arXiv subjects
Publications and source records attributed to Yan Liu.
In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.
We consider a fundamental algorithmic question in spectral graph theory: Compute a spectral sparsifier of random-walk matrix-polynomial $$L_α(G)=D-\sum_{r=1}^dα_rD(D^{-1}A)^r$$ where $A$ is the adjacency matrix of a weighted, undirected graph, $D$ is the diagonal matrix of weighted degrees, and $α=(α_1...α_d)$ are nonnegative coefficients with $\sum_{r=1}^dα_r=1$. Recall that $D^{-1}A$ is the transition matrix of random walks on the graph. The sparsification of $L_α(G)$ appears to be algorithmically challenging as the matrix power $(D^{-1}A)^r$ is defined by all paths of length $r$, whose precise calculation would be prohibitively expensive. In this paper, we develop the first nearly linear time algorithm for this sparsification problem: For any $G$ with $n$ vertices and $m$ edges, $d$ coefficients $α$, and $ε> 0$, our algorithm runs in time $O(d^2m\log^2n/ε^{2})$ to construct a Laplacian matrix $\tilde{L}=D-\tilde{A}$ with $O(n\log n/ε^{2})$ non-zeros such that $\tilde{L}\approx_εL_α(G)$. Matrix polynomials arise in mathematical analysis of matrix functions as well as numerical solutions of matrix equations. Our work is particularly motivated by the algorithmic problems for speeding up the classic Newton's method in applications such as computing the inverse square-root of the precision matrix of a Gaussian random field, as well as computing the $q$th-root transition (for $q\geq1$) in a time-reversible Markov model. The key algorithmic step for both applications is the construction of a spectral sparsifier of a constant degree random-walk matrix-polynomials introduced by Newton's method. Our algorithm can also be used to build efficient data structures for effective resistances for multi-step time-reversible Markov models, and we anticipate that it could be useful for other tasks in network analysis.
In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.
The layered 5d transition metal oxides like Sr2IrO4 have attracted significant interest recently due to a number of exotic and new phenomena induced by the interplay between the spin-orbit coupling, bandwidth W and on-site Coulomb correlation U. In contrast to a metallic behavior expected from the Mott-Hubbard model due to more spatially extended 5d orbitals and moderate U, an insulating ground state has been observed in Sr2IrO4. Such an insulating behavior can be understood by an effective J_eff=1/2 Mott insulator model by incorporating both electron correlation and strong spin-orbital coupling, although its validity remains under debate at present. In particular, Sr2IrO4 exhibits a number of similarities to the high temperature cuprate superconductors in the crystal structure, electronic structure, magnetic structure, and even possible high temperature superconductivity. Here we report a new observation of the anomalous high energy electronic structure in Sr2IrO4. By taking high-resolution angle-resolved photoemission measurements on Sr2IrO4 over a wide energy range, we have revealed that the high energy electronic structures show unusual nearly-vertical bands that extend over a large energy range. Such anomalous high energy behaviors resemble the high energy waterfall features observed in the cuprate superconductors, adding one more important similarity between these two systems. While strong electron correlation plays an important role in producing high energy waterfall features in the cuprate superconductors, the revelation of the high energy anomalies in Sr2IrO4 points to a novel route in generating exotic electronic excitations from the strong spin-orbit coupling and a moderate electron correlation.
We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and Hom-Novikov superalgebras with Rota-Baxter operators, respectively. We show that quadratic Hom-Novikov superalgebras are Hom-associative superalgebras and the sub-adjacent Hom-Lie superalgebras of Hom-Novikov superalgebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of Hom-Novikov superalgebras.
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf \mathbf{M}}$, and a constant $-1 \leq p \leq 1$, our algorithm gives efficient access to a sparse $n\times n$ linear operator $\tilde{\mathbf{C}}$ such that $${\mathbf{M}}^{p} \approx \tilde{\mathbf{C}} \tilde{\mathbf{C}}^\top.$$ The solution is based on factoring ${\bf \mathbf{M}}$ into a product of simple and sparse matrices using squaring and spectral sparsification. For ${\mathbf{M}}$ with $m$ non-zero entries, our algorithm takes work nearly-linear in $m$, and polylogarithmic depth on a parallel machine with $m$ processors. This gives the first sampling algorithm that only requires nearly linear work and $n$ i.i.d. random univariate Gaussian samples to generate i.i.d. random samples for $n$-dimensional Gaussian random fields with SDDM precision matrices. For sampling this natural subclass of Gaussian random fields, it is optimal in the randomness and nearly optimal in the work and parallel complexity. In addition, our sampling algorithm can be directly extended to Gaussian random fields with SDD precision matrices.
Traditional anomaly detection on social media mostly focuses on individual point anomalies while anomalous phenomena usually occur in groups. Therefore it is valuable to study the collective behavior of individuals and detect group anomalies. Existing group anomaly detection approaches rely on the assumption that the groups are known, which can hardly be true in real world social media applications. In this paper, we take a generative approach by proposing a hierarchical Bayes model: Group Latent Anomaly Detection (GLAD) model. GLAD takes both pair-wise and point-wise data as input, automatically infers the groups and detects group anomalies simultaneously. To account for the dynamic properties of the social media data, we further generalize GLAD to its dynamic extension d-GLAD. We conduct extensive experiments to evaluate our models on both synthetic and real world datasets. The empirical results demonstrate that our approach is effective and robust in discovering latent groups and detecting group anomalies.
Tumblr, as one of the most popular microblogging platforms, has gained momentum recently. It is reported to have 166.4 millions of users and 73.4 billions of posts by January 2014. While many articles about Tumblr have been published in major press, there is not much scholar work so far. In this paper, we provide some pioneer analysis on Tumblr from a variety of aspects. We study the social network structure among Tumblr users, analyze its user generated content, and describe reblogging patterns to analyze its user behavior. We aim to provide a comprehensive statistical overview of Tumblr and compare it with other popular social services, including blogosphere, Twitter and Facebook, in answering a couple of key questions: What is Tumblr? How is Tumblr different from other social media networks? In short, we find Tumblr has more rich content than other microblogging platforms, and it contains hybrid characteristics of social networking, traditional blogosphere, and social media. This work serves as an early snapshot of Tumblr that later work can leverage.
Topological insulators represent a new quantum state of matter that are insulating in the bulk but metallic on the edge or surface. In the Dirac surface state, it is well-established that the electron spin is locked with the crystal momentum. Here we report a new phenomenon of the spin texture locking with the orbital texture in a topological insulator Bi2Se3. We observe light-polarization-dependent spin texture of both the upper and lower Dirac cones that constitutes strong evidence of the orbital-dependent spin texture in Bi2Se3. The different spin texture detected in variable polarization geometry is the manifestation of the spin-orbital texture in the initial state combined with the photoemission matrix element effects. Our observations provide a new orbital degree of freedom and a new way of light manipulation in controlling the spin structure of the topological insulators that are important for their future applications in spin-related technologies.
The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One particular interest is to generate Dirac cone anisotropy so that the electrons can propagate differently from one direction to the other, creating an additional tunability for new properties and applications. While various theoretical approaches have been proposed to make the isotropic Dirac cones of graphene into anisotropic ones, it has not yet been met with success. There are also some theoretical predictions and/or experimental indications of anisotropic Dirac cone in novel topological insulators and AMnBi2 (A=Sr and Ca) but more experimental investigations are needed. Here we report systematic high resolution angle-resolved photoemission measurements that have provided direct evidence on the existence of strongly anisotropic Dirac cones in SrMnBi2 and CaMnBi2. Distinct behaviors of the Dirac cones between SrMnBi2 and CaMnBi2 are also observed. These results have provided important information on the strong anisotropy of the Dirac cones in AMnBi2 system that can be governed by the spin-orbital coupling and the local environment surrounding the Bi square net.
We study fermion pairing and condensation towards an ordered state in strongly coupled quantum critical systems with a holographic AdS/CFT dual. On the gravity side this is modeled by a system of charged fermion interacting through a BCS coupling. At finite density such a system has a BCS instability. We combine the relativistic version of mean-field BCS with the semi-classical fluid approximation for the many-body state of fermions. The resulting groundstate is the AdS equivalent of a charged neutron star with a superconducting core. The spectral function of the fermions confirms that the ground state is ordered through the condensation of the pair operator. A natural variant of the BCS star is shown to exist where the gap field couples Stueckelberg-like to the AdS Maxwell field. This enhances the tendency of the system to superconduct.
High resolution laser-based angle-resolved photoemission measurements have been carried out on Sb(111) single crystal. Two kinds of Fermi surface sheets are observed that are derived from the topological surface states: one small hexagonal electron-like Fermi pocket around $Γ$ point and the other six elongated lobes of hole-like Fermi pockets around the electron pocket. Clear Rashba-type band splitting due to the strong spin-orbit coupling is observed that is anisotropic in the momentum space. Our super-high-resolution ARPES measurements reveal no obvious kink in the surface band dispersions indicating a weak electron-phonon interaction in the surface states. In particular, the electron scattering rate for these topological surface states is nearly a constant over a large energy window near the Fermi level that is unusual in terms of the conventional picture.
The three-dimensional topological semimetals represent a new quantum state of matter. Distinct from the surface state in the topological insulators that exhibits linear dispersion in two-dimensional momentum plane, the three-dimensional semimetals host bulk band dispersions linearly along all directions, forming discrete Dirac cones in three-dimensional momentum space. In addition to the gapless points (Weyl/Dirac nodes) in the bulk, the three-dimensional Weyl/Dirac semimetals are also characterized by "topologically protected" surface state with Fermi arcs on their specific surface. The Weyl/Dirac semimetals have attracted much attention recently they provide a venue not only to explore unique quantum phenomena but also to show potential applications. While Cd3As2 is proposed to be a viable candidate of a Dirac semimetal, more experimental evidence and theoretical investigation are necessary to pin down its nature. In particular, the topological surface state, the hallmark of the three-dimensional semimetal, has not been observed in Cd3As2. Here we report the electronic structure of Cd3As2 investigated by angle-resolved photoemission measurements on the (112) crystal surface and detailed band structure calculations. The measured Fermi surface and band structure show a good agreement with the band structure calculations with two bulk Dirac-like bands approaching the Fermi level and forming Dirac points near the Brillouin zone center. Moreover, the topological surface state with a linear dispersion approaching the Fermi level is identified for the first time. These results provide strong experimental evidence on the nature of topologically non-trivial three-dimensional Dirac cones in Cd3As2.
The ability to steer light propagation inside scattering media has long been sought-after due to its potential widespread applications. To form optical foci inside scattering media, the only feasible strategy is to guide photons by using either implanted or virtual guide stars. However, all of these guide stars must be introduced extrinsically, either invasively or by physical contact, limiting the scope of their application. Here, we focus light inside scattering media by employing intrinsic dynamics as guide stars. By time-reversing the perturbed component of the scattered light adaptively, we concentrate light to the origin of the perturbation, where the permittivity varied spontaneously. We demonstrate dynamic light focusing onto moving targets and imaging of a time-variant object obscured by highly scattering media, without invasiveness and physical contact. Anticipated applications include all-weather optical communication with airplanes or satellites, tracking vehicles in thick fogs, and imaging and photoablation of angiogenic vessels in tumors.
The Low Energy X-ray Telescope is a main payload on the Hard X-ray Modulation Telescope satellite. The swept charge device is selected for the Low Energy X-ray Telescope. As swept charge devices are sensitive to proton irradiation, irradiation test was carried out on the HI-13 accelerator at the China Institute of Atomic Energy. The beam energy was measured to be 10 MeV at the SCD. The proton fluence delivered to the SCD was $3\times10^{8}\mathrm{protons}/\mathrm{cm}^{2}$ over two hours. It is concluded that the proton irradiation affects both the dark current and the charge transfer inefficiency of the SCD through comparing the performance both before and after the irradiation. The energy resolution of the proton-irradiated SCD is 212 eV@5.9 keV at $-60\,^{\circ}\mathrm{C}$, while it before irradiated is 134 eV. Moreover, better performance can be reached by lowering the operating temperature of the SCD on orbit.
In this paper, a family of reducible cyclic codes over GF(p) whose duals have four zeros is presented, where p is an odd prime. Furthermore, the weight distribution of these cyclic codes is determined.
The latest discovery of possible high temperature superconductivity in the single-layer FeSe film grown on a SrTiO3 substrate, together with the observation of its unique electronic structure and nodeless superconducting gap, has generated much attention. Initial work also found that, while the single-layer FeSe/SrTiO3 film exhibits a clear signature of superconductivity, the double-layer FeSe/SrTiO3 film shows an insulating behavior. Such a dramatic difference between the single-layer and double-layer FeSe/SrTiO3 films is surprising and the underlying origin remains unclear. Here we report our comparative study between the single-layer and double-layer FeSe/SrTiO3 films by performing a systematic angle-resolved photoemission study on the samples annealed in vacuum. We find that, like the single-layer FeSe/SrTiO3 film, the as-prepared double-layer FeSe/SrTiO3 film is insulating and possibly magnetic, thus establishing a universal existence of the magnetic phase in the FeSe/SrTiO3 films. In particular, the double-layer FeSe/SrTiO3 film shows a quite different doping behavior from the single-layer film in that it is hard to get doped and remains in the insulating state under an extensive annealing condition. The difference originates from the much reduced doping efficiency in the bottom FeSe layer of the double-layer FeSe/SrTiO3 film from the FeSe-SrTiO3 interface. These observations provide key insights in understanding the origin of superconductivity and the doping mechanism in the FeSe/SrTiO3 films. The property disparity between the single-layer and double-layer FeSe/SrTiO3 films may facilitate to fabricate electronic devices by making superconducting and insulating components on the same substrate under the same condition.
In high temperature cuprate superconductors, it is now generally agreed that the parent compound is a Mott insulator and superconductivity is realized by doping the antiferromagnetic Mott insulator. In the iron-based superconductors, however, the parent compound is mostly antiferromagnetic metal, raising a debate on whether an appropriate starting point should go with an itinerant picture or a localized picture. It has been proposed theoretically that the parent compound of the iron-based superconductors may be on the verge of a Mott insulator, but so far no clear experimental evidence of doping-induced Mott transition has been available. Here we report an electronic evidence of an insulator-superconductor transition observed in the single-layer FeSe films grown on the SrTiO3 substrate. By taking angle-resolved photoemission measurements on the electronic structure and energy gap, we have identified a clear evolution of an insulator to a superconductor with the increasing doping. This observation represents the first example of an insulator-superconductor transition via doping observed in the iron-based superconductors. It indicates that the parent compound of the iron-based superconductors is in proximity of a Mott insulator and strong electron correlation should be considered in describing the iron-based superconductors.