23,997 research outputs found
A graph theoretic characterization of the classical generalized hexagon on vertices
A tetravalent -arc-transitive graph of order is either the known
-arc-transitive incidence graph of the classical generalized hexagon
or a normal cover of a -transitive graph of order denoted
or in the list of Poto\v{c}nik.Comment: 11 page
Set-based differential covariance testing for high-throughput data
The problem of detecting changes in covariance for a single pair of features
has been studied in some detail, but may be limited in importance or general
applicability. In contrast, testing equality of covariance matrices of a {\it
set} of features may offer increased power and interpretability. Such
approaches have received increasing attention in recent years, especially in
the context of high-dimensional testing. These approaches have been limited to
the two-sample problem and involve varying assumptions on the number of
features vs. the sample size . In addition, there has been little
discussion of the motivating principles underlying various choices of
statistic, and no general approaches to test association of covariances with a
continuous outcome. We propose a uniform framework to test association of
covariance matrices with an experimental variable, whether discrete or
continuous. We describe four different summary statistics, to ensure power and
flexibility under various settings, including a new "connectivity" statistic
that is sensitive to changes in overall covariance magnitude. The approach is
not limited by the data dimensions, and is applicable to situations where . For several statistics we obtain asymptotic -values under relatively
mild conditions. For the two-sample special case, we show that the proposed
statistics are permutationally equivalent or similar to existing proposed
statistics. We demonstrate the power and utility of our approaches via
simulation and analysis of real data.Comment: arXiv admin note: substantial text overlap with arXiv:1609.0073
Estimation And Selection Via Absolute Penalized Convex Minimization And Its Multistage Adaptive Applications
The -penalized method, or the Lasso, has emerged as an important tool
for the analysis of large data sets. Many important results have been obtained
for the Lasso in linear regression which have led to a deeper understanding of
high-dimensional statistical problems. In this article, we consider a class of
weighted -penalized estimators for convex loss functions of a general
form, including the generalized linear models. We study the estimation,
prediction, selection and sparsity properties of the weighted
-penalized estimator in sparse, high-dimensional settings where the
number of predictors can be much larger than the sample size . Adaptive
Lasso is considered as a special case. A multistage method is developed to
apply an adaptive Lasso recursively. We provide oracle inequalities, a
general selection consistency theorem, and an upper bound on the dimension of
the Lasso estimator. Important models including the linear regression, logistic
regression and log-linear models are used throughout to illustrate the
applications of the general results
Communities of solutions in single solution clusters of a random K-Satisfiability formula
The solution space of a K-satisfiability (K-SAT) formula is a collection of
solution clusters, each of which contains all the solutions that are mutually
reachable through a sequence of single-spin flips. Knowledge of the statistical
property of solution clusters is valuable for a complete understanding of the
solution space structure and the computational complexity of the random K-SAT
problem. This paper explores single solution clusters of random 3- and 4-SAT
formulas through unbiased and biased random walk processes and the
replica-symmetric cavity method of statistical physics. We find that the giant
connected component of the solution space has already formed many different
communities when the constraint density of the formula is still lower than the
solution space clustering transition point. Solutions of the same community are
more similar with each other and more densely connected with each other than
with the other solutions. The entropy density of a solution community is
calculated using belief propagation and is found to be different for different
communities of the same cluster. When the constraint density is beyond the
clustering transition point, the same behavior is observed for the solution
clusters reached by several stochastic search algorithms. Taking together, the
results of this work suggests a refined picture on the evolution of the
solution space structure of the random K-SAT problem; they may also be helpful
for designing new heuristic algorithms.Comment: Extensively revised and expanded into 15 pages with 10 figures. New
mean-field calculations and simulation results adde
Where to Find Habitable "Earths" in Circumbinary Systems
Hitherto, six P-type planets are found around five binary systems, i.e.
Kepler-16 b, 34 b, 35 b, 38 b, 47 b, c, which are all Neptune or Jupiter-like
planets. The stability of planets and the habitable zones are influenced by the
gravitational and radiative perturbations of binary companions. In this Letter,
we check the stability of an additional habitable Earth-mass planet in each
system. Based on our simulations in 10 Myr, a habitable "Earth" is hardly
stable in Kepler-16 while a stable "Earth" in Kepler-47 close to the boundaries
of the habitable zone is possible. In contrast, Kepler-34, 35 and 38 seem to
have high probabilities of being able to tolerate a stable "Earth" in their
habitable zones. The affects of transit time variations are quite small due to
the small mass of an undetected "Earth", except that of Kepler-16 b. With a
time precision of 0.001 day(~ 88 s), an "Earth" in the corotational resonance
with Kepler-16 b can be detected in 3 years, while habitable "Earths" in
Kepler-34 and 38 systems can be detected in 10 years. Habitable "Earths" in
Kepler-35 and 47 are not likely to be detected in 10 years under this
precision.Comment: 7 pages, 3 figures, 2 table
An Explicit Cross Entropy Scheme for Mixtures
The key issue in importance sampling is the choice of the alternative
sampling distribution, which is often chosen from the exponential tilt family
of the underlying distribution. However, when the problem exhibits certain kind
of nonconvexity, it is very likely that a single exponential change of measure
will never attain asymptotic optimality and can lead to erroneous estimates. In
this paper we introduce an explicit iterative scheme which combines the
traditional cross-entropy method and the EM algorithm to find an efficient
alternative sampling distribution in the form of mixtures. We also study the
applications of this scheme to the estimation of rainbow option prices
Topological Superconductivity Intertwined with Broken Symmetries
Recently the superconductor and topological semimetal PbTaSe was
experimentally found to exhibit surface-only lattice rotational symmetry
breaking below . We exploit the Ginzburg-Landau free energy and propose a
microscopic two-channel model to study possible superconducting states on the
surface of PbTaSe. We identify two types of topological superconducting
states. One is time-reversal invariant and preserves the lattice hexagonal
symmetry while the other breaks both symmetries. We find that such
time-reversal symmetry breaking is unavoidable for a superconducting state in a
two dimensional irreducible representation of crystal point group in a system
where the spatial inversion symmetry is broken and the strong spin-orbit
coupling is present. Our findings will guide the search for topological chiral
superconductors.Comment: 4+5 pages, 5 figure
On the orbital evolution of a giant planet pair embedded in a gaseous disk. I: Jupiter-Saturn configuration
We carry out a series of high resolution () hydrodynamical
simulations to investigate the orbital evolution of Jupiter and Saturn embedded
in a gaseous protostellar disk. Our work extends the results in the classical
papers of Masset & Snellgrove (2001) and Morbidelli & Crida (2007) by exploring
various surface density profiles (), where . The stability of the mean motion resonances(MMRs) caused by the
convergent migration of the two planets is studied as well. Our results show
that:(1) The gap formation process of Saturn is greatly delayed by the tidal
perturbation of Jupiter. These perturbations cause inward or outward runaway
migration of Saturn, depending on the density profiles on the disk. (2) The
convergent migration rate increases as increases and the type of MMRs
depends on as well. When , the convergent migration speed
of Jupiter and Saturn is relatively slow, thus they are trapped into 2:1 MMR.
When , Saturn passes through the MMR with Jupiter and is
captured into the MMR. (3) The MMR turns out to be unstable when
the eccentricity of Saturn () increases too high. The critical value above
which instability will set in is . We also observe that the two
planets are trapped into MMR after the break of MMR. This process
may provide useful information for the formation of orbital configuration
between Jupiter and Saturn in the Solar System.Comment: 21 pages, 23 figure
Hypothesis testing at the extremes: fast and robust association for high-throughput data
A number of biomedical problems require performing many hypothesis tests,
with an attendant need to apply stringent thresholds. Often the data take the
form of a series of predictor vectors, each of which must be compared with a
single response vector, perhaps with nuisance covariates. Parametric tests of
association are often used, but can result in inaccurate type I error at the
extreme thresholds, even for large sample sizes. Furthermore, standard
two-sided testing can reduce power compared to the doubled -value, due to
asymmetry in the null distribution. Exact (permutation) testing is attractive,
but can be computationally intensive and cumbersome. We present an
approximation to exact association tests of trend that is accurate and fast
enough for standard use in high-throughput settings, and can easily provide
standard two-sided or doubled -values. The approach is shown to be
equivalent under permutation to likelihood ratio tests for the most commonly
used generalized linear models. For linear regression, covariates are handled
by working with covariate-residualized responses and predictors. For
generalized linear models, stratified covariates can be handled in a manner
similar to exact conditional testing. Simulations and examples illustrate the
wide applicability of the approach
HAWC Observation of Supernova Remnants and Pulsar Wind Nebulae
The majority of Galactic TeV gamma-ray sources are pulsar wind nebulae (PWNe)
and supernova remnants (SNRs), and the most common association for unidentified
sources is PWN. Many of these sources were discovered in TeV by imaging air
Cherenkov telescopes using overlapping pointed observations over sections of
the Galactic plane. The HAWC observatory is a survey type instrument in the
Northern hemisphere with an energy range of 100 GeV to 100 TeV. Preliminary
analysis of data recorded with the partially completed HAWC array taken since
2013 shows extended detections that are coincident with known TeV SNRs and
PWNe. The full array became operational in early 2015 and has been steadily
surveying the Northern sky since. I will discuss detections in HAWC data taken
since 2013 associated with PWNe and SNRs.Comment: Presented at the 34th International Cosmic Ray Conference (ICRC2015),
The Hague, The Netherlands. See arXiv:1508.03327 for all HAWC contribution
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