Sparsity Oriented Importance Learning for High-dimensional Linear Regression

With now well-recognized non-negligible model selection uncertainty, data analysts should no longer be satisfied with the output of a single final model from a model selection process, regardless of its sophistication. To improve reliability and reproducibility in model choice, one constructive approach is to make good use of a sound variable importance measure. Although interesting importance measures are available and increasingly used in data analysis, little theoretical justification has been done. In this paper, we propose a new variable importance measure, sparsity oriented importance learning (SOIL), for high-dimensional regression from a sparse linear modeling perspective by taking into account the variable selection uncertainty via the use of a sensible model weighting. The SOIL method is theoretically shown to have the inclusion/exclusion property: When the model weights are properly around the true model, the SOIL importance can well separate the variables in the true model from the rest. In particular, even if the signal is weak, SOIL rarely gives variables not in the true model significantly higher important values than those in the true model. Extensive simulations in several illustrative settings and real data examples with guided simulations show desirable properties of the SOIL importance in contrast to other importance measures

Branch and bound method for regression-based controlled variable selection

Self-optimizing control is a promising method for selection of controlled variables (CVs) from available measurements. Recently, Ye, Cao, Li, and Song (2012) have proposed a globally optimal method for selection of self-optimizing CVs by converting the CV selection problem into a regression problem. In this approach, the necessary conditions of optimality (NCO) are approximated by linear combinations of available measurements over the entire operation region. In practice, it is desired that a subset of available measurements be combined as CVs to obtain a good trade-off between the economic performance and the complexity of control system. The subset selection problem, however, is combinatorial in nature, which makes the application of the globally optimal CV selection method to large-scale processes difficult. In this work, an efficient branch and bound (BAB) algorithm is developed to handle the computational complexity associated with the selection of globally optimal CVs. The proposed BAB algorithm identifies the best measurement subset such that the regression error in approximating NCO is minimized and is also applicable to the general regression problem. Numerical tests using randomly generated matrices and a binary distillation column case study demonstrate the computational efficiency of the proposed BAB algorithm

Superconducting cosmic strings as sources of cosmological fast radio bursts

In this paper we calculate the radio burst signals from three kinds of structures of superconducting cosmic strings. By taking into account the observational factors including scattering and relativistic effects, we derive the event rate of radio bursts as a function of redshift with the theoretical parameters $G\mu$ and $\mathcal{I}$ of superconducting strings. Our analyses show that cusps and kinks may have noticeable contributions to the event rate and in most cases cusps would dominate the contribution, while the kink-kink collisions tend to have secondary effects. By fitting theoretical predictions with the normalized data of fast radio bursts, we for the first time constrain the parameter space of superconducting strings and report that the parameter space of $G\mu \sim [10^{-14}, 10^{-12}]$ and $\mathcal{I} \sim [10^{-1}, 10^{2}] ~ \rm{GeV}$ fit the observation well although the statistic significance is low due to the lack of observational data. Moreover, we derive two types of best fittings, with one being dominated by cusps with a redshift $z = 1.3$, and the other dominated by kinks at the range of the maximal event rate.Comment: 13 pages, 2 figures, 1 table; references update

Subset measurement selection for globally self-optimizing control of Tennessee Eastman process

The concept of globally optimal controlled variable selection has recently been proposed to improve self-optimizing control performance of traditional local approaches. However, the associated measurement subset selection problem has not be studied. In this paper, we consider the measurement subset selection problem for globally self-optimizing control (gSOC) of Tennessee Eastman (TE) process. The TE process contains substantial measurements and had been studied for SOC with controlled variables selected from individual measurements through exhaustive search. This process has been revisited with improved performance recently through a retrofit approach of gSOC. To extend the improvement further, the measurement subset selection problem for gSOC is considered in this work and solved through a modification of an existing partially bidirectional branch and bound (PB3) algorithm originally developed for local SOC. The modified PB3 algorithm efficiently identifies the best measurement candidates among the full set which obtains the globally minimal economic loss. Dynamic simulations are conducted to demonstrate the optimality of proposed results

Retrofit self-optimizing control of Tennessee Eastman process

This paper considers near-optimal operation of the Tennessee Eastman (TE) process by using a retrofit self-optimizing control (SOC) approach. Motivated by the factor that most chemical plants in operation have already been equipped with a workable control system for regulatory control, we propose to improve the economic performance by controlling some self-optimizing controlled variables (CVs). Different from traditional SOC methods, the proposed retrofit SOC approach improves economic optimality of operation through newly added cascaded SOC loops, where carefully selected SOC CVs are maintained at constant by adjusting set-points of the existing regulatory control loops. To demonstrate the effectiveness of the retrofit SOC proposed, we adopted measurement combinations as the CVs for the TE process, so that the economic cost is further reduced comparing to existing studies where single measurements are controlled. The optimality of the designed control architecture is validated through both steady state analysis and dynamic simulations

Modified evolution of stellar binaries from supermassive black hole binaries

The evolution of main sequence binaries resided in the galactic centre is influenced a lot by the central super massive black hole (SMBH). Due to this perturbation, the stars in a dense environment are likely to experience mergers or collisions through secular or non-secular interactions. In this work, we study the dynamics of the stellar binaries at galactic center, perturbed by another distant SMBH. Geometrically, such a four-body system is supposed to be decomposed into the inner triple (SMBH-star-star) and the outer triple (SMBH-stellar binary-SMBH). We survey the parameter space and determine the criteria analytically for the stellar mergers and the tidal disruption events (TDEs). For a relative distant and equal masses SMBH binary, the stars have more opportunities to merge as a result from the Lidov-Kozai(LK) oscillations in the inner triple. With a sample of tight stellar binaries, our numerical experiments reveal that a significant fraction of the binaries, ~70 per cent, experience merger eventually. Whereas the majority of the stellar TDEs are likely to occur at a close periapses to the SMBH, induced by the outer Kozai effect. The tidal disruptions are found numerically as many as ~10 per cent for a close SMBH binary that is enhanced significantly than the one without the external SMBH. These effects require the outer perturber to have an inclined orbit (>=40 degree) relatively to the inner orbital plane and may lead to a burst of the extremely astronomical events associated with the detection of the SMBH binary.Comment: 12 pages, 9 figures, MNRAS in pres