A theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions

In a recent study the initial rise of the mutual information between the firing rates of N neurons and a set of p discrete stimuli has been analytically evaluated, under the assumption that neurons fire independently of one another to each stimulus and that each conditional distribution of firing rates is gaussian. Yet real stimuli or behavioural correlates are high-dimensional, with both discrete and continuously varying features.Moreover, the gaussian approximation implies negative firing rates, which is biologically implausible. Here, we generalize the analysis to the case where the stimulus or behavioural correlate has both a discrete and a continuous dimension. In the case of large noise we evaluate the mutual information up to the quadratic approximation as a function of population size. Then we consider a more realistic distribution of firing rates, truncated at zero, and we prove that the resulting correction, with respect to the gaussian firing rates, can be expressed simply as a renormalization of the noise parameter. Finally, we demonstrate the effect of averaging the distribution across the discrete dimension, evaluating the mutual information only with respect to the continuously varying correlate.Comment: 20 pages, 10 figure

The Viscoelastic Properties of Passive Eye Muscle in Primates. III: Force Elicited by Natural Elongations

We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fung's quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant

Hypothetical membrane mechanisms in essential tremor

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Representational capacity of a set of independent neurons

The capacity with which a system of independent neuron-like units represents a given set of stimuli is studied by calculating the mutual information between the stimuli and the neural responses. Both discrete noiseless and continuous noisy neurons are analyzed. In both cases, the information grows monotonically with the number of neurons considered. Under the assumption that neurons are independent, the mutual information rises linearly from zero, and approaches exponentially its maximum value. We find the dependence of the initial slope on the number of stimuli and on the sparseness of the representation.Comment: 19 pages, 6 figures, Phys. Rev. E, vol 63, 11910 - 11924 (2000

Simultaneous recordings of ocular microtremor and microsaccades with a piezoelectric sensor and a video-oculography system

Our eyes are in continuous motion. Even when we attempt to fix our gaze, we produce so called “fixational eye movements”, which include microsaccades, drift, and ocular microtremor (OMT). Microsaccades, the largest and fastest type of fixational eye movement, shift the retinal image from several dozen to several hundred photoreceptors and have equivalent physical characteristics to saccades, only on a smaller scale (Martinez-Conde, Otero-Millan & Macknik, 2013). OMT occurs simultaneously with drift and is the smallest of the fixational eye movements (∼1 photoreceptor width, >0.5 arcmin), with dominant frequencies ranging from 70 Hz to 103 Hz (Martinez-Conde, Macknik & Hubel, 2004). Due to OMT’s small amplitude and high frequency, the most accurate and stringent way to record it is the piezoelectric transduction method. Thus, OMT studies are far rarer than those focusing on microsaccades or drift. Here we conducted simultaneous recordings of OMT and microsaccades with a piezoelectric device and a commercial infrared video tracking system. We set out to determine whether OMT could help to restore perceptually faded targets during attempted fixation, and we also wondered whether the piezoelectric sensor could affect the characteristics of microsaccades. Our results showed that microsaccades, but not OMT, counteracted perceptual fading. We moreover found that the piezoelectric sensor affected microsaccades in a complex way, and that the oculomotor system adjusted to the stress brought on by the sensor by adjusting the magnitudes of microsaccades

Learning the Optimal Control of Coordinated Eye and Head Movements

Various optimality principles have been proposed to explain the characteristics of coordinated eye and head movements during visual orienting behavior. At the same time, researchers have suggested several neural models to underly the generation of saccades, but these do not include online learning as a mechanism of optimization. Here, we suggest an open-loop neural controller with a local adaptation mechanism that minimizes a proposed cost function. Simulations show that the characteristics of coordinated eye and head movements generated by this model match the experimental data in many aspects, including the relationship between amplitude, duration and peak velocity in head-restrained and the relative contribution of eye and head to the total gaze shift in head-free conditions. Our model is a first step towards bringing together an optimality principle and an incremental local learning mechanism into a unified control scheme for coordinated eye and head movements