An Algorithm for Calculation of n-Dimensional Nonlinear Dependencies – Behaviour Tests on Rats

The evaluation of the data obtained during the behaviour tests always leads to the problem of multiple correlation, very often with non-linear dependencies on the target. All mathematical and statistical procedures that have been used so far are based on the assumption of an equation for the desired correlation for which parameters and related statistical equivalents are determined eventually. The MODAK system applied here (MODAK = algorithms of modelling for the calculation of multi-dimensional non-linear mathematical models) breaks down a complex correlation into individual dependencies in a mathematical and statistical way and selects suitable equations for each of them independently and determines the corresponding parameters. The numerical example evaluates data of behaviour tests on rats. First results obtained on the correlations of various behaviour tests indicate both the possibility of selecting suitable tests independent of each other and a better interpretation of the observed patterns of behaviour taking into account the interrelations between the tests. In addition, MODAK is a method which can be applied as a matter of course in a general way to all cases which call for the reduction and analysis of data occurring in process and system analysis and in the evaluation of test results requiring statistical modelling. So far, MODAK applications range from engineering sciences to medicine.     

Assessment of Optimal Selected Prognostic Factors

The identification and assessment of prognostic factors is one of the major tasks in clinical research. The assessment of one single prognostic factor can be done by recently established methods for using optimal cutpoints. Here, we suggest a method to consider an optimal selected prognostic factor from a set of prognostic factors of interest. This can be viewed as a variable selection method and is the underlying decision problem at each node of various tree building algorithms. We propose to use maximally selected statistics where the selection is defined over the set of prognostic factors and over all cutpoints in each prognostic factor. We demonstrate that it is feasible to compute the approximate null distribution. We illustrate the new variable selection test with data of the German Breast Cancer Study Group and of a small study on patients with diffuse large B‐cell lymphoma. Using the null distribution for a p‐value adjusted regression trees algorithm, we adjust for the number of variables analysed at each node as well. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical conformational analysis of phospholipids II. Role of hydration in the gel to liquid crystal transition of phospholipids

To obtain a satisfactory agreement between computed transition temperatures and those determined experimentally, we introduce explicitly water molecules which hydrate the polar headgroup of dipalmitoylphosphatidylethanolamine molecules. The calculated free energy curves as a function of the intermolecular interchain distance and the degree of hydration of the polar groups permit the determination of the transition of the phospholipid system from the gel to the liquid crystalline phase. The detailed structure of the hydration shell is defined using the supermolecular approach.     

Statistical treatment of VAM infection data

Summary The amount of vesicular-arbuscular mycorrhizal (VAM) infection, when expressed as length of infected roots, is commonly quite variable among replicate pots within an experimental treatment. In this paper we show that frequency distributions of VAM infection parameters are often non-normal in form and may follow the negative binomial, a distribution commonly associated with aggregated organisms in nature. The lack of normality means that statistical procedures should either be non-parametric or should include data transformations.     

Compositional statistics: An improvement of evolutionary parsimony and its application to deep branches in the tree of life

Summary We present compositional statistics, a new method of phylogenetic inference, which is an extension of evolutionary parsimony. Compositional statistics takes account of the base composition of the compared sequences by using nucleotide positions that evolutionary parsimony ignores. It shares with evolutionary parsimony the features of rate invariance and the fundamental distinction between transitions and transversions. Of the presently available methods of phylogenetic inference, compositional statistics is based on the fewest and mildest assumptions about the mode of DNA sequence evolution. It is therefore applicable to phylogenetic studies of the most distantly related organisms or molecules. This was illustrated by analyzing conservative positions in the DNA sequences of the large subunit of RNA polymerase from three archaebacterial groups, a eubacterium, a chloroplast, and the three eukaryotic polymerases. Internally consistent results, which are in accord with our knowledge of organelle origin and archaebacterial physiology, were achieved.     

Amino acid sequences of stomach and nonstomach lysozymes of ruminants

Summary Complete amino acid sequences are presented for lysozymesc from camel and goat stomachs and compared to sequences of other lysozymesc. Tree analysis suggests that the rate of amino acid replacement went up as soon as lysozyme was recruited for the stomach function in early ruminants. The two lysozymes from goat stomach are the products of a gene duplication that probably took place before the divergence of cow, goat, and deer about 25 million years ago. Partial sequences of three lysozymes from goat tears indicated that (a) the goat tear family of lysozymes may have diverged from the stomach lysozyme family by an ancient duplication and (b) later duplications are probably responsible for the multiple forms of tear and milk lysozymes in ruminants.     

Biological evaluation of trace element data in human ovaries by statistical analysis

Analysis of variance, analysis of covariance, correlation coefficient, multiple correlation, and partial correlation coefficient statistical tests were applied to Cs, Cr, Co, Fe, Rb, Sc, Se, and Zn content in human ovaries in order to evaluate statistically the possible relationships between these trace elements at: the ovary as an organ, each ovarian phase separately, each morphological part independent of the ovarian phase, and between cortex and medulla within the ovarian phases. The element Cs seems to have a homogenous distribution between cortex and medulla within reproductive and menopausal phase. Zinc shows a trend to have an antagonistic relation with Cs, Cr, Co, and Fe during fetal and reproductive phases and not during menopausal phase. The relationship between Zn and Cs when Fe is kept constant could be used as a tool for the decontamination of the ovary from an abnormal Cs content or for the inhibition of the accumulation of the same element to the ovarian tissue.