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The Statistical Consulting Center for Astronomy (SCCA)

The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.

Akritas, Michael↗

Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations

Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.

Bibb, Karen L.↗

The creation of local clusters in arbitrarily given grids

A method is presented to smoothly insert pointwise clusters into any given grid regardless of its origin, its topology, or its dimensionality. The process amounts to a local movement of the given coordinate curves or surfaces to more highly resolve an object. The object about which clustering is created can be a point, a curve, a surface, or segments of a curve or surface. The basic clustering capability is established by forming a grid operator for a single cluster. With a view toward multiple clusters being created about various objects, the basic operator is seen as an elementary operator. An algorithm is presented to execute the general elementary operation in three dimensions. In FORTRAN, this assumes the form of a subroutine which is fully operational and is presented to serve as a basic model for any such elementary clustering operation.

Eiseman, Peter R.↗

Value, Cost, and Sharing: Open Issues in Constrained Clustering

Clustering is an important tool for data mining, since it can identify major patterns or trends without any supervision (labeled data). Over the past five years, semi-supervised (constrained) clustering methods have become very popular. These methods began with incorporating pairwise constraints and have developed into more general methods that can learn appropriate distance metrics. However, several important open questions have arisen about which constraints are most useful, how they can be actively acquired, and when and how they should be propagated to neighboring points. This position paper describes these open questions and suggests future directions for constrained clustering research.

constraints↗

Using Clustering to Establish Climate Regimes from PCM Output

A multivariate statistical clustering technique--based on the k-means algorithm of Hartigan has been used to extract patterns of climatological significance from 200 years of general circulation model (GCM) output. Originally developed and implemented on a Beowulf-style parallel computer constructed by Hoffman and Hargrove from surplus commodity desktop PCs, the high performance parallel clustering algorithm was previously applied to the derivation of ecoregions from map stacks of 9 and 25 geophysical conditions or variables for the conterminous U.S. at a resolution of 1 sq km. Now applied both across space and through time, the clustering technique yields temporally-varying climate regimes predicted by transient runs of the Parallel Climate Model (PCM). Using a business-as-usual (BAU) scenario and clustering four fields of significance to the global water cycle (surface temperature, precipitation, soil moisture, and snow depth) from 1871 through 2098, the authors' analysis shows an increase in spatial area occupied by the cluster or climate regime which typifies desert regions (i.e., an increase in desertification) and a decrease in the spatial area occupied by the climate regime typifying winter-time high latitude perma-frost regions. The patterns of cluster changes have been analyzed to understand the predicted variability in the water cycle on global and continental scales. In addition, representative climate regimes were determined by taking three 10-year averages of the fields 100 years apart for northern hemisphere winter (December, January, and February) and summer (June, July, and August). The result is global maps of typical seasonal climate regimes for 100 years in the past, for the present, and for 100 years into the future. Using three-dimensional data or phase space representations of these climate regimes (i.e., the cluster centroids), the authors demonstrate the portion of this phase space occupied by the land surface at all points in space and time. Any single spot on the globe will exist in one of these climate regimes at any single point in time. By incrementing time, that same spot will trace out a trajectory or orbit between and among these climate regimes (or atmospheric states) in phase (or state) space. When a geographic region enters a state it never previously visited, a climatic change is said to have occurred. Tracing out the entire trajectory of a single spot on the globe yields a 'manifold' in state space representing the shape of its predicted climate occupancy. This sort of analysis enables a researcher to more easily grasp the multivariate behavior of the climate system.

Oglesby, Robert↗

X-ray luminosity functions of clusters of galaxies

Clusters of galaxies must have a considerable intrinsic spread in their X-ray luminosities at given mass if they are formed bottom-up by direct gravitational instability. The distributions of luminosities at given mass take on the general form of a flat power law with a sharp upper cutoff, consistent with the recently obtained luminosity functions for Abell clusters of given richness classes. The quantitative features depend on the specific hierarchical cosmogony, with models including mass accretion after first collapse providing the best agreement. The same clustering mechanism, after integrating over mass, yields a steep overall luminosity function consistent with existing measurements.

Cavaliere, A.↗

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

It was discovered that the nonlinear evolution of the two point correlation function in N-body experiments of galaxy clustering with Omega = 1 appears to be described to good approximation by a simple general formula. The underlying form of the formula is physically motivated, but its detailed representation is obtained empirically by fitting to N-body experiments. In this paper, the formula is presented along with an inverse formula which converts a final, nonlinear correlation function into the initial linear correlation function. The inverse formula is applied to observational data from the CfA, IRAs, and APM galaxy surveys, and the initial spectrum of fluctuations of the universe, if Omega = 1.

Hamilton, A. J. S.↗

The velocity-distance relation for galaxies on a bubble

The characteristic diameter of the most prominent void in the redshift survey of de Lapparent et al. (1986) is measured. Distances and peculiar velocities to individual galaxies are derived, and it is shown that the void is approximately a 'Hubble Bubble' in which the near and far edges are separating with the general expansion of the universe. At the 3 sigma level, infall toward the Coma cluster is detected for a portion of the bubble wall. Limits on the net outflow from the void and infall into Coma are used to estimate Omega.

Bothun, Gregory D.↗

Communicating Metrics of Land Surface Temperature Variability Using Multi-sensor Machine Learning

Land surface temperature (LST) is a key climate observable used to detect changes in the Earth’s surface energy budget that influence carbon and water cycles. Land surface temperature exhibits strong diurnal variability, which geostationary satellites can observe at scale thanks to their temporal resolution. Due to anthropogenic climate and land use changes, the surface energy balance has been considerably modified and may be described by changes in diurnal temperature range and extremes. Using high performance computing and datasets from the NASA Earth Exchange, we exploit co-located, co-temporal observations from low-earth orbit (LEO) and geostationary (GEO) sensors to develop a deep learning-based method for LEO-to-GEO algorithm emulation. Our model is trained to predict MODIS Terra LST from GOES-16 thermal bands and achieves validation error <2K. Application of the model to unseen times of day (observed by MODIS Aqua) and a new GEO sensor (Himawari-8) observing an unseen spatial domain, demonstrate the generalization of the deep learning model across space, time and spectra. Further, time series clustering approaches are examined with the objective of identifying key indicators of change in diurnal cycling and extremes on a continental scale. Communicating LST variability observed by geostationary satellites can have impacts in multiple disciplines, from understanding of snow, vegetation and soil dynamics, to recognizing trends in heat events relevant to human health.

Kate Duffy↗

Analysis of Fiber Clustering in Composite Materials Using High-Fidelity Multiscale Micromechanics

A new multiscale micromechanical approach is developed for the prediction of the behavior of fiber reinforced composites in presence of fiber clustering. The developed method is based on a coupled two-scale implementation of the High-Fidelity Generalized Method of Cells theory, wherein both the local and global scales are represented using this micromechanical method. Concentration tensors and effective constitutive equations are established on both scales and linked to establish the required coupling, thus providing the local fields throughout the composite as well as the global properties and effective nonlinear response. Two nondimensional parameters, in conjunction with actual composite micrographs, are used to characterize the clustering of fibers in the composite. Based on the predicted local fields, initial yield and damage envelopes are generated for various clustering parameters for a polymer matrix composite with both carbon and glass fibers. Nonlinear epoxy matrix behavior is also considered, with results in the form of effective nonlinear response curves, with varying fiber clustering and for two sets of nonlinear matrix parameters.

composite materials↗

Is There a Cosmological Constant?

The grant contributed to the publication of 18 refereed papers and 5 conference proceedings. The primary uses of the funding have been for page charges, travel for invited talks related to the grant research, and the support of a graduate student, Charles Keeton. The refereed papers address four of the primary goals of the proposal: (1) the statistics of radio lenses as a probe of the cosmological model (#1), (2) the role of spiral galaxies as lenses (#3), (3) the effects of dust on statistics of lenses (#7, #8), and (4) the role of groups and clusters as lenses (#2, #6, #10, #13, #15, #16). Four papers (#4, #5, #11, #12) address general issues of lens models, calibrations, and the relationship between lens galaxies and nearby galaxies. One considered cosmological effects in lensing X-ray sources (#9), and two addressed issues related to the overall power spectrum and theories of gravity (#17, #18). Our theoretical studies combined with the explosion in the number of lenses and the quality of the data obtained for them is greatly increasing our ability to characterize and understand the lens population. We can now firmly conclude both from our study of the statistics of radio lenses and our survey of extinctions in individual lenses that the statistics of optically selected quasars were significantly affected by extinction. However, the limits on the cosmological constant remain at lambda < 0.65 at a 2-sigma confidence level, which is in mild conflict with the results of the Type la supernova surveys. We continue to find that neither spiral galaxies nor groups and clusters contribute significantly to the production of gravitational lenses. The lack of group and cluster lenses is strong evidence for the role of baryonic cooling in increasing the efficiency of galaxies as lenses compared to groups and clusters of higher mass but lower central density. Unfortunately for the ultimate objective of the proposal, improved constraints on the cosmological constant, the next large survey for gravitational lenses did not release its results during the term of the proposal. The research supported the career development. of six graduate students (polar, Fletcher, Herold, Keeton, Deng and Rusin) and two post-docs (Labor and Munoz).

Kochanek, Christopher↗

General-relativistic astrophysics

The overall relevance of general relativity to astrophysics is considered, and some of the knowledge about the ways in which general relativity should influence astrophysical systems is reviewed. Attention is focused primarily on finite-sized astrophysical systems, such as stars, globular clusters, galactic nuclei, and primordial black holes. Stages in the evolution of such systems and tools for studying the effects of relativistic gravity in these systems are examined. Gravitational-wave astronomy is discussed in detail, with emphasis placed on estimates of the strongest gravitational waves that bathe earth, present obstacles and future prospects for detection of the predicted waves, the theory of small perturbations of relativistic stars and black holes, and the gravitational waves such objects generate. Characteristics of waves produced by black-hole events in general, pregalactic black-hole events, black-hole events in galactic nuclei and quasars, black-hole events in globular clusters, the collapse of normal stars to form black holes or neutron stars, and corequakes in neutron stars are analyzed. The state of the art in gravitational-wave detection and characteristics of various types of detector are described.

Thorne, K. S.↗

Pendulum Motion in Main Parachute Clusters

The coupled dynamics of a cluster of parachutes to a payload are notoriously difficult to predict. Often the payload is designed to be insensitive to the range of attitude and rates that might occur, but spacecraft generally do not have the mass and volume budgeted for this robust of a design. The National Aeronautics and Space Administration (NASA) Orion Capsule Parachute Assembly System (CPAS) implements a cluster of three mains for landing. During testing of the Engineering Development Unit (EDU) design, it was discovered that with a cluster of two mains (a fault tolerance required for human rating) the capsule coupled to the parachute cluster could get into a limit cycle pendulum motion which would exceed the spacecraft landing capability. This pendulum phenomenon could not be predicted with the existing models and simulations. A three phased effort has been undertaken to understand the consequence of the pendulum motion observed, and explore potential design changes that would mitigate this phenomenon. This paper will review the early analysis that was performed of the pendulum motion observed during EDU testing, summarize the analysis ongoing to understand the root cause of the pendulum phenomenon, and discuss the modeling and testing that is being pursued to identify design changes that would mitigate the risk.

Ray, Eric S.↗

Stellar populations in local group dwarf elliptical galaxies. I - NGC 147

A color-magnitude diagram of NGC 147 to an I magnitude of 23 is presented. The stellar population in the outer parts of this elliptical galaxy resembles that of the globular clusters of the Milky Way. Quantitative comparison of the giant branch with those of globular clusters yields a mean metallicity of -1.2 + or - 0.2, making NGC 147 a part of the general correlation between mass and metallicity seen in ellipticals. The giant branch appears to be broad, which suggests a metallicity dispersion. The absence of asymptotic giant branch stars at luminosities above that of the red giant branch tip sets an upper limit of 10 percent for the fraction of stars in this NGC 147 field that have ages less than 12 Gyr. This result contrasts with the situation in some of the related, but less massive, dwarf spheroidal systems. If the choice is made to assume, rather than determine the stellar content of NGC 147, a distance of 630 + or - 50 kpc is derived, similar to that of M31.

Mould, J. R.↗

Constraints on axions from the extragalactic background light

We consider the effect of dark matter in the form of multi-eV axions on the extragalactic background light. Our treatment differs from that of other workers in that we assume axions to be clustered in Galactic halos, with nonzero velocity dispersions. We also approach the problem in a fully general relativistic manner, treating the axion halos as luminous elements of a pressure-free perfect fluid in a standard Friedmann-Robertson-Walker universe. We find that the ultraviolet extragalactic background light places a firm upper limit of 9 eV on the axion rest energy, and that this drops to 4 eV for the simplest axion models, all but closing the multi-eV axion window (which begins at 3 eV). These results are close to earlier upper limits of 5 and 8 eV derived from the extragalactic background by Turner and Ressell, respectively. Although our methods differ somewhat from theirs, our findings support their conclusion that axions, if they exist, are likely to have rest energies well below the eV range.

Overduin, J. M.↗

A Hardware-in-the-Loop Testbed for Spacecraft Formation Flying Applications

The Formation Flying Test Bed (FFTB) at NASA Goddard Space Flight Center (GSFC) is being developed as a modular, hybrid dynamic simulation facility employed for end-to-end guidance, navigation, and control (GN&C) analysis and design for formation flying clusters and constellations of satellites. The FFTB will support critical hardware and software technology development to enable current and future missions for NASA, other government agencies, and external customers for a wide range of missions, particularly those involving distributed spacecraft operations. The initial capabilities of the FFTB are based upon an integration of high fidelity hardware and software simulation, emulation, and test platforms developed at GSFC in recent years; including a high-fidelity GPS simulator which has been a fundamental component of the Guidance, Navigation, and Control Center's GPS Test Facility. The FFTB will be continuously evolving over the next several years from a too[ with initial capabilities in GPS navigation hardware/software- in-the- loop analysis and closed loop GPS-based orbit control algorithm assessment to one with cross-link communications and relative navigation analysis and simulation capability. Eventually the FFT13 will provide full capability to support all aspects of multi-sensor, absolute and relative position determination and control, in all (attitude and orbit) degrees of freedom, as well as information management for satellite clusters and constellations. In this paper we focus on the architecture for the FFT13 as a general GN&C analysis environment for the spacecraft formation flying community inside and outside of NASA GSFC and we briefly reference some current and future activities which will drive the requirements and development.

Leitner, Jesse↗

Solution of the Neumann pressure problem in general orthogonal coordinates using the multigrid technique

The multigrid (MG) technique has been advanced for use with Neumann boundary-value problems in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of incompressible flow using the velocity-pressure formulation of the Navier-Stokes equations. The finite-difference representation of the problem and the formulation of the restriction and coarse-grid correction operators are examined in detail. Maintaining consistency between these and the integral constraint associated with the Neumann problem is found to be critical for the success of the MG technique. The influence of the smoothing operator is examined by employing Gauss-Seidel, alternating-direction implicit, and strongly implicit techniques. The MG procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 14, depending on the type of smoothing operator employed and the values of the problem parameters.

Ghia, U.↗