Completeness for nondeterministic complexity classes

We demonstrate differences between reducibilities and corresponding completeness notions for nondeterministic time and space classes. For time classes the studied completeness notions under polynomial-time bounded (even logarithmic-space bounded) reducibilities turn out to be different for any class containingNE. For space classes the completeness notions under logspace reducibilities can be separated for any class properly containingLOGSPACE. Key observation in obtaining the separations is the honesty property of reductions, which was recently observed to hold for the time classes and can be shown to hold for space classes.The work of S. Homer was supported in part by National Science Foundation Grants MIP-8608137 and CCR-8814339 and a Fulbright-Hays Research Fellowship. Some of this research was done while he was a Guest Professor at the Mathematics Institute of Heidelberg University.     

The importance of choosing attractors for optimizing chaotic communications

In this brief, we consider methods to improve the performance of chaotic communication schemes. We study a system using a receiver which explicitly includes the presence of noise in the channel. We show how the choice of chaotic dynamical system generating the transmitted signal is crucial. We observe a large variation in bit error rate performance of the system as parameters in the maps are changed, and we propose a simple explanation for this variation.     

Quantifying the effects of dimension on the convergence rate of theLMS adaptive FIR estimator

The convergence rate of an LMS adaptive FIR filter to an unknown stationary channel may be influenced by the filter parameter dimension as well as by the input signal's characteristics. This dimension influence may be of importance in applications, such as adaptive acoustic echo cancellation, in which the unknown channel is typically modeled as a “long” FIR filter. The paper includes the development and proposal of a novel measure of the expected convergence rate of the LMS/FIR filter followed by analysis of this convergence rate measure. The analysis indicates that unless the input signal is white, the expected convergence rate decreases with increasing dimension down to a limiting value, which is determined by the input signal's autocorrelation level