Generalized estimating equations (GEEs) are commonly used in the modelling of correlated data. However, in the presence of informative cluster sizes, estimates obtained using GEEs may be biased. In order to correct for this bias a weighted GEE may be used. Previous research has extended the use of weighted GEEs to a longitudinal setting but requires that cluster sizes remain constant over time. In this thesis, two new weighting schemes are investigated to allow for valid parameter estimation in a longitudinal setting where cluster sizes are informative and may change over time. Specifically, this thesis considers weighting by the inverse of the time-dependent cluster size, and by the total number of observations for a given cluster. Through Monte Carlo simulation, the performance of traditional GEEs, GEEs under previously proposed weighting schemes, and these two new models are compared. Results of these studies show that weighting by the total number of observations results in unbiased parameter estimates with excellent coverage.

This work reports an investigation of colloidal suspensions during sedimentation in what is known as the intermediate concentration range; one notoriously difficult to study. Two materials were examined: titanium dioxide P25 nanoparticles and magnesium hydroxide. The characterisation of these materials highlighted their high tendency to form aggregates under certain conditions. By the use of laser diffraction, measurements of the cluster size were conducted at under various conditions of shear. The use of sonication energy suggested the identification and classification of two classes of clusters related to their strength: high strength , and low strength clusters. A mathematical model which considered cluster formation and the occurrence of breakage predicted the aggregation and disaggregation kinetics. The approach was based on cluster-cluster interactions rather than particle-particle interactions. The results obtained by particle size analysis were compared with the size obtained using permeability analysis and settling velocity. In both cases the calculated sizes were comparable with the data obtained from size analysis; however, for magnesium hydroxide the predicted cluster size was a little higher and this may be due to the formation of channels giving faster settling. For the titanium dioxide it was noticeable that different mixing strategies exhibited different cluster size, network formation and settling behaviour. Finally, a novel modelling approach based on the presence of clusters rather than particles is presented. It is a combined model which considers the settling curve divided into two zones: a zone below the gel point modelled by a Kynch type approach and a zone above the gel point modelled by consolidation theory. This combined approach was only applicable to the settling data of titanium dioxide, where the settling data encompassed the gel point and the gel point could be identified by consideration of the Richardson and Zaki plots. For magnesium hydroxide, only the consolidation model was needed as all the initial settling concentrations were above the gel point.

Σε προβλήματα ερμηνείας βιολογικών δεδομένων όπου οι υπό μελέτη μονάδες εμφανίζονται κατά συστάδες (cluster) τυχαίου μεγέθους και πλήθους, ιδιαίτερο ρόλο παίζουν οι επιγενείς κατανομές. Συγκεκριμένα ως επιγενής Poisson κατανομή μπορεί να παρασταθεί κάθε μονοδιάστατη διακριτή κατανομή η οποία είναι άπειρα διαιρετή. Έχει μελετηθεί, η περίπτωση στην οποία η κατανομή του μεγέθους της συστάδας (csd) είναι μια γενικευμένη (εισάγεται νέα παράμετρος) εξαρτώμενη μεγέθους (gsb) λογαριθμική κατανομή. Παίρνοντας τα όρια αυτής της παραμέτρου ως οριακές κατανομές προκύπτουν η ΝΝΒD και η Pόlya-Aeppli. Στη παρούσα διπλωματική μελετάται η κατανομή που προκύπτει όταν ως csd χρησιμοποιείται η gsb μιας οιασδήποτε κατανομής. Δίνεται η πιθανογεννήτρια και προσδιορίζονται οι ασυμπτωτικές κατανομές στη γενικότερη περίπτωση. Μελετώνται επίσης, οι ιδιότητες της κατανομής και δίνονται εκτιμητές με τις μεθόδους των ροπών και της μέγιστης πιθανοφάνειας. Ειδικότερα, παρουσιάζεται η περίπτωση της ακρότμητης Poisson που δίνει ως οριακές κατανομές τις Νeyman και Thomas και προσομοιώνονται δεδομένα. Εξάγονται επίσης, ως ειδική περίπτωση των γενικών τύπων, τα αποτελέσματα που έχουν αποδειχθεί για τη λογαριθμική κατανομή. Στη συνέχεια αναπτύσσονται αντίστοιχα γενικευμένα διδιάστατα μοντέλα τέτοιων κατανομών. Δίνονται επίσης οι περιθώριες και οι δεσμευμένες κατανομές τους, υπολογίζονται οι ροπές, και χρήσιμες σχέσεις για τα διδιάστατα μοντέλα. Τέλος, παρουσιάζονται ειδικές περιπτώσεις, όπως οι Sum-Symmetric Power-Series και δίνονται εφαρμογές των διδιαστάτων κατανομών που μελετήθηκαν. / In biological data interpretation domains, where the units we exam come along as clusters of random size and number, generalized distributions have a very major role. In particular, every univariate discrete distribution that is infinite divisible can be formed like a generalized Poisson distribution. The case where the cluster-size distribution is a generalized (a new parameter has been inserted) size-biased log-series distribution has been studied. Taking the limits of this parameter, as limited cases we have the NNBD and Polya-Aeppli distribution. In this diplomatic work, we study the distribution which arises when as a csd we use the gsb of a random distribution. We give the pgf and we see the asymptotic distributions in the general case. We also see the attributes of the distribution and we give estimators with the method of moments and maximum likelihood estimators. Specially, we report the case of Truncated Poisson, which gives Neyman and Thomas as limiting cases and we simulate some data. Likewise, we also see the results that have been proofed for the Log-Series distribution as a special case of the general formulas. Then, we see correspond generalized Bivariate models of these distributions. We also give the marginals and the conditional distributions, we find the moments and some useful relations about the Bivariate models. Final, we present special cases, like Sum-Symmetric Power-Series and we give applications of the Bivariate distributions that we saw. In biological data interpretation domains, where the units we exam come along as clusters of random size and number, generalized distributions have a very major role. In particular, every univariate discrete distribution that is infinite divisible can be formed like a generalized Poisson distribution. The case where the cluster-size distribution is a generalized (a new parameter has been inserted) size-biased log-series distribution has been studied. Taking the limits of this parameter, as limited cases we have the NNBD and Polya-Aeppli distribution. In this diplomatic work, we study the distribution which arises when as a csd we use the gsb of a random distribution. We give the pgf and we see the asymptotic distributions in the general case. We also see the attributes of the distribution and we give estimators with the method of moments and maximum likelihood estimators. Specially, we report the case of Truncated Poisson, which gives Neyman and Thomas as limiting cases and we simulate some data. Likewise, we also see the results that have been proofed for the Log-Series distribution as a special case of the general formulas. Then, we see correspond generalized Bivariate models of these distributions. We also give the marginals and the conditional distributions, we find the moments and some useful relations about the Bivariate models. Final, we present special cases, like Sum-Symmetric Power-Series and we give applications of the Bivariate distributions that we saw.

Two different definitions of cluster-size heterogeneity are investigated as well as correlation time of different quantities using the Metropolis algorithm and the Wolff algorithm. It is confirmed that the correlation time multiplied by the computation time is lower for the Wolff algorithm in an area around the critical temperature. It is also confirmed that one definition of the heterogeneity has a local maximum at the critical temperature where as the other has an abrupt change in derivative. The local maximum appears with L ≥ 64 and it is predicted but not verified that systems with L > 43 have such a maximum. The relationship between the number of distinct cluster sizes for clusters with spin-up and spin-down is investigated and it is observed that these transition from being significantly different at lower temperatures to being mostly similar at higher temperatures. The point of transition appears to be near the critical temperature.

Les collisions d’ions lourds ultrarelativistes ont pour objectif principal l'étude des propriétés de la matière nucléaire soumise à températures et densités d'énergie extrêmes. La chromodynamique quantique (QCD) prédit, dans ces conditions, l’existence d’une nouvelle phase de la matière dans laquelle les constituants des hadrons sont déconfinés en un plasma de quarks et gluons (QGP). Les saveurs lourdes (charme et beauté) sont produites lors de processus durs aux premiers instants des collisions, avant de traverser le milieu. Par conséquent, la mesure des quarkonia (mésons cc et bb) est particulièrement intéressante pour l'étude du QGP : leur dissociation, due notamment à l’écrantage de couleur, est sensible à la température initiale du système. Les mesures effectuées au SPS et RHIC ont permis de mettre en évidence plusieurs caractéristiques du milieu produit, mais ont aussi laissé plusieurs questions sans réponse. Avec une énergie 14 fois supérieure à celle du RHIC, l’accélérateur LHC (Large Hadron Collider) au CERN, entré en fonctionnement fin 2009, a ouvert une nouvelle ère pour l'étude des propriétés du QGP. ALICE (A Large Ion Collider Experiment) est une des quatre grandes expériences fonctionnant auprès du LHC et dont le but principal est l'étude du plasma de quarks et gluons produit dans les collisions d'ions plomb à une énergie de 2.76 TeV par nucléon. Elle enregistre aussi des collisions pp afin de fournir la référence indispensable pour l'étude des collisions noyau-noyau et proton-noyau et de tester les calculs perturbatifs de QCD dans la région des faibles valeurs de la variable d'échelle x de Bjorken. Les quarkonia, ainsi que les saveurs lourdes ouvertes et les mésons légers, sont mesurés dans ALICE suivant leur mode de désintégration muonique avec le spectromètre à muons situé à petit angle polaire. Il est constitué d'un ensemble d’absorbeurs, d’un dipôle chaud, de cinq stations de trajectographie (Muon Tracking) et de deux stations de déclenchement (Muon Trigger). Le travail présenté dans cette thèse a été réalisé de 2011 à 2013 pendant les premières années de prise de données dans l’expérience ALICE. Après une introduction à la physique des ions lourds à hautes énergies et une description du setup expérimental, une étude des performances du Muon Trigger en Pb-Pb est proposée. En particulier, la stabilité dans le temps du détecteur et son efficacité de fonctionnement sont contrôlées. Le cluster size, correspondant au nombre moyen de voies adjacentes touchées par particule détectée, est étudié en fonction des différents variables. Les valeurs expérimentales sont comparées à des simulations afin de fournir une paramétrisation de cet effet. Finalement, la production du méson Ç en collisions Pb-Pb est analysée en détail et comparée à celle en collisions pp à la même énergie. Les résultats obtenus sont comparés aux mesures du J/ψ par ALICE, aux mesures par CMS et à des prédictions de modèles théoriques. / The main goal of ultrarelativistic heavy-ion collisions is the study of the properties of the matter at very high temperatures and energy densities. Quantum chromodynamics (QCD) predicts in these conditions the existence of a new phase of the matter whose components are deconfined in a Quark-Gluon Plasma (QGP). Heavy quarks (charm e bottom) are produced in the first stages of the collisions, before to interact with the medium. Therefore, the measurement of the quarkonia (cc and bb mesons) is of particular interest for the study of the QGP: their dissociation mainly due to the colour screening is sensible to the initial temperature of the medium. Previous measurements at the SPS and RHIC allowed to understand some characteristics of the system produced, but they also opened many questions. With an energy 14 times higher than RHIC, the LHC (Large Hadron Collider) at CERN opened a new era for the study of the QGP properties. ALICE (A Large Ion Collider Experiment) is the LHC experiment fully dedicated to the study of the Quark-Gluon Plasma produced in Pb-Pb collisions at an energy of 2.76 TeV per nucleon. The experiment also participates to the proton-proton data taking in order to obtain the fundamental reference for the study of ion-ion and proton-ion collisions and for testing the predictions at very small Bjorken-x values of the perturbative QCD. Quarkonia, D and B mesons and light vector mesons are measured at forward rapidity by a Muon Spectrometer exploiting their (di)muonic decay. This detector is composed of a front absorber, a dipole magnet, five stations of tracking (Muon Tracking) and two stations of trigger (Muon Trigger). The work presented in this thesis has been carried out from 2011 to 2013 during the first period of data taking of ALICE. After a detailed introduction of the heavy-ion physics and a description of the experimental setup, the performance of the Muon Trigger in Pb–Pb collisions are shown. A particular attention is devoted to the stability of the detector during the time and to the trigger effectiveness. Moreover, the cluster size, corresponding to the number of adjacent strips hit by a particle, is studied as a function of different variables. The experimental results will be compared to simulations in order to obtain a good parametrization of this phenomenon. Finally, the Ç production in Pb-Pb collisions is carefully analysed and compared to that in pp collisions at the same energy. The results are then compared to the J/ψ measurements obtained by ALICE, to the CMS results and to some theoretical predictions.

acase@tulane.edu

Multilevel datasets are commonly used and increasingly popular in research in the organizational and other social sciences. These models are complex and have many elements beyond those found in more traditional linear models. However, research on how multilevel models perform is lacking. The current paper examined the impact of common factors (average cluster size, cluster size distribution, average number of clusters, strength of the intraclass correlation coefficient, and effect sizes of individual and cluster level variables, and their interaction) in multilevel datasets. Monte Carlo data simulation was used across 6,144 factor-combination conditions. The results of study factors on observed intraclass correlation coefficients, calculated design effect, and empirical design effect are discussed. The results of this study have implications for both researchers in both academic and applied fields. The scale of the simulation variables allow it to be germane to datasets from across the social sciences. However, the nature of data simulation and analysis is such that there are still many elements that can and should be accounted for in future research.

The dust particles generated due to mechanical wear of iron ore pellets and clusters formed in molten stainless steel alloyed with rare earth metals (REM) are considered in this study. Firstly, the influence of the characteristics of iron ore pellets, applied load on a pellet bed and partial reduction of the pellets on the size distribution of the generated dust was investigated. Secondly, REM clusters are investigated to evaluate the size distribution of the clusters. Also, an extreme value distribution (EVD) analysis has been applied for the observed REM clusters. The large sized pellets showed 10-20% higher wear rate than small sized pellets during wear in a planetary mill. Moreover, an increase of ~67% was observed in the friction and dust generation in the pellet bed as the applied load increased from 1 to 3 kg. Also, it was observed that a higher friction in the pellet bed can lead to an increased amount of airborne particles. The mechanical wear experiments of pellets reduced at 500 °C (P500) and 850 °C (P850) showed that P500 pellets exhibit ~16-35% higher wear rate than unreduced pellets. For the P850 pellets, the wear is inhibited by formation of a metallic layer at the outer surface of the pellets. The mechanism of dust generation has been explained using the obtained results. A reliable cluster size distribution of REM clusters was obtained by improving the observation method and it was used to explicate the formation and growth mechanism of REM clusters. The results show that the growth of clusters is governed by different types of collisions depending on the size of the clusters. For EVD analysis three different size parameters were considered. Moreover, using the maximum length of clusters results in a better correlation of EVD regression lines compared to other size parameters. Moreover, a comparison of predicted and observed maximum lengths of clusters showed that further work is required for the application of EVD analyses for REM clusters. / Studien fokuserar på två olika typer av mikropartiklar som är valda från olika delar av järn- och ståltillverkningsprocessen. Dessa partiklar är dels stoft som genereras på grund av mekanisk nötning av partiklar och dels klusters som bildas i flytande rostfria stål legerade med sällsynta jordartsmetaller (REM). Inledningsvis så undersöktes inverkan av tre faktorer på storleksfördelningen hos stoft som bildas vid hantering av järnoxidpellets. De undersökta faktorerna inkluderade karakteristiken hos järnoxidpellets, det applicerade trycket på pelletsbädden och den partiella reduktionen av järnoxidpellets. Därefter så utfördes tredimensionella undersökningar av REM kluster som extraherats med hjälp av elektrolytisk extraction för att bestämma storleksfördelningen hos klustren. Dessutom så utfördes en extremvärdesdistribution (EVD) studie för de studerade klustren. En planetkvarn användes för att undersöka inverkan of karakeristiken hos pellets på stoftbildningen. Resultaten visade att storleken på pellets kan påverka nötningshastigheten under dessa försöksförhållanden. Pellets som hade en större storlek (13.5&lt; Deq &lt;15.0 mm) uppvisade en 10 till 20% högre nötningshastighet i jämförelse med mindre pellets (9.5&lt; Deq &lt;12.5 mm). Baserat på analyserna av stoftet som genererades under nötningsexperimenten så konstaterades att nötningsmekanismerna för dessa pellets var abrasions- och kollisionsnötning. En pelletsbädd skapades för att möjliggöra studier av inverkan av ett applicerat tryck på stoftbildningen och friktionskrafterna i en pelletsbädd. Ett varierat tryck på mellan 1 till 3 kg applicerades på pelletsbädden. Resultaten visade att en ökning på ~67% av friktionskraften och stoftbildningen ägde rum när det applicerade trycket ökades från 1 till 3kg. Dessutom så visade resultaten att en högre friktionskraft i pelletsbädden kan resultera in en ökad mängd luftburna partiklar. Den mekaniska nötningen av pellets som reducerats vid 500 °C (P500) och 850 °C (P850) studerades också genom användande av en planetkvarn. Resultaten visade att P500 pellets uppvisade en ~ 16 till 35% högre nötningshastighet i jämförelse med oreducerade referenspellets.  Resultaten för P850 pellets visade att den mekaniska nötningen motverkades genom bildningen av ett metalliskt skikt på den yttre delen av pelletsen. Resultaten visade också att stoftet som bildats pga mekanisk nötning av reducerade pellets innehöll 3 till 6 gånger mer grova partiklar  (&gt;20µm) i jämförelse med stoft som bildats från oreducerade pellets. Slutligen så diskuterades hur dessa resultat kan relateras till industriella förhållanden med avseende på mekanismerna som är involverade i den mekaniska nötningen av pellets samt med avseende på relationen mellan hastigheten av de utgående gaserna och storlken och morfologin hos stoftpartiklarna. Klusters innehållande REM-oxider som extraherats från en 253MA rostfri stålsort undersöktes med användande av en tredimensionell teknik. En trovärdig storleksfördelning av klusters (CSD) erhölls genom att förbättra undersökningsmetoden och denna användes för att studera bildningen och tillväxten av REM oxider. Dessutom så användes cirkularitetsfaktorn hos klusters för att dela in klustren i två olika grupper, vilka bildas och tillväxer enligt olika mekanismer. Resultaten visade också att tillväxten av klusters gynnas av olika typer av kollisioner som beror av av storleken på klusters. För REM-klusters så drogs slutsatsen att turbulenta kollisioner är den huvudsakliga mekanismen som påverkar tillväxten. Avhandlingen behandlar även problemet om hur det är möjligt att hantera synfält där det inte förekommer kluster vid en extremvärdesdistribution (EVD) analys. Tre olika parametrar undersöktes i EVD analysen. Resultaten visar att om den maximala längden på kluster (LC) används i analysen så erhålls den bästa korrelationen gällande regressionslinjen för en EVD analys. Specifikt så var R2 värdet upp till 0.9876 i jämförelse med de andra storleksparametrarna som har värden i intervallet 0.9656 – 0.9774. Slutligen så visar resultaten från en jämförelse mellan beräknade och observerade maximala klusterlängder att EVD analyser för studier av REM kluster behöver undersökas ytterligare i framtiden. / <p>QC 20161128</p>

In this study, we considered a heterogeneous, clustered WSN, which consists of two types of nodes (clusterheads and sensor nodes) deployed randomly over a sensing field. We investigated two cases based on how clusterheads can reach the sink: direct and multi-hop communication cases. Network dimensioning problems in randomly deployed WSNs are among the most challenging ones as the attributes of these networks are mostly non-deterministic. We focused on a number of network dimensioning problems based on the connected coverage concept, which is the degree of coverage achieved by only the connected devices. To evaluate connected coverage, we introduced the term cluster size, which is the expected value of the area covered by a clusterhead together with sensor nodes connected to it. We derived formulas for the cluster size and validated them by computer simulations. By using the cluster size formulas, we proposed a method to dimension a WSN for given targeted connected coverage. Furthermore, we formulated cost optimization problems for direct and multi-hop communication cases. These formulations utilize not only cluster size formulas but also the well-connectivity concept. We suggested some search heuristics to solve these optimization problems. Additionally, we justified that, in practical cases, node heterogeneity can provide lower cost solutions. We also investigated the lifetime of WSNs and for mulated a cost optimization problem with connected coverage and lifetime constraints. By solving this optimization problem, one can determine the number of nodes of each type and the initial energies of each type of node that leads to lowest cost solution while satisfying the minimum connected coverage and minimum lifetime requirements.

Conventional cellular systems have not taken full advantage of fractional frequency reuse and adaptive allocation due to the fixed cluster size and uniformed channel assignment procedures. This problem may cause more fatal consequences considering the cutting-edge 4G standards which have higher data rate requirements such as 3GPP-LTE and IEEE 802.16m (WiMAX). In this thesis, three different partitioning schemes for adaptive clustering with fractional frequency reuse were proposed and investigated. An overlaid cellular clustering scheme which uses adaptive fractional frequency reuse factors would provide a better end-user experience by exploiting the high level of signal to interference ratio (SIR). The proposed methods are studied via simulations and the results show that the adaptive clustering with different partitioning methods provide better capacity and grade of service (GoS) comparing to the conventional cellular architecture methodologies.