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.     

Pattern separability and the effect of the number of connections in a random neural net with inhibitory connections

It has been claimed that pattern separation in cerebellar cortex plays an important role in controlling movements and balance for vertebrates. A number of the neural models for cerebellar cortex have been proposed and their pattern separability has been analyzed. These results, however, only explain a part of pattern separability in random neural nets. The present paper is intended to study an extended theory of pattern separability in a new model with inhibitory connections. In addition to this, the effect of the number of connections on pattern separability is cleared up. It is also shown that the signal from the inhibitory connections has crucial importance for pattern separability.1977–1978 Exchange Visitor, on leave from the Department of Information Processing Engineering, Technical College, Yamaguchi University, Yamaguchi University     

Oscillations in a refractory neural net

A functional differential equation that arises from the classic theory of neural networks is considered. As the length of the absolute refractory period is varied, there is, as shown here, a super-critical Hopf bifurcation. As the ratio of the refractory period to the time constant of the network increases, a novel relaxation oscillation occurs. Some approximations are made and the period of this oscillation is computed.     

Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

The stability of brain networks with randomly connected excitatory and inhibitory neural populations is investigated using a simplified physiological model of brain electrical activity. Neural populations are randomly assigned to be excitatory or inhibitory and the stability of a brain network is determined by the spectrum of the network’s matrix of connection strengths. The probability that a network is stable is determined from its spectral density which is numerically determined and is approximated by a spectral distribution recently derived by Rajan and Abbott. The probability that a brain network is stable is maximum when the total connection strength into a population is approximately zero and is shown to depend on the arrangement of the excitatory and inhibitory connections and the parameters of the network. The maximum excitatory and inhibitory input into a structure allowed by stability occurs when the net input equals zero and, in contrast to networks with randomly distributed excitatory and inhibitory connections, substantially increases as the number of connections increases. Networks with the largest excitatory and inhibitory input allowed by stability have multiple marginally stable modes, are highly responsive and adaptable to external stimuli, have the same total input into each structure with minimal variance in the excitatory and inhibitory connection strengths, and have a wide range of flexible, adaptable, and complex behavior.     

Dynamic connections in neural networks

Massively parallel (neural-like) networks are receiving increasing attention as a mechanism for expressing information processing models. By exploiting powerful primitive units and stability-preserving construction rules, various workers have been able to construct and test quite complex models, particularly in vision research. But all of the detailed technical work was concerned with the structure and behavior offixed networks. The purpose of this paper is to extend the methodology to cover several aspects of change and memory.     

Response time and threshold of a random net

The response time of a random net is defined as the expected time (measured in the number of synaptic delays) required for the excitation in the net (measured by the fraction of neurons firing per unit time) to reach a certain level. The response time is calculated in terms of the net parameters as a function of the intensity of the outside stimulation. Two principal types of cases are studied, 1) an instantaneous initial stimulation, and 2) continuously applied stimulation. It is shown that for a certain type of net where the required level of excitation is small, the response time-intensity equation reduces to the one derived on the basis of the “one-factor” theory applied to a neural connection. More general assumptions, however, give different types of equations. The concept of the “net threshold” is defined, and its calculation indicated. The net threshold for instantaneous stimulation is, in general, greater than that for continuous stimulation. The results are discussed with reference to existing theories of reaction times.     

Wave speed in excitable random networks with spatially constrained connections

Very fast oscillations (VFO) in neocortex are widely observed before epileptic seizures, and there is growing evidence that they are caused by networks of pyramidal neurons connected by gap junctions between their axons. We are motivated by the spatio-temporal waves of activity recorded using electrocorticography (ECoG), and study the speed of activity propagation through a network of neurons axonally coupled by gap junctions. We simulate wave propagation by excitable cellular automata (CA) on random (Erdös-Rényi) networks of special type, with spatially constrained connections. From the cellular automaton model, we derive a mean field theory to predict wave propagation. The governing equation resolved by the Fisher-Kolmogorov PDE fails to describe wave speed. A new (hyperbolic) PDE is suggested, which provides adequate wave speed that saturates with network degree , in agreement with intuitive expectations and CA simulations. We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length. When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments rather than on mean degree , which is explained by general network theory. The wave speeds are strikingly similar in a diverse set of networks, including regular, Poisson, exponential and power law distributions, supporting our theory for various network topologies. Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.     

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.     

Energy coding in neural network with inhibitory neurons

This paper aimed at assessing and comparing the effects of the inhibitory neurons in the neural network on the neural energy distribution, and the network activities in the absence of the inhibitory neurons to understand the nature of neural energy distribution and neural energy coding. Stimulus, synchronous oscillation has significant difference between neural networks with and without inhibitory neurons, and this difference can be quantitatively evaluated by the characteristic energy distribution. In addition, the synchronous oscillation difference of the neural activity can be quantitatively described by change of the energy distribution if the network parameters are gradually adjusted. Compared with traditional method of correlation coefficient analysis, the quantitative indicators based on nervous energy distribution characteristics are more effective in reflecting the dynamic features of the neural network activities. Meanwhile, this neural coding method from a global perspective of neural activity effectively avoids the current defects of neural encoding and decoding theory and enormous difficulties encountered. Our studies have shown that neural energy coding is a new coding theory with high efficiency and great potential.     

Predicting net joint moments during a weightlifting exercise with a neural network model

The purpose of this study was to develop and train a Neural Network (NN) that uses barbell mass and motions to predict hip, knee, and ankle Net Joint Moments (NJM) during a weightlifting exercise. Seven weightlifters performed two cleans at 85% of their competition maximum while ground reaction forces and 3-D motion data were recorded. An inverse dynamics procedure was used to calculate hip, knee, and ankle NJM. Vertical and horizontal barbell motion data were extracted and, along with barbell mass, used as inputs to a NN. The NN was then trained to model the association between the mass and kinematics of the barbell and the calculated NJM for six weightlifters, the data from the remaining weightlifter was then used to test the performance of the NN – this was repeated 7 times with a k-fold cross-validation procedure to assess the NN accuracy. Joint-specific predictions of NJM produced coefficients of determination (r²) that ranged from 0.79 to 0.95, and the percent difference between NN-predicted and inverse dynamics calculated peak NJM ranged between 5% and 16%. The NN was thus able to predict the spatiotemporal patterns and discrete peaks of the three NJM with reasonable accuracy, which suggests that it is feasible to predict lower extremity NJM from the mass and kinematics of the barbell. Future work is needed to determine whether combining a NN model with low cost technology (e.g., digital video and free digitising software) can also be used to predict NJM of weightlifters during field-testing situations, such as practice and competition, with comparable accuracy.     

Disparity tuning as simulated by a neural net

Previous research has suggested that the processing of binocular disparity in complex cells may be described with an energy formalism. The energy formalism allows for a representation of disparity by differences in the position or in the phase of monocular receptive subfields of binocular cells, or by combination of these two types. We studied the coding of disparities with an approach complementary to previous algorithmic investigations. Since realization of these representations is probably not genetically determined but learned during ontogeny, we used backpropagation networks to study which of these three possibilities were realized within neural nets. Three types of networks were trained with noise patterns in analogy to the three types of energy models. The networks learned the task and generalized to untrained correlated noise pattern input. Outputs were broadly tuned to spatial frequency and did not respond to anti-correlated noise patterns. Although the energy model was not explicitly implemented, we could analyze the outputs of the networks using predictions of the energy formalism. After learning was completed, the model neurons preferred position shifts over phase shifts in representing disparity. We discuss the general meaning of these findings and the correspondences and deviations between the energy model, V1 neurons, and our networks. Received: 6 August 1999 / Accepted in revised form: 26 January 2000     

Cyclic modes in neural net models

Neural network models with possible cross-coupling from every neuron to every other neuron are condisered. The all-or-none law is assumed for firing of neurons. A network is shown to have a set of latent cyclic modes. If the net is stimulated briefly, it will subsequently either return to quiescence or settle into periodic activity in one of its cyclic modes. Realization of cyclic modes and analysis of nets are discussed. A learning rule for adjustment of synaptic strengths is presented.     

Further consideration of systematic errors present in protein-ligand interactions

Relatively minor systematic errors present during measurements of protein-ligand interaction can lead to large inaccuracies in the calculated values of the equilibrium dissociation constant and the total concentration of the binding protein. These errors, which include binding of the ligand to low affinity material and underestimation of bound ligand, cause the calculation of the concentration of free ligand at equilibrium to be overestimated. We report herein a model of ligandprotein binding which incorporates these errors into the mathematical formulation of the equilibrium binding equation. The effect of these errors on the Scatchard plot is presented.     

Further evidence for the inhibitory action of baclofen on a prolactin-releasing factor

The mechanism of action of a specific gamma-aminobutyric acid B receptor agonist, beta-p-chlorophenyl-gamma-aminobutyric acid or baclofen, in its inhibitory action on prolactin release, was studied. Dose-response studies of the effect of baclofen on prolactin (PRL) secretion were performed in stressed male rats. Furthermore, the action of the drug was evaluated in (i) rats treated with haloperidol or alpha-methyl-p-tyrosine, (ii) stressed or suckled rats pretreated with sulpiride, and (iii) animals treated with serotonin, alone, or with alpha-methyl-p-tyrosine. Baclofen showed a clear dose-dependent inhibition of prolactin secretion in males under stress. The drug was unable to inhibit the prolactin release induced by haloperidol or alpha-methyl-p-tyrosine, although it reduced the PRL secretion induced by serotonin. It also inhibited PRL release in sulpiride-pretreated stressed or suckled rats. These results suggest that the dose-dependent effect of baclofen on PRL secretion is the consequence of an inhibition exerted on the prolactin-releasing factor component of the neuroendocrine responses evoked by stress or suckling, possibly acting at the serotonergic system.     

Pharmacological dissection of a neural pattern generator

Summary Injection of picrotoxin solutions into the pericardium of lobsters,Homarus americanus, to produce final, estimated blood concentrations of between 8×10^–8M and 4.5×10^–6M led to disruption of the normal motor output to the scaphognathite. The phase separation of the starts of the bursts in the D1 and D2 muscles (Young, 1975) was reduced on the average by 49%; that of L1 and L2 muscles by 16%. The durations of the D1 and L1 bursts increased by 94% and 48% respectively. The phase separation between the starts of the levator and depressor portions of the cycle was not altered. Whilst rhythmic activity persisted ventilatory rates were depressed, and reversals and ventilatory pauses continued to occur. The rate of reversals and their pattern were not greatly altered. Inexplicably, tonic, synchronous spikes occurred in all four groups of muscles, levator and depressor, during periods of severe disruption. It was concluded that in spite of this, the observations supported the proposals of Young (1975) that (a) recruitment of the D2 and L2 bursts normally is delayed partly by inhibition from D1 and L1 units respectively, and (b) termination of D1 and L1 bursts results normally from inhibition due to activity in D2 and L2 units respectively. The findings also indicated that the synaptic mechanism determining timing within the depressor and levator sessions differs fundamentally from that operating between sessions. One mechanism may be based on picrotoxin-sensitive, and the other on picrotoxin-insensitive inhibition.Abbreviations GABA gamma-aminobutyric acid - SG scaphognathite     

Preliminary investigation into a neural net theory of color vision

Summary This paper reports results of an investigation of the problem of vertebrate color vision by means of a theoretical model, which, although it uses one kind of receptor, can be adapted to a multireceptor concept. It is assumed (1) that the time constant of the change of the receptor potential conveys the color information of the stimulus, whereas the magnitude of the potential is correlated with stimulus intensity and (2) that a group of cells, tentatively identified as ganglion cells, are associated with each receptor field. These cells fire only if the time constant falls within a certain range. Thus, the visual spectrum is divided into regions and the information is transmitted to the central nervous system. Wave length discrimination in the theoretical model is accomplished by one kind of retinal neural nets that are biased differentially. An analog computer was used in this initial phase of the investigation. Care has been taken to ensure that the model satisfies current anatomical and physiological knowledge. It has produced results similar to Granit's (1955) spectral sensitivity and Kelly's (1961) amplitude sensitivity curves. The model, which will predict subjective color phenomena at appropriate frequencies, has raised questions amenable to psychophysiological techniques.

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Zusammenfassung Dieser Bericht enthält die Ergebnisse einer Untersuchung des Farbensehens der Wirbeltiere, dargestellt in einem theoretischen Modell, das, obgleich es nur einen Receptor besitzt, auch auf mehrere Receptoren erweitert werden kann. Es wird angenommen 1., daß die Zeitkonstante der Veränderung des Receptor-Potentials die Farbeninformation des Lichtreizes überträgt, während die Potentialgröße mit der Intensität des Lichtreizes zusammenhängt, und 2., daß eine Gruppe von Zellen, die vorläufig als Ganglionzellen angenommen werden, mit jedem Receptorfeld assoziiert sind. Diese Zellen werden nur dann aktiviert, wenn die Zeitkonstante in einen bestimmten Bereich fällt. Demgemäß kann das visuelle Spektrum in Bereiche eingeteilt werden, die die Information aus diesem Bereich an das Zentralnervensystem weiterleiten. Die Unterscheidung der Wellenlängen in dem theoretischen Modell erreicht man durch ein Teilmodell der Retina, das differentiell beeinflußt wird. Ein Analogrechner wurde bei dieser Voruntersuchung verwandt. Es wurde besonders darauf geachtet, daß das Modell mit dem heutigen Stand des Wissens der Anatomie und Physiologie übereinstimmt. Die Ergebnisse ähneln den Verläufen von Granits Spektralempfindlichkeit und Kellys Amplitudenempfindlichkeit. Das Modell, das Subjektive Farben-Erscheinungen bei passenden Frequenzen voraussagt, wirft Fragen auf, die psychophysiologischen Methoden zugänglich sind.