Asymptotic normality of extreme value estimators on C[0,1]C[0,1]

Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution. A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on $[0,1]$. Detailed examples are also presented.Comment: Published at http://dx.doi.org/10.1214/009053605000000831 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Axial Anomaly and the Nucleon Spin

In this letter, we have taken a particular Lagrangian, which was introduced to resolve U(1) problem, as an effective QCD Lagrangian, and have derived a formula of the quark content of the nucleon spin. The difference between quark content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n) is evaluated by this formula. Neglecting the higher-order isospin corrections, this formula can reduce to Efremov's results in the large N_c limit.Comment: (1) A few changes and corrections made following Referee. (2) The difference between quark content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n) is evaluated. Neglecting the higher-order isospin corrections, this formula can reduce to Efremov's results in the large N_c limi

Building fault detection and diagnostics: Achieved savings, and methods to evaluate algorithm performance

Fault detection and diagnosis (FDD) represents one of the most active areas of research and commercial product development in the buildings industry. This paper addresses two questions concerning FDD implementation and advancement 1) What are today's users of FDD saving and spending on the technology? 2) What methods and datasets can be used to evaluate and benchmark FDD algorithm performance? Relevant to the first question, 26 organizations that use FDD across a total 550 buildings and 97 M sf achieved median savings of 8%. Twenty-seven FDD users reported that the median base cost for FDD software, annual recurring software cost, and annual labor cost were $8,$2.7 and $8 per monitoring point, with a median implementation size of approximately 1300 points. To address the second question, this paper describes a systematic methodology for evaluating the performance of FDD algorithms, curates an initial test dataset of air handling unit (AHU) system faults, and completes a trial to demonstrate the evaluation process on three sample FDD algorithms. The work provided a first step toward a standard evaluation of different FDD technologies. It showed the test methodology is indeed scalable and repeatable, provided an understanding of the types of insights that can be gained from algorithm performance testing, and highlighted the priorities for further expanding the test dataset