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.     

Statistical assessment of population variability: a methodological approach

We have implemented a multivariate statistical methodology to assess the degree and pattern of cranial variability in skeletal samples. Specifically, the method is designed to test whether variability in a skeletal sample exceeds "normal within-group variability" defined in the present instance as variability present among crania from a cemetery associated with a village. It involves comparing a covariance matrix derived from a sample of unknown composition to one representing "normal within-group variability." The method has been applied to two Plains Indian craniometric samples. The Leavenworth site (39CO9) represents the remnants of previously autonomous Arikara Indian villages devastated by epidemic diseases in the late 1700s. The Bad River 2 Phase is an archaeological designation grouping together closely related sites in the Bad-Cheyenne region of South Dakota dating from 1740-1795 AD. We were able to show substantial heterogeneity among crania from Leavenworth. District burial areas at Leavenworth account for some of the heterogeneity, supporting the notion that they represent an attempt to maintain former social distinctions. We were unable to differentiate among sites within the Bad River 2 Phase, suggesting that it is a valid biological unit.     

Performance evaluation of eight years experience of constructed wetland systems in Catalonia as alternative treatment for small communities

In Catalonia (Spain), a variety of different systems have been built to naturally treat liquid residues from small communities. Some of these wastewater treatment plants (WWTPs) include constructed wetlands with horizontal subsurface flow (HSSF) as secondary treatment. The present study described and characterized the performance of 11 WWTPs with secondary HSSF constructed wetland systems after an initial operating period of 8 years. The effluent concentrations of Biochemical Oxygen Demand (BOD₅), Total Suspended Solids (TSS), Total Nitrogen (TN) and Total Phosphorous (TP) were statistically analyzed, and removal efficiencies for all WWTPs including all stages in treatment were calculated. The accumulated probability functions of those parameters were evaluated to determine the influence of two different types of polishing units on the overall performance: (a) only lagoon systems and (b) lagoon systems with HSSF. The statistical analysis indicates good performance for BOD₅ and TSS. In the first case, mean concentrations below 25 mg/L were found in 9 of the 11 plants analyzed and removal efficiencies between 78 and 96% were observed. In the second case, mean concentrations below 35 mg/L were found in 8 of the 11 plants, and removal efficiencies were between 65 and 88%. For the nutrients, the removal efficiency for TN and TP were in the range of 48-66% and 39-58%, respectively. Additionally, the analysis of the influence of the polishing units did not show a significant improvement (α > 0.05) for any parameter in the wetland systems without a subsequent polishing unit. However, in the wetland systems with a polishing unit of HSSF, a significant improvement (α < 0.05) was found for the effluent's BOD₅, TN and TP concentrations but with no significant contribution in TSS management.     

Statistical inference for serial dilution assay data

Serial dilution assays are widely employed for estimating substance concentrations and minimum inhibitory concentrations. The Poisson-Bernoulli model for such assays is appropriate for count data but not for continuous measurements that are encountered in applications involving substance concentrations. This paper presents practical inference methods based on a log-normal model and illustrates these methods using a case application involving bacterial toxins.