Conservative Signal Processing Architectures For Asynchronous, Distributed Optimization Part II: Example Systems

This paper provides examples of various synchronous and asynchronous signal processing systems for performing optimization, utilizing the framework and elements developed in a preceding paper. The general strategy in that paper was to perform a linear transformation of stationarity conditions applicable to a class of convex and nonconvex optimization problems, resulting in algorithms that operate on a linear superposition of the associated primal and dual decision variables. The examples in this paper address various specific optimization problems including the LASSO problem, minimax-optimal filter design, the decentralized training of a support vector machine classifier, and sparse filter design for acoustic equalization. Where appropriate, multiple algorithms for solving the same optimization problem are presented, illustrating the use of the underlying framework in designing a variety of distinct classes of algorithms. The examples are accompanied by numerical simulation and a discussion of convergence

Influence of Rashba and Dresselhaus spin-orbit interactions of equal strengths on electron states in a circular quantum ring in the presence of a magnetic field

Solutions of the Schr\"odinger equation are obtained for an electron in a two-dimensional circular semiconductor quantum ring in the presence of both external uniform constant magnetic field and the Rashba and Dresselhaus spin-orbit interactions of equal strengths. Confinement is simulated by a realistic potential well of a finite depth. The dependence of the energy levels on a magnetic field strength, strength of spin-orbit interaction and a relative ring width is presented.Comment: 6 pages, 2 figures, 1 tabl