Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Poisson limits for a hard-core clustering model

Let X_1n,…,X_>nn denote the locations of n points in a bounded, γ-dimensional, Euclidean region D_n which has positive γ-dimensional Lebesgue measure μ(D_n). Let {Y_n(r): r > 0} be the interpoint distance process for these points where Y_n(r) is the number of pairs of points(X_in, X_in) which with i < j have Euclidean distance 6X_in ? X_>in6 < r. In this article we study the limiting distribution of Y_n(r) when n → ∞ and μ(D_n) → ∞, and the joint density of X_1n,…,X_nnis of the form

where r₀ is a positive constant and C_n is a normalizing constant. These joint densities modify the Strauss [11] clustering model densities by introducing a hard-core component (no two points can have 6X_in ? X_in6 < r₀) found in the Matérn [4] models. In our main result we show that the interpoint distance process converges to a non-homogeneous Poisson process for r values in a bounded interval 0 < r₀ < r < r₀₀ provided sparseness conditions discussed by Saunders and Funk [9] hold. The sparseness conditions which require $\text{μ(D}{}_{\mathrm{n}}\text{)}\text{n}{}^2$ converges to a positive constant and the boundary of D_n is negligible are essentially equivalent to requiring that although the number of points n is large the region is large enough so that the points are sparse in this region. That is, it is rare for a point to have another point close to it. These results extend results for v ? 0 given by Saunders and Funk [9] where it is shown that without the hard core component such results do not hold for v > 0. Statistical applications are discussed.     

变形镜高斯函数指数对迭代法自适应光学系统的影响

基于613单元自适应光学系统, 描述了迭代矩阵和斜率响应矩阵的特性. 在变形镜驱动器间距和交连值不变的情况下, 研究了变形镜高斯函数指数对迭代矩阵和斜率响应矩阵稀疏度的影响, 对自适应光学系统稳定性和校正能力的影响. 研究表明, 迭代矩阵和斜率响应矩阵的稀疏度随着变形镜高斯函数指数的增大而减小. 高斯函数指数过大或者过小都会影响自适应光学系统的稳定性和校正能力. 最后, 综合迭代矩阵和斜率响应矩阵的稀疏度、自适应光学系统的稳定性和校正能力, 给出了合理的变形镜高斯函数指数的取值范围.     

交连值对斜率响应矩阵和迭代矩阵稀疏度的影响

基于529单元自适应光学(AO)系统,分析了变形镜到哈特曼波前传感器的斜率响应矩阵的稀疏特性、波前复原中迭代矩阵的稀疏特性.在变形镜驱动器间距不变的条件下,研究了驱动器交连值对斜率响应矩阵稀疏度、迭代矩阵稀疏度以及AO系统校正能力的影响.研究表明,斜率响应矩阵和迭代矩阵的稀疏度随交连值的增大而减小;交连值过大或者过小都会影响AO系统的稳定性和校正能力.最后,综合斜率响应矩阵和迭代矩阵的稀疏度、系统稳定性和校正能力,给出了交连值的合理取值范围.     

美式看跌期权定价中的小波方法

本文采用有限差分格式和 Daubechies正交小波 ,提出了一种求解 Black- Scholes方程数值解新算法 .为美式看跌期定价提供了一条新的途径 .利用小波基的自适应性和消失矩特性 ,使偏微分算子矩阵和小波级数稀疏化 ,大大减少了计算量 .     

自适应光学系统中波前重建的快速求解

当激光在大气中传输时,光通道中介质折射率的随机变化,引起激光波前的畸变,导致激光的扭曲、畸变,降低了光学系统的性能.波前畸变可以由自适应光学进行补偿、校正.为了进行实时补偿,补偿必须能快速响应波前畸变的信息.基于这一思想,文章对有关波前重建的三种基本方式进行研究.利用变化矩阵的稀疏特性,根据各自的特点发展了存储单元少、反映速度快的计算方案.并分别对不同形状的波前进行了重建,以示对方案的检验.