Multi-Tree Methods for Statistics on Very Large Datasets in Astronomy

Alexander G. Gray; Andrew W. Moore; Robert C. Nichol; Andrew J. Connolly; Christopher Genovese; Larry Wasserman

Home/Archive/arXiv

arXiv · astro-ph/0401121

Multi-Tree Methods for Statistics on Very Large Datasets in Astronomy

Alexander G. Gray·Andrew W. Moore·Robert C. Nichol·Andrew J. Connolly·Christopher Genovese·Larry Wasserman

View original source ↗Read source document ↗Export metadata ↓

Abstract

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have dramatically reduced the computational complexity of 1) kernel density estimation (which also extends to nonparametric regression, classification, and clustering), and 2) the n-point correlation function for arbitrary n. These new multi-tree methods typically yield orders of magnitude in speedup over the previous state of the art for similar accuracy, making millions of data points tractable on desktop workstations for the first time.

Explore related subjects

astro-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Alexander G. Gray, Andrew W. Moore, Robert C. Nichol, Andrew J. Connolly, Christopher Genovese, Larry Wasserman. 2004-01-08. Multi-Tree Methods for Statistics on Very Large Datasets in Astronomy. https://arxiv.org/abs/astro-ph/0401121

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2023

Scaling of Black Hole Accretion Discs from Gamma-Ray Bursts and Black Hole X-Ray Binaries to Active Galactic Nuclei

I consider how physical processes scale over eight orders of magnitude in black hole mass, from stellar masses in gamma-ray bursts (GRB) and black-hole X-ray binaries (BHXRB) to supermassive active galactic nuclei (AGN). Accretion rates onto stellar mass black holes range over more than sixteen orders of magnitude, from the lower luminosity BHXRB to GRB. These enormous parameter ranges correspond to qualitative as well as quantitative differences in behavior. The fundamental questions involve the balance between nonequilibrium and thermalized plasmas. When energy fluxes exceed a critical value $\sim 10^{29}$ erg/cm$^2$s, as in GRB, a black-body equilibrium pair plasma forms. At the lower fluxes found in AGN, BHXRB and microquasars, accretion power electrodynamically accelerates a small number of very energetic particles, explaining their non-thermal spectra and the high energy gamma-ray emission of blazars. Ultra-high energy cosmic rays may be accelerated by massive black holes, otherwise undetectable, with very low thermal luminosities. New-born fast high-field pulsars may be in the black-body equilibrium regime, resembling SGR in permanent outburst. I also consider the question, significant for the acceleration of nonthermal particles in GRB outflows, of whether collisionless plasmas interpenetrate rather than forming hydrodynamic shocks, and propose this as an alternative to internal shock models of GRB. A new appendix attempts to explain why AGN are, proportionally, more efficient accelerators of energetic particles than stellar mass black holes.

astro-ph↗

arXiv2022

Two 3-Branes in Randall-Sundrum Setup and Current Acceleration of the Universe

Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that {\em the two 3-branes are spatially homogeneous, isotropic, and independent of time}, following the so-called "bulk-based" approach. The most general form of the metric is obtained, and the corresponding field equations are divided into three groups, one is valid on each of the two 3-branes, and the third is valid in the bulk. The Einstein tensor on the 3-branes is expressed in terms of the discontinuities of the first-order derivatives of the metric coefficients. Thus, once the metric is known in the bulk, the distribution of the Einstein tensor on the two 3-branes is uniquely determined. As applications, we consider two different cases, one is in which the bulk is locally $AdS_{5}$, and the other is where it is vacuum. In some cases, it is shown that the universe is first decelerating and then accelerating. The global structure of the bulk as well as the 3-branes is also studied, and found that in some cases the solutions may represent the collision of two orbifold 3-branes. The applications of the formulas to the studies of the cyclic universe and the cosmological constant problem are also pointed out.

astro-ph↗

arXiv2022

A Revolution in Science: the Eclipse Expeditions of 1919

The first direct experimental test of Einstein's theory of general relativity involved a pair of expeditions to measure the bending of light at a total solar eclipse that took place one hundred years ago, on 29 May 1919. So famous is this experiment, and so dramatic was the impact on Einstein himself, that history tends not to recognise the controversy that surrounded the results at the time. In this article, I discuss the experiment in its scientific and historical background context and explain why it was, and is, such an important episode in the development of modern physics.

astro-ph↗