Algebro-geometric Constructions to the Dym-type Hierarchy

Resorting to the characteristic polynomial of Lax matrix for the Dym-type hierarchy, we define a trigonal curve, on which appropriate vector-valued Baker-Akhiezer function and meromorphic function are introduced. Based on the theory of trigonal curve and three kinds of Abelian differentials, we obtain the explicit Riemann theta function representations of the meromorphic function, from which we get the algebro-geometric constructions for the entire Dym-type hierarch

The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces

We prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space. Admissible Hilbert-Hadamard spaces are a class of (possibly infinite-dimensional) non-positively curved metric spaces that contain dense sequences of closed convex subsets isometric to Riemannian manifolds. Examples of admissible Hilbert-Hadamard spaces include Hilbert spaces, certain simply connected and non-positively curved Riemannian-Hilbertian manifolds and infinite\-/dimensional symmetric spaces. Thus our main theorem can be considered as an infinite-dimensional analogue of Kasparov's theorem on the Novikov conjecture for groups acting properly and isometrically on complete, simply connected and non-positively curved manifolds. As a consequence, we show that the Novikov conjecture holds for geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a closed smooth manifold. This result is inspired by Connes' theorem that the Novikov conjecture holds for higher signatures associated to the Gelfand-Fuchs classes of groups of diffeormorphisms.Comment: 52 page

The diamagnetic phase transition in Magnetars

Neutron stars are ideal astrophysical laboratories for testing theories of the de Haas-van Alphen (dHvA) effect and diamagnetic phase transition which is associated with magnetic domain formation. The "magnetic interaction" between delocalized magnetic moments of electrons (the Shoenberg effect), can result in an effect of the diamagnetic phase transition into domains of alternating magnetization (Condon's domains). Associated with the domain formation are prominent magnetic field oscillation and anisotropic magnetic stress which may be large enough to fracture the crust of magnetar with a super-strong field. Even if the fracture is impossible as in "low-field" magnetar, the depinning phase transition of domain wall motion driven by low field rate (mainly due to the Hall effect) in the randomly perturbed crust can result in a catastrophically variation of magnetic field. This intermittent motion, similar to the avalanche process, makes the Hall effect be dissipative. These qualitative consequences about magnetized electron gas are consistent with observations of magnetar emission, and especially the threshold critical dynamics of driven domain wall can partially overcome the difficulties of "low-field" magnetar bursts and the heating mechanism of transient, or "outbursting" magnetar.Comment: 15pages, 4 fiures, accepted for publication in PAS

Impulse Control of Multidimensional Jump Diffusions

This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly `infinite-activity' jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrability conditions.Comment: 15 pages, 1 figur

Pseudorapidity dependence of short-range correlations from a multi-phase transport model

Using a multi-phase transport model (AMPT) that includes both initial partonic and hadronic interactions, we study neighboring bin multiplicity correlations as a function of pseudorapidity in Au+Au collisions at $\sqrt{s_{NN}} = 7.7-62.4$ GeV. It is observed that for $\sqrt{s_{NN}} <$19.6GeV Au+Au collisions, the short-range correlations of final particles have a trough at central pseudorapidity, while for $\sqrt{s_{NN}} >$19.6GeV AuAu collisions, the short-range correlations of final particles have a peak at central pseudorapidity. Our findings indicate that the pseudorapidity dependence of short-range correlations should contain some new physical information, and are not a simple result of the pseudorapidity distribution of final particles. The AMPT results with and without hadronic scattering are compared. It is found that hadron scattering can only increase the short-range correlations to some level, but is not responsible for the different correlation shapes for different energies. Further study shows that the different pseudorapidity dependence of short-range correlations are mainly due to partonic evolution and the following hadronization scheme.Comment: 5 pages, 3 figures, submitted to CP

RFP: A Remote Fetching Paradigm for RDMA-Accelerated Systems

Remote Direct Memory Access (RDMA) is an efficient way to improve the performance of traditional client-server systems. Currently, there are two main design paradigms for RDMA-accelerated systems. The first allows the clients to directly operate the server's memory and totally bypasses the CPUs at server side. The second follows the traditional server-reply paradigm, which asks the server to write results back to the clients. However, the first method has to expose server's memory and needs tremendous re-design of upper-layer software, which is complex, unsafe, error-prone, and inefficient. The second cannot achieve high input/output operations per second (IOPS), because it employs out-bound RDMA-write at server side which is not efficient. We find that the performance of out-bound RDMA-write and in-bound RDMA-read is asymmetric and the latter is 5 times faster than the former. Based on this observation, we propose a novel design paradigm named Remote Fetching Paradigm (RFP). In RFP, the server is still responsible for processing requests from the clients. However, counter-intuitively, instead of sending results back to the clients through out-bound RDMA-write, the server only writes the results in local memory buffers, and the clients use in-bound RDMA-read to remotely fetch these results. Since in-bound RDMA-read achieves much higher IOPS than out-bound RDMA-write, our model is able to bring higher performance than the traditional models. In order to prove the effectiveness of RFP, we design and implement an RDMA-accelerated in-memory key-value store following the RFP model. To further improve the IOPS, we propose an optimization mechanism that combines status checking and result fetching. Experiment results show that RFP can improve the IOPS by 160%~310% against state-of-the-art models for in-memory key-value stores.Comment: 11 pages, 10 figures; Key Words: RDMA and InfiniBand, Remote Fetching Paradigm, IOPS, and Small Dat

Singularities of plane gravitational waves and their memory effects

Similar to the Schwarzschild coordinates for spherical black holes, the Baldwin, Jeffery and Rosen (BJR) coordinates for plane gravitational waves are often singular, and extensions beyond such singularities are necessary, before studying asymptotic properties of such spacetimes at the null infinity of the plane, on which the gravitational waves propagate. The latter is closely related to the studies of memory effects and soft graviton theorems. In this paper, we point out that in the BJR coordinates all the spacetimes are singular physically at the focused point $u = u_s$, except for the two cases: (1) $\alpha =1/2, \; \forall \; \chi_n$; and (2) $\alpha =1, \; \chi_i = 0\; (i = 1, 2, 3)$, where $\chi_n$ are the coefficients in the expansion \chi \equiv \left[{\mbox{det}}\left(g_{ab}\right) \right]^{1/4} = \left(u - u_s\right)^{\alpha}\sum_{n = 0}^{\infty}\chi_n \left(u - u_s\right)^n with $\chi_0 \not= 0$, the constant $\alpha \in (0, 1]$ characterizes the strength of the singularities, and $g_{ab}$ denotes the reduced metric on the two-dimensional plane orthogonal to the propagation direction of the wave. Therefore, the hypersurfaces $u= u_s$ already represent the boundaries of such spacetimes, and the null infinity does not belong to them. As a result, they cannot be used to study properties of plane gravitational waves at null infinities, including memory effects and soft graviton theorems.Comment: revtex4-1, one figure. Corrected some typos. Gen. Relativ. Grav. 52 (2020) 2

Question Answering over Knowledge Base with Neural Attention Combining Global Knowledge Information

With the rapid growth of knowledge bases (KBs) on the web, how to take full advantage of them becomes increasingly important. Knowledge base-based question answering (KB-QA) is one of the most promising approaches to access the substantial knowledge. Meantime, as the neural network-based (NN-based) methods develop, NN-based KB-QA has already achieved impressive results. However, previous work did not put emphasis on question representation, and the question is converted into a fixed vector regardless of its candidate answers. This simple representation strategy is unable to express the proper information of the question. Hence, we present a neural attention-based model to represent the questions dynamically according to the different focuses of various candidate answer aspects. In addition, we leverage the global knowledge inside the underlying KB, aiming at integrating the rich KB information into the representation of the answers. And it also alleviates the out of vocabulary (OOV) problem, which helps the attention model to represent the question more precisely. The experimental results on WEBQUESTIONS demonstrate the effectiveness of the proposed approach

How does the electric current propagate through the fully-hydrogenated borophene?

We study the electronic transport properties of two-dimensional (2D) fully-hydrogenated borophene (namely, borophane), using the density functional theory and non-equilibrium Green's function approaches. Borophane shows a perfect electrical transport anisotropy and is promising for applications. Along the peak- or equivalently the valley-parallel direction, the 2D borophane exhibits a metallic characteristic and its current-voltage (I-V) curve shows a linear behavior, corresponding to the ON state in borophane-based nano-switch. In this case, electrons mainly propagate via the B-B bonds along the linear boron chains. In contrast, the electron transmission is almost forbidden along the perpendicular buckled direction (i.e., the OFF state), due to its semi-conductor property. Our work demonstrates that 2D borophane could combine the metal and semiconductor features and can be a promising candidate of nano-switching materials with stable structure and high ON/OFF ratio

Ultrafast Electronic Dynamics of a Weyl Semimetal MoTe2_2 Revealed by Time and Angle Resolved Photoemission Spectroscopy

A Weyl semimetal is a new type of topological quantum phase with intriguing physics near the Weyl nodes. Although the equilibrium state of Weyl semimetals has been investigated, the ultrafast dynamics near the Weyl node in the nonequilibrium state is still missing. Here by performing time and angle resolved photoemission spectroscopy on type-II Weyl semimetal MoTe$_2$, we reveal the dispersion of the unoccupied states and identify the Weyl node at 70 meV above E$_F$. Moreover, by tracking the ultrafast relaxation dynamics near the Weyl node upon photo-excitation with energy, momentum and temporal resolution, two intrinsic recovery timescales are observed, a fast one of 430 fs and a slow one of 4.1 ps, which are associated with hot electron cooling by optical phonon cascade emission and anharmonic decay of hot optical phonons respectively. The electron population shows a metallic response, and the two temperature model fitting of the transient electronic temperature gives an electron-phonon coupling constant of $\lambda\langle\Omega^2\rangle\simeq32$ $\textrm{meV}^2$. Our work provides important dynamic information for understanding the relaxation mechanism of a Weyl semimetal and for exploiting potential applications using ultrafast optical control.Comment: Submitted on 09/12/2017, including 16 pages, 4 figure