Diagnostic Applications for Micro-Synchrophasor Measurements

This report articulates and justifies the preliminary selection of diagnostic applications for data from micro-synchrophasors (µPMUs) in electric power distribution systems that will be further studied and developed within the scope of the three-year ARPA-e award titled Micro-synchrophasors for Distribution Systems

Bisimulation theory for switching linear systems

A general notion of hybrid bisimulation is proposed and related to the notions of algebraic, state-space and input-output equivalences for the class of switching linear systems. An algebraic characterization of hybrid bisimulations and a procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Bisimulation-based reduction and simulation-based abstraction are defined and characterized. Connections with observability are investigated

Oscillations, metastability and phase transitions in brain and models of cognition

Neuroscience is being practiced in many different forms and at many different organizational levels of the Nervous System. Which of these levels and associated conceptual frameworks is most informative for elucidating the association of neural processes with processes of Cognition is an empirical question and subject to pragmatic validation. In this essay, I select the framework of Dynamic System Theory. Several investigators have applied in recent years tools and concepts of this theory to interpretation of observational data, and for designing neuronal models of cognitive functions. I will first trace the essentials of conceptual development and hypotheses separately for discerning observational tests and criteria for functional realism and conceptual plausibility of the alternatives they offer. I will then show that the statistical mechanics of phase transitions in brain activity, and some of its models, provides a new and possibly revealing perspective on brain events in cognition

Optimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels

In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the method of Markovian jump linear systems, an optimal stationary estimator that minimizes the error variance in the steady state is obtained, based on the mean-square (MS) stabilizing solution to the coupled algebraic Riccati equations. An explicit necessary and sufficient condition is derived for the existence of the MS stabilizing solution, which coincides with that of the standard Kalman filter. More importantly, we provide a sufficient condition under which the MS detectability with multiple Markovian packet drop channels can be decoupled, and propose a locally optimal stationary estimator but computationally more tractable. Analytic sufficient and necessary MS detectability conditions are presented for the decoupled subsystems subsequently. Finally, numerical simulations are conducted to illustrate the results on the MS stabilizing solution, the MS detectability, and the performance of the optimal and locally optimal stationary estimators

Equivalence of switching linear systems by bisimulation

A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and input–output equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud \u

Effects of various generations of iterative CT reconstruction algorithms on low-contrast detectability as a function of the effective abdominal diameter: A quantitative task-based phantom study.

To investigate how various generations of iterative reconstruction (IR) algorithms impact low-contrast detectability (LCD) in abdominal computed tomography (CT) for different patient effective diameters, using a quantitative task-based approach. Investigations were performed using an anthropomorphic abdominal phantom with two optional additional rings to simulate varying patient effective diameters (25, 30, and 35 cm), and containing multiple spherical targets (5, 6, and 8 mm in diameter) with a 20-HU contrast difference. The phantom was scanned using routine abdominal protocols (CTDI <sub>vol</sub> , 5.9-16 mGy) on four CT systems from two manufacturers. Images were reconstructed using both filtered back-projection (FBP) and various IR algorithms: ASiR 50%, SAFIRE 3 (both statistical IRs), ASiR-V 50%, ADMIRE 3 (both partial model-based IRs), or Veo (full model-based IR). Section thickness/interval was 2/1 mm or 2.5/1.25 mm, except 0.625/0.625 mm for Veo. We assessed LCD using a channelized Hotelling observer with 10 dense differences of Gaussian channels, with the area under the receiver operating characteristic curve (AUC) as a figure of merit. For the smallest phantom (25-cm diameter) and smallest lesion size (5-mm diameter), AUC for FBP and the various IR algorithms did not significantly differ for any of the tested CT systems. For the largest phantom (35-cm diameter), Veo yielded the highest AUC improvement (8.5%). Statistical and partial model-based IR algorithms did not significantly improve LCD. In abdominal CT, switching from FBP to IR algorithms offers limited possibilities for achieving significant dose reductions while ensuring a constant objective LCD

Realization of multi-input/multi-output switched linear systems from Markov parameters

This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the submodels have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, zero sets of LTV Hankel matrices where the realized system has a linear time-invariant (LTI) pulse response matching that of the original SLS are exploited to extract the submodels, up to arbitrary similarity transformations, by a clustering algorithm using a statistics that is invariant to similarity transformations. Recovery is shown to be complete if the dwell times are sufficiently long and some mild identifiability conditions are met. In the third stage, the switching sequence is estimated by three schemes. The first scheme is based on forward/backward corrections and works on the short segments. The second scheme matches Markov parameter estimates to the true parameters for LTV systems and works on the medium-to-long segments. The third scheme also matches Markov parameters, but for LTI systems only and works on the very short segments. In the fourth stage, the submodels estimated in Stage~2 are brought to a common basis by applying a novel basis transformation method which is necessary before performing output predictions to given inputs. A numerical example illustrates the properties of the realization algorithm. A key role in this algorithm is played by time-dependent switching sequences that partition the state-space according to time, unlike many other works in the literature in which partitioning is state and/or input dependent