Astrophysically robust systematics removal using variational inference: application to the first month of Kepler data

Space-based transit search missions such as Kepler are collecting large numbers of stellar light curves of unprecedented photometric precision and time coverage. However, before this scientific goldmine can be exploited fully, the data must be cleaned of instrumental artefacts. We present a new method to correct common-mode systematics in large ensembles of very high precision light curves. It is based on a Bayesian linear basis model and uses shrinkage priors for robustness, variational inference for speed, and a de-noising step based on empirical mode decomposition to prevent the introduction of spurious noise into the corrected light curves. After demonstrating the performance of our method on a synthetic dataset, we apply it to the first month of Kepler data. We compare the results, which are publicly available, to the output of the Kepler pipeline's pre-search data conditioning, and show that the two generally give similar results, but the light curves corrected using our approach have lower scatter, on average, on both long and short timescales. We finish by discussing some limitations of our method and outlining some avenues for further development. The trend-corrected data produced by our approach are publicly available.Comment: 15 pages, 13 figures, accepted for publication in MNRA

Efficient state-space inference of periodic latent force models

Latent force models (LFM) are principled approaches to incorporating solutions to differen-tial equations within non-parametric inference methods. Unfortunately, the developmentand application of LFMs can be inhibited by their computational cost, especially whenclosed-form solutions for the LFM are unavailable, as is the case in many real world prob-lems where these latent forces exhibit periodic behaviour. Given this, we develop a newsparse representation of LFMs which considerably improves their computational efficiency,as well as broadening their applicability, in a principled way, to domains with periodic ornear periodic latent forces. Our approach uses a linear basis model to approximate onegenerative model for each periodic force. We assume that the latent forces are generatedfrom Gaussian process priors and develop a linear basis model which fully expresses thesepriors. We apply our approach to model the thermal dynamics of domestic buildings andshow that it is effective at predicting day-ahead temperatures within the homes. We alsoapply our approach within queueing theory in which quasi-periodic arrival rates are mod-elled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs.Further, we show that state estimates obtained using periodic latent force models can re-duce the root mean squared error to 17% of that from non-periodic models and 27% of thenearest rival approach which is the resonator model (S ̈arkk ̈a et al., 2012; Hartikainen et al.,2012.

National Geodetic Satellite Program /NGSP/ Station Solutions

Results derived from short arc, orbital solution of twelve stations, PAGEOS networ

EMPLOYEE STOCK OPTIONS

The taxation to an employee of the difference between the fair market value of a share of stock transferred to him by a corporate employer, pursuant to the employee\u27s exercise of an option to acquire it at a price below the value of the share, has for years been a matter of dispute between taxpayers and the Commissioner of Internal Revenue. This dispute has involved not merely, as in the case of many of the hardy tax perennials such as reasonableness of compensation, a question as to the application of facts to a well-defined principle of law, but rather a question of the correct legal concept. The deductibility of such difference by the corporate employer has been viewed as a corollary of the employee\u27s tax liability and hence in that field the same controversy has prevailed. That conflict has been in part, although only in part, resolved by the enactment of section 130A of the Internal Revenue Code, which under certain circumstances exempts income which might be derived by the employee from the exercise of a stock option, but at the sacrifice by the corporation of any deduction it might otherwise have. In cases where the corporation\u27s objective is to induce its employees to make an investment of their own funds in the stock of the corporation, in the belief that a proprietary interest in the enterprise will stimulate their efficiency and productivity, it will undoubtedly find it advantageous to devise a plan meeting all of the requirements of the new statutory provisions. On the other hand, if the arrangement is avowedly compensatory and a corporation in a 77 or 82 per cent tax bracket is more interested in securing a deduction than in protecting the employee from the realization of taxable income upon exercise of the option, it will have to be certain that the new statute will not apply. In either event, a full understanding of the statutory provisions is necessary. All of the implications of the statute, however, cannot be seen without an understanding of the evolution and status of the law as it existed prior to the enactment of the statute. Many able discussions have been written on the case law of employee stock options and, accordingly, only a relatively brief summary will be presented here

UAS Classification: Key to effective airworthiness and operational regulations

This presentation discusses some of the general issues relating to the classification of UAS for the purposes of defining and promulgating safety regulations. One possible approach for the definition of a classification scheme for UAS Type Certification Categories reviewed