Universal probability distribution function for bursty transport in plasma turbulence.

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.

Dust charge fluctuations in a magnetized dusty plasma.

Charging currents of electrons and ions to a spherical dust grain in a uniform magnetized dusty plasma have been examined. It is found that the external magnetic field reduces the charging currents, thereby decreasing the dust charge fluctuation damping of a low-frequency electrostatic wave in a dusty plasma.

Theory of cavitons in complex plasmas.

Nonlinear coupling between Langmuir waves with finite amplitude dispersive dust acoustic perturbations is considered. It is shown that the interaction is governed by a pair of coupled nonlinear differential equations. Numerical results reveal the formation of Langmuir envelope solitons composed of the dust density depression created by the ponderomotive force of bell-shaped Langmuir wave envelops. The associated ambipolar potential is positive. The present nonlinear theory should be able to account for the trapping of large amplitude Langmuir waves in finite amplitude dust density holes. This scenario may appear in Saturn's dense rings, and the Cassini spacecraft should be able to observe fully nonlinear cavitons, as presented herein. Furthermore, we propose that new electron-beam plasma experiments should be conducted to verify our theoretical prediction.

Radiation-condensation instability in a self-gravitating dusty astrophysical plasma.

Properties of radiation-condensation instability in a partially-ionized self-gravitating dusty astrophysical plasmas are studied. For this purpose, new dispersion relations for coupled dusty plasma and condensation modes in both unmagnetized and magnetized plasmas are derived. The dispersion relations are numerically analyzed to investigate the interplay between self-gravitation and impurity losses, as well as to study the effects of the external magnetic field and finite plasma beta on instabilities we found.

Comments on "Classification ability of single hidden layer feedforward neural networks".

A recent paper addresses a certain classification problem, and concludes that classification can be achieved using a single hidden layer neural network. We note here that conclusions along similar lines in a more general setting were reached in an earlier paper.

Complete memory structures for approximating nonlinear discrete-time mappings.

This paper introduces a general structure that is capable of approximating input-output maps of nonlinear discrete-time systems. The structure is comprised of two stages, a dynamical stage followed by a memoryless nonlinear stage. A theorem is presented which gives a simple necessary and sufficient condition for a large set of structures of this form to be capable of modeling a wide class of nonlinear discrete time systems. In particular, we introduce the concept of a "complete memory". A structure with a complete memory dynamical stage and a sufficiently powerful memoryless stage is shown to be capable of approximating arbitrarily wide class of continuous, causal, time invariant, approximately-finite-memory mappings between discrete-time signal spaces. Furthermore, we show that any bounded-input bounded output, time-invariant, causal memory structure has such an approximation capability if and only if it is a complete memory. Several examples of linear and nonlinear complete memories are presented. The proposed complete memory structure provides a template for designing a wide variety of artificial neural networks for nonlinear spatiotemporal processing.

Universal Approximation Using Radial-Basis-Function Networks.

There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.