7,672 research outputs found
Ellipsoidal classification via semidefinite programming
We propose a classification approach exploiting relationships between ellipsoidal separation and Support-vector Machine (SVM) with quadratic kernel. By adding a (Semidefinite Programming) SDP constraint to SVM model we ensure that the chosen hyperplane in feature space represents a non-degenerate ellipsoid in input space. This allows us to exploit SDP techniques within Support-vector Regression (SVR) approaches, yielding better results in case ellipsoid-shaped separators are appropriate for classification tasks. We compare our approach with spherical separation and SVM on some classification problems
Darwin-Riemann Problems in Newtonian Gravity
In this paper, we have reviewed the present status of the theory of
equilibrium configurations of compact binary star systems in Newtonian gravity.
Evolutionary processes of compact binary star systems due to gravitational wave
emission can be divided into three stages according to the time scales and
configurations. The evolution is quasi-stationary until a merging process
starts, since the time scale of the orbital change due to gravitational wave
emission is longer than the orbital period. In this stage, equilibrium
sequences can be applied to evolution of compact binary star systems. Along the
equilibrium sequences, there appear several critical states where some
instability sets in or configuration changes drastically. We have discussed
relations among these critical points and have stressed the importance of the
mass overflow as well as the dynamical instability of orbital motions.
Concerning the equilibrium sequences of binary star systems, we have summarized
classical results of incompressible ellipsoidal configurations. Recent results
of compressible binary star systems obtained by the ellipsoidal approximation
and by numerical computations have been shown and discussed. It is important to
note that numerical computational solutions to {\it exact equations} show that
compressibility may lead realistic neutron star binary systems to mass
overflows instead of dynamical disruptions for a wide range of parameters.Comment: 17 pages, 10 figures, PTPTeX style files are include
Selecting a Small Set of Optimal Gestures from an Extensive Lexicon
Finding the best set of gestures to use for a given computer recognition
problem is an essential part of optimizing the recognition performance while
being mindful to those who may articulate the gestures. An objective function,
called the ellipsoidal distance ratio metric (EDRM), for determining the best
gestures from a larger lexicon library is presented, along with a numerical
method for incorporating subjective preferences. In particular, we demonstrate
an efficient algorithm that chooses the best gestures from a lexicon of
gestures where typically using a weighting of both subjective and
objective measures.Comment: 27 pages, 7 figure
Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
The problem of the invariant classification of the orthogonal coordinate webs
defined in Euclidean space is solved within the framework of Felix Klein's
Erlangen Program. The results are applied to the problem of integrability of
the Calogero-Moser model
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
On Machine-Learned Classification of Variable Stars with Sparse and Noisy Time-Series Data
With the coming data deluge from synoptic surveys, there is a growing need
for frameworks that can quickly and automatically produce calibrated
classification probabilities for newly-observed variables based on a small
number of time-series measurements. In this paper, we introduce a methodology
for variable-star classification, drawing from modern machine-learning
techniques. We describe how to homogenize the information gleaned from light
curves by selection and computation of real-numbered metrics ("feature"),
detail methods to robustly estimate periodic light-curve features, introduce
tree-ensemble methods for accurate variable star classification, and show how
to rigorously evaluate the classification results using cross validation. On a
25-class data set of 1542 well-studied variable stars, we achieve a 22.8%
overall classification error using the random forest classifier; this
represents a 24% improvement over the best previous classifier on these data.
This methodology is effective for identifying samples of specific science
classes: for pulsational variables used in Milky Way tomography we obtain a
discovery efficiency of 98.2% and for eclipsing systems we find an efficiency
of 99.1%, both at 95% purity. We show that the random forest (RF) classifier is
superior to other machine-learned methods in terms of accuracy, speed, and
relative immunity to features with no useful class information; the RF
classifier can also be used to estimate the importance of each feature in
classification. Additionally, we present the first astronomical use of
hierarchical classification methods to incorporate a known class taxonomy in
the classifier, which further reduces the catastrophic error rate to 7.8%.
Excluding low-amplitude sources, our overall error rate improves to 14%, with a
catastrophic error rate of 3.5%.Comment: 23 pages, 9 figure
Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics
We investigate dynamics of probe particles moving in the near-horizon limit
of (2N+1)-dimensional extremal Myers-Perry black hole with arbitrary rotation
parameters. We observe that in the most general case with nonequal nonvanishing
rotational parameters the system admits separation of variables in
N-dimensional ellipsoidal coordinates. This allows us to find solution of the
corresponding Hamilton-Jacobi equation and write down the explicit expressions
of Liouville constants of motion.Comment: 9 pages, no figures, v2: Minor changes to match the published versio
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