Convex recovery of tensors using nuclear norm penalization

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining much interest due to its potential applications to signal processing, statistics and engineering. The goal of this paper is to present an applications to the problem of low rank tensor recovery based on linear random measurement by extending the results of Tropp to the tensors setting.Comment: To appear in proceedings LVA/ICA 2015 at Czech Republi

Complexity of linear circuits and geometry

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border) rigidity, (ii) compute degrees of varieties associated to rigidity, (iii) describe algebraic varieties associated to families of matrices that are expected to have super-linear rigidity, and (iv) prove results about the ideals and degrees of cones that are of interest in their own right.Comment: 29 pages, final version to appear in FOC

Real rank boundaries and loci of forms

In this article we study forbidden loci and typical ranks of forms with respect to the embeddings of $\mathbb P^1\times \mathbb P^1$ given by the line bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of $\mathbb P^n\times \mathbb P^1$. Finally, in connection with real rank boundaries, we give a new interpretation of the $2\times n \times n$ hyperdeterminant.Comment: 17 p

Distance Optimization and the Extremal Variety of the Grassmann Variety

The approximation of a multivector by a decomposable one is a distance-optimization problem between the multivector and the Grassmann variety of lines in a projective space. When the multivector diverges from the Grassmann variety, then the approximate solution sought is the worst possible. In this paper, it is shown that the worst solution of this problem is achieved, when the eigenvalues of the matrix representation of a related two-vector are all equal. Then, all these pathological points form a projective variety. We derive the equation describing this projective variety, as well as its maximum distance from the corresponding Grassmann variety. Several geometric and algebraic properties of this extremal variety are examined, providing a new aspect for the Grassmann varieties and the respective projective spaces

Light hadron, Charmonium(-like) and Bottomonium(-like) states

Hadron physics represents the study of strongly interacting matter in all its manifestations and the understanding of its properties and interactions. The interest on this field has been revitalized by the discovery of new light hadrons, charmonium- and bottomonium-like states. I review the most recent experimental results from different experiments.Comment: Presented at Lepton-Photon 2011, Mumbai, India; 21 pages, 18 figures; add more references; some correctio

Critical Trapped Surfaces Formation in the Collision of Ultrarelativistic Charges in (A)dS

We study the formation of marginally trapped surfaces in the head-on collision of two ultrarelativistic charges in $(A)dS$ space-time. The metric of ultrarelativistic charged particles in $(A)dS$ is obtained by boosting Reissner-Nordstr\"om $(A)dS$ space-time to the speed of light. We show that formation of trapped surfaces on the past light cone is only possible when charge is below certain critical - situation similar to the collision of two ultrarelativistic charges in Minkowski space-time. This critical value depends on the energy of colliding particles and the value of a cosmological constant. There is richer structure of critical domains in $dS$ case. In this case already for chargeless particles there is a critical value of the cosmological constant only below which trapped surfaces formation is possible. Appearance of arbitrary small nonzero charge significantly changes the physical picture. Critical effect which has been observed in the neutral case does not take place more. If the value of the charge is not very large solution to the equation on trapped surface exists for any values of cosmological radius and energy density of shock waves. Increasing of the charge leads to decrease of the trapped surface area, and at some critical point the formation of trapped surfaces of the type mentioned above becomes impossible.Comment: 30 pages, Latex, 7 figures, Refs. added and typos correcte

Limits on WWZ and WW\gamma couplings from p\bar{p}\to e\nu jj X events at \sqrt{s} = 1.8 TeV

We present limits on anomalous WWZ and WW-gamma couplings from a search for WW and WZ production in p-bar p collisions at sqrt(s)=1.8 TeV. We use p-bar p -> e-nu jjX events recorded with the D0 detector at the Fermilab Tevatron Collider during the 1992-1995 run. The data sample corresponds to an integrated luminosity of 96.0+-5.1 pb^(-1). Assuming identical WWZ and WW-gamma coupling parameters, the 95% CL limits on the CP-conserving couplings are -0.33<lambda<0.36 (Delta-kappa=0) and -0.43<Delta-kappa<0.59 (lambda=0), for a form factor scale Lambda = 2.0 TeV. Limits based on other assumptions are also presented.Comment: 11 pages, 2 figures, 2 table

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012

Search For Heavy Pointlike Dirac Monopoles

We have searched for central production of a pair of photons with high transverse energies in $p\bar p$ collisions at $\sqrt{s} = 1.8$ TeV using $70 pb^{-1}$ of data collected with the D\O detector at the Fermilab Tevatron in 1994--1996. If they exist, virtual heavy pointlike Dirac monopoles could rescatter pairs of nearly real photons into this final state via a box diagram. We observe no excess of events above background, and set lower 95% C.L. limits of $610, 870, or 1580 GeV/c^2$ on the mass of a spin 0, 1/2, or 1 Dirac monopole.Comment: 12 pages, 4 figure

The Dijet Mass Spectrum and a Search for Quark Compositeness in bar{p}p Collisions at sqrt{s} = 1.8 TeV

Using the DZero detector at the 1.8 TeV pbarp Fermilab Tevatron collider, we have measured the inclusive dijet mass spectrum in the central pseudorapidity region |eta_jet| < 1.0 for dijet masses greater than 200 Gev/c^2. We have also measured the ratio of spectra sigma(|eta_jet| < 0.5)/sigma(0.5 < |eta_jet| < 1.0). The order alpha_s^3 QCD predictions are in good agreement with the data and we rule out models of quark compositeness with a contact interaction scale < 2.4 TeV at the 95% confidence level.Comment: 11 pages, 4 figures, 2 tables, submitted to Phys. Rev. Let