Indiana University-Purdue University Indianapolis (IUPUI) / The aim of this study was to use multivariate statistical techniques to: (1) determine the reproducibility of fiber evidence analyzed by MSP, (2) determine whether XRF is an appropriate technique for forensic tape analysis, and (3) determine if DART/MS is an appropriate technique for forensic tape analysis. This was achieved by employing several multivariate statistical techniques including agglomerative hierarchical clustering, principal component analysis, discriminant analysis, and analysis of variance. First, twelve dyed textile fibers were analyzed by UV-Visible MSP. This analysis included an inter-laboratory study, external validations, differing preprocessing techniques, and color coordinates. The inter-laboratory study showed no statistically significant difference between the different instruments. The external validations had overall acceptable results. Using first derivatives as a preprocessing technique and color coordinates to define color did not result in any additional information. Next, the tape backings of thirty-three brands were analyzed by XRF. After chemometric analysis it was concluded that the 3M tapes with black adhesive can be classified by brand except for Super 33+ (Cold Weather) and Super 88. The colorless adhesive tapes were separated into two large groups which were correlated with the presence of aluminosilicate filler. Overall, no additional discrimination was seen by using XRF compared to the traditional instrumentation for tape analysis previously published. Lastly, the backings of eighty-nine brands of tape were analyzed by DART/MS. The analysis of the black adhesive tapes showed that again discrimination between brands is possible except for Super 33+ and Super 88. However, now Tartan and Temflex have become indistinguishable. The colorless adhesive tapes again were more or less indistinguishable from one another with the exception of Tuff Hand Tool, Qualpack, and a roll of 3M Tartan, which were found to be unique. It cannot be determined if additional discrimination was achieved with DART/MS because the multivariate statistical techniques have not been applied to the other instrumental techniques used during tape analysis.

Indiana University-Purdue University Indianapolis (IUPUI) / As medical data continues to transition to electronic formats, opportunities arise for researchers to use this microdata to discover patterns and increase knowledge that can improve patient care. Now more than ever, it is critical to protect the identities of the patients contained in these databases. Even after removing obvious “identifier” attributes, such as social security numbers or first and last names, that clearly identify a specific person, it is possible to join “quasi-identifier” attributes from two or more publicly available databases to identify individuals. K-anonymity is an approach that has been used to ensure that no one individual can be distinguished within a group of at least k individuals. However, the majority of the proposed approaches implementing k-anonymity have focused on improving the efficiency of algorithms implementing k-anonymity; less emphasis has been put towards ensuring the “utility” of anonymized data from a researchers’ perspective. We propose a new data utility measurement, called the research value (RV), which extends existing utility measurements by employing data constraints rules that are designed to improve the effectiveness of queries against the anonymized data. To anonymize a given raw dataset, two algorithms are proposed that use predefined generalizations provided by the data content expert and their corresponding research values to assess an attribute’s data utility as it is generalizing the data to ensure k-anonymity. In addition, an automated algorithm is presented that uses clustering and the RV to anonymize the dataset. All of the proposed algorithms scale efficiently when the number of attributes in a dataset is large.

No description available.

In this thesis, cluster analysis was applied to data comprising of customer spending habits at a retail chain in order to perform customer segmentation. The method used was a two-step cluster procedure in which the first step consisted of feature engineering, a square root transformation of the data in order to handle big spenders in the data set and finally principal component analysis in order to reduce the dimensionality of the data set. This was done to reduce the effects of high dimensionality. The second step consisted of applying clustering algorithms to the transformed data. The methods used were K-means clustering, Gaussian mixture models in the MCLUST family, t-distributed mixture models in the tEIGEN family and non-negative matrix factorization (NMF). For the NMF clustering a slightly different data pre-processing step was taken, specifically no PCA was performed. Clustering partitions were compared on the basis of the Silhouette index, Davies-Bouldin index and subject matter knowledge, which revealed that K-means clustering with K = 3 produces the most reasonable clusters. This algorithm was able to separate the customer into different segments depending on how many purchases they made overall and in these clusters some minor differences in spending habits are also evident. In other words there is some support for the claim that the customer segments have some variation in their spending habits. / I denna uppsats har klusteranalys tillämpats på data bestående av kunders konsumtionsvanor hos en detaljhandelskedja för att utföra kundsegmentering. Metoden som använts bestod av en två-stegs klusterprocedur där det första steget bestod av att skapa variabler, tillämpa en kvadratrotstransformation av datan för att hantera kunder som spenderar långt mer än genomsnittet och slutligen principalkomponentanalys för att reducera datans dimension. Detta gjordes för att mildra effekterna av att använda en högdimensionell datamängd. Det andra steget bestod av att tillämpa klusteralgoritmer på den transformerade datan. Metoderna som användes var K-means klustring, gaussiska blandningsmodeller i MCLUST-familjen, t-fördelade blandningsmodeller från tEIGEN-familjen och icke-negativ matrisfaktorisering (NMF). För klustring med NMF användes förbehandling av datan, mer specifikt genomfördes ingen PCA. Klusterpartitioner jämfördes baserat på silhuettvärden, Davies-Bouldin-indexet och ämneskunskap, som avslöjade att K-means klustring med K=3 producerar de rimligaste resultaten. Denna algoritm lyckades separera kunderna i olika segment beroende på hur många köp de gjort överlag och i dessa segment finns vissa skillnader i konsumtionsvanor. Med andra ord finns visst stöd för påståendet att kundsegmenten har en del variation i sina konsumtionsvanor.

Smokeless powders are a set of energetic materials, known as low explosives, which are typically utilized for reloading ammunition. There are three types which differ in their primary energetic materials; where single base powders contain nitrocellulose as their primary energetic material, double and triple base powders contain nitroglycerin in addition to nitrocellulose, and triple base powders also contain nitroguanidine. Additional organic compounds, while not proprietary to specific manufacturers, are added to the powders in varied ratios during the manufacturing process to optimize the ballistic performance of the powders. The additional compounds function as stabilizers, plasticizers, flash suppressants, deterrents, and opacifiers. Of the three smokeless powder types, single and double base powders are commercially available, and have been heavily utilized in the manufacture of improvised explosive devices. Forensic smokeless powder samples are currently analyzed using multiple analytical techniques. Combined microscopic, macroscopic, and instrumental techniques are used to evaluate the sample, and the information obtained is used to generate a list of potential distributors. Gas chromatography – mass spectrometry (GC-MS) is arguably the most useful of the instrumental techniques since it distinguishes single and double base powders, and provides additional information about the relative ratios of all the analytes present in the sample. However, forensic smokeless powder samples are still limited to being classified as either single or double base powders, based on the absence or presence of nitroglycerin, respectively. In this work, the goal was to develop statistically valid classes, beyond the single and double base designations, based on multiple organic compounds which are commonly encountered in commercial smokeless powders. Several chemometric techniques were applied to smokeless powder GC-MS data for determination of the classes, and for assignment of test samples to these novel classes. The total ion spectrum (TIS), which is calculated from the GC-MS data for each sample, is obtained by summing the intensities for each mass-to-charge (m/z) ratio across the entire chromatographic profile. A TIS matrix comprising data for 726 smokeless powder samples was subject to agglomerative hierarchical cluster (AHC) analysis, and six distinct classes were identified. Within each class, a single m/z ratio had the highest intensity for the majority of samples, though the m/z ratio was not always unique to the specific class. Based on these observations, a new classification method known as the Intense Ion Rule (IIR) was developed and used for the assignment of test samples to the AHC designated classes. Discriminant models were developed for assignment of test samples to the AHC designated classes using k-Nearest Neighbors (kNN) and linear and quadratic discriminant analyses (LDA and QDA, respectively). Each of the models were optimized using leave-one-out (LOO) and leave-group-out (LGO) cross-validation, and the performance of the models was evaluated by calculating correct classification rates for assignment of the cross-validation (CV) samples to the AHC designated classes. The optimized models were utilized to assign test samples to the AHC designated classes. Overall, the QDA LGO model achieved the highest correct classification rates for assignment of both the CV samples and the test samples to the AHC designated classes. In forensic application, the goal of an explosives analyst is to ascertain the manufacturer of a smokeless powder sample. In addition, knowledge about the probability of a forensic sample being produced by a specific manufacturer could potentially decrease the time invested by an analyst during investigation by providing a shorter list of potential manufacturers. In this work, Bayes* Theorem and Bayesian Networks were investigated as an additional tool to be utilized in forensic casework. Bayesian Networks were generated and used to calculate posterior probabilities of a test sample belonging to specific manufacturers. The networks were designed to include manufacturer controlled powder characteristics such as shape, color, and dimension; as well as, the relative intensities of the class associated ions determined from cluster analysis. Samples were predicted to belong to a manufacturer based on the highest posterior probability. Overall percent correct rates were determined by calculating the percentage of correct predictions; that is, where the known and predicted manufacturer were the same. The initial overall percent correct rate was 66%. The dimensions of the smokeless powders were added to the network as average diameter and average length nodes. Addition of average diameter and length resulted in an overall prediction rate of 70%.

Au niveau postsecondaire, les concepts mathématiques avancés seraient des concepts difficiles à appréhender pour beaucoup d’étudiants. Le concept de série fait partie de ces concepts avancés que les étudiants rencontrent pour la première fois de façon formelle dans leurs études postsecondaires (au niveau collégial, Cégep, dans le contexte québécois). Ce concept a un très grand nombre d’applications et ce, aussi bien en mathématiques que dans le domaine scientifique. Cependant, sa complexité propre et sa nature contre-intuitive font qu’il est très difficile à appréhender par certains étudiants. Parmi les difficultés d’appréhension, dans un grand nombre de cas, on peut trouver la conception que la somme d’une infinitude de termes donnera une quantité qui ne peut être qu’infiniment grande. Étant donné l’importance et la complexité de ce concept, on pourrait s’attendre à ce qu’il soit pris en compte avec une grande attention par la recherche. Cependant, notre recension d’écrits montre qu’il y a très peu d’études centrées sur le concept de somme infinie. Dans ce mémoire, nous allons présenter des résultats d’une analyse effectuée sur dix-sept manuels utilisés dans les Cégeps du Québec. Les résultats de cette analyse nous ont permis de prendre conscience que les manuels utilisés par l’enseignement actuel font rarement usage du registre graphique et que le registre algébrique est souvent privilégié. Ainsi, la plupart des manuels utilisés dans les Cégeps utilisent rarement les représentations visuelles qui pourraient être un outil important pouvant contribuer dans une appréhension complète du concept de série et les graphiques sont pratiquement absents dans tous les exercices et problèmes que ces manuels proposent. Par ailleurs, les résultats de notre recherche montre que les applications mathématiques et extramathématiques sont rares, et ce, bien que les sommes infinies soient un concept essentiel dans l’introduction d’autres concepts mathématiques et qu’elles permettent de modéliser plusieurs phénomènes. De plus, parmi le peu d’applications extramathématiques qui apparaissent dans les dix-sept manuels, beaucoup sont peu utiles à l’appréhension du concept en question étant donné que celles-ci sont artificielles (applications difficiles à réaliser dans la vie quotidienne). Enfin, nos résultats de recherche nous révèlent que le contenu des manuels en lien avec le concept de série mériterait d’être réajusté afin de permettre aux étudiants une meilleure appréhension de ce concept. / At the post high school level, advanced mathematical concepts are difficult to grasp for many students. The series concept is one such advanced concept that students meet for the first time formally in their postsecondary studies (Cégep in the Québec context). This concept has a very large number of applications both in mathematics and in science. However, its own complexity and nature against-intuitive make it very difficult to understand by some students. Among the difficulties to apprehend it, in many cases, we can find the idea that the sum of an infinite number of terms will give a quantity which will necessarily be infinitely large. Given the importance and complexity of this concept, one might expect it to be considered with great attention by the research. However, our literature review shows that there are very few studies focusing on the concept of infinite sum. In this Masters thesis, we will present the results of an analysis carried out on seventeen textbooks used in Cégeps in Quebec. The results of this analysis have allowed us to realize that the textbooks used by the current education rarely make use of the graphic register and that the algebraic register is often favored. Thus, most of the textbooks used in Cégeps rarely use visual representations that could be an important tool that can contribute to a comprehensive understanding of the concept of series and graphics are virtually absent in all the exercises and problems that these books offer. Furthermore, the results of our research show that mathematical and extramathematical applications are scarce, although infinite sums are a key concept in the introduction of other mathematical concepts and they allow modeling several phenomena. Moreover, among the few extramathematical applications that appear in the seventeen textbooks, many are of little use to the understanding of the concept in question since they are artificial (difficult applications to perform in daily life). Finally, our research results reveal that the content of textbooks in connection with the concept of series deserves to be readjusted to allow students a better understanding of this concept.

The study deals with the theory of optimal currency areas complemented with the EU's Maastricht criteria in order to investigate how today’s Economic and Monetary Union of the European Union can be divided into smaller unions with countries that are more homogeneous based on said criteria compared to the current larger currency union. To investigate this, we use cluster analysis as the method easily enables analysis of similarities and differences between countries. The results show that the optimal number of clusters for the nations in the EU in 2007, 2008, 2010 and 2015 is ten and that the optimal number of clusters in 2019 is seven. We also observe a relatively distinct division between western and eastern countries, which splits the countries in two clusters. These two clusters are consistent over the studied years, however not considered the most optimal according to cluster analysis. Nonetheless, with respect to political, geographical, and cultural aspects, we conclude that having two different currencies within the European Union being the most realistic. / Studien behandlar teorin om optimala valutaområden, kompletterat med EU:s Maastrichtkriterier för att undersöka hur den nuvarande ekonomiska och monetära unionen i EU kan delas in i mindre unioner med länder som är mer homogena utifrån nämnda kriterier jämfört med dagens större valutaunion. För att undersöka detta använder vi oss av klusteranalys eftersom metoden på ett enkelt sätt möjliggör analys av likheter och skillnader mellan länder. Resultatet visar att optimalt antal kluster för länderna i EU under åren 2007, 2008, 2010 och 2015 är tio och att optimalt antal kluster under år 2019 är sju. Vi observerar också en relativt tydlig uppdelning mellan de västra och östra länderna, som delar länderna i EU i två större kluster. Dessa två kluster är enhetliga över de undersökta åren, men inte helt optimala enligt klusteranalysen. Trots detta, så bedömer vi att dela in den Europeiska unionen i två valutaunioner är den mest realistiska slutsatsen utifrån politiska, geografiska, och kulturella skillnader. / Die Studie behandelt die Theorie der optimalen Währungsräume, ergänzt durch die Maastricht-Kriterien der EU, um zu untersuchen, wie die heutige europäische Wirtschafts-und Währungsunion in kleinere Unionen aufgeteilt werden kann. Diese Unionen sollten auf der Grundlage dieser Kriterien homogener als die heutige größere Währungsunion sein. Um dies zu untersuchen, verwenden wir Clusteranalyse, da diese Methode die Analyse von Ähnlichkeiten und Unterschieden zwischen den Ländern leicht ermöglicht. Die Studie zeigt, dass die optimale Anzahl von Clustern für die EU-Länder in den Jahren 2007, 2008, 2010 und 2015 bei einer Größe von zehn liegt und dass die optimale Anzahl von Clustern im Jahr 2019 bei sieben liegt. Wir finden auch eine ziemlich deutliche Aufteilung zwischen westlichen und östlichen Ländern. Diese zwei Clustern sind über den studierten Jahren durchgängig, aber laut der Klusteranalyse nicht völlig optimal. Dennoch finden wir, die Europäische Union in zwei Währungsunionen verteilen, die am meisten realistische Schlussfolge laut politische, geographische, und kulturellen Aspekten ist.

This research presented in this study demonstrates that county level population growth, economic growth, and localized social structure are interrelated. An analysis of the spatial distribution of these factors in the Southeast Region of the United States during the period of 1995-2000 also indicates the importance of differences in rural versus urban and coastal versus non-coastal areas as well as the importance of such factors as highways, large cities, and universities in economic, population, and social structure interrelationships. An extensive dataset is used in the analysis as a number of analysis tools including statistical analysis, econometric models, spatial econometric models, structural equation models, and GIS mapping.

No description available.

No description available.