Silicon and magnesium in planetary nebulae

The IUE satellite spectra of some planetary nebulae show features due to silicon and magnesium: Si III wavelengths 1883, 1892; Si IV wavelengths 1394, 1403; Mg II wavelengths 2796, 2804 and Mg V wavelengths 2784, 2929. With the aid of modeling techniques, the corresponding elemental abundances are found. In addition to previous observations of NGC 7662 and IC 418, data were found for NGC 2440, Hu 1-2, IC 2003 and IC 2165. Silicon appears depleted by up to an order of magnitude relative to the sun. Large variations of magnesium abundance are found, which are likely to reflect differing degrees of depletion due to grain formation

Elemental abundances in high-excitation planetary nebulae

The IUE satellite was used to obtain low dispersion spectra of the high excitation planetary nebulae IC 351, IC 2003, NGC 2022, IC 2165, NGC 2440, Hu 1-2, and IC 5217. Numerical modeling was undertaken to determine the chemical composition of these objects with particular emphasis on obtaining elemental carbon and nitrogen abundances. Large variations in the C/N ratio from object to object are suggested

Thrust performance of isolated 36-chute suppressor plug nozzles with and without ejectors at Mach numbers from 0 to 0.45

Plug nozzles with chute-type noise suppressors were tested with and without ejector shrouds at free-stream Mach numbers from 0 to 0.45 and over a range of nozzle pressure ratios from 2 to 4. A 36-chute suppressor nozzle with an ejector had an efficiency of 94.6 percent at an assumed takeoff pressure ratio of 3.0 and a Mach number of 0.36. This represents only a 3.4 percent performance penalty when compared with the 98 percent efficiency obtained with a previously tested unsuppressed plug nozzle

Thrust performance of isolated, two-dimensional suppressed plug nozzles with and without ejectors at Mach numbers from 0 to 0.45

A series of two-dimensional plug nozzles was tested with and without ejector shrouds at free stream Mach numbers from 0 to 0.45 and over a range of nozzle pressure ratios from 2 to 4. These nozzles were also tested with and without chute noise suppressors. A two-dimensional plug nozzle has an efficiency of 96.1 percent at an assumed takeoff pressure ratio of 3.0 and Mach 0.36. A 12-chute suppressed nozzle with sidewalls has an efficiency of 81.0 percent (15.1 percent below the unsuppressed nozzle)

Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions

Monte Carlo Simulation of Lyman Alpha Scattering and Application to Damped Lyman Alpha Systems

A Monte Carlo code to solve the transfer of Lyman alpha (Lya) photons is developed, which can predict the Lya image and two-dimensional Lya spectra of a hydrogen cloud with any given geometry, Lya emissivity, neutral hydrogen density distribution, and bulk velocity field. We apply the code to several simple cases of a uniform cloud to show how the Lya image and emitted line spectrum are affected by the column density, internal velocity gradients, and emissivity distribution. We then apply the code to two models for damped Lya absorption systems: a spherical, static, isothermal cloud, and a flattened, axially symmetric, rotating cloud. If the emission is due to fluorescence of the external background radiation, the Lya image should have a core corresponding to the region where hydrogen is self-shielded. The emission line profile has the characteristic double peak with a deep central trough. We show how rotation of the cloud causes the two peaks to shift in wavelength as the slit is perpendicular to the rotation axis, and how the relative amplitude of the two peaks is changed. In reality, damped Lya systems are likely to have a clumpy gas distribution with turbulent velocity fields, which should smooth the line emission profile, but should still leave the rotation signature of the wavelength shift across the system.Comment: 19 pages, 17 eps figures. One panel is added in Fig.1 to show the recoil effect. Revisions are made in response to the referee's comments. Accepted for publication in Ap

Numerical algebraic geometry for model selection and its application to the life sciences

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification

Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio

The development and evaluation of exercises for group response to word meaning for increasing the speed of word recognition in grade I

Thesis (Ed.M.)--Boston Universit