A positive linear recurrence sequence is of the form Hn+1 = c1Hn + · · · + cLHn+1−L with each ci ≥ 0 and c1cL > 0, with appropriately chosen initial conditions. There is a notion of a legal decomposition (roughly, given a sum of terms in the sequence we cannot use the recurrence relation to reduce it) such that every positive integer has a unique legal decomposition using terms in the sequence;...

The paper refers to the situation teaching basic statistics to students with little background in mathematics, especially no knowledge in differential calculus. Goal of the paper is to show that knowledge of basic linear algebra is sufficient to explain the problem and the solution of linear regression, and this in a closed form. This approach avoids black box teaching where students learn how ...

Mutual information (MI) is in increasing use as a way of quantifying neural responses. However, it is still considered with some doubts by many researchers, because it is not always clear what MI really measures, and because MI is hard to calculate in practice. This paper aims to clarify these issues. First, it provides an interpretation of mutual information as variability decomposition, simil...

Analysis of variance (ANOVA) is a statistical procedure for summarizing a classical linear model—a decomposition of sum of squares into a component for each source of variation in the model—along with an associated test (the F-test) of the hypothesis that any given source of variation in the model is zero. When applied to generalized linear models, multilevel models, and other extensions of cla...

The impurity of measures is considered as cause of erroneous interpretations of observed relationships. This paper concentrates on impurity with respect to the relationship between working memory and fluid intelligence. The means for the identification of impurity was the fixed-links model, which enabled the decomposition of variance into experimental and non-experimental parts. A substantial n...

Observed differences in phenotypic means between groups such as parents and their offspring or male and female twins can be decomposed into genetic and environmental components. The decomposition is based on the assumption that the difference in phenotypic means is due to a difference in the location of the normal genetic and environmental distributions underlying the phenotypic individual diff...

This paper empirically examines the dynamic causal link between business R&D expenditures and trade performance in Australia. Based on cointegration and errorcorrection modeling Granger causality tests, variance decomposition and impulse response functions are used for this purpose. The results show that there is a long-run relationship exists between the trade variables and R&D expenditure and...