119 research outputs found
Good methods for coping with missing data in decision trees
We propose a simple and effective method for dealing with missing data in decision trees used for classification. We call this approach 'missingness incorporated in attributes' (MIA). It is very closely related to the technique of treating 'missing' as a category in its own right, generalizing it for use with continuous as well as categorical variables. We show through a substantial data-based study of classification accuracy that MIA exhibits consistently good performance across a broad range of data types and of sources and amounts of missingness. It is competitive with the best of the rest (particularly, a multiple imputation EM algorithm method; EMMI) while being conceptually and computationally simpler. A simple combination of MIA and EMMI is slower but even more accurate
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MLB: multilevel load balancing for structured grid applications
The Multilevel Load Balancing algorithm (MLB) is a parallel algorithm that determines the communication schedule that is necessary to balance a distributed discrete load function. The MLB algorithm focuses on structured grid computations and their load balancing requirements, which we feel are largely unsupported within the load balancing community. The interface to MLB is inherently simple; a distributed discrete load function is provided by the user and a communication schedule is returned. The load function can, for example, map to one or more distributed arrays. So far the implementation includes a parallel version of only the one dimensional MLB algorithm and produces a communication schedule that requires at most log(p) communication steps, where p is the number of processors (log() stands for the logarithm of base two). This work forms just one of the object-oriented class libraries within the OVERTURE Framework, an object-oriented environment for the numerical solution of partial differential equations in serial and parallel environments
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Parallel object-oriented adaptive mesh refinement
In this paper we study adaptive mesh refinement (AMR) for elliptic and hyperbolic systems. We use the Asynchronous Fast Adaptive Composite Grid Method (AFACX), a parallel algorithm based upon the of Fast Adaptive Composite Grid Method (FAC) as a test case of an adaptive elliptic solver. For our hyperbolic system example we use TVD and ENO schemes for solving the Euler and MHD equations. We use the structured grid load balancer MLB as a tool for obtaining a load balanced distribution in a parallel environment. Parallel adaptive mesh refinement poses difficulties in expressing both the basic single grid solver, whether elliptic or hyperbolic, in a fashion that parallelizes seamlessly. It also requires that these basic solvers work together within the adaptive mesh refinement algorithm which uses the single grid solvers as one part of its adaptive solution process. We show that use of AMR++, an object-oriented library within the OVERTURE Framework, simplifies the development of AMR applications. Parallel support is provided and abstracted through the use of the P++ parallel array class
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Overture: an object-oriented software system for solving partial differential equations in serial and parallel environments
The OVERTURE Framework is an object-oriented environment for solving PDEs on serial and parallel architectures. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures, as well as the details of the parallel implementation. It is based on the A++/P++ array class library and is designed for solving problems on a structured grid or a collection of structured grids. In particular, it can use curvilinear grids, adaptive mesh refinement and the composite overlapping grid method to represent problems with complex moving geometry
Method for Measuring the Momentum-Dependent Relative Phase of the Superconducting Gap of High-Temperature Superconductors
The phase variation of the superconducting gap over the (normal) Fermi
surface of the high-temperature superconductors remains a significant
unresolved question. Is the phase of the gap constant, does it change sign, or
is it perhaps complex? A detailed answer to this question would provide
important constraints on various pairing mechanisms. Here we propose a new
method for measuring the relative gap PHASE on the Fermi surface which is
direct, is angle-resolved, and probes the bulk. The required experiments
involve measuring phonon linewidths in the normal and superconducting state,
with resolution available in current facilities. We primarily address the
La_1.85Sr_.15CuO_4 material, but also propose a more detailed study of a
specific phonon in Bi_2Sr_2CaCu_2O_8.Comment: 13 pages (revtex) + 5 figures (postscript-included), NSF-ITP-93-2
Quasi-particle Lifetimes in a d_{x^2-y^2} Superconductor
We consider the lifetime of quasi-particles in a d-wave superconductor due to
scattering from antiferromagnetic spin-fluctuations, and explicitly separate
the contribution from Umklapp processes which determines the electrical
conductivity. Results for the temperature dependence of the total scattering
rate and the Umklapp scattering rate are compared with relaxation rates
obtained from thermal and microwave conductivity measurements, respectively.Comment: 14 pages, 4 figure
Evolution of supermassive black holes
Supermassive black holes (SMBHs) are nowadays believed to reside in most
local galaxies, and the available data show an empirical correlation between
bulge luminosity - or stellar velocity dispersion - and black hole mass,
suggesting a single mechanism for assembling black holes and forming spheroids
in galaxy halos. The evidence is therefore in favour of a co-evolution between
galaxies, black holes and quasars. In cold dark matter cosmogonies, small-mass
subgalactic systems form first to merge later into larger and larger
structures. In this paradigm galaxy halos experience multiple mergers during
their lifetime. If every galaxy with a bulge hosts a SMBH in its center, and a
local galaxy has been made up by multiple mergers, then a black hole binary is
a natural evolutionary stage. The evolution of the supermassive black hole
population clearly has to be investigated taking into account both the
cosmological framework and the dynamical evolution of SMBHs and their hosts.
The seeds of SMBHs have to be looked for in the early Universe, as very
luminous quasars are detected up to redshift higher than z=6. These black holes
evolve then in a hierarchical fashion, following the merger hierarchy of their
host halos. Accretion of gas, traced by quasar activity, plays a fundamental
role in determining the two parameters defining a black hole: mass and spin. A
particularly intriguing epoch is the initial phase of SMBH growth. It is very
challenging to meet the observational constraints at z=6 if BHs are not fed at
very high rates in their infancy.Comment: Extended version of the invited paper to appear in the Proceedings of
the Conference "Relativistic Astrophysics and Cosmology - Einstein's Legacy
N-body simulations of gravitational dynamics
We describe the astrophysical and numerical basis of N-body simulations, both
of collisional stellar systems (dense star clusters and galactic centres) and
collisionless stellar dynamics (galaxies and large-scale structure). We explain
and discuss the state-of-the-art algorithms used for these quite different
regimes, attempt to give a fair critique, and point out possible directions of
future improvement and development. We briefly touch upon the history of N-body
simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu
Massive binary black holes in galactic nuclei and their path to coalescence
Massive binary black holes form at the centre of galaxies that experience a
merger episode. They are expected to coalesce into a larger black hole,
following the emission of gravitational waves. Coalescing massive binary black
holes are among the loudest sources of gravitational waves in the Universe, and
the detection of these events is at the frontier of contemporary astrophysics.
Understanding the black hole binary formation path and dynamics in galaxy
mergers is therefore mandatory. A key question poses: during a merger, will the
black holes descend over time on closer orbits, form a Keplerian binary and
coalesce shortly after? Here we review progress on the fate of black holes in
both major and minor mergers of galaxies, either gas-free or gas-rich, in
smooth and clumpy circum-nuclear discs after a galactic merger, and in
circum-binary discs present on the smallest scales inside the relic nucleus.Comment: Accepted for publication in Space Science Reviews. To appear in hard
cover in the Space Sciences Series of ISSI "The Physics of Accretion onto
Black Holes" (Springer Publisher
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