2,112 research outputs found
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 given by the line
bundles . 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 . Finally, in connection with real
rank boundaries, we give a new interpretation of the
hyperdeterminant.Comment: 17 p
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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 space-time. The metric of
ultrarelativistic charged particles in is obtained by boosting
Reissner-Nordstr\"om 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 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 collisions at TeV using 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 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
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