Multivariate Gini Indices

Two extensions of the univariate Gini index are considered:R_D, based on expected distance between two independent vectors from the same distribution with finite meanμ ^d; andR_V, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofR_Das proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.R_Vis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothR_DandR_Vequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:R_Dis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileR_Vis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces.     

Fermentation characteristics and the dynamic trend of chemical components during fermentation of Massa Medicata Fermentata

As a representative of traditionally fermented Chinese medicine, Massa Medicata Fermentata (MMF) shows the functions of invigorating the spleen and stomach and promoting digestion, which plays an important role in the treatment of gastrointestinal diseases. The fermentation mechanism and the key factors that affect the quality of MMF have not been revealed yet, which has become an urgent issue that limits its clinical application. This article aims to systematically and comprehensively reveal the transformation of physical properties and the dynamic trend of chemical components including substrate components, volatile components, and lactic acid as anaerobic fermentation product during MMF fermentation. Along with obvious hyphae growth observed for MMF, the weight of MMF decreased, and the moisture and temperature increased. Through the quantified 14 components from substrate, ferulic acid increased from 45.53 ± 6.94 to 141.89 ± 78.40 μg/g, while glycosides and phenolic acids declined except caffeic acid. Also, within the 66 volatile components analyzed, alcohols and acids increased, while aldehydes and ketones decreased. Lactic acid was not detected in the fermentation substrate, but an apparent increase in lactic acid content was observed along with the increased fermentation days, resulting in 2.54 ± 0.15 mg/g on day 8. Based on the tested components, the fermentation process of MMF was discriminated into three distinct stages by principal component analysis, and an optimal fermentation time of four days was proposed. The results of this study will be of great significance to clarify the characteristics of fermentation and conduce to improving quality standards of MMF.     

Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm

We present a Monte Carlo algorithm to find approximate solutions of the traveling salesman problem. The algorithm generates randomly the permutations of the stations of the traveling salesman trip, with probability depending on the length of the corresponding route. Reasoning by analogy with statistical thermodynamics, we use the probability given by the Boltzmann-Gibbs distribution. Surprisingly enough, using this simple algorithm, one can get very close to the optimal solution of the problem or even find the true optimum. We demonstrate this on several examples.We conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.The author acknowledges stimulating discussions with J. Piút concerning the main ideas of the present paper. The author is also indebted to P. Brunovský, J. erný, M. Hamala, . Peko, . Znám, and R. Zajac for useful comments.     

π-CONJUGATED OLIGOMERS IN SUPRAMOLECULAR CRYSTALS AND THEIR OPTOELECTRONIC FUNCTIONS

Functional organic molecular materials and conjugated oligomers or polymers now allow the low-cost fabrication of thin films for insertion into new generations of electronic and optoelectronic devices. The performance of these devices relies on the understanding and optimization of several complementary processes. Our goal is to discuss the relationship between the molecular stacking structures and their optoelectronic properties that are of importance in all these areas. The concept of intermolecular interaction should be taken here in the special sense that is inter-dipole coupling. Specifically, we will address the impact of inter-dipole interaction between adjacent molecules in aggregate state on the solid-state emission properties.     

Firm size distribution and mobility of the top 500 firms in China,the United States and the world

This paper considers the macroscopic and microscopic statistical features of the top 500 firms in China, the United States and the world, denoted as China 500 (CH500), Fortune 500 (US500) and Fortune Global 500 (FG500). From a macroscopic perspective, the firm size distribution of each category, when measured by revenue, is steadily distributed over the observed period, even during periods of financial crises. As is evidenced by the Gini coefficient, divergences between firm scales are most significant for the CH500. From a microscopic perspective, the underlying micro-dynamics are volatile and often turbulent due to the exit and entry of firms as well as shifts in their revenues and ranks. Such fluctuations, or mobility, are visualized in rank/revenue/share clocks. We also propose a revenue/rank/share mobility index that is a quantitative measurement of mobility. Among these, we find that the share mobility acts as an effective indicator of economic status; where there is a share mobility spike, there is an ailing economy. The share mobility indexes indicate that the 2008 Financial Crisis had little impact on the Chinese economy, while it triggered violent changes in the top 500 firms in the United States and the world.     

Advances in 1,8-Naphthyridines Chemistry

This review reports a broad overview of the synthetic procedures of 1,8-naphthyridines, dibenzo[b,g][1,8]naphthyridine, dibenzo[c,f][1,8]naphthyridine, 1,8-naphthyridine-3-carboxylic acid, 1,8-naphthyridine-3-carboxamide, and 1,8-naphthyridine-3-carbohydrazide compounds and their reactions. The physical properties, spectral data, and biological importance of naphthyridines are discussed.     

IMPORTANCE MEASURE OF CORRELATED VARIABLES IN POLYNOMIAL OUTPUT

为了解决一般工程问题中输出量为多项式情况下相关正态输入变量的贡献识别问题，以二次不含交叉项的多项输出量为例，利用多维相关正态分布及其条件分布的性质，解析地推导了相关正态输入变量对输出量总方差的独立贡献及相关贡献，采用算例验证了所推导的解析表达式的正确性．文中所推导的相关正态变量独立贡献和相关贡献的表达式可直接用于输出量为二次不含交叉项多项式或一次多项式情况下的输入变量贡献的识别，并且为其他新的算法提供了对照解，另外此方法亦可以推广至含交叉项的高阶多项式，解决更为复杂输出量情况下输入量的贡献识别问题．     

A note on random walks with absorbing barriers and sequential Monte Carlo methods

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman–Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.     

Recent Progress in the Chemistry of 2-Tosylacetonitrile

This review is a broad overview of the chemistry of 2-tosylacetonitrile, which considered as a very reactive synthetic compound. The synthetic methods are reported. The reactions of the title compound lead to the preparation of a variety of heterocyclic ring systems, such as five- and six-membered ring systems containing one, two, or three heteroatoms. The reaction mechanisms are discussed.