Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA

Observation of Fermi-energy dependent unitary impurity resonances in a strong topological insulator Bi_2Se_3 with scanning tunneling spectroscopy

Scanning tunneling spectroscopic studies of Bi_2Se_3 epitaxial films on Si (111) substrates reveal highly localized unitary impurity resonances associated with non-magnetic quantum impurities. The strength of the resonances depends on the energy difference between the Fermi level (E_F) and the Dirac point (E_D) and diverges as E_F approaches E_D. The Dirac-cone surface state of the host recovers within ~ 2Å spatial distance from impurities, suggesting robust topological protection of the surface state of topological insulators against high-density impurities that preserve time reversal symmetry

An authentication scheme to defend against UDP DrDoS attacks in 5G networks

5th generation wireless systems are coming. While we are excited about the delay-free high speeds 5G will bring, security problems are becoming more and more serious. Increasingly rampant Distributed Denial of service (DDoS) attacks, particularly Distributed Reflection Denial of Service (DrDoS) attacks with User Datagram Protocols (UDPs) have developed into a global problem. This article presents a design, implementation, analysis, and experimental evaluation of an authentication scheme, a defense against UDP DrDoS attacks, by which attackers cleverly use rebound server farms to bounce a flood of packets to a target host. We call our solution IEWA because it combines the concepts of increasing expenses and weak authentication. In this paper, we apply IEWA to Network Time Protocol (NTP). First, we simulate and compare the original and improved protocols. Next, we verify the effectiveness of our proposed scheme. We show that our improved scheme is safer than the original scheme. Finally, we compare our solution with existing state-of-the-art schemes, using indicators such as communication overhead, server storage costs, client storage costs, computation costs of server and computation costs of client. We find that our scheme improves system stability and security, reduces communication overhead, server storage cost and computational costs. Our solution not only improves the NTP protocol to mitigate DrDoS attacks, but also strengthens other UDP protocols that are vulnerable to DrDoS attacks. Therefore, our solution can be used as a solution to UDP DrDoS attacks in 5G Network

An Economic Aspect of Device-to-Device Assisted Offloading in Cellular Networks

Traffic offloading via device-to-device (D2D) communications has been proposed to alleviate the traffic burden on base stations (BSs) and to improve the spectral and energy efficiency of cellular networks. The success of D2D communications relies on the willingness of users to share contents. In this paper, we study the economic aspect of traffic offloading via content sharing among multiple devices and propose an incentive framework for D2D assisted offloading. In the proposed incentive framework, the operator improves its overall profit, defined as the network economic efficiency (ECE), by encouraging users to act as D2D transmitters (D2D-Txs) which broadcast their popular contents to nearby users. We analytically characterize D2D assisted offloading in cellular networks for two operating modes: 1) underlay mode and 2) overlay mode. We model the optimization of network ECE as a two-stage Stackelberg game, considering the densities of cellular users and D2D-Tx’s, the operator’s incentives and the popularity of contents. The closedform expressions of network ECE for both underlay and overlay modes of D2D communications are obtained. Numerical results show that the achievable network ECE of the proposed incentive D2D assisted offloading network can be significantly improved with respect to the conventional cellular networks where the D2D communications are disabled

Chaotic Properties of Subshifts Generated by a Non-Periodic Recurrent Orbit

The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a non-periodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts

Computation Offloading and Resource Allocation in Mixed Fog/Cloud Computing Systems with Min-Max Fairness Guarantee

Cooperation between the fog and the cloud in mobile cloud computing environments could offer improved offloading services to smart mobile user equipment (UE) with computation intensive tasks. In this paper, we tackle the computation offloading problem in a mixed fog/cloud system by jointly optimizing the offloading decisions and the allocation of computation resource, transmit power and radio bandwidth, while guaranteeing user fairness and maximum tolerable delay. This optimization problem is formulated to minimize the maximal weighted cost of delay and energy consumption (EC) among all UEs, which is a mixed-integer non-linear programming problem. Due to the NP-hardness of the problem, we propose a low-complexity suboptimal algorithm to solve it, where the offloading decisions are obtained via semidefinite relaxation and randomization and the resource allocation is obtained using fractional programming theory and Lagrangian dual decomposition. Simulation results are presented to verify the convergence performance of our proposed algorithms and their achieved fairness among UEs, and the performance gains in terms of delay, EC and the number of beneficial UEs over existing algorithms

An Economic Aspect of Device-to-Device Assisted Offloading in Cellular Networks

Traffic offloading via device-to-device (D2D) communications has been proposed to alleviate the traffic burden on base stations (BSs) and to improve the spectral and energy efficiency of cellular networks. The success of D2D communications relies on the willingness of users to share contents. In this paper, we study the economic aspect of traffic offloading via content sharing among multiple devices and propose an incentive framework for D2D assisted offloading. In the proposed incentive framework, the operator improves its overall profit, defined as the network economic efficiency (ECE), by encouraging users to act as D2D transmitters (D2D-Txs) which broadcast their popular contents to nearby users. We analytically characterize D2D assisted offloading in cellular networks for two operating modes: 1) underlay mode and 2) overlay mode. We model the optimization of network ECE as a two-stage Stackelberg game, considering the densities of cellular users and D2D-Tx’s, the operator’s incentives and the popularity of contents. The closedform expressions of network ECE for both underlay and overlay modes of D2D communications are obtained. Numerical results show that the achievable network ECE of the proposed incentive D2D assisted offloading network can be significantly improved with respect to the conventional cellular networks where the D2D communications are disabled