Meyniel's conjecture holds for random d‐regular graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In a separate paper, we showed that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. The result was obtained by showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. In this paper, this deterministic result is used to show that the conjecture holds asymptotically almost surely for random d‐regular graphs when d = d(n) ≥ 3.     

Conditionally Specified Space-Time Models for Multivariate Processes

This article proposes a class of conditionally specified models for the analysis of multivariate space-time processes. Such models are useful in situations where there is sparse spatial coverage of one of the processes and much more dense coverage of the other process(es). The dependence structure across processes and over space, and time is completely specified through a neighborhood structure. These models are applicable to both point and block sources; for example, multiple pollutant monitors (point sources) or several county-level exposures (block sources). We introduce several computational tricks that are integral for model fitting, give some simple sufficient and necessary conditions for the space-time covariance matrix to be positive definite, and implement a Gibbs sampler, using Hybrid MC steps, to sample from the posterior distribution of the parameters. Model fit is assessed via the DIC. Predictive accuracy, over both time and space, is assessed both relatively and absolutely via mean squared prediction error and coverage probabilities. As an illustration of these models, we fit them to particulate matter and ozone data collected in the Los Angeles, CA, area in 1995 over a three-month period. In these data, the spatial coverage of particulate matter was sparse relative to that of ozone.     

Using random forest to classify T-cell epitopes based on amino acid properties and molecular features

T-lymphocyte (T-cell) is a very important component in human immune system. T-cell epitopes can be used for the accurately monitoring the immune responses which activation by major histocompatibility complex (MHC), and rationally designing vaccines. Therefore, accurate prediction of T-cell epitopes is crucial for vaccine development and clinical immunology. In current study, two types peptide features, i.e., amino acid properties and chemical molecular features were used for the T-cell epitopes peptide representation. Based on these features, random forest (RF) algorithm, a powerful machine learning algorithm, was used to classify T-cell epitopes and non-T-cell epitopes. The classification accuracy, sensitivity, specificity, Matthews correlation coefficient (MCC), and area under the curve (AUC) values for proposed method are 97.54%, 97.22%, 97.60%, 0.9193, and 0.9868, respectively. These results indicate that current method based on the combined features and RF is effective for T-cell epitopes prediction.     

基于邻域贡献权值细化的圆心亚像素定位算法

针对传统的圆心算法过程复杂、定位精度受初始边缘提取效果影响较大等问题,提出了一种基于邻域贡献权值细化的圆心亚像素定位算法。首先引入邻域贡献权值系数,改进传统非极大值抑制法,细化边缘;然后在边缘点的梯度方向对灰度值进行高斯拟合,确定亚像素边缘位置;最后针对边缘突变点提出了基于随机抽样一致的最小二乘法来拟合圆心。实验结果表明,该算法具有较好的精度和稳定性,圆心的提取精度可以达到0.1个像素。     

随机变量变换分布的若干推论及应用

给出了随机变量变换分布的三个推论，这些推论提供了在不同变换下求二维随机变量的函数的概率密度的计算公式，实例应用表明，这些公式应用简便，灵活，实用．     

Book review of spectral theory of linear operators and spectral systems in banach algebras,operator theory: advances and applications,Vladimir Müller,Birkhäuser Verlag,Basel-Boston-Berlin, 2003, Volume 139, 381 pages. ISBN 3-7643-6912-4

We explore how randomization can help asymptotic convergence properties of simple directional search-based optimization methods. Specifically, we develop a cheap, iterative randomized Hessian estimation scheme. We then apply this technique and analyse how it enhances a random directional search method. Then, we proceed to develop a conjugate-directional search method that incorporates estimated Hessian information without requiring the direct use of gradients.     

Supramolecular complexes of poly(3‐Hexylthiophene)‐block (and random)‐poly[3‐(2‐(6‐carboxyhexyl)methyl)thiophene] copolymers with perylene bisimide

Block and random copolymers of poly(3‐hexylthiophene) and poly[3‐(2‐(6‐carboxyhexyl)methyl)thiophene] with side‐chain carboxylic functionality ((P3HT‐b‐P3COOH) and (P3HT‐r‐P3COOH) were developed by Grignard Metathesis (GRIM) polymerization. The carboxylic functionality was introduced in the side chain via the oxazoline route. Both the block and random polythiophene copolymers were complexed with pyridine functionalized perylene bisimide to obtain supramolecular block and random polymer complexes. The complex formation in both systems was confirmed by ¹H NMR, WXRD and SAXS studies. An expansion of d spacing upon complex formation was observed in both the block and random copolymer, which could be traced by WXRD. Hole and electron mobilities measured for the supramolecular complexes indicated values which were higher by an order of magnitude for the supramolecular block complex (μ_h ≈ 2.9 × 10⁻⁴ cm²/Vs; μ_e ≈ 3.1 × 10⁻⁶ cm²/Vs) as compared to the random (μ_h ≈ 1.4 × 10⁻⁵ cm²/Vs; μ_e ≈ 4.7 × 10⁻⁷ cm²/Vs) copolymer. These results are indicative of the higher degree of disorder prevailing in the films of random copolymer system compared to the block copolymer. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1574–1583     

A scaling limit for the length of the longest cycle in a sparse random digraph

We discuss the length of the longest directed cycle in the sparse random digraph , constant. We show that for large there exists a function such that a.s. The function where is a polynomial in . We are only able to explicitly give the values , although we could in principle compute any .     

An improved watermarking method based on double random phase encoding technique

An improved watermarking method, based on the double random phase encoding technique and the cascaded-phases iterative algorithm and random-phase-shift algorithm, is proposed. This method can significantly reduce the needs of watermarking information storage for different multimedia products, and provide a reasonable criterion of determining the authenticity of a product for the copyright owner. This method can also be applied to track the source of copies. The effectiveness of this method was verified through numerical simulations.     

Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg