We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where the dimension of the observed variables exceeds the sample size. Based on previous work, we postulate conditions that characterize a causal relation between X ...

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a...

Stabilization involves finding feedback controllers which stabilize the closed-loop system in the finite-time sense. Stability and control have been developed in the literature using Lyapunov-like method. In this paper, we develop a general framework for stabilization of linear differential-algebraic equations with time-varying delay. Based on Lyapunov-like function method and new bound estimat...

Abstract. In this paper, we address the problem for enumerating the number of finite field elements with prescribed trace and co-trace in case of arbitrary characteristic p. We show that this problem can be reduced to solving a system of p − 1 linear equations with matrix of coefficients a slight modification of circulant matrix formed by the Kloosterman sums over the field Fp. The presented ap...

Convergence of a matrix dynamics for online LDA is analyzed. Especially, stable spurious solutions are pointed out and two schemes to prevent the spurious solutions are proposed. The performance of the algorithm is confirmed by simulations of face identification.

We present a novel class of real symmetric matrices in arbitrary dimension d, linearly dependent on a parameter x. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such matrices for all x, and an intuitive sufficiency condition for the solvability of certain linear equations that arise therefrom. This class of matrices generically vi...

We give an unconditional version of a conditional, on the Extended Riemann Hypothesis, result of L. Babai, A. Banerjee, R. Kulkarni and V. Naik (2010) on the evasiveness of sparse graphs.

For solving large sparse non-Hermitian positive definite linear equations, Bai et al. proposed the Hermitian and skew-Hermitian splitting methods (HSS). They recently generalized this technique to the normal and skew-Hermitian splitting methods (NSS). In this paper, we present an accelerated normal and skew-Hermitian splitting methods (ANSS) which involve two parameters for the NSS iteration. W...

The estimation of the positive definite solutions to perturbed discrete Lyapunov equations is discussed. Several upper bounds of the positive definite solutions are obtained when the perturbation parameters are norm-bounded uncertain. In the derivation of the bounds, one only needs to deal with eigenvalues of matrices and linear matrix inequalities, and thus avoids solving high-order algebraic ...