The continuous Wagon wheel illusion and the 'when' pathway of the right parietal lobe: a repetitive transcranial magnetic stimulation study

A continuous periodic motion stimulus can sometimes be perceived moving in the wrong direction. These illusory reversals have been taken as evidence that part of the motion perception system samples its inputs as a series of discrete snapshots -although other explanations of the phenomenon have been proposed, that rely on the spurious activation of low-level motion detectors in early visual areas. We have hypothesized that the right inferior parietal lobe ('when' pathway) plays a critical role in timing perceptual events relative to one another, and thus we examined the role of the right parietal lobe in the generation of this "continuous Wagon Wheel Illusion" (c-WWI). Consistent with our hypothesis, we found that the illusion was effectively weakened following disruption of right, but not left, parietal regions by low frequency repetitive transcranial magnetic stimulation (1 Hz, 10 min). These results were independent of whether the motion stimulus was shown in the left or the right visual field. Thus, the c-WWI appears to depend on higher-order attentional mechanisms that are supported by the 'when' pathway of the right parietal lobe.     

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

 Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train. Received: 30 March 1993/Accepted in revised form: 16 April 1994     

Categorization of environmental sounds

Sounds in the natural environment are non-stationary, in that their spectral dynamics is time-dependent. We develop measures to analyze the spectral dynamics of environmental sound signals and find that they fall into two categories—simple sounds with slowly varying spectral dynamics and complex sounds with rapidly varying spectral dynamics. Based on our results and those from auditory processing we suggest rate of spectral dynamics as a possible scheme to categorize sound signals in the environment.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist ‘What’ and ‘Where’ pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives ‘where’, for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The computational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

Mathematical modeling and parameter estimation of axonal cargo transport

This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the γ-band (25–90 Hz) of the LFP power spectrum in macaque V1. The height and location of the γ-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model’s resonance frequency (ResF) was in the γ-band and varied up or down in frequency depending on cortical feedback. The model’s ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for γ-band peaks in the LFP power spectrum of the primary visual cortex.     

Sociability leads to instability

We present a general stochastic model showing that colonial breeding can lead to complex multi-colony population dynamics when combined with nothing more than (inevitably) imperfect decision-making by individuals. In particular, frequent “switching cascades”—mass movement of individuals between locations from one breeding season to the next—arise naturally from our model, bringing into question the need to invoke a separate, fitness-based explanation for this commonly observed real-world phenomenon. A key component of the model is the development, at the beginning of each breeding season, of a set of colonies, based on sequential choices by individuals about where to breed. Individuals favor the colony they bred in previously, but are also attracted to colonies that are rapidly establishing, and may switch locations. This provides a positive feedback that leads to switching cascades. We examine the effect on the dynamics of individuals’ access to (and ability to act on) information, as well as the overall size of the colony system and of individual colonies. We compare the model’s dynamics to the observed population dynamics of a set of heron and egret breeding colonies in New York Harbor.     

Nested reentrant and recurrent computation in early vision: a Bayesian neuromorphic model applied to hyperacuity

 Hyperacuity is demonstrated in a neuromorphic model of the early visual system. The model incorporates Bayesian principles which are embodied in the dynamics of reentrant and recurrent feedback processes. Each retinotopically mapped area in the model represents a transformation of data from the visual field. Sensory information propagates in a bottom-up direction from one area to the next, while information based on Bayesian priors propagates in a top-down direction through reentrant connections. The ‘bottom-up’ and ‘top-down’ information maintain a separate existence in distinct layers of the model, but they interact through local connections within each area. Transformations between one area and the next are defined by the reentrant synaptic connections between areas, while local prior probability maps are defined by local recurrent connections within layers. The representation of hyperacuity is accomplished using a model of functional multiplicity: the large ratio of neurons in striate cortex compared with the number of afferent fibers projecting from the lateral geniculate nucleus. High functional multiplicity, in conjunction with hierarchical reentrant processing, allows the model to represent a fine-grained restoration of the line structure of visual input. Received : 26 April 1995 / Accepted in revised form : 27 July 1996     

Target-Specific Expression of Presynaptic NMDA Receptors in Neocortical Microcircuits

Traditionally, NMDA receptors are located postsynaptically; yet, putatively presynaptic NMDA receptors (preNMDARs) have been reported. Although implicated in controlling synaptic plasticity, their function is not well understood and their expression patterns are debated. We demonstrate that, in layer 5 of developing mouse visual cortex, preNMDARs specifically control synaptic transmission at pyramidal cell inputs to other pyramidal cells and to Martinotti cells, while leaving those to basket cells unaffected. We also reveal a type of interneuron that mediates ascending inhibition. In agreement with synapse-specific expression, we find preNMDAR-mediated calcium signals in a subset of pyramidal cell terminals. A tuned network model predicts that preNMDARs specifically reroute information flow in local circuits during high-frequency firing, in particular by impacting frequency-dependent disynaptic inhibition mediated by Martinotti cells, a finding that we experimentally verify. We conclude that postsynaptic cell type determines presynaptic terminal molecular identity and that preNMDARs govern information processing in neocortical columns.     

Learning invariant object recognition in the visual system with continuous transformations

The cerebral cortex utilizes spatiotemporal continuity in the world to help build invariant representations. In vision, these might be representations of objects. The temporal continuity typical of objects has been used in an associative learning rule with a short-term memory trace to help build invariant object representations. In this paper, we show that spatial continuity can also provide a basis for helping a system to self-organize invariant representations. We introduce a new learning paradigm “continuous transformation learning” which operates by mapping spatially similar input patterns to the same postsynaptic neurons in a competitive learning system. As the inputs move through the space of possible continuous transforms (e.g. translation, rotation, etc.), the active synapses are modified onto the set of postsynaptic neurons. Because other transforms of the same stimulus overlap with previously learned exemplars, a common set of postsynaptic neurons is activated by the new transforms, and learning of the new active inputs onto the same postsynaptic neurons is facilitated. We demonstrate that a hierarchical model of cortical processing in the ventral visual system can be trained with continuous transform learning, and highlight differences in the learning of invariant representations to those achieved by trace learning.     

Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal''s position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat''s velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.     

Motor-maps, navigation and implicit space representation in the hippocampus

Multiple sensory-motor maps located in the brainstem and the cortex are involved in spatial orientation. Guiding movements of eyes, head, neck and arms they provide an approximately linear relation between target distance and motor response. This involves especially the superior colliculus in the brainstem and the parietal cortex. There, the natural frame of reference follows from the retinal representation of the environment. A model of navigation is presented that is based on the modulation of activity in those sensory-motor maps. The actual mechanism chosen was gain-field modulation, a process of multimodal integration that has been demonstrated in the parietal cortex and superior colliculus, and was implemented as attraction to visual cues (colour). Dependent on the metric of the sensory-motor map, the relative attraction to these cues implemented as gain field modulation and their position define a fixed point attractor on the plane for locomotive behaviour. The actual implementation used Kohonen-networks in a variant of reinforcement learning that are well suited to generate such topographically organized sensory-motor maps with roughly linear visuo-motor response characteristics. In the following, it was investigated how such an implicit coding of target positions by gain-field parameters might be represented in the hippocampus formation and under what conditions a direction-invariant space representation can arise from such retinotopic representations of multiple cues. Information about the orientation in the plane—as could be provided by head direction cells—appeared to be necessary for unambiguous space representation in our model in agreement with physiological experiments. With this information, Gauss-shaped “place-cells” could be generated, however, the representation of the spatial environment was repetitive and clustered and single cells were always tuned to the gain-field parameters as well     

A model of the cerebellum in adaptive control of saccadic gain

 We review data showing that the cerebellum is required for adaptation of saccadic gain to repeated presentations of dual-step visual targets and thus, presumably, for providing adaptive corrections for the brainstem saccade generator in response to any error created by the open-loop saccadic system. We model the adaptability of the system in terms of plasticity of synapses from parallel fibers to Purkinje cells in cerebellar cortex, stressing the integration of cerebellar cortex and nuclei in microzones as the units for correction of motor pattern generators. We propose a model of the inferior olive as an error detector, and use a ‘window of eligibility’ to insure that error signals that elicit a corrective movement are used to adjust the original movement, not the secondary movement. In a companion paper we simulate this large, realistic network of neural-like units to study the complex spatiotemporal behavior of neuronal subpopulations implicated in the control and adaptation of saccades. Received: 25 November 1994/Accepted in revised form: 6 February 1996     

Encoding of Naturalistic Stimuli by Local Field Potential Spectra in Networks of Excitatory and Inhibitory Neurons

Recordings of local field potentials (LFPs) reveal that the sensory cortex displays rhythmic activity and fluctuations over a wide range of frequencies and amplitudes. Yet, the role of this kind of activity in encoding sensory information remains largely unknown. To understand the rules of translation between the structure of sensory stimuli and the fluctuations of cortical responses, we simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population, and we determined how the LFPs generated by the network encode information about input stimuli. We first considered simple static and periodic stimuli and then naturalistic input stimuli based on electrophysiological recordings from the thalamus of anesthetized monkeys watching natural movie scenes. We found that the simulated network produced stimulus-related LFP changes that were in striking agreement with the LFPs obtained from the primary visual cortex. Moreover, our results demonstrate that the network encoded static input spike rates into gamma-range oscillations generated by inhibitory–excitatory neural interactions and encoded slow dynamic features of the input into slow LFP fluctuations mediated by stimulus–neural interactions. The model cortical network processed dynamic stimuli with naturalistic temporal structure by using low and high response frequencies as independent communication channels, again in agreement with recent reports from visual cortex responses to naturalistic movies. One potential function of this frequency decomposition into independent information channels operated by the cortical network may be that of enhancing the capacity of the cortical column to encode our complex sensory environment.     

Trade-Offs Between Efficiency and Robustness in Bacterial Metabolic Networks Are Associated with Niche Breadth

The relation between structure and function in biologic networks is a central point of systems biology research. Key functional features—notably, efficiency and robustness—are linked to the topologic structure of a network, and there appears to be a degree of trade-off between these features, i.e., simulation studies indicate that more efficient networks tend to be less robust. Here, we investigate this issue in metabolic networks from 105 lineages of bacteria having a wide range of ecologies. We take quantitative measurements on each network and integrate this network data with ecologic data using a phylogenetic comparative model. In this setting, we find that biologic conclusions obtained with classical phylogenetic comparative methods are sensitive to correlations between model covariates and phylogenetic branch length. To avoid this problem, we propose a revised statistical framework—hierarchical mixed-effect regression—to accommodate phylogenetic nonindependence. Using this approach, we show that the cartography of metabolic networks does indeed reflect a trade-off between efficiency and robustness. Furthermore, ecologic characteristics related to niche breadth are strong predictors of network shape. Given the broad variation in niche breadth seen among species, we predict that there is no universally optimal balance between efficiency and robustness in bacterial metabolic networks and, thus, no universally optimal network structure. These results highlight the biologic relevance of variation in network structure and the potential role of niche breadth in shaping metabolic strategies of efficiency and robustness. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. Ransom A. Myers Died March 27th, 2007. He will be missed.     

Transient Responses to Spatial Perturbations in Advective Systems

We study the transient dynamics, following a spatially-extended perturbation of models describing populations residing in advective media such as streams and rivers. Our analyses emphasize metrics that are independent of initial perturbations—resilience, reactivity, and the amplification envelope—and relate them to component spatial wavelengths of the perturbation using spatial Fourier transforms of the state variables. This approach offers a powerful way of understanding the influence of spatial scale on the initial dynamics of a population following a spatially variable environmental perturbation, an important property in determining the ecological implications of transient dynamics in advective systems. We find that asymptotically stable systems may exhibit transient amplification of perturbations (i.e., have positive reactivity) for some spatial wavelengths and not others. Furthermore, the degree and duration of amplification varies strongly with spatial wavelength. For two single-population models, there is a relationship between transient dynamics and the response length that characterizes the steady state response to spatial perturbations: a long response length implies that peak amplification of perturbations is small and occurs fast. This relationship holds less generally in a specialist consumer-resource model, likely due to the model’s tendency for flow-induced instabilities at an alternative characteristic spatial scale.     

Neural network model of the primary visual cortex: From functional architecture to lateral connectivity and back

The role of intrinsic cortical dynamics is a debatable issue. A recent optical imaging study (Kenet et al., 2003) found that activity patterns similar to orientation maps (OMs), emerge in the primary visual cortex (V1) even in the absence of sensory input, suggesting an intrinsic mechanism of OM activation. To better understand these results and shed light on the intrinsic V1 processing, we suggest a neural network model in which OMs are encoded by the intrinsic lateral connections. The proposed connectivity pattern depends on the preferred orientation and, unlike previous models, on the degree of orientation selectivity of the interconnected neurons. We prove that the network has a ring attractor composed of an approximated version of the OMs. Consequently, OMs emerge spontaneously when the network is presented with an unstructured noisy input. Simulations show that the model can be applied to experimental data and generate realistic OMs. We study a variation of the model with spatially restricted connections, and show that it gives rise to states composed of several OMs. We hypothesize that these states can represent local properties of the visual scene. Action Editor: Jonathan D. Victor     

Responses of blowfly motion-sensitive neurons to reconstructed optic flow along outdoor flight paths

The retinal image flow a blowfly experiences in its daily life on the wing is determined by both the structure of the environment and the animal’s own movements. To understand the design of visual processing mechanisms, there is thus a need to analyse the performance of neurons under natural operating conditions. To this end, we recorded flight paths of flies outdoors and reconstructed what they had seen, by moving a panoramic camera along exactly the same paths. The reconstructed image sequences were later replayed on a fast, panoramic flight simulator to identified, motion sensitive neurons of the so-called horizontal system (HS) in the lobula plate of the blowfly, which are assumed to extract self-motion parameters from optic flow. We show that under real life conditions HS-cells not only encode information about self-rotation, but are also sensitive to translational optic flow and, thus, indirectly signal information about the depth structure of the environment. These properties do not require an elaboration of the known model of these neurons, because the natural optic flow sequences generate—at least qualitatively—the same depth-related response properties when used as input to a computational HS-cell model and to real neurons.     

Neural network model of visual cortex for determining surface curvature from images of shaded surfaces

The visual system can extract information about shape from the pattern of light and dark surface shading on an object. Very little is known about how this is accomplished. We have used a learning algorithm to construct a neural network model that computes the principal curvatures and orientation of elliptic paraboloids independently of the illumination direction. Our chief finding is that receptive fields developed by units of such model network are surprisingly similar to some found in the visual cortex. It appears that neurons that can make use of the continuous gradations of shading have receptive fields similar to those previously interpreted as dealing with contours (i.e. 'bar' detectors or 'edge' detectors). This study illustrates the difficulty of deducing neuronal function within a network solely from receptive fields. It is also important to consider the pattern of connections a neuron makes with subsequent stages, which we call the 'projective field'.     

Using extracellular action potential recordings to constrain compartmental models

We investigate the use of extracellular action potential (EAP) recordings for biophysically faithful compartmental models. We ask whether constraining a model to fit the EAP is superior to matching the intracellular action potential (IAP). In agreement with previous studies, we find that the IAP method under-constrains the parameters. As a result, significantly different sets of parameters can have virtually identical IAP’s. In contrast, the EAP method results in a much tighter constraint. We find that the distinguishing characteristics of the waveform—but not its amplitude- resulting from the distribution of active conductances are fairly invariant to changes of electrode position and detailed cellular morphology. Based on these results, we conclude that EAP recordings are an excellent source of data for the purpose of constraining compartmental models. Action Editor: Alain Destexhe