Switching systems with dwell time: Computing the maximal Lyapunov exponent

We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete–continuous) linear switching systems on graphs, in which some modes correspond to discrete actions and some others correspond to continuous-time evolutions. Each discrete action has its own positive weight which accounts for its time-duration. We develop a theory of stability for the mixed systems; in particular, we prove the existence of an invariant Lyapunov norm for mixed systems on graphs and study its structure in various cases, including discrete-time systems for which discrete actions have inhomogeneous time durations. This allows us to adapt recent methods for the joint spectral radius computation (Gripenberg’s algorithm and the Invariant Polytope Algorithm) to compute the Lyapunov exponent of mixed systems on graphs.     

三维荧光结合化学多维校正快速灵敏测定环境水样中的噻菌灵和双酚A

随着经济的高速发展,环境问题正在日益引起人们的广泛关注。在实际生产中,农药和塑化剂长期存在滥用的问题,使其成为最为广泛的环境污染源并对生态环境、食品、人畜等造成严重的危害。针对环境中农药和塑化剂的残留问题,开发一种灵敏、快速的高效检测分析方法,采用三维荧光结合化学计量学方法用于环境水样中噻菌灵（TBZ）与双酚A（BPA）的快速灵敏分析。兼顾了三维荧光分析的灵敏度高、信息丰富及化学多维校正方法“数学分离”的显著优势,仅需要简单的预处理过程即可实现TBZ和BPA的痕量检测。即使分析物之间以及分析物和水样中未知背景干扰之间的光谱存在严重的重叠,基于交替三线性分解（ATLD）算法的二阶校正方法仍能借助其显著的“二阶优势”对其进行解析,并获得可靠的定性定量结果。其中,TBZ在20~200 ng·mL-1范围内线性关系良好（r=0.9999）,而BPA在40~280 ng·mL-1范围内线性关系良好（r=0.999 1）。TBZ和BPA在两种水样中的平均加标回收率分别为96.3%~99.1%和90.0%~90.8%,且标准偏差均低于7.2%。另外,计算品质因子,如灵敏度（SEN）、选择性（SEL）、检测限（LOD）和定量限（LOQ）,评估了该方法的准确性。所得结果均令人满意,表明所提出的方法能够用于环境水样中TBZ和BPA的准确、快速定量分析,为环境中农药和塑化剂的残留问题提供了一种科学有效的监测手段。     

基于遗传算法-支持向量机的兔肝VX2肿瘤光谱鉴别

兔肝VX２肿瘤是一种快速生长的肿瘤模型,可以在多种器官如肝、肺、直肠等快速生长,常用于肿瘤研究。采用可见-近红外高光谱技术对四只兔子的兔肝VX２肿瘤和正常组织进行活体和离体的反射光谱检测,然后采用支持向量机分别实现了二分类(正常肝组织和肝VX2肿瘤组织)和四分类(未出血活体正常肝组织、未出血活体VX2肿瘤组织、出血离体正常肝组织和出血离体肝VX2肿瘤组织)。根据其光谱反射曲线的特征,选择了400～1 800 nm区间的数据为特征变量。为进一步提高分类准确率,分别采用5折交叉验证和遗传算法对支持向量机的核函数参数g和惩罚因子c进行了优化。其中5折交叉验证优化参数和分类结果为：二分类优化的惩罚参数c为4,核函数参数g为0.125 0,其校正集和预测集的准确率都达到了100%;四分类中优化出的参数c为8,g为0.121 1,其校正集和预测集的准确率分别达到了99.242 4%和93.333%。遗传算法优化参数和结果为：二分类中优化的参数c为0.845 6,g为0.062 5,其校正集和预测集的准确率同样都达到了100%;四分类中优化的参数c为5.5307,g为0.068 5,其校正集和预测集的准确率分别达到了99.242 4%和100%。结果显示两种优化方法都取得了很好的效果,遗传算法优化参数对四分类的分类更为精确。为进一步提升算法速度,采用间隔选取变量的方法来不断减少特征变量,最终每隔100 nm谱段选择一个变量,共选择14个谱段作为特征变量。采用遗传算法优化支持向量机参数并对其分类进行了研究,结果表明：二分类和四分类的校正集和预测集结果准确率均为99.242 4%,而且运行时间分别为11.4和20.0 s, 与选择全波段的运行时间：340.3和491.0 s相比, 说明多光谱技术可以进行肝VX2肿瘤组织和正常肝组织的鉴别,且分类准确率可达99%以上,而且运行时间缩短了很多。为未来多光谱技术在未来临床肿瘤诊断中实现肿瘤组织的快速实时在线检测和分类奠定了基础,显示出巨大的应用潜力。     

Apollonian packings as physical fractals

The Apollonian packings (APs) of spheres are fractals that result from a space-filling procedure. We discuss the finite size effects for finite intervals s?∈?[s _min,?s _max] between the largest and the smallest sizes of the filling spheres. We derive a simple analytical generalization of the scale-free laws, which allows a quantitative study of such physical fractals. To test our result, a new efficient space-filling algorithm has been developed which generates random APs of spheres with a finite range of diameters: the correct asymptotic limit s _min/s _max?→?0 and the known APs' fractal dimensions are recovered and an excellent agreement with the generalized analytic laws is proved within the overall range of sizes.     

A segmentation method for noisy photoelectric image

In order to improve the ability of noisy photoelectric image segmentation and satisfy the requirement of human visual apperception, a noisy photoelectric image segmentation method is proposed in this paper. Firstly, the basic principle of FCM algorithm is analyzed in detail. Secondly, on the basis of PCM algorithm, only such pixels affected by noise lesser that centralized in the diagonal area of two-dimensional histogram is actualized image processing, and the probability of the pixel that lie in such area is obtained. Thirdly, objective function, membership matrix and cluster centers are renovated on the basis of PCM algorithm. Finally, experiment contrast between our method and other methods is executed, the results of experiment indicate that our method has relatively better segmentation quality and faster segmentation speed.     

A novel construction algorithm of the LDPC code for high-speed long-haul optical transmission systems

According to the transmission characteristics of high-speed long-haul optical transmission system, the main construction method of Low-Density Parity-Check (LDPC) code for optical transmission system is presented and a novel construction algorithm of LDPC code is proposed, the theoretical analysis shows that the parity check matrix of the LDPC code constructed by the proposed construction algorithm has no four-girth phenomenon, this is also theoretically proved out. Both the novel LDPC(3969,3720) code with 6.69% redundancy and the novel LDPC(8281,7920) code with 4.56% redundancy for optical transmission systems are constructed by using the presented construction method and proposed construction algorithm. The simulation results show that the net coding gain (NCG) of the two novel LDPC codes at the eighteenth iteration for the BER of 10^?12 are respectively 1.63 dB and 1.49 dB more than that of the RS(255,239) code in ITU-T G.975. Moreover, the decoding of the LDPC code in the hardware can parallel be implemented, so the decoding speed of the two novel LDPC codes are very rapid, the complexities of implementing the two novel LDPC codes, compared with the concatenated codes in ITU-T G.975.1, are relatively lower, furthermore, the hardware overhead and storage space can relatively be saved and the computation complexity can be reduced in implementing the hardware in the future. As a result, the two novel LDPC codes can better be suitable for high-speed long-haul optical transmission systems.     

FFT-based convolution algorithm for fast and precise numerical evaluating diffracted field by photon sieve

FFT-based convolution is proposed to numerical solve Fresnel–Kirchhoff integral in Fresnel regime carefully and in a very shorter time in comparison to direct solving convolution. To show its capability, the algorithm was implemented to evaluate amplitude of a diffracted plane wave at the focal plane of photon sieves with different focal lengths. The calculated amplitudes are completely the same calculated via convolving operation but has advantageous of taking very very shorter time. The calculation was also repeated using single-FFT algorithm that produce same result for all ranges either below or upper the sampling criteria and different results in comparison to the other two methods.     

潘宁源放电的全三维电磁粒子模拟/蒙特卡罗碰撞数值算法研究

深入研究潘宁放电的物理机制, 研制了全三维高品质算法粒子模拟软件(PIC), 设计并添加了相应物理情景的蒙特卡罗碰撞模块(MCC), 并对电子、氢分子离子(H₂⁺)、氢正离子(H⁺)、氢三正离子(H₃⁺)同时进行了跟踪, 成功研制了全三维电磁PIC/MCC数值算法. 结合国内研究较热的潘宁放电模型, 对该算法进行模拟验证. 模拟结果显示: 采用有效的滤波算法能抑制电磁数值噪声, 电子能量呈麦克斯韦分布, 由于电子的径向漂移和加速导致离子源顶端H₂⁺产量较大. 关键词： 潘宁离子源 高品质算法 粒子模拟/蒙特卡罗     

一种基于角谱理论的改进型相位恢复迭代算法

进行星间激光通信的光学发射天线光束整形器设计时, 首要解决的问题是根据输入光场及理想的输出光场, 确定整形器的相位分布, 其核心就是相位恢复. 基于角谱传播理论, 在传统 Gerchberg-Saxton (G-S)迭代算法的基础上, 提出了一种幅度梯度加成迭代算法, 给出了算法的详细流程与分析. 与G-S相比, 新算法利用迭代过程, 构建光场幅度反馈回路, 利用梯度搜索最佳迭代路径, 两者的联合作用加速其迭代收敛进程. 数值仿真表明, 新算法的单位迭代次数所引起迭代误差下降的速度是G-S算法的1.7倍, 其收敛速度明显优于G-S算法; 对不同的随机初始相位, 新算法都能进行有效迭代, 表现出适应性强, 且收敛一致性好的优点. 幅度梯度加成迭代算法为复杂光场的高效相位恢复提供了一种新思路, 为设计各种衍射光学元件提供了技术支持. 关键词： 相位恢复 迭代算法 角谱理论 光通信