The Gentlest Ascent Dynamics

Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations to high index saddle points are discussed. Both gradient and non-gradient systems are considered. Preliminary results on the nature of the dynamical behavior are presented

Exotic mesons from quantum chromodynamics with improved gluon and quark actions on the anisotropic lattice

Hybrid (exotic) mesons, which are important predictions of quantum chromodynamics (QCD), are states of quarks and anti-quarks bound by excited gluons. First principle lattice study of such states would help us understand the role of ``dynamical'' color in low energy QCD and provide valuable information for experimental search for these new particles. In this paper, we apply both improved gluon and quark actions to the hybrid mesons, which might be much more efficient than the previous works in reducing lattice spacing error and finite volume effect. Quenched simulations were done at $\beta=2.6$ and on a $\xi=3$ anisotropic $12^3\times36$ lattice using our PC cluster. We obtain $2013 \pm 26 \pm 71$ MeV for the mass of the $1^{-+}$ hybrid meson ${\bar q}qg$ in the light quark sector, and $4369 \pm 37 \pm 99$Mev in the charm quark sector; the mass splitting between the $1^{-+}$ hybrid meson ${\bar c}c g$ in the charm quark sector and the spin averaged S-wave charmonium mass is estimated to be $1302 \pm 37 \pm 99$ MeV. As a byproduct, we obtain $1438 \pm 32 \pm 57$ MeV for the mass of a P-wave $1^{++}$ ${\bar u}u$ or ${\bar d}d$ meson and $1499 \pm 28 \pm 65$ MeV for the mass of a P-wave $1^{++}$ ${\bar s}s$ meson, which are comparable to their experimental value 1426 MeV for the $f_1(1420)$ meson. The first error is statistical, and the second one is systematical. The mixing of the hybrid meson with a four quark state is also discussed.Comment: 12 pages, 3 figures. Published versio

Sound propagation in density wave conductors and the effect of long-range Coulomb interaction

We study theoretically the sound propagation in charge- and spin-density waves in the hydrodynamic regime. First, making use of the method of comoving frame, we construct the stress tensor appropriate for quasi-one dimensional systems within tight-binding approximation. Taking into account the screening effect of the long-range Coulomb interaction, we find that the increase of the sound velocity below the critical temperature is about two orders of magnitude less for longitudinal sound than for transverse one. It is shown that only the transverse sound wave with displacement vector parallel to the chain direction couples to the phason of the density wave, therefore we expect significant electromechanical effect only in this case.Comment: revtex, 14 pages (in preprint form), submitted to PR

Metamagnetic Transition in Na0.85_{0.85}CoO2_2 Single Crystals

We report the magnetization, specific heat and transport measurements of high quality Na$_{0.85}$CoO$_2$ single crystals in applied magnetic fields up to 14T. In high temperatures, the system is in a paramagnetic phase. It undergoes a magnetic phase transition below about 20K. When the field is applied along the c-axis, the measurement data of magnetization, specific heat and magnetoresistance reveal a metamagnetic transition from an antiferromagnetic state to a quasi-ferromagnetic state at about 8T in low temperatures. However, no transition is observed in the magnetization measurements up to 14T when the field is applied perpendicular to the c-axis. The low temperature magnetic phase diagram of Na$_{0.85}$CoO$_2$ is determined.Comment: 4 pages, 5 figure

Low frequency noise peak near magnon emission energy in magnetic tunnel junctions

We report on the low frequency (LF) noise measurements in magnetic tunnel junctions (MTJs) below 4 K and at low bias, where the transport is strongly affected by scattering with magnons emitted by hot tunnelling electrons, as thermal activation of magnons from the environment is suppressed. For both CoFeB/MgO/CoFeB and CoFeB/AlO$_{x}$/CoFeB MTJs, enhanced LF noise is observed at bias voltage around magnon emission energy, forming a peak in the bias dependence of noise power spectra density, independent of magnetic configurations. The noise peak is much higher and broader for unannealed AlO$_{x}$-based MTJ, and besides Lorentzian shape noise spectra in the frequency domain, random telegraph noise (RTN) is visible in the time traces. During repeated measurements the noise peak reduces and the RTN becomes difficult to resolve, suggesting defects being annealed. The Lorentzian shape noise spectra can be fitted with bias-dependent activation of RTN, with the attempt frequency in the MHz range, consistent with magnon dynamics. These findings suggest magnon-assisted activation of defects as the origin of the enhanced LF noise.Comment: 6 pages, 5 figure

Sequential Recommendation Based on Multivariate Hawkes Process Embedding With Attention.

Recommender systems are important approaches for dealing with the information overload problem in the big data era, and various kinds of auxiliary information, including time and sequential information, can help improve the performance of retrieval and recommendation tasks. However, it is still a challenging problem how to fully exploit such information to achieve high-quality recommendation results and improve users' experience. In this work, we present a novel sequential recommendation model, called multivariate Hawkes process embedding with attention (MHPE-a), which combines a temporal point process with the attention mechanism to predict the items that the target user may interact with according to her/his historical records. Specifically, the proposed approach MHPE-a can model users' sequential patterns in their temporal interaction sequences accurately with a multivariate Hawkes process. Then, we perform an accurate sequential recommendation to satisfy target users' real-time requirements based on their preferences obtained with MHPE-a from their historical records. Especially, an attention mechanism is used to leverage users' long/short-term preferences adaptively to achieve an accurate sequential recommendation. Extensive experiments are conducted on two real-world datasets (lastfm and gowalla), and the results show that MHPE-a achieves better performance than state-of-the-art baselines