Estimation for bilinear stochastic systems

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed

A class of finite dimensional optimal nonlinear estimators

Finite dimensional optimal nonlinear state estimators are derived for bilinear systems evolving on nilpotent and solvable Lie groups. These results are extended to other classes of systems involving polynomial nonlinearities. The concepts of exact differentials and path-independent integrals are used to derive optimal finite dimensional estimators for a further class of nonlinear systems

A High Reliability Asymptotic Approach for Packet Inter-Delivery Time Optimization in Cyber-Physical Systems

In cyber-physical systems such as automobiles, measurement data from sensor nodes should be delivered to other consumer nodes such as actuators in a regular fashion. But, in practical systems over unreliable media such as wireless, it is a significant challenge to guarantee small enough inter-delivery times for different clients with heterogeneous channel conditions and inter-delivery requirements. In this paper, we design scheduling policies aiming at satisfying the inter-delivery requirements of such clients. We formulate the problem as a risk-sensitive Markov Decision Process (MDP). Although the resulting problem involves an infinite state space, we first prove that there is an equivalent MDP involving only a finite number of states. Then we prove the existence of a stationary optimal policy and establish an algorithm to compute it in a finite number of steps. However, the bane of this and many similar problems is the resulting complexity, and, in an attempt to make fundamental progress, we further propose a new high reliability asymptotic approach. In essence, this approach considers the scenario when the channel failure probabilities for different clients are of the same order, and asymptotically approach zero. We thus proceed to determine the asymptotically optimal policy: in a two-client scenario, we show that the asymptotically optimal policy is a "modified least time-to-go" policy, which is intuitively appealing and easily implementable; in the general multi-client scenario, we are led to an SN policy, and we develop an algorithm of low computational complexity to obtain it. Simulation results show that the resulting policies perform well even in the pre-asymptotic regime with moderate failure probabilities

On the Phenomenology of Hydrodynamic Shear Turbulence

The question of a purely hydrodynamic origin of turbulence in accretion disks is reexamined, on the basis of a large body of experimental and numerical evidence on various subcritical (i.e., linearly stable) hydrodynamic flows. One of the main points of this paper is that the length scale and velocity fluctuation amplitude which are characteristic of turbulent transport in these flows scale like $Re_m^{-1/2}$, where $Re_m$ is the minimal Reynolds number for the onset of fully developed turbulence. From this scaling, a simple explanation of the dependence of $Re_m$ with relative gap width in subcritical Couette-Taylor flows is developed. It is also argued that flows in the shearing sheet limit should be turbulent, and that the lack of turbulence in all such simulations performed to date is most likely due to a lack of resolution, as a consequence of the effect of the Coriolis force on the large scale fluctuations of turbulent flows. These results imply that accretion flows should be turbulent through hydrodynamic processes. If this is the case, the Shakura-Sunyaev $\alpha$ parameter is constrained to lie in the range $10^{-3}-10^{-1}$ in accretion disks, depending on unknown features of the mechanism which sustains turbulence. Whether the hydrodynamic source of turbulence is more efficient than the MHD one where present is an open question.Comment: 31 pages, 3 figures. Accepted for publication in Ap

Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N

Using optimized perturbation theory, we evaluate the effective potential for the massless two dimensional Gross-Neveu model at finite temperature and density containing corrections beyond the leading large-N contribution. For large-N, our results exactly reproduce the well known 1/N leading order results for the critical temperature, chemical potential and tricritical points. For finite N, our critical values are smaller than the ones predicted by the large-N approximation and seem to observe Landau's theorem for phase transitions in one space dimension. New analytical results are presented for the tricritical points that include 1/N corrections. The easiness with which the calculations and renormalization are carried out allied to the seemingly convergent optimized results displayed, in this particular application, show the robustness of this method and allows us to obtain neat analytical expressions for the critical as well as tricritical values beyond the results currently known.Comment: 29 pages, 14 figure

Co-Clinical Imaging Resource Program (CIRP): Bridging the translational divide to advance precision medicine

The National Institutes of Health\u27s (National Cancer Institute) precision medicine initiative emphasizes the biological and molecular bases for cancer prevention and treatment. Importantly, it addresses the need for consistency in preclinical and clinical research. To overcome the translational gap in cancer treatment and prevention, the cancer research community has been transitioning toward using animal models that more fatefully recapitulate human tumor biology. There is a growing need to develop best practices in translational research, including imaging research, to better inform therapeutic choices and decision-making. Therefore, the National Cancer Institute has recently launched the Co-Clinical Imaging Research Resource Program (CIRP). Its overarching mission is to advance the practice of precision medicine by establishing consensus-based best practices for co-clinical imaging research by developing optimized state-of-the-art translational quantitative imaging methodologies to enable disease detection, risk stratification, and assessment/prediction of response to therapy. In this communication, we discuss our involvement in the CIRP, detailing key considerations including animal model selection, co-clinical study design, need for standardization of co-clinical instruments, and harmonization of preclinical and clinical quantitative imaging pipelines. An underlying emphasis in the program is to develop best practices toward reproducible, repeatable, and precise quantitative imaging biomarkers for use in translational cancer imaging and therapy. We will conclude with our thoughts on informatics needs to enable collaborative and open science research to advance precision medicine

The evolution of bits and bottlenecks in a scientific workflow trying to keep up with technology: Accelerating 4D image segmentation applied to nasa data

In 2016, a team of earth scientists directly engaged a team of computer scientists to identify cyberinfrastructure (CI) approaches that would speed up an earth science workflow. This paper describes the evolution of that workflow as the two teams bridged CI and an image segmentation algorithm to do large scale earth science research. The Pacific Research Platform (PRP) and The Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI) resources were used to significantly decreased the earth science workflow's wall-clock time from 19.5 days to 53 minutes. The improvement in wall-clock time comes from the use of network appliances, improved image segmentation, deployment of a containerized workflow, and the increase in CI experience and training for the earth scientists. This paper presents a description of the evolving innovations used to improve the workflow, bottlenecks identified within each workflow version, and improvements made within each version of the workflow, over a three-year time period

Constraints on relaxation rates for N-level quantum systems

We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open N-level systems. The Lindblad operators that govern the evolution of the system are expressed in terms of observable relaxation rates, explicit formulas for the decoherence rates due to population relaxation are derived, and it is shown that there are additional, non-trivial constraints on the pure dephasing rates for N>2. Explicit experimentally testable inequality constraints for the decoherence rates are derived for three and four-level systems, and the implications of the results are discussed for generic ladder-, Lambda- and V-systems, and transitions between degenerate energy levels.Comment: 10 pages, RevTeX, 4 figures (eps/pdf

Exact 1/N and Optimized Perturbative Evaluation of mu_c for Homogeneous Interacting Bose Gases

In the framework of the O(N) three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the 1/N expansion to evaluate, within the large N limit, the parameter r_c which is directly related to the critical chemical potential mu_c. This quantity enters the order-a^2 n^{2/3} coefficient contributing to the critical temperature shift Delta T_c where a represents the s-wave scattering length and n represents the density. Compared to the recent precise numerical lattice simulation results, our calculation suggests that the large N approximation performs rather well even for the physical case N=2. We then calculate the same quantity but using different forms of the optimized perturbative (variational) method, showing that these produce excellent results both for the finite N and large-N cases.Comment: 12 pages, 2 figures. We have performed a refined and extended numerical analysis to take into account the very recent results of Ref. [15