An axisymmetric meniscus converges particles for microscopy.

Capillary rise on a tapered cylindrical rod creates a static axisymmetric meniscus that quantitatively attracts buoyant particles into a single microscopic field of view, providing a new method for small particle microscopy. This approach simplifies the visualization of micrometre-sized particles, such as pollen and parasite eggs, and has potential utility in remote location monitoring and clinical diagnosis.

An upper-body can improve the stability and efficiency of passive dynamic walking.

The compass-gait walker proposed by McGeer can walk down a shallow slope with a self-stabilizing gait that requires no actuation or control. However, as the slope goes to zero so does the walking speed, and dynamic gait stability is only possible over a very narrow range of slopes. Gomes and Ruina have results demonstrating that by adding a torso to the compass-gait walker, it can walk passively on level-ground with a non-infinitesimal constant average speed. However, the gait involves exaggerated joint movements, and for energetic reasons horizontal passive dynamic walking cannot be stable. We show in this research that in addition to collision-free walking, adding a torso improves stability and walking speed when walking downhill. Furthermore, adding arms to the torso results in a collision-free periodic gait with natural-looking torso and limb movements. Overall, in contrast to the suggestions that active control may be needed to balance an upper-body on legs, it turns out that the upper and lower bodies can be integrated to improve the stability, efficiency and speed of a passive dynamic walker.

Evolution of the cerebellum as a neuronal machine for Bayesian state estimation.

The cerebellum evolved in association with the electric sense and vestibular sense of the earliest vertebrates. Accurate information provided by these sensory systems would have been essential for precise control of orienting behavior in predation. A simple model shows that individual spikes in electrosensory primary afferent neurons can be interpreted as measurements of prey location. Using this result, I construct a computational neural model in which the spatial distribution of spikes in a secondary electrosensory map forms a Monte Carlo approximation to the Bayesian posterior distribution of prey locations given the sense data. The neural circuit that emerges naturally to perform this task resembles the cerebellar-like hindbrain electrosensory filtering circuitry of sharks and other electrosensory vertebrates. The optimal filtering mechanism can be extended to handle dynamical targets observed from a dynamical platform; that is, to construct an optimal dynamical state estimator using spiking neurons. This may provide a generic model of cerebellar computation. Vertebrate motion-sensing neurons have specific fractional-order dynamical characteristics that allow Bayesian state estimators to be implemented elegantly and efficiently, using simple operations with asynchronous pulses, i.e. spikes. The computational neural models described in this paper represent a novel kind of particle filter, using spikes as particles. The models are specific and make testable predictions about computational mechanisms in cerebellar circuitry, while providing a plausible explanation of cerebellar contributions to aspects of motor control, perception and cognition.

Optimal firing rate estimation.

We define a measure for evaluating the quality of a predictive model of the behavior of a spiking neuron. This measure, information gain per spike (Is), indicates how much more information is provided by the model than if the prediction were made by specifying the neuron's average firing rate over the same time period. We apply a maximum Is criterion to optimize the performance of Gaussian smoothing filters for estimating neural firing rates. With data from bullfrog vestibular semicircular canal neurons and data from simulated integrate-and-fire neurons, the optimal bandwidth for firing rate estimation is typically similar to the average firing rate. Precise timing and average rate models are limiting cases that perform poorly. We estimate that bullfrog semicircular canal sensory neurons transmit in the order of 1 bit of stimulus-related information per spike.

State-space receptive fields of semicircular canal afferent neurons in the bullfrog.

Receptive fields are commonly used to describe spatial characteristics of sensory neuron responses. They can be extended to characterize temporal or dynamical aspects by mapping neural responses in dynamical state spaces. The state-space receptive field of a neuron is the probability distribution of the dynamical state of the stimulus-generating system conditioned upon the occurrence of a spike. We have computed state-space receptive fields for semicircular canal afferent neurons in the bullfrog (Rana catesbeiana). We recorded spike times during broad-band Gaussian noise rotational velocity stimuli, computed the frequency distribution of head states at spike times, and normalized these to obtain conditional pdfs for the state. These state-space receptive fields quantify what the brain can deduce about the dynamical state of the head when a single spike arrives from the periphery.

A model of cerebellar computations for dynamical state estimation.

The cerebellum is a neural structure that is essential for agility in vertebrate movements. Its contribution to motor control appears to be due to a fundamental role in dynamical state estimation, which also underlies its role in various non-motor tasks. Single spikes in vestibular sensory neurons carry information about head state. We show how computations for optimal dynamical state estimation may be accomplished when signals are encoded in spikes. This provides a novel way to design dynamical state estimators, and a novel way to interpret the structure and function of the cerebellum.

Modelling the firing pattern of bullfrog vestibular neurons responding to naturalistic stimuli.

We have developed a neural system identification method for fitting models to stimulus-response data, where the response is a spike train. The method involves using a general nonlinear optimisation procedure to fit models in the time domain. We have applied the method to model bullfrog semicircular canal afferent neuron responses during naturalistic, broad-band head rotations. These neurons respond in diverse ways, but a simple four parameter class of models elegantly accounts for the various types of responses observed.

Neural representations of moving systems.

The cerebellum is necessary for moving smoothly and accurately, but this does not imply that the cerebellum generates or modifies movement control signals. Cerebellar function can be explained by assuming that it is involved in constructing neural representations of moving systems, including the body, its parts, and objects in the environment. To draw a technological analogy, the cerebellum could be a neural analogue of a dynamical state estimator, or a part of one. This explanation is able to account not only for cerebellar involvement in motor control, motor learning, and certain kinds of reflex conditioning, but also cerebellar involvement in certain kinds of perceptual and cognitive tasks unrelated to the production of movements. Evidence for the hypothesis that the cerebellum is involved in a neural analogue of state estimation is (1) across phylogeny, cerebellar morphology reflects animals' use of particular sensory systems for analyzing their own movements and the movements of objects in the environment; (2) cerebellar "oculomotor" neurons are active in relation to movements of salient objects in the environment, regardless of whether the animal moves its eyes to look at them; (3) compensatory eye movements have dynamic characteristics indicating that the control signals are constructed from an underlying optimal head state representation; and (4) the motor symptoms of cerebellar dysfunction resemble the effects of faulty state estimation in artificial control systems. The state estimator hypothesis explains the participation of the cerebellum in controlling, perceiving, and imagining systems that move.

Neural simulations of adaptive reafference suppression in the elasmobranch electrosensory system.

The electrosensory system of elasmobranchs is extremely sensitive to weak electric fields, with behavioral thresholds having been reported at voltage gradients as low as 5 nV/cm. To achieve this amazing sensitivity, the electrosensory system must extract weak extrinsic signals from a relatively large reafferent background signal associated with the animal's own movements. Ventilatory movements, in particular, strongly modulate the firing rates of primary electrosensory afferent nerve fibers, but this modulation is greatly suppressed in the medullary electrosensory processing nucleus, the dorsal octavolateral nucleus. Experimental evidence suggests that the neural basis of reafference suppression involves a common-mode rejection mechanism supplemented by an adaptive filter that fine tunes the cancellation. We present a neural model and computer simulation results that support the hypothesis that the adaptive component may involve an anti-Hebbian form of synaptic plasticity at molecular layer synapses onto ascending efferent neurons, the principal output neurons of the nucleus. Parallel fibers in the molecular layer carry a wealth of proprioceptive, efference copy, and sensory signals related to the animal's own movements. The proposed adaptive mechanism acts by canceling out components of the electrosensory input signal that are consistently correlated with these internal reference signals.

A method for constructing data-based models of spiking neurons using a dynamic linear-static nonlinear cascade.

This paper describes a general nonlinear dynamical model for neural system identification. It describes an algorithm for fitting a simple form of the model to spike train data, and reports on this algorithm's performance in identifying the structure and parameters of simulated neurons. The central element of the model is a Wiener-Bose dynamic nonlinearity that ensures that the model is able to approximate the behaviour of an arbitrary nonlinear dynamical system. Nonlinearities associated with spike generation and transmission are treated by placing the Wiener-Bose system in cascade with pulse frequency modulators and demodulators, and the static nonlinearity at the output of the Wiener-Bose system is decomposed into a rectifier and a multinomial. This simplifies the model without reducing its generality for neuronal system identification. Model elements can be characterised using standard methods of dynamical systems analysis, and the model has a simple form that can be implemented and simulated efficiently. This model bears a structural resemblance to real neurons; it may be regarded as a connectionist "neuron" that has been generalized in a realistic way to enable it to mimic the behaviour of an arbitrary nonlinear system, or conversely as a general nonlinear model that has been constrained to make it easy to fit to spike train data. Tests with simulated data show that the identification algorithm can accurately estimate the structure and parameters of neuron-like nonlinear dynamical systems using data sets containing only a few hundred spikes.

The role of the cerebellum in motor control and perception.

The cerebellum has an important role in control and coordination of movements, but in some species, notably weakly electric fish of the family Mormyridae, anatomical, electrophysiological and behavioural evidence indicates that parts of cerebellar cortex are concerned with tracking movements of objects around the animal, rather than with controlling movements of the animal itself. The existence of such anomalies suggests that the cerebellum may not be exclusively, or even primarily, a structure for motor control. Evidence reviewed in this paper shows that the cerebellum is associated with sensory systems used for tracking movements of targets in the environment, as well as movements made by the animal itself, in all vertebrates, not just in a few isolated cases. The evidence indicates that the standard theory that the function of the cerebellum is control and coordination of movements only partially characterises cerebellar function. The cerebellum may be better characterised as a tracking system, with an important role in control and coordination of movements which arises because of an animal's need to track moving objects, to track its own movements, and to analyse the sensory consequences of movements in order to control movements. This theory not only predicts the known motor consequences of cerebellar dysfunction, it also predicts a specific kind of perceptual deficit caused by cerebellar dysfunction, namely an inability to accurately follow and predict trajectories of objects moving in the environment. A variety of behavioural and perceptual tasks in addition to motor control and movement tracking may require dynamical state estimation, and therefore may involve the cerebellum.

Digital filters for firing rate estimation.

When a rate histogram is used to represent the firing pattern of a neuron there is the potential for serious error due to aliasing, and because of this the rate histogram is a very poor way to represent neural activity. It is theoretically possible to encode a signal in a spike train and decode it without error by filtering and sampling. There is no natural optimal filter design for this problem, but it is possible to specify the characteristics of a good rate estimating filter heuristically and design a filter with these characteristics. Two rate estimating filters are described here. Their performance has been tested, and compared to the rate histogram and the French-Holden rate estimating algorithm, by measuring their ability to recover signals encoded as impulse sequences by Integral Pulse Frequency Modulation (IPFM). These filters are simple to implement and perform well. They should be used in preference to the rate histogram.

Adaptation of sleep and circadian rhythms to the Antarctic summer: a question of zeitgeber strength.

Adaptation of sleep and circadian rhythms was examined in three temperate zone dwellers arriving in Antarctica during summer. Rectal temperature, wrist activity, and heart rate were monitored continuously, sleep timing and quality noted on awakening, and mood and fatigue rated every 2 h while awake. Sleep was poorer in 2/3 subjects in Antarctica, where all subjects reported more difficulty rising. Sleep occurred at the same clock times in New Zealand and Antarctica, however, the rhythms of temperature, activity, and heart rate underwent a delay of about 2 h. The subject with the most Antarctic experience had the least difficulty adapting to sleeping during constant daylight. The subject with the most delayed circadian rhythms had the most difficulty. The delay in the circadian system with respect to sleep and clock time is hypothesized to be due to differences in zeitgeber strength and/or zeitgeber exposure between Antarctica and New Zealand.

Elasmobranch eye motor dynamics characterised using pseudorandom stimulus.

A pseudorandom binary sequence electrical pulse rate stimulus was delivered to the abducens nerve of an elasmobranch preparation. Ipsilateral eye movements were recorded using a position-sensitive photodiode to measure the position of a reflective patch attached to the fish's eye. Eye position data was cross-correlated with the stimulus pattern, and exponential decay curves were fitted to the cross-correlograms to estimate the time constant of a linear first order low-pass filter model. The cross-correlograms were transformed into the frequency domain using a Digital Fourier Transform, and Bode plots of eye dynamics were plotted. Eye motor plant dynamics in the elasmobranch Cephaloscyllium isabella can be accurately characterised by a linear first order low-pass filter model with a corner frequency of 0.73 +/- 0.10 Hz. Non-minimum phase lag reaches 90 degrees at about 4 Hz, indicating a time delay of some 50-60 ms. Integration of the canal signal is not required for producing compensatory eye movements above the characteristic frequency of the eye motor plant. However, the canal signal may be integrated to ensure that the vestibulo-ocular reflex is compensatory at lower frequencies. Substantial phase compensation or prediction is required for effective control of the vestibulo-ocular reflex.

A vestibulo-ocular reflex with no head movement.

Eye movements were produced in an elasmobranch preparation by electrical stimulation of the horizontal canal ampullary nerves. A pseudorandom binary sequence of stimulus pulse trains was delivered bilaterally. Eye position during this stimulus was cross-correlated with the stimulus pattern to obtain a linear model of the response. Sums of exponential functions were fitted to the crosscorrelogram data to estimate time-constants and transfer functions. The data was examined in the frequency domain by using Fourier transformation. The response is accurately described by a second order linear filter, which is essentially a low pass filter with a cutoff at 0.22 Hz. This nearly two octaves below the cutoff frequency of the eye motor plant, which has been estimated by the same method. Our data shows that there is no central phase compensation or prediction which might offset the substantial delay in eye motor plant response. We hypothesise that the necessary phase compensation may be achieved by driving the vestibulo-ocular reflex with sensory neurons having a phase advance at high frequency.