1 Summary The goal of blind deconvolution and source separation is to unravel the effects of an unknown linear transformation on a unknown signal source. For blind deconvolution, the transformation is a linear finite-impulse response (FIR) filter, and for blind source separation it is a matrix of mixing coefficients. A general architecture for these blind adaptive algorithms consists of an adju...

Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields. While FPR can express most of the known queries that separate FPC from Ptime, nearly nothing was known about the limitations of its expressive power. In our first main result we show that the e...

We analyse the elastic properties of a class cylindrical cloaks deduced from linear geometric transforms x→x′ in framework Milton–Briane–Willis cloaking theory [New Journal Physics 8, 248, 2006]. More precisely, we assume that mapping between displacement fields u(x)→u′(x′) is such u′(x′)=A−tu(x), where A either transformation gradient Fij=∂xi′/∂xj or second order identity tensor I. The nature ...

In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is n...

We present a low-rank transformation approach to compensate for face variations due to changes in visual domains, such as pose and illumination. The key idea is to learn discriminative linear transformations for face images using matrix rank as the optimization criteria. The learned linear transformations restore a shared low-rank structure for faces from the same subject, and, at the same time...

The nonparanormal model assumes that variables follow a multivariate normal distribution after a set of unknown monotone increasing transformations. It is a flexible generalization of the normal model but retains the nice interpretability of the latter. In this paper we propose a rank-based tapering estimator for estimating the correlation matrix in the nonparanormal model in which the variable...

Linear spaces of n× n× n tensors over finite fields are investigated where the rank of every nonzero tensor in the space is bounded from below by a prescribed number μ. Such linear paces can recover any n × n × n error tensor of rank ≤ (μ−1)/2, and, as such, they can be used to correct three-way crisscross errors. Bounds on the dimensions of such spaces are given for μ ≤ 2n+1, and constructions...

a celebrated result of i. schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the theory of groups. in this paper we exhibit a similar result to schur's theorem for vector spaces, acted upon by certain groups. the proof of this analogous result depends on the characteristic o...

We propose an exact nonparametric inference scheme for the detection of nonlinearity. The essential fact utilized in our scheme is that, for a linear stochastic process with jointly symmetric innovations, its ordinary least square (OLS) linear prediction error is symmetric about zero. Based on this viewpoint, a class of linear signed rank statistics, e.g. the Wilcoxon signed rank statistic, can...

Bruyère and Carton lifted the notion of finite automata reading infinite words to finite automata reading words with shape an arbitrary linear order L. Automata on finite words can be used to represent infinite structures, the socalled word-automatic structures. Analogously, for a linear order L there is the class of L-automatic structures. In this paper we prove the following limitations on th...