Several methods are available to predict cis-regulatory modules in DNA based on position weight matrices. However, the performance of these methods generally depends on a number of additional parameters that cannot be derived from sequences and are difficult to estimate because they have no physical meaning. As the best way to detect cis-regulatory modules is the way in which the proteins recog...

This paper presents a new classification framework for brain-computer interface (BCI) based on motor imagery. This framework involves the concept of Riemannian geometry in the manifold of covariance matrices. The main idea is to use spatial covariance matrices as EEG signal descriptors and to rely on Riemannian geometry to directly classify these matrices using the topology of the manifold of s...

The investigation of a distance{based regression model, using a one{dimensional set of equally spaced points as regressor values, and p jx ? yj as a distance function, leads to the study of a family of matrices which is closely related to a discrete analog of the Brownian Bridge stochastic process. We describe its eigenstructure and several properties, recovering in particular well{known result...

We define the notion of a random metric space and prove that with probability one such a space is isometric to the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particular, universal) spaces to the properties of distance matrices. We give examples of other categories in which the randomness and u...

This work applies earlier results on Quasi-Cyclic (QC) LDPC codes to the codes specified in six separate IEEE 802 standards, specifying wireless communications from 54 MHz to 60 GHz. First, we examine the weight matrices specified to upper bound the codes’ minimum distance independent of block length. Next, we search for the minimum distance achieved for the parity check matrices selected at ea...

In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is inconsistency of given PCM. In such a situation it is important to approximate the PCM with a consistent one. The most common way is to minimize the Euclidean distance between the matrices. In the paper we consider minimization of th...

In this paper we investigate partial spreads of H(2n− 1, q2) through the related notion of partial spread sets of hermitian matrices, and the more general notion of constant rank-distance sets. We prove a tight upper bound on the maximum size of a linear constant rank-distance set of hermitian matrices over finite fields, and as a consequence prove the maximality of extensions of symplectic sem...

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, in the case of Pauli measurements) with explicit dependence of the bounds on t...

We define a geodesic distance associated with the polarization space of non-singular coherency matrices. Its introduction on HPD(2) (the manifold of Hermitian positive definite matrices of dimension 2) can be directly related to the Jones calculus. The expression of distance and related notion of mean value in this particular metric space are also presented. We investigate the properties of thi...