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An experiment using a multisensor SQUID (superconducting quantum interference device) array was performed by Kelso and colleagues (1992) which combined information from three different sources: perception, motor response, and brain signals. When an acoustic stimulus frequency is changed systematically, a spontaneous transition in coordination occurs at a critical frequency in both motor behavior and brain signals. Qualitatively analogous transitions are known for physical and biological systems such as changes in the coordination of human hand movements (Kelso 1981, 1984). In this paper we develop a theoretical model based on methods from the interdisciplinary field of synergetics (Haken 1983, 1987) and nonlinear oscillator theory that reproduces the main experimental features very well and suggests a formulation of a fundamental biophysical coupling.

Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm.

The response characteristics of an electronic neuron model proposed by the authors are investigated. Periodic stimulating pulse sequences with a fixed frequency are applied to the analog neuron model and the response pulse sequences are studied. In the degenerate case, the state transition of the neuron model during one period of the stimulating pulse sequence is described by a first order piecewise linear difference equation with a jump. It is shown that the periodic response pulse sequences of the neuron model belong to a special class of pulse sequences generated by a simple algorithm, and that the relation between the pulse width (or amplitude) of the stimulating pulse and the firing rate of the neuron model takes the form of an extended Cantor function.

Klinokinesis is a behavioral mechanism in which an organism moves toward or away from a stimulus source by altering its frequency of change of direction without biasing its turns with respect to the stimulus field. Previous studies of a variety of organisms have demonstrated that rates of adaptation (or other information processing features) for increases and decreases in stimulus intensity are often very different from one another. In order to determine if such asymmetric signal processing could improve the efficiency of klinokinesis, computer modeling studies were performed. The model involved a simple generic version of klinokinesis in 2 dimensions with the rate of adaptation for increasing intensity varied independently of the rate for decreasing intensity. The effects of three types of noise that limit the performance of the model were tested-intensity noise, motor noise, and developmental noise. The results demonstrated that, with all three types of noise, the two adaptation rates had quite different effects on efficiency. The overall pattern of effects was different for each type of noise. In the cases of intensity noise and motor noise, the optimum combination of adaptation rates had a 3-to 5-fold higher rate for decreases in attractant than for increases, which is similar to what has previously been found with bacteria and nematodes.

Nonlinear systems that require discrete inputs can be characterized by using random impulse train (Poisson process) inputs. The method is analagous to the Wiener method for continuous input systems, where Gaussian white-noise is the input. In place of the Wiener functional expansion for the output of a continuous input system, a new series for discrete input systems is created by making certain restrictions on the integrals in a Volterra series. The kernels in the new series differ from the Wiener kernels, but also serve to identify a system and are simpler to compute. For systems whose impulse responses vary in amplitude but maintain a similar shape, one argument may be held fixed in each kernel. This simplifies the identification problem. As a test of the theory presented, the output of a hypothetical second order nonlinear system in response to a random impulse train stimulus was computer simulated. Kernels calculated from the simulated data agreed with theoretical predictions. The Poisson impulse train method is applicable to any system whose input can be delivered in discrete pulses. It is particularly suited to neuronal synaptic systems when the pattern of input nerve impulses can be made random.

The cross-correlation between output and input of a system containing nonlinearities, when that system is stimulated with Gaussian white noise, is a good estimate of the linear properties of the system. In practice, however, when sequences of pseudonoise are used, great errors may be introduced in the estimate of the linear part depending on the properties of the noise. This consideration assumes special importance in the analysis of the linear properties of the peripheral auditory system, where the rectifying properties of the haircells constitute a second order nonlinearity. To explore this problem, a simple model has been designed, consisting of a second order nonlinearity without memory and sandwiched between two bandpass filters. Different types of pseudonoise are used as input whereupon it is shown that noise based on binary m-sequences, which is commonly used in noise generators, will yield totally incorrect information about this system. Somewhat better results are achieved with other types of noise. By using inverse-repeat sequences the results are greatly improved. Furthermore, certain anomalies obtained in the analysis of responses from single fibers in the auditory nerve are viewed in the light of the present results. The theoretical analysis of these anomalies reveals some information about the organization of the peripheral auditory system. For example, the possibility of the existence of a second bandpass filter in the auditory periphery seems to be excluded.

In this study, the amplitude frequency characteristics, which are obtained by application of Fourier transform to the selectively averaged evoked potentials (SAEPs) recorded from human vertex and occipital scalp electrodes upon acoustical step stimulation, are given and discussed. The resonance phenomena which we have observed in the cat brain are also demonstrated in humans by comparing the components of the single EPs with those of the spontaneous activity (EEG) just preceding the stimulus and by using the concept of amplification factor which we have recently introduced. Besides other types, special emphasis is given to the resonance phenomena in the alpha frequency range (alpha resonances). Various forms of alpha resonances are described and quantitatively demonstrated by using the data recorded during closed-eye and open-eye experiments on eight subjects. A strong resonance phenomenon is also noted in the 2–9 Hz frequency range.

In binocular fusion, pairs of left and right stimuli yielding the same brightness perception constitute an equibrightness curve in a coordinate system whose ordinate and abscissa correspond to the left and right stimulus strengths. A neural network model is presented to elucidate the characteristics of the curve. According to the model, Fechner's paradox is due to the threshold characteristics of the neuron. If the shapes or movements are radically different between the left and right stimuli, the retinal rivalry is caused. That is, only the left stimulus is perceived at one moment and the right stimulus at another moment. The period of left or right eye dominance alternates randomly from time to time. The distribution of the period is approximate to the gamma distribution. In order to account for this fact, a neural network model is proposed, which consists of a pair of neurons receiving inputs with stochastic fluctuations. The computer simulation was carried out with satisfactory results. The model of retinal rivalry is integrated with that of brightness perception.