The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

基于实际路网情境的配送车辆调度优化

在实际路网情境下结合车道数、车道宽度、路口信号灯设置等路网物理特性,构建了考虑综合交通阻抗的多车型车辆调度模型,提出了两阶段求解策略:第1阶段设计了改进A-star精确解算法用于计算客户时间距离矩阵;第2阶段针对实际路网的特征设计了混合模拟退火算法求解调度方案。以大连市某配送中心运营实例进行路网情境仿真试验,结果表明:改进A-star算法较改进Dijkstra算法具有更短的路径搜索时间;混合模拟退火算法求解结果较实际调度方案优化了13.1% 的综合成本;路网增流、区域拥堵和路段禁行三类路网情境均能对配送方案的车辆配置、路径选择、客户服务次序、作业时间和违约费用等5方面内容产生干扰,调度计划的制定需要详细考虑这些因素的变化。     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

Novel matrix invariants for characterization of changes of proteomics maps

Previous studies on mathematical characterization of proteomics maps by sets of map invariants were based on the construction of a set of distance-related matrices obtained by matrix multiplication of a single matrix by itself. Here we consider an alternative characterization of proteomics maps based on a set of matrices characterizing local features of an embedded zigzag curve over the map. It is shown that novel invariants can well characterize proteomics maps. Advantages of the novel approach are discussed.     

Compressed matrix thin film (CMTF)-assisted laser desorption ionization mass spectrometric analysis

The inhomogeneous re-crystallization process of matrix materials is the major concerns associated with matrix assisted laser desorption/ionization (MALDI) analysis. We describe here the approach termed compressed matrix thin film (CMTF) in order to make a uniform matrix deposition. In this approach, solid matrix particles are compressed under 10 MPa of pressure by a compressor that is regularly used in infrared spectroscopic analysis. Then aqueous samples can be deposited on the surface of the matrix film. Major advantages of the CMTF approach are summarized as follows. (1) Reproducible sample preparation procedure. Size and thickness of matrix thin films can be controlled by using a fixed mold.force and known amount of matrix materials. (2) Significantly decreased shot-to-shot variations and enhanced reproducibility. (3) Tolerance for in situ salt washing. Because matrix materials are hydrophobic, salts can be washed away while proteins or peptides are retained on the surface of matrix thin films through hydrophobic interactions. (4) Improved sensitivity. The hydrophobic coating of MALDI sample plate by matrix thin films prevents the spreading of samples across the plate and confines analytes to a small area, leading to increased local concentration. (5) A new means for tissue analysis. Tissue sections can be directly transferred to the uniform surface of matrix materials for reproducible and quantitative comparison of different molecules in different localization. The proposed CMTF should be an enabling technique for mass spectrometric analysis with improved correlations between signal intensities and sample quantities.     

Development of a Sensitive Method for the Determination of 4‐(Methylnitrosamino)‐1‐(3‐pyridyl)‐1‐butanol in Human Urine Using Solid‐phase Extraction Combined with Ultrasound‐assisted Dispersive Liquid–liquid Microextraction and LC‐MS/MS Detection

An efficient and sensitive analytical method based on molecularly imprinted solid‐phase extraction (MISPE) and reverse‐phase ultrasound‐assisted dispersive liquid–liquid microextraction (USA‐DLLME) coupled with LC–MS/MS detection was developed and validated for the analysis of urinary 4‐(methylnitrosamino)‐1‐(3‐pyridyl)‐1‐butanol (NNAL), a tobacco‐specific nitrosamine metabolite. The extraction performances of NNAL on three different solid‐phase extraction (SPE) sorbents including the hydrophilic‐lipophilic balanced sorbent HLB, the mixed mode cationic MCX sorbent and the molecularly imprinted polymers (MIP) sorbent were evaluated. Experimental results showed that the analyte was well retained with the highest extraction recovery and the optimum purification effect on MIP. Under the optimized conditions of MIP and USA‐DLLME, an enrichment factor of 23 was obtained. Good linearity relationship was obtained in the range of 5‐1200 pg/mL with a correlation coefficient of 0.9953. The limit of detection (LOD) was 0.35 pg/mL. The recoveries at three spiked levels ranged between 88.5% and 93.7%. Intra‐ and inter‐day relative standard deviations varied from 3.6% to 7.4% and from 5.4% to 9.7%, respectively. The developed method combing the advantages of MISPE and DLLME significantly improves the purification and enrichment of the analyte and can be used as an effective approach for the determination of ultra‐trace NNAL in complex biological matrices.     

Highly unsaturated pyranone derivatives from the basidiomycete Junghuhnianitida

Four new highly unsaturated pyranone derivatives A–D (1–4), together with one known compound 5 (−)-nitidon were isolated from cultures of the fungus Junghuhnianitida. Planar structures of the new compounds were elucidated on the basis of extensive NMR spectroscopic and mass spectrometric analyses. Absolute configurations of the new compounds were determined on the basis of biosynthetic considerations and quantum chemistry theory. Compound 1 exhibited almost the same cytotoxic activities as cis-platin.     

Determination of four sulfonylurea herbicides in tea by matrix solid‐phase dispersion cleanup followed by dispersive liquid–liquid microextraction

Matrix solid‐phase dispersion combined with dispersive liquid–liquid microextraction has been developed as a new sample pretreatment method for the determination of four sulfonylurea herbicides (chlorsulfuron, bensulfuron‐methyl, chlorimuron‐ethyl, and pyrazosulfuron) in tea by high‐performance liquid chromatography with diode array detection. The extraction and cleanup by matrix solid‐phase dispersion was carried out by using CN‐silica as dispersant and carbon nanotubes as cleanup sorbent eluted with acidified dichloromethane. The eluent of matrix solid‐phase dispersion was evaporated and redissolved in 0.5 mL methanol, and used as the dispersive solvent of the following dispersive liquid–liquid microextraction procedure for further purification and enrichment of the target analytes before high‐performance liquid chromatography analysis. Under the optimum conditions, the method yielded a linear calibration curve in the concentration range from 5.0 to 10 000 ng/g for target analytes with a correlation coefficients (r²) ranging from 0.9959 to 0.9998. The limits of detection for the analytes were in the range of 1.31–2.81 ng/g. Recoveries of the four sulfonylurea herbicides at two fortification levels were between 72.8 and 110.6% with relative standard deviations lower than 6.95%. The method was successfully applied to the analysis of four sulfonylurea herbicides in several tea samples.     

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.