A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.     

Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by $\pi (G,R)$. The edge-forwarding index $\pi (G)$ is the minimum of $\pi (G,R)$ over all possible all-to-all routings R, and the arc-forwarding index $\overrightarrow{\pi }(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible R, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs.     

Evaluation of Multi-Objective Optimization Algorithms for NMR Chemical Shift Assignment

An automated NMR chemical shift assignment algorithm was developed using multi-objective optimization techniques. The problem is modeled as a combinatorial optimization problem and its objective parameters are defined separately in different score functions. Some of the heuristic approaches of evolutionary optimization are employed in this problem model. Both, a conventional genetic algorithm and multi-objective methods, i.e., the non-dominated sorting genetic algorithms II and III (NSGA2 and NSGA3), are applied to the problem. The multi-objective approaches consider each objective parameter separately, whereas the genetic algorithm followed a conventional way, where all objectives are combined in one score function. Several improvement steps and repetitions on these algorithms are performed and their combinations are also created as a hyper-heuristic approach to the problem. Additionally, a hill-climbing algorithm is also applied after the evolutionary algorithm steps. The algorithms are tested on several different datasets with a set of 11 commonly used spectra. The test results showed that our algorithm could assign both sidechain and backbone atoms fully automatically without any manual interactions. Our approaches could provide around a 65% success rate and could assign some of the atoms that could not be assigned by other methods.     

A method for C(alpha) direct-detection in protonless NMR

Attempts are made to efficiently decouple (13)C nuclei without significant loss of coherence during the application of the decoupling package. Such attempts are based on the S(3)E spin-state selection method. A newly developed double S(3)E (DS(3)E) is particularly efficient for C(alpha) detection for proteins as large as 480 kDa.     

一种新的六氢喹啉衍生物的NMR研究

应用¹H NMR,¹³C NMR,DEPT,¹H-¹H COSY,HSQC,HMBC等多种NMR实验测试分析方法,确证了一种新的六氢喹啉衍生物2,7,7-三甲基-4-(4-羟基-3-甲氧基）苯基-5-氧代-1,4,5,6,7,8-六氢喹啉-3-羧酸甲酯的结构,并对它的¹H、¹³C信号进行了归属.     

Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.     

Comprehensive 1H and 13C NMR assignment of 13 protobassic acid saponins

This study aimed to carry out complete ¹H and ¹³C NMR assignment of 13 protobassic acid saponins, including arganins A–C ( 1 – 3 ) and F ( 4 ), butyrosides B–D ( 5 – 7 ), tieghemelin ( 8 ), 3′-O-glucosyl-arganin C ( 9 ), Mi-saponins A–C ( 10 – 12 ), and mimusopsin ( 13 ), recorded in methanol-d₄. This was accomplished by the analysis of high-resolution one-dimensional (1D) NMR (¹H and ¹³C), two-dimensional (2D) NMR (¹H–¹H COSY, HSQC, and HMBC), and selectively excited 1D TOCSY spectra. Before this study, ¹H and ¹³C NMR data of arganins A–C ( 1 – 3 ) and F ( 4 ) were partially assigned. Our effort leads to their complete assignment, especially the glycon residue, and revises some reported data. Some revisions of the ¹H and ¹³C NMR data in the glycon part of butyroside C ( 6 ), tieghemelin ( 8 ), Mi-saponin A ( 10 ), and mimusopsin ( 13 ) were made. Those data of butyrosides B and D ( 5 & 7 ) and Mi-saponin B ( 11 ), which had not been recorded in methanol-d₄, are provided. In addition, the ¹H and ¹³C NMR data of Mi-saponin C ( 12 ) are reported for the first time. These data, being recorded in methanol-d₄, should be more friendly for use as a reference for identifying the related triterpenoid saponins.     

Cheminformatics in MS-based environmental exposomics: Current achievements and future directions

Compound annotation using MS/MS data is the major bottleneck in interpretation of mass spectrometry data during non-targeted screening and suspect screening exposomics studies. Apart from compound identification using available databases or mass spectral libraries, the true challenge comes when completely new compounds have to be identified. Along with recent advances in MS instrumentation that set grounds to a new revolutionary age in environmental exposomics, a multitude of cheminformatics annotation approaches has been developed. Herein, we review the basic principles of the cutting-edge cheminformatics MS-based approaches employed in eco-exposome annotation.We give a solid background discussing the eco-exposome concept in relation to the advances in MS instrumentation, and define the three crucial cheminformatics tasks used in the eco-exposome annotation: molecular formula assignment, compound prioritization and compound annotation. The basic principles of compound annotation are discussed, which are based on three approaches of utilizing structural information inherent to MS data. These involve direct, indirect and joint annotation approaches. We assess their performance through the ability to annotate eco-exposome constituents. We discuss future perspectives and give directions to new annotation strategies and performance evaluation protocols aiming to solve current issues hampering the incorporation of cheminformatics annotation approaches in regular eco-exposome annotation workflows.     

脯氨酸类N-酰胺衍生物的核磁共振研究

脯氨酸类衍生物结构独特,鲜有报道利用核磁共振（nuclear magnetic resonance,NMR）技术对氨基酸的手性进行鉴别.利用多种NMR技术:1H NMR、1H-1H同核位移相关谱（1H-1H COSY）、1H-1H质子全相关谱（1H-1H TOCSY）、1H-1H核Overhauser效应谱（1H-1H NOESY）、13C NMR、无畸变的极化转移增强法（DEPT135°）、1H-13C检出1H的异核单量子相干（1H-13C HSQC）和1H-13C检出1H的异核多键相关（1H-13C HMBC）,对脯氨酸类N-酰胺衍生物两种构象异构体的1H和13C NMR进行了全归属,确定了室温下在二甲基亚砜（DMSO）中L型和D型的顺反异构体以相同的比例同时存在.     

非平衡指派模型及其在航空机务维修中的应用

非平衡指派问题是最优平衡指派问题的推广与深化,在航空机务维修工作中,维修任务的合理配置对及时完成维修任务,保障训练作战计划非常重要.本文从装备完好率和人力资源的优化配置角度出发,按照不考虑维修任务等待时间和考虑维修任务等待时间两种情况分别建立了非平衡指派优化模型,并给出了这两种情况下效益矩阵的构造方法,进而将优化模型转化为最优平衡指派模型进行求解,从而为航空机务维修工作中维修人员的优化配置提供了一种科学、合理的决策方法.