The multivariate L1-median and associated data depth

This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in ℝd, a problem that can be traced to Fermat and has fascinated applied mathematicians for over three centuries; (ii) a new general definition for depth functions, as functions of multivariate medians, so that different definitions of medians will, correspondingly, give rise to different dept functions; and (iii) a simple closed-form formula of the L1-depth function for a given data cloud in ℝd.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.

Microwave-Assisted Extraction of Phenolic Compounds from Almond Skin Byproducts (Prunus amygdalus): A Multivariate Analysis Approach

A microwave-assisted extraction (MAE) procedure to isolate phenolic compounds from almond skin byproducts was optimized. A three-level, three-factor Box–Behnken design was used to evaluate the effect of almond skin weight, microwave power, and irradiation time on total phenolic content (TPC) and antioxidant activity (DPPH). Almond skin weight was the most important parameter in the studied responses. The best extraction was achieved using 4 g, 60 s, 100 W, and 60 mL of 70% (v/v) ethanol. TPC, antioxidant activity (DPPH, FRAP), and chemical composition (HPLC-DAD-ESI-MS/MS) were determined by using the optimized method from seven different almond cultivars. Successful discrimination was obtained for all cultivars by using multivariate linear discriminant analysis (LDA), suggesting the influence of cultivar type on polyphenol content and antioxidant activity. The results show the potential of almond skin as a natural source of phenolics and the effectiveness of MAE for the reutilization of these byproducts.

Multi-Element Analysis of Spanish Date Palm (Phoenix dactylifera L.) by Inductively Coupled Plasma-Based Techniques. Discrimination Using Multivariate Statistical Analysis

The elemental analysis of Spanish palm dates by inductively coupled plasma atomic emission spectrometry and inductively coupled plasma mass spectrometry is reported for the first time. To complete the information about the mineral composition of the samples, C, H, and N are determined by elemental analysis. Dates from Israel, Tunisia, Saudi Arabia, Algeria and Iran have also been analyzed. The elemental composition have been used in multivariate statistical analysis to discriminate the dates according to its geographical origin. A total of 23 elements (As, Ba, C, Ca, Cd, Co, Cr, Cu, Fe, H, In, K, Li, Mg, Mn, N, Na, Ni, Pb, Se, Sr, V, and Zn) at concentrations from major to ultra-trace levels have been determined in 13 date samples (flesh and seeds). A careful inspection of the results indicate that Spanish samples show higher concentrations of Cd, Co, Cr, and Ni than the remaining ones. Multivariate statistical analysis of the obtained results, both in flesh and seed, indicate that the proposed approach can be successfully applied to discriminate the Spanish date samples from the rest of the samples tested.

Coreferentiality: A New Method for the Hypothesis-Based Analysis of Phenotypes Characterized by Multivariate Data

Many multifactorial biologic effects, particularly in the context of complex human diseases, are still poorly understood. At the same time, the systematic acquisition of multivariate data has become increasingly easy. The use of such data to analyze and model complex phenotypes, however, remains a challenge. Here, a new analytic approach is described, termed coreferentiality, together with an appropriate statistical test. Coreferentiality is the indirect relation of two variables of functional interest in respect to whether they parallel each other in their respective relatedness to multivariate reference data, which can be informative for a complex effect or phenotype. It is shown that the power of coreferentiality testing is comparable to multiple regression analysis, sufficient even when reference data are informative only to a relatively small extent of 2.5%, and clearly exceeding the power of simple bivariate correlation testing. Thus, coreferentiality testing uses the increased power of multivariate analysis, however, in order to address a more straightforward interpretable bivariate relatedness. Systematic application of this approach could substantially improve the analysis and modeling of complex phenotypes, particularly in the context of human study where addressing functional hypotheses by direct experimentation is often difficult.

Entwicklung und Vergleich von Methoden zur Bestimmung des DE-Wertes von Zuckersirupen

Die EU-Zuckermarktverordnung gibt Quoten für den Verbrauch und Import von Zucker und Isoglucose, einem durch enzymatische Stärkehydrolyse gewonnenen Sirup, vor. Die Quotenregelung entfällt 2017, so dass damit gerechnet wird, dass bei der Verarbeitung von Lebensmitteln, Isoglucose Zucker anteilig substituiert. Die vorliegende Bachelorarbeit gibt einen Überblick über Zucker und Zuckeralternativen, wobei sich insbesondere dem Thema Industriesirupe gewidmet wurde. Nach einer theoretischen Heranführung an die Bachelorthesis, erfolgten experimentelle Untersuchungen. Hierbei wurden die DE-Werte unbekannter Zuckersirupe untersucht und miteinander verglichen. Beim DE-Wert handelt es sich um das Dextrose-Äquivalent, das den Verzuckerungsgrad angibt. Die Standardmethode Lane-Eynon wurde im Vergleich zu den Bestimmungsmethoden Luff-Schoorl und HPLC (High Performance Liquid Chromatography) betrachtet und ausgewertet.

Multivariate statistical analysis of highway accident and highway conditions. Final report.

Transportation Department, Office of University Research, Washington, D.C.

Vergleich der methoden Kants und Hegels auf grund ihrer behandlung der kategorie der quantität.

Vita.

Über die Eulerschen und Gaussschen Methoden der Primzahlbestimmung /

Inaug.-diss.--Kaiser-Wilhelms-Universität Strassburg.