43,038 research outputs found
Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy
We determine positive-dimensional G-periodic proper subvarieties of an
n-dimensional normal projective variety X under the action of an abelian group
G of maximal rank n-1 and of positive entropy. The motivation of the paper is
to understand the obstruction for X to be G-equivariant birational to the
quotient variety of an abelian variety modulo the action of a finite group.Comment: Asian Journal of Mathematics (to appear), Special issue on the
occasion of Prof N. Mok's 60th birthda
Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates
The problem of learning forest-structured discrete graphical models from
i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu
tree through adaptive thresholding is proposed. It is shown that this algorithm
is both structurally consistent and risk consistent and the error probability
of structure learning decays faster than any polynomial in the number of
samples under fixed model size. For the high-dimensional scenario where the
size of the model d and the number of edges k scale with the number of samples
n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy
structural and risk consistencies. In addition, the extremal structures for
learning are identified; we prove that the independent (resp. tree) model is
the hardest (resp. easiest) to learn using the proposed algorithm in terms of
error rates for structure learning.Comment: Accepted to the Journal of Machine Learning Research (Feb 2011
High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
We consider the problem of high-dimensional Gaussian graphical model
selection. We identify a set of graphs for which an efficient estimation
algorithm exists, and this algorithm is based on thresholding of empirical
conditional covariances. Under a set of transparent conditions, we establish
structural consistency (or sparsistency) for the proposed algorithm, when the
number of samples n=omega(J_{min}^{-2} log p), where p is the number of
variables and J_{min} is the minimum (absolute) edge potential of the graphical
model. The sufficient conditions for sparsistency are based on the notion of
walk-summability of the model and the presence of sparse local vertex
separators in the underlying graph. We also derive novel non-asymptotic
necessary conditions on the number of samples required for sparsistency
Astrochemical confirmation of the rapid evolution of massive YSOs and explanation for the inferred ages of hot cores
Aims. To understand the roles of infall and protostellar evolution on the
envelopes of massive young stellar objects (YSOs).
Methods. The chemical evolution of gas and dust is traced, including infall
and realistic source evolution. The temperatures are determined
self-consistently. Both ad/desorption of ices using recent laboratory
temperature-programmed-desorption measurements are included.
Results. The observed water abundance jump near 100 K is reproduced by an
evaporation front which moves outward as the luminosity increases. Ion-molecule
reactions produce water below 100 K. The age of the source is constrained to t
\~ 8 +/- 4 x 10^4 yrs since YSO formation. It is shown that the chemical
age-dating of hot cores at ~ few x 10^3 - 10^4 yr and the disappearance of hot
cores on a timescale of ~ 10^5 yr is a natural consequence of infall in a
dynamic envelope and protostellar evolution. Dynamical structures of ~ 350AU
such as disks should contain most of the complex second generation species. The
assumed order of desorption kinetics does not affect these results.Comment: Accepted by A&A Letters; 4 pages, 5 figure
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An agent-based DDM for high level architecture
The Data Distribution Management (DDM) service is one of the six services provided in the Runtime Infrastructure (RTI) of High Level Architecture (HLA). Its purpose is to perform data filtering and reduce irrelevant data communicated between federates. The two DDM schemes proposed for RTI, region based and grid based DDM, are oriented to send as little irrelevant data to subscribers as possible, but only manage to filter part of this information and some irrelevant data is still being communicated. Previously (G. Tan et al., 2000), we employed intelligent agents to perform data filtering in HLA, implemented an agent based DDM in RTI (ARTI) and compared it with the other two filtering mechanisms. The paper reports on additional experiments, results and analysis using two scenarios: the AWACS sensing aircraft simulation and the air traffic control simulation scenario. Experimental results show that compared with other mechanisms, the agent based approach communicates only relevant data and minimizes network communication, and is also comparable in terms of time efficiency. Some guidelines on when the agent based scheme can be used are also give
Learning Latent Tree Graphical Models
We study the problem of learning a latent tree graphical model where samples
are available only from a subset of variables. We propose two consistent and
computationally efficient algorithms for learning minimal latent trees, that
is, trees without any redundant hidden nodes. Unlike many existing methods, the
observed nodes (or variables) are not constrained to be leaf nodes. Our first
algorithm, recursive grouping, builds the latent tree recursively by
identifying sibling groups using so-called information distances. One of the
main contributions of this work is our second algorithm, which we refer to as
CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree
over the observed variables is constructed. This global step groups the
observed nodes that are likely to be close to each other in the true latent
tree, thereby guiding subsequent recursive grouping (or equivalent procedures)
on much smaller subsets of variables. This results in more accurate and
efficient learning of latent trees. We also present regularized versions of our
algorithms that learn latent tree approximations of arbitrary distributions. We
compare the proposed algorithms to other methods by performing extensive
numerical experiments on various latent tree graphical models such as hidden
Markov models and star graphs. In addition, we demonstrate the applicability of
our methods on real-world datasets by modeling the dependency structure of
monthly stock returns in the S&P index and of the words in the 20 newsgroups
dataset
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