Dissertations / Theses on the topic 'Optimal clusters'

We developed a new version of a C++ code, Get the Halo 2021, that implements the optimal linear matched filter presented in Maturi et al.(2005). Our aim is to detect dark matter haloes of clusters of galaxies through their weak gravitational lensing signatures applying the filter to a catalogue of simulated galaxy ellipticities. The dataset represents typical data that will be available thanks to the Euclid mission, thus we are able to forecast the filter performances on weak lensing data obtained by Euclid. The linear matched filter is optimised to maximise the signal-to-noise ratio (S/N) of the detections and minimise the number of spurious detections caused by superposition of large-scale structures; this is achieved by suppressing those spatial frequencies dominated by the large-scale structure contamination. We compared our detections with the true population of dark matter haloes used to produce the catalogue of ellipticities. We confirmed the expectations on the filter performance raised by Maturi et al.(2005) and Pace et al.(2007). We found that S/N 7 can be considered as a reliable threshold to detect haloes through weak lensing as 83% of our detections with S/N>7 were matched to the haloes; this is consistent with Pace et al.(2007). The purity of our catalogues of detections increases as a function of S/N and reaches 100% at S/N 10.5-11. We also confirmed that the filter selects preferentially haloes with redshift between 0.2 and 0.5, that have an intermediate distance between observer and background sources, condition that maximises the lensing effects. The completeness of our catalogues is a steadily growing function of the mass until 4-5Msun/h, where it reaches values 58-68%. Our algorithm might be used to enhance the reliability of the detections of the AMICO code (Bellagamba et al.2018), the optimal linear matched filter implemented in the Euclid data analysis pipeline to identify galaxy clusters in photometric data (Euclid Collaboration et al.2019).

The aim of this thesis is to examine the cluster analysis ability segment the data set by selected methods. The data sets are consisting of quantitative variables. The basic criterion for the data sets is that the number of classes has to be known and the next criterion is that the membership of all object to each class has to be known too. Execution of the cluster analysis was based on knowledge about the number of classes. Classified objects to individual clusters were compared with its original classes. The output was the relative success of classification by selected methods. Cluster analysis methods are not able to determine an optimal number of clusters. Estimates of the optimal number of clusters were the second step in analysis for each data set. The ability of selected criteria identify the original number of classes was analyzed by comparing numbers of original classes and numbers of optimal clusters. The main contribution of this thesis is the validation of the ability of selected cluster analysis methods to identify similar objects and verify the ability of selected criteria to estimate the number of clusters corresponding to the real file distribution. Moreover, this work provides a structured overview of the basic cluster analysis methods and indicators for estimating the optimal number of clusters.

The objective of this thesis is the evaluation of selected coefficients of the cluster analysis when determining the optimal number of clusters. The analytical evaluation is performed on 20 independent real datasets. The analysis is made in statistical SYSTAT 13.1 Software. The application of coefficients RMSSTD, CHF, PTS, DB and Dunn's index on real datasets is the main part of this thesis, because the issue of evaluating the results of clustering is not devoted sufficient attention in scientific publications. The main goal is whether the selected coefficients of clustering can be applied in the real situations. The second goal is to compare selected clustering methods and their corresponding metrics when determining the optimal number of clusters. In conclusion, it is found that the optimal number of clusters determined by the coefficients mentioned above cannot be considered to be correct since, after application to the real data, none of the selected coefficients overcome the success rate of 40%, hence, the use of these coefficients in practice is very limited. Based on the practical analysis, the best method in identifying the known number of clusters is the average linkage in connection with the Euclidean distance, while the worst is the Ward's method in connection with the Euclidean distance.

La BPCO est une pathologie hétérogène responsable d’une morbidité et d’une mortalité importante. La classification GOLD de la sévérité de la BPCO introduit des incertitudes, son applicabilité dans la pratique est plus que douteuse. Les exacerbations et les comorbidités contribuent à la sévérité globale de l'affection, au complexe des symptômes et à l'évolution de la maladie. L’évaluation de la dyspnée en pratique clinique n’est pas chose aisée, et il est difficile d’apprécier la part attribuable respiratoire de la dyspnée chez des patients ayant des comorbidités. Les données actuelles restent insuffisantes pour affirmer ou infirmer l’importance de la majorité des candidats phénotypes. Principalement, ce travail a pour buts de caractériser l’évolution des trajectoires des patients BPCO et d’identifier des candidats phénotypes chez des patients BPCO. Secondairement, ce travail a pour buts : d’identifier les clusters stables de comorbidités, de caractériser les déterminants de la dyspnée, de déterminer les facteurs associés aux phénotypes des Exacerbateurs fréquents et d'évaluer l'impact des symptômes, des fonctions pulmonaires et des comorbidités sur la mortalité. Les patients BPCO (VEMS/CVF<70% post-BD) ont été inclus depuis Janvier 2014 par leur pneumologue en utilisant le questionnaire de la cohorte PALOMB. Ce questionnaire comprenait les domaines suivants : les critères démographiques, les symptômes cliniques, les tests fonctionnels, les comorbidités, les vaccinations et les traitements inhalés. Après cinq ans de suivi, les données sur leur statut vital ont été obtenues en utilisant le RNIPP. L’identifier des clusters stables de comorbidités a été réalisé à partir des modèles de classification supervisée sur les composantes principales. L’analyse de sensibilité et l’estimateur des moindres carrés pénalisé (modèle LASSO) ont ensuite été utilisés afin d’évaluer les déterminants de la dyspnée. Le suivi longitudinal de la fréquence des exacerbations a permis d’identifier trois phénotypes à partir d’une classification non-supervisée. De plus, Le modèle de Cox a été utilisé afin d’identifier les facteurs associés à la mortalité toute cause. Les arbres de classification et de régression (CART) ont été utilisés pour répartir les patients dans des sous-groupes et la pertinence clinique a été déterminée en comparant la mortalité à 5 ans. L’analyse en cluster la plus optimale (supervisé vs non-supervisé) a été utilisée pour identifier de façon robuste les phénotypes cliniques. L’analyse en cluster a permis de différencier 5 clusters de comorbidités : cardiovasculaire ; syndrome métabolique et SAOS ; dénutrition ; patients avec bronchectasie et un cluster de patients ayant moins de comorbidités. Nos résultats suggèrent que la dyspnée est liée à la sévérité de la BPCO, au sexe, aux exacerbations, aux comorbidités et à l'hyperinflation statique. Révélant que l'hyperinflation statique définie par le rapport IC/TLC était un meilleur déterminant de l'échelle de dyspnée mMRC comparativement aux rapports RV/TLC et FRC/TLC. Sur la base de notre hypothèse, nous avons pu déterminer quatre phénotypes : le phénotype A (Exacerbateurs non fréquents), B (exacerbations fréquentes chez les patients en sous poids), C (transitoires) et D (exacerbations fréquentes chez les patients obèses). Les déterminants les plus importants du phénotype exacerbateur fréquent sont les antécédents d’exacerbations, l’absence de vaccination antigrippale annuelle et l’anxiété. Le cancer et les comorbidités cardiovasculaires contribuent à l’augmentation de la mortalité, en plus des critères connus en rapport avec la sévérité de la maladie. Nos résultats montrent que la multimorbidité est fréquente, hétérogène et varie en fonction du stade de sévérité de la BPCO. Ils illustrent l’aspect plurifactoriel de la dyspnée chez les patients BPCO, confirment l’existence et la pertinence clinique d’un phénotype d’Exacerbateurs fréquents de patients BPCO
COPD is a heterogeneous and multisystemic disease with progressive increasing morbidity and mortality. The GOLD classification introduces uncertainties, its validity in predicting mortality is still uncertain, and its applicability in practice is more than questionable. Our understanding of the longitudinal determinants of COPD exacerbations remains unclear. COPD patients frequently suffer from comorbidities, with a significant impact on mortality. Evaluating dyspnea in clinical practice is not easy, and it is difficult to assess the respiratory attributable part of dyspnea in patients with comorbidities. Current data remains insufficient to confirm the importance of the majority of candidate phenotypes. Mainly, this work aims to characterize the evolution of the trajectories of COPD patients and to identify candidate phenotypes in COPD patients. Secondly, this work aims to: identify stable clusters of comorbidities, characterize the determinants of dyspnoea, determine the factors associated with the phenotypes of frequent exacerbators and assess the impact of symptoms, pulmonary functions and comorbidities on mortality. Diagnosis of COPD was made using spirometry with post-BD FEV1/FVC <70%. Since January 2014, pulmonologists have been using the PALOMB web site questionnaire to include COPD patients. This questionnaire included the following domains: demographic criteria, clinical symptoms, lung function, comorbidities and therapeutic management. After 5 years of follow-up, vital status was recorded through the RNIPP. Stable clusters of comorbidities were identified using the supervised classification models on the principal components. The sensitivity analysis and the least absolute shrinkage and selection operator (LASSO) were then used to assess the determinants of dyspnea. The unsupervised classification was used to identify three phenotypes by modelling the longitudinal changes in the frequency of COPD exacerbations. In addition, the Cox model was used to identify factors associated with all-cause mortality. Classification and regression trees (CART) were used for allocating patients to the subgroups and clinical relevance was determined by comparing 5-year mortality. The most optimal cluster analysis (supervised vs unsupervised) was used to robustly identify clinical phenotypes. The cluster analysis showed five phenotypes of comorbidities: cluster 1 included cardiac profile; cluster 2 included less comorbidities; cluster 3 included metabolic syndrome, apnea and anxiety-depression; cluster 4 included malnutrition and osteoporosis and cluster 5 included bronchiectasis. Regardless of the cut-off values set to identify higher dyspnoea, our results suggested that dyspnoea is related to the severity of airflow limitation, gender, exacerbations, comorbidities and hyperinflation. Revealing that the hyperinflation defined by IC/TLC ratio was a better determinant of the mMRC dyspnoea scale in comparison to both RV/TLC and FRC/TLC ratio. Based on our hypothesis, we were able to determine four phenotypes: A (infrequent), B (frequent in underweight patients), C (transient), and D (frequent in obese patients). The most important determinants of the frequent exacerbating phenotype are: the presence of anxiety, chronic sputum, and unvaccinated against influenza. In addition to known criteria related to COPD severity, cancer and cardiovascular comorbidities contribute to increased mortality in COPD patients. Our results show that within the Palomb cohort (a large clinic-based cohort) multimorbidity is frequent, heterogeneous and varies according to the stage of COPD severity. The presence of comorbidities should therefore be included in any assessment of COPD severity. These cohort results illustrate in real-life the multifactorial aspect of dyspnoea in COPD patients, confirm the existence and clinical relevance of two frequent exacerbators’ phenotypes and the currently used threshold to define this phenotype

Mestrado em Economia
Com a aproximação da data de adesão formal dos dez Países em Adesão à União Europeia, muitos autores têm-se debruçado sobre a questão da adesão prospectiva destes países à Zona Euro. À luz da teoria das Zonas Monetárias Óptimas, a perda da autonomia na condução da política monetária e cambial constitui o principal custo económico associado à adopção do euro por parte destes países, ao limitar os instrumentos disponíveis aos Estados-membros para acomodar eventuais choques assimétricos. Neste trabalho, considerei um modelo vector autoregressivo (VAR) estrutural para identificar e comparar os choques de procura e de oferta entre os Estados-membros da Zona Euro e os Países em Adesão. De forma a avaliar o grau de simetria entre os choques da Zona Euro e dos Países em Adesão, considerei duas abordagens distintas: o cálculo das correlações dos choques de procura e oferta entre os vários países e a UEM e a análise de clusters. Recorrendo ainda à análise de clusters, procurei também identificar grupo homogéneos de países dentro da futura UE e analisar a sua evolução ao longo do tempo. Os resultados obtidos neste estudo relativamente ao período 1996-2002 revelam que os Países em Adesão estão, em geral, menos correlacionados com os choques de oferta e de procura da Zona Euro que os actuais Estados-membros da UEM. No entanto, o cenário em termos individuais é bastante heterogéneo. Em particular, alguns Países em Adesão mais avançados, a Hungria e a Polónia, já se encontram ao nível dos países de menor dimensão da UEM (nomeadamente Portugal e a Grécia). Em contrapartida, em países como Lituânia e a Eslováquia, a correlação entre os choques permanece baixa, o que implica que um avanço rápido para a adopção do euro traria eventualmente elevados custos de estabilização para estes países.
On the eve of the formal accession of the ten Accession Countries into the European Union, many authors have been discussing the implications of the upcoming integration of these countries in the Euro Area. Under the Optimum Currency Areas (OCA) theory, the loss of monetary autonomy and exchange rate flexibility constitutes the main economic cost associated with the adoption of the euro, thus limiting the instruments for adjusting asymmetric shocks available to member countries. In this paper, I used a structural vector autoregression model to identify and compare demand and supply shocks between euro area countries and the accession countries. In order to assess the degree of symmetry between euro area and accession countries shocks, 1 considered two ditterent approaches: the correlation between shocks and cluster analysis. With the help of cluster analysis, I also tried to identify homogenous groups of countries within the future EU, and analyse their evolution through time. Focusing on the period 1996-2002, the results show that the accession countries are generally less correlated with euro area supply and demand shocks than the EMU Member Countries. However, when considering individual countries, a different picture emerges. The more advanced Accession Countries (namely Hungary and Poland) are hardly different in the correlation of their shocks vis-a-vis the euro area than the smaller countries of the EMU (i.e. Portugal and Greece). At the same time, countries like Lithuania and Slovakia show a low correlation with euro area shocks, implying that moving fast towards the adoption of the euro may eventually generate high stabilization costs for these countries.

The diploma thesis explores with the evaluation of the success of selected indices for determining the number of clusters used in cluster analysis. The aim of this thesis is on the basis of various combinations of clustering methods and distances verify whether, alternatively using which clustering methods and distances is it possible to rely on the results of indices for determining the number of clusters. The results of success rate presented in the third chapter suggest that not all of indices for determining the number of clusters can be used universally. The most successful index is Dunn index, which was able to determine the correct number of clusters in 37 % of cases, respectively Davies-Bouldin index with the share of 70 % when including deviation of one cluster. The success rate is affected by both used method and selected distance.

Les dynamiques d'opinions suscitent un regain d'intérêt de la part des communautés d'Automatique et de Mathématiques Appliquées. Cela peut s'expliquer par l'émergence des réseaux sociaux en ligne et de la possibilité d'exploiter et comprendre les comportements et données associés. Les modèles de dynamiques d'opinions sont des cas particuliers de systèmes multi-agents. Ces systèmes ont des applications diverses comme par exemple le contrôle du comportement d'une flotte de robots collaboratifs. Un système de dynamique d'opinions est ainsi constitué de plusieurs agents. L'état de chaque agent est alors modélisé par un réel qui représente l'opinion de celui-ci à propos d'un certain sujet. Les modèles mathématiques de dynamiques d'opinions décrivent alors l'évolution des opinions des agents dans le temps. De nombreux résultats ont été obtenus sur le régime asymptotique de ces systèmes, notamment sur la convergence vers le consensus, lorsque les opinions de tous les agents du système tendent vers la même valeur. Le régime transitoire, moins bien connu, présente également des phénomènes intéressants comme la formation d'accords locaux transitoires mais qui sont plus délicats à définir. Une étude de ces phénomènes est présentée pour des systèmes de dynamiques d'opinions à temps discret avec fonctions d'influence génériques dépendant de l'état. La contribution principale propose un critère de détection de la formation de ces accords locaux, ainsi que la prédiction de la durée pendant laquelle ce critère est vérifié. La seconde partie de cette thèse se concentre sur les dynamiques d'opinions en temps continu dont un des agents, appelé leader, a un rôle particulier : l'évolution de son opinion est contrôlable. Le leader est utilisé pour rassembler tous les agents dans son voisinage en temps fini, puis pour les amener vers une valeur de consensus désirée. La loi de commande proposée est valide pour des systèmes à fonctions d'influence dépendant du temps et de l'état et sous certaines conditions. De plus, le problème de contrôle en temps optimal consistant à rassembler tous les agents dans le voisinage du leader en temps minimal est examiné. Ceci est effectué dans le cas particulier de fonctions d'influence dépendant uniquement de l'état. Afin de déterminer la classe des commandes optimales admissible, le Principe du Maximum de Pontryagin est utilisé. Dans un cadre général, la commande optimale est précisée sous la forme de relations implicites. Pour le cas particulier où il n'y a pas d'interaction entre les agents, la loi de commande en temps optimal a été obtenue en pratique pour toute condition initiale
Opinion dynamics systems aroused renewed interest in the Control System Theory and Applied Mathematics communities. This can be explained by the emergence of online social networks and the possibility of exploiting and understanding associated behaviours and data. Opinion dynamic models are special cases of multi-agent systems. These systems have various applications such as controlling the behaviour of a fleet of collaborative robots. A system of opinion dynamics is thus composed of several agents. The state of each agent is then modeled by a real number, which represents the agent's opinion on a certain subject. The mathematical models of opinion dynamics then describe the evolution of agents' opinions over time. Many results have been obtained on the asymptotic behaviour of these systems, notably on convergence towards consensus, when the opinion of all agents of the system tend towards the same value. The less well known transient state also presents interesting phenomena such as the formation of local transient agreements, which are more tricky to define. A study of these phenomena is presented for discrete-time opinion dynamics systems with generic state dependent influence functions. The main contribution proposes a criterion for detecting the formation of these local agreements, as well as a prediction of the duration during which this criterion is verified. The second part of this thesis focuses on opinion dynamics in continuous time in which one of the agents, called leader, has a particular role: the evolution of its opinion is controllable. For systems with time and state-dependent influence functions and under certain conditions, a control law is presented that allows the leader to gather all agents in its neighbourhood in finite time and then steer them to a desired consensus value. In addition, the problem of time optimal control which consists in bringing all agents together in the neighborhood of the leader in minimal time is also examined for the case of only state-dependent influence functions. The Pontryagin Maximum Principle specifies the class of admissible optimal controls with implicit expressions within a general framework. For the particular case where there is no interaction between agents, the time-optimal control law has been obtained in practice for any initial conditions

Dissertation follows up cluster analysis of European Union states using social and economical indicators. In the first part all the social and economical indicators are defined. In the second part of the dissertation all these indicators in time of economical and financial and later debt crisis in years from 2007 to 2012 in European Union states are analysed. In the third part the cluster analysis is applicated for the social and economical indicators of the European Union states. Five clusters were identified using cluster analysis. Structure of these clusters was changing during years 2007 and 2012. First cluster contained developed Western European countries (Belgium, Denmark, Germany, Ireland, France, Netherlands, Austria, Finland, Sweden and United Kingdom). The second cluster was created from countries, that entered to European Union after year 2004 (Bulgaria, Estonia, Croatia, Latvia, Lithuania, Hungary, Poland, Romania and Slovakia). The third cluster contained Czech Republic, Estonia, Greece, Lithuania, Portugal, Slovakia and Slovenia. In the fourth cluster were Southern European countries Greece, Spain, Italy, Cyprus and Malta and the fifth cluster contained only Luxembourg.

Cluster analysis includes a range of methods and practices that are used primarily for classification of objects. It takes an important role in many areas. Since the resulting distribution of objects into clusters may vary depending on the selected methods and specifications, it is appropriate to assess the results obtained. This paper proposes new ways of evaluating these results in a situation where objects are characterized by qualitative variables or by variables of different types. These coefficients can be used either to compare different methods (in terms of better outcomes) or for finding of the optimal number of clusters. All of them are based on the detection of variability which is also used for measuring of dissimilarity of objects and clusters. The newly proposed evaluation methods are applied to real data sets (of different sizes, with different number of variables, including variables of different types) and the behavior of these coefficients in different conditions is being examined. These data sets have known as well as unknown classification of objects into clusters. The best coefficient for evaluating clustering results with different types of variables can be considered, based on the analysis carried out, the modified coefficient of CHF. Local maximum value according to which the results of the clustering are evaluated, almost always exists. The analysis has proven that in most cases this value meets the expected results of the well-known classification of objects into clusters. The existence of local extremes of the other coefficients depends on specific data sets and is not always feasible.

This thesis first presents a relatively straight forward approach for detecting galaxy clusters using spectroscopic data. A friend-of-friends algorithm based on that of Huchra & Geller (1982) is implemented with linking parameters that take into account selection effects on the the 2dF-SDSS and QSO (2SLAQ) Luminous Red Galaxy Survey (Cannon et al. 2006). The linking parameters are constrained using a mock halo catalogue. The galaxy groups and clusters found with this method have an average velocity dispersion of \sigma v = 467:97 kms-1 and an average size of R clt = 0:78 h-1Mpc. Cluster masses are estimated using the cluster velocity dispersions and appear consistent with values expected for genuine structures. The spectroscopic cluster catalogue is then used to calibrate and compare with a more complex method for detecting clusters using photometric redshifts based on the method of Botzler et al. (2004). The spectroscopic cluster catalogue can be reproduced by around 38% and up to 80% if matching is made only to groups and clusters with six or more members. This code is also applied to the Megaz-LRG DR7 catalogue (Collister & Lahav 2004) producing two catalogues. One that appears to have a good level of completeness relative to the 2SLAQ spectroscopic catalogue. A spectroscopic follow up of some preliminary results from the photometric cluster finder was made using the Anglo-Australian Telescope, which show that the majority of the clusters analysed are genuine and approximate masses can be estimated from the cluster velocity dispersions. Finally, some initials results from on going work in the Dark Energy Survey collaboration are presented, which cover simulated galaxy photometric redshift and colour analysis as well as cluster detection.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Os aglomerados de galáxias são os maiores objetos ligados que observamos no universo. Dado que as galáxias são consideradas traçadores de matéria escura, os aglomerados de galáxias nos permitem estudar a formação e a evolução de estruturas em grande escala. As contagens do número de aglomerados de galáxias são sensı́veis ao modelo cosmológico, portanto são usadas como observáveis para restringir os parâmetros cosmológicos. Nesta tese estudamos os aglomerados de galáxias óticos. Iniciamos o trabalho analisando a degradação da precisão e a exatidão no desvio para o vermelho fotométrico estimado através de métodos de aprendizagem de máquina (machine learning) ANNz2 e GPz. Além do valor singular do desvio para o vermelho fotométrico clássico (isto é, valor médio ou máximo da distribuição), implementamos um estimador baseado em uma amostragem de Monte Carlo usando a função de distribuição cumulativa. Mostramos que este estimador para o algoritmo ANNz2 apresenta a melhor concorância com a distribuição do desvio para o vermelho espectroscópico, no entanto, uma maior dispersão. Por outro lado, apresentamos o buscador de aglomerados VT-FOFz, o qual combina as técnicas de Voronoi Tessellation e Friends of Friends. Estimamos seu desempenho através de catálogos simulados. Calculamos a completeza e a pureza usando uma região de cilindrica no espaço 2+1 (ou seja, coordenadas angulares e desvio para o vermelho). Para halos maciços e aglomerados com alta riqueza, obtemos valores elevados de completeza e pureza. Comparamos os grupos de galáxias detectados através do buscador de aglomera- dos VT-FOFz com o catálogo RedMaPPer SDSS DR8. Recuperamos ∼ 90% dos aglomerados de galáxias do catálogo RedMaPPer até o desvio para o vermelho de z ≈ 0.33 considerando galáxias mais brilhantes com r < 20.6. Finalmente, realizamos uma previsão cosmológica usando um método MCMC para um modelo plano de wCDM por meio da abundância de aglomerados de galáxias. O modelo fiducial é um universo ΛCDM plano. Os efeitos devidos à massa observável estimada e aos deslocamentos para o vermelho fotométricos são incluı́dos através de um modelo de auto-calibração. Empregamos a função de massa de Tinker para estimar o número de contagens em uma faixa de massa e um bin de deslocamento para o vermelho. Assumimos que a riqueza e a massa do aglomerado estejam relacionadas através de uma lei de potência. Recuperamos os valores fiduciais com nı́vel de confiança de até 2σ para os testes considerados.
The galaxy clusters are the largest bound objects observed in the universe. Given that the galaxies are considered as tracers of dark matter, the galaxy clusters allow us to study the formation and evolution of large-scale structures. The cluster number counts are sensitive to the cosmological model, hence they are used as probes to constrain the cosmological parameters. In this work we focus on the study of optical galaxy clusters. We start analyzing the degradation of both precision and accuracy in the estimated photometric redshift via ANNz2 and GPz machine learning methods. In addition to the classical singular value for the photometric redshift (i.e., mean value or maximum of the distribution), we implement an estimator based on a Monte Carlo sampling by using the cumulative distribution function. We show that this estimator for the ANNz2 algorithm presents the best agreement with the distribution for spectroscopic redshift, nonetheless a higher scattering. On the other hand, we present the VT-FOFz cluster finder, which combines the techniques Voronoi Tessellation and Friends of Friends. Through mock catalogs, we estimate its performance. We compute the completeness and purity by using a cylindrical region in the 2+1 space (i.e., angular coordinates and redshift). For massive haloes and clusters with high richness, we obtain high values of completeness and purity. We compare the detected galaxy clusters via the VT-FOFz cluster finder with the redMaPPer SDSS DR8 cluster catalog. We recover ∼ 90% of the galaxy clusters of the redMaPPer catalog until the redshift z ≈ 0.33 considering brighter galaxies with r < 20.6. Finally, we perform a cosmological forecasting by using a MCMC method, for a flat wCDM model through galaxy cluster abundance. The fiducial model is a flat ΛCDM Universe. The effects due to the estimated observable mass and the photometric redshifts are included via a self-calibriation model. We employ the Tinker’s mass function to estimate the number counts in a range of mass and a redshift bin. We assume that the richness and the cluster mass are related through a power law. We recover the fiducial values at 2σ confindence level for the considered tests.

Orientador: Maria Cristina Batoni Abdalla Ribeiro
Coorientador: Filipe Batoni Abdalla
Banca: Filipe Batoni Abdalla
Banca: Laerte Sodré Júnior
Banca: Marcos Vinícius Borges Teixeira Lima
Banca: Martín Makler
Resumo: Os aglomerados de galáxias são os maiores objetos ligados que observamos no universo. Dado que as galáxias são consideradas traçadores de matéria escura, os aglomerados de galáxias nos permitem estudar a formação e a evolução de estruturas em grande escala. As contagens do número de aglomerados de galáxias são sensı́veis ao modelo cosmológico, portanto são usadas como observáveis para restringir os parâmetros cosmológicos. Nesta tese estudamos os aglomerados de galáxias óticos. Iniciamos o trabalho analisando a degradação da precisão e a exatidão no desvio para o vermelho fotométrico estimado através de métodos de aprendizagem de máquina (machine learning) ANNz2 e GPz. Além do valor singular do desvio para o vermelho fotométrico clássico (isto é, valor médio ou máximo da distribuição), implementamos um estimador baseado em uma amostragem de Monte Carlo usando a função de distribuição cumulativa. Mostramos que este estimador para o algoritmo ANNz2 apresenta a melhor concorância com a distribuição do desvio para o vermelho espectroscópico, no entanto, uma maior dispersão. Por outro lado, apresentamos o buscador de aglomerados VT-FOFz, o qual combina as técnicas de Voronoi Tessellation e Friends of Friends. Estimamos seu desempenho através de catálogos simulados. Calculamos a completeza e a pureza usando uma região de cilindrica no espaço 2+1 (ou seja, coordenadas angulares e desvio para o vermelho). Para halos maciços e aglomerados com alta riqueza, obtemos valores elevados de ... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The galaxy clusters are the largest bound objects observed in the universe. Given that the galaxies are considered as tracers of dark matter, the galaxy clusters allow us to study the formation and evolution of large-scale structures. The cluster number counts are sensitive to the cosmological model, hence they are used as probes to constrain the cosmological parameters. In this work we focus on the study of optical galaxy clusters. We start analyzing the degradation of both precision and accuracy in the estimated photometric redshift via ANNz2 and GPz machine learning methods. In addition to the classical singular value for the photometric redshift (i.e., mean value or maximum of the distribution), we implement an estimator based on a Monte Carlo sampling by using the cumulative distribution function. We show that this estimator for the ANNz2 algorithm presents the best agreement with the distribution for spectroscopic redshift, nonetheless a higher scattering. On the other hand, we present the VT-FOFz cluster finder, which combines the techniques Voronoi Tessellation and Friends of Friends. Through mock catalogs, we estimate its performance. We compute the completeness and purity by using a cylindrical region in the 2+1 space (i.e., angular coordinates and redshift). For massive haloes and clusters with high richness, we obtain high values of completeness and purity. We compare the detected galaxy clusters via the VT-FOFz cluster finder with the redMaPPer SDSS DR8 cluster catalog. We recover ∼ 90% of the galaxy clusters of the redMaPPer catalog until the redshift z ≈ 0.33 considering brighter galaxies with r < 20.6. Finally, we perform a cosmological forecasting by using a MCMC method, for a flat wCDM model through galaxy cluster abundance. The fiducial model is a flat ΛCDM Universe. The effects due to the estimated observable mass and (Complete abstract click electronic access below)
Doutor

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.

The properties of galaxy clusters, such as abundance and mass to light ratios, have long been used to investigate and constrain cosmology. With vast numbers of newly detected clusters, such as from the Planck mission (Planck Collaboration et al., 2013), full determination of cluster properties, particularly mass, can be hugely expensive and time consuming. Optical characterisation o ers a cheap solution, using optical data alone to estimate cluster properties such as redshift. With the abundance of current optical data, such as from the Sloan Digital Sky Survey (SDSS), (Ahn et al., 2012) and upcoming all sky surveys, such as the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) 3 survey (Magnier et al., 2013), optical characterisation will play a key role in the investigation of the latest clusters. Presented in this thesis is the Gaussian Mixture full Photometric Red sequence Cluster Characteriser (GMPhoRCC), which aims to provide such an analysis, o ering substantial advantages over existing algorithms. GMPhoRCC identi es and models the red sequence, early-type galaxies which dominate the cluster, and uses the properties of this to estimate cluster redshift and richness, an optical mass proxy based on the number of cluster members. The main features include, full treatment of multi-modal distributions by modelling properties with error-corrected Gaussian Mixtures, model independence by using empirical photometric redshifts rather than assumed colour-redshift relations and quality control used to identify probable catastrophic failures in order to clean the characterisations. Using a sample of 5500 clusters taken from the GMBCG (Hao et al., 2010), NORAS (Bohringer et al., 2000), REFLEX (Bohringer et al., 2004) and XCS (Mehrtens et al., 2012) catalogues, GMPhoRCC redshift estimates are compared to spectra showing low scatter ( σ∆z~ 0:042) around the actual value. In addition applying the quality control to produce a clean subset removes most outliers (|zGMPhoRCC-zspec| > 0:03) gives a much tighter agreement, σ∆z~ 0:018 showing signi cant improvement over maxBCG, σ∆z~ 0:025, and XCS, σ∆z~ 0:050. In addition to comparisons with real clusters, an extensive evaluation of the GMPhoRCC selection function is presented using mock clusters. These mocks are produced by stacking red sequence galaxies from existing clusters, analysed using the SDSS DR9, in redshift-richness bins from which new sequences are resampled. This extends the similar approach of maxBCG and GMBCG where only rich clusters are used as seeds to generate mocks with a range of properties. Comparisons with mocks agree well with real clusters attaining low redshift scatters ( σ∆z~ 0:01) with the clean subset removing the majority of outliers. In addition, with a de nitive mock value, richness comparisons are possible and although show a larger fractional scatter (σ∆z n200 ~ 0:12) are centred on the mock value. Richness estimates are shown to be more sensitive to discrepancies in redshift, background uctuations and poor modelling of the red sequence than redshift. Completeness is estimated by considering the fraction of clusters found with characterisations within given bounds. First incomplete photometry, simulated by an i-band < 21 cut, is shown to remove members for clusters with z > 0:45. Redshift completeness, the fraction of clusters within 0:03 of the mock value, is not immediately hindered by the photometry, attaining 93% for 0:05 < z < 0:62 for clusters with a richness greater than 20, showing improvement over maxBCG (with 90% for 0:1 < z < 0:3) and a larger range than GMBCG (with 96% for 0:1 < z < 0:46). Similar to results from GMBCG, richness attains lower completeness rates due to discrepancies introduced by projection e ects, background uctuations, and redshift errors. The fraction of clusters within 25% of the mock value, de ning completeness, is measured as 91% for 0:07 < z < 0:45 for clusters with richness greater than 20, 78% for those with richness between 10 and 20, and 64% for those with richnesses less than 10. The application of GMPhoRCC follows, where characterisations are found for new XCS X-ray extended sources (Lloyd-Davies et al., 2011). Applying GMPhoRCC to these preliminary DR2 candidates ( 10 times larger than the current catalogue) using the VLT Survey Telescope (VST) ATLAS catalogue (Shanks & Metcalfe, 2012) and the much deeper Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) (Heymans et al., 2012) provides characterisations beyond the SDSS footprint. Of the 13; 956 candidates, 6124 have optical coverage, 5580 in the SDSS, 523 in ATLAS and 819 in CFHTLenS with some overlap. Overall characterisations are found for 4365 candidates, 1893 of which have an associated spectroscopic redshift. The clean subset comprises 1203 candidates, 904 with spectra. Considering XCS DR1, Mehrtens et al. (2012) presented 503 optically con rmed X-ray clusters of which 258 have spectroscopic redshifts and 108 have SDSS characterisations. GMPhoRCC provides characterisations for 360, 232 of which have spectroscopic redshifts. Overall GMPhoRCC provides 260 (149 of which are clean) new SDSS characterisations and 91 (61 of which are clean) new spectroscopic redshifts. Finally this thesis concludes with a discussion of future research, focusing mainly on a preliminary analysis of a clean spectroscopic subset of XCS DR1 in order to illustrate the potential to constrain X-ray scaling relations with the upcoming XCS DR2. Additionally, potential research into the e ect of environment on the red sequence is illustrated using the dependence of the CMR slope on X-ray temperature. While a slight dependence is found, the cluster sample is insu cient to contradict the independence on environment found by Hogg et al. (2004) and Hao et al. (2009).

In this study, Amsterdam Density Functional software is used to model bimetallic and ligated aluminum clusters. The stability of the bimetallic clusters is well described by the Jellium model, and the nature of bonding between dopants and aluminum in the bimetallic clusters is analyzed using different criteria. We find that sodium tends to bind ionically, while the bonding of magnesium is not so obvious. We also determine that examining the Mulliken population is the most useful parameter in differentiating bonding character. Calculations on ligated aluminum clusters reveal it behaves fundamentally different than the bimetallic clusters studied in the first part. The ligated clusters contained a high HOMO-LUMO gap regardless of size and the aluminum showed a high 3p Mulliken population. These results show ligated aluminum clusters behave according to Wade-Mingos counting rules.

We present the design and the first results of a program of optical spectroscopy of galaxies in clusters detected in South Pole Telescope (SPT) data using the Sunyaev-Zel'dovich (SZ) effect, the spectral distortion of the cosmic microwave background from galaxy clusters. We use resampling for an empirical determination of the uncertainty in cluster velocity dispersion calculated from galaxy redshift measurements. We discuss outstanding questions that need answering in order to reach the goal of using cluster velocity dispersion measurements to calibrate scaling relation between the SZ observable and the cluster mass.
Physics

This thesis is comprised of X-ray and optical studies of 27 X-ray selected galaxy clusters from the XMM-LSS survey. These systems are mostly groups and poor clusters, with temperatures 0.6-4.8 keV, spanning the redshift range 0.05 to 1.05, hence these are some of the highest redshift X-ray selected clusters to have been studied. In the X-ray study, the evolution in the X-ray surface brightness profiles of the hot intracluster plasma is studied. Comparing the profiles with a standard -model it is found that 54% of the sample possess cuspy (cool) cores. Trends with both temperature and redshift in the outer slope beta of the X-ray surface brightness and in the incidence of cuspy cores are investigated. Fits indicate that the incidence of cuspy cores does not decline at high redshifts, as has been reported in rich clusters. Rather such cores become more prominent with increasing redshift. It is also found that has a positive correlation with temperature. In the optical study, CFHTLS optical photometry has been used to study the galaxy luminosity functions of 14 members of the sample. Individual luminosity functions (LFs) as well as redshift-stacked and temperature-stacked LFs in three filters, g', r' and z', down to M = -14:5 are derived. All LFs were fitted by Schechter functions which well-constrained the faint-end slope, . Derived values of ranged from -:03 to as steep as -2:1. No evidence is found for upturns at faint magnitudes. Evolution in was apparent in all bands: it becomes shallower with increasing redshift. It is found that at z~0:3, alpha is steeper (-1.67) in the green (g') band than it is (-1.30) in the red (z') band. This colour trend disappears at low redshift, which is attributed to reddening of faint blue galaxies from z ~0.3 to z~0. Also, the total optical luminosity is calculated and is found to correlate strongly with X-ray luminosity and temperature, which is consistent with expectations for self-similar clusters with constant mass-to-light ratio.

L'intérêt de la recherche fondamentale pour les morceaux nanométriques de métaux nobles est principalement dû à la résonance localisée des plasmons de surface (LSPR) dans l'absorption optique. Différents aspects, liés à la compréhension théorique de la LSPR dans le cas de clusters de métaux nobles de taille dite intermédiaire, sont étudiés dans ce manuscrit. Afin d'avoir une vision plus large nous utilisons deux approches : l'approche électromagnétique classique et le formalisme ab initio en temps réel de la théorie de la fonctionnelle de la densité dépendant du temps (RT-TDDFT). Une comparaison systématique et détaillée de ces deux approches souligne et quantifie les limitations de l'approche électromagnétique lorsqu'elle est appliquée à des systèmes de taille quantique. Les différences entre les excitations plasmoniques collectives et celles impliquant les électrons d, ainsi que leurs interactions, sont étudiées grâce au comportement spatial des densités correspondantes. Ces densités sont obtenues en appliquant une transformée de Fourier dans l'espace à la densité obtenue par les simulations DFT utilisant une perturbation delta-kick. Dans ce manuscrit, des clusters de métaux nobles nus et protégés par des ligands sont étudiés. En particulier, motivé par de récents travaux sur les phénomènes d'émergence de plasmon, l'étude par TD-DFT de nano-alliages Au-Cu de taille tout juste inférieure à 2nm à fourni de subtiles connaissances sur les effets d'alliages sur la réponse optique de tels systèmes
The fundamental research interest in nanometric pieces of noble metals is mainly due to the localized surface-plasmon resonance (LSPR) in the optical absorption. Different aspects related to the theoretical understanding of LSPRs in `intermediate-size' noble-metal clusters are studied in this thesis. To gain a broader perspective both the real-time \ai formalism of \td density-functional theory (RT-TDDFT) and the classical electromagnetics approach are employed. A systematic and detailed comparison of these two approaches highlights and quantifies the limitations of the electromagnetics approach when applied to quantum-sized systems. The differences between collective plasmonic excitations and the excitations involving $d$-electrons, as well as the interplay between them are explored in the spatial behaviour of the corresponding induced densities by performing the spatially resolved Fourier transform of the time-dependent induced density obtained from a RT-TDDFT simulation using a $\delta$-kick perturbation. In this thesis, both bare and ligand-protected noble-metal clusters were studied. In particular, motivated by recent experiments on plasmon emergence phenomena, the TDDFT study of Au-Cu nanoalloys in the size range just below 2~nm produced subtle insights into the general effects of alloying on the optical response of these systems

En tant que structures gravitationnellement liées les plus massives, les amas de galaxies permettent de poser des contraintes fortes sur les structures à grande échelle prédites par le modèle cosmologique standard. Ils permettent aussi de comprendre l'influence de l'environnement sur l'évolution des galaxies. Pour mener ce type d'étude et obtenir des résultats robustes, il est impératif de construire des catalogues d'amas complets et purs. Dans le présent manuscrit, je décris l'algorithme de détection d'amas que j'ai développé lors de ma thèse de doctorat -Red GOLD ainsi que les résultats que j'ai obtenus en l'appliquant aux relevés multi-longueur d'onde. Mon algorithme est fondé sur la détection de surdensités de galaxies et la caractérisation de leur séquence rouge : il détecte les surdensités de galaxies rouges par rapport à la distribution moyenne des galaxies. Je sélectionne les galaxies rouges à l'aide des couleurs prédites par les modèles de population stellaire, en imposant des coupes en couleur en fonction du redshift. Parmi ces galaxies, j'identifie celles ayant un type spectral correspondant à des galaxies de type précoce. J'ai appliqué Red-GOLD à des données dans le visible venant de deux relevés diférents, le Next Generation Virgo Cluster Survey (NGVS) et le Canada-France-Hawaii Telescope Lensing Survey (CFHTLS) et j'ai détecté des candidats amas jusqu'à z~1. J'ai estimé les performances de mon algorithme en l'appliquant aux catalogues de galaxies simulées issus des simulations Millenium. Mon catalogue d'amas est complet à ~ 80 % jusqu'à z=1 et pur à 81%
Being galaxy clusters the most massive bound structures in the Universe, they represent a powerful tool to probe the large-scale structure predicted by the standard cosmological model, and to understand how environmental effects affect galaxy evolution. To conduct these studies and obtain reliable results, it is important to build complete and pure cluster catalogs. The use of these catalogs for cosmology requires accurate estimates of cluster mass. In this work, I describe the cluster detection algorithm that I developed during my PhD thesis : Red-GOLD, and the results that I obtained by applying i to current multi-wavelength surveys. My algorithm is based on the detection of galaxy overdensities and the characterisation of their red-sequence. The algorithm finds red galaxy overdensities with respect to the mean background. I select red galaxies using color predictions given by stellar population synthesis models and impose color limits as a function of redshift. Among those galaxies, I discern the early-type galaxies from their spectral type. I then identify cluster members using accurate photometric redshifts, and estimate the cluster candidate richness. I applied Red-GOLD to optical data coming from two different surveys, the Next Generatiôn Virgo Cluster Survey (NGVS) and the Canada-France-Hawaii Telescope Lensing Survey (CFHTLS) and detected galaxy cluster candidates up to redshift z=1. I assessed the performances of my algorithm by applying it to simulated galaxy catalogs from the Millennium simulations. My cluster catalogue is complete at the 80% up to redshift z=1 and pure at 81%

Die Untersuchungen der nichtskalierbaren Eigenschaften von Clustern in dem Größenregime, in dem jedes Atom zählt, zeigten, daß hier neuartige Phänomene und Funktionalität entstehen können. Dadurch motiviert wurden in dieser Arbeit: i) strukturelle und elektronische Eigenschaften sowie die Reaktivität von Metall Clustern, ii) stationäre optische Eigenschaften und iii) zeitabhängige Eigenschaften und optimale Kontrolle von ultraschnellen Prozessen in Edelmetallcluster und in nonstoichiometrischen Natrium-Fluorid Cluster, untersucht.
The study of the nonscalable properties of clusters in the size regime in which each atom counts have shown that fully new phenomena and striking new unexpected properties of small clusters can emerge. In this work three aspects have been addressed: i) the structural and electronic properties and reactivity of metal clusters, ii) stationary optical propertis and iii) real time investigation and control of ultrafast processes in noble metal and in nonstoichiometric sodium fluoride clusters.

In this work we made use of the AMICO algorithm to detect clusters in COSMOS2015, a photometric galaxy catalogue of the COSMOS field (Laigle+16). We divided our study in two different analyses being the cluster search on r-band photometry in the range 0