arXiv subjects

Christopher Miller

Publications and source records attributed to Christopher Miller.

25 records · Page 2Linked to original sources

arXiv2015

Examples of $k$-regular maps and interpolation spaces

A continous map $f: \mathbb{C}^n \rightarrow \mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev, to construct $k$-regular maps with small $N$ and only a few nontrivial examples are known so far. Applying tools from algebraic geometry we construct a 4-regular polynomial map $\mathbb{C}^3\rightarrow \mathbb{C}^{11}$ and a 5-regular polynomial map $\mathbb{C}^3\rightarrow \mathbb{C}^{14}$.

math.AG↗

arXiv2012

Prime tight frames

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two.

math.FA↗

arXiv2009

Inference for the dark energy equation of state using Type IA supernova data

The surprising discovery of an accelerating universe led cosmologists to posit the existence of "dark energy"--a mysterious energy field that permeates the universe. Understanding dark energy has become the central problem of modern cosmology. After describing the scientific background in depth, we formulate the task as a nonlinear inverse problem that expresses the comoving distance function in terms of the dark-energy equation of state. We present two classes of methods for making sharp statistical inferences about the equation of state from observations of Type Ia Supernovae (SNe). First, we derive a technique for testing hypotheses about the equation of state that requires no assumptions about its form and can distinguish among competing theories. Second, we present a framework for computing parametric and nonparametric estimators of the equation of state, with an associated assessment of uncertainty. Using our approach, we evaluate the strength of statistical evidence for various competing models of dark energy. Consistent with current studies, we find that with the available Type Ia SNe data, it is not possible to distinguish statistically among popular dark-energy models, and that, in particular, there is no support in the data for rejecting a cosmological constant. With much more supernova data likely to be available in coming years (e.g., from the DOE/NASA Joint Dark Energy Mission), we address the more interesting question of whether future data sets will have sufficient resolution to distinguish among competing theories.

astro-ph↗

arXiv2005

Massive Science with VO and Grids

There is a growing need for massive computational resources for the analysis of new astronomical datasets. To tackle this problem, we present here our first steps towards marrying two new and emerging technologies; the Virtual Observatory (e.g, AstroGrid) and the computational grid (e.g. TeraGrid, COSMOS etc.). We discuss the construction of VOTechBroker, which is a modular software tool designed to abstract the tasks of submission and management of a large number of computational jobs to a distributed computer system. The broker will also interact with the AstroGrid workflow and MySpace environments. We discuss our planned usages of the VOTechBroker in computing a huge number of n-point correlation functions from the SDSS data and massive model-fitting of millions of CMBfast models to WMAP data. We also discuss other applications including the determination of the XMM Cluster Survey selection function and the construction of new WMAP maps.

astro-ph↗

arXiv2003

Eccentricity Evolution in Simulated Galaxy Clusters

Strong cluster eccentricity evolution for $z \le 0.13$ has appeared in a variety of observational data sets. We examine the evolution of eccentricity in simulated galaxy clusters using a variety of simulation methodologies, amplitude normalizations, and background cosmologies. We do not find find such evolution for $z < 0.1$ in any of our simulation ensembles. We suggest a systematic error in the form of a redshift-dependent selection effect in cluster catalogs or missing physics in cluster simulations important enough to modify the cluster morphology.

astro-ph↗

arXiv2001

Weak Lensing Measurements of 42 SDSS/RASS Galaxy Clusters

We present a lensing study of 42 galaxy clusters imaged in Sloan Digital Sky Survey (SDSS) commissioning data. Cluster candidates are selected optically from SDSS imaging data and confirmed for this study by matching to X-ray sources found independently in the ROSAT all sky survey (RASS). Five color SDSS photometry is used to make accurate photometric redshift estimates that are used to rescale and combine the lensing measurements. The mean shear from these clusters is detected to 2 h-1 Mpc at the 7-sigma level, corresponding to a mass within that radius of 4.2 +/- 0.6 x 10^14 h-1 M_sun. The shear profile is well fit by a power law with index -0.9 +/- 0.3, consistent with that of an isothermal density profile. This paper demonstrates our ability to measure ensemble cluster masses from SDSS imaging data.

astro-ph↗

arXiv1999

Cluster Winds Blow along Supercluster Axes

Within Abell galaxy clusters containing wide-angle tailed radio sources, there is evidence of a ``prevailing wind'' which directs the WAT jets. We study the alignment of WAT jets and nearby clusters to test the idea that this wind may be a fossil of drainage along large-scale supercluster axes. We also test this idea with a study of the alignment of WAT jets and supercluster axes. Statistical test neighbours indicate no alignment of WAT jets towards nearest clusters, but do indicate approximately 98% confidence in alignment with the long axis of the supercluster in which the cluster lies. We find a preferred scale for such superclusters of order 25 Mpc $h^{-1}$.

astro-ph↗