42,393 research outputs found
Resampling methods for spatial regression models under a class of stochastic designs
In this paper we consider the problem of bootstrapping a class of spatial
regression models when the sampling sites are generated by a (possibly
nonuniform) stochastic design and are irregularly spaced. It is shown that the
natural extension of the existing block bootstrap methods for grid spatial data
does not work for irregularly spaced spatial data under nonuniform stochastic
designs. A variant of the blocking mechanism is proposed. It is shown that the
proposed block bootstrap method provides a valid approximation to the
distribution of a class of M-estimators of the spatial regression parameters.
Finite sample properties of the method are investigated through a moderately
large simulation study and a real data example is given to illustrate the
methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000000551 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exact heat kernel on a hypersphere and its applications in kernel SVM
Many contemporary statistical learning methods assume a Euclidean feature
space. This paper presents a method for defining similarity based on
hyperspherical geometry and shows that it often improves the performance of
support vector machine compared to other competing similarity measures.
Specifically, the idea of using heat diffusion on a hypersphere to measure
similarity has been previously proposed, demonstrating promising results based
on a heuristic heat kernel obtained from the zeroth order parametrix expansion;
however, how well this heuristic kernel agrees with the exact hyperspherical
heat kernel remains unknown. This paper presents a higher order parametrix
expansion of the heat kernel on a unit hypersphere and discusses several
problems associated with this expansion method. We then compare the heuristic
kernel with an exact form of the heat kernel expressed in terms of a uniformly
and absolutely convergent series in high-dimensional angular momentum
eigenmodes. Being a natural measure of similarity between sample points
dwelling on a hypersphere, the exact kernel often shows superior performance in
kernel SVM classifications applied to text mining, tumor somatic mutation
imputation, and stock market analysis
Open string instantons and relative stable morphisms
We show how topological open string theory amplitudes can be computed by
using relative stable morphisms in the algebraic category. We achieve our goal
by explicitly working through an example which has been previously considered
by Ooguri and Vafa from the point of view of physics. By using the method of
virtual localization, we successfully reproduce their results for multiple
covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold
of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of
boundary components. In particular we show that in the case we consider there
are no open string instantons with more than one boundary component ending on
the Lagrangian submanifold.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
A Low-order Model of Water Vapor, Clouds, and Thermal Emission for Tidally Locked Terrestrial Planets
In the spirit of minimal modeling of complex systems, we develop an idealized
two-column model to investigate the climate of tidally locked terrestrial
planets with Earth-like atmospheres in the habitable zone of M-dwarf stars. The
model is able to approximate the fundamental features of the climate obtained
from three-dimensional (3D) atmospheric general circulation model (GCM)
simulations. One important reason for the two-column model's success is that it
reproduces the high cloud albedo of the GCM simulations, which reduces the
planet's temperature and delays the onset of a runaway greenhouse state. The
two-column model also clearly illustrates a secondary mechanism for determining
the climate: the nightside acts as a ``radiator fin'' through which infrared
energy can be lost to space easily. This radiator fin is maintained by a
temperature inversion and dry air on the nightside, and plays a similar role to
the subtropics on modern Earth. Since 1D radiative-convective models cannot
capture the effects of the cloud albedo and radiator fin, they are
systematically biased towards a narrower habitable zone. We also show that
cloud parameters are most important for determining the day--night thermal
emission contrast in the two-column model, which decreases and eventually
reverses as the stellar flux increases. This reversal is important because it
could be detected by future extrasolar planet characterization missions, which
would suggest that the planet has Earth-like water clouds and is potentially
habitable.Comment: The Astrophysical Journal (in press), 14 pages, 11 figures, 1 tabl
Entanglement and spin-squeezing in a network of distant optical lattice clocks
We propose an approach for collective enhancement of precision for remotely
located optical lattice clocks and a way of generation of the
Einstein-Podolsky-Rosen state of remote clocks. Close to Heisenberg scaling of
the clock precision with the number of clocks M can be achieved even for an
optical channel connecting clocks with substantial losses. This scenario
utilizes a collective quantum nondemolition measurement on clocks with parallel
Bloch vectors for enhanced measurement precision. We provide an optimal network
solution for distant clocks as well as for clocks positioned in close proximity
of each other. In the second scenario, we employ collective dissipation to
drive two clocks with oppositely oriented Bloch vectors into a steady state
entanglement. The corresponding EPR entanglement provides enhanced time sharing
beyond the projection noise limit between the two quantum synchronized clocks
protected from eavesdropping, as well as allows better characterization of
systematic effects
Complexity Results for MCMC derived from Quantitative Bounds
This paper considers how to obtain MCMC quantitative convergence bounds which
can be translated into tight complexity bounds in high-dimensional settings. We
propose a modified drift-and-minorization approach, which establishes a
generalized drift condition defined in a subset of the state space. The subset
is called the ``large set'' and is chosen to rule out some ``bad'' states which
have poor drift property when the dimension gets large. Using the ``large set''
together with a ``centered'' drift function, a quantitative bound can be
obtained which can be translated into a tight complexity bound. As a
demonstration, we analyze a certain realistic Gibbs sampler algorithm and
obtain a complexity upper bound for the mixing time, which shows that the
number of iterations required for the Gibbs sampler to converge is constant
under certain conditions on the observed data and the initial state. It is our
hope that this modified drift-and-minorization approach can be employed in many
other specific examples to obtain complexity bounds for high-dimensional Markov
chains.Comment: 42 page
Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory
The ubiquitous ADE classification has induced many proposals of often
mysterious correspondences both in mathematics and physics. The mathematics
side includes quiver theory and the McKay Correspondence which relates finite
group representation theory to Lie algebras as well as crepant resolutions of
Gorenstein singularities. On the physics side, we have the graph-theoretic
classification of the modular invariants of WZW models, as well as the relation
between the string theory nonlinear -models and Landau-Ginzburg
orbifolds. We here propose a unification scheme which naturally incorporates
all these correspondences of the ADE type in two complex dimensions. An
intricate web of inter-relations is constructed, providing a possible guideline
to establish new directions of research or alternate pathways to the standing
problems in higher dimensions.Comment: 35 pages, 4 figures; minor corrections, comments on toric geometry
and references adde
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