Equivalences among Z2s-linear Hadamard codes

The ${\mathbb{Z}}_{2^s}$-additive codes are subgroups of ${\mathbb{Z}}_{2^s}^n$, and can be seen as a generalization of linear codes over ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$. A ${\mathbb{Z}}_{2^s}$-linear Hadamard code is a binary Hadamard code which is the Gray map image of a ${\mathbb{Z}}_{2^s}$-additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some ${\mathbb{Z}}_{2^s}$-linear Hadamard codes of length $2^t$ are equivalent, once $t$ is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to $t=11$, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on $s\in \{2,3\}$, the full classification of the ${\mathbb{Z}}_{2^s}$-linear Hadamard codes of length $2^t$ is established by giving the exact number of such codes.     

Generating 2-Gray codes for ballot sequences in constant amortized time

We present a simple algorithm that generates a cyclic 2-Gray code for ballot sequences. The algorithm generates each ballot sequence in constant amortized time using a linear amount of space. This is the first known cyclic 2-Gray code for ballot sequences that achieves this time bound. In addition, the algorithm can be easily modified to output ballot sequences in binary reflected Gray code order in constant amortized time per string using a linear amount of space.     

铜黄公路某滑坡安全监测及预测研究

铜黄公路全长93.9km,其中遇到的各种滑坡30余处。为了研究这些滑坡的治理效果,对其变形与稳定进行了检测。以川口滑坡检测为例,运用灰色理论建立铜黄滑坡安全监控的GM(2,1)模型,其中非等时距位移序列采用拉格朗日插值函数转变为等时距序列。采用非等时距GM(2,1)和GM(1,1)模型对铜黄公路川口滑坡观测点进行安全预测。非等时距GM(2,1)模型预测滑坡变形精度总体较GM(1,1)模型高。由预测结果可见,治理后该滑坡是稳定的,预测结果和实际吻合良好。     

STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS

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Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

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.     

Integrated Digital Image Correlation considering gray level and blur variations: Application to distortion measurements of IR camera

The acquisition of images with different modalities may involve different alterations with respect to an ideal model. Inhomogeneous brightness and contrast, blur due to non-ideal focusing, distortions are common. It is proposed herein to account for such effects for instance by registering a calibration target image with an actual optical image to measure lens distortions. An Integrated Digital Image Correlation (I-DIC) algorithm is proposed to account for the above artifacts and the algorithm is detailed. The resolution and uncertainty of the technique are first investigated on synthetic images, and then applied to the measurement of distortions for infrared (IR) images. The procedure is shown to reduce drastically the residual level assessing the validity of the image formation model, but more importantly allowing for a much improved registration of images.     

Parallel bucket sorting on graphics processing units based on convex optimization

We found an interesting relation between convex optimization and sorting problem. We present a parallel algorithm to compute multiple order statistics of the data by minimizing a number of related convex functions. The computed order statistics serve as splitters that group the data into buckets suitable for parallel bitonic sorting. This led us to a parallel bucket sort algorithm, which we implemented for many-core architecture of graphics processing units (GPUs). The proposed sorting method is competitive to the state-of-the-art GPU sorting algorithms and is superior to most of them for long sorting keys.