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Shu Wang

Publications and source records attributed to Shu Wang.

At least 235 records · Page 13Linked to original sources
arXiv2016

Visual Tracking via Reliable Memories

In this paper, we propose a novel visual tracking framework that intelligently discovers reliable patterns from a wide range of video to resist drift error for long-term tracking tasks. First, we design a Discrete Fourier Transform (DFT) based tracker which is able to exploit a large number of tracked samples while still ensures real-time performance. Second, we propose a clustering method with temporal constraints to explore and memorize consistent patterns from previous frames, named as reliable memories. By virtue of this method, our tracker can utilize uncontaminated information to alleviate drifting issues. Experimental results show that our tracker performs favorably against other state of-the-art methods on benchmark datasets. Furthermore, it is significantly competent in handling drifts and able to robustly track challenging long videos over 4000 frames, while most of others lose track at early frames.

cs.CV↗
arXiv2015

Very Large Interstellar Grains as Evidenced by the Mid-Infrared Extinction

The sizes of interstellar grains are widely distributed, ranging from a few angstroms to a few micrometers. The ultraviolet (UV) and optical extinction constrains the dust in the size range of a couple hundredth micrometers to several submicrometers. The near and mid infrared (IR) emission constrains the nanometer-sized grains and angstrom-sized very large molecules. However, the quantity and size distribution of micrometer-sized grains remain unknown as they are gray in the UV/optical extinction and they are too cold and emit too little in the IR to be detected by IRAS, Spitzer, or Herschel. In this work, we employ the ~3-8 micron mid-IR extinction which is flat in both diffuse and dense regions to constrain the quantity, size, and composition of the micron-sized grain component. We find that, together with nano- and submicron-sized silicate and graphite (as well as PAHs), micron-sized graphite grains with C/H=137 ppm and a mean size of ~1.2 micron closely fit the observed interstellar extinction of the Galactic diffuse interstellar medium from the far-UV to the mid-IR as well as the near-IR to millimeter thermal emission obtained by COBE/DIRBE, COBE/FIRAS, and Planck up to lambda < 1000 micron. The micron-sized graphite component accounts for ~14.6% of the total dust mass and ~2.5% of the total IR emission.

astro-ph.GA↗
arXiv2015

The Interstellar Oxygen Crisis, or Where Have All the Oxygen Atoms Gone?

The interstellar medium (ISM) seems to have a significant surplus of oxygen which was dubbed as the "O crisis": independent of the adopted interstellar reference abundance, the total number of O atoms depleted from the gas phase far exceeds that tied up in solids by as much as ~160ppm of O/H. Recently, it has been hypothesized that the missing O could be hidden in micrometer-sized H2O ice grains. We examine this hypothesis by comparing the infrared (IR) extinction and far-IR emission arising from these grains with that observed in the Galactic diffuse ISM. We find that it is possible for the diffuse ISM to accommodate ~160ppm of O/H in micron-sized H2O ice grains without violating the observational constraints including the absence of the 3.1micron O-H absorption feature. More specifically, H2O ice grains of radii ~4micron and O/H = 160 ppm are capable of accounting for the observed flat extinction at ~ 3-8 micron and produce no excessive emission in the far-IR. These grains could be present in the diffuse ISM through rapid exchange of material between dense molecular clouds where they form and diffuse clouds where they are destroyed by photosputtering.

astro-ph.GA↗
arXiv2015

Uniform Quadratic Optimization and Extensions

The uniform quadratic optimizatin problem (UQ) is a nonconvex quadratic constrained quadratic programming (QCQP) sharing the same Hessian matrix. Based on the second-order cone programming (SOCP) relaxation, we establish a new sufficient condition to guarantee strong duality for (UQ) and then extend it to (QCQP), which not only covers several well-known results in literature but also partially gives answers to a few open questions. For convex constrained nonconvex (UQ), we propose an improved approximation algorithm based on (SOCP). Our approximation bound is dimensional independent. As an application, we establish the first approximation bound for the problem of finding the Chebyshev center of the intersection of several balls.

math.OC↗
arXiv2015

Dust in the Local Group

How dust absorbs and scatters starlight as a function of wavelength (known as the interstellar extinction curve) is crucial for correcting for the effects of dust extinction in inferring the true luminosity and colors of reddened astrophysical objects. Together with the extinction spectral features, the extinction curve contains important information about the dust size distribution and composition. This review summarizes our current knowledge of the dust extinction of the Milky Way, three Local Group galaxies (i.e., the Small and Large Magellanic Clouds, and M31), and galaxies beyond the Local Group.

astro-ph.GA↗
arXiv2015

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $μ$ such that $f(x) + μh(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + μh(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $μ\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.

math.OC↗
arXiv2015

Capability of Quasar Selection by Combining the SCUSS and SDSS Observations

The South Galactic Cap $u$-band Sky Survey (SCUSS) provides a deep $u$-band imaging of about 5000 deg$^2$ in south Galactic cap. It is about 1.5 mag deeper than the SDSS $u$-band. In this paper we evaluate the capability of quasar selection using both SCUSS and SDSS data, based on considerations of the deep SCUSS $u$-band imaging and two-epoch $u$-band variability. We find that the combination of the SCUSS $u$-band and the SDSS $griz$ band allows us to select more faint quasars and more quasars at redshift around 2.2 than the selection only with the SDSS $ugriz$ data. Quasars have significant $u$-band variabilities. The fraction of quasars with large two-epoch variability is much higher than that of stars. The selection by variability can select both low-redshift quasars with ultraviolet excess and mid-redshift ($2 < z <3.5$) quasars where quasar selection by optical colors is inefficient. The above two selections are complementary and make full use of the SCUSS u-band advantages.

astro-ph.GA↗
arXiv2014

An Improved Analysis of Semidefinite Approximation Bound for Nonconvex Nonhomogeneous Quadratic Optimization with Ellipsoid Constraints

We consider the problem of approximating nonconvex quadratic optimization with ellipsoid constraints (ECQP). We show some SDP-based approximation bounds for special cases of (ECQP) can be improved by trivially applying the extened Pataki's procedure. The main result of this paper is to give a new analysis on approximating (ECQP) by the SDP relaxation, which greatly improves Tseng's result [SIAM Journal Optimization, 14, 268-283, 2003]. As an application, we strictly improve the approximation ratio for the assignment-polytope constrained quadratic program.

math.OC↗
arXiv2014

Indeterminate Strings, Prefix Arrays & Undirected Graphs

An integer array y = y[1..n] is said to be feasible if and only if y[1] = n and, for every i \in 2..n, i \le i+y[i] \le n+1. A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater than one of a given alphabet Sigma; otherwise it is said to be regular. A feasible array y is said to be regular if and only if it is the prefix array of some regular string. We show using a graph model that every feasible array of integers is a prefix array of some (indeterminate or regular) string, and for regular strings corresponding to y, we use the model to provide a lower bound on the alphabet size. We show further that there is a 1-1 correspondence between labelled simple graphs and indeterminate strings, and we show how to determine the minimum alphabet size |Sigma| of an indeterminate string x based on its associated graph Gx. Thus, in this sense, indeterminate strings are a more natural object of combinatorial interest than the strings on elements of Sigma that have traditionally been studied.

cs.DM↗
arXiv2014

Universality of the Near-Infrared Extinction Law Based on the APOGEE Survey

Whether the near-infrared (NIR) extinction law is universal has been a long debated topic. Based on the APOGEE H-band spectroscopic survey as a key project of SDSS-III, the intrinsic colors of a large number of giant stars are accurately determined from the stellar effective temperature. Taking this advantage and using a sample of 5942 K-type giants, the NIR extinction law is carefully re-visited. The color excess ratio E(J-H)/E(J-Ks), representative of the NIR extinction law, shows no dependence on the color excess when E(J-Ks) changes from ~0.3 to ~4.0, which implies a universal NIR extinction law from diffuse to dense regions. The constant value of E(J-H)/E(J-Ks), 0.64, corresponds to a power law index of 1.95. The other two ratios, E(H-Ks)/E(J-Ks) and E(J-H)/E(H-Ks), are 0.36 and 1.78 respectively. The results are consistent with the MRN dust size distribution.

astro-ph.GA↗
arXiv2014

Modeling the Infrared Interstellar Extinction

How dust scatters and absorbs starlight in the interstellar medium (ISM) contains important clues about the size and composition of interstellar dust. While the ultraviolet (UV) and visible interstellar extinction is well studied and can be closely fitted in terms of various dust mixtures (e.g., the silicategraphite mixture), the infrared (IR) extinction is not well understood, particularly, the mid-IR extinction in the 3-8 micron wavelength range is rather flat (or "gray") and is inconsistent with the standard Mathis, Rumpl, & Nordsieck (MRN) silicate-graphite dust model. We attempt to reproduce the flat IR extinction by exploring various dust sizes and species, including amorphous silicate, graphite, amorphous carbon and iron. We find that the flat IR extinction is best explained in terms of micrometer-sized amorphous carbon dust which consumes ~ 60 carbon atoms per million hydrogen atoms (i.e., C/H ~ 60 ppm). To account for the observed UV/visible and near-IR extinction, the silicate-graphite model requires Si/H ~ 34 ppm and C/H ~ 292 ppm. We conclude that the extinction from the UV to the mid-IR could be closely reproduced by a mixture of submicrometer-sized amorphous silicate dust, submicrometer-sized graphitic dust, and micrometer-sized amorphous carbon dust, at the expense of excess C available in the ISM (i.e., this model requires a solid-phase C abundance of C/H ~ 352 ppm, considerably exceeding what could be available in the ISM).

astro-ph.GA↗
arXiv2013

On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In \cite{HL09}, Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler and Navier-Stokes equations is that the convection term is neglected in the 3D model. In \cite{HSW09}, the authors proved that the 3D inviscid model can develop a finite time singularity starting from smooth initial data on a rectangular domain. A global well-posedness result was also proved for a class of smooth initial data under some smallness condition. The analysis in \cite{HSW09} does not apply to the case when the domain is axisymmetric and unbounded in the radial direction. In this paper, we prove that the 3D inviscid model with an appropriate Neumann-Robin boundary condition will develop a finite time singularity starting from smooth initial data in an axisymmetric domain. Moreover, we prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition.

math.AP↗
arXiv2013

The Mid-Infrared Extinction Law and its Variation in the Coalsack Nebula

In recent years the wavelength dependence of interstellar extinction from the ultraviolet (UV), optical, through the near- and mid-infrared (IR) has been studied extensively. Although it is well established that the UV/optical extinction law varies significantly among the different lines of sight, it is not clear how the IR extinction varies among various environments. In this work, using the color-excess method and taking red giants as the extinction tracer, we determine the interstellar extinction Alambda in the four Spitzer/IRAC bands of the Coalsack nebula, a nearby starless dark cloud, based on the data obtained from the 2MASS and Spitzer/GLIMPSE surveys. We select five individual regions across the nebula that span a wide variety of physical conditions, ranging from diffuse, translucent to dense environments, as traced by the visual extinction, the Spitzer/MIPS 24micron emission, and CO emission. We find that Alambda/AKs, the mid-IR extinction relative to AKs, decreases from diffuse to dense environments, which may be explained in terms of ineffective dust growth in dense regions. The mean extinction (relative to AKs) is calculated for the four IRAC bands as well, which exhibits a flat mid-IR extinction law, consistent with previous determinations for other regions. The extinction in the IRAC 4.5micron band is anomalously high, much higher than that of the other three IRAC bands. It cannot be explained in terms of CO and CO2 ices. The mid-IR extinction in the four IRAC bands have also been derived for four representative regions in the Coalsack Globule 2 which respectively exhibit strong ice absorption, moderate or weak ice absorption, and very weak or no ice absorption. The derived mid-IR extinction curves are all flat, with Alambda/AKs increasing with the decrease of the H2O ice absorption optical depth.

astro-ph.GA↗
arXiv2012

On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei in [16] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier-Stokes equations. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the 3D inviscid model for a class of initial boundary value problems with smooth initial data of finite energy. We also prove the global regularity of the 3D inviscid model for a class of small smooth initial data.

math.AP↗
arXiv2012

The asymptotic behavior of globally smooth solutions of bipolar non-isentropic compressible Euler-Maxwell system for plasma

The bipolar non-isentropic compressible Euler-Maxwell system is investigated in $R^3$ in the present paper, and the $L^q$ time decay rate for the global smooth solution is established. It is shown that the total densities, total temperatures and magnetic field of two carriers converge to the equilibrium states at the same rate $(1+t)^{-3/2+3q/2}$ in $L^q$ norm. But, both the difference of densities and the difference of temperatures of two carriers decay at the rate $(1+t)^{-2-\frac{1}{q}}$, and the velocity and electric field decay at the rate $(1+t)^{-3/2+\frac{1}{2q}}$. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar Euler-Maxwell and the bipolar isentropic Euler-Maxwell system.

math.AP↗
arXiv2012

On one multidimensional compressible nonlocal model of the dissipative QG equations

In this paper we study the Cauchy problem for one multidimensional compressible nonlocal model of the dissipative quasi-geostrophic equations. First, we obtain the local existence and uniqueness of the smooth non-negative solution or the strong solution in time. Secondly, for the sub-critical and critical case $1\leα\leq 2$, we obtain the global existence and uniqueness results of the nonnegative smooth solution. Then, we prove the global existence of the weak solution for $0\le α\le 2$ and $ν\ge 0$. Finally, for the sub-critical case, we establish the global $H^1$ and $L^p, p>2,$ decay rate of the smooth solution as $t\to\infty$.

math.AP↗