栎黄枯叶蛾幼虫寄主选择机制的光谱学研究

栎黄枯叶蛾(Trabala vishnou gigantina Yang)是一种多寄主林业害虫,在我国常造成多种经济作物的减产甚至绝收。为了对栎黄枯叶蛾幼虫的寄主选择机制进行深入了解,该研究在室内条件下,选取刺槐、柠条、旱柳、山杨、山杏和沙棘六种植物,采用双向选择实验方法,研究了栎黄枯叶蛾幼虫对六种植物的取食偏好性。并利用傅里叶变换红外光谱(FTIR)和X射线衍射(XRD)对六种供选植物的化学成分和物理结构进行了光谱学研究。研究结果表明,当寄主沙棘与山杏、山杨、旱柳、柠条、刺槐存在时,幼虫比较倾向于选择沙棘。栎黄枯叶蛾幼虫对六种植物的取食偏好性的顺序依次为：沙棘>山杏>旱柳>山杨>刺槐>柠条。FTIR谱图显示,六种植物在光谱特征吸收峰的位置、数目及形状上基本相似,差异不明显。通过对三个FTIR吸光度比率的分析后发现：植物中的脂类和多糖含量是影响幼虫取食选择的关键因素。通过XRD检测,测得了六种供试植物的结晶度。通过对结晶度变化趋势和幼虫取食偏好性的对比发现：结晶度可能一定程度上影响植物的适口性,进而影响了幼虫对寄主植物的取食偏好。该研究是光谱学分析方法首次应用于昆虫寄主选择机制的研究,将为深入研究昆虫与植物在分子层面上的互相影响开辟蹊径。     

考虑背景风险的高阶矩三角模糊随机投资组合模型

在已有的大部分投资组合模型中,证券的收益服从随机分布或者模糊分布。然而,在实际的市场中存在大量的不确定性,市场不仅具有内在的风险,也存在由投资者个体差异产生的背景风险。本文推导随机模糊数的高阶矩性质,构建一个考虑背景风险的高矩三角模糊随机投资组合风险模型,采用沪深股市的数据分析背景风险对投资组合的影响。     

Perspectives on CUR decompositions

This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization of CUR decompositions which synergizes these viewpoints and shows that they are indeed the same in the exact decomposition case.     

Maps of several variables of finite total variation. I. Mixed differences and the total variation

Given two points a=(a₁,…,an) and b=(b₁,…,bn) from Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), we study properties of the total variation of f on introduced by the first author in [V.V. Chistyakov, A selection principle for mappings of bounded variation of several variables, in: Real Analysis Exchange 27th Summer Symposium, Opava, Czech Republic, 2003, pp. 217-222] such as the additivity, generalized triangle inequality and sequential lower semicontinuity. This extends the classical properties of C. Jordan's total variation (n=1) and the corresponding properties of the total variation in the sense of Hildebrandt [T.H. Hildebrandt, Introduction to the Theory of Integration, Academic Press, 1963] (n=2) and Leonov [A.S. Leonov, On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle, Math. Notes 63 (1998) 61-71] (n∈N) for real-valued functions of n variables.     

Analysis of the reproduction operator in an artificial bacterial foraging system

In his seminal paper published in 2002, Passino pointed out how individual and groups of bacteria forage for nutrients and how to model it as a distributed optimization process, which he called the Bacterial Foraging Optimization Algorithm (BFOA). One of the major driving forces of BFOA is the reproduction phenomenon of virtual bacteria each of which models a trial solution of the optimization problem. During reproduction, the least healthier bacteria (with a lower accumulated value of the objective function in one chemotactic lifetime) die and the other healthier bacteria each split into two, which then starts exploring the search place from the same location. This keeps the population size constant in BFOA. The phenomenon has a direct analogy with the selection mechanism of classical evolutionary algorithms. In this letter we provide a simple mathematical analysis of the effect of reproduction on bacterial dynamics. Our analysis reveals that the reproduction event contributes to the quick convergence of the bacterial population near optima.     

Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria

This paper deals with two criteria for selection of variables for the discriminant analysis in the case of two multivariate normal populations with different means and a common covariance matrix. One is based on the estimated error rate of misclassification. The other uses Akaike's information criterion. The asymptotic distributions and error rate risks of the criteria are obtained. The result will prove that the two criteria are asymptotically equivalent in the sense of their asymptotic distributions and error rate risks being identical.     

Nuclear spin selection rules in chemical reactions by angular momentum algebra

The detailed selection rules for reactive collisions reported by Quack using molecular symmetry group are derived by using angular momentum algebra. Instead of the representations of the permutation-inversion group for both nuclear spin and rovibronic coordinate wavefunctions, those of the rotation group for nuclear spin wavefunction only are used. The method allows more straightforward derivation of Quack’s results and further extension of the calculation for separating elementary reactions and application to higher proton systems.     

球形阵列自适应网格分层定位算法

刚性球形传声器阵列可以在无空间模糊的条件下进行球谐域数据处理,基于球形阵列的可控波束形成器导向响应功率(SRP)算法定位精度高,但是计算量大,计算效率低。通过将球面致密的全局网格搜索替换为分层搜索策略可以有效减小SRP算法的计算量。提出MRE-SRP算法保持球形阵列SRP定位精度的同时降低计算量,首先通过球谐域MUSIC(SH-MUSIC)算法判断入射声源的数量减小搜索区域;其次将相对熵模型引入球谐域SRP(SH-SRP)定位算法中,提取网格分层前后的信息增益,设计自适应网格选择判据,实现分层多分辨率网格的精准再细分,从而降低计算量。实验验证了所提出算法的性能,结果显示在单双声源定位中,该算法可以实现较高的定位精度,精准选择分层网格,计算量减少75%以上。     

Selections of bounded variation under the excess restrictions

Let X be a metric space with metric d, c(X) denote the family of all nonempty compact subsets of X and, given F,G∈c(X), let e(F,G)=supx∈Finfy∈Gd(x,y) be the Hausdorff excess of F over G. The excess variation of a multifunction , which generalizes the ordinary variation V of single-valued functions, is defined by where the supremum is taken over all partitions of the interval [a,b]. The main result of the paper is the following selection theorem: If,V₊(F,[a,b])<∞,t₀∈[a,b]andx₀∈F(t₀), then there exists a single-valued functionof bounded variation such thatf(t)∈F(t)for allt∈[a,b],f(t₀)=x₀,V(f,[a,t₀))?V₊(F,[a,t₀))andV(f,[t₀,b])?V₊(F,[t₀,b]). We exhibit examples showing that the conclusions in this theorem are sharp, and that it produces new selections of bounded variation as compared with [V.V. Chistyakov, Selections of bounded variation, J. Appl. Anal. 10 (1) (2004) 1-82]. In contrast to this, a multifunction F satisfying e(F(s),F(t))?C(t−s) for some constant C?0 and all s,t∈[a,b] with s?t (Lipschitz continuity with respect to e(⋅,⋅)) admits a Lipschitz selection with a Lipschitz constant not exceeding C if t₀=a and may have only discontinuous selections of bounded variation if a<t₀?b. The same situation holds for continuous selections of when it is excess continuous in the sense that e(F(s),F(t))→0 as s→t−0 for all t∈(a,b] and e(F(t),F(s))→0 as s→t+0 for all t∈[a,b) simultaneously.     

Evolving window zone selection method followed by independent component analysis as useful chemometric tools to discriminate between grapefruit juice, orange juice and blends

This study investigates the use of high resolution ¹H NMR as a suitable alternative to the standard chromatographic method for the determination of adulteration of orange juice (Citrus sinensis) with grapefruit juice (Citrus paradisi) based on flavonoid glycoside content. Fifty-nine orange juices (OJ), 23 grapefruit juices (GJ) and 10 blends (OG), obtained from local retail outlets were used to assess the performance of the ¹H NMR method. The work presented here introduces the Evolving Window Zone Selection (EWZS) function that holds promise for the automatic detection of spectral regions tailored to discriminate predefined groups. This technique was applied on the pre-processed ¹H NMR spectra of the 92 juices. Independent Component Analysis (ICA) is a good alternative to Principal Component Analysis (PCA) for recovering linearly-mixed unobserved multidimensional independent signals and has been used in this study to build supervised models that classify the samples into three categories, OJ, GJ, OG. The regions containing the known flavonoid glycoside markers were selected as well as another zone containing the signals of sucrose, α-glucose and other components that were tentatively attributed. ICA was applied on three different groups of selected variables and showed good results for both discrimination and interpretation of the signals. Up to 97.8% of the juices were correctly attributed. This method gave better results than the commonly used PCA method. In addition, the time required to carry out the ¹H NMR analysis was less than half the time of the standard chromatographic method.