The Young-Householder algorithm and the least squares multidimensional scaling of squared distances

It is shown that replacement of the zero diagonal elements of the symmetric data matrix of approximate squared distances by certain other quantities in the Young-Householder algorithm will yield a least squares fit to squared distances instead of to scalar products. Iterative algorithms for obtaining these replacement diagonal elements are described and relationships with the ELEGANT algorithm (de Leeuw 1975; Takane 1977) are discussed. In large residual situations a penalty function approach, motivated by the ELEGANT algorithm, is adopted. Empirical comparisons of the algorithms are given.An early version of this paper was presented at the Multidimensional Data Analysis Workshop, Pembroke College, Cambridge, July 1985. I want to thank Jan de Leeuw and Yoshio Takane for bringing the ELEGANT algorithm to my attention and for clarifying its rationale and notation. My thanks go also to Stephen du Toit for help with the ALSCAL computations reported in Section 7.     

用爆炸波起爆癸烷云雾的两种模式

用垂直激波管研究了400μm癸烷液滴与空气混合物的爆炸波起爆。每种混合物有两个极限起爆能值,即高值Ecu,和低值Ecl。当起爆能的值高于Ecu时,观察到100%发生爆轰;而当其低于Ecl时,就不会发生爆轰。有趣的是,当起爆能水平在Ecu和Ecl之间时观察到对应于不同的起爆能水平有不同的起爆行为。如实验结果所表明的,爆轰的激发不仅是由于直接起爆,而且也由于“爆燃”到爆轰的转变。     

Regulation of cellulose synthesis in Acetobacter xylinum by cyclic diguanylic acid

Cellulose is the most abundant renewable carbon resource on earth and is an indispensable raw material for the wood, paper, and textile industries. A model system to study the mechanism of cellulose biogenesis is the bacterium Acetobacter xylinum which produces pure cellulose as an extracellular product. It was from this organism that in vitro preparations which possessed high levels of cellulose synthase activity were first obtained in both membranous and soluble forms. We recently demonstrated that this activity is subject to a complex multi-component regulatory system, in which the synthase is directly affected by an unusual cyclic nucleotide activator enzymatically formed from GTP, and indirectly by a Ca (2+) -sensitive phosphodiesterase which degrades the activator. The cellulose synthase activator (CSA) has now been identified as bis-(3' 5')-cyclic diguanylic acid (5'G3'p5'G3'p) on the basis of mass spectroscopic data, nuclear magnetic resonance analysis and comparison with chemically synthesized material. We also report here on intermediary steps in the synthesis and degradation of this novel circular dinucleotide, which have been integrated into a model for the regulation of cellulose synthesis.