204,113 research outputs found
ATRo and Some Related Theories
The main point of interest of this dissertation is to study theories related to the theory ATRo in the realm of second order arithmetic. It is divided into two parts. In Part I, the equivalence of several axiom schemas to (ATR) over ACAo is proven. In particular, so-called reduction principles – also known as separation principles – are discussed. Part I is then concluded with an analysis of set-parameter free variants of ATRo and related systems. In Part II we are interested in set-theoretic analogues of questions that were treated in Part I. To this end, a range of basic set theories featuring the natural numbers as urelements and induction principles on sets and the natural numbers of various strengths are introduced. To interpret set-theoretic objects within second order arithmetic, we adapt the method of representation trees introduced by Jäger and Simpson. Making use of representation trees, the effect on proof-theoretic strength when adding reduction principles to our basic set theories is discussed. Finally, the effect of adding Axiom Beta is examined
Labeling Schemes with Queries
We study the question of ``how robust are the known lower bounds of labeling
schemes when one increases the number of consulted labels''. Let be a
function on pairs of vertices. An -labeling scheme for a family of graphs
\cF labels the vertices of all graphs in \cF such that for every graph
G\in\cF and every two vertices , the value can be inferred
by merely inspecting the labels of and .
This paper introduces a natural generalization: the notion of -labeling
schemes with queries, in which the value can be inferred by inspecting
not only the labels of and but possibly the labels of some additional
vertices. We show that inspecting the label of a single additional vertex (one
{\em query}) enables us to reduce the label size of many labeling schemes
significantly
Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems
We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for
the kernels associated with power-law fundamental solutions of the polyharmonic
equation on d-dimensional Euclidean space. From these series representations we
derive Fourier expansions in certain rotationally-invariant coordinate systems
and Gegenbauer polynomial expansions in Vilenkin's polyspherical coordinates.
We compare both of these expansions to generate addition theorems for the
azimuthal Fourier coefficients
Optimization of Signal Significance by Bagging Decision Trees
An algorithm for optimization of signal significance or any other
classification figure of merit suited for analysis of high energy physics (HEP)
data is described. This algorithm trains decision trees on many bootstrap
replicas of training data with each tree required to optimize the signal
significance or any other chosen figure of merit. New data are then classified
by a simple majority vote of the built trees. The performance of this algorithm
has been studied using a search for the radiative leptonic decay B->gamma l nu
at BaBar and shown to be superior to that of all other attempted classifiers
including such powerful methods as boosted decision trees. In the B->gamma e nu
channel, the described algorithm increases the expected signal significance
from 2.4 sigma obtained by an original method designed for the B->gamma l nu
analysis to 3.0 sigma.Comment: 8 pages, 2 figures, 1 tabl
A Multi-variate Discrimination Technique Based on Range-Searching
We present a fast and transparent multi-variate event classification
technique, called PDE-RS, which is based on sampling the signal and background
densities in a multi-dimensional phase space using range-searching. The
employed algorithm is presented in detail and its behaviour is studied with
simple toy examples representing basic patterns of problems often encountered
in High Energy Physics data analyses. In addition an example relevant for the
search for instanton-induced processes in deep-inelastic scattering at HERA is
discussed. For all studied examples, the new presented method performs as good
as artificial Neural Networks and has furthermore the advantage to need less
computation time. This allows to carefully select the best combination of
observables which optimally separate the signal and background and for which
the simulations describe the data best. Moreover, the systematic and
statistical uncertainties can be easily evaluated. The method is therefore a
powerful tool to find a small number of signal events in the large data samples
expected at future particle colliders.Comment: Submitted to NIM, 18 pages, 8 figure
Robust Machine Learning Applied to Astronomical Datasets I: Star-Galaxy Classification of the SDSS DR3 Using Decision Trees
We provide classifications for all 143 million non-repeat photometric objects
in the Third Data Release of the Sloan Digital Sky Survey (SDSS) using decision
trees trained on 477,068 objects with SDSS spectroscopic data. We demonstrate
that these star/galaxy classifications are expected to be reliable for
approximately 22 million objects with r < ~20. The general machine learning
environment Data-to-Knowledge and supercomputing resources enabled extensive
investigation of the decision tree parameter space. This work presents the
first public release of objects classified in this way for an entire SDSS data
release. The objects are classified as either galaxy, star or nsng (neither
star nor galaxy), with an associated probability for each class. To demonstrate
how to effectively make use of these classifications, we perform several
important tests. First, we detail selection criteria within the probability
space defined by the three classes to extract samples of stars and galaxies to
a given completeness and efficiency. Second, we investigate the efficacy of the
classifications and the effect of extrapolating from the spectroscopic regime
by performing blind tests on objects in the SDSS, 2dF Galaxy Redshift and 2dF
QSO Redshift (2QZ) surveys. Given the photometric limits of our spectroscopic
training data, we effectively begin to extrapolate past our star-galaxy
training set at r ~ 18. By comparing the number counts of our training sample
with the classified sources, however, we find that our efficiencies appear to
remain robust to r ~ 20. As a result, we expect our classifications to be
accurate for 900,000 galaxies and 6.7 million stars, and remain robust via
extrapolation for a total of 8.0 million galaxies and 13.9 million stars.
[Abridged]Comment: 27 pages, 12 figures, to be published in ApJ, uses emulateapj.cl
Cascade Training Technique for Particle Identification
The cascade training technique which was developed during our work on the
MiniBooNE particle identification has been found to be a very efficient way to
improve the selection performance, especially when very low background
contamination levels are desired. The detailed description of this technique is
presented here based on the MiniBooNE detector Monte Carlo simulations, using
both artifical neural networks and boosted decision trees as examples.Comment: 12 pages and 4 EPS figure
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