Blind separation of fluorescence spectra using sparse non‐negative matrix factorization on right hand factor

Sparse non‐negative matrix factorization on right side factor (SNMF/R) has better performance in feature extraction than non‐negative matrix factorization. In this work, SNMF/R was first used to separate the overlapped three‐dimensional fluorescence spectra of polycyclic aromatic hydrocarbons mixtures in pure water, lake water, and river water, respectively. It is found that the similarity coefficients between the acquired three‐dimensional spectra and the corresponding reference spectra with random initials are all above 0.80; the recognition rate of SNMF/R is higher than that of PARAFAC and non‐negative matrix factorization algorithms, especially in the case of lake water and river water samples. In addition, SNMF/R does not need any initialization scheme designing during spectra separation. These results demonstrate that SNMF/R is an appropriate algorithm to separate the overlapped fluorescence spectra of polycyclic aromatic hydrocarbons in aquatic environment accurately and effectively. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

The Order of Automorphisms of Quasigroups

We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D.  Stones.     

Perfect 1‐Factorizations of a Family of Cayley Graphs

A 1‐factorization of a graph G is a decomposition of G into edge‐disjoint 1‐factors (perfect matchings), and a perfect 1‐factorization is a 1‐factorization in which the union of any two of the 1‐factors is a Hamilton cycle. We consider the problem of the existence of perfect 1‐factorizations of even order 4‐regular Cayley graphs, with a particular interest in circulant graphs. In this paper, we study a new family of graphs, denoted , which are Cayley graphs if and only if k is even or . By solving the perfect 1‐factorization problem for a large class of graphs, we obtain a new class of 4‐regular bipartite circulant graphs that do not have a perfect 1‐factorization, answering a problem posed in 7 . With further study of graphs, we prove the nonexistence of P1Fs in a class of 4‐regular non‐bipartite circulant graphs, which is further support for a conjecture made in 7 .     

基于非负矩阵分解技术探寻早期阿尔茨海默症基因表达调控网络

本文利用非负矩阵分解(NMF)技术,依据加强算法的稀疏性对患早期阿尔茨海默 症(Alzheimer’s Disease,AD)样本的基因表达数据进行了分析,提取了对疾病早期诊断具有重 要意义的显著基因,样本分类实验结果证明了算法的有效性。在此基础上,结合与炎症反应 有重要关系的 NF-κB 等基因初步建立了与早期 AD 密切相关的基因表达调控网络结构图, 为 AD 致病机理的探询、早期诊断与治疗等提供了有益的途径和方法。     

LU和Cholesky分解的向前舍入误差分析

1引言LU分解可用于解可逆线性系统Ax=b．作为数值代数领域中的重要工具,其舍入误差分析一直为众多学者所关注．事实上,长方矩阵的LU分解也有着广泛的应用,如,确定矩阵数值秩的LU分解(RRLU)[5,7],解等式约束最小二乘问题的直接消去法[3]等问题中都涉及到长方矩阵的LU分解．当A∈Rm×n且秩r≤min{m,n},则在考虑A的LU分解时[4],一般需要确定置换阵∏L,∏R使得A(1):=∏L-A∏R的LU分解能持续qr步,这里当A为亏秩矩阵时,qr=r;否贝qr=r-1．在．A(1)的LU分解的第k(k≤qr)步,需执行如下Gauss消去过程:     

余因子系的等价定义与树形表示

利用图论的方法,讨论了余因子系的性质,分析了余因子系的等价定义,给出了几种重要的等价形式.并利用树的特殊结构,给出了余因子系的树形表示,为引入多项式系各种形式的结式矩阵做了理论准备.     

Revisiting radiative leptonic B decay

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist \begin{document}$B$\end{document}-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors \begin{document}$F_{A,V}$\end{document} in the \begin{document}$B \to \gamma \ell\nu$\end{document} decay at leading power in \begin{document}$\Lambda/m_b$\end{document}. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by \begin{document}$1/E_\gamma$\end{document} and \begin{document}$1/m_b$\end{document}), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.     

NONCOMMUTATIVE ORLICZ-HARDY SPACES

Let(Φ, Ψ) be a pair of complementary N-functions and HΦ(A) and HΨ(A) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg and innerouter type factorization theorems of Hp(A) to this case.