Finding Y‐relevant part of X by use of PCR and PLSR model reduction methods

The paper is considering the following question: using principal component regression (PCR) or partial least squares regression (PLSR), how much data can be removed from X while retaining the original ability to predict Y ? Two model reduction methods using similarity transformations are discussed, one giving projections of original loadings onto the column space of the fitted response matrix (essentially the orthogonal signal correction (OSC) methods), and one giving projections of original scores onto the column space of the coefficient matrix (essentially the net analyte signal (NAS) methods). The loading projection method gives model residuals that are orthogonal to Y and , which is valuable in certain applications. The score projection method, on the other hand, gives model residuals that are orthogonal to , which is essential in other applications. It is shown that the reduced matrix X from the score projection method is a subset of the reduced matrix X from the loading projection method. It therefore has the smallest Frobenius norm, and thus the smallest total column variance, assuming centered data. Copyright © 2007 John Wiley & Sons, Ltd.     

On the Mössbauer studies of harmonically bound quantum oscillators in Brownian motion

In many biological systems like whole cells, membranes or proteins and some of the polymeric systems, dynamics reveals itself in M?ssbauer spectra as a non Lorentzian behaviour above some particular temperature which is characteristic of the system. Moreover mean square displacement and line width show temperature dependence above the characteristic temperature. Brownian motion of harmonically bound oscillator has been able to explain the non-Lorentzian behaviour. In the present paper, a quantum picture of the above model is discussed and lineshape is expressed as the closed form for the extreme overdamping case. In addition to the non-Lorentzian behaviour, the present model also predicts a temperature dependence of mean square displacement and linewidth. Received 16 July 1997 and Received in final form 2 September 1998     

Deterministic group selection model for the evolution of altruism

We study the evolution of an infinite population of asexually reproducing individuals, each of which can be either altruist or non-altruist, subdivided into reproductively isolated groups (demes) of finite size under the action of two opposed selective pressures, namely, differential individual reproduction and differential deme extinction. We derive a recursion equation for the deterministic, discrete time evolution of the frequencies of the different types of demes, classified according to the number of altruistic individuals they have. We give emphasis to the detrimental effects of mutation and migration on the stability of the altruistic demes, which are the only stable demes in the absence of these processes. Furthermore, we draw an analogy between the proposed deterministic group selection model and the quasispecies model for molecular evolution. Received: 22 May 1998 / Accepted: 18 August 1998     

聚偏二氯乙烯负载金鸡纳碱催化剂的合成及其对不对称Michael反应的催化性能

将天然的金鸡纳碱——辛可宁与聚偏二氯乙烯进行接枝反应,制备了聚偏二氯乙烯负载辛可宁的催化剂.将制备的催化剂用于催化不对称Michael反应,并探索了溶剂、催化剂用量、温度、底物等不同条件对其催化性能的影响.结果表明,该催化剂在甲苯中有很高的催化活性和较好的立体选择性,Michael反应中部分产率达到80%以上,e.e值达到72%,且该催化剂具有一定的重复使用性能.     

A chain rule for first- and second-order epiderivatives and hypoderivatives

A chain rule is established for contingent and adjacent epiderivatives and hypoderivatives of compositions g○h, where h is assumed to be Hadamard directionally differentiable. Corollaries include a formula for the contingent and adjacent cones of an equality constraint set defined by a Hadamard directionally differentiable function. An analogous chain rule for second-order contingent and adjacent epiderivatives and hypoderivatives is also developed.     

Matching in 3-uniform hypergraphs

A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. We use $E_3(2d?1,n?2d+1)$ to denote the 3-uniform hypergraph whose vertex set can be partitioned into two vertex classes $V_1$ and $V_2$ of size $2d?1$ and $n?2d+1$, respectively, and whose edge set consists of all the triples containing at least two vertices of $V_1$. Let $H$ be a 3-uniform hypergraph of order $n\ge 13d$ with no isolated vertex and $\text{deg}\left(u\right)+\text{deg}\left(v\right)>2\left(\left(\genfrac{}{}{0ex}{}{n?1}{2}\right)?\left(\genfrac{}{}{0ex}{}{n?d}{2}\right)\right)$ for any two adjacent vertices $u,v\in V\left(H\right)$. In this paper, we show that $H$ contains a matching of size $d$ if and only if $H$ is not a subgraph of $E_3(2d?1,n?2d+1)$. This result improves our previous one in Zhang and Lu (2018).     

图的邻点可区别无圈边染色的一个界

图G的一个正常边染色被称作邻点可区别无圈边染色,如果G中无二色圈,且相邻点关联边的色集合不同.应用概率的方法得到了图G的一个邻点可区别无圈边色数的上界,其中图G为无孤立边的图.     

Concise proofs for adjacent vertex-distinguishing total colorings

Let G=(V,E) be a graph and f:(V∪E)→[k] be a proper total k-coloring of G. We say that f is an adjacent vertex- distinguishing total coloring if for any two adjacent vertices, the set of colors appearing on the vertex and incident edges are different. We call the smallest k for which such a coloring of G exists the adjacent vertex-distinguishing total chromatic number, and denote it by χ_at(G). Here we provide short proofs for an upper bound on the adjacent vertex-distinguishing total chromatic number of graphs of maximum degree three, and the exact values of χ_at(G) when G is a complete graph or a cycle.