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.     

An enzyme immunoassay for mouse epidermal growth factor utilizing a liquid phase double-antibody system

Summary An enzyme immunoassay for mouse epidermal growth factor (EGF) involving a liquid phase double-antibody system was developed. The EGF--galactosidase conjugate prepared was stable for at least 8 months. By this method, EGF was detectable at a concentration as low as 20 pg per tube. The concentrations of EGF in various tissues of mice are also presented.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.     

Binding of 11-cis retinaldehyde to the partially purified cellular retinaldehyde binding protein from bovine retinal pigment epithelium

Summary 11-cis retinaldehyde binding analysis was performed on a bovine retinal pigment epithelium preparation of cellular retinaldehyde binding protein (CRALBP), whose purity degree was estimated as 75%. Equilibrium binding studies were carried out measuring the replacement of tritium-labeled with unlabeled 11-cis retinaldehyde at 25°C. Analysis of the experimental data both by a direct curve-fitting procedure utilizing a non linear least square regression analysis and by a conventional Scatchard plot revealed a single non-interacting binding site with an apparent equilibrium constant of 0.9×10^–7 M.A binding stoichiometry of approximately 1 mol of 11-cis retinaldehyde/mol of binding protein can be calculated from the experimental data. Competition studies carried out in the presence of unlabeled trans and cis isomers of Vitamin A derivatives confirm the high degree of specificity of the 11-cis retinaldehyde binding.