Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure

Experimental modification and identification of the DSS-13 antenna control system model

This work is the first step toward increasing the bandwidth of the DSS-13 antenna position loop controller. A wider bandwidth of the controller allows for faster tracking rates and better pointing performance under windy conditions. To achieve this goal, the antenna control system model has to be improved, such that it will accurately reflect the dynamic properties of the antenna. The existing analytical model, due to its many uncertainties, could not be used in the design of the controller. However, by using experimental data, the analytical model is modified and improved, and a new model is obtained through system identification techniques

Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna

The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller

Reducing stigma and punitive attitudes toward pedophiles through narrative humanization

Stigmatization and societal punitiveness about pedophilia has a range of potential consequences, such as the social isolation of people with sexual interest in children, and the formation of policies that are not consistent with empirical research findings. Previous research has shown that people with pedophilic sexual interests use societal thinking to self-stigmatize, which in turn may actually serve to increase their risk of committing a sexual offense. In this study, we compared two attitudinal interventions (first-person narrative vs. expert opinion) using a student sample(N = 100). It was hypothesized that both interventions would lead to reductions in stigmatization and punitive attitudes about pedophiles on an explicit (self-report) level, but that only the narrative intervention would lead to reductions of these constructs at the implicit level. Our findings supported both hypotheses. We further discuss the role of narrative humanization in this area, and offer suggestions for further research based upon the theoretical and methodological implications of the findings

A functional-cognitive framework for attitude research

In attitude research, behaviours are often used as proxies for attitudes and attitudinal processes. This practice is problematic because it conflates the behaviours that need to be explained (explanandum) with the mental constructs that are used to explain these behaviours (explanans). In the current chapter we propose a meta-theoretical framework that resolves this problem by distinguishing between two levels of analysis. According to the proposed framework, attitude research can be conceptualised as the scientific study of evaluation. Evaluation is defined not in terms of mental constructs but in terms of elements in the environment, more specifically, as the effect of stimuli on evaluative responses. From this perspective, attitude research provides answers to two questions: (1) Which elements in the environment moderate evaluation? (2) What mental processes and representations mediate evaluation? Research on the first question provides explanations of evaluative responses in terms of elements in the environment (functional level of analysis); research on the second question offers explanations of evaluation in terms of mental processes and representations (cognitive level of analysis). These two levels of analysis are mutually supportive, in that better explanations at one level lead to better explanations at the other level. However, their mutually supportive relation requires a clear distinction between the concepts of their explanans and explanandum, which are conflated if behaviours are treated as proxies for mental constructs. The value of this functional-cognitive framework is illustrated by applying it to four central questions of attitude research

Social Balance on Networks: The Dynamics of Friendship and Enmity

How do social networks evolve when both friendly and unfriendly relations exist? Here we propose a simple dynamics for social networks in which the sense of a relationship can change so as to eliminate imbalanced triads--relationship triangles that contains 1 or 3 unfriendly links. In this dynamics, a friendly link changes to unfriendly or vice versa in an imbalanced triad to make the triad balanced. Such networks undergo a dynamic phase transition from a steady state to "utopia"--all friendly links--as the amount of network friendliness is changed. Basic features of the long-time dynamics and the phase transition are discussed.Comment: 16 pages, 11 figures, paper based on an invited talk at Dyonet06, Dynamics on Complex Networks and Applications, Dresden, Germany, Feburary 200

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this paper, we show that using the Eigensystem Realization Algorithm (ERA) \citep{JuPa-85}, one can theoretically obtain exactly the same reduced order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure

The 2010 nova outburst of the symbiotic Mira V407 Cyg

The nova outburst experienced in 2010 by the symbiotic binary Mira V407 Cyg has been extensively studied at optical and infrared wavelengths with both photometric and spectroscopic observations. This outburst, reminiscent of similar events displayed by RS Oph, can be described as a very fast He/N nova erupting while being deeply embedded in the dense wind of its cool giant companion. The hard radiation from the initial thermonuclear flash ionizes and excites the wind of the Mira over great distances (recombination is observed on a time scale of 4 days). The nova ejecta is found to progressively decelerate with time as it expands into the Mira wind. This is deduced from line widths which change from a FWHM of 2760 km/s on day +2.3 to 200 km/s on day +196. The wind of the Mira is massive and extended enough for an outer neutral and unperturbed region to survive at all outburst phases.Comment: MNRAS Letter, in pres