Asymptotic Validity of the Bayes-Inspired Indifference Zone Procedure: The Non-Normal Known Variance Case

We consider the indifference-zone (IZ) formulation of the ranking and selection problem in which the goal is to choose an alternative with the largest mean with guaranteed probability, as long as the difference between this mean and the second largest exceeds a threshold. Conservatism leads classical IZ procedures to take too many samples in problems with many alternatives. The Bayes-inspired Indifference Zone (BIZ) procedure, proposed in Frazier (2014), is less conservative than previous procedures, but its proof of validity requires strong assumptions, specifically that samples are normal, and variances are known with an integer multiple structure. In this paper, we show asymptotic validity of a slight modification of the original BIZ procedure as the difference between the best alternative and the second best goes to zero,when the variances are known and finite, and samples are independent and identically distributed, but not necessarily normal

A note on discrete R symmetries in Z6-II orbifolds with Wilson lines

We re-derive the R symmetries for the Z6-II orbifold with non-trivial Wilson lines and find expressions for the R charges which differ from those in the literature.Comment: 13 pages, 3 figure

The Role of Planning Contracts in the Conduct of French Industrial Policy

The French have a long history of state economic planning, of comprehensive industrial policy, and of contractualised relations between the state and firms, though the links between them have not always been close. In the following section we review the relevant history of French planning and industrial policy. We focus in the second section on the development of contractual relations between corporations and the state in postwar France until the Socialists took office in 1981. In the third section we discuss recent developments, and we conclude with a theoretical appraisal of the experience

The Flavor Puzzle: Textures and Symmetries

We discuss aspects of a promising top-down origin of flavor symmetries in particle physics. Modular transformations originating from string theory dualities are shown to play a crucial role. We introduce the notion of an "eclectic" flavor scheme that unifies traditional flavor symmetries, modular symmetries and CP-transformations. It exhibits the phenomenon of "Local Flavor Unification" with enhanced flavor symmetries at fixed points or lines in moduli space. Successful fits of masses and mixing angles of quarks and leptons are found in the vicinity of these points and lines.Comment: 14 pages, 10 figures; contribution to the "Memorial volume with World Scientific in honor of Harald Fritzsch

First Weak-lensing Results from "See Change": Quantifying Dark Matter in the Two Z>1.5 High-redshift Galaxy Clusters SPT-CL J2040-4451 and IDCS J1426+3508

We present a weak-lensing study of SPT-CLJ2040-4451 and IDCSJ1426+3508 at z=1.48 and 1.75, respectively. The two clusters were observed in our "See Change" program, a HST survey of 12 massive high-redshift clusters aimed at high-z supernova measurements and weak-lensing estimation of accurate cluster masses. We detect weak but significant galaxy shape distortions using IR images from the WFC3, which has not yet been used for weak-lensing studies. Both clusters appear to possess relaxed morphology in projected mass distribution, and their mass centroids agree nicely with those defined by both the galaxy luminosity and X-ray emission. Using an NFW profile, for which we assume that the mass is tightly correlated with the concentration parameter, we determine the masses of SPT-CL J2040-4451 and IDCS J1426+3508 to be M_{200}=8.6_{-1.4}^{+1.7}x10^14 M_sun and 2.2_{-0.7}^{+1.1}x10^14 M_sun, respectively. The weak-lensing mass of SPT-CLJ2040-4451 shows that the cluster is clearly a rare object. Adopting the central value, the expected abundance of such a massive cluster at z>1.48 is only ~0.07 in the parent 2500 sq. deg. survey. However, it is yet premature to claim that the presence of this cluster creates a serious tension with the current LCDM paradigm unless that tension will remain in future studies after marginalizing over many sources of uncertainties such as the accuracy of the mass function and the mass-concentration relation at the high mass end. The mass of IDCSJ1426+3508 is in excellent agreement with our previous ACS-based weak-lensing result while the much higher source density from our WFC3 imaging data makes the current statistical uncertainty ~40% smaller.Comment: Accepted to Ap