We consider the problem of estimating a random vector x, with covariance uncertainties, that is observed through a known linear transformation H and corrupted by additive noise. We first develop the linear estimator that minimizes the worst-case meansquared error (MSE) across all possible covariance matrices. Although the minimax approach has enjoyed widespread use in the design of robust metho...

We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-le...

We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the...

The multiscale entropy (MSE) is a novel method for quantifying the intrinsic dynamical complexity of physiological systems over several scales. To evaluate this method as a promising way to explore the neural mechanisms in ADHD, we calculated the MSE in EEG activity during the designed task. EEG data were collected from 13 outpatient boys with a confirmed diagnosis of ADHD and 13 age- and gende...

OBJECTIVE: To examine the association between movie smoking exposure (MSE) and adolescent smoking according to rating category. METHODS: A total of 6522 US adolescents were enrolled in a longitudinal survey conducted at 8-month intervals; 5503 subjects were followed up at 8 months, 5019 subjects at 16 months, and 4575 subjects at 24 months. MSE was estimated from 532 recent box-office hits, blo...

Diierent predictors and their approximators in nonlinear prediction regression models are studied. The minimal value of the mean squared error (MSE) is derived. Some approximate formulae for the MSE of ordinary and weighted least squares predictors are given.

In the present paper we compute the geometric minimum mean square error for the vector linear estimation problem. We do this by proving that the vector linear estimator that minimizes the mean square error (MSE) also minimizes the geometric MSE.

The Saccharomyces cerevisiae transcription factor Ndt80 selectively binds a DNA consensus sequence (the middle sporulation element [MSE]) to activate gene expression after the successful completion of meiotic recombination. Here we report the X-ray crystal structures of Ndt80 bound to ten distinct MSE variants. Comparison of these structures with the structure of Ndt80 bound to a consensus MSE ...

We address the problem of reconstructing a random signal from samples of its filtered version using a given interpolation kernel. In order to reduce the mean squared error (MSE) when using a non-optimal interpolation kernel we propose using a scheme with reconstruction rate that is greater than the sampling rate. A digital correction system that processes the samples prior to their multiplicati...