Samplers and Extractors for Unbounded Functions

Blasiok (SODA\u2718) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions f from {0,1}^m to the real numbers such that f(U_m) has subgaussian tails, and asked for explicit constructions. In this work, we give the first explicit constructions of subgaussian samplers (and in fact averaging samplers for the broader class of subexponential functions) that match the best known constructions of averaging samplers for [0,1]-bounded functions in the regime of parameters where the approximation error epsilon and failure probability delta are subconstant. Our constructions are established via an extension of the standard notion of randomness extractor (Nisan and Zuckerman, JCSS\u2796) where the error is measured by an arbitrary divergence rather than total variation distance, and a generalization of Zuckerman\u27s equivalence (Random Struct. Alg.\u2797) between extractors and samplers. We believe that the framework we develop, and specifically the notion of an extractor for the Kullback-Leibler (KL) divergence, are of independent interest. In particular, KL-extractors are stronger than both standard extractors and subgaussian samplers, but we show that they exist with essentially the same parameters (constructively and non-constructively) as standard extractors

A Novel Algorithm to Minimize the Excitation of Undesirable Oscillations-State Space

A new state-space type stabilizer to minimize low frequency oscillation is proposed. The proposed Power System Stabilizer (PSS) design not only damps the oscillations by moving the Eigen-values to desired left hand plane locations but additionally reduces the excitation of the mode itself through optimization of the left eigenvector of the poorly damped electro-mechanical mode. The stabilizer is implemented as a State-Space (SS) type controller which is optimized using a constrained optimization procedure. Two possible inputs, speed and electrical power are considered as candidate inputs to the stabilizers. The state-space design is also compared with one based on traditional lead-lag compensation. The SS type stabilizer with electrical power input is shown to perform better compared to any other type of PSS by minimizing low frequency oscillations