Supervisor Localization of Discrete-Event Systems based on State Tree Structures

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems in the Ramadge-Wonham supervisory control framework. Its essence is the decomposition of monolithic (global) control action into local control strategies for the individual agents. In this paper, we establish a counterpart supervisor localization theory in the framework of State Tree Structures, known to be efficient for control design of very large systems. In the new framework, we introduce the new concepts of local state tracker, local control function, and state-based local-global control equivalence. As before, we prove that the collective localized control behavior is identical to the monolithic optimal (i.e. maximally permissive) and nonblocking controlled behavior. In addition, we propose a new and more efficient localization algorithm which exploits BDD computation. Finally we demonstrate our localization approach on a model for a complex semiconductor manufacturing system

Resolving single molecule structures with Nitrogen-vacancy centers in diamond.

We present theoretical proposals for two-dimensional nuclear magnetic resonance spectroscopy protocols based on Nitrogen-vacancy (NV) centers in diamond that are strongly coupled to the target nuclei. Continuous microwave and radio-frequency driving fields together with magnetic field gradients achieve Hartmann-Hahn resonances between NV spin sensor and selected nuclei for control of nuclear spins and subsequent measurement of their polarization dynamics. The strong coupling between the NV sensor and the nuclei facilitates coherence control of nuclear spins and relaxes the requirement of nuclear spin polarization to achieve strong signals and therefore reduced measurement times. Additionally, we employ a singular value thresholding matrix completion algorithm to further reduce the amount of data required to permit the identification of key features in the spectra of strongly sub-sampled data. We illustrate the potential of this combined approach by applying the protocol to a shallowly implanted NV center addressing a small amino acid, alanine, to target specific hydrogen nuclei and to identify the corresponding peaks in their spectra

Multiple passages of light through an absorption inhomogeneity in optical imaging of turbid media

The multiple passages of light through an absorption inhomogeneity of finite size deep within a turbid medium is analyzed for optical imaging using the ``self-energy'' diagram. The nonlinear correction becomes more important for an inhomogeneity of a larger size and with greater contrast in absorption with respect to the host background. The nonlinear correction factor agrees well with that from Monte Carlo simulations for CW light. The correction is about $50$ in near infrared for an absorption inhomogeneity with the typical optical properties found in tissues and of size of five times the transport mean free path.Comment: 3 figure

Signed q-Analogs of Tornheim's Double Series

We introduce signed q-analogs of Tornheim's double series, and evaluate them in terms of double q-Euler sums. As a consequence, we provide explicit evaluations of signed and unsigned Tornheim double series, and correct some mistakes in the literature.Comment: 12 pages, AMSLaTeX. The multinomial notation introduced on page 3 just before Theorem 1 is insufficiently general in version 1, since it may happen that the upper number is negative. This is corrected in version 2, which allows for a negative or even complex upper argumen