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A fast method is presented for simulating a class of systems that includes certain regular neural networks based on neurons that perform a weighted spatial summation as a part of their operation. The method employs high-speed convolution via the Fast Fourier Transform. Some important aspects are emphasized: first, even though the FFT is essential, the neurons do not need to be completely linear (they can have time varying thresholds for example); second, simulations of networks with very dense interconnections are encouraged (they take no more time then sparse ones using this method); and finally, the method is suggestive of similar but more general computational schemes.

Two new methods are presented in order to determine the behavior of a structure carrying moving masses. The first method is analytic in nature and represents a modified asymptotic method in the theory of nonlinear phenomena. The second method is an exact numerical technique general enough to be used for solving exactly a set of differential equations with singular coefficients.

Recently, Little demonstrated the existence of persistent states in a neural network when a certain transfer matrix has approximately degenerate maximum eigenvalues. He showed the direst analogy of the persistence of the neuronal firing patterns considered in discrete time steps, to the long range apatial order in an Ising spin crystal system. The ordered phase of the spin system occurs below the Curie point temparature. Hence in analogy, a factor representing the temparature of the neural network is assumed in Little's model for the transfer matrix. We derive his transfer matrix for a neural network and explicitly relate this temperature or “smearing” phenomenon to the experimentally observed fluctuations in the postsynaptic potentials.

A number of neural networks, with direct lateral couplings, have been simulated digitally. The operation of each of these networks has been investigated with regard to the form of interconnection between neurons and the shape of input excitation front to the network. One multilayer network investigated had properties which may duplicate the frequency and intensity coding properties of the mammalian auditory system. As such this network forms the basis of a conceptual model of the processing of sound signals in the auditory system. It is a source of great controversy as to whether the organisation of the auditory system can be copied and understood. However, the neural networks investigated could produce output excitation patterns in which frequency and intensity information was coded with position. Such a system of speech coding, if not a true analogue of the auditory system, has immense potential in the field of speech recognition.

SUMMARYA neural net model with random interconnections is shown capable of exhibiting the features of Parkinson’s disease, including cogwheel rigidity, resting tremor, and dysdiadochokinesis. These properties are simulated uniquely for extrapyramidal disease, with spasticity and hypereflexia predicted for other upper motoneuron lesions.

A central theme of both Cybernetics and Systems Research has been the study of complex, richly-interconnected systems, particularly those having properties of self-organization. Although social and economic systems are frequently mentioned in the literature, the systems which have been studied most have been the nervous system and artificial systems of neuron-like elements.

The mixed problem for strictly hyperbolic first order systems in regions containing a multiple corner is considered. Geometric optics approximations are studied and in certain cases are used to construct counter-examples. (Author)

Plastic change is introduced and discussed as the property of the brain cell that is responsible for the self‐organizing capabilities of neural nets. Three models of this phenomenon are described. The models are of increasing complexity, and the reasons for the three different models are given. The emergence of association as a property of a plastic neuron is illustrated.

The Wiener theory of nonlinear system identification is extended to multi-input-output systems and experimentally applied. The experimental applicability of the method is discussed with regard to biological systems. It is shown that the method is well suited for the treatment of the idiosyncratic features of such systems: nonlinearities, short lifetimes of experimental preparations, and high noise content. A preliminary analysis is outlined, taking into account the characteristics of the system under study, which results in the determination of the parameters of the identifying experiment. An error analysis is made which can be used to increase the accuracy of the derived model within certain constraints. Several examples are given of the experimental application of the method to certain neural networks in a vertebrate retina (the catfish, Ictalurus punctatus, retina was used for these experiments). In addition to functional identification through white-noise stimulation, these same retinal neurons are identified morphologically through intracellular dye injection. The performance of the derived functional models, as compared to the physical system, is evaluated through a variety of tests and it is found to be very satisfactory.

The field of the randomly connected neural network is approximately formulated by Griffith's equation, regarding the network as being continuous. An integral representation of Griffith's equation is derived. If a relative refractory period can be ignored, it is X(x,t) =1 ∫ o ∞ ds ∫ −vs vs dn kv 2t e −avs X(x−n, t−s) − θ where X(x, t) corresponds to the firing rate and θ means the threshold of the neural firing, τ the absolute refractory period and v the velocity for the spike potential travelling down the axon. The above equation is formally analogous to Caianiello's equation, but the former describes the more macroscopic behaviour of the neural network than the latter. With the aid of computer simulation, appropriate solutions are successfully obtained. In regions where X = 1, neurones are firing at a high constant rate of 1 τ (active regions). In regions where X = 0, there is no firing of neurones (resting regions). In the neural net for which 0 a 2 τθ k , the net is generally a mixture of the active regions and of the resting regions. In the case that a large active region is in contact with a large resting region, the propagation velocity of boundary between the two regions tends to the velocity u given by u = (1 − 2a 2 τθ k )v . This expression of velocity u was deduced from the fact that there exists a solution of the type X(x, t) = 1 (ut − x) for equation (A). In the case of 0 a 2 τθ k , the active region grows and in the case of 0 · 5 a 2 τθ k , the resting region grows. A fatigue effect is introduced, for which it is hard for neurones to maintain firing states. In this case an active region of definite width L propagates with constant velocity u′. The dependence of L and u′ on characteristics of neural network and on the fatigue effect is investigated.

This report describes a theory and corresponding model for the neural basis of language. A detailed functional description will be given for the following elementary visual-linguistic processes: (1) the selection and neural encoding of patterns from the visual field; (2) the representation of visual experience in memory; (3) the mechanisms of association between different types of visual and verbal information including (a) naming of visual images, (b) naming of positional relationships between objects, (c) naming of size and shape attributes of objects, and (d) imaging of pictorial information which was previously stored in memory; (4) the neural representation of phrases and simple sentences; (5) the recognition of simple sentences and the concept of meaning; and (b) verballydirected recall of visual experience. Strengths and weaknesses of the model are discussed. Part 1 of this paper contains a complete set of operational definitions. The neural networks aie described, and several alternate control strategies for these networks are considered. Part 2 gives a detailed description of computersimulation studies of the proposed model. Processes demonstrated by the computer simulations are: (1) verbally directed recall of visual experience; (2) understanding of verbal information; (3) aspects of learning and forgetting; (4) the dependence of, recognition and understanding on, contextual information; and (5) elementary concepts of sentence generation. The simulation studies are based on one particular choice of control functions.

As a prelude to the study of the adaptive-behavior and data-handling characteristics of natural and artificial neural networks, an analog model of a single neuron was developed. An analog computer was employed to reproduce the known electrical characteristics of a neuron in a qualitative simulation study of neuronal behavior. A self-imposed criterion of a minimum number of analog-computer components was adopted for the single-neuron simulation in anticipation of network studies. This criterion led to the development of a simple analog circuit which has qualitatively reproduced some of the known electrical characteristics of a neuron, such as: initiation of an action potential in the presence of suprathreshold depolarizing (or excitatory) inputs; strength-duration relationship; accommodation; refractoriness; rate of pulse repetition as a function of the input depolarization level; and prolonged action potentials. The simulation method adopted consisted of four major analog-computer components, three operational amplifiers and a single-shot multivibrator. The circuit developed has a linear forward path with a nonlinear form of feedback. A discussion is given of the properties exhibited by the simulated neuron with and without the nonlinear feedback. A mathematical method for linearly approximating nonlinear behavior is presented. This method is known as the "describing function technique," and its application to the analysis of neuronal behavior is described, as well as the technique's application to the synthesis of simulation networks.

It is believed that all practical cases of notch shapes are covered by the above analysis. The experiments are in favour of the upper bound solution, though, for practical cases, the mean value derived from the limit analysis differs very little from that of the bounds, and it can be used with confidence.

This paper presents analytical stabiltity analysis of turning using non-linear force-feed model in two dimensions. Most of the existing analytical models ignored the effect of static feed term on the regeneration phenomenon. In practice there is a marked effect of feed on stability due to force variation. The modified analytical equations for cutting insert using three dimensional too geometry are obtained by considering relative motion of tool with respect to a two dimensional elastic model of work-piece. The critical stability limits obtained as a function of feed are confirmed with time domain analysis. Experiments are conducted on a flexible work-piece at varying feed conditions. The measured cutting forces show a marked effect of feed on stability. A neural network models developed to obtain the critical depth of cut at various values of operating speeds and feeds. Key words: Dynamics modeling; Tool geometry; Force-feed; Stab. DOI: 10.3329/bjsir.v45i2.5710Bangladesh J. Sci. Ind. Res. 45(2), 129-132, 2010

A mathematical framework for a rigorous theory of general systems is constructed, using the notions of the theory of Categories and Functors introduced by Eilenberg and MacLane (1945,Trans. Am. Math. Soc.,58, 231–94). A short discussion of the basic ideas is given, and their possible application to the theory of biological systems is discussed. On the basis of these considerations, a number of results are proved, including the possibility of selecting a unique representative (a “canonical form”) from a family of mathematical objects, all of which represent the same system. As an example, the representation of the neural net and the finite automaton is constructed in terms of our general theory.

Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.

A mathematical model for learning of a conditioned avoidance behavior is presented. An identification of the net excitation of a neural model (Rashevsky, N., 1960.Mathematical Biophysics. Vol. II. New York: Dover Publications, Inc.) with the instantaneous probability of response is introduced and its usefulness in discussing block-trial learning performances in the conditioned avoidance situation is outlined for normal and brain-operated animals, using experimental data collected by the author. Later, the model is applied to consecutive trial learning and connection is made with the approach of H. D. Landahl (1964. “An Avoidance Learning Situation. A Neural Net Model.”Bull. Math. Biophysics,26, 83–89; and 1965, “A Neural Net Model for Escape Learning.”Bull. Math. Biophysics,27, Special Edition, 317–328) wherein lie further data with which the model can be compared.

Concepts of random neural nets, as treated in mathematical biophysics, are used to describe the random behavior of communication nets. Application of the steady-state as well as message spread threshold concepts to communication nets are considered. The steady state here implies a systematic and regular spread of the message while the spread threshold, referred to as the "ignition" threshold in neural nets, determines the required threshold minimum number of links ensuring, eventually, a steady-state activity, namely, a regular spread of the message throughout the net. The derived formulas offer useful computational tools in the treatment of strategic nondirectory nets in random behavior. Section II discusses the use of the spread of contagion theory and Section III deals with the random behavior of mobile communication nets, with directional and nondirectional antennas.

By “neural net” will be meant “neural net without circles.” Every neural net effects a transformation from inputs (i.e., firing patterns of the input neurons) to outputs (firing patterns of the output neurons). Two neural nets will be calledequivalent if they effect the same transformation from inputs to outputs.

Meaningful factor analysis and algebraic operations during stimulation, learning, and discrimination experiments have been performed on averaged evoked potential responses, suggesting that, at least under some circumstances, the signal space of average evoked potentials is linear. Alternatively, the "behavior" of simulated neural nets is defined as the observation of an average over an ensemble of the trajectories of solutions of interconnected nonlinear dynamical systems. This behavior is a mathematical counterpart of the physiological macropotential observations. In this paper, a mathematical model corresponding to the ensemble average over an unconnected set of statistically distributed linear elements suggests duplication of both the simulated neural net and the neurophysiological findings. In contrast with the simulated neural network, the statistical properties of this model are amenable to analysis. The model suggests experiments of the prediction and control of multidiscrimination experiments in cats and provokes questions on the significance of the specification of detail in different levels on the structural hierarchy of the brain.

The paper presents the fundamentals of the theory of neural nets with loops based on functional matrices, which are a generalization of the state transition matrices for a net. Problems of analysis and synthesis; given a net, find its functional matrix and vice versa, are treated for probabilistic and deterministic nets. Questions about universal nets, oscillations, and stability are studied for deterministic nets. Reduction of probabilistic nets with loops is considered. It is shown that any probabilistic net with loops can be duplicated by a deterministic net with loops plus a probabilistic loop-free encoder. The motivation for the work is a search for formulation of the general theory of neural nets that could be tied to the theory of triadic intensional relations, as suggested by Warren S. McCulloch.

A parallel processing algorithm for shrinking binary patterns to obtain single isolated elements, one for each pattern, is presented. This procedure may be used for counting patterns on a matrix, and a hardware implementation of the algorithm using large scale integrated tecnology is envisioned. The principal features of this method are the very small window employed (two-by-two elements), the parallel nature of the process, and the possibility of shrinking any pattern, regardless of the complexity of its configuration. Problems regarding merging and disconnection of patterns during the process as well as the determination of the maximum number of steps necessary to obtain a single isolated element from a pattern, are reviewed and discussed. An analogy with a neural network description, in terms of McCulloch-pitts “neurons” is presented.

Neural networks are introduced which can be taught by classical or instrumental conditioning to fire in response to arbitrary learned classes of patterns. The filters of output cells are biased by presetting cells whose activation prepares the output cell to “expect” prescribed patterns. For example, an animal that learns to expect food in response to a lever press becomes frustrated if food does not follow the lever press. It's expectations are thereby modified, since frustration is negatively reinforcing. A neural analog with aspects of cerebellar circuitry is noted, including diffuse mossy fiber inputs feeding parallel fibers that end in Purkinje cell dendrites, climbing fiber inputs ending in Purkinje cell dendrites and giving off collaterals to nuclear cells, and inhibitory Purkinje cell outputs to nuclear cells. The networks are motivated by studying mechanisms of pattern discrimination that require no learning. The latter often use two successive layers of inhibition, analogous to horizontal and amacrine cell layers in vertebrate retinas. Cells exhibiting hue (in)constancy, brightness (in)constancy, or movement detection properties are included. These results are relevant to Land's retinex theory and to the existence of opponent- and nonopponent-type cell responses in retinal cells. Some adaptation mechanisms, and arousal mechanisms for crispening the pattern weights that can fire a given cell, are noted.

In connection with some problems that arise in the study of neural networks random matrices are considered and the probability for them to have certain rank is investigated. Two models are studied in a simple-minded approach to problems of this type.

The results from a study by M. F. Morales on the labyrinthine response to motion are used, together with results of neural net theory, to enable one to calculate, in terms of a small number of parameters, the percentage of individuals who have motion sickness when exposed to rather general patterns of motion which may vary with time.

In a previous paper a method was given by which the efferent activity of an idealized neural net could be calculated from a given afferent pattern. Those results are extended in the present paper. Conditions are given under which nets may be considered equivalent. Rules are given for the reduction or extension of a net to an equivalent net. A procedure is given for constructing a net which has the property of converting each of a given set of afferent activity patterns into its corresponding prescribed efferent activity pattern.

An escape learning situation is discussed in terms of a neural model in which a stimulus can result in a conditioned excitement and a specific conditioned response. By using the simplest relations between the strengths of conditioning and the number of reinforcements and by introducing a distribution of fluctuations occurring regularly in time, one can calculate the probabilities of various responses, as well as the various latencies, in successive trials. The results are in moderately satisfactory agreement with the data of R. L. Solomon and L. C. Wynne (Psychol. Monogr.,67, No. 4, 1953). Consequences of the model for various experimental situations are discussed.

Adaptive neural nets are collections of threshold logic units (TLU) connected by variable weights. They are often compared to biological systems, serving as models for memory and perception, and are frequently used for Optical Character Recognition (OCR). The Perceptron is the most commonly used model among these nets. Taking it as an example we will show it to be inadequate to account for perception. The following notation is used: “ φ,φ ....“ denotes individual characters φ,φ 2....; denotes the class of all characters φ, φ2.

Aggregates of neurons are considered in which the frequency of occurrence of neurons with a specified value of the refractory period follows certain probability distributions. Input-output functions are derived for such aggregates. In particular, if input and output intensities are defined in terms of stimulus frequencies and firing frequencies per neuron respectively, it is shown that a rectangular distribution of refractory periods leads to a logarithmic input-output curve. If input and output are defined in terms of the total number of stimuli and firings in the aggregate, it is shown how the “mobilization” picture leads to the logarithmic input-output curve.

A neural net is taken to consist of a semi-infinite chain of neurons with connections distributed according to a certain probability frequency of the lengths of the axones. If an input of excitation is “fed” into the net from an outside source, the statistical properties of the net determine a certain steady state output. The general functional relation between the input and the output is derived as an integral equation. For a certain type of probability distribution of connections, this equation is reducible to a differential equation. The latter can be solved by elementary methods for the output in terms of the input in general and for the input in terms of the output in special cases.

Learning of patterns by neural networks obeying general rules of sensory transduction and of converting membrane potentials to spiking frequencies is considered. Any finite number of cellsA can sample a pattern playing on any finite number of cells ∇ without causing irrevocable sampling bias ifA = ℬ orA ∩ ℬ = . Total energy transfer from inputs ofA to outputs of ℬ depends on the entropy of the input distribution. Pattern completion on recall trials can occur without destroying perfect memory even ifA = ℬ by choosing the signal thresholds sufficiently large. The mathematical results are global limit and oscillation theorems for a class of nonlinear functional-differential systems.