Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints

A new smoothing approach based on entropic perturbationis proposed for solving mathematical programs withequilibrium constraints. Some of the desirableproperties of the smoothing function are shown. Theviability of the proposed approach is supported by acomputationalstudy on a set of well-known test problems.mathematical programs with equilibrium constraints;entropic regularization;smoothing approach

Entropic regularization approach for mathematical programs with equilibrium constraints

A new smoothing approach based on entropic perturbation is proposed for solving mathematical programs with equilibrium constraints. Some of the desirable properties of the smoothing function are shown. The viability of the proposed approach is supported by a computational study on a set of well-known test problems.Entropic regularization;Smoothing approach;Mathematical programs with equilibrium constraints

The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behavior, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behavior of the isochore heat capacity for a trapped unitary Fermi gas is also analyzed.Comment: 6 pages, 6 figure

On the finite termination of an entropy function based smoothing Newton method for vertical linear complementarity problems

By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that the proposed algorithm finds an exact solution of VLCP in a finite number of iterations, under some conditions milder than those assumed in literature. Some computational results are included to illustrate the potential of this approach.Newton method;Finite termination;Entropy function;Smoothing approximation;Vertical linear complementarity problems

Transfer Learning for Multi-language Twitter Election Classification

Both politicians and citizens are increasingly embracing social media as a means to disseminate information and comment on various topics, particularly during significant political events, such as elections. Such commentary during elections is also of interest to social scientists and pollsters. To facilitate the study of social media during elections, there is a need to automatically identify posts that are topically related to those elections. However, current studies have focused on elections within English-speaking regions, and hence the resultant election content classifiers are only applicable for elections in countries where the predominant language is English. On the other hand, as social media is becoming more prevalent worldwide, there is an increasing need for election classifiers that can be generalised across different languages, without building a training dataset for each election. In this paper, based upon transfer learning, we study the development of effective and reusable election classifiers for use on social media across multiple languages. We combine transfer learning with different classifiers such as Support Vector Machines (SVM) and state-of-the-art Convolutional Neural Networks (CNN), which make use of word embedding representations for each social media post. We generalise the learned classifier models for cross-language classification by using a linear translation approach to map the word embedding vectors from one language into another. Experiments conducted over two election datasets in different languages show that without using any training data from the target language, linear translations outperform a classical transfer learning approach, namely Transfer Component Analysis (TCA), by 80% in recall and 25% in F1 measure

Inferring effective interactions from the local density of states: application to STM data from Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

While the influence of impurities on the local density of states (LDOS) in a metal is notoriously non-local due to interference effects, low order moments of the LDOS in general can be shown to depend only on the local structure of the Hamiltonian. Specifically, we show that an analysis of the spatial variations of these moments permits one to ``work backwards'' from scanning tunneling microscopy (STM) data to infer the local structure of the underlying effective Hamiltonian. Applying this analysis to STM data from the high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we find that the variations of the electro-chemical potential are remarkably small (i.e., the disorder is, in a sense, weak) but that there are large variations in the local magnitude of the d-wave gap parameter.Comment: 7 pages, 7 figure