13,580 research outputs found
A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently
solve the Radial Basis Function (RBF) interpolation problem with variable
polynomial order. The HB forms an orthogonal set and is adapted to the kernel
seed function and the placement of the interpolation nodes. Moreover, this
basis is orthogonal to a set of polynomials up to a given order defined on the
interpolating nodes. We are thus able to decouple the RBF interpolation problem
for any order of the polynomial interpolation and solve it in two steps: (1)
The polynomial orthogonal RBF interpolation problem is efficiently solved in
the transformed HB basis with a GMRES iteration and a diagonal, or block SSOR
preconditioner. (2) The residual is then projected onto an orthonormal
polynomial basis. We apply our approach on several test cases to study its
effectiveness, including an application to the Best Linear Unbiased Estimator
regression problem
The counterrotating core and the black hole mass of IC1459
The E3 giant elliptical galaxy IC1459 is the prototypical galaxy with a fast
counterrotating stellar core. We obtained one HST/STIS long-slit spectrum along
the major axis of this galaxy and CTIO spectra along five position angles. We
present self-consistent three-integral axisymmetric models of the stellar
kinematics, obtained with Schwarzschild's numerical orbit superposition method.
We study the dynamics of the kinematically decoupled core (KDC) in IC1459 and
we find it consists of stars that are well-separated from the rest of the
galaxy in phase space. The stars in the KDC counterrotate in a disk on orbits
that are close to circular. We estimate that the KDC mass is ~0.5% of the total
galaxy mass or ~3*10^9 Msun. We estimate the central black hole mass M_BH of
IC1459 independently from both its stellar and its gaseous kinematics. Some
complications probably explain why we find rather discrepant BH masses with the
different methods. The stellar kinematics suggest that M_BH = (2.6 +/-
1.1)*10^9 Msun (3 sigma error). The gas kinematics suggests that M_BH ~
3.5*10^8 Msun if the gas is assumed to rotate at the circular velocity in a
thin disk. If the observed velocity dispersion of the gas is assumed to be
gravitational, then M_BH could be as high as ~1.0*10^9 Msun. These different
estimates bracket the value M_BH = (1.1 +/- 0.3)*10^9 Msun predicted by the
M_BH-sigma relation. It will be an important goal for future studies to assess
the reliability of black hole mass determinations with either technique. This
is essential if one wants to interpret the correlation between the BH mass and
other global galaxy parameters (e.g. velocity dispersion) and in particular the
scatter in these correlations (believed to be only ~0.3 dex). [Abridged]Comment: 51 pages, LaTeX with 19 PostScript figures. Revised version, with
three new figures and data tables. To appear in The Astrophysical Journal,
578, 2002 October 2
Searching for Exoplanets Using Artificial Intelligence
In the last decade, over a million stars were monitored to detect transiting
planets. Manual interpretation of potential exoplanet candidates is labor
intensive and subject to human error, the results of which are difficult to
quantify. Here we present a new method of detecting exoplanet candidates in
large planetary search projects which, unlike current methods uses a neural
network. Neural networks, also called "deep learning" or "deep nets" are
designed to give a computer perception into a specific problem by training it
to recognize patterns. Unlike past transit detection algorithms deep nets learn
to recognize planet features instead of relying on hand-coded metrics that
humans perceive as the most representative. Our convolutional neural network is
capable of detecting Earth-like exoplanets in noisy time-series data with a
greater accuracy than a least-squares method. Deep nets are highly
generalizable allowing data to be evaluated from different time series after
interpolation without compromising performance. As validated by our deep net
analysis of Kepler light curves, we detect periodic transits consistent with
the true period without any model fitting. Our study indicates that machine
learning will facilitate the characterization of exoplanets in future analysis
of large astronomy data sets.Comment: Accepted, 16 Pages, 14 Figures,
https://github.com/pearsonkyle/Exoplanet-Artificial-Intelligenc
System- and Data-Driven Methods and Algorithms
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques
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