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Crayfish swimmeret system shows rhythmic, coordinated behavior when the command fibers are stimulated chronically by electrical pulses, and the oscillating frequency becomes faster with increasing stimulus frequency. This behavior is organized by the distributed neural oscillators in the abdominal ganglia. We investigated the dynamics of the neural oscillators which are controlled by command fibers. Phase resetting experiment technique was used for this purpose; a temporary cessation of commanding pulses, which was regarded as suppressive perturbation for the neural oscillator, was applied to the chronically stimulated oscillator, and phase transition curves (PTCs) were measured. For the short cessation of command pulses, type 1 PTCs were obtained. With increasing cessation length, the PTC shifted downward, and finally changed into type 0. We also measured PTCs for temporarily increased stimulus frequency, which was an excitatory perturbation for the neural oscillator and increased the frequency of the oscillation transiently. For the short excitatory perturbation, the PTCs were also type 1 and shifted upward. PTCs changed their shapes from type 1 into type 0, as increasing the perturbation length. These shapes of the PTCs contain important information about the properties of the neural oscillator. Analyzing these PTCs, we present a phase plane diagram which describes the character of the command control of the neural oscillator.

The processing of visual information for collision avoidance has been investigated at the biophysical level in several model systems. In grasshoppers, the (so-called) $$\eta $$ model captures reasonably well the visual processing performed by an identified neuron called the lobular giant movement detector as it tracks approaching objects. Similar phenomenological models have been used to describe either the firing rate or the membrane potential of neurons responsible for visually guided collision avoidance in other animals. Specifically, in goldfish, the $$\kappa $$ model has been proposed to describe the Mauthner cell, an identified neuron involved in startle escape responses. In the vinegar fly, a third model was developed for the giant fiber neuron, which triggers last resort escapes immediately before an impending collision. One key property of these models is their prediction that peak neuronal responses occur at a fixed delay after the simulated approaching object reaches a threshold angular size on the retina. This prediction is valid for simulated objects approaching at a constant speed. We tested whether it remains valid when approaching objects accelerate. After characterizing and comparing the models’ responses to accelerating and constant speed stimuli, we find that the prediction holds true for the $$\kappa $$ and the giant fiber model, but not for the $$\eta $$ model. These results suggest that acceleration in the approach trajectory of an object may help distinguish and further constrain the neuronal computations required for collision avoidance in grasshoppers, fish and vinegar flies.

We describe a method for the characterization of electroencephalographic (EEG) signals based on a model which features nonlinear feedback. The characteristic EEG ‘fingerprints’ obtained through this approach display the time-course of nonlinear interactions, rather than aspects susceptible to standard spectral analysis. Fingerprints of seizure discharges in six patients (five with typical absence seizures, one with complex partial seizures) revealed significant nonlinear interactions. The timing and pattern of these interactions correlated closely with the seizure type. Nonlinear autoregressive (NLAR) analysis is compared with other nonlinear dynamical measures that have been applied to the EEG.

A special class of stochastic processes with optimization (SPO) is considered and their long-run behaviour is investigated. At each step of the process {X h} h ≧0 (where X h is a discrete random variable) a loss function expressing the distance with respect to the moments in the previous step is minimized. The transformation leading from a certain probability distribution F k (step k) to the next probability distribution F k+1 (step k+1) is accomplished by means of an optimization operator, or simply optimator, that is, a nonlinear operator performing an optimization. The constraints involved by the optimator are typically regarded as a message conveying the information needed for the stepwise evolution of the system. In other words, the behaviour of the system is expressed by an ordered set of events (actions) to be realized with given probabilities and minimum losses, while the message is viewed as a set of constraints providing an inferior bound for that probabilities, hence, ensuring that the required actions are performed. Besides, in order to account for some relaxation phenomena taking place in higher systems each active step (active optimator) is followed by a relaxation step (recovery optimator). Under these conditions it is shown that repeated presentation of a stimulus pattern leads to a convergent process, so that the action is finally performed with minimum minimorum losses. This reveals some fundamental relations between optimization and learning in higher systems, highlighting also the key role of the relaxation processes. Further the behaviour of the system is described in terms of a special class of Non-Markovian processes termed stochastic processes with optimization and relaxation (SPORs). It is shown that two basic subclasses of SPORs exist, namely the monoergodic and the biergodic SPORs. Sufficient conditions for both monoergodicity and biergodicity are given. Finally, a particular feature of the optimators, the so-called nonredundancy is shown to be relevant with respect to the influence of the past on the current evolution of the system.

The myoskeletal inverse dynamics problem and the myocybernetic control inverse problem were investigated with respect to their ill-posedness. The first problem consists of finding from observed experimental motion and reaction force data the resultant muscle moments that generated the observed motion, while the second aims at finding the corresponding neural controls. It is shown that both problems belong to the class of incorrectly posed (ill-posed) problems that, by definition, do not possess unique solutions. To illustrate this point, results of a forward dynamics simulation of a comprehensive neuromusculoskeletal model of the human body are presented. These results demonstrate that fairly chaotic neural control perturbations have very little influence on the resulting motion trajectory, at least in the present example. While a regularization procedure may be applied to solve successfully the myoskeletal inverse dynamics problem, the myocybernetic control inverse problem is unsolvable. The latter fact has the important implication that, based on the somatosensory inputs it receives, the pars intermedia in the cerebellum is not able to control individual motor unit stimulation rates and recruitment patterns but only whole muscles by means of a single compound signal. The latter signal is identified as the “common drive.” Presumably at the spinal level, special neural circuits are used to decompose the common drive signal into motor unit recruitment patterns and stimulation rates that are specific for a given mode of contraction and probably obey certain optimality principles.

This manuscript proposes a method to directly transfer the features of horse walking, trotting, and galloping to a quadruped robot, with the aim of creating a much more natural (horse-like) locomotion profile. A principal component analysis on horse joint trajectories shows that walk, trot, and gallop can be described by a set of four kinematic Motion Primitives (kMPs). These kMPs are used to generate valid, stable gaits that are tested on a compliant quadruped robot. Tests on the effects of gait frequency scaling as follows: results indicate a speed optimal walking frequency around 3.4 Hz, and an optimal trotting frequency around 4 Hz. Following, a criterion to synthesize gait transitions is proposed, and the walk/trot transitions are successfully tested on the robot. The performance of the robot when the transitions are scaled in frequency is evaluated by means of roll and pitch angle phase plots.

This study deals with neurophysiologically based models simulating electrical brain activity (i.e., the electroencephalogram or EEG, and evoked potentials or EPs). A previously developed lumped-parameter model of a single cortical column was implemented using a more accurate computational procedure. Anatomically acceptable values for the various model parameters were determined, and a multi-dimensional exploration of the model parameter-space was conducted. It was found that the model could produce a large variety of EEG-like waveforms and rhythms. Coupling two models, with delays in the interconnections to simulate the synaptic connections within and between cortical areas, made it possible to replicate the spatial distribution of alpha and beta activity. EPs were simulated by presenting pulses to the input of the coupled models. In general, the responses were more realistic than those produced using a single model. Our simulations also suggest that the scalp-recorded EP is at least partially due to a phase reordering of the ongoing activity.

Bees on a horizontal comb can orient their dances by a field of polarized light in the zenith even when the degree of polarization of this light field is modulated from 0 to 100%, at frequencies between 0.05 and 25 Hz, with the direction of polarization and the intensity kept constant. The result suggests that bees use a process of polarized light evaluation which probes simultaneously with three or more differently oriented analyser channels. It would follow that, in this experimental situation, time is not a component of sampling.