The congruence coefficient was first introduced by Burt (1948) under the name of unadjusted correlation as a measure of the similarity of two factorial configurations. The name congruence coefficient was later tailored by Tucker (1951, see also Harman, 1976). The congruence coefficient is also sometimes called a monotonicity coefficient (Borg & Groenen, 1997, p. 203). The congruence coefficient...

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an Fσ-subset of a “smaller” dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces. The classical Hurewicz-Menger-Tumarkin theorem in dimension theory says that connected topological n-manifolds (with or without boundary) are Cantor manifo...

The congruence between two configurations of points quantifies their similarity. The configurations to be compared are, in general, produced by factor analytic methods which decompose an “observations by variables” data matrix and produce one set of factor scores for the observations and one set of factor scores (i.e., the “loadings”) for the variables. The congruence between two sets of factor...

Phosphofructokinase (PFK), a regulatory enzyme in glycolytic pathway, has been purified to electrophoretic homogeneity from adult female Setaria cervi and partially characterized. For this enzyme, the Lineweaver-Burk's double reciprocal plots of initial rates and D-fructose-6-phosphate (F-6-P) or Mg-ATP concentrations for varying values of cosubstrate concentration gave intersecting lines indic...

Meta-analysis has become an indispensable tool for reaching accurate and representative conclusions about phenomena of interest within a research literature. However, in order for meta-analytic computations to provide accurate estimates of population parameters (e.g., a population correlation), underlying statistical models need to be both efficient and unbiased. Current fixed-effect (i.e., con...

We present a consistent, geometric notion of homogeneity, for vector elds (diierential equations and control systems), functions, diierential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly, a coordinate-free characterization is given, and shown to yield the desired/expected results. This also addresses: \When do there ex...

The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontinuous setting: the equivalence of the global asymptotic stability and the existence o...

Sufficient as well as necessary conditions are studied for a dendrite or a dendroid to be homogeneous with respect to monotone mappings. The obtained results extend ones due to H. Kato and the first named author. A number of open problems are asked.