Stochastic resonance at phase noise in signal transmission

A model is developed for a periodic signal corrupted by an arbitrarily distributed phase noise and transmitted by an arbitrary memoryless system. The model establishes a new form of the phenomenon of stochastic resonance, whereby signal transmission can be enhanced by addition of noise. This is revealed by the standard signal-to-noise ratio of stochastic resonance, which here receives an explicit theoretical expression, and which is shown improvable via noise addition. This model is the first to propose a theory of stochastic resonance with phase noise. It represents a unique framework for further investigations on stochastic resonance and its applications.

Signal transcoding by nonlinear sensory neurons: information-entropy maximization, optimal transfer function, and anti-Hebbian adaptation.

A principle of information-entropy maximization is introduced in order to characterize the optimal representation of an arbitrarily varying quantity by a neural output confined to a finite interval. We then study the conditions under which a neuron can effectively fulfil the requirements imposed by this information-theoretic optimal principle. We show that this can be achieved with the natural properties available to the neuron. Specifically, we first deduce that neural (monotonically increasing and saturating) nonlinearities are potentially efficient for achieving the entropy maximization, for any given input signal. Secondly, we derive simple laws which adaptively adjust modifiable parameters of a neuron toward maximum entropy. Remarkably, the adaptation laws that realize entropy maximization are found to belong to the class of anti-Hebbian laws (a class having experimental groundings), with a special, yet simple, nonlinear form. The present results highlight the usefulness of general information-theoretic principles in contributing to the understanding of neural systems and their remarkable performances for information processing.

Synapse models for neural networks: from ion channel kinetics to multiplicative coefficient wij.

This paper relates different levels at which the modeling of synaptic transmission can be grounded in neural networks: the level of ion channel kinetics, the level of synaptic conductance dynamics, and the level of a scalar synaptic coefficient. The important assumptions to reduce a synapse model from one level to the next are explicitly exhibited. This coherent progression provides control on what is discarded and what is retained in the modeling process, and is useful to appreciate the significance and limitations of the resulting neural networks. This methodic simplification terminates with a scalar synaptic efficacy as it is very often used in neural networks, but here its conditions of validity are explicitly displayed. This scalar synapse also comes with an expression that directly relates it to basic quantities of synaptic functioning, and it can be endowed with meaningful physical units and realistic numerical values. In addition, it is shown that the scalar synapse does not receive the same expression in neural networks operating with spikes or with firing rates. These coherent modeling elements can help to improve, adjust, and refine the investigation of neural systems and their remarkable collective properties for information processing.

Information processing in neural networks by means of controlled dynamic regimes.

This paper is concerned with the modeling of neural systems regarded as information processing entities. I investigate the various dynamic regimes that are accessible in neural networks considered as nonlinear adaptive dynamic systems. The possibilities of obtaining steady, oscillatory or chaotic regimes are illustrated with different neural network models. Some aspects of the dependence of the dynamic regimes upon the synaptic couplings are examined. I emphasize the role that the various regimes may play to support information processing abilities. I present an example where controlled transient evolutions in a neural network, are used to model the regulation of motor activities by the cerebellar cortex.

A neural network model of the cerebellar cortex performing dynamic associations.

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber--Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.

A theoretical model of acoustoelectric transducer with a nonuniform distribution of piezoelectric coefficient: application to transducer optimization.

A general equation is derived that describes the behavior of a piezoelectric transducer with a nonuniform distribution of piezoelectric coefficient within its bulk, when submitted to an arbitrary distribution of acoustic pressure. Based on this equation, an expression for the receiving transfer function of the transducer is calculated. The results demonstrate the dependence of the transfer function on the distribution of piezoelectric coefficient, and that it is possible to benefit from a nonuniform distribution to optimize the transfer function. The general equation also describes the influence of the external electric circuit loading the transducer, which leads to another independent means of optimizing the transfer function. The proposed model combines effects of piezoelectric material characteristics, acoustic backing, and electric loading, without resorting to Mason or other equivalent circuits for the transducer.

An experimental study of acoustoelectric transducers with nonuniform distribution of the piezoelectric coefficient.

In this paper, an experimental test of a theoretical model published previously is presented that describes the behavior of an acoustoelectric transducer with a nonuniform distribution of the piezoelectric coefficient within its bulk. Results of this theoretical model are first reviewed. Uniform and nonuniform piezoelectric transducers were fabricated, following a procedure described herein. The receive transfer functions of the transducers were recorded experimentally, and a comparison is made with the theoretical transfer functions predicted by the model, which shows good agreement. The transmit transfer functions of the uniform and nonuniform transducers were also measured and are reported. Numerical calculations of the different transfer functions given by the theoretical model for a uniform transducer associated with different backing materials are also presented, and the results are shown to be equivalent to the results following from the Mason equivalent circuit. Comparisons with experimental results and with Mason's equivalent circuit verified the new theoretical model.