Parameter estimation in spiking neural networks: a reverse-engineering approach.

This paper presents a reverse engineering approach for parameter estimation in spiking neural networks (SNNs). We consider the deterministic evolution of a time-discretized network with spiking neurons, where synaptic transmission has delays, modeled as a neural network of the generalized integrate and fire type. Our approach aims at by-passing the fact that the parameter estimation in SNN results in a non-deterministic polynomial-time hard problem when delays are to be considered. Here, this assumption has been reformulated as a linear programming (LP) problem in order to perform the solution in a polynomial time. Besides, the LP problem formulation makes the fact that the reverse engineering of a neural network can be performed from the observation of the spike times explicit. Furthermore, we point out how the LP adjustment mechanism is local to each neuron and has the same structure as a 'Hebbian' rule. Finally, we present a generalization of this approach to the design of input-output (I/O) transformations as a practical method to 'program' a spiking network, i.e. find a set of parameters allowing us to exactly reproduce the network output, given an input. Numerical verifications and illustrations are provided.

Use of target velocity in saccadic programming.

Previous studies indicate that in response to a step-ramp visual target movement, the saccade amplitude approximates target displacement 100 ms before saccade onset. This study examines whether the saccadic system takes target motion into consideration when computing saccadic amplitude, if target movement is seen by the subject before he is requested to make a saccade. In the first experiment, while the subject fixated at the target (laser dot) and maintained fixation, the target jumped to the left and moved to the right at a fixed velocity. At some predetermined site, the target jumped a step to the right and continued to move in that direction. After the target step, the subject had to make a saccade and follow target motion. In the second experiment, while the subject fixated at the target and maintained fixation, the target jumped to the right and up and moved down at a fixed velocity. At some predetermined site, an auditory signal was given, and the subject had to make a saccade and follow target motion. Results in both experiments showed that the eye position was statistically different from the target displacement at 100 ms before saccade onset, indicating that the saccadic system uses target velocity in computing saccade amplitude.

Target velocity based prediction in saccadic vector programming.

Two experiments have been designed to test whether the saccadic system takes target motion into consideration in computing saccade amplitude. In one experiment, while the subject fixated straight ahead, either a horizontal ramp-step-ramp or a horizontal step-ramp target moved from left to right. After the step, the subject had to make a saccade and follow the target. In the second set of experiments, the target, after an initial step, moved extrafoveally from up to down at fixed velocity; a tone, signaling the subject to make a saccade to the target and follow it, was delivered either after a variable delay (previewed condition) or simultaneously with the initial target step (non-previewed condition). In both experiments, eye position at saccade end was statistically different from target position 100 msec before saccade onset only when the target slow motion was presented before the step (i.e. in horizontal ramp-step-ramp and in previewed H-step V-ramp paradigms), suggesting that target motion could be used by the saccadic system to extrapolate the future target position, only if the subject is given enough time to observe the target ramp motion before the step.

Linear head displacement measured by the otoliths can be reproduced through the saccadic system.

Normal subjects seated on a moving cart have been submitted to horizontal linear accelerations in the frontal plane. They were shown an earth-fixed target at a distance of 63 cm before the onset of cart motion, which occurred in total darkness. They were asked to keep their gaze on the imagined target. The main result is that, in spite of a low gain otolith-ocular reflex, they could reproduce their motion with great accuracy by saccades (a small overestimation was, however, observed). It is concluded that otolith information is used by probably cortical spatial analysers which can derive a precise measurement of linear displacement and feed this information in the saccadic system.

Ocular counter-rolling during active head tilting in humans.

Human ocular counter-rolling has been measured by means of an infra-red video based system: EMIRAT. This method of three-dimensional eye angular displacement recording has an overall precision of 0.5 degrees, is calibrated and is completely non-invasive. Dynamic counter-rolling gain is about 0.5, increasing with head roll oscillation frequency from 0.3 at 0.1 Hz, to 0.7 at 1 Hz. Otolithic contribution to this reflex has been taken into consideration.

Ocular Counter-rolling during Active Head Tilting in Humans.

Human ocular counter-rolling has been measured by means of an infra-red video based system: EMIRAT. This method of three-dimensional eye angular displacement recording has an overall precision of 0.5°, is calibrated and is completely non-invasive. Dynamic counter-rolling gain is about 0.5, increasing with head roll oscillation frequency from 0.3 at 0.1 Hz, lo 0.7 at 1 Hz. Otolithic contribution to this reflex has been taken into consideration.

European vestibular experiments on the Spacelab-1 mission: 2. Experimental equipment and methods.

A series of vestibular experiments were performed in conjunction with the first Spacelab mission, consisting of sets of pre-, in- and postflight tests. A multipurpose experimental apparatus used for the diverse flight and ground tests is presented. Additional apparatus together with the multi-purpose package were used in the baseline data collection facility at the landing site at NASA Dryden Flight Research Facility for the ground tests. The tests involved optokinetic, caloric and mechanical (whole-body or head-alone) stimulation. The latter included linear acceleration in the subject's x, y and z axes, static roll and yaw about an earth-vertical axis. Physiological parameters such as electro-oculogram (EOG), blood-volume-pulse (BVP), respiration, as well as the stimulus variables such as acceleration and caloric temperature were transmitted to the ground and recorded there. The flight and ground testing schedules are outlined. Problems arising from this complex venture are discussed, and some suggestions are made for future improvement.

European vestibular experiments on the Spacelab-1 mission: 5. Contribution of the otoliths to the vertical vestibulo-ocular reflex.

The gain of the vestibulo-ocular reflex in the sagittal plane may be due to a cooperation between otoliths and the vertical semi-circular canals. The present space experiment was aimed at studying the influence of the absence of gravity stimulation on the otoliths, by comparing VOR gain and phase in space and on ground. Measurements were taken the 5th and the 7th day of flight, the subject being asked to perform, eyes closed, active head oscillations in pitch while fixating an imaginary target in front of him. No significant decrease of the VOR gain was found in space, but a change in phase was noted. A significant increase of the VOR gain was found 14 h after landing. Control experiments have been done on ground on several subjects. They indicate that pitch VOR gain during active head movements is about one, with eyes open in darkness at 1 Hz.

European vestibular experiments on the Spacelab-1 mission: 6. Yaw axis vestibulo-ocular reflex.

In two Spacelab-1 crew members the lateral eye movements evoked by active angular oscillation of the head in yaw at 1 Hz were recorded in-flight and post-flight. In one, the responses to passive angular oscillation in yaw at 0.2-1 Hz were also studied pre- and post-flight. In the absence of visual fixation there was no significant change in the gain of either the active or passive vestibulo-ocular reflex (VOR) attributable to exposure to microgravity. However, when the subject fixated on a visual target that moved with his head the suppressed VOR gain was lower on the first post-flight test (performed 16 h after landing) than that obtained pre-flight or on subsequent post-flight tests.

Modifications of gain asymmetry and beating field of vertical optokinetic nystagmus in microgravity.

Optokinetic nystagmus (OKN) was measured in human subjects before, during and after exposure to microgravity induced by either parabolic flight or space flight. The downward (slow phase up) OKN gain was greater than upward gain in normal gravity. On first exposure to microgravity this asymmetry was reversed. In addition, the beating field of OKN tended to shift downward, and the vertical optokinetic after nystagmus (OKAN) time constant was increased. This reversed asymmetry disappeared after 3 days of space flight. On return to 1 g gravity, there was a general drift of the eye in the upward direction during either spontaneous eye movements or OKN. This suggests that the sacculus normally influences mean vertical eye position and the perception of the subjective horizontal direction, both of which are gravity dependent.

The European vestibular experiments in Spacelab-1.

A series of experiments were performed in the Spacelab-1 mission on November/December, 1983, pre-, in-, and postflight. These experiments covered various aspects of the functions of the vestibular system, the inflight tests comprising threshold measurements for linear movements in three orthogonal axes, optokinetic stimulation, vestibulo-ocular reflexes under linear and angular accelerations, caloric stimulation with and without linear accelerations; pre- and postflight tests repeated the inflight protocol with the addition of subjective vertical and eye counter-rotation measurements using a tilt table. One of the most surprising and significant results was the caloric test: strong caloric nystagmus on the two subjects tested was recorded inflight; this was contrary to what was expected from Barany's convection hypothesis for caloric nystagmus.