Loop-Erasure of Plane Brownian Motion

We use the coupling technique to prove that there exists a loop-erasure of a plane Brownian motion stopped on exiting a simply connected domain, and the loop-erased curve is the reversal of a radial SLE$_2$ curve.Comment: 10 page

On defining partition entropy by inequalities

Partition entropy is the numerical metric of uncertainty within a partition of a finite set, while conditional entropy measures the degree of difficulty in predicting a decision partition when a condition partition is provided. Since two direct methods exist for defining conditional entropy based on its partition entropy, the inequality postulates of monotonicity, which conditional entropy satisfies, are actually additional constraints on its entropy. Thus, in this paper partition entropy is defined as a function of probability distribution, satisfying all the inequalities of not only partition entropy itself but also its conditional counterpart. These inequality postulates formalize the intuitive understandings of uncertainty contained in partitions of finite sets.We study the relationships between these inequalities, and reduce the redundancies among them. According to two different definitions of conditional entropy from its partition entropy, the convenient and unified checking conditions for any partition entropy are presented, respectively. These properties generalize and illuminate the common nature of all partition entropies

Modeling and Detecting False Data Injection Attacks against Railway Traction Power Systems

Modern urban railways extensively use computerized sensing and control technologies to achieve safe, reliable, and well-timed operations. However, the use of these technologies may provide a convenient leverage to cyber-attackers who have bypassed the air gaps and aim at causing safety incidents and service disruptions. In this paper, we study false data injection (FDI) attacks against railways' traction power systems (TPSes). Specifically, we analyze two types of FDI attacks on the train-borne voltage, current, and position sensor measurements - which we call efficiency attack and safety attack -- that (i) maximize the system's total power consumption and (ii) mislead trains' local voltages to exceed given safety-critical thresholds, respectively. To counteract, we develop a global attack detection (GAD) system that serializes a bad data detector and a novel secondary attack detector designed based on unique TPS characteristics. With intact position data of trains, our detection system can effectively detect the FDI attacks on trains' voltage and current measurements even if the attacker has full and accurate knowledge of the TPS, attack detection, and real-time system state. In particular, the GAD system features an adaptive mechanism that ensures low false positive and negative rates in detecting the attacks under noisy system measurements. Extensive simulations driven by realistic running profiles of trains verify that a TPS setup is vulnerable to the FDI attacks, but these attacks can be detected effectively by the proposed GAD while ensuring a low false positive rate.Comment: IEEE/IFIP DSN-2016 and ACM Trans. on Cyber-Physical System

Many-body dynamics of a Bose system with attractive interactions on a ring

We investigate the many-body dynamics of an effectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theory predicts that a bright-soliton state will be formed when increasing the interparticle interaction over a critical point. The study of quantum many-body dynamics in this paper reveals that there is a modulation instability in a finite Bose system correspondingly. We show that Shannon entropy becomes irregular near and above the critical point due to quantum correlations. We also study the dynamical behavior of the instability by exploring the momentum distribution and the fringe visibility, which can be verified experimentally by releasing the trapComment: 6 pages,5 figure

Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems

We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making singleshot polarization-dependent measurements, as well as for providing a means of preparing samples with position-dependent spin.Comment: 8 pages, 5 figures. Accepted in Optics Expres