Binary matrices of optimal autocorrelations as alignment marks

We define a new class of binary matrices by maximizing the peak-sidelobe distances in the aperiodic autocorrelations. These matrices can be used as robust position marks for in-plane spatial alignment. The optimal square matrices of dimensions up to 7 by 7 and optimal diagonally-symmetric matrices of 8 by 8 and 9 by 9 were found by exhaustive searches.Comment: 8 pages, 6 figures and 1 tabl

Fabrication of photovoltaic laser energy converterby MBE

A laser-energy converter, fabricated by molecular beam epitaxy (MBE), was developed. This converter is a stack of vertical p-n junctions connected in series by low-resistivity, lattice matched CoSi2 layers to achieve a high conversion efficiency. Special high-temperature electron-beam (e-beam) sources were developed especially for the MBE growth of the junctions and CoSi2 layers. Making use of the small (greater than 1.2 percent) lattice mismatch between CoSi2 and Si layers, high-quality and pinhole-free epilayers were achieved, providing a capability of fabricating all the junctions and connecting layers as a single growth process with one pumpdown. Well-defined multiple p-n junctions connected by CoSi2 layers were accomplished by employing a low growth temperature (greater than 700 C) and a low growth rate (less than 0.5 microns/hour). Producing negligible interdiffusion, the low growth temperature and rate also produced negligible pinholes in the CoSi2 layers. For the first time, a stack of three p-n junctions connected by two 10(exp -5) Ohm-cm CoSi2 layers was achieved, meeting the high conversion efficiency requirement. This process can now be optimized for high growth rate to form a practical converter with 10 p-n junctions in the stack

Experimental Observation of Large Chern numbers in Photonic Crystals

Despite great interest in the quantum anomalous Hall phase and its analogs, all experimental studies in electronic and bosonic systems have been limited to a Chern number of one. Here, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Bandgaps with large Chern numbers of 2, 3, and 4 are present in the experimental results which show excellent agreement with theory. We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations.Comment: This experimental work was accepted to PRL on Oct. 13, 2015. Our theoretical work from PRL http://dx.doi.org/10.1103/PhysRevLett.113.11390

ON THE EQUIVALENCE OF CASE-CROSSOVER AND TIME SERIES METHODS IN ENVIRONMENTAL EPIDEMIOLOGY

Time series and case-crossover methods are often viewed as competing alternatives in environmental epidemiologic studies. Several recent studies have compared the time series and case-crossover methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for over-dispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF UNMEASURED TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data