Abstract:
The local field correction to the spontanous dacay rate of an impurity source atom imbedded in a disordered dielectric is calculated to second order in the dielectric density. The result is found to differ from predictions associated with both "virtual" and "real" cavity models of this decay process. However, if the contributions from two dielectric atoms at the same position are included, the virtual cavity result is reproduced.

Abstract:
An atom recoils when it undergoes spontaneous decay. In this paper we present a microscopic calculation of the recoil of a source atom imbedded in a dielectric medium. We find that the source atom recoils with the canonical photon momentum $n\hbar k_{0,}$ where $n$ is the index of refraction and $\hbar k_{0}$ is the photon momentum calculated at the source atom atomic frequency $\omega_{0}$. We also show explicitly how the energy is conserved with the photon inside the medium.

Abstract:
When releasing data to the public, data stewards are ethically and often legally obligated to protect the confidentiality of data subjects' identities and sensitive attributes. They also strive to release data that are informative for a wide range of secondary analyses. Achieving both objectives is particularly challenging when data stewards seek to release highly resolved geographical information. We present an approach for protecting the confidentiality of data with geographic identifiers based on multiple imputation. The basic idea is to convert geography to latitude and longitude, estimate a bivariate response model conditional on attributes, and simulate new latitude and longitude values from these models. We illustrate the proposed methods using data describing causes of death in Durham, North Carolina. In the context of the application, we present a straightforward tool for generating simulated geographies and attributes based on regression trees, and we present methods for assessing disclosure risks with such simulated data.

Abstract:
A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e.g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting recursion relations for Legendre functions. Numerical examples illustrate the performance of the scheme; in particular, it is demonstrated that for a BIE associated with Laplace's equation on a surface discretized using 320,800 points, the set-up phase of the algorithm takes 1 minute on a standard laptop, and then solves can be executed in 0.5 seconds.

Abstract:
Cyanobacteria are a rich source of natural products with interesting biological activities. Many of these are peptides and the end products of a non-ribosomal pathway. However, several cyanobacterial peptide classes were recently shown to be produced through the proteolytic cleavage and post-translational modification of short precursor peptides. A new class of bacteriocins produced through the proteolytic cleavage and heterocyclization of precursor proteins was recently identified from marine cyanobacteria. Here we show the widespread occurrence of bacteriocin gene clusters in cyanobacteria through comparative analysis of 58 cyanobacterial genomes. A total of 145 bacteriocin gene clusters were discovered through genome mining. These clusters encoded 290 putative bacteriocin precursors. They ranged in length from 28 to 164 amino acids with very little sequence conservation of the core peptide. The gene clusters could be classified into seven groups according to their gene organization and domain composition. This classification is supported by phylogenetic analysis, which further indicated independent evolutionary trajectories of gene clusters in different groups. Our data suggests that cyanobacteria are a prolific source of low-molecular weight post-translationally modified peptides.

Abstract:
Invasive exotic species pose a growing threat to the economy, public health, and ecological integrity of nations worldwide. Explaining and predicting the spatial distribution of invasive exotic species is of great importance to prevention and early warning efforts. We are investigating the potential distribution of invasive exotic species, the environmental factors that influence these distributions, and the ability to predict them using statistical and information-theoretic approaches. For some species, detailed presence/absence occurrence data are available, allowing the use of a variety of standard statistical techniques. However, for most species, absence data are not available. Presented with the challenge of developing a model based on presence-only information, we developed an improved logistic regression approach using Information Theory and Frequency Statistics to produce a relative suitability map. This paper generated a variety of distributions of ragweed (Ambrosia artemisiifolia L.) from logistic regression models applied to herbarium specimen location data and a suite of GIS layers including climatic, topographic, and land cover information. Our logistic regression model was based on Akaike’s Information Criterion (AIC) from a suite of ecologically reasonable predictor variables. Based on the results we provided a new Frequency Statistical method to compartmentalize habitat-suitability in the native range. Finally, we used the model and the compartmentalized criterion developed in native ranges to “project” a potential distribution onto the exotic ranges to build habitat-suitability maps.

Abstract:
Thermodynamic property calculations of mixtures containing carbon dioxide (CO$_2$) and water, including brines, are essential in theoretical models of many natural and industrial processes. The properties of greatest practical interest are density, solubility, and enthalpy. Many models for density and solubility calculations have been presented in the literature, but there exists only one study, by Spycher and Pruess, that has compared theoretical molar enthalpy predictions with experimental data. In this report, we recommend two different models for enthalpy calculations: the CPA equation of state by Li and Firoozabadi, and the CO$_2$ activity coefficient model by Duan and Sun. We show that the CPA equation of state, which has been demonstrated to provide good agreement with density and solubility data, also accurately calculates molar enthalpies of pure CO$_2$, pure water, and both CO$_2$-rich and aqueous (H$_2$O-rich) mixtures of the two species. It is applicable to a wider range of conditions than the Spycher and Pruess model. In aqueous sodium chloride (NaCl) mixtures, we show that Duan and Sun's model yields accurate results for the partial molar enthalpy of CO$_2$. It can be combined with another model for the brine enthalpy to calculate the molar enthalpy of H$_2$O-CO$_2$-NaCl mixtures. We conclude by explaining how the CPA equation of state may be modified to further improve agreement with experiments. This generalized CPA is the basis of our future work on this topic.

Abstract:
We developed a method to automatically detect and trace solar filaments in H\alpha\ full-disk images. The program is able not only to recognize filaments and determine their properties, such as the position, the area, the spine, and other relevant parameters, but also to trace the daily evolution of the filaments. The program consists of three steps: First, preprocessing is applied to correct the original images; Second, the Canny edge-detection method is used to detect filaments; Third, filament properties are recognized through the morphological operators. To test the algorithm, we applied it to the observations from the Mauna Loa Solar Observatory (MLSO), and the program is demonstrated to be robust and efficient. H\alpha\ images obtained by MLSO from 1998 to 2009 are analyzed, and a butterfly diagram of filaments is obtained. It shows that the latitudinal migration of solar filaments has three trends in the Solar Cycle 23: The drift velocity was fast from 1998 to the solar maximum; After the solar maximum, it became relatively slow. After 2006, the migration became divergent, signifying the solar minimum. About 60% filaments with the latitudes larger than $50^{\circ}$ migrate towards the polar regions with relatively high velocities, and the latitudinal migrating speeds in the northern and the southern hemispheres do not differ significantly in the Solar Cycle 23.

Abstract:
Invasive exotic species pose a growing threat to the economy, public health, and ecological integrity of nations worldwide. Explaining and predicting the spatial distribution of invasive exotic species is of great importance to prevention and early warning efforts. We are investigating the potential distribution of invasive exotic species, the environmental factors that influence these distributions, and the ability to predict them using statistical and information-theoretic approaches. For some species, detailed presence/absence occurrence data are available, allowing the use of a variety of standard statistical techniques. However, for most species, absence data are not available. Presented with the challenge of developing a model based on presence-only information, we developed an improved logistic regression approach using Information Theory and Frequency Statistics to produce a relative suitability map. This paper generated a variety of distributions of ragweed (Ambrosia artemisiifolia L.) from logistic regression models applied to herbarium specimen location data and a suite of GIS layers including climatic, topographic, and land cover information. Our logistic regression model was based on Akaike’s Information Criterion (AIC) from a suite of ecologically reasonable predictor variables. Based on the results we provided a new Frequency Statistical method to compartmentalize habitat-suitability in the native range. Finally, we used the model and the compartmentalized criterion developed in native ranges to “project” a potential distribution onto the exotic ranges to build habitat-suitability maps. Supported by the National Natural Science Foundation of China (Grant No. 40371084), U.S. Geological Survey (Grant No. 03CRCN0001), and UW-Madison funded under U.S. Geological Survey cooperative agreement (Grant No. 03CRAG0016)

Abstract:
Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarithmically-singular kernels. Only smooth boundaries are considered, but some of the techniques extend straightforwardly to the case of corners. Three are modifications of the global periodic trapezoid rule, due to Kapur-Rokhlin, to Alpert, and to Kress. The fourth is a modification to a quadrature based on Gauss-Legendre panels due to Kolm-Rokhlin; this formulation allows adaptivity. We compare in numerical experiments the convergence of the four schemes in various settings, including low- and high-frequency planar Helmholtz problems, and 3D axisymmetric Laplace problems. We also find striking differences in performance in an iterative setting. We summarize the relative advantages of the schemes.