Sampling-based proofs of almost-periodicity results and algorithmic applications

We give new combinatorial proofs of known almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask, whose almost-periodicity lemma has had far-reaching implications in additive combinatorics. We provide an alternative (and L^p-norm free) point of view, which allows for proofs to easily be converted to probabilistic algorithms that decide membership in almost-periodic sumsets of dense subsets of F_2^n. As an application, we give a new algorithmic version of the quasipolynomial Bogolyubov-Ruzsa lemma recently proved by Sanders. Together with the results by the last two authors, this implies an algorithmic version of the quadratic Goldreich-Levin theorem in which the number of terms in the quadratic Fourier decomposition of a given function is quasipolynomial in the error parameter, compared with an exponential dependence previously proved by the authors. It also improves the running time of the algorithm to have quasipolynomial dependence instead of an exponential one. We also give an application to the problem of finding large subspaces in sumsets of dense sets. Green showed that the sumset of a dense subset of F_2^n contains a large subspace. Using Fourier analytic methods, Sanders proved that such a subspace must have dimension bounded below by a constant times the density times n. We provide an alternative (and L^p norm-free) proof of a comparable bound, which is analogous to a recent result of Croot, Laba and Sisask in the integers.Comment: 28 page

CONTROLLING WILDLIFE AND LIVESTOCK DISEASE WITH ENDOGENOUS ON-FARM BIOSECURITY

The spread of infectious disease among and between wild and domesticated animals has become a major problem worldwide. We analyze the socially optimal management of wildlife and livestock, including choices involving environmental habitat variables and on-farm biosecurity controls, when wildlife and livestock can spread an infectious disease to each other. The model is applied to the problem of bovine tuberculosis among Michigan white-tailed deer. The optimum is a cycle in which the disease remains endemic in the wildlife, but in which the cattle herd is depleted when the prevalence rate in deer grows too large.Research Methods/ Statistical Methods,

Analytical Approximations for Calculating the Escape and Absorption of Radiation in Clumpy Dusty Environments

We present analytical approximations for calculating the scattering, absorption and escape of nonionizing photons from a spherically symmetric two-phase clumpy medium, with either a central point source of isotropic radiation, a uniform distribution of isotropic emitters, or uniformly illuminated by external sources. The analytical approximations are based on the mega-grains model of two-phase clumpy media, as proposed by Hobson & Padman, combined with escape and absorption probability formulae for homogeneous media. The accuracy of the approximations is examined by comparison with 3D Monte Carlo simulations of radiative transfer, including multiple scattering. Our studies show that the combined mega-grains and escape/absorption probability formulae provide a good approximation of the escaping and absorbed radiation fractions for a wide range of parameters characterizing the medium. A realistic test is performed by modeling the absorption of a starlike source of radiation by interstellar dust in a clumpy medium, and by calculating the resulting equilibrium dust temperatures and infrared emission spectrum of both the clumps and the interclump medium. In particular, we find that the temperature of dust in clumps is lower than in the interclump medium if clumps are optically thick. Comparison with Monte Carlo simulations of radiative transfer in the same environment shows that the analytic model yields a good approximation of dust temperatures and the emerging UV to FIR spectrum of radiation for all three types of source distributions mentioned above. Our analytical model provides a numerically expedient way to estimate radiative transfer in a variety of interstellar conditions and can be applied to a wide range of astrophysical environments, from star forming regions to starburst galaxies.Comment: 55 pages, 27 figures. ApJ 523 (1999), in press. Corrected equations and text so as to be same as ApJ versio

Photoacoustic ultrasound sources from diffusion-limited aggregates

Metallic diffusion-limited aggregate (DLA) films are well-known to exhibit near-perfect broadband optical absorption. We demonstrate that such films also manifest a substantial and relatively material-independent photoacoustic response, as a consequence of their random nanostructure. We theoretically and experimentally analyze photoacoustic phenomena in DLA films, and show that they can be used to create broadband air- coupled acoustic sources. These sources are inexpensive and simple to fabricate, and work into the ultrasonic regime. We illustrate the device possibilities by building and testing an optically-addressed acoustic phased array capable of producing virtually arbitrary acoustic intensity patterns in air.Comment: 5 pages, 5 figure

Solar Contamination in Extreme-precision Radial-velocity Measurements: Deleterious Effects and Prospects for Mitigation

Solar contamination, due to moonlight and atmospheric scattering of sunlight, can cause systematic errors in stellar radial velocity (RV) measurements that significantly detract from the ~10 cm s−1 sensitivity required for the detection and characterization of terrestrial exoplanets in or near habitable zones of Sun-like stars. The addition of low-level spectral contamination at variable effective velocity offsets introduces systematic noise when measuring velocities using classical mask-based or template-based cross-correlation techniques. Here we present simulations estimating the range of RV measurement error induced by uncorrected scattered sunlight contamination. We explore potential correction techniques, using both simultaneous spectrometer sky fibers and broadband imaging via coherent fiber imaging bundles, that could reliably reduce this source of error to below the photon-noise limit of typical stellar observations. We discuss the limitations of these simulations, the underlying assumptions, and mitigation mechanisms. We also present and discuss the components designed and built into the NEID (NN-EXPLORE Exoplanet Investigations with Doppler spectroscopy) precision RV instrument for the WIYN 3.5 m telescope, to serve as an ongoing resource for the community to explore and evaluate correction techniques. We emphasize that while "bright time" has been traditionally adequate for RV science, the goal of 10 cm s−1 precision on the most interesting exoplanetary systems may necessitate access to darker skies for these next-generation instruments

Influence of sulfur oxidation state and substituents on sulfur-bridged luminescent copper(I) complexes showing thermally activated delayed fluorescence

C.M.B. thanks Dr. Maria B. Ezhova for helpful discussions regarding NMR spectra, and Dr. Saeid Kamal for assistance with the TCSPC data. C.M.B. and M.O.W. acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Peter Wall Institute for Advanced Studies for financial support and the Laboratory for Advanced Spectroscopy for Imaging Research (LASIR) for facilities access. Z.X. thanks Compute Canada for computing resources for DFT calculations. C.L. thanks the Prof. & Mrs. Purdie Bequests Scholarship and AstraZeneca PhD Studentship. E.Z.-C. and I.D.W.S thank EPSRC (grants EP/R035164/1 and EP/L017008/1) for financial support.Copper(I) complexes are seen as more sustainable alternatives to those containing metal ions such as iridium and platinum for emitting devices. Copper(I) complexes have the ability to radiatively decay via a thermally activated delayed fluorescence (TADF) pathway, leading to higher photoluminescent quantum yields. In this work we discuss six new heteroleptic Cu(I) complexes of the diphosphine–diimine motif. The diphosphine ligands employed are (oxydi- 2,1-phenylene)bis(diphenylphosphine) (DPEPhos) and the diimine fragments are sulfur- bridged dipyridyl ligands (DPS) which are functionalized at the 6,6′-positions of the pyridyl rings (R = H, Me, Ph), and have varying oxidation states at the bridging sulfur atom (S, SO2). The proton ( Cu-DPS, Cu-DPSO2 ) and phenyl ( Cu-Ph-DPS, Cu-Ph-DPSO2 ) substituted species are found to form monometallic complexes, while those with methyl substitution ( Cu-Me-DPS, Cu-Me-DPSO2 ) are found to have a “Goldilocks” degree of steric bulk leading to bimetallic species. All six Cu(I) complexes show emission in the solid state, with the photophysical properties characterized by low temperature steady-state and time-resolved spectroscopies and variable temperature time-correlated single photon counting (TCSPC). Cu- DPS , Cu-DPSO2 , Cu-Me-DPS , Cu-Me-DPSO2 and Cu-Ph-DPSO2 were shown to emit via a TADF mechanism, while Cu-Ph-DPS showed photoluminescence properties consistent with triplet ligand-centered (3LC) emission.PostprintPeer reviewe

Solar Contamination in Extreme-precision Radial-velocity Measurements: Deleterious Effects and Prospects for Mitigation

Solar contamination, due to moonlight and atmospheric scattering of sunlight, can cause systematic errors in stellar radial velocity (RV) measurements that significantly detract from the ~10 cm s−1 sensitivity required for the detection and characterization of terrestrial exoplanets in or near habitable zones of Sun-like stars. The addition of low-level spectral contamination at variable effective velocity offsets introduces systematic noise when measuring velocities using classical mask-based or template-based cross-correlation techniques. Here we present simulations estimating the range of RV measurement error induced by uncorrected scattered sunlight contamination. We explore potential correction techniques, using both simultaneous spectrometer sky fibers and broadband imaging via coherent fiber imaging bundles, that could reliably reduce this source of error to below the photon-noise limit of typical stellar observations. We discuss the limitations of these simulations, the underlying assumptions, and mitigation mechanisms. We also present and discuss the components designed and built into the NEID (NN-EXPLORE Exoplanet Investigations with Doppler spectroscopy) precision RV instrument for the WIYN 3.5 m telescope, to serve as an ongoing resource for the community to explore and evaluate correction techniques. We emphasize that while "bright time" has been traditionally adequate for RV science, the goal of 10 cm s−1 precision on the most interesting exoplanetary systems may necessitate access to darker skies for these next-generation instruments

Solar Contamination in Extreme Precision Radial Velocity Measurements: Deleterious Effects and Prospects for Mitigation

Solar contamination, due to moonlight and atmospheric scattering of sunlight, can cause systematic errors in stellar radial velocity (RV) measurements that significantly detract from the ~10cm/s sensitivity required for the detection and characterization of terrestrial exoplanets in or near Habitable Zones of Sun-like stars. The addition of low-level spectral contamination at variable effective velocity offsets introduces systematic noise when measuring velocities using classical mask-based or template-based cross-correlation techniques. Here we present simulations estimating the range of RV measurement error induced by uncorrected scattered sunlight contamination. We explore potential correction techniques, using both simultaneous spectrometer sky fibers and broadband imaging via coherent fiber imaging bundles, that could reliably reduce this source of error to below the photon-noise limit of typical stellar observations. We discuss the limitations of these simulations, the underlying assumptions, and mitigation mechanisms. We also present and discuss the components designed and built into the NEID precision RV instrument for the WIYN 3.5m telescope, to serve as an ongoing resource for the community to explore and evaluate correction techniques. We emphasize that while "bright time" has been traditionally adequate for RV science, the goal of 10cm/s precision on the most interesting exoplanetary systems may necessitate access to darker skies for these next-generation instruments