracted at random locations or at the observed fixation locations using an image-shuffled database. Contrary to some results and in agreement with other results in the literature, a significant decorrelation of image intensity is observed between the locations of fixation and other neighboring locations. A discussion and analysis of methodological techniques is given that provides an explanation for the discrepancy in results. The results of our analyses indicate that both the local contrast and correlation at the points of fixation are a function of image type and, furthermore, that the magnitude of these effects depend on the levels of contrast and correlation present overall in the images. Finally, the largest effect sizes in local contrast and correlation are found at distances of approximately 1 deg of visual angle, which agrees well with measures of optimal spatial scale selectivity in the visual periphery where visual information for potential saccade targets is processed.

The effects of input rate and synchrony on a coincidence detector: analytical solution

We derive analytically the solution for the output rate of the ideal coincidence detector. The solution is for an arbitrary number of input spike trains with identical binomial count distributions (which includes Poisson statistics as a special case) and identical arbitrary pairwise cross-correlations, from zero correlation (independent processes) to complete correlation (identical processes).

Electrophysiological correlates of synchronous neural activity and attention: a short review

Attentional selection implies preferential treatment of some sensory stimuli over others. This requires differential representation of attended and unattended stimuli. Most previous research has focused on pure rate codes for this representation but recent evidence indicates that a mixed code, involving both mean firing rate and temporal codes, may be employed. Of particular interest is a distinction of attended from unattended stimuli based on synchrony within neural populations. I review electrophysiological evidence at macroscopic, mesoscopic and microscopic spatial scales showing that the degree of synchronous activity varies with the attentional state of the perceiving organism.

Synchrony: a neuronal mechanism for attentional selection?

Attentional selection involves brain processes that select and control the flow of information into the mechanisms that underlie perception and consciousness. One theory proposes that the neural activity that represents the stimuli or events to be attended to is selected through modification of its synchrony. Recent experimental evidence supports this theory, by showing that changes in attentional focus increase the synchrony of neural firing in some neuron pairs and decrease it in others.

Modeling the role of salience in the allocation of overt visual attention

A biologically motivated computational model of bottom-up visual selective attention was used to examine the degree to which stimulus salience guides the allocation of attention. Human eye movements were recorded while participants viewed a series of digitized images of complex natural and artificial scenes. Stimulus dependence of attention, as measured by the correlation between computed stimulus salience and fixation locations, was found to be significantly greater than that expected by chance alone and furthermore was greatest for eye movements that immediately follow stimulus onset. The ability to guide attention of three modeled stimulus features (color, intensity and orientation) was examined and found to vary with image type. Additionally, the effect of the drop in visual sensitivity as a function of eccentricity on stimulus salience was examined, modeled, and shown to be an important determiner of attentional allocation. Overall, the results indicate that stimulus-driven, bottom-up mechanisms contribute significantly to attentional guidance under natural viewing conditions.

Variable-resolution displays: a theoretical, practical, and behavioral evaluation

Variable-resolution display techniques present visual information in a display using more than one resolution. For example, gaze-contingent variable-resolution displays allocate computational resources for image generation preferentially to the area around the center of gaze, where visual sensitivity to detail is the greatest. Using such displays reduces the amount of computational resources required as compared with traditional uniform-resolution displays. The theoretical benefits, implementational issues, and behavioral consequences of variable-resolution displays are reviewed. A mathematical analysis of computational efficiency for a two-region variable-resolution display is conducted. The results are discussed in relation to applications that are limited by computational resources, such as virtual reality, and applications that are limited by bandwidth, such as internet image transmission. The potential for variable-resolution display techniques as a viable future technology is discussed.

Rate limitations of unitary event analysis

Unitary event analysis is a new method for detecting episodes of synchronized neural activity (Riehle, Grün, Diesmann, & Aertsen, 1997). It detects time intervals that contain coincident firing at higher rates than would be expected if the neurons fired as independent inhomogeneous Poisson processes; all coincidences in such intervals are called unitary events (UEs). Changes in the frequency of UEs that are correlated with behavioral states may indicate synchronization of neural firing that mediates or represents the behavioral state. We show that UE analysis is subject to severe limitations due to the underlying discrete statistics of the number of coincident events. These limitations are particularly stringent for low (0-10 spikes/s) firing rates. Under these conditions, the frequency of UEs is a random variable with a large variation relative to its mean. The relative variation decreases with increasing firing rate, and we compute the lowest firing rate, at which the 95% confidence interval around the mean frequency of UEs excludes zero. This random variation in UE frequency makes interpretation of changes in UEs problematic for neurons with low firing rates. As a typical example, when analyzing 150 trials of an experiment using an averaging window 100 ms wide and a 5 ms coincidence window, firing rates should be greater than 7 spikes per second.

Attention modulates synchronized neuronal firing in primate somatosensory cortex

A potentially powerful information processing strategy in the brain is to take advantage of the temporal structure of neuronal spike trains. An increase in synchrony within the neural representation of an object or location increases the efficacy of that neural representation at the next synaptic stage in the brain; thus, increasing synchrony is a candidate for the neural correlate of attentional selection. We investigated the synchronous firing of pairs of neurons in the secondary somatosensory cortex (SII) of three monkeys trained to switch attention between a visual task and a tactile discrimination task. We found that most neuron pairs in SII cortex fired synchronously and, furthermore, that the degree of synchrony was affected by the monkey's attentional state. In the monkey performing the most difficult task, 35% of neuron pairs that fired synchronously changed their degree of synchrony when the monkey switched attention between the tactile and visual tasks. Synchrony increased in 80% and decreased in 20% of neuron pairs affected by attention.

Modeling the Temporal Dynamics of IT Neurons in Visual Search: A Mechanism for Top-Down Selective Attention

We propose a neural model for object-oriented attention in which various visual stimuli (shapes, colors, letters, etc.) are represented by competing, mutually inhibitory, cell assemblies. The model's response to a sequence of cue and target stimuli mimics the neural responses in infero temporal (IT) visual cortex of monkeys performing a visual search task: enhanced response during the display of the stimulus, which decays but remains above a spontaneous rate after the cue disappears. When, subsequently, a display consisting of the target and several distractors is presented, the activity of all stimulus-driven cells is initially enhanced. After a short period of time, however, the activity of the cell assembly representing the cue stimulus is enhanced while the activity of the distractors decays because of mutual competition and a small top-down “expectational” input. The model fits the measured delayed activity in IT-cortex, recently reported by Chelazzi, Miller, Duncan, and Desimone (1993a), and we suggest that such a process, which is largely independent of the number of distractors, may be used by the visual system for selecting an expected target (appearing at an uncertain location) among distractors.

Lateral interactions in primary visual cortex: a model bridging physiology and psychophysics

Recent physiological studies show that the spatial context of visual stimuli enhances the response of cells in primary visual cortex to weak stimuli and suppresses the response to strong stimuli. A model of orientation-tuned neurons was constructed to explore the role of lateral cortical connections in this dual effect. The differential effect of excitatory and inhibitory current and noise conveyed by the lateral connections explains the physiological results as well as the psychophysics of pop-out and contour completion. Exploiting the model's property of stochastic resonance, the visual context changes the model's intrinsic input variability to enhance the detection of weak signals.

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.

A model for the neuronal implementation of selective visual attention based on temporal correlation among neurons

We propose a model for the neuronal implementation of selective visual attention based on temporal correlation among groups of neurons. Neurons in primary visual cortex respond to visual stimuli with a Poisson distributed spike train with an appropriate, stimulus-dependent mean firing rate. The spike trains of neurons whose receptive fields do not overlap with the "focus of attention" are distributed according to homogeneous (time-independent) Poisson process with no correlation between action potentials of different neurons. In contrast, spike trains of neurons with receptive fields within the focus of attention are distributed according to non-homogeneous (time-dependent) Poisson processes. Since the short-term average spike rates of all neurons with receptive fields in the focus of attention covary, correlations between these spike trains are introduced which are detected by inhibitory interneurons in V4. These cells, modeled as modified integrate-and-fire neurons, function as coincidence detectors and suppress the response of V4 cells associated with non-attended visual stimuli. The model reproduces quantitatively experimental data obtained in cortical area V4 of monkey by Moran and Desimone (1985).

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, 782-784] using the "temporal tagging" hypothesis of Crick and Koch [(1990a) Cold Spring Harbor Symposiums in Quantitative Biology, LV, 953-962; (1990b) Seminars in the neurosciences (pp. 1-36)]. 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 "focus of attention" 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 "non-attended" 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.

Theory of the locomotion of nematodes: control of the somatic motor neurons by interneurons

The only animal of which the complete neural circuitry is known at the submicroscopical level is the nematode Caenorhabditis elegans. This anatomical knowledge is complemented by functional insight from electrophysiological experiments in the related nematode Ascaris lumbricoides, which show that Ascaris motor neurons transmit signals electrotonically and not with unattenuated spikes. We developed a mathematical model for electrotonic neural networks and applied it to the motor nervous system of nematodes. This enabled us to reproduce experimental results in Ascaris quantitatively. In particular, our computed result of the velocity v approximately equal to 6 cm/s of neural excitations in the Ascaris interneurons supports the simple hypothesis that the so-called rapidly moving muscular wave is produced by a neural excitation traveling at the same speed in the interneuron as the muscular wave. In C. elegans, the computed velocity v approximately equal to 8-30 cm/s of signals in the interneurons is much larger than the observed velocity v approximately equal to 0.2 cm/s of the body wave. Therefore, the hypothesis that the muscular wave is produced by a synchronous neural excitation wave cannot hold for C. elegans. We argue that stretch receptor control is the most likely mechanism for the generation of body waves used in the locomotion of C. elegans. Extending the simulation to larger groups of neurons, we found that the neural system of C. elegans can operate purely electrotonically. We demonstrate that the same conclusion cannot be drawn for the nervous system of Ascaris, because in the long (l approximately equal to 30 cm) interneurons the electrotonic signals would be too strongly attenuated. This conclusion is not in contradiction with the experimental findings of electrotonic signal propagation in the motor neurons of Ascaris because the latter are shorter (l approximately equal to 5 cm) than the interneurons.

Dynamics of Populations of Integrate-and-Fire Neurons, Partial Synchronization and Memory

We study the dynamics of completely connected populations of refractory integrate-and-fire neurons in the presence of noise. Solving the master equation based on a mean-field approach, and by computer simulations, we find sustained states of activity that correspond to fixed points and show that for the same value of external input, the system has one or two attractors. The dynamic behavior of the population under the influence of external input and noise manifests hysteresis effects that might have a functional role for memory. The temporal dynamics at higher temporal resolution, finer than the transmission delay times and the refractory period, are characterized by synchronized activity of subpopulations. The global activity of the population shows aperiodic oscillations analogous to experimentally found field potentials.

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.

Numerical implementation of sealed-end boundary conditions in cable theory

We show that a frequently used numerical implementation of von Neumann boundary conditions (zero inflowing current) in cable theory is incorrect. Correct implementations are given and it is shown that they yield results in good agreement with known analytical solutions.

Isotropic connections generate functional asymmetrical behavior in visual cortical cells

1. We study the relationship between structure and function in inhibitory long-range interactions in visual cortex. The sharpening of orientation tuning with "cross-orientation inhibition" is used as an example to discuss anisotropies that are generated by long-range connections. 2. In this study, as opposed to the detailed cortex model described in a previous report, a model of the cortical orientation column structure is proposed in which cortical cells are described only by their orientation preference. 3. We present results using different geometric arrangements of orientation columns. In the simplest case, straight parallel orientation columns were used. We also utilized more realistic, curved columns generated by a simple algorithm. The results were confirmed by the study of a patch of real column structure, determined experimentally by Swindale et al. 4. A given cell receives functionally defined cross-orientation inhibition if the cell receives inhibitory input that is strongest along its nonpreferred orientation. On the other hand, a cell is said to receive structurally defined cross-orientation inhibition if the inhibition arises from source cells with an orientation preference orthogonal to that of the target cell. Even though those definitions seem to describe similar situations, we show that, in the general case, structurally defined cross-orientation inhibition does not efficiently sharpen orientation selectivity. In particular, for straight and parallel columns, structurally defined cross-orientation inhibition results in unequal amounts of inhibition for whole cell populations with different preferred orientations. 5. In more realistic column structures, we studied the question of whether structural cross-orientation inhibition could be implemented in a more efficient way. However, for the majority of cells, it is demonstrated that their nonpreferred stimulus will not preferably excite "cross-oriented" cells. Thus structural cross-orientation inhibition is not efficient in real cortical columns. 6. We propose a new mechanism called circular inhibition. In this connection scheme, a target cell receives inhibitory input from source cells that are located at a given distance (the same for all cells) from the target cell. Circular inhibition can be regarded as two-dimensional long-range lateral inhibition. As opposed to structural cross-orientation inhibition, this mechanism does not introduce unwanted anisotropies in the orientation tuning of the target cells. It is also conceptually much simpler and developmentally advantageous. It is shown that this connection scheme results in a net functional cross-orientation inhibition in all realistic column geometries. The inhibitory tuning strength obtained with circular inhibition is weak and similar to that measured in reality.(ABSTRACT TRUNCATED AT 400 WORDS)