Factor analytical study on water quality in Lake Saimaa, Finland

Multivariate data analysis methods (4-way Candecomp-PARAFAC model solved with Multilinear Engine (ME-1)) were used to interpret the data of over two decades to study the changes in the water of Lake Saimaa in Finland. Earlier studies have shown that it is difficult to extract the natural background from the other sources of variation. By using the multilinear model three interpretable factors representing natural and anthropogenic processes could be extracted. The natural long-term variation, seasonal fluctuation and dilution of discharges in the recipient area could be extracted into their own factors, which could be easily visualized. The variation could be also presented with estimated variation in the water quality parameters caused by each of these natural or anthropogenic processes. Received: 27 September 2000 / Revised: 11 January 2001 / Accepted: 14 January 2001     

Grab vs. composite sampling of particulate materials with significant spatial heterogeneity—A simulation study of “correct sampling errors”

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.     

A tensile testing machine for a scanning electron microscope; Its structure,properties and applications

This work introduces a micro tensile testing machine built in to an ISI 40 SEM scanning electron microscope. With additional accessories (an anticontamination system and a Robinson detector), the machine is suitable for studying non-conductive materials, such as polymers, plastics and non-metallic composites, without coating, during tension or compression.With regard to its properties, the micro tensile testing machine developed in this context can structurally be compared in all aspects to normal mechanical universal tensile testing machines. The difference is that in this case, in addition to the conventional information (force, deformation), a continuing picture of the surface of test materials can be recorded from the area where the most interesting changes are happening. With the micro tensile testing machine it has been possible to retain all movements of the specimen stage, which enables the efficient observation of the specimen in a scanning electron microscope.The examples of applications presented in this paper show that the tensile machine is suitable and useful in studies of plastics and plastic-based composites in a very wide area.     

Magnetic resonance imaging of the uterus in vivo and in vitro at an ultra low magnetic field (0.02 T): Assessment of its normal structure and of leiomyomas

The purpose of this investigation was to analyze the normal anatomy and leiomyomas of the uterus with an ultra low field (0.02 T) magnetic resonance imaging (MRI) device. MR imaging was performed on 18 uteri, 11 of which were imaged both preoperatively (in vivo) and as an operative specimen (in vitro), 6 only as an operative specimen, and 1 only preoperatively. All uteri were examined histologically after imaging. The junctional zone was much better delineated in vivo than in vitro, indicating that its appearance on MR is partly due to blood flow. No structures contributing to its visibility in vitro could be demonstrated histologically. Twenty leiomyomas (size range 7–79 mm) in 12 uteri were found with MRI. They were slightly better discerned in vivo than in vitro. The leiomyomas, having no degenerative changes, had a signal intensity which was the same or lower than that of the myometrium. On images obtained in vitro the signal intensity of these leiomyomas relative to that of myometrium correlated directly with their muscular content (R = 0.74, p = .002). The authors conclude that the junctional zone is a sum of physiological and structural factors, the latter being responsible for its in vitro delineation. MR imaging of the uterus in vitro did not give more information than MR imaging in vivo. All leiomyomas larger than 10 mm could be detected, indicating that MR imaging at 0.02 T is an accurate method for the imaging of the uterine leiomyomas.     

Rotational tools for factor analytic models

Rotational ambiguity is a major problem in the application of factor analysis to a variety of multivariate mixture resolution problems and particularly important in the analysis of environmental data. As part of the development of an implementation of positive matrix factorization for the U.S. Environmental Protection Agency to distribute in support of airborne particle source identification and apportionment, several tools have been developed to control the rotations and explore the extent of rotational solution space. This discussion of the nature of the rotational tools provides an understanding of these rotational tools as well as the basis for their incorporation into other implementations of least‐squares based solutions to the factor analysis problem. Several example algorithms are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Cholesterol supports headgroup superlattice domain formation in fluid phospholipid/cholesterol bilayers

Fluorescence and Fourier transform infrared (FTIR) spectroscopic techniques were used to explore the effect of added cholesterol on the composition-dependent formation of putative phospholipid headgroup superlattices in fluid 1-palmitoyl-2-oleoyl-phosphatidylethanolamine/1-palmitoyl-2-oleoyl-phosphatidylcholine/cholesterol (POPE/POPC/CHOL) bilayers. Steady-state fluorescence anisotropy measurements of diphenylhexatriene (DPH) chain-labeled phosphatidylcholine (DPH-PC) revealed significant dips at several POPE-to-phospholipid mole fractions (X(PE)'s) when the cholesterol-to-lipid mole fraction (X(CHOL)) was fixed at 0.00, 0.35, 0.40, and 0.50. Most of the observed dips occur at or close to critical X(PE)'s predicted by the Headgroup Superlattice (SL) model, suggesting that phospholipid headgroups of different structures tend to adopt regular distributions even in the presence of cholesterol. Time-resolved fluorescence anisotropy measurements revealed that DPH-PC senses a disordered and highly mobile microenvironment in the POPE/POPC/CHOL bilayers at those critical X(PE)'s, indicating that this probe may partition to defect regions in the bilayers. The presence of coexisting packing defect regions and regularly distributed SL domains is a key feature predicted by the Headgroup SL model. Importantly, probe-free FTIR measurements of acyl chain C-H, interfacial carbonyl, and headgroup phosphate stretching peak frequencies revealed the presence of abrupt changes at X(PE)'s close to those observed in the fluorescence data. When X(PE) was varied from 0.60 to 0.72 and X(CHOL) from 0.34 to 0.46, a clear dip at the lipid composition coordinates (X(PE), X(CHOL)) approximately (0.68, 0.40) was observed in the three-dimensional surface plots of DPH-PC anisotropy as well as the carbonyl and phosphate stretching frequencies. The critical X(CHOL) at 0.40 agrees with the Cholesterol SL model, which assumes that cholesterol and phospholipid form SL domains at the lipid acyl chain level. In conclusion, this study provides evidence that cholesterol supports formation of phospholipid headgroup SLs in fluid state ternary lipid bilayers. The feasibility of the parallel existence of SLs at the lipid headgroup and acyl chain levels supports the relevance of the lipid SL model for the membranes of eukaryotic cells that typically contain significant amounts of cholesterol. We speculate that lipid SL formation may play a central role in the regulation of membrane lipid compositions, maintenance of organelle boundaries, and other crucial phenomena in those cells.     

On unitary analogs of GCD reciprocal LCM matrices

A divisor d ∈ ?₊ of n ∈ ?₊ is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.     

A topological approach to divisibility of arithmetical functions and GCD matrices

Considering lower closed sets as closed sets on a preposet (P, ≤), we obtain an Alexandroff topology on P. Then order preserving functions are continuous functions. In this article we investigate order preserving properties (and thus continuity properties) of integer-valued arithmetical functions under the usual divisibility relation of integers and power GCD matrices under the divisibility relation of integer matrices.