Thesis (M.S.) -- Mississippi State University. Department of Computer Science and Engineering. / Title from title screen. Includes bibliographical references.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-04-24T14:03:12Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertacao-mestrado.pdf: 2772669 bytes, checksum: 25b575026c012270168ca5a4c397d063 (MD5) / Made available in DSpace on 2017-04-24T14:03:12Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertacao-mestrado.pdf: 2772669 bytes, checksum: 25b575026c012270168ca5a4c397d063 (MD5) Previous issue date: 2015-07-29 / CNPQ / N-Graphs is a multiple conclusion natural deduction with proofs as directed graphs, motivated by the idea of proofs as geometric objects and aimed towards the study of the geometry of Natural Deduction systems. Following that line of research, this work revisits the system under a purely combinatorial perspective, determining geometrical conditions on the graphs of proofs to explain its soundness criterion and proof growth during normalization. Applying recent developments in the fields of proof graphs, proof-nets and N-Graphs itself, we propose a linear time algorithm for proof verification of the full system, a result that can be related to proof-nets solutions from Murawski (2000) and Guerrini (2011), and a normalization procedure based on the notion of sub-N-Graphs, introduced by Carvalho, in 2014. We first present a new soundness criterion for meta-edges, along with the extension of Carvalho’s sequentization proof for the full system. For this criterion we define an algorithm for proof verification that uses a DFS-like search to find invalid cycles in a proof-graph. Since the soundness criterion in proof graphs is analogous to the proof-nets procedure, the algorithm can also be extended to check proofs in the multiplicative linear logic without units (MLL−) with linear time complexity. The new normalization proposed here combines a modified version of Alves’ (2009) original beta and permutative reductions with an adaptation of Carbone’s duplication operation on sub-N-Graphs. The procedure is simpler than the original one and works as an extension of both the normalization defined by Prawitz and the combinatorial study developed by Carbone, i.e. normal proofs enjoy the separation and subformula properties and have a structure that can represent how patterns lying in normal proofs can be recovered from the graph of the original proof with cuts. / N-Grafos é uma dedução natural de múltiplas conclusões onde provas são representadas como grafos direcionados, motivado pela idéia de provas como objetos geométricos e com o objetivo de estudar a geometria de sistemas de Dedução Natural. Seguindo esta linha de pesquisa, este trabalho revisita o sistema sob uma perpectiva puramente combinatorial, determinando condições geométricas nos grafos de prova para explicar seu critério de corretude e crescimento da prova durante a normalização. Aplicando desenvolvimentos recentes nos campos de grafos de prova, proof-nets e dos próprios N-Grafos, propomos um algoritmo linear para verificação de provas para o sistema completo, um resultado que pode ser comparado com soluções para roof-nets desenvolvidas por Murawski (2000) e Guerrini (2011), e um procedimento de normalização baseado na noção de sub-N-Grafos, introduzidas por Carvalho, em 2014. Apresentamos primeiramente um novo critério de corretude para meta-arestas, juntamente com a extensão para todo o sistema da prova da sequentização desenvolvida por Carvalho. Para este critério definimos um algoritmo para verificação de provas que utiliza uma busca parecida com a DFS (Busca em Profundidade) para encontrar ciclos inválidos em um grafo de prova. Como o critério de corretude para grafos de provas é análogo ao procedimento para proof-nets, o algoritmo pode também ser estendido para validar provas em Lógica Linear multiplicativa sem units (MLL−) com complexidade de tempo linear. A nova normalização proposta aqui combina uma versão modificada das reduções beta e permutativas originais de Alves com uma adaptação da operação de duplicação proposta por Carbone para ser aplicada a sub-N-Grafos. O procedimento é mais simples do que o original e funciona como uma extensão da normalização definida por Prawitz e do estudo combinatorial desenvolvido por Carbone, i.e. provas em forma normal desfrutam das propriedades da separação e subformula e possuem uma estrutura que pode representar como padrões existentes em provas na forma normal poderiam ser recuperados a partir do grafo da prova original com cortes.

Made available in DSpace on 2014-07-29T16:02:19Z (GMT). No. of bitstreams: 1 Dissertacao Bruno Trindade Reis.pdf: 1549283 bytes, checksum: 850cae1de80dba723aabf95e990ddd6a (MD5) Previous issue date: 2011-08-31 / We begin with a definition of the algebras Qn, who originated the study of algebra associated to directed graphs. Then, we define key concepts such as Hilbert series, graded and filtered algebras. Among the quadratic algebras, we introduce the Koszul algebras. The Hilbert series is a useful tool to study the Koszulity of a quadratic algebra. The homological interpretation of the coefficients of the Hilbert series of algebras associated with direct graphs allowed us to give conditions Koszulity these algebras in terms of the homological properties of the graph. We use this interpretation to construct algebras with Hilbert series prescribed. / Começamos definindo as álgebras Qn, que originaram o estudo das álgebras associadas a grafos orientados em níveis. Em seguida, definimos conceitos importantes, tais como séries de Hilbert , álgebras graduadas e álgebras filtradas. Entre as álgebras quadráticas, introduzimos as álgebras de Koszul. As séries de Hilbert são instrumentos úteis para estudar a Koszulidade de álgebras quadráticas. A interpretação homológica dos coeficientes da série de Hilbert de álgebras associadas a grafos em níveis nos permite dar condições de Koszulidade dessas álgebras em termos das propriedades homológicas do grafo. Usamos essa interpretação para construir álgebras com séries de Hilbert préestabelecidas.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2015-04-22T21:00:51Z No. of bitstreams: 2 Tese - José Eder Salvador de Vasconcelos - 2014.pdf: 10572296 bytes, checksum: 40616b346bd2479e01caf5eeea4cfe68 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2015-04-22T21:03:08Z (GMT) No. of bitstreams: 2 Tese - José Eder Salvador de Vasconcelos - 2014.pdf: 10572296 bytes, checksum: 40616b346bd2479e01caf5eeea4cfe68 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-04-22T21:03:08Z (GMT). No. of bitstreams: 2 Tese - José Eder Salvador de Vasconcelos - 2014.pdf: 10572296 bytes, checksum: 40616b346bd2479e01caf5eeea4cfe68 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-11-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study classes of algebras associated with layered directed graphs. Let 􀀀 be a layered directed graph. We determine the algebra Ap􀀀q; generated by the edges of the graph, satisfying a set of quadratic relations R; and the dual algebra Ap􀀀q!, associated with grpAp􀀀qq. For each P Autp􀀀q we determine: the algebra Ap􀀀 q; where 􀀀 is the subgraph of 􀀀 whose vertices are xed by ; the graded trace generating functions Tr pAp􀀀q; tq and Tr pAp􀀀q!; tq: We also determine the multiplicities of the irreducible representations of AutpAp􀀀qq acting on Ap􀀀q and Ap􀀀q!: We show that for a layered directed graph 􀀀, satisfying some hypotheses, AutpAp􀀀qq K Autp􀀀q. Finally, we verify the property Tr pAp􀀀q; tq Tr pAp􀀀q!; tq 1 for all P Autp􀀀q, called koszulity property. We consider two classes of algebras, the algebra associated to the Hasse graph of the partially ordered set of faces of a star polygon, Ap􀀀 q; and the algebra associated with the Hasse graph of the lattice of subespaces of a nite dimensional vector space over Fq; ApLpn; qqq: / Este trabalho apresenta o estudo de algumas classes de álgebras associadas a grafos orientados em níveis. Dado um grafo orientado em níveis 􀀀 (satisfazendo algumas propriedades) determinamos a álgebra Ap􀀀q gerada pelas arestas do grafo, satisfazendo um conjunto de relações quadráticas R, e a álgebra dual Ap􀀀q!, associada a grpAp􀀀qq. Para cada P Autp􀀀q determinamos o grafo 􀀀 ; o subgrafo de 􀀀 dos vértices xados por ; que dá origem à álgebra Ap􀀀 q e calculamos as funções geradoras do traço graduado Tr pAp􀀀q; tq e Tr pAp􀀀q!; tq: Determinamos as multiplicidades das representações irredutíveis de AutpAp􀀀qq sobre Ap􀀀q e Ap􀀀q!. Mostramos que para um grafo orientado em níveis 􀀀, satisfazendo certas hipóteses, tem-se AutpAp􀀀qq K Autp􀀀q. Finalmente, veri camos a validade da equação Tr pAp􀀀q; tq Tr pAp􀀀q!; tq 1 para todo P Autp􀀀q; a qual denominamos propriedade da koszulidade. Fazemos isso para duas classes de álgebras, a álgebra associada ao grafo de Hasse do conjunto parcialmente ordenado das faces de um polígono estrelado, Ap􀀀 q, e a álgebra associada ao grafo de Hasse do reticulado dos subespaços vetoriais de um espaço vetorial de dimensão nita sobre Fq, ApLpn; qqq.

La recherche menée dans cette thèse a pour but de développer une analyse harmonique pour des fonctions définies sur les sommets d'un graphe orienté. À l'ère du déluge de données, de nombreuses données sont sous forme de graphes et données sur ce graphe. Afin d'analyser d'exploiter ces données de graphes, nous avons besoin de développer des méthodes mathématiques et numériquement efficientes. Ce développement a conduit à l'émergence d'un nouveau cadre théorique appelé le traitement de signal sur graphe dont le but est d'étendre les concepts fondamentaux du traitement de signal classique aux graphes. Inspirées par l'aspect multi échelle des graphes et données sur graphes, de nombreux constructions multi-échelles ont été proposé. Néanmoins, elles s'appliquent uniquement dans le cadre non orienté. L'extension d'une analyse harmonique sur graphe orienté bien que naturelle, s'avère complexe. Nous proposons donc une analyse harmonique en utilisant l'opérateur de marche aléatoire comme point de départ de notre cadre. Premièrement, nous proposons des bases de type Fourier formées des vecteurs propres de l'opérateur de marche aléatoire. De ces bases de Fourier, nous en déterminons une notion fréquentielle en analysant la variation de ses vecteurs propres. La détermination d'une analyse fréquentielle à partir de la base des vecteurs de l'opérateur de marche aléatoire nous amène aux constructions multi-échelles sur graphes orientés. Plus particulièrement, nous proposons une construction en trames d'ondelettes ainsi qu'une construction d'ondelettes décimées sur graphes orientés. Nous illustrons notre analyse harmonique par divers exemples afin d'en montrer l'efficience et la pertinence. / The research conducted in this thesis aims to develop a harmonic analysis for functions defined on the vertices of an oriented graph. In the era of data deluge, much data is in the form of graphs and data on this graph. In order to analyze and exploit this graph data, we need to develop mathematical and numerically efficient methods. This development has led to the emergence of a new theoretical framework called signal processing on graphs, which aims to extend the fundamental concepts of conventional signal processing to graphs. Inspired by the multi-scale aspect of graphs and graph data, many multi-scale constructions have been proposed. However, they apply only to the non-directed framework. The extension of a harmonic analysis on an oriented graph, although natural, is complex. We, therefore, propose a harmonic analysis using the random walk operator as the starting point for our framework. First, we propose Fourier-type bases formed by the eigenvectors of the random walk operator. From these Fourier bases, we determine a frequency notion by analyzing the variation of its eigenvectors. The determination of a frequency analysis from the basis of the vectors of the random walk operator leads us to multi-scale constructions on oriented graphs. More specifically, we propose a wavelet frame construction as well as a decimated wavelet construction on directed graphs. We illustrate our harmonic analysis with various examples to show its efficiency and relevance.

Introdução: O número de estudos relacionados à Síndrome Metabólica (SM) vem aumentando nos últimos anos, muitas vezes motivados pelo aumento do número de casos de sobrepeso/obesidade e diabetes Tipo II levando ao desenvolvimento de doenças cardiovasculares e, como consequência, infarto agudo do miocárdio e AVC, dentre outros desfechos desfavoráveis. A SM é uma doença multifatorial composta de cinco características, porém, para que um indivíduo seja diagnosticado com ela, possuir pelo menos três dessas características torna-se condição suficiente. Essas cinco características são: Obesidade visceral, caracterizada pelo aumento da circunferência da cintura, Glicemia de jejum elevada, Triglicérides aumentado, HDL-colesterol reduzido, Pressão Arterial aumentada. Objetivo: Estabelecer a rede de associações entre os fenótipos que compõem a Síndrome Metabólica através do aprendizado de estruturas de dependência, decompor a rede em componentes de correlação genética e ambiental e avaliar o efeito de ajustes por covariáveis e por variantes genéticas exclusivamente relacionadas à cada um dos fenótipos da rede. Material e Métodos: A amostra do estudo corresponderá a 79 famílias da cidade mineira de Baependi, composta por 1666 indivíduos. O aprendizado de estruturas de redes será feito por meio da Teoria de Grafos e Modelos de Equações Estruturais envolvendo o modelo linear misto poligênico para determinar as relações de dependência entre os fenótipos que compõem a Síndrome Metabólica / Introduction: The number of studies related to Metabolic Syndrome (MetS) has been increasing in the last years, encouraged by the increase on the overweight / obesity and Type II Diabetes cases, leading to the development of cardiovascular disease and, therefore, acute myocardial infarction and stroke, and others unfavorable outcomes. MetS is a multifactorial disease containing five characteristics, however, for an individual to be diagnosed with MetS, he/she may have at least three of them. These characteristics are: Truncal Obesity, characterized by increasing on the waist circumference, increasing on Fasting Blood Glucose, increasing on Triglycerides, decreasing on HDL cholesterol and increasing on Blood Pressure. Aims: Establish the best association network between MetS phenotypes through structured dependency learning between phenotypes considering genetic variants exclusively related to each phenotype. Materials and Methods: The study sample is composed of 79 families, 1666 individuals of a city in a rural area of Brazil, called Beapendi. Structured learning will use graph theory and Structural Equations Models to establish the dependency relations between MetS phenotypes

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-22T11:27:19Z No. of bitstreams: 2 Dissertação - Kariny de Andrade Dirino - 2017.pdf: 1986993 bytes, checksum: fd843aaf3aee361fd3b4dd512828d8f0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-22T11:27:47Z (GMT) No. of bitstreams: 2 Dissertação - Kariny de Andrade Dirino - 2017.pdf: 1986993 bytes, checksum: fd843aaf3aee361fd3b4dd512828d8f0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-09-22T11:27:47Z (GMT). No. of bitstreams: 2 Dissertação - Kariny de Andrade Dirino - 2017.pdf: 1986993 bytes, checksum: fd843aaf3aee361fd3b4dd512828d8f0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-08-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Considering a layered directed graphs we may associate it to an algebra, denoted as , whose generators are the edges of the graph and the relations are defined through: every ways with the same initial vertex and the same final vertex determine different fractorizations for the same polynomial with coefficients in a non-commutative ring. We present a study about these algebras and their main properties, presenting some classes of examples and having as central focus the Hasse graph of the partially ordered set of k -faces of Petersen graph, . We discuss the results on basis for algebras of type we calculate their Hilbert series and the automorphisms group of these algebras, we determine the subgraphs induced by the set of vertices fixed by each and we calculate the graded trace generating functions, in order to introduce problems related to koszulity. / Dado um grafo orientado em níveis podemos associar a ele uma álgebra, denotada por cujos geradores são as arestas do grafo e as relações são definidas mediante: todos os caminhos com o mesmo vértice inicial e mesmo vértice final determinam fatorações distintas para o mesmo polinômio com coeficientes em um anel não comutativo. Exibimos um estudo sobre essas álgebras e suas principais propriedades, apresentando algumas classes de exemplos e tendo como foco central o grafo de Hasse do conjunto parcialmente ordenado das k-faces do grafo de Petersen, . Abordamos resultados sobre bases para álgebras do tipo , calculamos as suas séries de Hilbert e o grupo dos automorfismos dessas álgebras, determinamos os subgrafos induzidos pelo conjunto dos vértices fixados por cada e calculamos as funções geradoras do traço graduado, a fim de introduzirmos problemas relacionados à koszulidade.

Introdução: O número de estudos relacionados à Síndrome Metabólica (SM) vem aumentando nos últimos anos, muitas vezes motivados pelo aumento do número de casos de sobrepeso/obesidade e diabetes Tipo II levando ao desenvolvimento de doenças cardiovasculares e, como consequência, infarto agudo do miocárdio e AVC, dentre outros desfechos desfavoráveis. A SM é uma doença multifatorial composta de cinco características, porém, para que um indivíduo seja diagnosticado com ela, possuir pelo menos três dessas características torna-se condição suficiente. Essas cinco características são: Obesidade visceral, caracterizada pelo aumento da circunferência da cintura, Glicemia de jejum elevada, Triglicérides aumentado, HDL-colesterol reduzido, Pressão Arterial aumentada. Objetivo: Estabelecer a rede de associações entre os fenótipos que compõem a Síndrome Metabólica através do aprendizado de estruturas de dependência, decompor a rede em componentes de correlação genética e ambiental e avaliar o efeito de ajustes por covariáveis e por variantes genéticas exclusivamente relacionadas à cada um dos fenótipos da rede. Material e Métodos: A amostra do estudo corresponderá a 79 famílias da cidade mineira de Baependi, composta por 1666 indivíduos. O aprendizado de estruturas de redes será feito por meio da Teoria de Grafos e Modelos de Equações Estruturais envolvendo o modelo linear misto poligênico para determinar as relações de dependência entre os fenótipos que compõem a Síndrome Metabólica / Introduction: The number of studies related to Metabolic Syndrome (MetS) has been increasing in the last years, encouraged by the increase on the overweight / obesity and Type II Diabetes cases, leading to the development of cardiovascular disease and, therefore, acute myocardial infarction and stroke, and others unfavorable outcomes. MetS is a multifactorial disease containing five characteristics, however, for an individual to be diagnosed with MetS, he/she may have at least three of them. These characteristics are: Truncal Obesity, characterized by increasing on the waist circumference, increasing on Fasting Blood Glucose, increasing on Triglycerides, decreasing on HDL cholesterol and increasing on Blood Pressure. Aims: Establish the best association network between MetS phenotypes through structured dependency learning between phenotypes considering genetic variants exclusively related to each phenotype. Materials and Methods: The study sample is composed of 79 families, 1666 individuals of a city in a rural area of Brazil, called Beapendi. Structured learning will use graph theory and Structural Equations Models to establish the dependency relations between MetS phenotypes

Dans cette thèse, nous cherchons à caractériser les facteurs de transcription de la plante Arabidopsis thaliana, gènes importants pour la régulation de l'expression du génome. À l'aide de données d'expression, notre objectif biologique est de classer ces facteurs de transcription en groupes de gènes co-régulateurs et en groupes de gènes co-régulés. Nous procédons en deux phases pour y parvenir. La première phase consiste à construire un réseau de régulation entre les facteurs de transcription. La seconde phase consiste en la classification des facteurs de transcription selon les liens de régulation établis par ce réseau. D'un point de vue statistique, les facteurs de transcription sont les variables et les données d'expression sont les observations. Nous représentons le réseau à inférer par un graphe orienté dont les nœuds sont les variables. L'estimation de ses arêtes est vue comme un problème de sélection de variables en grande dimension avec un faible nombre d'unités statistiques. Nous traitons ce problème à l'aide de régressions linéaires pénalisées de type LASSO. Une approche préliminaire qui consiste à sélectionner un ensemble de variables du chemin de régularisation par le biais de critères de vraisemblance pénalisée s'avère être instable et fournit trop de variables explicatives. Pour contrecarrer cela, nous proposons et mettons en compétition deux procédures de sélection, adaptées au problème de la haute dimension et mêlant régression linéaire pénalisée et rééchantillonnage. L'estimation des différents paramètres de ces procédures a été effectuée dans le but d'obtenir des ensembles de variables stables. Nous évaluons la stabilité des résultats à l'aide de jeux de données simulés selon notre modèle graphique. Nous faisons appel ensuite à une méthode de classification non supervisée sur chacun des graphes orientés obtenus pour former des groupes de nœuds vus comme contrôleurs et des groupes de nœuds vus comme contrôlés. Pour évaluer la proximité entre les classifications doubles des nœuds obtenus sur différents graphes, nous avons développé un indice de comparaison de couples de partition dont nous éprouvons et promouvons la pertinence. D'un point de vue pratique, nous proposons une méthode de simulation en cascade, exigée par la complexité de notre modèle et inspirée du bootstrap paramétrique, pour simuler des jeux de données en accord avec notre modèle. Nous avons validé notre modèle en évaluant la proximité des classifications obtenues par application de la procédure statistique sur les données réelles et sur ces données simulées. / This thesis deals with the characterisation of key genes in gene expression regulation, called transcription factors, in the plant Arabidopsis thaliana. Using expression data, our biological goal is to cluster transcription factors in groups of co-regulator transcription factors, and in groups of co-regulated transcription factors. To do so, we propose a two-step procedure. First, we infer the network of regulation between transcription factors. Second, we cluster transcription factors based on their connexion patterns to other transcriptions factors.From a statistical point of view, the transcription factors are the variables and the samples are the observations. The regulatory network between the transcription factors is modelled using a directed graph, where variables are nodes. The estimation of the nodes can be interpreted as a problem of variables selection. To infer the network, we perform LASSO type penalised linear regression. A preliminary approach selects a set of variable along the regularisation path using penalised likelihood criterion. However, this approach is unstable and leads to select too many variables. To overcome this difficulty, we propose to put in competition two selection procedures, designed to deal with high dimension data and mixing linear penalised regression and subsampling. Parameters estimation of the two procedures are designed to lead to select stable set of variables. Stability of results is evaluated on simulated data under a graphical model. Subsequently, we use an unsupervised clustering method on each inferred oriented graph to detect groups of co-regulators and groups of co-regulated. To evaluate the proximity between the two classifications, we have developed an index of comparaison of pairs of partitions whose relevance is tested and promoted. From a practical point of view, we propose a cascade simulation method required to respect the model complexity and inspired from parametric bootstrap, to simulate data under our model. We have validated our model by inspecting the proximity between the two classifications on simulated and real data.

Software systems can be represented as directed graphs where components are nodes and dependencies between components are edges. Improvement in system complexity and reduction of interference between development teams can be achieved by applying hidden structure analysis. However, since systems can contain thousands of dependencies, a concrete method for selecting which dependencies that are most beneficial to remove is needed. In this thesis two solutions to this problem are introduced; dominator- and cluster analysis. Dominator analysis examines the cost/gain ratio of detaching individual components from a cyclic group. Cluster analysis finds the most beneficial subgroups to split in a cyclic group. The aim of the methods is to reduce the size of cyclic groups, which are sets of co- dependent components. As a result, the system architecture will be less prone to propagating errors, caused by modifications of components. Both techniques derive from graph theory and data science but have not been applied to the area of hidden structures before. A subsystem at Ericsson is used as a testing environment. Specific dependencies in the structure which might impede the development process have been discovered. The outcome of the thesis is four to-be scenarios of the system, displaying the effect of removing these dependencies. The to-be scenarios show that the architecture can be significantly improved by removing few direct dependencies. / Mjukvarusystem kan representeras som riktade grafer där komponenter är noder och beroenden mellan komponenter är kanter. Förbättrad systemkomplexitet och minskad mängd störningar mellan utvecklingsteam kan åstadkommas genom att applicera teorin om gömda beroende. Eftersom system kan innehålla tusentals beroenden behövs en konkret metod för att hitta beroenden i systemet som är fördelaktiga att ta bort. I den här avhandlingen presenteras två lösningar till problemet; dominator- och klusteranalys. Dominatoranalys undersöker kostnad/vinst ration av att ta bort individuella komponenter i systemet från en cyklisk grupp. Klusteranalys hittar de mest lönsamma delgrupperna att klyva isär i en cyklisk grupp. Metodernas mål är att minska storleken på cykliska grupper. Cykliska grupper är uppsättningar av komponenter som är beroende av varandra. Som resultat blir systemarkitekturen mindre benägen till propagering av fel, orsakade av modifiering av komponenter. Båda metoderna härstammar från grafteori och datavetenskap men har inte applicerats på området kring gömda strukturer tidigare. Ett subsystem på Ericsson användes som testmiljö. Specifika beroenden i strukturen som kan vara hämmande för utvecklingsprocessen har identifierats. Resultatet av avhandlingen är fyra potentiella framtidsscenarion av systemet som visualiserar effekten av att ta bort de funna beroendena. Framtidsscenariona visar att arkitekturen kan förbättras markant genom att avlägsna ett fåtal direkta beroenden.