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PubMed1990

Structural classification of multi-input nonlinear systems.

We present new structural classification and parameter estimation results that are applicable to multi-input nonlinear systems. The mathematical relationships between the self- and cross-(Volterra and Wiener) kernels are derived for a basic two-input nonlinear structure. These results are then used to develop classification methods for more complicated two-input structures. Algorithms for estimating the parameters (linear and nonlinear subsystems) of these structures are also presented.

Cybernetics↗
PubMed1990

Some conjectures on the design of a rod outer segment.

Photoreceptor diameter and spacing have been extensively analyzed with respect to diffraction, wave-guiding and other phenomena and have been found to be consistent with optimal design criteria. Photoreceptor length, on the other hand, has received but little attention. It is proposed here that the outer segment length of rods is optimal with respect to the competing demands of maximal photon absorption and minimal noise. This is borne out by our calculations based on the experimental data.

Animals↗
PubMed1990

Postural maintenance during movement: simulations of a two joint model.

Voluntary movements of the upper body are accompanied by anticipatory postural adjustments to the lower body in a standing subject. The long-standing hypothesis is that these anticipatory adjustments serve to counteract the perturbation to the body's center of gravity caused by the voluntary arm movement. This paper presents model simulations investigating the possible roles of anticipatory postural activity that accompanies a rapid, upward arm swing. The model incorporates two (idealized) antagonistic muscle pairs controlling the movements of a double-joint system, with a "shoulder joint" between the arm and stiff body links, and an "ankle joint" between the stiff body-leg segment and the ground. Each muscle is represented by a nonlinear viscoelastic element and also includes proprioceptive feedback. Four inputs to the model define the motor control signals for muscle force generation in both the arm and the postural muscle pairs. The neurological component of the model describes consequences of alternate strategies for cocontractions, stretch reflex activity, and anticipatory and synchronous postural activities (or combinations thereof). Simulations with this model show that: (1) none of the postural maintenance schemes considered in these simulations (including varying anticipation) could suppress the initial backward thrust on the body link; (2) the more important destabilizing perturbation is a subsequent forward sway that, left uncountered by postural activity, would eventually leave the body to fall flat on its face; and (3) anticipatory silencing of the postural extensor followed by a brief period of extensor activation (descending control) and synchronous reflex activity (feedback control) appears to be the most likely postural stabilizing strategy that inhibits the continuous forward sway and is consistent with the experimental evidence.

Arm↗
PubMed1992

A new algorithm for the identification of multiple input Wiener systems.

Multiple-input Wiener systems consist of two or more linear dynamic elements, whose outputs are transformed by a multiple-input static non-linearity. Korenberg (1985) demonstrated that the linear elements of these systems can be estimated using either a first order input-output cross-covariance or a slice of the second, or higher, order input-output cross-covariance function. Korenberg's work used a multiple input LNL structure, in which the output of the static nonlinearity was then filtered by a linear dynamic system. In this paper we show that by restricting our study to the slightly simpler Wiener structure, it is possible to improve the linear subsystem estimates obtained from the measured cross-covariance functions. Three algorithms, which taken together can identify any multiple-input Wiener system, have been developed. We present the theory underlying these algorithms and detail their implementation. Simulation results are then presented which demonstrate that the algorithms are robust in the presence of output noise, and provide good estimates of the system dynamics under a wide set of conditions.

Algorithms↗
PubMed1990

Simulation study on dynamics transition in neuronal activity during sleep cycle by using asynchronous and symmetry neural network model.

We have found that single neuronal activities in different regions in the brain commonly exhibit the distinct dynamics transition during sleep-waking cycle in cats. Especially, power spectral densities of single neuronal activities change their profiles from the white to the 1/f along with sleep cycle from slow wave sleep (SWS) to paradoxical sleep (PS). Each region has different neural network structure and physiological function. This suggests a globally working mechanism may be underlying the dynamics transition we concern. Pharmacological studies have shown that a change in a wide-spread serotonergic input to these regions possibly causes the neuronal dynamics transition during sleep cycle. In this paper, based on these experimental results, an asynchronous and symmetry neural network model including inhibitory input, which represents the role of the serotonergic system, is utilized to examine the reality of our idea that the inhibitory input level varying during sleep cycle induce that transition. Simulation results show that the globally applied inhibitory input can control the dynamics of single neuronal state evolution in the artificial neural network: 1/f-like power spectral density profiles result under weak inhibition, which possibly corresponds to PS, and white profiles under strong inhibition, which possibly corresponds to SWS. An asynchronous neural network is known to change its state according to its energy function. The geometrical structure of network energy function is thought to vary along with the change in inhibitory level, which is expected to cause the dynamics transition of neuronal state evolution in the network model. These simulation results support the possibility that the serotonergic system is essential for the dynamics transition of single neuronal activities during sleep cycle.

Animals↗
PubMed1990

Spectral analysis on fluctuation of heart period in paralyzed, vagotomized, and unanesthetized decerebrate cats.

Spectral analysis was performed on the heart period fluctuation in vagotomized, paralyzed, and unanesthetized decerebrate cats. The heart period was measured as the time interval between successive R waves of the electrocardiograms. When end-tidal PCO2 was set at the same level as that before immobilization, the power spectral density plot of the heart period fluctuation showed several distinct peaks: one peak corresponded to the frequency of the artificial ventilator and the others to its harmonics. In addition, the spectral density plot had another peak centered at the intrinsic respiratory frequency evaluated by recording efferent phrenic neural discharges. The amplitude of these spectral peaks tended to become greater when the end-tidal PCO2 was increased by adding CO2 to the input gas. Our results, therefore, provide evidence that the heart period is modulated not only by the artificial ventilation rhythm but also by the centrally generated respiratory rhythm, and suggested that the strength of such central interactions between cardiac and respiratory rhythms varies depending on the end-tidal PCO2 level.

Animals↗
PubMed1990

A dynamic theory of coordination of discrete movement.

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.

Cybernetics↗
PubMed1990

The study of locomotion by finite state models.

A methodology to derive finite state models of legged locomotion is outlined. Background data for model derivation are joint angle functions and gait diagrams. The method is used to describe the walking of the cat in terms of an abstract automaton. The main features of finite state descriptions of legged locomotion are described. Such models are presenting locomotion invariants of a species in explicit form. It is emphasized that finite state models provide insight into structural features of motor control organization such as decomposition into subsystems, interaction between centralized and decentralized control, and the role of control levels. The finite state model of locomotion can be helpful in suggesting experiments pertinent to the study of motor control and interpretation of experimental results.

Animals↗
PubMed1990

Synaptic rectification model equivalent to the correlation-type movement detector.

Neural models which are equivalent to the correlation-type movement detector are described. The models involve contrast-coding channels which comprise bandpass linear filters followed by synaptic retifiers. Linear, one-directional lateral interactions are assumed among the contrast-coding channels. Synaptic rectifiers convert linear spatial interaction into a multiplication-like (quadratic) interaction, which is the core of the correlation-type movement detector. One of the neural models (E-I model) well approximates the correlation model in both time-averaged and dynamic (instantaneous) responses. Possible applicability of the model to movement detection by insects is discussed.

Animals↗
PubMed1990

Creative dynamics approach to neural intelligence.

The thrust of this paper is to introduce and discuss a substantially new type of dynamical system for modelling biological behavior. The approach was motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks-their rigid behavior compared with even simplest biological systems. This approach exploits a novel paradigm in nonlinear dynamics based upon the concept of terminal attractors and repellers. It was demonstrated that non-Lipschitzian dynamics based upon the failure of Lipschitz condition exhibits a new qualitative effect--a multi-choice response to periodic external excitations. Based upon this property, a substantially new class of dynamical systems--the unpredictable systems--was introduced and analyzed. These systems are represented in the form of coupled activation and learning dynamical equations whose ability to be spontaneously activated is based upon two pathological characteristics. Firstly, such systems have zero Jacobian. As a result of that, they have an infinite number of equilibrium points which occupy curves, surfaces or hypersurfaces. Secondly, at all these equilibrium points, the Lipschitz conditions fails, so the equilibrium points become terminal attractors or repellers depending upon the sign of the periodic excitation. Both of these pathological characteristics result in multi-choice response of unpredictable dynamical systems. It has been shown that the unpredictable systems can be controlled by sign strings which uniquely define the system behaviors by specifying the direction of the motions in the critical points. By changing the combinations of signs in the code strings the system can reproduce any prescribed behavior to a prescribed accuracy.(ABSTRACT TRUNCATED AT 250 WORDS)

Artificial Intelligence↗
PubMed1990

Population coding of stimulus orientation by striate cortical cells.

I have examined the performance of a population coding model of visual orientation discrimination, similar to the population coding models proposed for the coding of limb movements. The orientation of the stimulus is not represented by a single unit but by an ensemble of broadly tuned units in a distributed way. Each unit is represented by a vector whose magnitude and direction correspond to the response magnitude and preferred orientation of the unit, respectively. The orientation of the population vector, i.e. the vector sum of the ensemble of units, is the signalled orientation on a particular trial. The accuracy of this population vector orientation coding was determined as a function of a number of parameters by computer simulation. I have shown that even with broadly orientation tuned units possessing considerable response variance, the accuracy of the orientation of the population vector can be as good as behaviorally measured just noticeable differences in orientation. The accuracy of the population code is shown to depend upon the number of units, the average response strength, the orientation band-width, response variability and the response covariance. The results of these simulations were also compared to predictions derived from psychophysical studies of orientation discrimination.

Animals↗
PubMed1990

A model of the mechanisms of long-term potentiation in the hippocampus.

Long-Term Potentiation (LTP) in the hippocampus has been considered to be a phenomenon closely related to learning and memory in the brain. In this paper, an integrated model of LTP is constructed based on hypotheses about both the mechanism of LTP induction and that of LTP maintenance, that is, the NMDA-receptor channel, protein phosphorylation and protein turnover. The validity of the model is discussed based on the results of computer simulations.

Animals↗
PubMed1990

Applicability of quadratic and threshold models to motion discrimination in the rabbit retina.

Computational and behavioral studies suggest that visual motion discrimination is based on quadratic nonlinearities. This raises the question of whether the behavior of motion sensitive neurons early in the visual system is actually quadratic. Theoretical studies show that mechanisms proposed for retinal directional selectivity do not behave quadratically at high stimulus contrast. However, for low contrast stimuli, models for these mechanisms may be grouped into three categories: purely quadratic, quadratic accompanied by a rectification, and models mediated by a high level threshold. We discriminated between these alternatives by analyzing the extracellular responses of ON-OFF directionally selective ganglion cells of the rabbit retina to drifting periodic gratings. The data show that purely-quadratic or high-threshold systems do not account for the behavior of these cells. However, their behavior is consistent with a rectified-quadratic model.

Animals↗
PubMed1990

A sensitive estimator for crosscorrelograms.

The best established method for finding interactions between extracellularly recorded neurons is the crosscorrelation technique. The method is simple and useful, but it has some drawbacks. One of them is its limited sensitivity to weak interactions, which are common in the mammalian cerebral cortex. In the present paper a new method for the estimation of interaction strength is presented. This method is based on the intensity representation of point processes, and provides an optimal estimator for the intensity of the postsynaptic spike train. The estimator is complicated to use, but it can be approximated by a simple estimator, similar to ordinary measures of synaptic efficacy like the area under the crosscorrelogram peak. Simulation results, showing the advantage of the new estimator over the commonly used efficacy estimators and some measure of its robustness to deviations from model assumptions, are presented. Finally, application of the estimator to the analysis of simultaneous recordings of physiological single units is demonstrated.

Animals↗
PubMed1990

Effects of paranodal potassium permeability on repetitive activity of mammalian myelinated nerve fiber models.

Almost all potassium channels within mammalian myelinated nerve fibers are covered by the myelin sheath and their majority is concentrated in a small paranodal region. In order to investigate effects of this paranodal potassium permeability on nerve fiber behavior via a simulation approach, a myelinated fiber model is required that treats myelin sheath and internodal axolemma as separate entities. Such a fiber description was developed by Blight (1985) and his model was used to investigate the effects paranodal potassium channels have on the ability of maintaining repetitive firing in response to a constant current injected into the fiber. It was found that increasing the potassium channel density at the paranode from low to moderate values widened the range of injected currents with a repetitive response. This promotion of repetitive activity by the introduction of additional potassium channels occurred up to an "optimal" value beyond which a further increase in paranodal potassium permeability narrowed the range of currents with a repetitive response. Finally, if a certain limit in paranodal potassium channel density was exceeded, repetitive activity was abolished completely. These results were obtained regardless of the assumptions about the electrical resistance of the myelin sheath. On the other hand, in the absence of potassium channels repetitive firing could be observed only when a high resistance myelin sheath was assumed, whereas a nerve fiber model with electrical properties inferred from intracellular recordings needed at least some potassium channels within the paranodal region for repetitive firing in response to an injected current.

Animals↗
PubMed1990

A model for neuronal oscillations in the visual cortex. 1. Mean-field theory and derivation of the phase equations.

We study a neural network consisting of model neurons whose efferent synapses are either excitatory or inhibitory. They are densely interconnected on a local scale, but only sparsely on a larger scale. The local clusters are described by the mean activities of excitatory and inhibitory neurons. The equations for these activities define a neuronal oscillator, which can be switched between an active and a passive state by an external input. Investigating the coupling of two of these oscillators we found their coupling behaviour to be activity-dependent. They are tightly coupled and almost synchronized if both oscillators are active, but weakly coupled if one or both oscillators are passive. This activity-dependent coupling is independent of the underlying connectivities, which are fixed. Finally, for coupled active oscillators we derive a simplified description by disregarding the amplitudes of the oscillators and working with their phases. We use this simplified description in a compagnion article to model the oscillations in the visual cortex.

Animals↗
PubMed1990

A model for neuronal oscillations in the visual cortex. 2. Phase description of the feature dependent synchronization.

In a previous paper we have shown, that it is possible to model the oscillations observed in an orientation specific column in the visual cortex by coupling excitatory and inhibitory subpopulations of neurons which compose the column, and that these oscillations can be described by the phases of the corresponding limit cycle oscillators. By coupling different columns via long but finite range sparse interactions, we generate in the phase description stimulus dependent multiplicative couplings which explain experimentally observed synchronization effects.

Animals↗
PubMed1995

A model of the neuro-musculo-skeletal system for human locomotion. I. Emergence of basic gait.

The generation of human locomotion was examined by linking computational neuroscience with biomechanics from the perspective of nonlinear dynamical theory. We constructed a model of human locomotion, which includes a musculo-skeletal system with 8 segments and 20 muscles, a neural rhythm generator composed of 7 pairs of neural oscillators, and mechanisms for processing and transporting sensory and motor signals. Using a computer simulation, we found that locomotion emerged as a stable limit cycle that was generated by the global entrainment between the musculo-skeletal system, the neural system, and the environment. Moreover, the walking movements of the model could be compared quantitatively with those of experimental studies in humans.

Biomechanical Phenomena↗