Canonical Field Theory -- A Prototype Example

The equations of a field may be put into a standard Lagrangian form from which several conservation laws follow directly. As an illustrative example, a string free to vibrate in two directions is investigated; this example clearly illustrates the outstanding features of the canonical theory, while avoiding the notational and physical complications encountered in most systems of practical interest. The conservation laws are interpreted for the string. The theory is further developed to express the field\u27s behavior in terms of canonical coordinates and momenta. Quantum conditions are introduced, as in meson theory and quantum electrodynamics. It is shown that the mathematics of the quantized string is that of several charged particles occupying a set of energy states

The Relationship between the Firing Rate of a Single Neuron and the Level of Activity in a Population of Neurons : Experimental Evidence for Resonant Enhancement in the Population Response

A quantitative comparison is made between experiment and the theoretically predicted dynamics of a neuron population. The experiment confirms the theoretical prediction that under appropriate conditions an enlarged resonant response should appear in the activity of the neuron population, near the frequency at which there is minimum modulation in the instantaneous rate of a single neuron. These findings bear on the relationship between the firing rate of a single neuron and the firing rate of a population of neurons

Dynamics of Encoding in Neuron Populations: Some General Mathematical Features

The use of a population dynamics approach promises efficient simulation of large assemblages of neurons. Depending on the issues addressed and the degree of realism incorporated in the simulated neurons, a wide range of different population dynamics formulations can be appropriate. Here we present a common mathematical structure that these various formulations share and that implies dynamical behaviors that they have in common. This underlying structure serves as a guide toward efficient means of simulation. As an example, we derive the general population firing-rate frequency-response and show how it may be used effectively to address a broad range of interacting-population response and stability problems. A few specific cases will be worked out. A summary of this work appears at the end, before the appendix

Dynamics of Encoding in a Population of Neurons

A simple encoder model, which is a reasonable idealization from known electrophysiological properties, yields a population in which the variation of the firing rate with time is a perfect replica of the shape of the input stimulus. A population of noise-free encoders which depart even slightly from the simple model yield a very much degraded copy of the input stimulus. The presence of noise improves the performance of such a population. The firing rate of a population of neurons is related to the firing rate of a single member in a subtle way