Submodularity of Energy Related Controllability Metrics

The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.Comment: 7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision and Contro

On Submodularity and Controllability in Complex Dynamical Networks

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary documents) that explains an error in a proof of the original paper and provides a counterexample to the corresponding resul

Anger, Quality of Life and Mood in Multiple Sclerosis

This research was funded by The Multiple Sclerosis Society (UK).Peer reviewedPublisher PD

Ionization state, excited populations and emission of impurities in dynamic finite density plasmas: I. The generalized collisional-radiative model for light elements

The paper presents an integrated view of the population structure and its role in establishing the ionization state of light elements in dynamic, finite density, laboratory and astrophysical plasmas. There are four main issues, the generalized collisional-radiative picture for metastables in dynamic plasmas with Maxwellian free electrons and its particularizing to light elements, the methods of bundling and projection for manipulating the population equations, the systematic production/use of state selective fundamental collision data in the metastable resolved picture to all levels for collisonal-radiative modelling and the delivery of appropriate derived coefficients for experiment analysis. The ions of carbon, oxygen and neon are used in illustration. The practical implementation of the methods described here is part of the ADAS Project

Nuance and behavioral cogency: How the Visible Burrow System inspired the Stress-Alternatives Model and conceptualization of the continuum of anxiety

By creating the Visible Burrow System (VBS) Bob Blanchard found a way to study the interaction of genetics, physiology, environment, and adaptive significance in a model with broad validity. The VBS changed the way we think about anxiety and affective disorders by allowing the mechanisms which control them to be observed in a dynamic setting. Critically, Blanchard used the VBS and other models to show how behavioral systems like defense are dependent upon context and behavioral elements unique to the individual. Inspired by the VBS, we developed a Stress Alternatives Model (SAM) to further explore the multifaceted dynamics of the stress response with a dichotomous choice condition. Like the VBS, the SAM is a naturalistic model built upon risk assessment and defensive behavior, but with a choice of response: escape or submission to a large conspecific aggressor. The anxiety of novelty during the first escape must be weighed against fear of the aggressor, and a decision must be made. Both outcomes are adaptively significant, evidenced by a 50/50 split in outcome across several study systems. By manipulating the variables of the SAM, we show that a gradient of anxiety exists that spans the contextual settings of escaping an open field, escaping from aggression, and submitting to aggression. These findings correspond with increasing levels of corticosterone and increasing levels of NPS and BDNF in the central amygdala as the context changes.Whereas some anxiolytics were able to reduce the latency to escape for some animals, only with the potent anxiolytic drug antalarmin (CRF1R-blocker) and the anxiogenic drug yohimbine (α2 antagonist) were we able to reverse the outcome for a substantial proportion of individuals. Our findings promote a novel method for modeling anxiety, offering a distinction between low-and-high levels, and accounting for individual variability. The translational value of the VBS is immeasurable, and it guided us and many other researchers to seek potential clinical solutions through a deeper understanding of regional neurochemistry and gene expression in concert with an ecological behavioral model

Charge dependence of neoclassical and turbulent transport of light impurities on MAST

Carbon and nitrogen impurity transport coefficients are determined from gas puff experiments carried out during repeat L-mode discharges on the Mega-Amp Spherical Tokamak (MAST) and compared against a previous analysis of helium impurity transport on MAST. The impurity density profiles are measured on the low-field side of the plasma, therefore this paper focuses on light impurities where the impact of poloidal asymmetries on impurity transport is predicted to be negligible. A weak screening of carbon and nitrogen is found in the plasma core, whereas the helium density profile is peaked over the entire plasma radius.Comment: 17 pages, 7 figure

Site-Selective Spectroscopy And Crystal-Field Analysis For Nd3+ In Strontium Fluorovanadate

Site‐selective spectroscopy reveals that Nd3+ ions occupy more than 40 different crystal‐field environments in Sr5(VO4)3F. Preferential energy transfer to the site responsible for 1 μm lasing occurs but becomes less complete with increasing temperature. The 4I and 4F3/2 Stark levels of the lasing site have been determined and an analysis of the crystal field performed. From the crystal‐field fitting parameters Bkq, a calculated energy‐level spectrum is determined up to 17 500 cm−1 with a rms deviation from the available experimental levels of 6 cm−1

Learning and CRF-Induced Indecision during Escape and Submission in Rainbow Trout during Socially Aggressive Interactions in the Stress-Alternatives Model

Socially stressful environments induce a phenotypic dichotomy of coping measures for populations in response to a dominant aggressor and given a route of egress. This submission- (Stay) or escape-oriented (Escape) dichotomy represents individual decision-making under the stressful influence of hostile social environments. We utilized the Stress-Alternatives Model (SAM) to explore behavioral factors which might predict behavioral phenotype in rainbow trout. The SAM is a compartmentalized tank, with smaller and larger trout separated by an opaque divider until social interaction, and another divider occluding a safety zone, accessible by way of an escape route only large enough for the smaller fish. We hypothesized that distinctive behavioral responses during the first social interaction would indicate a predisposition for one of the behavioral phenotypes in the subsequent interactions. Surprisingly, increased amount or intensity of aggression received had no significant effect on promoting escape in test fish. In fact, during the first day of interaction, fish that turned toward their larger opponent during attack eventually learned to escape. Escaping fish also learn to monitor the patrolling behavior of aggressors, and eventually escape primarily when they are not being observed. Escape per se, was also predicted in trout exhibiting increased movements directed toward the escape route. By contrast, fish that consistently remained in the tank with the aggressor (Stay) showed significantly higher frequency of swimming in subordinate positions, at the top or the bottom of the water column, as well as sitting at the bottom. In addition, a corticotropin-releasing factor (CRF)-induced behavior, snap-shake, was also displayed in untreated fish during aggressive social interaction, and blocked by a CRF1 receptor antagonist. Especially prevalent among the Stay phenotype, snap-shake indicates indecision regarding escape-related behaviors. Snap-shake was also exhibited by fish of the Escape phenotype, showing a positive correlation with latency to escape. These results demonstrate adaptive responses to stress that reflect evolutionarily conserved stress neurocircuitry which may translate to psychological disorders and decision-making across vertebrate taxa