Scattering on two Aharonov-Bohm vortices with opposite fluxes

The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations

A new class of (2+1)(2+1)-d topological superconductor with Z8\mathbb{Z}_8 topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.Comment: 5 pages main text and 3 pages appendix. 1 figur

Top-N Recommendation on Graphs

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well-known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.Comment: CIKM 201

Dislocation nucleation in shocked fcc solids: effects of temperature and preexisting voids

Quantitative behaviors of shock-induced dislocation nucleation are investigated by means of molecular dynamics simulations on fcc Lennard-Jones solids: a model Argon. In perfect crystals, it is found that Hugoniot elastic limit (HEL) is a linearly decreasing function of temperature: from near-zero to melting temperatures. In a defective crystal with a void, dislocations are found to nucleate on the void surface. Also HEL drastically decreases to 15 percent of the perfect crystal when a void radius is 3.4 nanometer. The decrease of HEL becomes larger as the void radius increases, but HEL becomes insensitive to temperature.Comment: 4 pages. (ver.2) All figures have been revised. Two citations are newly added. Numerical unit is unified in the context of solid argon. (ver. 3) A minor revision including new reference

Neural adaptive sequential Monte Carlo

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods, performance is critically dependent on the proposal distribution: a bad proposal can lead to arbitrarily inaccurate estimates of the target distribution. This paper presents a new method for automatically adapting the proposal using an approximation of the Kullback-Leibler divergence between the true posterior and the proposal distribution. The method is very flexible, applicable to any parameterized proposal distribution and it supports online and batch variants. We use the new framework to adapt powerful proposal distributions with rich parameterizations based upon neural networks leading to Neural Adaptive Sequential Monte Carlo (NASMC). Experiments indicate that NASMC significantly improves inference in a non-linear state space model outperforming adaptive proposal methods including the Extended Kalman and Unscented Particle Filters. Experiments also indicate that improved inference translates into improved parameter learning when NASMC is used as a subroutine of Particle Marginal Metropolis Hastings. Finally we show that NASMC is able to train a latent variable recurrent neural network (LV-RNN) achieving results that compete with the state-of-the-art for polymorphic music modelling. NASMC can be seen as bridging the gap between adaptive SMC methods and the recent work in scalable, black-box variational inference

Converting Your Thoughts to Texts: Enabling Brain Typing via Deep Feature Learning of EEG Signals

An electroencephalography (EEG) based Brain Computer Interface (BCI) enables people to communicate with the outside world by interpreting the EEG signals of their brains to interact with devices such as wheelchairs and intelligent robots. More specifically, motor imagery EEG (MI-EEG), which reflects a subjects active intent, is attracting increasing attention for a variety of BCI applications. Accurate classification of MI-EEG signals while essential for effective operation of BCI systems, is challenging due to the significant noise inherent in the signals and the lack of informative correlation between the signals and brain activities. In this paper, we propose a novel deep neural network based learning framework that affords perceptive insights into the relationship between the MI-EEG data and brain activities. We design a joint convolutional recurrent neural network that simultaneously learns robust high-level feature presentations through low-dimensional dense embeddings from raw MI-EEG signals. We also employ an Autoencoder layer to eliminate various artifacts such as background activities. The proposed approach has been evaluated extensively on a large- scale public MI-EEG dataset and a limited but easy-to-deploy dataset collected in our lab. The results show that our approach outperforms a series of baselines and the competitive state-of-the- art methods, yielding a classification accuracy of 95.53%. The applicability of our proposed approach is further demonstrated with a practical BCI system for typing.Comment: 10 page

Electronic correlations and unusual superconducting response in the optical properties of the iron-chalcogenide FeTe0.55Se0.45

The in-plane complex optical properties of the iron-chalcogenide superconductor FeTe0.55Se0.45 have been determined above and below the critical temperature Tc = 14 K. At room temperature the conductivity is described by a weakly-interacting Fermi liquid; however, below 100 K the scattering rate develops a frequency dependence in the terahertz region, signaling the increasingly correlated nature of this material. We estimate the dc conductivity just above Tc to be sigma_dc ~ 3500 Ohm-1cm-1 and the superfluid density rho_s0 ~ 9 x 10^6 cm-2, which places this material close to the scaling line rho_s0/8 ~ 8.1 sigma_dc Tc for a BCS dirty-limit superconductor. Below Tc the optical conductivity reveals two gap features at Delta_1,2 ~ 2.5 and ~ 5.1 meV.Comment: Minor revisions, 5 pages, 4 figure