Quantum anomalies in superconducting Weyl metals

We theoretically study the quantum anomalies in the superconducting Weyl metals based on the topological field theory. It is demonstrated that the Fermi arc and the surface Andreev bound state, characteristic of the superconducting Weyl metals, are the manifestations of two underlying phenomenon, namely the chiral anomaly and the parity-like anomaly, respectively. The first anomaly is inherited from the Berry curvature around the original Weyl points, while the second is the result of the superconductivity. We show that, all the fascinating topological behavior of the superconducting Weyl metals, either intranode FFLO or the internode BCS pairing state, can be satisfactorily described and predicted by our topological field theory

Qubit-loss-free fusion of W states employing weak cross-Kerr nonlinearities

With the assistance of weak cross-Kerr nonlinearities, we introduce an optical scheme to fuse two small-size polarization entangled W states into a large-scale W state without qubit loss, i.e.,$\mathrm{W}_{n+m}$ state can be generated from an $n$-qubit W state and a $m$-qubit W state. To complete the fusion task, two polarization entanglement processes and one spatial entanglement process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. We analyze the resource cost and the success probability of the scheme. There is no complete failure output in our fusion mechanism, and all the garbage states are recyclable. In addition, there is no need for any controlled quantum gate and any ancillary photon, so it is simple and feasible under the current experiment technology.Comment: 7 pages, 3 figure

Eigenvalue, Quadratic Programming, and Semidefinite Programming Bounds for a Cut Minimization Problem

We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex separator. This problem is closely related to the graph partitioning problem. In fact, the model we use is the same as that for the graph partitioning problem except for a different \emph{quadratic} objective function. We look at known and new bounds obtained from various relaxations for this NP-hard problem. This includes: the standard eigenvalue bound, projected eigenvalue bounds using both the adjacency matrix and the Laplacian, quadratic programming (QP) bounds based on recent successful QP bounds for the quadratic assignment problems, and semidefinite programming bounds. We include numerical tests for large and \emph{huge} problems that illustrate the efficiency of the bounds in terms of strength and time.Comment: 32 pages, Department of Combinatorics & Optimization, University of Waterloo, Canad

Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the k\it{\textbf{k}}-space

Two common approaches of studying theoretically the property of a superconductor are shown to have significant differences, when they are applied to the Larkin-Ovchinnikov state of Weyl metals. In the first approach the pairing term is restricted by a cutoff energy to the neighborhood of the Fermi surface, whereas in the second approach the pairing term is extended to the whole Brillouin zone. We explore their difference by considering two minimal models for the Weyl metal. For a model giving a single pair of Weyl pockets, both two approaches give a partly-gapped (fully-gapped) bulk spectrum for small (large) pairing amplitude. However, for very small cutoff energy, a portion of the Fermi surface can be completely unaffected by the pairing term in the first approach. For the other model giving two pairs of Weyl pockets, while the bulk spectrum for the first approach can be fully gapped, the one from the second approach has a robust line node, and the surface states are also changed qualitatively by the pairing. We elucidate the above differences by topological arguments and analytical analyses. A factor common to both of the two models is the tilting of the Weyl cones which leads to asymmetric normal state band structure with respect to the Weyl nodes. For the Weyl metal with two pairs of Weyl pockets, the band folding leads to a double degeneracy in the effective model, which distinguishes the pairing of the second approach from all others.Comment: 27 pages, 11 figure

The Design of Circuit-Measuring Collaborative Learning System with Embedded Broker

Recently, the academic community has been giving much attention to Cooperative Learning System, a group learning method combined with pedagogy and social psychology. It allows group members to gain knowledge through collaborations and interactions. Nowadays, most Internet cooperative learning systems are designed to provide students mainly with a convenient online environment to study theoretical courses but rarely with an online environment to operate practical instruments. Hence, this paper designed a 3D online cooperative learning system for operating virtual instruments with circuit-measuring function. By integrating with Virtual Reality, Remote Control Parameter Transmission and embedded system techniques, this system gives learners not only a cooperative learning environment via networking to jointly operate the 3D virtual instruments (for example, multi-meters, power supplies and oscilloscopes) but also the functions of instant messages and 3D puzzles to interact with one another. Therefore, learners can effectively improve learning interests and results.Comment: International Journal of Computer Science Issues, IJCSI, Vol. 7, Issue 1, No. 3, January 2010, http://ijcsi.org/articles/The-Design-of-Circuit-Measuring-Collaborative-Learning-System-with-Embedded-Broker.ph

Ferromagnetism and superconductivity with possible p+ipp+ip pairing symmetry in partially hydrogenated graphene

By means of first-principles calculations, we predict two new types of partially hydrogenated graphene systems: C$_{6}$H$_{1}$ and C$_{6}$H$_{5}$, which are shown to be ferromagnetic (FM) semimetal and FM narrow-gap semiconductor, respectively. When properly doped, the Fermi surface of the two systems consists of an electron pocket or six hole patches in the first Brillouin zone with completely spin-polarized charge carries. If superconductivity exists in these systems, the stable pairing symmetries are shown to be $p+ip$ for electron doped case, and anisotropic $p+ip$ for hole doped case. The predicted systems may provide fascinating platforms for studying the novel properties of ferromagnetism and triplet-pairing superconductivity as well as two-dimensional spintronics

Growth on Two Limiting Essential Resources in a Self-Cycling Fermentor

A system of impulsive differential equations with state-dependent impulses is used to model the growth of a single population on two limiting essential resources in a self-cycling fermentor. Potential applications include water purification and biological waste remediation. The self-cycling fermentation process is a semi-batch process and the model is an example of a hybrid system. In this case, a well-stirred tank is partially drained, and subsequently refilled using fresh medium when the concentration of both resources (assumed to be pollutants) falls below some acceptable threshold. We consider the process successful if the threshold for emptying/refilling the reactor can be reached indefinitely without the time between successive emptying/refillings becoming unbounded and without interference by the operator. We prove that whenever the process is successful, the model predicts that the concentrations of the population and the resources converge to a positive periodic solution. We derive conditions for the successful operation of the process that are shown to be initial condition dependent and prove that if these conditions are not satisfied, then the reactor fails. We show numerically that there is an optimal fraction of the medium drained from the tank at each impulse that maximizes the output of the process.Comment: 21 pages, 6 figure

A Detection and Segmentation Architecture for Skin Lesion Segmentation on Dermoscopy Images

This report summarises our method and validation results for the ISIC Challenge 2018 - Skin Lesion Analysis Towards Melanoma Detection - Task 1: Lesion Segmentation. We present a two-stage method for lesion segmentation with optimised training method and ensemble post-process. Our method achieves state-of-the-art performance on lesion segmentation and we win the first place in ISIC 2018 task1.Comment: 5 pages, 9 figures, Ranked 1st place in ISIC 2018 task1, title updated and results adde

SimGNN: A Neural Network Approach to Fast Graph Similarity Computation

Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), is the core operation of graph similarity search and many other applications, but very costly to compute in practice. Inspired by the recent success of neural network approaches to several graph applications, such as node or graph classification, we propose a novel neural network based approach to address this classic yet challenging graph problem, aiming to alleviate the computational burden while preserving a good performance. The proposed approach, called SimGNN, combines two strategies. First, we design a learnable embedding function that maps every graph into a vector, which provides a global summary of a graph. A novel attention mechanism is proposed to emphasize the important nodes with respect to a specific similarity metric. Second, we design a pairwise node comparison method to supplement the graph-level embeddings with fine-grained node-level information. Our model achieves better generalization on unseen graphs, and in the worst case runs in quadratic time with respect to the number of nodes in two graphs. Taking GED computation as an example, experimental results on three real graph datasets demonstrate the effectiveness and efficiency of our approach. Specifically, our model achieves smaller error rate and great time reduction compared against a series of baselines, including several approximation algorithms on GED computation, and many existing graph neural network based models. To the best of our knowledge, we are among the first to adopt neural networks to explicitly model the similarity between two graphs, and provide a new direction for future research on graph similarity computation and graph similarity search.Comment: WSDM 201

Novel anisotropic spin singlet pairings in Cux_xBi2_2Se3_3 and Bi2_2Te3_3

Possible anisotropic spin singlet pairings in Bi$_2$X$_3$ (X is Se or Te) are studied. Among six pairings compatible with the crystal symmetry, two novel pairings show nontrivial surface Andreev bound states, which form flat bands and could produce zero bias conductance peak in measurements like point contact spectroscopy. By considering purely repulsive short range Coulomb interaction as the pairing mechanism, the dominant superexchange terms are all antiferromagnetic, which would usually favor spin singlet pairing in Bi$_2$X$_3$. Mean field analyses show that the interorbital pairing interaction favors a mixed spatial-parity anisotropic pairing state, and one pairing channel with zero energy surface states has a sizable component. The results provide important new information for future experiments.Comment: 13 pages, 2 figures, 3 table