Covariance Steering of Discrete-Time Linear Systems with Mixed Multiplicative and Additive Noise

In this paper, we study the covariance steering (CS) problem for discrete-time linear systems subject to multiplicative and additive noise. Specifically, we consider two variants of the so-called CS problem. The goal of the first problem, which is called the exact CS problem, is to steer the mean and the covariance of the state process to their desired values in finite time. In the second one, which is called the ``relaxed'' CS problem, the covariance assignment constraint is relaxed into a positive semi-definite constraint. We show that the relaxed CS problem can be cast as an equivalent convex semi-definite program (SDP) after applying suitable variable transformations and constraint relaxations. Furthermore, we propose a two-step solution procedure for the exact CS problem based on the relaxed problem formulation which returns a feasible solution, if there exists one. Finally, results from numerical experiments are provided to show the efficacy of the proposed solution methods

Density Steering of Gaussian Mixture Models for Discrete-Time Linear Systems

In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems. Specifically, we focus on steering probability densities represented as Gaussian mixture models which are known to give good approximations for general smooth probability density functions. We then revisit the covariance steering problem for Gaussian distributions and derive its optimal control policy. Subsequently, we propose a randomized policy to enhance the numerical tractability of the problem and demonstrate that under this policy the state distribution remains a Gaussian mixture. By leveraging these results, we reduce the Gaussian mixture steering problem to a linear program. We also discuss the problem of steering general distributions using Gaussian mixture approximations. Finally, we present results of non-trivial numerical experiments and demonstrate that our approach can be applied to general distribution steering problems

Evolution of Superconductivity in Electron-Doped Cuprates: Magneto-Raman Spectroscopy

The electron-doped cuprates Pr_{2-x}Ce_xCuO_4 and Nd_{2-x}Ce_xCuO_4 have been studied by electronic Raman spectroscopy across the entire region of the superconducting (SC) phase diagram. The SC pairing strength is found to be consistent with a weak-coupling regime except in the under-doped region where we observe an in-gap collective mode at 4.5 k_{B}T_c while the maximum amplitude of the SC gap is ~8 k_{B}T_{c}. In the normal state, doped carriers divide into coherent quasi-particles (QPs) and carriers that remain incoherent. The coherent QPs mainly reside in the vicinity of (\pi/2, \pi/2) regions of the Brillouin zone (BZ). We find that only coherent QPs contribute to the superfluid density in the B_{2g} channel. The persistence of SC coherence peaks in the B_{2g} channel for all dopings implies that superconductivity is mainly governed by interactions between the hole-like coherent QPs in the vicinity of (\pi/2, \pi/2) regions of the BZ. We establish that superconductivity in the electron-doped cuprates occurs primarily due to pairing and condensation of hole-like carriers. We have also studied the excitations across the SC gap by Raman spectroscopy as a function of temperature (T) and magnetic field (H) for several different cerium dopings (x). Effective upper critical field lines H*_{c2}(T, x) at which the superfluid stiffness vanishes and H^{2\Delta}_{c2}(T, x) at which the SC gap amplitude is suppressed by field have been determined; H^{2\Delta}_{c2}(T, x) is larger than H*_{c2}(T, x) for all doping concentrations. The difference between the two quantities suggests the presence of phase fluctuations that increase for x< 0.15. It is found that the magnetic field suppresses the magnitude of the SC gap linearly at surprisingly small fields.Comment: 13 pages, 8 figures; submitted to Phys. Rev.

A rare cause of blepharoconjunctivitis: Phthiriasis palpebrarum

Letter to Edito

Polypyrrole grafts with poly[(methyl methacrylate)-CO-(2-(N-pyrrolyl)ethyl methacrylate)]

Cataloged from PDF version of article.Conducting polymer grafts of pyrrole and poly[(methyl methacrylate)-co-(2- (N-pyrrolyl) ethyl methacrylate)] containing 0.7% PEMA units were prepared by potentiostatic anodic polymerization of pyrrole in different electrolytic media. Grafting between copolymer and pyrrole was achieved in media where tetrabutylammonium fluoroborate and sodium perchlorate were used as the supporting electrolytes. Characterizations were made by using IT-IR, DSC, TGA, SEM, CV, and elemental analysis. The conductivities of the resultant polymers seemed to be in the order of pure polypyrrole prepared under the same conditions. Copyright o 1997 Elsevier Scienc