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.     

Channel capacities via p-summing norms

In this paper we show how the metric theory of tensor products developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in Shannon's information theory. Furthermore, in the last years Shannon's theory has been fully generalized to the quantum setting, and revealed qualitatively new phenomena in comparison. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. These capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. Our approach to restricted capacities is based on tools from functional analysis, and in particular the notion of p  -summing maps going back to Grothendieck's work. Pisier's noncommutative vector-valued _Lp$L_p$ spaces allow us to establish the new connection between functional analysis and information theory in the quantum setting.     

Non-integrability vs. integrability in pentagram maps

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.     

Comparison of criteria used to access carcinogenicity in CPANN QSAR models versus the knowledge-based expert system Toxtree

The primary goal of this study was to describe and compare the criteria used to assess carcinogenic activity. The statistically-based predictive quantitative structure–activity relationship (QSAR) models based on the counter propagation artificial neural network (CPANN) algorithm, and knowledge-based expert systems based on a decision tree structural alert (SA) approach (Toxtree application), were considered. The integration of the QSAR (CPANN models) and SAR (Toxtree SA application) approach contributed to the mechanistic understanding of the QSAR model considered. The mapping technique inherent to CPANN Kohonen enables us to relate the similarities or dissimilarities within a congeneric set of chemicals with particular SAs for carcinogenicity. The focus of our investigations was the similarities and dissimilarities of the features used in the QSAR and SAR methods. Due to the complexity of the carcinogenic endpoint, the integration of different approaches allows the models to be improved and provides a valuable technique for evaluating the safety of chemicals.     

振荡Robin混合边值齐次化问题

该文研究了振荡Robin混合边值齐次化问题解的收敛率.该工作的困难之处在于Robin边值上出现的振荡因子以及边界交叉项的处理.该文利用对偶方法巧妙得对振荡积分进行了估计.文中建立了解的H1和L2收敛率,所得结果明显地依赖于维数.该文可以视为将对偶方法和光滑算子,延拓到处理振荡Robin混合边值问题的情形.     

Nonequilibrium Time Reversibility with Maps and Walks

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt’s and Zermélo’s paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the irreversible Second Law of Thermodynamics (Loschmidt’s) as well as periodic in the time (Zermélo’s, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals’ information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here.     

Static Theory for Planar Ferromagnets and Antiferromagnets

Here we generalize the “BBH”-asymptotic analysis to a simplified mathematical model for the planar ferromagnets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathematical justification of dynamical laws for the magnetic vortices formally derived in [1] and [2]. Received March 15, 2001, Accepted May 16, 2001     

全连续弱内向映象的不动点指数及多重不动点定理

本文通过研究与全连续弱内向映象相应的Banach空间中凸闭集上常微分方程解的性质，定义了有界凸闭集上局部Lip.全连续弱内向映象的不动点指数并利用它给出了一个弱内向映象的三解定理．     

基于拉曼光谱法的降糖类药物的判别方法比较

采用了四种聚类方法对降糖类药物拉曼光谱进行了快速、无损判别。采集九种降糖类药品共48个样品的拉曼光谱,经截波、基线校正、平滑、矢量归一化等预处理后,分别采用K-均值、系统聚类法、自组织图(SOM)及PCA-SOM四种不同聚类方法做聚类判别。结果表明,自组织图与K-均值、系统聚类法相比,聚类结果较好,并且SOM结合PCA后的PCA-SOM结果最优。为降糖类药品的快速判别从聚类的角度提供了一种新的方法。     

Collisional effects in the tokamap

Plasmas confined in tokamaks with non-symmetric perturbations are surrounded by a chaotic layer of magnetic field lines that guide charged particles to the tokamak wall. We use an analytical two-dimensional symplectic mapping to study the resulting fractal patterns of field line escape. However, particles may experience several collisions before escaping toward the tokamaks wall. We add a random collisional term to the field line mapping to investigate how the particle collisions modify their escape patterns.