Using a factored dual in augmented Lagrangian methods for semidefinite programming

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further use the approximate maximum of the augmented Lagrangian with the aim of improving the convergence rate of alternating direction augmented Lagrangian frameworks. Numerical results are reported, showing the benefits of the approach.     

Optical Diagnosis for Thyroid and Parathyroid Tissues—A Review

Abstract

This article presents an overview of optical methodologies to aid the diagnosis and differentiation of thyroid and parathyroid tissues. In particular, we review the several techniques and associated methodologies that allow in vivo and ex vivo optical characterization of thyroid and parathyroid tissues. Emphasis is placed on the research potential of these techniques and whether intrinsic characteristics can provide useful contrast for the diagnosis of human thyroid and parathyroid malignant lesions.     

Universally programmable quantum cellular automaton

We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton with external classical control into an autonomous one, thereby proving the computational equivalence of these two models. We use this technique to construct a universally programmable cellular automaton on a one-dimensional lattice with single cell dimension 12.     

Phase Retrieval for Probability Distributions on Quantum Groups and Braided Groups

For nilpotent quantum groups [as introduced by Franz et al. ⁽⁷⁾], we show that (in sharp contrast to the classical case) the symmetrization of a probability distribution and the first moments of together determine uniquely the original distribution .