Pattern separability in a random neural net with inhibitory connections

Some interesting properties on pattern separation have been shown through researches by neural models of cerebellar cortex. It seems to us that those results are a part of the properties of pattern separation. A two layer random nerve net with inhibitory connections is given as a model of the cerebellar cortex. The model is composed of threshold elements there. A more general theory of pattern separation than those studied earlier is given, and the pattern separability of the model is considered. It is revealed that the standard deviation of threshold values of threshold elements has a great effect on the pattern separability and the control of the firing rate. The present study is also intended to investigate the pattern separability in such a case that the firing rate of input patterns are not equal, and a pattern includes the other pattern. It is assumed there that the standard deviation is small. Some properties of the degree of pattern separation are cleaned up.     

Further consideration on pattern separability in a random neural net with inhibitory connections

A two-layer random neural net with inhibitory connections composing of threshold elements has been regarded as a model of the cerebellar cortex. Many properties of pattern separation with the model have been disclosed through consideration on the degree of pattern separation. However, we have not shown yet that the degree of pattern separation is given by some different functions which are decided by the relation between the firing rates of input patterns. The present study is intended to reveal that the functions of the degree of pattern separation are synthesized with some different partial functions, and they are differently given on the relation between the firing rates of input patterns. Simultaneously, it is proved that the number of the functions also depend on the number of connections between two layers in the model. We also disclose the properties of the degree of pattern separation, and give some suggestions on the sizes of the firing rates of mossy fibers and granule cells under the knowledge about them.     

The functional geometry of local and horizontal connections in a model of V1.

A mathematical model of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the geometry of local and long-range horizontal connections. Each hypercolumn is modeled as a network of interacting excitatory and inhibitory neural populations with orientation and spatial frequency preferences organized around a pair of pinwheels. The pinwheels are arranged on a planar lattice, reflecting the crystalline-like structure of cortex. Local interactions within a hypercolumn generate orientation and spatial frequency tuning curves, which are modulated by horizontal connections between different hypercolumns on the lattice. The symmetry properties of the local and long-range connections play an important role in determining the types of spontaneous activity patterns that can arise in cortex.     

An analysis of interneuronal connections in the auditory cortex of awake cats]

A statistical analysis has been made of the interaction of the auditory cortex units in alert cats with chronically implanted electrodes. Three neurones with an amplitude ratio of 4:2:1 were singled out from the multineuronal activity. The dependence between the firing of two neurones was determined by the cross interval histograms. The relationships between 78 pairs of units were studied in 26 three units microsystems. About a third of the studied pairs functioned independently. The number of pairs with one-way and two-way connections was about equal (26 and 30 respectively). The neurones which generated spikes of high and medium amplitude, had the largest number of two-way connections. One-way connections were equally represented in all the three neurones, though with regard to direction they depended on the amplitude characteristics of the spikes. In neurones with large and medium spikes, output connections predominated, while in neurones with small spikes input connections predominated considerably. The connection could be of inhibitory, excitatory or mixed type. The inhibitory type of connections was the most frequent occurrence (57 out of 86). At prolonged recording (6 to 16 min) of spike activity, most of the functional connections persisted.     

A recurrent system incorporating characteristics of the visual system: a model for the function of backward neural connections in the visual system

A recurrent system is constructed in order to investigate the role of the backward neural connections found in the primate visual system. The system incorporates a layer to perform localized spatial frequency analysis of input images, a function which has been assumed to take place in the primary visual cortex. The function of the system is examined by simulation. The results show that the system can separate an object pattern from its background, irrespective of its precise position. The acceptable displacement range for input images is determined from the width of the window function used to calculate the local Fourier transform. A multilayer version of the above recurrent system is also constructed.     

Effect of interruption of descending cortical connections on unit responses to extracellular polarization in the lateral geniculate body

Acute experiments on cats showed that unilateral division of projection connections from the cerebral cortex gives rise to definite changes in the effects of extracellular polarization of lateral geniculate neurons: in 40% of cells the regular firing pattern is disturbed in the initial period of action of anodal polarization, the number of cells with after-responses and prolonged changes in spontaneous firing pattern is significantly reduced, and the number of neurons capable of modifying their type of activity under the influence of an incoming polarizing current is also reduced. After interruption of the descending cortical connections the functional characteristics of the lateral geniculate neurons are altered, with a resulting narrowing of the range of their physiological responses to the polarizing current. These facts suggest that the most complex processes of tonic regulation of unit activity in the lateral geniculate bodies require the active participation of the cerebral cortex.Institute of Experimental Medicine, Academy of Medical Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 4, No. 6, pp. 629–635, November-December, 1972.     

Development of longitudinal patterns in the cerebellum of the chicken (Gallus domesticus): a cytoarchitectural study on the genesis of cerebellar modules.

The cytoarchitecture of the cerebellum has been studied in chicken embryos from day 3-20 using serial sections stained with cresylviolet, haematoxylin-eosin and toluidine blue. Three periods have been distinguished in cerebellar development on a basis of cytoarchitectonic characteristics. Of these periods the middle one, which lasts from the 8th to the 15th day, is marked by two subsequent transient longitudinal cytoarchitectonic patterns in the cortical anlage. The first pattern, which exists between days 8 and 11, consists of 4 longitudinal Purkinje cell clusters (of the first order) at either side of the midline. The second pattern, which is most distinct and complete during embryonic days 12-14, is caused by specific localizations of otherwise few, early inwardly migrating granule cells from the external cerebellar matrix (so-called granule raphes), which pass through the layer of Purkinje cell clusters of the first order and thus subdivide these latter into smaller entities: Purkinje cell clusters of the second order. The number of these latter (6 or 7 and 11 or 12 in the anterior and posterior lobes, respectively) correspond to the number of parasagittal modules, which can be discerned on a basis of the organization of fiber connections of the adult cerebellar cortex. Thanks to this similarity various hypotheses can be formulated concerning the significance of the transient cytoarchitectonic patterns in the primitive cortex for the genesis of the modular organization of the cerebellum.     

Post-tetanic modification of the efficacy of excitatory transmission in neuronal networks with interhemispheric connections

The modifiable reciprocal transcallosal monosynaptic excitatory connections were for the first time detected in vivo experiments in rat motor cortex using multiunit recording and crosscorrelation analysis, It was shown that high-frequency microstimulation (MCS) of a small group of cortical cells of one hemisphere produces long-term changes in the efficacy of transcallosal excitatory connections, and also ipsilateral connections in both hemispheres. The posttetanic changes appear as long-term potentiation (LTP) and long-term depression (LTD). The bursting neurons were found to have more favorable conditions for the induction of LTP of most converging inputs (in contrast to cells with other discharge patterns). Both LTP and LTD could be simultaneously induced in synapses formed by axon collaterals of a callosal cell on several neurons. LTP and LTD could be simultaneously obtained at diverse synapses of the same cell. The number of spontaneously active callosal neurons as well as the number and efficacy of transcallosal connections increased after the MCS, whereas the number and efficacy of ipsilateral connections decreased. Basing on these data we assume that the ipsilateral inhibition is more effective than the transcallosal inhibition. MCS results in the modification of the pattern of initially existing connections between numerous neurons of an ensemble including cells of both hemispheres.     

Two-point heterogeneous connections in a continuum neural field model

We examine a novel heterogeneous connection scheme in a 1D continuum neural field model. Multiple two-point connections are added to a local connection function in order to model the “patchy” connections seen in, for example visual cortex. We use a numerical approach to solve the equations, choosing the locations of the two-point connections stochastically. We observe self-sustained persistent fluctuations of activity which can be classified into two types (one of which is similar to that seen in network models of discrete excitable neurons, the other being particular to this model). We study the effect of parameters such as system size and the range, number and strength of connections, on the probability that a particular realisation of the connections is able to exhibit persistent fluctuations.     

Dynamics of pattern formation in lateral-inhibition type neural fields

The dynamics of pattern formation is studied for lateral-inhibition type homogeneous neural fields with general connections. Neural fields consisting of single layer are first treated, and it is proved that there are five types of pattern dynamics. The type of the dynamics of a field depends not only on the mutual connections within the field but on the level of homogeneous stimulus given to the field. An example of the dynamics is as follows: A fixed size of localized excitation, once evoked by stimulation, can be retained in the field persistently even after the stimulation vanishes. It moves until it finds the position of the maximum of the input stimulus. Fields consisting of an excitatory and an inhibitory layer are next analyzed. In addition to stationary localized excitation, fields have such pattern dynamics as production of oscillatory waves, travelling waves, active and dual active transients, etc.This research was supported in part by a Sloan Foundation grant to the Center for Systems Neuroscience, University of Massachusetts at AmherstOn sabbatical leave from the University of Tokyo     

Neuronal interaction in the cat cerebellar cortex: A cross correlation analysis

Neuronal interaction in the cat cerebellum was investigated by cross correlation analysis techniques. Excitatory connections of varying effectiveness were found between neurons of 13 out of 90 pairs investigated (or 14%). Inhibitory interaction was observed in 38 pairs, or 42%. Neurons of 26 pairs (40%) had shared inputs. Effectiveness of connections between cerebellar cortex neurons was demonstrated by changing stimulus parameters. Findings obtained agree with existing data on the functional organization of the cerebellar cortex. Possible reasons for the large numbers of inhibitory connections discovered are discussed.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow, Institute of Experimental Biology, Polish Academy of Sciences, Warsaw. Translated from Neirofiziologiya, Vol. 19, No. 5, pp. 672–678, September–October, 1987.     

Origin of orientation tuning in the visual cortex.

The results of recent experiments have thrown new light on the neuronal connections underlying orientation-selective responses in the primary visual cortex of adult animals. The pattern of afferent input from the lateral geniculate nucleus to the cortex appears to be specific for orientation, while intracortical inhibitory connections appear to be non-specific in this respect. Experimental and theoretical studies have suggested that the development of cortical cell orientation tuning is an activity-dependent process.     

Cerebellar Cortex Granular Layer Interneurons in the Macaque Monkey Are Functionally Driven by Mossy Fiber Pathways through Net Excitation or Inhibition

The granular layer is the input layer of the cerebellar cortex. It receives information through mossy fibers, which contact local granular layer interneurons (GLIs) and granular layer output neurons (granule cells). GLIs provide one of the first signal processing stages in the cerebellar cortex by exciting or inhibiting granule cells. Despite the importance of this early processing stage for later cerebellar computations, the responses of GLIs and the functional connections of mossy fibers with GLIs in awake animals are poorly understood. Here, we recorded GLIs and mossy fibers in the macaque ventral-paraflocculus (VPFL) during oculomotor tasks, providing the first full inventory of GLI responses in the VPFL of awake primates. We found that while mossy fiber responses are characterized by a linear monotonic relationship between firing rate and eye position, GLIs show complex response profiles characterized by “eye position fields” and single or double directional tunings. For the majority of GLIs, prominent features of their responses can be explained by assuming that a single GLI receives inputs from mossy fibers with similar or opposite directional preferences, and that these mossy fiber inputs influence GLI discharge through net excitatory or inhibitory pathways. Importantly, GLIs receiving mossy fiber inputs through these putative excitatory and inhibitory pathways show different firing properties, suggesting that they indeed correspond to two distinct classes of interneurons. We propose a new interpretation of the information flow through the cerebellar cortex granular layer, in which mossy fiber input patterns drive the responses of GLIs not only through excitatory but also through net inhibitory pathways, and that excited and inhibited GLIs can be identified based on their responses and their intrinsic properties.     

Association connections of the cat's parietal cortex

Intercortical connections of primary sensory (visual, auditory, somatosensory) areas with the parietal association cortex were studied in cats by the retrograde axonal transport of horseradish peroxidase and the Fink-Heimer silver impregnation of degenerated fibers techniques. This combined study revealed the shape, size, and intracortical location of cells connecting the primary sensory areas monosynaptically with the parietal cortex and also the distribution of preterminals and terminals of the fibers of these cells in the parietal association cortex. The greatest number of cells forming connections with area 7 of the parietal association cortex was shown to occur in visual area V1, and with area 5 in somatosensory area S1. Besides pyramidal neurons tagged with horseradish peroxidase, which were located mainly in layers II–IV, a few tagged stellate and fusiform cells also were found. The results supplement and confirm data on afferent connections of the parietal association cortex in cats.M. Gor'kii Donetsk Medical Institute. Translated from Neirofiziologiya, Vol. 13, No. 1, pp. 3–6, January, 1981.     

Afferent and efferent connections of cortical transplants implanted into the damaged sensorimotor area of the cerebral cortex of mature rats

Afferent and efferent connections of the transplant, implanted in the previously damaged sensorimotor area of the mature rat cerebral cortex have been studied by means of axonal transport of horseradish peroxidase. For 5 months after transplantation neural axons of the transplant are capable to reach the caudo-putamen and thalamic structures, while connections with the spinal cord are absent. The afferent connections of the transplant are minimal and belong only to the neighbouring areas of the cortex and the caudo-putamen of the recipient brain. Presence of efferent projections to the striate and thalamic structures demonstrates specificity of the projections formed; this can be a morphological base for restoration of the functions lost after the damage of the sensorimotor area of the cortex in mature animals.     

Cooperative self-organization of afferent and lateral connections in cortical maps

A self-organizing neural network model called LISSOM for the synergetic development of afferent and lateral connections in cortical feature maps is presented. The weight adaptation process is purely activity-dependent, unsupervised, and local. The afferent input weights self-organize into a topological map of the input space. At the same time, the lateral interconnection weights adapt, and a unique lateral interaction profile develops for each neuron. Weak lateral connections die off, leaving a pattern of connections that represents the significant long-term correlations of activity on the feature map. LISSOM demonstrates how self-organization can bootstrap based on input information only, without global supervision or predetermined lateral interaction. The model gives rise to a nontopographically organized lateral connectivity similar to that observed in the mammalian neocortex as illustrated by a LISSOM model of ocular dominance column formation in the primary visual cortex. In addition, LISSOM can potentially account for the development of multiple maps of different modalities on the same undifferentiated cortical architecture. Received: 12 May 1993/Accepted in revised form: 22 September 1993     

Laminar specificity of extrinsic cortical connections studied in coculture preparations.

The formation of specific neural connections in the cerebral cortex was studied using organotypic coculture preparations composed of subcortical and cortical regions. Morphological and electrophysiological analysis indicated that several cortical efferent and afferent connections, such as the corticothalamic, thalamocortical, corticocortical, and corticotectal connections, were established in the cocultures with essentially the same laminar specificity as that found in the adult cerebral cortex, but without specificity of sensory modality. This suggests the existence of a cell-cell recognition system between cortical or subcortical neurons and their final targets. This interaction produces lamina-specific connections, but is probably insufficient for the formation of the modality-specific connections.     

A neural network model of the cerebellar cortex performing dynamic associations

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber — Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.     

Spike suppression in a local cortical circuit induced by transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) noninvasively interferes with human cortical function, and is widely used as an effective technique for probing causal links between neural activity and cognitive function. However, the physiological mechanisms underlying TMS-induced effects on neural activity remain unclear. We examined the mechanism by which TMS disrupts neural activity in a local circuit in early visual cortex using a computational model consisting of conductance-based spiking neurons with excitatory and inhibitory synaptic connections. We found that single-pulse TMS suppressed spiking activity in a local circuit model, disrupting the population response. Spike suppression was observed when TMS was applied to the local circuit within a limited time window after the local circuit received sensory afferent input, as observed in experiments investigating suppression of visual perception with TMS targeting early visual cortex. Quantitative analyses revealed that the magnitude of suppression was significantly larger for synaptically-connected neurons than for isolated individual neurons, suggesting that intracortical inhibitory synaptic coupling also plays an important role in TMS-induced suppression. A conventional local circuit model of early visual cortex explained only the early period of visual suppression observed in experiments. However, models either involving strong recurrent excitatory synaptic connections or sustained excitatory input were able to reproduce the late period of visual suppression. These results suggest that TMS targeting early visual cortex disrupts functionally distinct neural signals, possibly corresponding to feedforward and recurrent information processing, by imposing inhibitory effects through intracortical inhibitory synaptic connections.     

The functional logic of cortico-pulvinar connections

The pulvinar is an 'associative' thalamic nucleus, meaning that most of its input and output relationships are formed with the cerebral cortex. The function of this circuitry is little understood and its anatomy, though much investigated, is notably recondite. This is because pulvinar connection patterns disrespect the architectural subunits (anterior, medial, lateral and inferior pulvinar nuclei) that have been the traditional reference system. This article presents a simplified, global model of the organization of cortico-pulvinar connections so as to pursue their structure-function relationships. Connections between the cortex and pulvinar are topographically organized, and as a result the pulvinar contains a 'map' of the cortical sheet. However, the topography is very blurred. Hence the pulvinar connection zones of nearby cortical areas overlap, allowing indirect transcortical communication via the pulvinar. A general observation is that indirect cortico-pulvino-cortical circuits tend to mimic direct cortico-cortical pathways: this is termed 'the replication principle'. It is equally apt for certain pairs (or groups) of nearby cortical areas that happen not to connect with each other. The 'replication' of this non-connection is achieved by discontinuities and dislocations of the cortical topography within the pulvinar, such that the associated pair of connection zones do not overlap. Certain of these deformations can be used to divide the global cortical topography into specific sub-domains, which form the natural units of a connectional subdivision of the pulvinar. A substantial part of the pulvinar also expresses visual topography, reflecting visual maps in occipital cortex. There are just two well-ordered visual maps in the pulvinar, that both receive projections from area V1, and several other occipital areas; the resulting duplication of cortical topography means that each visual map also acts as a separate connection domain. In summary, the model identifies four topographically ordered connection domains, and reconciles the coexistence of visual and cortical maps in two of them. The replication principle operates at and below the level of domain structure. It is argued that cortico-pulvinar circuitry replicates the pattern of cortical circuitry but not its function, playing a more regulatory role instead. Thalamic neurons differ from cortical neurons in their inherent rhythmicity, and the pattern of cortico-thalamic connections must govern the formation of specific resonant circuits. The broad implication is that the pulvinar acts to coordinate cortical information processing by facilitating and sustaining the formation of synchronized trans-areal assemblies; a more pointed suggestion is that, owing to the considerable blurring of cortical topography in the pulvinar, rival cortical assemblies may be in competition to recruit thalamic elements in order to outlast each other in activity.