No abstract

[1] Pulsar detection and timing experiments are applications where adaptive filters seem eminently suitable tools for radio frequency interference (RFI) mitigation. We describe a novel variant which works well in field trials of pulsar observations centered on an observing frequency of 675 MHz and a bandwidth of 64 MHz and with 2-bit sampling. Adaptive filters have generally received bad press for RFI mitigation in radio astronomical observations with their most serious drawback being a spectral echo of the RFI embedded in the filtered signals. Pulsar observations are intrinsically less sensitive to this as they operate in the (pulsar period) time domain. The field trials have allowed us to identify those issues which limit the effectiveness of the adaptive filter. We conclude that adaptive filters can significantly improve pulsar observations in the presence of RFI.

Experiments have been performed on unanaesthetized and paralysed cats. The tuning curves for spatial frequency of retinal, lateral geniculate and simple and complex cells of the cortex have been determined in response to sinusoidal gratings of various spatial frequencies at different levels of mean luminance. For all neurones, decreasing the mean luminance leads to a progressive loss of spatial resolution and contrast sensitivity. Retinal ganglion cells of type X show, for scotopic levels of luminance, a flattening of their spatial frequency tuning curves in the low spatial frequency range. For geniculate and cortical neurones, on the contrary, the spatial frequency characteristics at the various levels of luminance remain practically invariant in their bandwidth. On the average, complex cells still respond to mean luminances ten times lower than simple cells. The tuning curves for orientation of cortical cells maintain, to a first approximation, the same shape at the various levels of mean luminance. The results are discussed comparing the electrophysiological with psychophysical data.

Congenital nystagmus is an oculomotor disorder in which fixation is disrupted by rhythmical, bilateral involuntary oscillations. Clinically these eye movements have been described with some degree of success in terms of their peak-to-peak amplitude, frequency, mean velocity and waveform shape. However, it has not proved possible to diagnose any underlying pathology from the nystagmus characteristics. Here, we propose a new approach to understanding the nystagmus using dynamical systems theory. Our approach is based on the use of delay embedding techniques, which allow one to relate a time series of scalar observations to the state space dynamics of the underlying dynamical system. Using this approach we quantify the dynamics of the nystagmus in the region of foveation and present evidence to suggest that it is low-dimensional and deterministic. Our results put new constraints on acceptable models of nystagmus and suggest a way to make a closer link between data analysis and model development. This approach raises the hope that techniques originally developed to stabilise chaotic systems, by using small perturbations, may prove useful in the control of nystagmus.

The study of eye movement control and oculomotor disorders has, for four decades, relied on control theoretic concepts for its theoretical foundation. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus.The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. * Now at: Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK 1The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles.In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.

Dynamic overshoots are seen after voluntary re-fixation saccades. They are microsaccadic movements which follow primary saccades and have no delay. The purpose of this study was to examine the prevalence and metrics of the dynamic overshoots seen after involuntary saccades. Using infra-red oculography we demonstrate that dynamic overshoots are a common occurrence in physiological square-wave jerks, congenital nystagmus and manifest latent nystagmus and that these overshoots are saccadic in nature and have the same dynamic characteristics as those seen following voluntary saccades. It is therefore likely that they share common neural commands to those dynamic overshoots seen after a volitional saccade. All dynamic overshoots are postulated to be the unwanted consequence of making a saccade and are simulated in a model of fast oculomotor behaviour which is consistent with known experimental results.

Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to both recorded jerk CN waveforms and simulated waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the time series analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system. This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses.

Because the oscillatory eye movements of congenital nystagmus vary from cycle to cycle, there is no clear relationship between the waveform produced and the underlying abnormality of the ocular motor system. We consider the durations of successive cycles of nystagmus which could be (1) completely determined by the lengths of the previous cycles, (2) completely independent of the lengths of the previous cycles or (3) a mixture of the two. The behaviour of a deterministic system can be characterised in terms of a collection of (unstable) oscillations, referred to as periodic orbits, which make up the system. By using a recently developed technique for identifying periodic orbits in noisy data, we find evidence for periodic orbits in nystagmus waveforms, eliminating the possibility that each cycle is independent of the previous cycles. The technique also enables us to identify the waveforms which correspond to the deterministic behaviour of the ocular motor system. These waveforms pose a challenge to our understanding of the ocular motor system because none of the current extensions to models of the normal behaviour of the ocular motor system can explain the range of identified waveforms.