Combined Descriptors in Spatial Pyramid Domain for Image Classification

Recently spatial pyramid matching (SPM) with scale invariant feature transform (SIFT) descriptor has been successfully used in image classification. Unfortunately, the codebook generation and feature quantization procedures using SIFT feature have the high complexity both in time and space. To address this problem, in this paper, we propose an approach which combines local binary patterns (LBP) and three-patch local binary patterns (TPLBP) in spatial pyramid domain. The proposed method does not need to learn the codebook and feature quantization processing, hence it becomes very efficient. Experiments on two popular benchmark datasets demonstrate that the proposed method always significantly outperforms the very popular SPM based SIFT descriptor method both in time and classification accuracy.Comment: 9 pages, 5 figure

Variation of the Gieseker and Uhlenbeck Compactifications

In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some {\it canonical} rational morphisms among the Gieseker compactifications are proved to exist and their fibers are studied. As a consequence of studying the morphisms from the Gieseker compactifications to the Uhlebeck compactifications, we show that there is an everywhere-defined {\it canonical} algebraic map between two adjacent Uhlenbeck compactifications which restricts to the identity on some Zariski open subset.Comment: 24 pages, AmsLaTe

Diversity in Machine Learning

Machine learning methods have achieved good performance and been widely applied in various real-world applications. They can learn the model adaptively and be better fit for special requirements of different tasks. Generally, a good machine learning system is composed of plentiful training data, a good model training process, and an accurate inference. Many factors can affect the performance of the machine learning process, among which the diversity of the machine learning process is an important one. The diversity can help each procedure to guarantee a total good machine learning: diversity of the training data ensures that the training data can provide more discriminative information for the model, diversity of the learned model (diversity in parameters of each model or diversity among different base models) makes each parameter/model capture unique or complement information and the diversity in inference can provide multiple choices each of which corresponds to a specific plausible local optimal result. Even though the diversity plays an important role in machine learning process, there is no systematical analysis of the diversification in machine learning system. In this paper, we systematically summarize the methods to make data diversification, model diversification, and inference diversification in the machine learning process, respectively. In addition, the typical applications where the diversity technology improved the machine learning performance have been surveyed, including the remote sensing imaging tasks, machine translation, camera relocalization, image segmentation, object detection, topic modeling, and others. Finally, we discuss some challenges of the diversity technology in machine learning and point out some directions in future work.Comment: Accepted by IEEE Acces

On the connection between radiative outbursts and timing irregularities in magnetars

Magnetars are strongly magnetized pulsars and they occasionally show violent radiative outbursts. They also often exhibit glitches which are sudden changes in the spin frequency. It was found that some glitches were associated with outbursts but their connection remains unclear. We present a systematic study to identify possible correlations between them. We find that the glitch size of magnetars likely shows a bimodal distribution, different from the distribution of the Vela-like recurrent glitches but consistent with the high end of that of normal pulsars. A glitch is likely a necessary condition for an outburst but not a sufficient condition because only 30\% of glitches were associated with outbursts. In the outburst cases, the glitches tend to induce larger frequency changes compared to those unassociated ones. We argue that a larger glitch is more likely to trigger the outburst mechanism, either by reconfiguration of the magnetosphere or deformation of the crust. A more frequent and deeper monitoring of magnetars is necessary for further investigation of their connection.Comment: Accepted for publication in Astronomische Nachrichten (proceedings of XMM-Newton workshop 'Time-Domain Astronomy: A High Energy View' in ESAC, Madrid, Spain, June 2018

The Donaldson-Thomas invariants under blowups and flops

Using the degeneration formula for Doanldson-Thomas invariants, we proved formulae for blowing up a point and simple flops.Comment: Latex, 15 page

Birational Models of the Moduli Spaces of Stable Vector Bundles over Curves

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in connection with rationality of moduli spaces of stable vector bundles.Comment: To appear in Intern. Journal of Math., AMS-LaTe

Mantel's Theorem for Random Hypergraphs

A classical result in extremal graph theory is Mantel's Theorem, which states that every maximum triangle-free subgraph of $K_n$ is bipartite. A sparse version of Mantel's Theorem is that, for sufficiently large $p$, every maximum triangle-free subgraph of $G(n,p)$ is w.h.p. bipartite. Recently, DeMarco and Kahn proved this for $p > K \sqrt{\log n/n}$ for some constant $K$, and apart from the value of the constant this bound is best possible. We study an extremal problem of this type in random hypergraphs. Denote by $F_5$, which sometimes called as the generalized triangle, the 3-uniform hypergraph with vertex set {a,b,c,d,e} and edge set {abc, ade, bde}. One of the first extremal results in extremal hypergraph theory is by Frankl and F\"{u}redi, who proved that the maximum 3-uniform hypergraph on n vertices containing no copy of $F_5$ is tripartite for n>3000. A natural question is for what p is every maximum $F_5$-free subhypergraph of $G^3(n,p)$ w.h.p. tripartite. We show this holds for $p>K\log n/n$ for some constant K and does not hold for $p=0.1\sqrt{\log n}/n$.Comment: 15 pages, 1 figur

Modeling Collective Behavior of Posting Microblog by Stochastic Differential Equation with Jump

The characterization and understanding of online social network behavior is of importance from both the points of view of fundamental research and realistic utilization. In this manuscript, we propose a stochastic differential equation to describe the online microblogging behavior. Our analysis is based on the microblog data collected from Sina Weibo which is one of the most popular microblogging platforms in China. Especially, we focus on the collective nature of the microblogging behavior reflecting itself in the analyzed data as the characters of the periodic pattern, the stochastic fluctuation around the baseline, and the extraordinary jumps. Compared with existing works, we use in our model time dependent parameters to facilitate the periodic feature of the microblogging behavior and incorporate a compound Poisson process to describe the extraordinary spikes in the Sina Weibo volume. Such distinct merits lead to significant improvement in the prediction performance, thus justifying the validity of our model. This work may offer potential application in the future detection of the anomalous behavior in online social network platforms

The CL and PL characteristic of different scale CsI:Na crystals

We investigate the luminescence characteristic of different scale CsI:Na crystals excited via photoluminescence(PL) and cathodoluminescence (CL). The CsI:Na crystals are processed to three samples with different diameter, decreasing from micro-scale to nano-scale. It is found that the nano-scale CsI:Na crystal emits 420nm luminescence by PL, while its emission band is at 315nm and 605nm by CL. The reason for this phenomenon relates to the energy and density of incident particles, and the diameter of CsI:Na crystal. When crystal diameter decreases to nano-scale, the number of surface defects relatively increases, leading to the Na-relative luminescence decreasing. In addition, we have also investigated the CsI:Tl crystal with the same experiment condition. The result indicates that the emission almost has nothing to do with the crystal diameter.Comment: 6 pages,5 figures,1 tabl

Symmetry-protected topological phase in a one-dimensional correlated bosonic model with a synthetic spin-orbit coupling

By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the insulating regime, this model exhibits a symmetry-protected topological phase. This symmetry-protected topological phase is stabilized by time-reversal symmetry and it is identified as a Haldane phase. We confirm our conclusions further by analyzing the entanglement spectrum. In addition, we find four conventional phases: a Mott insulating phase with no long range order, a ferromagnetic superfluid phase, a ferromagnetic insulating phase and a density-wave phase.Comment: Submitted on April 12, 2015, accepted by PR