Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data spaces. This paper provides an introductory overview of the mathematical underpinnings of Topological Data Analysis, the workflow to convert samples of data to topological summary statistics, and some of the statistical methods developed for performing inference on these topological summary statistics. The intention of this non-technical overview is to motivate statisticians who are interested in learning more about the subject.Comment: 15 pages, 7 Figures, 27th Annual Conference on Applied Statistics in Agricultur

Ion-by-Ion DEM Determination: I. Method

We describe a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission line spectra. This technique involves fitting spectra using a number of components, each of which is the entire X-ray line emission spectrum for a single ion. It is applicable to high-resolution X-ray spectra of any collisionally ionized plasma and particularly useful for spectra in which the emission lines are broadened and blended such as those of the winds of hot stars. This method does not require that any explicit assumptions about the form of the DEM distribution be made and is easily automated.Comment: This paper was split in two. This version is part I. Part II may be found at astro-ph/050343

Reconstructing the free-energy landscape of Met-enkephalin using dihedral Principal Component Analysis and Well-tempered Metadynamics

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers however from the same limitation, i.e. the non trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachadran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates. We illustrate the robustness of this method in the case of the small and very diffusive Metenkephalin pentapeptide, and highlight a criterion to limit the number of CVs necessary to biased the metadynamics simulation. The free-energy landscape (FEL) of Met-enkephalin built on CVs generated from dPCA is found rugged compared with the FEL built on CVs extracted from PCA of the Cartesian coordinates of the atoms.Comment: 17 pages, 9 figures (4 in color

2MASS 1315-2649: A High Proper Motion L Dwarf with Strong H-alpha Emission

In Hall (2002) I reported that 2MASSI J1315309-264951 is an L dwarf with strong H-alpha emission. Two spectroscopic epochs appeared to show that the H-alpha was variable, decreasing from 121 Angstroms to 25 Angstroms EW, which I interpreted as a flare during the first observation. Gizis (2002) independently discovered this object, and his intermediate spectroscopic epoch shows H-alpha with 97 Angstroms EW. A new fourth epoch of spectroscopy again shows a very large H-alpha EW (124 Angstroms), confirming this object to be a persistent, strong H-alpha emitter. Whether the H-alpha is steady (like 2MASS 1237+6526) or from continuous strong flaring (like PC0025+0447) remains unclear. Imaging confirms that 2MASS 1315-2649 has a high proper motion (0.71"/year), corresponding to a transverse velocity of ~76 km/s at its distance of ~23 pc. Thus 2MASS 1315-2649 is consistent with being >~2 Gyr old and therefore relatively massive. If that is so, the correlation of H-alph activity with mass found by Gizis et al. (2000) would seem to support the continuous strong flaring scenario, though it does not rule out a brown dwarf binary accretion scenario.Comment: 2 pages, ApJL accepte

Constraints on the Velocity and Spatial Distribution of Helium-like Ions in the Wind of SMC X-1 from Observations with XMM-Newton/RGS

We present here X-ray spectra of the HMXB SMC X-1 obtained in an observation with the XMM observatory beginning before eclipse and ending near the end of eclipse. With the Reflection Grating Spectrometers (RGS) on board XMM, we observe emission lines from hydrogen-like and helium-like ions of nitrogen, oxygen, neon, magnesium, and silicon. Though the resolution of the RGS is sufficient to resolve the helium-like n=2->1 emission into three line components, only one of these components, the intercombination line, is detected in our data. The lack of flux in the forbidden lines of the helium-like triplets is explained by pumping by ultraviolet photons from the B0 star and, from this, we set an upper limit on the distance of the emitting ions from the star. The lack of observable flux in the resonance lines of the helium-like triplets indicate a lack of enhancement due to resonance line scattering and, from this, we derive a new observational constraint on the distribution of the wind in SMC X-1 in velocity and coordinate space. We find that the solid angle subtended by the volume containing the helium-like ions at the neutron star multiplied by the velocity dispersion of the helium-like ions must be less than 4pi steradians km/s. This constraint will be satisfied if the helium-like ions are located primarily in clumps distributed throughout the wind or in a thin layer along the surface of the B0 star.Comment: 22 pages, 17 figures, ApJ accepted, discussion of relevant other work adde

Computing the merger of black-hole binaries: the IBBH problem

Gravitational radiation arising from the inspiral and merger of binary black holes (BBH's) is a promising candidate for detection by kilometer-scale interferometric gravitational wave observatories. This paper discusses a serious obstacle to searches for such radiation and to the interpretation of any observed waves: the inability of current computational techniques to evolve a BBH through its last ~10 orbits of inspiral (~100 radians of gravitational-wave phase). A new set of numerical-relativity techniques is proposed for solving this ``Intermediate Binary Black Hole'' (IBBH) problem: (i) numerical evolutions performed in coordinates co-rotating with the BBH, in which the metric coefficients evolve on the long timescale of inspiral, and (ii) techniques for mathematically freezing out gravitational degrees of freedom that are not excited by the waves.Comment: 6 pages RevTe

MECHANICAL DAMPING SYSTEM FOR STRUCTURES

A mechanical damping system for a structure is provided. The mechanical damping system comprises a tubular impact frame secured to the structure. A support frame is secured to the structure with the support frame spaced from the impact frame. An elongated member is provided having a first end and a second end. The first end is secured within the support frame and the second end is free from connection and extends into the impact frame. At least one impact mass is secured to the second end of the elongated member, the impact mass movable within and contactable with the impact frame

A Deep Multicolor Survey V: The M Dwarf Luminosity Function

We present a study of M dwarfs discovered in a large area, multicolor survey. We employ a combination of morphological and color criteria to select M dwarfs to a limiting magnitude in V of 22, the deepest such ground-based survey for M dwarfs to date. We solve for the vertical disk stellar density law and use the resulting parameters to derive the M dwarf luminosity and mass functions from this sample. We find the stellar luminosity function peaks at M_V = 12 and declines thereafter. Our derived mass function for stars with M < 0.6 M_sun is inconsistent with a Salpeter function at the 3 sigma level; instead, we find the mass function is relatively flat for 0.6 M_sun > M > 0.1 M_sun.Comment: Accepted for publication in AJ. 19 pages including 4 embedded postscript figures (AASTEX