We study the Hilbert series of the graded algebra of regular functions on a symplectic quotient of a unitary circle representation and elaborate explicit formulas for the lowest coefficients of the Laurent expansion of such a Hilbert series in terms of rational symmetric functions of the weights. Considerable efforts are devoted to including the cases where the weights are degenerate. We find t...

We derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution, and we observe n i.i.d copies of it. The confidence regions are built using a data-dependent threshold based on a weighted bootstrap procedure. We consider two approach...

This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability distributions on strings, a representation which occurs naturally in spectral learning, can be computed by a negative mixture of at most two probabilistic a...

In this article we show that VLSI efficient implementations of certain classes of Boolean functions using threshold gates are possible. It is a challenging open problem to find algorithms to synthesize simple neural networks using threshold gates for VLSI implementation. We first investigate depth-size tradeoffs for symmetric functions, detailing two algorithms: one based on the divide-and-conq...

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

In this correspondence, we give a new definition of generalized Hamming weights of nonlinear codes and a new interpretation connected with it. These generalized weights are determined by the entropy/length profile of the code. We show that this definition characterizes the performance of nonlinear codes on the wire-tap channel of type II. The new definition is invariant under translates of the ...

The existence of (standard) Gauss quadrature rules with respect to a nonnegative measure dμ with support on the real axis easily can be shown with the aid of orthogonal polynomials with respect to this measure. Efficient algorithms for computing the nodes and weights of an n-point Gauss rule use the n × n symmetric tridiagonal matrix determined by the recursion coefficients for the first n orth...

We propose a general method to combine several estimators of the same quantity in order to produce a better estimate. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained to sum to one. In this framework, the optimal weights, minimizing the quadratic loss, are entirely determined by the mean s...

Recursive Least Square (RLS) is one of the algorithms that can be used to update array weights in adaptive array antennas. Although the calculation load is large, it achieves fast convergence and is thus effective under fading environments; it shows great promise in mobile communication applications [1]. We first constructed a fully functional testbed in which the RLS algorithm is implemented u...

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non-asymptotic control of the confidence level,...