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PubMed1997

Visual space distortion.

We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics, and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distored version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters causes distortion of the computed depth of the scene. The unified framework introduced here describes this distortion in computational terms. We characterize the space of distortions by its level sets, that is, we characterize the systematic distortion via a family of iso-distortion surfaces which describes the locus over which depths are distorted by some multiplicative factor. Given that humans' estimation of egomotion or estimation of the extrinsic parameters of the stereo apparatus is likely to be imprecise, the framework is used to explain a number of psychophysical experiments on the perception of depth from motion or stereo.

Cybernetics↗
PubMed1997

Use of the fractal dimension for the analysis of electroencephalographic time series.

Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out.

Algorithms↗
PubMed1997

Timing of neural commands: a model study with neuronal networks.

Networks constructed of biologically realistic model neurons (neuroids) were used to study how in a neural assembly using pulse (interval)-coded information slow rhythmical oscillations with possible mode transitions might occur and how the efferent commands might be structured and their phase-shifts created. The simulations show that slow oscillations (in the hertz range) can be derived from reverberatory spiking in relatively short closed loops (fewer than ten neuroids) with the inputs protected against disturbing afferent signals and the outputs coupled by convergence on a common neuroid. Slow oscillations can be modified by a tonic activity entering the network; this activity changes the transmission time in the coupled loops involved. The structuring of the regulatory commands (in the millisecond range) was achieved by simulation of sequential activity propagation in a non-ring neuronal assembly supervised by a tonic activity in a set of inputs. The tonic activity acted as an instructive signal influencing the pattern of the functional connectivity in such a way that a particular efferent command was generated by the instructed network.

Central Nervous System↗
PubMed1998

Tests of a linear model of visual-vestibular interaction using the technique of parameter estimation.

The goal of this study was to test whether a superposition model of smooth-pursuit and vestibuloocular reflex (VOR) eye movements could account for the stability of gaze that subjects show as they view a stationary target, during head rotations at frequencies that correspond to natural movements. Horizontal smooth-pursuit and the VOR were tested using sinusoidal stimuli with frequencies in the range 1.0-3.5 Hz. During head rotation, subjects viewed a stationary target either directly or through an optical device that required eye movements to be approximately twice the amplitude of head movements in order to maintain foveal vision of the target. The gain of compensatory eye movements during viewing through the optical device was generally greater than during direct viewing or during attempted fixation of the remembered target location in darkness. This suggests that visual factors influence the response, even at high frequencies of head rotation. During viewing through the optical device, the gain of compensatory eye movements declined as a function of the frequency of head rotation (P < 0.001) but, at any particular frequency, there was no correlation with peak head velocity 9P > 0.23), peak head acceleration (P > 0.22) or retinal slip speed (P > 0.22). The optimal values of parameters of smooth-pursuit and VOR components of a simple superposition model were estimated in the frequency domain, using the measured responses during head rotation, as each subject viewed the stationary target through the optical device. We then compared the model's prediction of smooth-pursuit gain and phase, at each frequency, with values obtained experimentally. Each subject's pursuit showed lower gain and greater phase lag than the model predicted. Smooth-pursuit performance did not improve significantly if the moving target was a 10 deg x 10 deg Amsler grid, or if sinusoidal oscillation of the target was superimposed on ramp motion. Further, subjects were still able to modulate the gain of compensatory eye movements during pseudo-random head perturbations, making improved predictor performance during visual-vestibular interactions unlikely. We conclude that the increase in gain of eye movements that compensate for head rotations when subjects view, rather than imagine, a stationary target cannot be adequately explained by superposition of VOR and smooth-pursuit signals. Instead, vision may affect VOR performance by determining the context of the behavior.

Adult↗
PubMed1998

Learning and stabilization of altruistic behaviors in multi-agent systems by reciprocity.

Optimization of performance in collective systems often requires altruism. The emergence and stabilization of altruistic behaviors are difficult to achieve because the agents incur a cost when behaving altruistically. In this paper, we propose a biologically inspired strategy to learn stable altruistic behaviors in artificial multi-agent systems, namely reciprocal altruism. This strategy in conjunction with learning capabilities make altruistic agents cooperate only between themselves, thus preventing their exploitation by selfish agents, if future benefits are greater than the current cost of altruistic acts. Our multi-agent system is made up of agents with a behavior-based architecture. Agents learn the most suitable cooperative strategy for different environments by means of a reinforcement learning algorithm. Each agent receives a reinforcement signal that only measures its individual performance. Simulation results show how the multi-agent system learns stable altruistic behaviors, so achieving optimal (or near-to-optimal) performances in unknown and changing environments.

Altruism↗
PubMed1998

A locally inhibited lateral neural network: on the fundamental features of a network consisting of neurons with a restricted range of interaction.

A network model that consists of neurons with a restricted range of interaction is presented. The neurons are connected mutually by inhibition weights. The inhibition of the whole network can be controlled by the range of interaction of a neuron. By this local inhibition mechanism, the present network can produce patterns with a small activity from input patterns with various large activities. Moreover, it is shown in simulation that the network has attractors for input patterns. The appearance of attractors is caused by the local interaction of neurons. Thus, we expect that the network not only works as a kind of filter, but also as a memory device for storing the produced patterns. In the present paper, the fundamental features and behavior of the network are studied by using a simple network structure and a simple rule of interaction of neurons. In particular, the relation between the interaction range of a neuron and the activity of input-output patterns is shown in simulation. Furthermore, the limit of the transformation and the size of basin are studied numerically.

Computer Simulation↗
PubMed1998

Quantification of emotion by nonlinear analysis of the chaotic dynamics of electroencephalograms during perception of 1/f music.

The goal of this study is to quantify and determine the way in which the emotional response to music is reflected in the electrical activities of the brain. When the power spectrum of sequences of musical notes is inversely proportional to the frequency on a log-log plot, we call it 1/f music. According to previous research, most listeners agree that 1/f music is much more pleasing than white (1/f0) or brown (1/f2) music. Based on these studies, we used nonlinear methods to investigate the chaotic dynamics of electroencephalograms (EEGs) elicited by computer-generated 1/f music, white music, and brown music. In this analysis, we used the correlation dimension and the largest Lyapunov exponent as measures of complexity and chaos. We developed a new method that is strikingly faster and more accurate than other algorithms for calculating the nonlinear invariant measures from limited noisy data. At the right temporal lobe, 1/f music elicited lower values of both the correlation dimension and the largest Lyapunov exponent than white or brown music. We observed that brains which feel more pleased show decreased chaotic electrophysiological behavior. By observing that the nonlinear invariant measures for the 1/f distribution of the rhythm with the melody kept constant are lower than those for the 1/f distribution of melody with the rhythm kept constant, we could conclude that the rhythm variations contribute much more to a pleasing response to music than the melody variations do. These results support the assumption that chaos plays an important role in brain function, especially emotion.

Auditory Perception↗
PubMed1998

An equivalent cable model for neuronal trees with active membrane.

A non-uniform equivalent cable model of membrane voltage changes in branching neuronal trees with active ion channels has been developed. A general branching condition is formulated, extending Rall's 3/2 power rule for passive dendritic trees so that non-uniform cable segments can be treated. The theoretical results support the use of the dendritic profile model of Clements and Redman. The theory is then applied to dendrites of different morphological type yielding qualitative different response behaviour.

Computer Simulation↗
PubMed1998

How to "hear" visual disparities: real-time stereoscopic spatial depth analysis using temporal resonance.

In a stereoscopic system, both eyes or cameras have a slightly different view. As a consequence, small variations between the projected images exist ('disparities') which are spatially evaluated in order to retrieve depth information (Sanger 1988; Fleet et al. 1991). A strong similarity exists between the analysis of visual disparities and the determination of the azimuth of a sound source (Wagner and Frost 1993). The direction of the sound is thereby determined from the temporal delay between the left and right ear signals (Konishi and Sullivan 1986). Similarly, here we transpose the spatially defined problem of disparity analysis into the temporal domain and utilize two resonators implemented in the form of causal (electronic) filters to determine the disparity as local temporal phase differences between the left and right filter responses. This approach permits real-time analysis and can be solved analytically for a step function contrast change, which is an important case in all real-world applications. The proposed theoretical framework for spatial depth retrieval directly utilizes a temporal algorithm borrowed from auditory signal analysis. Thus, the suggested similarity between the visual and the auditory system in the brain (Wagner and Frost 1993) finds its analogy here at the algorithmical level. We will compare the results from the temporal resonance algorithm with those obtained from several other techniques like cross-correlation or spatial phase-based disparity estimation showing that the novel algorithm achieves performances similar to the 'classical' approaches using much lower computational resources.

Algorithms↗
PubMed1998

A mathematical model of adaptive behavior in quadruped locomotion.

Locomotion involves repetitive movements and is often executed unconsciously and automatically. In order to achieve smooth locomotion, the coordination of the rhythms of all physical parts is important. Neurophysiological studies have related that basic rhythms are produced in the spinal network called, the central pattern generator (CPG), where some neural oscillators interact to self-organize coordinated rhythms. We present a model of the adaptation of locomotion patterns to a variable environment, and attempt to elucidate how the dynamics of locomotion pattern generation are adjusted by the environmental changes. Recent experimental results indicate that decerebrate cats have the ability to learn new gait patterns in a changed environment. In those experiments, a decerebrate cat was set on a treadmill consisting of three moving belts. This treadmill provides a periodic perturbation to each limb through variation of the speed of each belt. When the belt for the left forelimb is quickened, the decerebrate cat initially loses interlimb coordination and stability, but gradually recovers them and finally walks with a new gait. Based on the above biological facts, we propose a CPG model whose rhythmic pattern adapts to periodic perturbation from the variable environment. First, we design the oscillator interactions to generate a desired rhythmic pattern. In our model, oscillator interactions are regarded as the forces that generate the desired motion pattern. If the desired pattern has already been realized, then the interactions are equal to zero. However, this rhythmic pattern is not reproducible when there is an environmental change. Also, if we do not adjust the rhythmic dynamics, the oscillator interactions will not be zero. Therefore, in our adaptation rule, we adjust the memorized rhythmic pattern so as to minimize the oscillator interactions. This rule can describe the adaptive behavior of decerebrate cats well. Finally, we propose a mathematical framework of an adaptation in rhythmic motion. Our framework consists of three types of dynamics: environmental, rhythmic motion, and adaptation dynamics. We conclude that the time scale of adaptation dynamics should be much larger than that of rhythmic motion dynamics, and the repetition of rhythmic motions in a stable environment is important for the convergence of adaptation.

Adaptation, Physiological↗
PubMed1998

Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized electromyogram.

We investigate the relationship between the extensor electromyogram (EMG) and tremor times series in physiological hand tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and the effects of observational noise. We calculate the theoretical phase spectrum for a second-order linear stochastic process and compare the results to measured tremor data recorded from subjects who did not show a synchronized EMG activity in the corresponding extensor muscle. The results show that physiological tremor is well described by the proposed model and that the measured EMG represents a Newtonian force by which the muscle acts on the hand.

Biomechanical Phenomena↗
PubMed1998

Cross-spectral analysis of physiological tremor and muscle activity. II. Application to synchronized electromyogram.

We investigated the relationship between synchronized muscle activity and tremor time series in (enhanced) physiological tremor by cross-spectral analysis. Special attention was directed to the phase spectrum and its potential to clarify the contribution of reflex mechanisms to physiological tremor. The phase spectra are investigated assuming that the electromyogram (EMG) synchronization was caused by a reflex or a central oscillator. Comparing these results to phase spectra of measured data, we found a significant contribution of reflexes. But reflexes only modify existing peaks in the power spectrum. The main agents of physiological tremor are an efferent pace and the resonant behavior of the biomechanical system.

Biomechanical Phenomena↗
PubMed1998

Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model.

We consider how the output of the perfect integrate-and-fire (I&F) model of a single neuron is affected by the properties of the input, first of all by the distribution of afferent excitatory and inhibitory postsynaptic potential (EPSP, IPSP) inter-arrival times, discriminating particularly between short- and long-tailed forms, and by the degree of balance between excitation and inhibition (as measured by the ratio, r, between the numbers of inhibitory and excitatory inputs). We find that the coefficient of variation (CV; standard deviation divided by mean) of efferent interspike interval (ISI) is an increasing function of the length of the tail of the distribution of EPSP inter-arrival times and the ratio r. There is a range of values of r in which the CV of output ISIs is between 0.5 and 1. Too tight a balance between EPSPs and IPSPs will cause the model to produce a CV outside the interval considered to correspond to the physiological range. Going to the extreme, an exact balance between EPSPs and IPSPs as considered in [24] ensures a long-tailed ISI output distribution for which the moments such as mean and variance cannot be defined. In this case it is meaningless to consider quantities like output jitter, CV, etc. of the efferent ISIs. The longer the tail of the input inter-arrival time distribution, the less is the requirement for balance between EPSPs and IPSPs in order to evoke output spike trains with a CV between 0.5 and 1. For a given short-tailed input distribution, the range of values of r in which the CV of efferent ISIs is between 0.5 and 1 is almost completely inside the range in which output jitter (standard deviation of efferent ISI) is greater than input jitter. Only when the CV is smaller than 0.5 or the input distribution is a long-tailed one is output less than input jitter [21]. The I&F model tends to enlarge low input jitter and reduce high input jitter. We also provide a novel theoretical framework, based upon extreme value theory in statistics, for estimating output jitter, CV and mean firing time.

Action Potentials↗
PubMed1998

A neural network model for the emergence of grating cells.

A correlation-based learning (CBL) neural network model is proposed, which simulates the emergence of grating cells as well as some of their response characteristics to periodic pattern stimuli. These cells, found in areas V1 and V2 of the visual cortex of monkeys, respond vigorously and exclusively to bar gratings of a preferred orientation and periodicity. Their non-linear behaviour differentiates grating cells from other orientation-selective cells, which show linear spatial frequency filtering.

Animals↗
PubMed1998

Neural network model of on-off units in the fly visual system: simulations of dynamic behavior.

We analyze the dynamic properties of a neural network model for on-off spiking neurons recorded in the first optic chiasm of the fly visual system. The model consists of two parallel pathways and three sequential processing stages. The first stage models photoreceptors. At the second stage, the signal is segregated into on- and off-pathways. These pathways are proposed to correspond to two populations of amacrine cells. At the third stage, the on- and off-pathways converge to on-off neurons. Furthermore, according to the model, on-off neurons interact via recurrent connections. This stage is proposed to correspond to lamina L4 neurons. In response to luminance increments and decrements, the model exhibits a three-component response and suggests pathways for each of the components. When stimulated by a train of pulses, the model exhibits fast adaptation for frequencies higher than about 5 Hz. Furthermore, adaptation to on- and off-pulses occurs independently. When the frequency of stimulation is reduced, the unit recovers rapidly from its adapted state. The temporal modulation transfer function has its peak around 7 Hz. The phase characteristics show a phase lead for low temporal frequencies changing to a phase lag for high frequencies. These model predictions are compared with data from Jansonius and van Hateren (1991).

Adaptation, Physiological↗
PubMed1998

Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator.

The neuronal network underlying lamprey swimming has stimulated extensive modelling on different levels of abstraction. The lamprey swims with a burst frequency ranging from 0.3 to 8-10 Hz with a rostrocaudal lag between bursts in each segment along the spinal cord. The swimming motor pattern is characterized by a burst proportion that is independent of burst frequency and lasts around 30%-40% of the cycle duration. This also applies in preparations in which the reciprocal inhibition in the spinal cord between the left and right side is blocked. A network of coupled excitatory neurons producing hemisegmental oscillations may form the basis of the lamprey central pattern generator (CPG). Here we explored how such networks, in principle, could produce a large frequency range with a constant burst proportion. The computer simulations of the lamprey CPG use simplified, graded output units that could represent populations of neurons and that exhibit adaptation. We investigated the effect of an active modulation of the degree of adaptation of the CPG units to accomplish a constant burst proportion over the whole frequency range when, in addition, each hemisegment is assumed to be self-oscillatory. The degree of adaptation is increased with the degree of stimulation of the network. This will make the bursts terminate earlier at higher burst rates, allowing for a constant burst proportion. Without modulated adaptation the network operates in a limited range of swimming frequencies due to a progressive increase of burst duration with increasing background stimulation. By introducing a modulation of the adaptation, a broad burst frequency range can be produced. The reciprocal inhibition is thus not the primary burst terminating factor, as in many CPG models, and it is mainly responsible for producing alternation between the left and right sides. The results are compared with the Morris-Lecar oscillator model with parameters set to produce a type A and type B oscillator, in which the burst durations stay constant or increase, respectively, when the background stimulation is increased. Here as well, burst duration can be controlled by modulation of the slow variable in a similar way as above. When oscillatory hemisegmental networks are coupled together in a chain a phase lag is produced. The production of a phase lag in chains of such oscillators is compared with chains of Morris-Lecar relaxation oscillators. Models relating to the intact versus isolated spinal cord preparation are discussed, as well as the role of descending inhibition.

Adaptation, Physiological↗
PubMed1998

Dynamics extraction in multivariate biomedical time series.

A nonlinear analysis of the underlying dynamics of a biomedical time series is proposed by means of a multi-dimensional testing of nonlinear Markovian hypotheses in the observed time series. The observed dynamics of the original N-dimensional biomedical time series is tested against a hierarchy of null hypotheses corresponding to N-dimensional nonlinear Markov processes of increasing order, whose conditional probability densities are estimated using neural networks. For each of the N time series, a measure based on higher order cumulants quantifies the independence between the past of the N-dimensional time series, and its value r steps ahead. This cumulant-based measure is used as a discriminating statistic for testing the null hypotheses. Experiments performed on artificial and real world examples, including autoregressive models, noisy chaos, and nonchaotic nonlinear processes, show the effectiveness of the proposed approach in modeling multivariate systems, predicting multidimensional time series, and characterizing the structure of biological systems. Electroencephalogram (EEG) time series and heart rate variability trends are tested as biomedical signal examples.

Aged↗
PubMed1998

Sensitivity analysis of a model of mammalian neural membrane.

The sensitivity of the strength-duration (S-D) relationship to changes in the parameters describing the sodium channel of mammalian neuronal membrane was determined by computer simulation. A space-clamped patch of neuronal membrane was modeled by a parallel nonlinear sodium conductance, linear leakage conductance, and membrane capacitance. Each parameter that governs the activation (m) and inactivation (h) variables of the sodium channel was varied from -50% to +50% of its default value, and for each variation a S-D relationship was generated. Individual changes in six of the eleven parameters (alpha mA, alpha mD, alpha hA, beta mA, beta mB, and beta hB) generated substantial changes in the rheobase current and chronaxie time (Tch) of the model. Changing the parameter values individually did not correct for the model's failure to generate excitation after the release from a long duration hyperpolarization (anode break excitation). Scaling a combination of five parameters (alpha mA, alpha mB, alpha hA, beta mA, and beta hB) by an equal amount produced a model that generated anode break excitation and increased Tch, but also decreased the amplitude of the action potential. To reproduce the amplitude of the action potential, the maximum sodium conductance and sodium Nernst potential were increased. These modifications generated a model that had S-D properties closer to experimental results, could produce anode break excitation, and reproduced the action potential amplitude.

Action Potentials↗