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

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

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

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

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

Tilings in graphons

We introduce a counterpart to the notion of vertex disjoint tilings by copy of a fixed graph F to the setting of graphons. The case F=K_2 gives the notion of matchings in graphons. We give a transference statement that allows us to switch between the finite and limit notion, and derive several favorable properties, including the LP-duality counterpart to the classical relation between the fractional vertex covers and fractional matchings/tilings, and discuss connections with property testing. As an application of our theory, we determine the asymptotically almost sure F-tiling number of inhomogeneous random graphs \mathbb{G}(n,W). As another application, in an accompanying paper [Hladky, Hu, Piguet: Komlos's tiling theorem via graphon covers, preprint] we give a proof of a strengthening of a theorem of Komlos [Komlos: Tiling Tur\'an Theorems, Combinatorica, 2000].Comment: 25 pages, 5 figure

The Gromov-Witten invariants of the Hilbert schemes of points on surfaces with pg>0p_g > 0

In this paper, we study the Gromov-Witten theory of the Hilbert schemes X^{[n]} of points on smooth projective surfaces X with positive geometric genus p_g. Using cosection localization technique due to Y. Kiem and J. Li [KL1, KL2], we prove that if X is a simply connected surface admitting a holomorphic differential two-form with irreducible zero divisor, then all the Gromov-Witten invariants of X^{[n]} defined via the moduli space \Mbar_{g, r}(X^{[n]}, \beta) vanish except possibly when $\beta = d_0 \beta_{K_X} - d \beta_n$ where d is an integer, $d_0 \ge 0$ is a rational number, and $\beta_n$ and $\beta_{K_X}$ are defined in (3.2) and (3.3) respectively. When $n=2$, the exceptional cases can be further reduced to the invariants: $_{0, \beta_{K_X} - d\beta_2}^{X^{[2]}}$ with $K_X^2 = 1$ and $d \le 3$, and $_{1, d\beta_2}^{X^{[2]}}$ with $d \ge 1$. We show that when $K_X^2 = 1$, $$_{0, \beta_{K_X} - 3 \beta_2}^{X^{[2]}} = (-1)^{\chi(\mathcal O_X)}$$ which is consistent with a well-known formula of Taubes [Tau]. In addition, for an arbitrary smooth projective surface X and $d \ge 1$, we verify that $$_{1, d\beta_2}^{X^{[2]}} = K_X^2/(12d).$$Comment: 24 pages. Comments are welcom

Role of weak measurements on states ordering and monogamy of quantum correlation

The information-theoretic definition of quantum correlation, e.g., quantum discord, is measurement dependent. By considering the more general quantum measurements, weak measurements, which include the projective measurement as a limiting case, we show that while weak measurements can enable one to capture more quantumness of correlation in a state, it can also induce other counterintuitive quantum effects. Specifically, we show that the general measurements with different strengths can impose different orderings for quantum correlations of some states. It can also modify the monogamous character for certain classes of states as well which may diminish the usefulness of quantum correlation as a resource in some protocols. In this sense, we say that the weak measurements play a dual role in defining quantum correlation.Comment: 6 pages, 5 figures, the final version as that published in Int. J. Theor. Phy