Theoretical study on dispersion compensation in air-core Bragg fibers

In a previous paper we developed a matrix theory that applies to any cylindrically symmetric fiber surrounded by Bragg cladding. Using this formalism, along with Finite Difference Time Domain (FDTD) simulations, we study the waveguide dispersion for the m = 1 mode in an air-core Bragg fiber and showed it is possible to achieve very large negative dispersion values (~ -20,000 ps/(nm.km)) with significantly reduced absorption loss and non-linear effects

Comparative study of air-core and coaxial Bragg fibers: single-mode transmission and dispersion characteristics

Using an asymptotic formalism we developed in an earlier paper, we compare the dispersion properties of the air-core Bragg fiber with those of the coaxial Bragg fiber. In particular we are interested in the way the inner core of the coaxial fiber influence the dispersion relation. It is shown that, given appropriate structural parameters, large single-mode frequency windows with a zero-dispersion point can be achieved for the TM mode in coaxial fibers. We provide an intuitive interpretation based on perturbation analysis and the results of our asymptotic calculations are confirmed by Finite Difference Time Domain (FDTD) simulations

GENOME-WIDE SCREENING FOR FUNCTIONAL FACTORS IN LISTERIA MONOCYTOGENES BIOFILM FORMATION

ABSTRACT Listeria monocytogenes is a ubiquitous gram positive food borne pathogen. Ingestion of L.monocytogenes contaminated food can cause serious infections in immune-compromised persons. In addition to planktonic growth, this pathogen can also grow as biofilms under adverse conditions, which has been proved to be more resistant than its planktonic counterpart to various eradications, such as antibiotic treatments. Compared with the extensively studied intracellular replication mechanisms, L.monocytogenes biofilm developmental process is not well understood. Our research group initiated a systemic study on the molecular mechanisms of L.monocytogenes biofilm formation. A whole genome-scale screening for functional factors involved in L.monocytogenes biofilm development was carried out by means of transposon mutagenesis in combination with microtiter plate assay. 14 mutants with an at least 50% decreased biofilm formation were selected from 10,000 transposon mutants. Transposon locations in these 14 mutants were identified through NEST-PCR and sequencing. The in-frame deletion mutant of two genes, lmo2553 and lmo2554, were generated and showed similar biofilm formation defects as the transposon mutant. The roles of these genes in L.monocytogenes biofilm development will be further pursued in the future

Asymptotic Matrix Theory of Bragg Fibers

We developed a matrix theory that applies to any cylindrically symmetric fiber surrounded with Bragg cladding, which includes both the Bragg fibers and the recently proposed dielectric coaxial fibers. In this formalism,an arbitrary number of inner dielectric layers are treated exactly and the outside cladding structure is approximated in the asymptotic limit. An estimate of the radiation loss of such fibers is given. We compare the asymptotic results with those obtained from the finite difference time domain (FDTD) calculations and find excellent agreement between the two approaches

Travelling Wave Solutions of Nonlinear Dynamical Equations in a Double-Chain Model of DNA

We consider the nonlinear dynamics in a double-chain model of DNA which consists of two long elastic homogeneous strands connected with each other by an elastic membrane. By using the method of dynamical systems, the bounded traveling wave solutions such as bell-shaped solitary waves and periodic waves for the coupled nonlinear dynamical equations of DNA model are obtained and simulated numerically. For the same wave speed, bell-shaped solitary waves of different heights are found to coexist

Understanding the Generalization Performance of Spectral Clustering Algorithms

The theoretical analysis of spectral clustering mainly focuses on consistency, while there is relatively little research on its generalization performance. In this paper, we study the excess risk bounds of the popular spectral clustering algorithms: \emph{relaxed} RatioCut and \emph{relaxed} NCut. Firstly, we show that their excess risk bounds between the empirical continuous optimal solution and the population-level continuous optimal solution have a $\mathcal{O}(1/\sqrt{n})$ convergence rate, where $n$ is the sample size. Secondly, we show the fundamental quantity in influencing the excess risk between the empirical discrete optimal solution and the population-level discrete optimal solution. At the empirical level, algorithms can be designed to reduce this quantity. Based on our theoretical analysis, we propose two novel algorithms that can not only penalize this quantity, but also cluster the out-of-sample data without re-eigendecomposition on the overall sample. Experiments verify the effectiveness of the proposed algorithms

Enhancing The Performance of Membrane Introduction Mass Spectrometry by Organic Carrier and Liquid Chromatographic Separation

A method of membrane introduction mass spectrometry with liquid chromatographic separation (LC/MIMS) for the analysis of volatile organic compounds (VOCs) in water has been developed. The method not only inherited all the advantages of membrane introduction mass spectrometry by flow-injection analysis (FIA/MIMS), but also expanded the application of MIMS to the determination of compounds with identical quantitation ions. Because the quantitation by LC/MIMS is based on two-dimensional identification (retention time (tr) and mass-to-charge ratio ()), it provides a tangible approach to the analysis of VOCs in complex aqueous samples. In this work, a C18 column and a mobile phase (methanol/water) were used for chromatographic separation. A mixture of eighteen VOCs was determined within 28 min. The method has linear dynamic ranges of 3–4 orders of magnitude and sub-ppb-level detection limits. In comparison with the EPA method 524.2 (a purge-and-trap GC/MS method), it requires less analysis time and no sample pretreatment

VIGraph: Self-supervised Learning for Class-Imbalanced Node Classification

Class imbalance in graph data poses significant challenges for node classification. Existing methods, represented by SMOTE-based approaches, partially alleviate this issue but still exhibit limitations during imbalanced scenario construction. Self-supervised learning (SSL) offers a promising solution by synthesizing minority nodes from the data itself, yet its potential remains unexplored. In this paper, we analyze the limitations of SMOTE-based approaches and introduce VIGraph, a novel SSL model based on the self-supervised Variational Graph Auto-Encoder (VGAE) that leverages Variational Inference (VI) to generate minority nodes. Specifically, VIGraph strictly adheres to the concept of imbalance when constructing imbalanced graphs and utilizes the generative VGAE to generate minority nodes. Moreover, VIGraph introduces a novel Siamese contrastive strategy at the decoding phase to improve the overall quality of generated nodes. VIGraph can generate high-quality nodes without reintegrating them into the original graph, eliminating the "Generating, Reintegrating, and Retraining" process found in SMOTE-based methods. Experiments on multiple real-world datasets demonstrate that VIGraph achieves promising results for class-imbalanced node classification tasks

The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box

In this paper, we study the Newtonian limit for relativistic Boltzmann equation in a periodic box $\mathbb{T}^3$. We first establish the global-in-time mild solutions of relativistic Boltzmann equation with uniform-in-$\mathfrak{c}$ estimates and time decay rate. Then we rigorously justify the global-in-time Newtonian limits from the relativistic Boltzmann solutions to the solution of Newtonian Boltzmann equation in $L^1_pL^{\infty}_x$. Moreover, if the initial data of Newtonian Boltzmann equation belong to $W^{1,\infty}(\mathbb{T}^3\times\mathbb{R}^3)$, based on a decomposition and $L^2-L^\infty$ argument, the global-in-time Newtonian limit is proved in $L^{\infty}_{x,p}$. The convergence rates of Newtonian limit are obtained both in $L^1_pL^{\infty}_x$ and $L^{\infty}_{x,p}$.Comment: 56 pages, All comments are welcom