arXiv subjects
Publications and source records attributed to Shuo Zhang.
In this paper, a finite element space is presented on quadrilateral grids which can provide consistent discretization for the biharmonic equations. The space consists of piecewise quadratic polynomials and is of minimal degree for the variational problem.
The symmetrized bidisc ${\textbf{G}}_{2}$ is defined by $${\textbf{G}}_{2}:=\{(z_1+z_2,z_1z_2)\in\mathbb{C}^2: |z_1|<1,|z_2|<1,\; z_1,z_2\in\mathbb{C}\}.$$ It is a bounded inhomogeneous pseudoconvex domain without $\mathcal{C}^1$ boundary, and especially the symmetrized bidisc hasn't any strongly pseudoconvex boundary point and the boundary behavior of both Carathéodory and Kobayashi metrics over the symmetrized bidisc is hard to describe precisely. In this paper, we study the boundary Schwarz lemma for holomorphic self-mappings of the symmetrized bidisc ${\textbf{G}}_2$, and our boundary Schwarz lemma in the paper differs greatly from the earlier related results.
The wide adoption of smartphones and mobile applications has brought significant changes to not only how individuals behave in the real world, but also how groups of users interact with each other when organizing group events. Understanding how users make event decisions as a group and identifying the contributing factors can offer important insights for social group studies and more effective system and application design for group event scheduling. In this work, we have designed a new mobile application called OutWithFriendz, which enables users of our mobile app to organize group events, invite friends, suggest and vote on event time and venue. We have deployed OutWithFriendz at both Apple App Store and Google Play, and conducted a large-scale user study spanning over 500 users and 300 group events. Our analysis has revealed several important observations regarding group event planning process including the importance of user mobility, individual preferences, host preferences, and group voting process.
We present a hard X-ray observation of the TeV gamma-ray binary candidate HESS J1832-093 coincident with supernova remnant (SNR) G22.7-0.2 using the Nuclear Spectroscopic Telescope Array (NuSTAR). Non-thermal X-ray emission from XMMU J183245-0921539, the X-ray source associated with HESS J1832-093, is detected up to ~30 keV and is well-described by an absorbed power-law model with the best-fit photon index $Γ= 1.5\pm0.1$. A re-analysis of archival Chandra and XMM-Newton data finds that the long-term X-ray flux increase of XMMU J183245-0921539 is $50^{+40}_{-20}$% (90% C.L.), much less than previously reported. A search for a pulsar spin period or binary orbit modulation yields no significant signal to a pulse fraction limit of fp < 19% in the range 4 ms < P < 40 ks. No red noise is detected in the FFT power spectrum to suggest active accretion from a binary system. While further evidence is required, we argue that the X-ray and gamma-ray properties of XMMU J183245-0921539 are most consistent with a non-accreting binary generating synchrotron X- rays from particle acceleration in the shock formed as a result of the pulsar and stellar wind collision. We also report on three nearby hard X-ray sources, one of which may be associated with diffuse emission from a fast-moving supernova fragment interacting with a dense molecular cloud.
We address the task of ranking objects (such as people, blogs, or verticals) that, unlike documents, do not have direct term-based representations. To be able to match them against keyword queries, evidence needs to be amassed from documents that are associated with the given object. We present two design patterns, i.e., general reusable retrieval strategies, which are able to encompass most existing approaches from the past. One strategy combines evidence on the term level (early fusion), while the other does it on the document level (late fusion). We demonstrate the generality of these patterns by applying them to three different object retrieval tasks: expert finding, blog distillation, and vertical ranking.
Tables are among the most powerful and practical tools for organizing and working with data. Our motivation is to equip spreadsheet programs with smart assistance capabilities. We concentrate on one particular family of tables, namely, tables with an entity focus. We introduce and focus on two specific tasks: populating rows with additional instances (entities) and populating columns with new headings. We develop generative probabilistic models for both tasks. For estimating the components of these models, we consider a knowledge base as well as a large table corpus. Our experimental evaluation simulates the various stages of the user entering content into an actual table. A detailed analysis of the results shows that the models' components are complimentary and that our methods outperform existing approaches from the literature.
Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM's cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.
Understanding the origin of the flaring activity from the Galactic center supermassive black hole, Sagittarius A*, is a major scientific goal of the NuSTAR Galactic plane survey campaign. We report on the data obtained between July 2012 and April 2015, including 27 observations on Sgr A* with a total exposure of ~ 1 Ms. We found a total of ten X-ray flares detected in the NuSTAR observation window, with luminosities in the range of $L_{3-79~keV}$~$(0.2-4.0) \times 10^{35}~erg~s^{-1}$. With this largest hard X-ray Sgr A* flare dataset to date, we studied the flare spectral properties. Seven flares are detected above 5σ significance, showing a range of photon indices (Γ ~ 2.0-2.8) with typical uncertainties of +/-0.5 (90% confidence level). We found no significant spectral hardening for brighter flares as indicated by a smaller sample. The accumulation of all the flare spectra in 1-79 keV can be well fit with an absorbed power-law model with Γ=2.2+/-0.1, and does not require the existence of a spectral break. The lack of variation in X-ray spectral index with luminosity would point to a single mechanism for the flares and is consistent with the synchrotron scenario. Lastly, we present the quiescent state spectrum of Sgr A*, and derived an upper limit on the quiescent luminosity of Sgr A* above 10 keV to be $L_{Xq, 10-79 keV}$ < $(2.9{\pm}0.2) \times 10^{34}~erg~s^{-1}$.
In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. By a regular decomposition of $H_0({\rm rot},Ω)$ and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. A framework of designing uniformly stable finite element schemes is presented, and a specific example is given.
Silicon Photo-Multipliers (SiPM) are regarded as novel photo-detectors to replace conventional Photo-Multiplier Tubes (PMTs). However, the breakdown voltage dependence on the ambient temperature results in a gain variation of $\sim$3$\% /^{\circ} \mathrm C$. This severely limits the application of this device in experiments with wide range of operating temperature, especially in space missions. An experimental setup was established to investigate the temperature and bias voltage dependence of gain for the Multi-Pixel Photon Counter (MPPC). The gain and breakdown voltage dependence on operating temperature of an MPPC can be approximated by a linear function, which is similar to the behavior of a zener diode. The measured temperature coefficient of the breakdown voltage is $(59.4 \pm 0.4$ mV)$/^{\circ} \mathrm C$. According to this fact, an analog power supply based on two zener diodes and an operational amplifier was designed with a positive temperature coefficient. The measured temperature dependence for the designed power supply is between 63.65 to 64.61~mV/$^{\circ} \mathrm C$ at different output voltages. The designed power supply can bias the MPPC at an over-voltage with a temperature variation of $\sim$ 5~mV$/^{\circ} \mathrm C$. The gain variation of the MPPC biased at over-voltage of 2~V was reduced from 2.8$\% /^{\circ} \mathrm C$ to 0.3$\% /^{\circ} \mathrm C$ when biased the MPPC with the designed power supply for gain control. Detailed design and performance of the analog power supply in the temperature range from -42.7$^{\circ}\mathrm{C}$ to 20.9$^{\circ}\mathrm{C}$ will be discussed in this paper.
Energy resolution is an important figure of merit for TES microcalorimeter. We propose a laser system to measure the energy resolution of TES microcalorimeter with a 1550 nm laser source. Compared to method that characterizes the performance by irradiating the detector using X-ray photons from a radioactive source placed inside the refrigerator, our system is safer and more convenient. The feasibility of this system has been demonstrated in the measurement of an Al/Ti bilayer TES microcalorimeter. In this experiment, the tested detector showed a energy resolution of 72 eV in the energy range from 0.2 keV to 0.9 keV
In this paper, we study decoupled mixed element schemes for fourth order problems. A general process is designed such that an elliptic problem on high-regularity space is transformed to a decoupled system with spaces of low order involved only and is further discretised by low-degree finite elements. The process can be fit for various fourth order problems, and is used in the remaining of the paper particularly for three-dimensional bi-Laplacian equation to conduct a family of mixed element discretisation schemes.
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three low-regularity spaces which are connected by a regular decomposition, which is corresponding to a decomposition of the figuration of the regularity of the high order space. The framework is fit for various fourth order problems, and the numerical schemes based on the deduced problems can be of lower complicacy. Two fourth order problems in three dimensional are discussed under the framework. They are each corresponding to a regular decomposition, and thus are discretised based on the discretised analogues of the regular decompositions constructed; optimal error estimates are given.
In this paper, amiable mixed schemes are presented for two variants of fourth order curl equations. Specifically, mixed formulations for the problems are constructed, which are well-posed in Babuska-Brezzi's sense and admit stable discretizations by finite element spaces of low smoothness and of low degree. The regularities of the mixed formulations and thus equivalently the primal problems are established, and some finite elements examples are given which can exploit the regularity of the solutions to an optimal extent.
In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization. Then, we construct multi-level finite element schemes by implementing the algorithm as in [33] to the nested discretizations on series of nested grids. The multi-level mixed scheme for biharmonic eigenvalue problem possesses optimal convergence rate and optimal computational cost. Both theoretical analysis and numerical verifications are presented.
In this paper, we present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of $\mathcal{O}(h)$ order in energy norm and of $\mathcal{O}(h^2)$ order in $L^2$ norm on general $d$-rectangular grids. Moreover, when the grid is uniform, the convergence rate can be of $\mathcal{O}(h^2)$ order in energy norm, and the convergence rate in $L^2$ norm is still of $\mathcal{O}(h^2)$ order, which can not be improved. Numerical examples are presented to demonstrate our theoretical results.
Cooling vibrational degrees of freedom down to ground states is essential to observation of quantum properties of systems with mechanical vibration. We propose two cooling schemes employing four internal levels of the systems, which achieve the ground-state cooling in an efficient fashion by completely deleting the carrier and first-order blue-sideband transitions. The schemes, based on the quantum interference and Stark-shift gates, are robust to fluctuation of laser intensity and frequency. The feasibility of the schemes is justified using current laboratory technology. In practice, our proposal readily applies to an nano-diamond nitrogen-vacancy center levitated in an optic trap or attached to a cantilever.
Recently, unresolved hard (20-40 keV) X-ray emission has been discovered within the central 10 pc of the Galaxy, possibly indicating a large population of intermediate polars (IPs). Chandra and XMM-Newton measurements in the surrounding ~50 pc imply a much lighter population of IPs with $\langle M_{\rm WD} \rangle \approx 0.5 M_\odot$. Here we use broad-band NuSTAR observations of two IPs: TV Columbae, which has a fairly typical but widely varying reported mass of $M_{\rm WD} \approx 0.5-1.0 M_\odot$, and IGR J17303-0601, with a heavy reported mass of $M_{\rm WD} \approx 1.0-1.2 M_\odot$. We investigate how varying spectral models and observed energy ranges influence estimated white dwarf mass. Observations of the inner 10 pc can be accounted for by IPs with $\langle M_{\rm WD} \rangle \approx 0.9 M_\odot$, consistent with that of the CV population in general, and the X-ray observed field IPs in particular. The lower mass derived by Chandra and XMM-Newton appears to be an artifact of narrow energy band fitting. To explain the (unresolved) CHXE by IPs requires an X-ray (2-8 keV) luminosity function (XLF) extending down to at least $5\times10^{31}$ erg/s. The CHXE XLF, if extended to the surrounding ~50 pc observed by Chandra and XMM-Newton, requires at least ~20-40% of the $\sim$9000 point sources are IPs. If the XLF extends just a factor of a few lower in luminosity, then the vast majority of these sources are IPs. This is in contrast to recent observations of the Galactic ridge, where the bulk of the 2-8 keV emission is ascribed to dwarf novae.