Title: Cluster analysis of dynamic data Author: Bc. Michal Marko Department: Department of Software and Computer Science Education Supervisor: RNDr. František Mráz, CSc. Supervisor's e-mail address: Frantisek.Mraz@mff.cuni.cz Abstract: The mail goal of this thesis is to choose or eventually to propose own modifications to some of the cluster analysis methods in order to observe the progress of dynamic data and its clusters. The chosen ones are applied to the real data. The dynamic data denotes series of information that is created periodically over the time describing the same characteristics of the given set of data objects. When applied to such data, the problem of classic clustering algorithm is the lack of coherence between the results of particular data set from the series which can be illustrated via application to our artificial data. We discuss the idea of proposed modifications and compare the progress of the methods based on them. In order to be able to use our modified methods on the real data, we examine their applicability to the multidimensional artificial data. Due to the complications caused by multidimensional space we develop our own validation criterion. Once the methods are approved for use in such space, we apply our modified methods on the real data, followed by the visualization and...

Nowdays, coupled cluster method belongs to one of the most used quantum chemical methods. However, the single-reference coupled cluster methods are not able to describe systems where the static correlation have an important role. Multireference coupled cluster methods developed in our group can describe both static and dy- namic correlation and can be used for problematic systems. Together with explicitly correlated wavefunction, which can properly describe the electronic cusp and speed up the convergence to the complete ba- sis set limit, they are able to calculate computationally demanding diradicals. Multireference CC calculations of tetramethylenethane have been perforemd and the performance of explicitly correlated version is discussed. Calculations of the isomerization of bicyclobu- tane using the multireference approach are presented as well. 1

Approved for public release; distribution is unlimited. / (DFAS) vendor payment transactions through Unsupervised Modeling (cluster analysis). Clementine Data Mining software is used to construct unsupervised models of vendor payment data using the K-Means, Two Step, and Kohonen algorithms. Cluster validation techniques are applied to select the most useful model of each type, which are then combined to select candidate records for physical examination by a DFAS auditor. Our unsupervised modeling technique utilizes all the available valid transaction data, much of which is not admitted under the current supervised modeling procedure. Our procedure standardizes and provides rigor to the existing unsupervised modeling methodology at DFAS. Additionally, we demonstrate a new clustering approach called Tree Clustering, which uses Classification and Regression Trees to cluster data with automatic variable selection and scaling. A Recommended SOP for Unsupervised Modeling, detailed explanation of all Clementine procedures, and implementation of the Tree Clustering algorithm are included as appendices. / Major, United States Marine Corps

Doctor of Philosophy / Department of Mathematics / Zongzhu Lin / Let A[subscript]n(S) be a coefficient free commutative cluster algebra over a field K. A cluster automorphism is an element of Aut.[subscript]KK(t[subscript]1,[dot, dot, dot],t[subscript]n) which leaves the set of all cluster variables, [chi][subscript]s invariant. In Chapter 2, the group of all such automorphisms is studied in terms of the orbits of the symmetric group action on the set of all seeds of the field K(t[subscript]1,[dot,dot, dot],t[subscript]n). In Chapter 3, we set up for a new class of non-commutative algebras that carry a non-commutative cluster structure. This structure is related naturally to some hyperbolic algebras such as, Weyl Algebras, classical and quantized universal enveloping algebras of sl[subscript]2 and the quantum coordinate algebra of SL(2). The cluster structure gives rise to some combinatorial data, called cluster strings, which are used to introduce a class of representations of Weyl algebras. Irreducible and indecomposable representations are also introduced from the same data. The last section of Chapter 3 is devoted to introduce a class of categories that carry a hyperbolic cluster structure. Examples of these categories are the categories of representations of certain algebras such as Weyl algebras, the coordinate algebra of the Lie algebra sl[subscript]2, and the quantum coordinate algebra of SL(2).

The study is about enterprises in the formal and informal sectors in sub-Saharan Africa and consists of three separate but connected essays. The first essay examines whether or not structural reforms in the business regulatory environment, trade sector, and the financial sector, can influence access to debt financing for investment by enterprises in sub-Sahara Africa. The data is from the World Bank Enterprise Surveys. The analyses involve panel data models. The results are indicative that taken together; structural policy reforms reduce debt-financing constraints. Reforms in the business regulatory environment and the financial sector increase the likelihood of access to debt financing. However, for trade, beyond a threshold, further reductions in the tariff and non-tariff barriers make it harder for enterprises to obtain debt financing. These results have implications for the type of reforms pursued in various countries. The second essay examines how social capital, education, and liquidity constraints influence the decision of an entrepreneur to operate either in the formal or informal sector. For enterprises that did not register and operating for less than five years, there is evidence that the likelihood of running in the informal sector, as opposed to the formal sector, decreases with the entrepreneurial level of education while social capital increases this likelihood. However, for enterprises in the informal sector, operating for over five years, liquidity constraints impedes formalisation. In the long run, the decision to stay informal or formalise depends on funding constraints, the incidence of taxes in the formal sector and the perception that there are no benefits from operating in the formal sector. The third essay is about the relationship between enterprises in the formal and informal sector and aims to uncover, at least in part, whether or not social and human capitals are important in facilitating the linkages between enterprises in the formal and the informal sectors. The analysis involves flexible binary generalised extreme value models. The results are indicative that for both male and female entrepreneurs, social and human capitals have significant positive real effects on the likelihood of linkages. / October 2016

The studies presented in this thesis deal with resonant and non-resonant excitation of free variable size clusters using synchrotron radiation in the soft X-ray regime. The post collision interaction (PCI) effect is investigated in free variable size krypton and argon clusters near the Kr 3d and Ar 2p ionization energies. The core ionization energies of surface and bulk sites in variable size clusters can be clearly distinguished. This is mostly due to the polarization screening. It is found that the asymmetry, which is a consequence of PCI, is characteristically smaller for clusters than for isolated atoms. Moreover, there is less asymmetry for bulk sites than for surface sites in variable size rare gas clusters. We assign the results in terms of mechanisms that are based on quantum mechanical models of post collision interaction. Complementary experiments on the photoionization of free van der Waals clusters are performed by using zero kinetic energy (ZEKE) photoelectron spectroscopy in the Ar 2p-, Kr 3d-, Ne 1s-, and N2-regimes. The experimental approach is also suitable to detect cluster size dependent changes in electronic structure. This also allows us to study post collision interaction in variable size clusters. The parameters of the PCI profiles deduced for ZEKE experiments indicate that there are no significant changes in core ionization dynamics compared to near-threshold experiments. Results from model calculations in Kr 3d ionization energy indicate that different geometric sites can be clearly distinguished from each other by their substantial shift in Kr 3d ionization energy, though the dimer shows almost the same Kr 3d ionization energy as the free atom. A comparison with the experimental results indicates that there is resemblance with the model calculations, even though close-lying ionization energies are blended and require deconvolutions of the experimental spectra. It is evident from the present work that one can observe distinct shifts in core ionization energies in van der Waals clusters that are formed in wide size distributions of a jet expansion. The emission of ultraviolet fluorescence radiation from variable size argon clusters is investigated with high spectral resolution in the Ar 2p-excitation regime. The fluorescence excitation spectra reveal strong fluorescence intensity in the Ar 2p-continuum, but no evidence for the occurrence of discrete low-lying core-exciton states in the near-edge regime. This finding is different from the absorption and photoionization cross sections of argon clusters and the solid. The dispersed fluorescence shows a broad molecular band centered near 280 nm. The present results are consistent with the formation of singly charged, excited moieties within the clusters, which are assigned as sources of the radiative relaxation in the 280 nm regime. A fast energy transfer process (interatomic Coulombic decay, ICD) is assigned to be primarily the origin of these singly charged, excited cations besides intra-cluster electron impact ionization by Auger electrons. Our findings give possibly the first experimental evidence for ICD in the core level regime. Free, variable size nitrogen clusters are investigated in the N 1s excitation regime in comparison with the free molecule and solid nitrogen. The conversion of Rydberg states into core excitons, surface and bulk, was studied. The experimental results are simulated by ab initio calculations using (N2)13 as a reasonable prototype cluster structure that allows us to simulate both surface and bulk properties in comparison with the isolated molecule. The present results clearly show that there are specific properties, such as molecular orientation, in molecular van der Waals clusters, which do not exist in atomic van der Waals clusters. It is shown that inner and outer surface sites give rise to distinct energy shifts of the low lying surface core excitons. / In der vorliegenden Dissertation wurden Experimente zur resonanten und nicht-resonanten Anregung von Clustern variabler Größe durchgeführt. Hierzu kam Synchrotronstrahlung im weichen Röntgenbereich zum Einsatz. Der "Post-Collision Interaction"-Effekt (PCI) wurde im Detail am Beispiel von Krypton und Argon-Clustern im Bereich der Kr 3d- und Ar 2p-Anregung studiert. Es lassen sich die Ionisierungsenergien von Atomen, die an der Oberfläche bzw. im Volumen gebunden sind, klar unterscheiden. Dies ist aufgrund der unterschiedlichen Polarisationsabschirmung möglich, die zu einer Verschiebung der Innerschalen-Ionisierungsenergien führt. Die Linienformen der Photoelektronenbanden werden asymmetrisch, wenn die Anregungsenergie geringfügig über der Ionisierungsenergie liegt. Dies lässt sich auf den PCI-Effekt zurückführen. Es wird beobachtet, dass die Asymmetrie vom isolierten Atom über Oberflächenatome zu den im Volumen gebundenen Atomen abnimmt. Diese Veränderung der Linienformen wird mit Hilfe von Mechanismen, die auf Grundlage von quantenmechanischen Modellen basieren, interpretiert. Komplementäre Experimente wurden an Argon- und Neon-Clustern zur Nullvolt-Photoelektronen-Spektroskopie (ZEKE) durchgeführt (Anregung der Ar 2p-Kante, Kr 3d-Kante, N2 1s und Ne 1s-Kante). Auch mit diesem Ansatz lassen sich größenabhängige Veränderungen der elektronischen Struktur in Clustern sowie die Bedeutung des PCI Effektes bestimmen. Ein Vergleich dieser Resultate mit der Anregung, die nahe der Ionisationsschwelle liegt, zeigt, dass es zu keiner signifikanten Veränderung der Ionisationsdynamik als Funktion der Anregungsenergie kommt. Berechnungen zur Ioniserungsenergien von Krypton-Clustern im Bereich der Kr 3d-Anregung zeigen, dass sich einzelne geometrische Orte klar in ihrer Ionisierungsenergie unterscheiden. Das Krypton-Dimer zeigt allerdings fast dieselbe 3d-Ioniserungsenergie wie das freie Atom. Der Vergleich mit den experimentellen Resultaten zeigt, dass eine gute übereinstimmung zwischen Modell und Experiment besteht. Allerdings müssen die experimentellen Spektren entfaltet werden, da die relativen Verschiebungen der Ionisierungsenergien zu gering sind und die Rumpflochlebensdauer zu einer Verbreiterung der Banden führt. Die Resultate belegen, dass sich ausgezeichnete Werte für Rumpfniveau-Ionisierungsenergien bestimmen lassen, obwohl die Cluster in breiten Größenverteilungen vorliegen. Dies lässt sich durch die ortsspezifische Photoionisation erklären. Die Emission von Fluoreszenzstrahlung im ultravioletten Spektralbereich nach Rumpfniveauanregung wurde im Fall von 2p-angeregten Argon-Clustern untersucht. Die hochaufgel östen Spektren zeigen hohe Intensität im 2p-Kontinuum, jedoch keinen Hinweis auf signifikante Beiträge im Bereich der Rumpfniveau-Excitonen. Dieses Ergebnis unterscheidet sich vom Absoprtions- und Photoionisationsquerschnitt von Argon-Clustern sowie festem Argon. Die dispergierte Fluoreszenz liefert eine intensive Bande bei 280 nm. Dieses Resultat lässt sich mit der Fluoreszenz von einfach geladenen, angeregten Argon-Clustern erklären. Die Bildung von einfach geladenen Ionen nach primärer Doppelionisation im Ar 2p-Kontinuum wird durch einen schnellen Energietransfer-Prozess (Interatomic Coulombic Decay, ICD) erklärt. Er läuft nach der Rumpfniveauanregung ab und liefert, neben der Elektronenstoßionisation durch schnelle Auger-Elektronen, einfach geladene Clusterfragmente, die nachfolgend strahlend relaxieren. Dieses Ergebnis ist als erster Hinweis darauf zu werten, dass der ICD-Prozess auch im Bereich der Innerschalenanregung auftritt. Freie Stickstoff-Cluster variabler Größe wurden im Bereich der N 1s-Anregung untersucht. Hier stand die Umwandlung der Rydberg-Zustände in die entsprechenden Oberflächen- und Volumen-Excitonen in Fokus der Studien. Die Resultate wurden mit denen zu freiem und kondensiertem Stickstoff verglichen. Die experimentellen Resultate lassen auch einen Vergleich mit ab initio Rechnungen zu, wofür (N2)13 als Prototyp-Cluster genutzt wurde, da hier sowohl oberflähen - als auch volumengebundene Moleküle auftreten. Diese Resultate zeigen signifikante Unterschiede im Vergleich zu atomaren Clustern. Es zeigt sich, dass die molekulare Orientierung die Lage der Excitonenbanden beeinflusßt. Ebenso treten signifikante Energieverschiebungen relativ zum isolierten Molekül auf, die sich durch Absorption von Zentren erklären lassen, die entweder auf der inneren bzw. äußeren Oberfläche der Cluster gebunden sind.

The theoretical work presented in this thesis is concerned with the highest possible oxidation states of the 5d transition metal row. Based on a validation study of several DFT functionals against accurate coupled-cluster CCSD(T) methods we will present calculations on a series of new high oxidation state HgIV species. Quantum-chemical calculations have also been applied to various fluoro complexes of gold in oxidation states +V through +VII to evaluate the previously claimed existence of AuF7. The calculations indicate clearly that the oxidation state (+V), e.g., in [AuF5]2, remains the highest well-established gold oxidation state. Further calculations on iridium in oxidation state (+VII) show that IrF7 and IrOF5 are viable synthetic targets, whereas higher oxidation states of iridium appear to be unlikely. Structures and stabilities of several osmium fluorides and oxyfluorides were also studied in this thesis. It is shown that homoleptic fluorides all the way up to OsF8 may exist. Combining the results of the most accurate quantum-chemical predictions of this thesis and of the most reliable experimental studies, we observe a revised trend of the highest oxidation states of the 5d transition metal row. From lanthanum (+III) to osmium (+VIII), there is a linear increase of the highest oxidation states with increasing atomic number. Thereafter, we observe a linear descent from osmium (+VIII) to mercury (+IV). We will also present a short outlook to the transition metals of the 3d and 4d row and their highest reachable oxidation states. / In der vorliegenden theoretischen Arbeit wurden mittels quantenchemischer Methoden die höchsten Oxidationsstufen der späten Übergangselemente untersucht. Um eine adäquate Beschreibung dieser Systeme zu gewährleisten, wurde zuerst eine Validierungsstudie verschiedener Dichtefunktionale, die mit hochgenauen coupled-cluster CCSD(T) Berechnungen verglichen wurden, durchgeführt. Das zugrundeliegende Referenzsystem war Quecksilber in der Oxidationsstufe +IV (HgF4, HgCl4, HgH4). Es wurden Strukturoptimierungen von Minima und Übergangszuständen, Atomisierungsenergien sowie die entsprechenden Zerfallsreaktionen für die Systeme betrachtet. Basierend auf diesen Ergebnissen konnten weitere HgIV Systeme mit sogenannten „Weakly Coordinating Anions“ wie z.B. [OTeF5]-, [AsF6]-, [Sb2F11]- usw. unter Verwendung von Dichtefunktionalmethoden untersucht werden. Die beiden Verbindungen Hg[OTeF5]4 und Hg[AsF6]4 scheinen dabei die Oxidationsstufe +IV am besten zu stabilisieren. Quantenchemische Methoden wurden ebenfalls zur Berechnung von Fluorkomplexen des Goldes in den Oxidationsstufen von +V bis +VII verwendet. Dabei wurde insbesondere überprüft, ob das angeblich experimentell gefundene AuF7 tatsächlich existiert. Es konnte gezeigt werden, dass eine Existenz von AuF7 unter den in der Literatur angegebenen Bedingungen sehr wahrscheinlich ausgeschlossen werden kann. Diese Instabilität wird ebenfalls für das quantenchemisch untersuchte AuF6 beobachtet. Somit bleibt die Oxidationsstufe +V in [AuF5]2 die höchste erreichbare Oxidationsstufe für Gold. Basierend auf coupled-cluster CCSD(T) Berechnungen konnten die Verbindungen des Iridiums in der Oxidationsstufe +VII (IrF7, IrOF5) als thermochemisch stabil vorhergesagt werden, wohingegen die höheren Iridiumverbindungen des IrVIII und IrIX sehr unwahrscheinlich sind. Außerdem wurden Strukturen und Stabilitäten verschiedener Osmiumfluoride und Oxyfluoride in dieser Arbeit diskutiert. Es konnte gezeigt werden, dass ausgehend von OsF6 auch die höheren Verbindungen OsF7 und OsF8 experimentell zugänglich sein sollten. Kombiniert man die in dieser Arbeit vorhergesagten Verbindungen in ihren höchsten Oxidationsstufen mit den verlässlichsten experimentellen Untersuchungen, so beobachtet man einen revidierten Trend der höchsten Oxidationsstufen der 5d-Übergangsmetallreihe: Direkt proportional zur Ordnungszahl steigen die höchsten Oxidationszahlen zunächst linear an, von Os (+VIII) bis hin zu Hg (+IV) kann ein linearer Abfall beobachtet werden. Abschließend werden in dieser Arbeit die höchsten Oxidationsstufen der 3d und 4d Übergangsmetalle in einer kurzen Übersicht vorgestellt.

As cloud computing has become the more popular choice to host clusters in recent times there are multiple providers that offer their services to the public such as Amazon web services, Google cloud platform and Microsoft Azure. The decision of cluster provider is not only a decision of provider, it is also an indirect decision of cluster infrastructure. The indirect choice of infrastructure makes it important to consider any potential differences in cluster performance caused by the infrastructure in combination with the workload type, but also the cost of the infrastructure on the available public cloud providers. To evaluate whether or not there are any significant differences in either cluster cost or performance between the available public cloud providers, a performance comparison study was conducted. The study consisted of multiple clusters hosted on Amazon Web Services and the Google Cloud Platform. The clusters had access to five different instance types that each correspond to a specific number of available cores, amount of memory and storage. All clusters executed a CPU intensive, I/O intensive, and MapReduce workload while simultaneously having its performance monitored with regard to CPU, memory, and disk usage. The performance comparison study revealed that there are significant performance differences between clusters hosted on Amazon web services and Google cloud platform for the chosen workload types. Since there are significant differences it can be concluded that the choice of provider is crucial as it impacts the cluster performance. Comparing the selected instance types against each other with regard to performance and cost, reveals that a subset of them have better performance as well as lower cost. The instance types that is not a part of this subset, have either better performance or lower cost than its counterpart on the other provider.

A análise de agrupamento de dados é uma tarefa fundamental em mineração de dados e aprendizagem de máquina. Ela tem por objetivo encontrar um conjunto finito de categorias que evidencie as relações entre os objetos (registros, instâncias, observações, exemplos) de um conjunto de dados de interesse. Os algoritmos de agrupamento podem ser divididos em particionais e hierárquicos. Uma das vantagens dos algoritmos hierárquicos é conseguir representar agrupamentos em diferentes níveis de granularidade e ainda serem capazes de produzir partições planas como aquelas produzidas pelos algoritmos particionais, mas para isso é necessário que seja realizado um corte (por exemplo horizontal) sobre o dendrograma ou hierarquia dos grupos. A escolha de como realizar esse corte é um problema clássico que vem sendo investigado há décadas. Mais recentemente, este problema tem ganho especial importância no contexto de algoritmos hierárquicos baseados em densidade, pois somente estratégias mais sofisticadas de corte, em particular cortes não-horizontais denominados cortes locais (ao invés de globais) conseguem selecionar grupos de densidades diferentes para compor a solução final. Entre as principais vantagens dos algoritmos baseados em densidade está sua robustez à interferência de dados anômalos, que são detectados e deixados de fora da partição final, rotulados como ruído, além da capacidade de detectar clusters de formas arbitrárias. O objetivo deste trabalho foi adaptar uma variante da medida da Modularidade, utilizada amplamente na área de detecção de comunidades em redes complexas, para que esta possa ser aplicada ao problema de corte local de hierarquias de agrupamento. Os resultados obtidos mostraram que essa adaptação da modularidade pode ser uma alternativa competitiva para a medida de estabilidade utilizada originalmente pelo algoritmo estado-da-arte em agrupamento de dados baseado em densidade, HDBSCAN*. / Cluster Analysis is a fundamental task in Data Mining and Machine Learning. It aims to find a finite set of categories that evidences the relationships between the objects (records, instances, observations, examples) of a data set of interest. Clustering algorithms can be divided into partitional and hierarchical. One of the advantages of hierarchical algorithms is to be able to represent clusters at different levels of granularity while being able to produce flat partitions like those produced by partitional algorithms. To achieve this, it is necessary to perform a cut (for example horizontal) through the dendrogram or cluster tree. How to perform this cut is a classic problem that has been investigated for decades. More recently, this problem has gained special importance in the context of density-based hierarchical algorithms, since only more sophisticated cutting strategies, in particular nonhorizontal cuts (instead of global ones) are able to select clusters with different densities to compose the final solution. Among the main advantages of density-based algorithms is their robustness to noise and their capability to detect clusters of arbitrary shape. The objective of this work was to adapt a variant of the Q Modularity measure, widely used in the realm of community detection in complex networks, so that it can be applied to the problem of local cuts through cluster hierarchies. The results show that the proposed measure can be a competitive alternative to the stability measure, originally used by the state-of-the-art density-based clustering algorithm HDBSCAN*.

Completely inorganic nanoscale clusters play an essential role in many aspects of inorganic chemistry, materials chemistry, and geochemistry. The underlying dynamic behavior of these species in solution defines how and why they make successful thin film precursors as well as exist naturally in the environment. There have been a limited number of previous solution studies involving inorganic nanoscale clusters due to the lack of spectroscopic handles and availability of analytical techniques. This dissertation outlines the available and appropriate characterization techniques needed for identifying and studying inorganic nanoscale species and then uses proton Nuclear Magnetic Resonance (1H-NMR) and Diffusion Ordered Spectroscopy (DOSY) to fully characterize the Ga13-xInx(µ3-OH)6(µ-OH)18(H2O)24(NO3)15 (0 ≤ x ≤ 6) cluster series in solution. This research lays a foundation for a multitude of future studies on the dynamic behavior of these species that was previously unachievable. This dissertation includes previously published and unpublished co-authored material.