Spectrum of a Rudin–Shapiro-like sequence

We show that a recently proposed Rudin–Shapiro-like sequence, with balanced weights, has purely singular continuous diffraction spectrum, in contrast to the well-known Rudin–Shapiro sequence whose diffraction is absolutely continuous. This answers a question that had been raised about this new sequence.     

Real‐Time Measurement of the Size Distribution of Diesel Exhaust Particles using a Portable 4‐stage Electrical Low Pressure Impactor

For this study, a 4 stage electrical low pressure impactor was designed to measure the real‐time size distribution of diesel particulate matter (DPM). For the performance evaluation, sodium chloride (NaCl) particles and dioctyl sebacate (DOS) particles were used. After evaluating the collection efficiency of each stage of the impactor, the size distributions of test particles were estimated using electrical current data and their inversion algorithm, and this was found to agree with the results obtained by a scanning mobility particle sizer (SMPS). For measurement of DPM, a common‐rail direct injection (CRDI) diesel engine, for engine speeds of 1,200 rpm and 1,500 rpm at 2.7 kgf·m, was used. Therefore, it was found that the size distribution of the DPM could be easily obtained, with the currents measured by the impactor and the data inversion algorithm, in less than 5 seconds. Furthermore, the effective density of the DPM could be obtained using the calculated results and the SMPS data.     

Parallel Schwarz alternating methods for anisotropic diffusion of speckled medical images

This paper deals with ultrasound medical image processing, particularly to filter the noise while preserving the edges and structures of information. The mathematical processing consists in solving by a numerical way a nonlinear evolutive boundary value problem. Several numerical semi-implicit time marching schemes are considered and analyzed. At each time step, parallel synchronous or asynchronous Schwarz alternating methods are used to solve the linear system and its convergence is studied. Lastly, the results of sequential and parallel simulations are presented.      

字符串匹配算法在DNA序列比对中的应用

高通量测序技术的飞速发展让生物信息领域迎来了大数据时代。新技术在提供海量生物遗传信息的同时,也给分析这些数据带来了新的挑战。DNA序列比对是信息分析流程中的关键步骤,为后续的变异检测提供序列比对信息。2015“深圳杯”数学建模夏令营B题以DNA序列比对为研究课题,希望参赛学生给出序列快速比对的最佳方案。本文简要点评了各参赛队伍的解答情况,然后介绍了现有DNA序列比对软件中用到的算法和数据结构。     

汽车租赁调度多目标优化模型

本文考虑一个周期的汽车租赁调度问题,在直接调运的前提下,首先以汽车租赁公司的总收益最大和总短缺损失最小为目标,建立多目标优化模型;然后提出了基于启发式的双层排序综合择优算法;最后对汽车租赁案例进行了实证研究。     

A conformal mapping approach for investigating the free-boundary seepage from symmetric channels

We present a new method to investigate the two-dimensional free-boundary groundwater seepage from symmetric soil channels into a homogeneous isotropic porous medium. We use Levi–Civitá’s function to construct an integral representation for the conformal mapping of the complex potential domain onto the physical flow domain. A genetic algorithm (GA) is used to calculate the coefficients of the Maclaurin series expansion of Levi–Civitá’s function. The coordinates of the points from the channel contour, calculated by means of the integral representation, must satisfy the analytic equation of the contour. We use this condition to define the objective function of the genetic algorithm. Levi–Civitá’s function is afterwards used to calculate the seepage loss, the free lines, the streamlines, the equipotential lines, the isobars and the velocity field. Some examples illustrate the method.     

Rivality index neighbourhood algorithm with density and distances weighted schemes for the building of robust QSAR classification models with high reliable applicability domain

The rivality index (RI) is a normalized distance measurement between a molecule and their first nearest neighbours providing a robust prediction of the activity of a molecule based on the known activity of their nearest neighbours. Negative values of the RI describe molecules that would be correctly classified by a statistic algorithm and, vice versa, positive values of this index describe those molecules detected as outliers by the classification algorithms. In this paper, we have described a classification algorithm based on the RI and we have proposed four weighted schemes (kernels) for its calculation based on the measuring of different characteristics of the neighbourhood of molecules for each molecule of the dataset at established values of the threshold of neighbours. The results obtained have demonstrated that the proposed classification algorithm, based on the RI, generates more reliable and robust classification models than many of the more used and well-known machine learning algorithms. These results have been validated and corroborated by using 20 balanced and unbalanced benchmark datasets of different sizes and modelability. The classification models generated provide valuable information about the molecules of the dataset, the applicability domain of the models and the reliability of the predictions.