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 $n$ 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