Cover and Pack Inequalities for (Mixed) Integer Programming

We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0-1 knapsack set, the mixed 0-1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a unified presentation of the inequalities based on covers and packs and highlight the connections among them. The focus of the paper is on recent research on the use of superadditive functions for the analysis of knapsack polyhedra. We also present some new results on integer knapsacks. In particular, we give an integer version of the cover inequalities and describe a necessary and sufficient facet condition for them. This condition generalizes the well-known facet condition of minimality of covers for 0-1 knapsacks. The author is supported, in part, by NSF Grants 0070127 and 0218265.     

Higher Power Residue Codes and the Leech Lattice

We shall consider higher power residue codes over the ring Z₄. We will briefly introduce these codes over Z₄ and then we will find a new construction for the Leech lattice. A similar construction is used to construct some of the other lattices of rank 24.     

Weak compactness of certain sets of measures

For a compact Hausdorff space and a Montel Hausdorff locally convex space , let being the uniform topology. We determine the necessary and sufficient conditions for an equicontinuous to be -compact. Special results are obtained when is an -space or a -Stonian space.

     

Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms

We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables. We develop a lifting theory for the continuous variables. In particular, we present a pseudo-polynomial algorithm for the sequential lifting of the continuous variables and we discuss its practical use.This research was supported by NSF grants DMI-0100020 and DMI-0121495Mathematics Subject Classification (2000): 90C11, 90C27     

The optimal differentiation basis and liftings of

There is an optimal way to differentiate measures when given a consistent choice of where zero limits must occur. The appropriate differentiation basis is formed following the pattern of an earlier construction by the authors of an optimal approach system for producing boundary limits in potential theory. Applications include the existence of Lebesgue points, approximate continuity, and liftings for the space of bounded measurable functions - all aspects of the fact that for every point outside a set of measure , a given integrable function has small variation on a set that is ``big' near the point. This fact is illuminated here by the replacement of each measurable set with the collection of points where the set is ``big', using a classical base operator. Properties of such operators and of the topologies they generate, e.g., the density and fine topologies, are recalled and extended along the way. Topological considerations are simplified using an extension of base operators from algebras of sets on which they are initially defined to the full power set of the underlying space.

     

二维提升的CDF(1,3)小波结合改进的SPIHT的渐进性无损图像压缩方法

针对传统小波变换计算复杂的缺点和多级树集合分裂算法(SPIHT)编码过程重复运算、存储量大的问题,提出了一种二维提升的CDF(1,3)小波结合改进的SPIHT的渐进性无损图像压缩方法。对整数CDF(1,3)双正交小波变换实现二维提升,利用提升的小波对图像做变换,提高了运算速度、便于硬件实现。对SPIHT算法加以改进,根据各个子图像的不同特点,改变扫描路线,采用四路并行分块处理的方法,提高了编码速度,降低了编解码过程的运算复杂度和时间消耗。利用提升的CDF(1,3)小波变换结合改进的SPIHT实现了渐进性无损图像压缩,证明了二维提升方案的有效性。     

基于相对失真测度的感兴趣区域编码

提出了一种基于相对失真测度的率失真斜率提升感兴趣区域编码算法.通过计算感兴趣区域与背景之间的相对失真确定感兴趣区域的率失真斜率提升幅度,使得实际感兴趣区域与背景的相对失真尽可能逼近给定值.本算法不需要对小波域的系数进行比特平面提升,而是通过提升率失真斜率实现.解码器不需要进行小波域系数的逆提升,且提升大小不受比特平面限制, 可以精确到步骤.适合给定感兴趣区域与背景之间的相对失真,也适合交互式图像等感兴趣区域编码.相对失真改变时,不需要重新对图像进行比特平面编码,只要提升感兴趣区域斜率然后重新组织码流即可, 避免了比特平面提升的感兴趣区域编码算法缺陷.仿真结果表明,本算法能够精确根据给定感兴趣区域与背景的平均相对失真组织码流,实际结果十分接近给定值.     

基于提升小波的红外图像去噪算法与实现

介绍了提升小波原理,以及把提升小波应用于红外图像去噪的算法.研究了提升小波的硬件实现方法,根据FPGA器件具有快速逻辑处理能力的特点,采用流水线的加法及桶状移位操作指令,设计了一种适合FPGA实现的提升小波图像去噪的硬件结构.实验结果表明,以FPGA来实现基于小波变换的图像去噪方法与传统方法相比,在速度方面得到了很大的提高.     

一类正的K_0-群同态的提升

设0→I→A■B→0为C~*-代数扩张,其中I为AF-代数,A为有单位元的C~*-代数.设D为一类AF-代数.本文利用投影元的保序提升和K_0-群的归纳极限来研究K_0(D)到K_0(B)的群同态被K_0(π)提升的问题.从而得到,如果Φ为从K_0(D)到K_0(B)的正的群同态且Φ([1_D]_0)=[1_B]_0,则Φ可以被K_0(π)提升.     

基于提升小波与灰色神经网络的光纤陀螺振动误差建模

光纤陀螺在振动环境下的输出具有噪声大、漂移强的特性,必须建立合理的振动误差模型,以便使用精确的算法进行补偿,从而提高光纤陀螺的输出精度。文中首先使用Allan方差分析法分析了某型号的数字闭环光纤陀螺在振动环境下的输出信号,随后利用提升小波分离出了光纤陀螺误差模型中的白噪声及漂移误差,并提出了基于灰色理论和RBF神经网络的漂移误差建模方法。仿真结果表明,相较于传统的RBF神经网络模型,基于提升小波的灰色RBF神经网络的漂移误差建模方法能有效滤除白噪声,并将漂移误差模型的建模精度提高了一倍左右。该方法能够有效提高光纤陀螺在振动环境下的输出精度,对光纤陀螺在振动环境下的误差研究具有重要指导意义。