Mbius-invariant curve and surface energies and their applications

Curvature-based surface energies are frequently used in mathematics, physics, thin plate and shell engineering, and membrane chemistry and biology studies. Invariance under rotations and shifts makes curvature-based energies very attractive for modeling various phenomena. In computer-aided geometric design, the Willmore surfaces and the so-called minimum variation surfaces （MVS） are widely used for shape modeling purposes. The Willmore surfaces are invariant w.r.t conformal transformations （Mbius or conformal invariance）, and studied thoroughly in differential geometry and related disciplines. In contrast, the minimum variation surfaces are not conformal invariant. In this paper, we suggest a simple modification of the minimum variation energy and demonstrate that the resulting modified MVS enjoy Mbius invariance （so we call them conformal-invariant MVS or, shortly, CI-MVS）. We also study connections of CI-MVS with the cyclides of Dupin. In addition, we consider several other conformal-invariant curve and surface energies involving curvatures and curvature derivatives. In particular, we show how filtering with a conformal-invariant curve energy can be used for detecting salient subsets of the principal curvature extremum curves used by Hosaka and co-workers for shape quality inspection purposes.     

Energy-efficient communication in wireless cable sensor networks

In this paper, we introduce a new type of sensor: cable sensor. Unlike traditional point sensors, this type of sensor has a rectangular sensing region with a processor installed on it to do processing and communication. The wireless network formed by this kind of sensor is called wireless cable sensor network (WCSN). We study energy-efficient communication algorithms in WCSNs. We address it in two ways: one is through reducing the total transmission power of processors while maintaining the connectivity of the network and the other is through scheduling cable sensors to let them take turns to go to sleep without affecting the coverage and connectivity of the network. In the first approach, we initially develop a distributed algorithm called DTRNG based on the relative neighbourhood graph. Later we enhance it to Algorithm determine the transmission power by removing the largest edge in CYCles (DTCYC). Mathematical proofs show that Algorithm DTCYC provides an optimal solution that can not only minimise the total processor transmission power but maintain the connectivity of the network as well. In the second approach, we propose a cable mode transition algorithm which determines the minimum number of active sensors to maintain K-coverage as well as K-connectivity required by the application. We discuss the relationship between coverage and connectivity and prove the theorems that lay the foundation for our algorithm. Simulation results demonstrate that our algorithm is efficient in saving energy.     

基于土拱理论的土体坍塌机理研究

在均质堤基或典型双层堤基中由于各种原因形成土洞,其轮廓线是拱形.将土拱近似为三铰拱,应用结构力学中三铰拱合理拱轴线的求解方法,推导了土拱的近似合理拱轴线方程.应用太沙基提出的土拱效应存在条件,推导了在粘性土和无粘性土的土拱的最小拱高和最小拱厚计算公式,分析了拱形参数的合理性及形成稳定土拱的条件.应用本文的土体坍塌机理研...     

输出本质安全型准谐振反激变换器分析

在给定的输入电压和负载变化范围内,分析了准谐振反激变换器的输入电压和负载电阻对其开关频率、输出纹波电压和峰值电感电流的影响,总结了其变化规律,得出了满足电气指标要求的电感和输出滤波电容最小设计值,使得最大输出短路释放能量最小。     

无回路网络中的最小费用流算法

针对无回路网络的特殊性,利用广探法的思想,提出了无回路网络最短路的有效算法,并在此基础之上提出了最小费用流的有效算法.其算法的复杂性分别为o(m)和o(mvo),相比拓扑排序法和最小费用路算法,本文提出的算法更为简练、易懂且复杂性低.     

灰度图像二维最小类方差递推及差分演化的快速分割

为克服Otsu法阈值偏离及一维最小类方差法在含噪图像分割中性能不佳的问题,基于图像灰度级二维直方图,提出一种二维最小类方差快速阈值化方法.通过递推方式计算得到图像前景及背景在不同阈值向量上的灰度级类概率及类均值,在此基础上,应用差分演化算法搜寻使图像类方差最小的阈值向量,并用该阈值向量对图像实施分割.在合成及真实图像上的实验结果表明,采用文中方法可获得良好的分割性能,有效地克服了Otsu法及一维最小类方差法的不足;采用递推及差分演化算法使计算时间大幅降低,可满足工程应用需求.     

四水箱控制系统的性能评价

针对基于最小方差的性能评价准则由于只考虑时滞引起的性能限制,不适合对PID控制回路进行性能评价的问题,本文采用PID能实现最小方差控制准则,对四水箱控制系统进行性能分析,得到的性能指标比传统最小方差准则明显提高,控制器参数大大改善了过程的输出方差。实验表明,PID能实现最小方差准则能够为PID控制器的性能评价提供一个合理的评价基准,更说明其对特定类型控制器性能评价所具有的实际意义。     

Bad:基于最小描述长度的均衡离散化方法

连续数据离散化是数据挖掘分类方法中的重要预处理过程。本文提出一种基于最小描述长度原理的均衡离散化方法,该方法基于最小描述长度理论提出一种均衡的离散化函数,很好地衡量了离散区间与分类错误之间的关系。同时,基于均衡函数提出一种有效的启发式算法,寻找最佳的断点序列。仿真结果表明,在C5.0决策树和Naive贝叶斯分类器上,提出的算法有较好的分类学习能力。     

最小描述长度优化下的医学图像统计形状建模

统计形状模型(SSM)是有效的图像处理与分析方法。为了建立模型,需要从形状样本集中提取出具有对应关系的轮廓采样点集合,这是决定模型性能的关键。传统的手动标定这些点集来确保对应关系枯燥耗时且带有主观性,更难以向高维拓展。对形状建立逐层的多尺度参数表示,基于最小描述长度(MDL),在粗尺度上建立反映点对应程度的目标函数并最小化,提出首先确保粗尺度上具有最优意义的点对应,同时在精尺度上使用最便捷的弧长参数函数来确定特征点,完成感兴趣目标的快速统计形状建模,进而统计分析以验证模型性能,为后续图像分割或定量分析打下基础。实验对肌肉骨骼核磁共振成像(MRI)中椎骨、椎间盘以及半月板等具有临床意义的结构建立了统计形状模型,验证了本文方法与手动取点相比具有客观可重复性且更加简洁,与单一尺度下的MDL方法相比时间效率更高。基于此模型的图像分割与基于手动建模的分割相比,误差相当或有所降低。     

高维空间球集覆盖问题的改进1+ε近似算法

高维空间球集的覆盖问题是指对高维空间中多个球构成的集合S,构造一个直径最小的球来覆盖S中所有已知球。本文提出了球集直径的概念,给出求解球集直径的1/3~(1/2)近似算法。基于此算法求解球集实例集合S的初始核心集,进而给出高维空间球集覆盖问题的1+ε近似算法,算法时间复杂度为O(nd/ε+d2/ε3/2(1/ε+d)lg1/ε)。算法保证核心集中球的个数为O(1/ε),与S中球的个数和空间维数无关。