This work applies complex network theory to the problem of semi-supervised and unsupervised learning in networks that are representations of multivariate datasets. Complex networks allow the use of nonlinear dynamical systems to represent behaviors according to the connectivity patterns of networks. Inspired by behavior observed in nature, such as competition for limited resources, dynamical system models can be employed to uncover the organizational structure of a network. In this dissertation, we develop a technique for classifying data represented as interaction networks. As part of the technique, we model a dynamical system inspired by the biological dynamics of resource competition. So far, similar methods have focused on vertices as the resource of competition. We introduce edges as the resource of competition. In doing so, the connectivity pattern of a network might be used not only in the dynamical system simulation but in the learning task as well. / Este trabalho aplica a teoria de redes complexas para o estudo de uma técnica aplicada ao problema de aprendizado semissupervisionado e não-supervisionado em redes, especificamente, aquelas que representam conjuntos de dados multivariados. Redes complexas permitem o emprego de sistemas dinâmicos não-lineares que podem apresentar comportamentos de acordo com os padrões de conectividade de redes. Inspirado pelos comportamentos observados na natureza, tais como a competição por recursos limitados, sistema dinâmicos podem ser utilizados para revelar a estrutura da organização de uma rede. Nesta dissertação, desenvolve-se uma técnica aplicada ao problema de classificação de dados representados por redes de interação. Como parte da técnica, um sistema dinâmico inspirado na competição por recursos foi modelado. Métodos similares concentraram-se em vértices como o recurso da concorrência. Neste trabalho, introduziu-se arestas como o recurso-alvo da competição. Ao fazê-lo, utilizar-se-á o padrão de conectividade de uma rede tanto na simulação do sistema dinâmico, quanto na tarefa de aprendizado.

Uma das etapas mais importantes da análise de imagens e, que conta com uma enorme quantidade de aplicações, é a segmentação. No entanto, uma boa parte das técnicas tradicionais apresenta alto custo computacional, dificultando sua aplicação em imagens de alta resolução como, por exemplo, as imagens de ninhais de aves do Pantanal que também serão analisadas neste trabalho. Diante disso, é proposta uma nova abordagem de segmentação que combina algoritmos de detecção de comunidades, pertencentes à teoria das redes complexas, com técnicas de extração de superpixels. Tal abordagem é capaz de segmentar imagens de alta resolução mantendo o compromisso entre acurácia e tempo de processamento. Além disso, como as imagens de ninhais analisadas apresentam características peculiares que podem ser mais bem tratadas por técnicas de segmentação por textura, a técnica baseada em Markov Random Fields (MRF) é proposta, como um complemento à abordagem de segmentação inicial, para realizar a identificação final das aves. Por fim, devido à importância de avaliar quantitativamente a qualidade das segmentações obtidas, um nova métrica de avaliação baseada em ground-truth foi desenvolvida, sendo de grande importância para a área. Este trabalho contribuiu para o avanço do estado da arte das técnicas de segmentação de imagens de alta resolução, aprimorando e desenvolvendo métodos baseados na combinação de redes complexas com superpixels, os quais alcançaram resultados satisfatórios com baixo tempo de processamento. Além disso, uma importante contribuição referente ao censo demográfico de aves por meio da análise de imagens aéreas de ninhais foi viabilizada por meio da aplicação da técnica de segmentação MRF. / Segmentation is one of the most important steps in image analysis with a large range of applications. However, some traditional techniques exhibit high computational costs, hindering their application in high resolution images such as the images of birds nests from Pantanal, one of Brazilian most important wetlands. Therefore, we propose a new segmentation approach that combines community detection algorithms, originated from the theory of the complex networks, with superpixels extraction techniques. This approach is capable of segmenting high resolution images while maintaining the trade-off between accuracy and processing time. Moreover, as the nest images exhibit peculiar characteristics that can be better dealt with texture segmentation techniques, the Markov Random Fields (MRF) technique is proposed, as a complement to the initial approach, to perform the final identification of the birds. Finally, due to the importance of the quantitatively evaluation of the segmentation quality, a new evaluation metric based on ground-truth was developed, being of great importance to the segmentation field. This work contributed to the state of art of high resolution images segmentation techniques, improving and developing methods based on combination of complex networks and superpixels, which generated satisfactory results within low processing time. Moreover, an important contribution for the birds census by the analysis of aerial images of birds nests was made possible by application of the MRF technique.

Nas últimas décadas, testemunhou-se um crescente interesse no estudo de sistemas complexos. Tais sistemas são compostos por pelo menos dois componentes fundamentais: elementos dinâmicos individuais e uma estrutura de organização definindo a forma de interação entre estes. Devido a dinâmica de cada elemento e a complexidade de acoplamento, uma grande variedade de fenômenos espaço-temporais podem ser observados. Esta tese tem como objetivo principal explorar o uso da dinâmica espaço-temporal em redes visando a solução de alguns problemas computacionais. Com relação aos mecanismos dinâmicos, a sincronização entre osciladores acoplados, a caminhada aleatória-determinística e a competição entre elementos na rede foram considerados. Referente à parte estrutural da rede, tanto estruturas regulares baseadas em reticulados quanto redes com estruturas mais gerais, denominadas redes complexas, foram abordadas. Este estudo é concretizado com o desenvolvimento de modelos aplicados a dois domínios específicos. O primeiro refere-se à utilização de redes de osciladores acoplados para construção de modelos de atenção visual. Dentre as principais características desses modelos estão: a seleção baseada em objetos, a utilização da sincronização/ dessincronização entre osciladores neurais como forma de organização perceptual, a competição entre objetos para aquisição da atenção. Além disso, ao comparar com outros modelos de seleção de objetos baseados em redes osciladores, um número maior de atributos visuais é utilizado para definir a saliência dos objetos. O segundo domínio está relacionado ao desenvolvimento de modelos para detecção de comunidades em redes complexas. Os dois modelos desenvolvidos, um baseado em competição de partículas e outro baseado em sincronização de osciladores, apresentam alta precisão de detecção e ao mesmo tempo uma baixa complexidade computacional. Além disso, o modelo baseado em competição de partículas não só oferece uma nova técnica de detecção de comunidades, mas também apresenta uma abordagem alternativa para realização de aprendizado competitivo. Os estudos realizados nesta tese mostram que a abordagem unificada de dinâmica e estrutura é uma ferramenta promissora para resolver diversos problemas computacionais / In the last decades, an increasing interest in complex system study has been witnessed. Such systems have at least two integrated fundamental components: individual dynamical elements and an organizational structure which defines the form of interaction among those elements. Due to the dynamics of each element and the coupling complexity, various spatial-temporal phenomena can be observed. The main objective of this thesis is to explore spatial-temporal dynamics in networks for solving some computational problems. Regarding the dynamical mechanisms, the synchronization among coupled oscillators, deterministic-random walk and competition between dynamical elements are taken into consideration. Referring to the organizational structure, both regular network based on lattice and more general network, called complex networks, are studied. The study of coupled dynamical elements is concretized by developing computational models applied to two specific domains. The first refers to the using of coupled neural oscillators for visual attention. The main features of the developed models in this thesis are: object-based visual selection, realization of visual perceptual organization by using synchronization / desynchronization among neural oscillators, competition among objects to achieve attention. Moreover, in comparison to other object-based selection models, more visual attributes are employed to define salience of objects. The second domain is related to the development of computational models applied to community detection in complex networks. Two developed models, one based on particle competition and another based on synchronization of Integrate-Fire oscillators, present high detection rate and at the same time low computational complexity. Moreover, the model based on particle competition not only offers a new community detection technique, but also presents an alternative way to realize artificial competitive learning. The study realized in this thesis shows that the unified scheme of dynamics and structure is a powerful tool to solve various computational problems

Depuis 2004, les médias sociaux en ligne ont connu une croissance considérable. Ce développement rapide a eu des effets intéressants pour augmenter la connexionet l'échange d'informations entre les utilisateurs, mais certains effets négatifs sont également apparus, dont le nombre de faux comptes grandissant jour après jour.Les sockpuppets sont les multiples faux comptes créés par un même utilisateur. Ils sont à l'origine de plusieurs types de manipulations comme la création de faux comptes pour louer, défendre ou soutenir une personne ou une organisation, ou pour manipuler l'opinion publique. Dans cette thèse, nous présentons SocksCatch, un processus complet de détection et de groupage des sockpuppets composé de trois phases principales : la première phase a pour objectif la préparation du processus et le pré-traitement des données; la seconde phase a pour objectif la détection des comptes sockpuppets à l'aide d'algorithmes d'apprentissage automatique; la troisième phase a pour objectif le regroupement des comptes sockpuppets créés par un même utilisateur à l'aide d'algorithmes de détection de communautés. Ces phases sont déclinées en trois étapes : une étape "modèle" pour représenter les médias sociaux en ligne, où nous proposons un modèle général de médias sociaux dédié à la détection et au regroupement des sockpuppets ; une étape d'adaptation pour ajuster le processus à un média social spécifique, où nous instancions et évaluons le modèle SocksCatch sur un média social sélectionné ; et une étape en temps réel pour détecter et grouper les sockpuppets en ligne, où SocksCatch est déployé en ligne sur un média social sélectionné. Des expérimentations ont été réalisées sur l'étape d'adaptation en utilisant des données réelles extraites de Wikipédia anglais. Afin de trouver le meilleur algorithme d'apprentissage automatique pour la phase de détection de sockpuppet, les résultats de six algorithmes d'apprentissage automatique sont comparés. En outre, ils sont comparés à la littérature où les résultats de la comparaison montrent que notre proposition améliore la précision de la détection des sockpuppets. De plus, les résultats de cinq algorithmes de détection de communauté sont comparés pour la phase de regroupement de Sockpuppet, afin de trouver le meilleur algorithme de détection de communauté qui sera utilisé en temps réel. / Since 2004, online social medias have grown hugely. This fast development had interesting effects to increase the connection and information exchange between users, but some negative effects also appeared, including fake accounts number growing day after day. Sockpuppets are multiple fake accounts created by a same user. They are the source of several types of manipulation such as those created to praise, defend or support a person or an organization, or to manipulate public opinion. In this thesis, we present SocksCatch, a complete process to detect and group sockpuppets, which is composed of three main phases: the first phase objective is the process preparation and data pre-processing; the second phase objective is the detection of the sockpuppet accounts using machine learning algorithms; the third phase objective is the grouping of sockpuppet accounts created by a same user using community detection algorithms. These phases are declined in three stages: a model stage to represent online social medias, where we propose a general model of social media dedicated to the detection and grouping of sockpuppets; an adaptation stage to adjust the process to a particular social media, where we instantiate and evaluate the SocksCatch model on a selected social media; and a real-time stage to detect and group the sockpuppets online, where SocksCatch is deployed online on a selected social media. Experiments have been performed on the adaptation stage using real data crawled from English Wikipedia. In order to find the best machine learning algorithm for sockpuppet's detection phase, the results of six machine learning algorithms are compared. In addition, they are compared with the literature, and the results show that our proposition improves the accuracy of the detection of sockpuppets. Furthermore, the results of five community detection algorithms are compared for sockpuppet's grouping phase, in order to find the best community detecton algorithm that will be used in real-time stage.

Dans cette thèse, nous étudions les graphes aléatoires en utilisant des outils de la théorie des matrices aléatoires et l’analyse probabilistique afin de résoudre des problèmes clefs dans le domaine des réseaux complexes et Big Data. Le premier problème qu’on considère est de détecter un sous graphe Erdős–Rényi G(m,p) plante dans un graphe Erdős–Rényi G(n,q). Nous dérivons les distributions d’une statistique basée sur les propriétés spectrales d’une matrice définie du graphe. Ensuite, nous considérons le problème de la récupération des sommets du sous graphe en présence de l’information supplémentaire. Pour cela nous utilisons l’algorithme «Belief Propagation». Le BP sans informations supplémentaires ne réussit à la récupération qu’avec un SNR effectif lambda au-delà d’un seuil. Nous prouvons qu’en présence des informations supplémentaires, ce seuil disparaît et le BP réussi pour n’importe quel lambda. Finalement, nous dérivons des expressions asymptotiques pour PageRank sur une classe de graphes aléatoires non dirigés appelés « fast expanders », en utilisant des techniques théoriques à la matrice aléatoire. Nous montrons que PageRank peut être approché pour les grandes tailles du graphe comme une combinaison convexe du vecteur de dégré normalisé et le vecteur de personnalisation du PageRank, lorsque le vecteur de personnalisation est suffisamment délocalisé. Par la suite, nous caractérisons les formes asymptotiques de PageRank sur le Stochastic Block Model (SBM) et montrons qu’il contient un terme de correction qui est fonction de la structure de la communauté. / In this thesis, we study random graphs using tools from Random Matrix Theory and probability to tackle key problems in complex networks and Big Data. First we study graph anomaly detection. Consider an Erdős-Rényi (ER) graph with edge probability q and size n containing a planted subgraph of size m and probability p. We derive a statistical test based on the eigenvalue and eigenvector properties of a suitably defined matrix to detect the planted subgraph. We analyze the distribution of the derived test statistic using Random Matrix Theoretic techniques. Next, we consider subgraph recovery in this model in the presence of side-information. We analyse the effect of side-information on the detectability threshold of Belief Propagation (BP) applied to the above problem. We show that BP correctly recovers the subgraph even with noisy side-information for any positive value of an effective SNR parameter. This is in contrast to BP without side-information which requires the SNR to be above a certain threshold. Finally, we study the asymptotic behaviour of PageRank on a class of undirected random graphs called fast expanders, using Random Matrix Theoretic techniques. We show that PageRank can be approximated for large graph sizes as a convex combination of the normalized degree vector and the personalization vector of the PageRank, when the personalization vector is sufficiently delocalized. Subsequently, we characterize asymptotic PageRank on Stochastic Block Model (SBM) graphs, and show that it contains a correction term that is a function of the community structure.

Statistical analysis of networks has grown rapidly over the last few years with increasing number of applications. Graph-valued data carries additional information of dependencies which opens the possibility of modeling highly complex objects in vast number of fields such as biology (e.g. brain networks , fungi networks, genes co-expression), chemistry (e.g. molecules fingerprints), psychology (e.g. social networks) and many others (e.g. citation networks, word co-occurrences, financial systems, anomaly detection). While the inclusion of graph structure in the analysis can further help inference, simple statistical tasks in a network is very complex. For instance, the assumption of exchangeability of the nodes or the edges is quite strong, and it brings issues such as sparsity, size bias and poor characterization of the generative process of the data. Solutions to these issues include adding specific constraints and assumptions on the data generation process. In this work, we approach this problem by assuming graphs are globally sparse but locally dense, which allows exchangeability assumption to hold in local regions of the graph. We consider problems with two types of locality structure: block structure (also framed as multiple graphs or population of networks) and unstructured sparsity which can be seen as missing data. For the former, we developed a hypothesis testing framework for weighted aligned graphs; and a spectral clustering method for community detection on population of non-aligned networks. For the latter, we derive an efficient spectral clustering approach to learn the parameters of the zero inflated stochastic blockmodel. Overall, we found that incorporating multiple local dense structures leads to a more precise and powerful local and global inference. This result indicates that this general modeling scheme allows for exchangeability assumption on the edges to hold while generating more realistic graphs. We give theoretical conditions for our proposed algorithms, and we evaluate them on synthetic and real-world datasets, we show our models are able to outperform the baselines on a number of settings. <br>

Les travaux présentés dans la thèse s'inscrivent dans le cadre de l'analyse des graphes de terrain (complex networks) et plus précisément de la tâche de détection de communautés, c'est-à-dire la reconnaissance algorithmique de sous-graphes particulièrement denses. Nous nous intéressons spécifiquement à l'implémentation d'une telle méthode dans un contexte fortement décentralisé et distribué : des réseaux MANET opportunistes formés par de petits objets connectés communiquant en pair-à-pair. Afin de tenir compte des contraintes d'exécution d'algorithme dans de tels réseaux, les travaux présentés dans la thèse proposent des méthodes conçues selon le paradigme récent et actif nommé orienté sommet, en alliant le traitement de graphes Think-Like-a-Vertex aux méthodes de détection de communautés basées sur des leaders ou des graines : celles-ci présentent en effet des propriétés de décentralisation qui autorisent des implémentations parallèles et distribuées appropriées au cadre applicatif considéré. Dans ce contexte, nous proposons d'une part un principe global de fonctionnement original que nous mettons en oeuvre et déclinons dans trois algorithmes dédiés à trois configurations différentes de la tâche de détection de communautés : l'algorithme VOLCAN considère le cas de référence des communautés disjointes dans un graphe statique. Nous l'étendons ensuite avec l'algorithme LOCNeSs au cas des communautés recouvrantes, qui autorisent un sommet à appartenir à plusieurs communautés simultanément : cette généralisation donne plus de flexibilité à la détection et la rend plus appropriée au cadre applicatif considéré. Nous examinons également le cas des graphes dynamiques, c'est-à-dire dont les sommets et les arêtes évoluent au cours du temps, auquel est consacré l'algorithme DynLOCNeSs. Chacun des algorithmes est associé à une implémentation décentralisée et fait l'objet d'une étude théorique ainsi qu'expérimentale sur des données artificielles et réelles permettant d'évaluer la qualité des résultats fournis et de les comparer aux méthodes de l'état de l'art. Nous considérons également, dans un cas particulier de réseau mobile ad-hoc spontané et décentralisé issu d'une application réelle de vêtements intelligents et communicants, une tâche de cheminement permettant d'identifier des interlocuteurs. Nous proposons une stratégie de recommandation utilisant la structure communautaire, modélisée et évaluée à travers un algorithme nommé SWAGG. / Our research is in the field of complex network analysis and mining, specifically addressing the communit detection task, ie. algorithms aiming to uncover particularly dense subgraphs. We focus on the implementation of such an algorithm in a decentralised and distributed context : opportunistic MANET constituted of small wireless devices using peer-to-peer communication. To tackle the implementation constraints in such networks, we propose several methods designed according to the novel and trending vertex-centred paradigm, by combining Think-Like-a-Vertex graph processing with vertex-centred community detection methods based on leaders or seeds : they show specific properties allowing dsitributed implementations suiting the opportunistic MANET case. In this context, we first a global working principle and implement it in three different algorithms dedicated to three different configurations of community detection : the VOLCAN algorithm manages the classical disjoint community detection task in a static graph. We extend it with the LOCNeSs algorithm, that is dealing with overlapping communities which means that one vertex can belong to several communities. It adds more flexibility to the method and more significance to produced results. We also tackle the dynamic graphe case (graph evolving over time), addressed by the DynLOCNeSs algorithm.Each algorithm comes with a decentralised implementation and theoretical as well as experimental studies conducted both on real and synthetic benchmark data, allowing to evaluate the quality of the results and compare to existing state-of-the-art methods. Finally, we consider a special case of opportunistic decentralised MANET developped as a part of a research project about smart and communicating clothing. We formalise a task of path finding between smart t-shirts holders and propose a recommandation strategy using community structure, that we model and evaluate through an algorithm named SWAGG.

L’analyse des réseaux sociaux a conduit à la découverte d’une propriété très intéressante : ces réseaux se caractérisent par l’existence de zones de forte densité constituées d’éléments fortement connectés entre eux. Ces zones appelées "communautés", évoluent au cours du temps suivant la dynamique des acteurs sociaux et de leurs interactions. L’identification de ces communautés offre un éclairage intéressant sur la structure du réseau et permet de suivre leur évolution au fil du temps. Bien que ce problème ait donné lieu à de très nombreux travaux ces dernières années, la détection des communautés dynamiques reste encore un problème ouvert et aucune solution entièrement satisfaisante n’est encore proposée. Dans ce travail, nous proposons une approche multi-agents pour la détection des communautés dans les réseaux sociaux dynamiques. Les entités de notre approche observent l’évolution du réseau, et en conséquence, elles adaptent en temps réel le graphe représentant le réseau et elles engendrent les modifications adéquates sur les communautés précédemment détectées. Cette approche permet de modéliser le réseau par un graphe dynamique qui s’adapte en fonction l’évolution observée dans le réseau. Pour cette modélisation, plusieurs aspects du réseau sont intégrés : la structure topologique du graphe, la similarité sémantiques des membres sociaux et la communication entre eux. Cette modélisation se base sur le concept d’homophilie et sur une stigmergie à base des phéromones. Afin d’étudier les performances de l’approche proposée, nous l’avons appliquée sur un ensemble très varié de graphes réels et artificiels. Les résultats ont été suffisamment satisfaisants et montrent la bonne performance de notre modèle. / Analysis of social networks has led to the discovery of a very interesting property : these networks are characterized by the existence of areas with high density composed of highly interconnected elements. These areas called "communities", evolve over time according to the dynamic of social members and their interactions. The identification of these communities offers an interesting light on the network structure and it allows to track their progress over time. Although this problem has been the subject of numerous studies in recent years, the detection of dynamic communities remains an open problem and no fully satisfactory solution has yet been proposed. In this work, we propose a multi-agent approach for the detection of communities in dynamic social networks. The entities of our approach observe the evolution of the network and consequently they adapt in real time the graph representing the network and they generate the appropriate changes on previously identified communities. This approach allows to model the network by a graph that dynamically adapts according to the evolution of the network. For this modeling, several network’s aspects are integrated: the topological structure of the graph, the semantic similarity of social members and the communication between them. This modeling is based on the concept of homophily and a pheromone based stigmergy. In order to study the performances of the proposed approach, we applied it to a divers set of real and artificial graphs. The results were satisfactory enough and show the good performance of our model.

Motivée par les récentes avancées dans l'analyse théorique des performances des algorithmes d'apprentissage automatisé, cette thèse s'intéresse à l'analyse de performances et à l'amélioration de la classification nonsupervisée de données et graphes en grande dimension. Spécifiquement, dans la première grande partie de cette thèse, en s'appuyant sur des outils avancés de la théorie des grandes matrices aléatoires, nous analysons les performances de méthodes spectrales sur des modèles de graphes réalistes et denses ainsi que sur des données en grandes dimensions en étudiant notamment les valeurs propres et vecteurs propres des matrices d'affinités de ces données. De nouvelles méthodes améliorées sont proposées sur la base de cette analyse théorique et démontrent à travers de nombreuses simulations que leurs performances sont meilleures comparées aux méthodes de l'état de l'art. Dans la seconde partie de la thèse, nous proposons un nouvel algorithme pour la détection de communautés hétérogènes entre plusieurs couches d'un graphe à plusieurs types d'interaction. Une approche bayésienne variationnelle est utilisée pour approximer la distribution apostériori des variables latentes du modèle. Toutes les méthodes proposées dans cette thèse sont utilisées sur des bases de données synthétiques et sur des données réelles et présentent de meilleures performances en comparaison aux approches standard de classification dans les contextes susmentionnés. / Spurred by recent advances on the theoretical analysis of the performances of the data-driven machine learning algorithms, this thesis tackles the performance analysis and improvement of high dimensional data and graph clustering. Specifically, in the first bigger part of the thesis, using advanced tools from random matrix theory, the performance analysis of spectral methods on dense realistic graph models and on high dimensional kernel random matrices is performed through the study of the eigenvalues and eigenvectors of the similarity matrices characterizing those data. New improved methods are proposed and are shown to outperform state-of-the-art approaches. In a second part, a new algorithm is proposed for the detection of heterogeneous communities from multi-layer graphs using variational Bayes approaches to approximate the posterior distribution of the sought variables. The proposed methods are successfully applied to synthetic benchmarks as well as real-world datasets and are shown to outperform standard approaches to clustering in those specific contexts.

Die Verbreitung von Social Media und damit verbunden die entstehenden und wachsenden Communities im Internet führen zu einer Zunahme von auswertbaren, digitalen Spuren, die häufig öffentlich zugänglich sind. Diese lassen sich durch verschiedene analytische Verfahren wie z.B. die Methode der Sozialen Netzwerkanalyse [1] auswerten. Insbesondere Ansätze für „Community Detection“ erfreuen sich besonderer Beliebtheit, wodurch sich unter anderem innovative Untergemeinschaften und Subgruppen beispielsweise in großen „Open Source“-Projekten identifizieren lassen [2]. Im Rahmen dieser Anwendungen ergeben sich neue methodische und grundlegende Fragen, darunter die nach der Rolle der von Zeit in solchen Analysen. Während die Darstellung dynamischer Effekte (z.B. durch Animationen) die Zeit als expliziten Parameter enthält, geht die Wahl der Zeitintervalle für die Aggregation von Daten, aus denen dann Netzwerke gewonnen werden, nur implizit in die Prämissen des Verfahrens ein. Diese Effekte wurden im Gegensatz zur Analyse von Dynamik bisher kaum untersucht. Im Fall der Sozialen Netzwerkanalyse ist die Zielrepräsentation selbst nicht mehr zeitbehaftet sondern sozusagen ein „statischer Schnappschuss“, wodurch etwa zeitabhängige Interaktionsmuster nicht erkannt werden können. (...)