Mathematical theory for the interface mode in a waveguide bifurcated from a Dirac point

In this paper, we prove the existence of a bound state in a waveguide that consists of two semi-infinite periodic structures separated by an interface. The two periodic structures are perturbed from the same periodic medium with a Dirac point and they possess a common band gap enclosing the Dirac point. The bound state, which is called interface mode here, decays exponentially away from the interface with a frequency located in the common band gap and can be viewed as a bifurcation from the Dirac point. Using the layer potential technique and asymptotic analysis, we first characterize the band gap opening for the two perturbed periodic media and derive the asymptotics of the Bloch modes near the band gap edges. By formulating the eigenvalue problem for the waveguide with two semi-infinite structures using a boundary integral equation over the interface and analyzing the characteristic values of the associated boundary integral operator, we prove the existence of the interface mode for the waveguide when the perturbation of the periodic medium is small

The C0C^0-convergence at the Neumann boundary for Liouville equations

In this paper, we study the blow-up analysis for a sequence of solutions to the Liouville type equation with exponential Neumann boundary condition. For interior case, i.e. the blow-up point is an interior point, Li \cite{Li} gave a uniform asymptotic estimate. Later, Zhang \cite{Zhang} and Gluck \cite{Gluck} improved Li's estimate in the sense of $C^0$-convergence by using the method of moving planes or classification of solutions of the linearized version of Liouville equation. If the sequence blows up at a boundary point, Bao-Wang-Zhou \cite{Bao-Wang-Zhou} proved a similar asymptotic estimate of Li \cite{Li}. In this paper, we will prove a $C^0$-convergence result in this boundary blow-up process. Our method is different from \cite{Zhang,Gluck}.Comment: 26 page

Charge transport and electron-hole asymmetry in low-mobility graphene/hexagonal boron nitride heterostructures

Graphene/hexagonal boron nitride (G/$h$-BN) heterostructures offer an excellent platform for developing nanoelectronic devices and for exploring correlated states in graphene under modulation by a periodic superlattice potential. Here, we report on transport measurements of nearly $0^{\circ}$-twisted G/$h$-BN heterostructures. The heterostructures investigated are prepared by dry transfer and thermally annealing processes and are in the low mobility regime (approximately $3000~\mathrm{cm}^{2}\mathrm{V}^{-1}\mathrm{s}^{-1}$ at 1.9 K). The replica Dirac spectra and Hofstadter butterfly spectra are observed on the hole transport side, but not on the electron transport side, of the heterostructures. We associate the observed electron-hole asymmetry to the presences of a large difference between the opened gaps in the conduction and valence bands and a strong enhancement in the interband contribution to the conductivity on the electron transport side in the low-mobility G/$h$-BN heterostructures. We also show that the gaps opened at the central Dirac point and the hole-branch secondary Dirac point are large, suggesting the presence of strong graphene-substrate interaction and electron-electron interaction in our G/$h$-BN heterostructures. Our results provide additional helpful insight into the transport mechanism in G/$h$-BN heterostructures.Comment: 7 pages, 4 figure

PhaBOX: A web server for identifying and characterizing phage contigs in metagenomic data

Motivation: There is accumulating evidence showing the important roles of bacteriophages (phages) in regulating the structure and functions of microbiome. However, lacking an easy-to-use and integrated phage analysis software hampers microbiome-related research from incorporating phages in the analysis. Results: In this work, we developed a web server, PhaBOX, to comprehensively identify and analyze phage contigs in metagenomic data. To our best knowledge, this is the first web server that supports integrated phage analysis, including detecting phage contigs from the metagenomic assembly, lifestyle prediction, taxonomic classification, and host prediction. Instead of treating the algorithms as a black box, PhaBOX also supports visualization of the essential features for making predictions. With the user-friendly graphical interface, users with or without informatics training can easily use the web server for analyzing phages in microbiome data. Availability: The web server of PhaBOX is available via: https://phage.ee.cityu.edu.hk. The source code of PhaBOX is available via: https://github.com/KennthShang/PhaBOXComment: 5 pages, 1 figur

COMPUTE N-WAY DE-DUPLICATED REACH USING PRIVACY SAFE VECTOR OF COUNTS

Systems and methods for determining the union of the set of user identifiers across multiple publishers are described. Each publisher computing device can use a list of hash functions to hash the respective set of de-duplicated user identifiers. Each publisher can assemble a vector of counts using the respective hashed set of user identifiers, where each coordinate in the vector of counts corresponds to a select of bit positions from the hashed set of user identifiers. Each publisher can add noise to each of the vector of counts to enhance the privacy of the system. Each publisher can transmit the respective vector of counts to a server to compute the union of the multiset without exposing any private or protected information about the user identifiers to any third-party. The server can compute the union of the sets described by the vectors of counts from each of the publishers using at least one of the methods described herein

Phage family classification under Caudoviricetes: A review of current tools using the latest ICTV classification framework

Bacteriophages, which are viruses infecting bacteria, are the most ubiquitous and diverse entities in the biosphere. There is accumulating evidence revealing their important roles in shaping the structure of various microbiomes. Thanks to (viral) metagenomic sequencing, a large number of new bacteriophages have been discovered. However, lacking a standard and automatic virus classification pipeline, the taxonomic characterization of new viruses seriously lag behind the sequencing efforts. In particular, according to the latest version of ICTV, several large phage families in the previous classification system are removed. Therefore, a comprehensive review and comparison of taxonomic classification tools under the new standard are needed to establish the state-of-the-art. In this work, we retrained and tested four recently published tools on newly labeled databases. We demonstrated their utilities and tested them on multiple datasets, including the RefSeq, short contigs, simulated metagenomic datasets, and low-similarity datasets. This study provides a comprehensive review of phage family classification in different scenarios and a practical guidance for choosing appropriate taxonomic classification pipelines. To our best knowledge, this is the first review conducted under the new ICTV classification framework. The results show that the new family classification framework overall leads to better conserved groups and thus makes family-level classification more feasible

Managing rather than Avoiding “Difficulties” in Building Landscape Resilience

Building landscape resilience inspires the cultivation of the landscape’s capacity to recover from disruption and live with changes and uncertainties. However, integrating ecosystem and society within such a unified lens—that is, socio–ecological system (SES) resilience—clashes with many cornerstone concepts in social science, such as power, democracy, rights, and culture. In short, a landscape cannot provide the same values to everyone. However, can building landscape resilience be an effective and just environmental management strategy? Research on this question is limited. A scoping literature review was conducted first to synthesise and map landscape management change based on 111,653 records. Then, we used the Nuozhadu (NZD) catchment as a case study to validate our findings from the literature. We summarised current critiques and created a framework including seven normative categories, or common difficulties, namely resilience for “whom”, “what”, “when”, “where”, “why”, as well as “can” and “how” we apply resilience normatively. We found that these difficulties are overlooked and avoided despite their instructive roles to achieve just landscape management more transparently. Without clear targets and boundaries in building resilience, we found that some groups consume resources and services at the expense of others. The NZD case demonstrates that a strategy of building the NZD’s resilience has improved the conservation of the NZD’s forest ecosystems but overlooked trade-offs between sustaining people and the environment, and between sustainable development for people at different scales. Future researchers, managers, and decision-makers are thereby needed to think resilience more normatively and address the questions in the “seven difficulties” framework before intervening to build landscape resilience.This work was supported by the Key Foundation of China Academy of Engineering Physics, China (Grant No. 2019-ZD-012); the China Postdoctoral Innovative Talents Program (Grant No. BX201907170); and the China Scholarship Council (CSC) (Grant No. 201808190012)