COSMOLOGY FROM ALPHA TO OMEGA

Abstract. This paper focuses on four passages in the journey of the universe from beginning to end: its origin in the Big Bang, the production of heavy elements in first generation stars, the buzzing symphony of life on earth, and the distant future of the cosmos. As a physicist and a Christian theologian, I will ask how each of these passages casts light on the deepest questions of existence and our relation to God, and in turn how these questions are being explored through ongoing research into the interaction between Christian theology and the natural sciences.     

A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Zellini (1979, Theorem 3.1) has shown how to decompose an arbitrary symmetric matrix of ordern ×n as a linear combination of 1/2n(n+1) fixed rank one matrices, thus constructing an explicit tensor basis for the set of symmetricn ×n matrices. Zellini's decomposition is based on properties of persymmetric matrices. In the present paper, a simplified tensor basis is given, by showing that a symmetric matrix can also be decomposed in terms of 1/2n(n+1) fixed binary matrices of rank one. The decomposition implies that ann ×n ×p array consisting ofp symmetricn ×n slabs has maximal rank 1/2n(n+1). Likewise, an unconstrained INDSCAL (symmetric CANDECOMP/PARAFAC) decomposition of such an array will yield a perfect fit in 1/2n(n+1) dimensions. When the fitting only pertains to the off-diagonal elements of the symmetric matrices, as is the case in a version of PARAFAC where communalities are involved, the maximal number of dimensions can be further reduced to 1/2n(n–1). However, when the saliences in INDSCAL are constrained to be nonnegative, the tensor basis result does not apply. In fact, it is shown that in this case the number of dimensions needed can be as large asp, the number of matrices analyzed.     

Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. The number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping-rule validity. Equal and unequal population base rates were also considered. Both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space. The replication criterion, which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set, was superior as the degree of overlap in population distributions increased. Neither method performed adequately when overlap obliterated visually discernible density nodes.This research was supported in part by NIMH grant 5R01 MH 32457 14.     

Vasopressin, glucose homeostasis, and sucrose taste preferences

Previous research indicates that vasopressin-containing (LE) rats are capable of adapting to the stress of food restriction, whereas vasopressin-deficient (DI) rats cannot adapt to this stressor. It has been postulated that abnormalities in glucose metabolism may be one of the factors leading to the demise of food-restricted DI rats. The present study was conducted to determine if taste preferences are altered in DI animals and if the presentation of exogenous glucose, in the form of sucrose solutions, can ameliorate the effects of the stress of food restriction. Four different concentrations of sucrose solutions were presented to LE and DI rats under the food-restricted condition. In both strains, an 8% sucrose solution was preferred over 0%, 16%, and 32% concentrations, with DI rats consuming more of this concentration than LE rats. Thus, when DI rats had the opportunity of maintaining glucose homeostasis by exogenous supplements, they maintained body weight, displayed no stomach pathology, and survived.     

Showing Clients What Their Profiles Mean

This article suggests that counselors might profitably investigate new graphic approaches to showing clients what their multivariate profiles mean. An illustration is given in terms of Holland's RIASEC (Realistic, Investigative, Artistic, Social, Enterprising, Conventional; 1985) model of vocational interests.