Paraxial full-field cloaking

We complete the `paraxial' (small-angle) ray optics cloaking formalism presented previously [Choi and Howell, Opt. Express 22, 29465 (2014)], by extending it to the full-field of light. Omnidirectionality is then the only relaxed parameter of what may be considered an ideal, broadband, field cloak. We show that an isotropic plate of uniform thickness, with appropriately designed refractive index and dispersion, can match the phase over the whole visible spectrum. Our results support the fundamental limits on cloaking for broadband vs. omnidirectionality, and provide insights into when anisotropy may be required

R.A.Fisher, design theory, and the Indian connection

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R. A. Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.Comment: 11 pages, 3 figure

Extensions of D-optimal Minimal Designs for Symmetric Mixture Models.

The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé\u27s linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. IN THIS PAPER EXTENSIONS OF THE D-OPTIMAL MINIMAL DESIGNS ARE DEVELOPED FOR A GENERAL MIXTURE MODEL TO ALLOW ADDITIONAL INTERIOR POINTS IN THE DESIGN SPACE TO ENABLE PREDICTION OF THE ENTIRE RESPONSE SURFACE: Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two ten-point designs for the Lack of Fit test by simulations

Randomization tests for peer effects in group formation experiments

Measuring the effect of peers on individual outcomes is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by randomly assigning individuals to groups and observing their responses; for example, do first-year students have better grades when they are randomly assigned roommates who have stronger academic backgrounds? Standard approaches for analyzing these experiments, however, are heavily model-dependent and generally fail to exploit the randomized design. In this paper, we extend methods from randomization-based testing under interference to group formation experiments. The proposed tests are justified by the randomization itself, require relatively few assumptions, and are exact in finite samples. First, we develop procedures that yield valid tests for arbitrary group formation designs. Second, we derive sufficient conditions on the design such that the randomization test can be implemented via simple random permutations. We apply this approach to two recent group formation experiments