Matrix-Variate Regressions and Envelope Models

Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for matrix-valued responses. In this article, we study matrix-variate regressions for such data, where the response Y on each experimental unit is a random matrix and the predictor X can be either a scalar, a vector, or a matrix, treated as non-stochastic in terms of the conditional distribution Y|X. We propose models for matrix-variate regressions and then develop envelope extensions of these models. Under the envelope framework, redundant variation can be eliminated in estimation and the number of parameters can be notably reduced when the matrix-variate dimension is large, possibly resulting in significant gains in efficiency. The proposed methods are applicable to high dimensional settings.Comment: 28 pages, 4 figure

Manin-Olshansky triples for Lie superalgebras

Following V. Drinfeld and G. Olshansky, we construct Manin triples (\fg, \fa, \fa^*) such that \fg is different from Drinfeld's doubles of \fa for several series of Lie superalgebras \fa which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception. Straightforward superization of suitable Etingof--Kazhdan's results guarantee then the uniqueness of $q$-quantization of our Lie bialgebras. Our examples give solutions to the quantum Yang-Baxter equation in the cases when the classical YB equation has no solutions. To find explicit solutions is a separate (open) problem. It is also an open problem to list (\`a la Belavin-Drinfeld) all solutions of the {\it classical} YB equation for the Poisson superalgebras \fpo(0|2n) and the exceptional Lie superalgebra \fk(1|6) which has a Killing-like supersymmetric bilinear form but no Cartan matrix

Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one-deimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure

The Transmission Property of the Discrete Heisenberg Ferromagnetic Spin Chain

We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic spin chain (DHF) via a geometric approach. By the aid of a discrete nonlinear Schr\"odinger-like equation which is the discrete gauge equivalent to the DHF, we show that the determination of transmitting coefficients in the transmission problem is always bistable. Thus a definite algorithm and general stochastic algorithms are presented. A new invariant periodic phenomenon of the non-transmitting behavior for the DHF, with a large probability, is revealed by an adoption of various stochastic algorithms.Comment: 16 pages, 7 figure

Novel Gas-Doping Technique for Local Spectroscopic Measurements in Pulsed-Power Systems

A novel method for doping plasmas in pulsed-power experiments with gaseous elements has been developed. A fast gas valve, a nozzle, and a skimmer are used to generate an ultrasonic gas beam that is injected into a planar-geometry microsecond plasma-opening-switch (POS). An array of ionization probes with relatively high spatial and temporal resolutions was developed for diagnosing the absolute injected-gas density and its spatial profile. The properties of the gas column were also studied using spectroscopy of line emission that results from the interaction of the doped gas with the POS prefilled plasma. The doped column is found to have a width of ~1 cm and a density of (0.8-1.7)*10^14 cm-3. Observations of characteristic emission lines from the doped atoms and their ions allow for various spectroscopic measurements, such as the magnetic field from Zeeman splitting and the ion velocity distributions from Doppler shifts, that are local in three dimensions. It is shown that this gas doping technique can also be used to study proton-dominated plasmas that cannot be studied with simple emission spectroscopy due to the lack of light emitting ions. The variety of gases used with this method, together with the small valve dimensions and its fast opening, make it potentially useful for broad diagnostics of various short-duration plasma experiments.Comment: 5 pages, 7 figures in 1 pdf file from Rev. Sci. Inst

Hot Spots on the Fermi Surface of Bi2212: Stripes versus Superstructure

In a recent paper Saini et al. have reported evidence for a pseudogap around (pi,0) at room temperature in the optimally doped superconductor Bi2212. This result is in contradiction with previous ARPES measurements. Furthermore they observed at certain points on the Fermi surface hot spots of high spectral intensity which they relate to the existence of stripes in the CuO planes. They also claim to have identified a new electronic band along Gamma-M1 whose one dimensional character provides further evidence for stripes. We demonstrate in this Comment that all the measured features can be simply understood by correctly considering the superstructure (umklapp) and shadow bands which occur in Bi2212.Comment: 1 page, revtex, 1 encapsulated postscript figure (color