We study the dynamics and evolution of Nambu-Goto strings in a warped spacetime, where the warp factor is a function of the internal coordinates giving rise to a ‘throat’ region. The microscopic equations of motion for strings in this background include potential and friction terms, which attract the strings towards the bottom of the warping throat. However, by considering the resulting macrosc...

In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, Xi(z) and Xi(s), where Xi(z) = Var[Z(ij)]/{Var[Z(ii)]Var[Z(jj)]}1/2, Xi(s) = Var[S(ij)]/{Var[S(ii)]Var[S(...

This paper studies the fundamental issue of determining if a linear precoder, such as a filter bank, introduces enough redundancy to enable the receiver to identify the unknown finite impulse response channel. Prior to the work herein, identifiability had only been resolved for specially designed linear precoders for which linear algebra or z-matrix theory sufficed.

In this brief note it is shown that the linear matrix inequalities that result from the application of interconnection and damping assignment passivity–based control to general linear time–invariant systems are feasible if and only if the system is stabilizable. A very simple proof of this fact is given that, in contrast to previous results, does not require the assumption that the system has n...

We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the renormalization of the ε-scalar mass. As a by-product we obtain the three-loop on-shell renormalization constants ZOS m and Z OS 2 in dimensional regularization a...

Several recent works have discussed tree structured sparse coding [8, 10, 7, 3], where N data points in R written as the d × N matrix X are approximately decomposed into the product of matrices WZ . HereW is a d×K dictionary matrix, and Z is a K×N matrix of coefficients. In tree structured sparse coding, the rows of Z correspond to nodes on a tree, and the columns of Z are encouraged to be nonz...

We implement a flexible Z-matrix approach in the Density Functional Theory (DFT) periodic boundary conditions code, SIESTA. This allows a mixture of Z-matrix and Cartesian coordinates to be used for geometry specification and optimisation. In addition, geometry constraints in the form of fixed coordinates and fixed linear relationships between coordinates can be specified. A Z-matrix approach i...

A proof is given for the preferred basis theorem for the generalized nullspace of a given M-matrix. The theorem is then generalized and extended to the case of a Z-matrix.

We consider the problem of characterizing nonnegativity of the Moore-Penrose inverse for matrix perturbations of the type A − XGY, when the Moore-Penrose inverse of A is nonnegative. Here, we say that a matrix B = (b ij ) is nonnegative and denote it by B ≥ 0 if b ij ≥ 0, ∀i, j. This problemwasmotivated by the results in [1], where the authors consider an M-matrix A and find sufficient conditio...

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P, Q] = P , where P flows according to the KP hierarchy ∂P/∂t n = [(P n/p) + , P ], with p := ord P ≥ 2; (ii) find a matrix integral representation for the associated τ-function. First we construct an infinite dimensional space W = span C ψ 0 (z), ψ 1 (z),. .. of functions of z ∈ C invariant u...