Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States

The boundary of symmetry-protected topological states (SPTs) can harbor new quantum anomaly phenomena. In this work, we characterize the bosonic anomalies introduced by the 1+1D non-onsite-symmetric gapless edge modes of 2+1D bulk bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to $G=\prod_i Z_{N_i}=Z_{N_1} \times Z_{N_2} \times Z_{N_3} \times ...$). We demonstrate that some classes of SPTs (termed "Type II") trap fractional quantum numbers (such as fractional $Z_N$ charges) at the 0D kink of the symmetry-breaking domain walls; while some classes of SPTs (termed "Type III") have degenerate zero energy modes (carrying the projective representation protected by the unbroken part of the symmetry), either near the 0D kink of a symmetry-breaking domain wall, or on a symmetry-preserving 1D system dimensionally reduced from a thin 2D tube with a monodromy defect 1D line embedded. More generally, the energy spectrum and conformal dimensions of gapless edge modes under an external gauge flux insertion (or twisted by a branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish many SPT classes. We provide a manifest correspondence from the physical phenomena, the induced fractional quantum number and the zero energy mode degeneracy, to the mathematical concept of cocycles that appears in the group cohomology classification of SPTs, thus achieving a concrete physical materialization of the cocycles. The aforementioned edge properties are formulated in terms of a long wavelength continuum field theory involving scalar chiral bosons, as well as in terms of Matrix Product Operators and discrete quantum lattice models. Our lattice approach yields a regularization with anomalous non-onsite symmetry for the field theory description. We also formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.Comment: 29 pages, 12 Figures. v3 clarification to be accessible for both HEP and CMT. Thanks to Roman Jackiw for introducing new Ref

Multiple Timescale Energy Scheduling for Wireless Communication with Energy Harvesting Devices

The primary challenge in wireless communication with energy harvesting devices is to efficiently utilize the harvesting energy such that the data packet transmission could be supported. This challenge stems from not only QoS requirement imposed by the wireless communication application, but also the energy harvesting dynamics and the limited battery capacity. Traditional solar predictable energy harvesting models are perturbed by prediction errors, which could deteriorate the energy management algorithms based on this models. To cope with these issues, we first propose in this paper a non-homogenous Markov chain model based on experimental data, which can accurately describe the solar energy harvesting process in contrast to traditional predictable energy models. Due to different timescale between the energy harvesting process and the wireless data transmission process, we propose a general framework of multiple timescale Markov decision process (MMDP) model to formulate the joint energy scheduling and transmission control problem under different timescales. We then derive the optimal control policies via a joint dynamic programming and value iteration approach. Extensive simulations are carried out to study the performances of the proposed schemes

Emergence of hysteresis loop in social contagions on complex networks

Understanding the spreading mechanisms of social contagions in complex network systems has attracted much attention in the physics community. Here we propose a generalized threshold model to describe social contagions. Using extensive numerical simulations and theoretical analyses, we find that a hysteresis loop emerges in the system. Specifically, the steady state of the system is sensitive to the initial conditions of the dynamics of the system. In the steady state, the adoption size increases discontinuously with the transmission probability of information about social contagions, and trial size exhibits a non-monotonic pattern, i.e., it first increases discontinuously then decreases continuously. Finally we study social contagions on heterogeneous networks and find that network topology does not qualitatively affect our results.This work was funded in part by the National Key Research and Development Program (Grant No. 2016YFB0800602), the National Natural Science the Foundation of China (Grant Nos 61472045,61573067), and the China Scholarship Council. (2016YFB0800602 - National Key Research and Development Program; 61472045 - National Natural Science the Foundation of China; 61573067 - National Natural Science the Foundation of China; China Scholarship Council)Published versio

Cyber Insurance for Heterogeneous Wireless Networks

Heterogeneous wireless networks (HWNs) composed of densely deployed base stations of different types with various radio access technologies have become a prevailing trend to accommodate ever-increasing traffic demand in enormous volume. Nowadays, users rely heavily on HWNs for ubiquitous network access that contains valuable and critical information such as financial transactions, e-health, and public safety. Cyber risks, representing one of the most significant threats to network security and reliability, are increasing in severity. To address this problem, this article introduces the concept of cyber insurance to transfer the cyber risk (i.e., service outage, as a consequence of cyber risks in HWNs) to a third party insurer. Firstly, a review of the enabling technologies for HWNs and their vulnerabilities to cyber risks is presented. Then, the fundamentals of cyber insurance are introduced, and subsequently, a cyber insurance framework for HWNs is presented. Finally, open issues are discussed and the challenges are highlighted for integrating cyber insurance as a service of next generation HWNs.Comment: IEEE Communications Magazine (Heterogeneous Ultra Dense Networks

Discrimination of Xihulongjing tea grade using an electronic tongue

Five grades of Xihulongjing tea (grade: AAA, AA, A, B and C, from the same region and processed with the same processing method) were discriminated using -Astree II electronic tongue (e-tongue) coupled with pattern recognition methods including principal component analysis (PCA), canonical discriminant analysis (CDA) and back-propagation neural networks (BPNN). Results of PCA and CDA showed that the grades of the samples were discriminated with the exception of a few overlap samples between grade AA and grade A. The discrimination of accuracy of the training sample set and the predicted sample set was 95.7 and 97.5%, respectively, by the analysis of BPNN. 92.9% of all the crossvalidated training sample set and 100% of the predicted sample set were exactly grouped by CDA. The sensory evaluation of the samples was consistent with the evaluation based on the e-tongue. Theresults show that the e-tongue is a potential tool to identify the tea quality