3,459 research outputs found
Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time
Consider a branching random walk in which the offspring distribution and the
moving law both depend on an independent and identically distributed random
environment indexed by the time.For the normalised counting measure of the
number of particles of generation in a given region, we give the second and
third orders asymptotic expansions of the central limit theorem under rather
weak assumptions on the moments of the underlying branching and moving laws.
The obtained results and the developed approaches shed light on higher order
expansions. In the proofs, the Edgeworth expansion of central limit theorems
for sums of independent random variables, truncating arguments and martingale
approximation play key roles. In particular, we introduce a new martingale,
show its rate of convergence, as well as the rates of convergence of some known
martingales, which are of independent interest.Comment: Accepted by Bernoull
Memory-Efficient Topic Modeling
As one of the simplest probabilistic topic modeling techniques, latent
Dirichlet allocation (LDA) has found many important applications in text
mining, computer vision and computational biology. Recent training algorithms
for LDA can be interpreted within a unified message passing framework. However,
message passing requires storing previous messages with a large amount of
memory space, increasing linearly with the number of documents or the number of
topics. Therefore, the high memory usage is often a major problem for topic
modeling of massive corpora containing a large number of topics. To reduce the
space complexity, we propose a novel algorithm without storing previous
messages for training LDA: tiny belief propagation (TBP). The basic idea of TBP
relates the message passing algorithms with the non-negative matrix
factorization (NMF) algorithms, which absorb the message updating into the
message passing process, and thus avoid storing previous messages. Experimental
results on four large data sets confirm that TBP performs comparably well or
even better than current state-of-the-art training algorithms for LDA but with
a much less memory consumption. TBP can do topic modeling when massive corpora
cannot fit in the computer memory, for example, extracting thematic topics from
7 GB PUBMED corpora on a common desktop computer with 2GB memory.Comment: 20 pages, 7 figure
Heterogeneous Multi-task Learning for Human Pose Estimation with Deep Convolutional Neural Network
We propose an heterogeneous multi-task learning framework for human pose
estimation from monocular image with deep convolutional neural network. In
particular, we simultaneously learn a pose-joint regressor and a sliding-window
body-part detector in a deep network architecture. We show that including the
body-part detection task helps to regularize the network, directing it to
converge to a good solution. We report competitive and state-of-art results on
several data sets. We also empirically show that the learned neurons in the
middle layer of our network are tuned to localized body parts
Fermi Large Area Telescope observations of the supernova remnant HESS J1731-347
Context: HESS J1731-347 has been identified as one of the few TeV-bright
shell-type supernova remnants (SNRs). These remnants are dominated by
nonthermal emission, and the nature of TeV emission has been continuously
debated for nearly a decade.
Aims: We carry out the detailed modeling of the radio to gamma-ray spectrum
of HESS J1731-347 to constrain the magnetic field and energetic particles
sources, which we compare with those of the other TeV-bright shell-type SNRs
explored before.
Methods: Four years of data from Fermi Large Area Telescope (LAT)
observations for regions around this remnant are analyzed, leading to no
detection correlated with the source discovered in the TeV band. The Markov
Chain Monte Carlo method is used to constrain parameters of one-zone models for
the overall emission spectrum.
Results: Based on the 99.9% upper limits of fluxes in the GeV range, one-zone
hadronic models with an energetic proton spectral slope greater than 1.8 can be
ruled out, which favors a leptonic origin for the gamma-ray emission, making
this remnant a sibling of the brightest TeV SNR RX J1713.7-3946, the Vela
Junior SNR RX J0852.0-4622, and RCW 86. The best-fit leptonic model has an
electron spectral slope of 1.8 and a magnetic field of about 30 muG, which is
at least a factor of 2 higher than those of RX J1713.7-3946 and RX
J0852.0-4622, posing a challenge to the distance estimate and/or the energy
equipartition between energetic electrons and the magnetic field of this
source. A measurement of the shock speed will address this challenge and has
implications on the magnetic field evolution and electron acceleration driven
by shocks of SNRs.Comment: 7 pages, 3 fogures, A&A in pres
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