Communities and beyond: mesoscopic analysis of a large social network with complementary methods

Community detection methods have so far been tested mostly on small empirical networks and on synthetic benchmarks. Much less is known about their performance on large real-world networks, which nonetheless are a significant target for application. We analyze the performance of three state-of-the-art community detection methods by using them to identify communities in a large social network constructed from mobile phone call records. We find that all methods detect communities that are meaningful in some respects but fall short in others, and that there often is a hierarchical relationship between communities detected by different methods. Our results suggest that community detection methods could be useful in studying the general mesoscale structure of networks, as opposed to only trying to identify dense structures.Comment: 11 pages, 10 figures. V2: typos corrected, one sentence added. V3: revised version, Appendix added. V4: final published versio

The scaling of human contacts and epidemic processes in metapopulation networks

We study the dynamics of reaction-diffusion processes on heterogeneous metapopulation networks where interaction rates scale with subpopulation sizes. We first present new empirical evidence, based on the analysis of the interactions of 13 million users on Twitter, that supports the scaling of human interactions with population size with an exponent γ ranging between 1.11 and 1.21, as observed in recent studies based on mobile phone data. We then integrate such observations into a reaction- diffusion metapopulation framework. We provide an explicit analytical expression for the global invasion threshold which sets a critical value of the diffusion rate below which a contagion process is not able to spread to a macroscopic fraction of the system. In particular, we consider the Susceptible-Infectious-Recovered epidemic model. Interestingly, the scaling of human contacts is found to facilitate the spreading dynamics. This behavior is enhanced by increasing heterogeneities in the mobility flows coupling the subpopulations. Our results show that the scaling properties of human interactions can significantly affect dynamical processes mediated by human contacts such as the spread of diseases, ideas and behaviors

Characteristics of cardiorespiratory output determining factors among 11–19-year-old boys at rest and during maximal load: Its impact on systolic hypertension

As consequence of the expansion of sedentary lifestyle among schoolchildren the prevalence of particular symptoms related to decreased cardiorespiratory fitness increases. The purpose of this study was twofolds, on one hand to compare boys in three developmental groups: second childhood (G1), puberty (G2), young adult (G3) and on the other hand to compare groups classified on resting systolic blood pressure (RSBP) to differentiate cardiorespiratory output determining factors both at rest and at maximal load. Randomly selected apparently healthy boys were assessed, all subjects (n = 282) performed an incremental treadmill test until fatigue. Heart rate (HR), systolic and diastolic blood pressure (SBP and DBP), and oxygen consumption were measured. Resting HR was higher and resting SBP and DBP were lower in the G1 as compared to G2 and G3 (p < 0.05) but not differed at maximal loads. However indicators of cardiovascular load differed between groups. The oxygen pulse and Q were the lowest in the G1 and increased significantly between groups (p < 0.05). In conclusion based on our data we can suggest that there is an observable development of hypertension associated with maturation and cardiac output determining factors

Efficient limited-time reachability estimation in temporal networks

Time-limited states characterize many dynamical processes on networks: disease-infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These dynamics can be described as limited-waiting-time processes, and they are particularly important for systems modeled as temporal networks. These processes have been studied via simulations, which is equivalent to repeatedly finding all limited-waiting-time temporal paths from a source node and time. We propose a method yielding an orders-of-magnitude more efficient way of tracking the reachability of such temporal paths. Our method gives simultaneous estimates of the in- or out-reachability (with any chosen waiting-time limit) from every possible starting point and time. It works on very large temporal networks with hundreds of millions of events on current commodity computing hardware. This opens up the possibility to analyze reachability and dynamics of spreading processes on large temporal networks in completely new ways. For example, one can now compute centralities based on global reachability for all events or can find with high probability the infected node and time, which would lead to the largest epidemic outbreak.Peer reviewe

Comportement coopératif dans des systèmes complexes

Ma motivation lors de mon doctorat fut d'examiner le comportement coopératif dans des systèmes complexes en utilisant les méthodes de la physique statistique et de l'informatique. Le but de mon travail fut d'étudier le comportement critique des systèmes à N corps durant leurs transitions de phase et de décrire de façon analytique leurs caractéristiques universelles, au moyen de calculs numériques. Afin d'y arriver j'ai effectue des études dans quatre sujets différents qui sont présentés dans la dissertation de la manière suivante. Après une brève introduction, j'ai résumé les points capitaux en relation avec les résultats théoriques. J'ai brièvement abordé le sujet des transitions de phase et des phénomènes critiques, de même que la théorie des classes d'universalité et des exposants critiques. Ensuite j'ai introduit les modèles statistiques important qui sont examinés plus tard dans la thèse et j'ai donné une petite description des modèles désordonnés. Dans le chapitre suivant, j'ai tout d'abord mis en avant les définitions de la théorie des graphes dont j'ai eu besoin pour introduire les structures géométriques appliquées et j'ai passé en revue les principales propriétés des réseaux régulières et j'ai défini les conditions de bord généralement utilisées. J'ai terminé ce chapitre avec une petite introduction sur les réseaux complexes. Le chapitre suivant contient les méthodes numériques appliquées que j'ai utilisées au cours des études numériques. J'ai écrit quelques mots sur les méthodes de Monte-Carlo et j'ai introduit l'algorithme d'optimisation combinatoire utilisé, et ses justifications mathématiques. Pour terminer j'ai décrit mes propres techniques pour générer des réseaux sans échelle. Suite à cette introduction théorique les résultats scientifiques ont été présentés de la manière suivante. Le 1er sujet auquel je me suis intéressé est une étude des transitions de phase hors équilibre dans les réseaux sans échelle de longueur, où la distribution des connectivités était ajustée, de telle façon qu'une transition de phase puisse être réalisée même dans les réseaux réalistes ayant un degré exposant g <= 3. Le système hors équilibre étudié était le "contact process" qui est un modèle de réaction-diffusion appartenant à la classe d'universalité de la percolation dirigé. Le deuxième problème que j'ai étudié fut le modèle de Potts aléatoire ferromagnétique avec de grandes valeurs de q sur des réseaux évolutifs sans échelle. Ce problème est équivalent à un problème de coopération optimale, où les agents essaient de trouver une situation optimale, où les bénéfices de coopération de paire (ici les couplages de Potts) et la somme totale du support, qui est la même pour tous les projets (introduite ici comme la température), sont maximisés. Une transition de phase apparaît dans le système entre un état où tous les agents sont corrélés, et un état désordonné à haute température. J'ai examiné ce modèle en utilisant un algorithme d'optimisation combinatoire sur les réseaux de Barabási-Albert sans échelle de longueur avec des couplages homogènes et aussi avec des couplages pondérés par des variables aléatoires indépendantes, suivant une distribution quasi-continue avec différents intensité de désordre. Le troisième problème examiné fut en rapport également avec le modèle de Potts ferromagnétique aléatoire à grand nombre d'états. J'ai examiné la densité critique des amas qui touchent l'un ou l'autre des bords dans une géométrie rectangulaire. Conformément à une prédiction de la théorie conforme je me suis attendu au même comportement que celui dérivé exactement pour la percolation critique dans des bandes infinies. J'ai calculé des moyennes à l'aide de l'algorithme d'optimisation combinatoire mentionné ci-dessus et j'ai comparé les moyennes numériques aux courbes théoriques attendues. Le dernier problème que j'ai étudié fut le modèle antiferromagnétique d'Ising bidimensionnel sur réseau triangulaire à température zéro en l'absence de champ extérieur. Ce modèle a été intensément étudié au cours des deux dernières décennies, dans la mesure où il montre les caractéristiques exotiques à l'équilibre due à la frustration géométrique. Cependant des explications contradictoires ont été publiées dans la littérature à propos du comportement dynamique en hors équilibre, suivant qu'il était caractérisé par une croissance diffusive avec correction logarithmique ou par une dynamique sous diffusives avec des exposants effectifs. Mon but fut de trouver des preuves indépendantes pour l'une des explications et d'examiner le comportement dynamique dans le régime de vieillissement.My motivation during my PhD studies was to examine cooperative behaviour in complex systems using the methods of statistical and computational physics. The aim of my work was to study the critical behaviour of interacting many-body systems during their phase transitions and describe their universal features analytically and by means of numerical calculations. In order to do so I completed studies in four different subjects which are presented in the dissertation as follows. After a short introduction I summarized the capital points of the related theoretical results. I shortly discussed the subjects of phase transitions and critical phenomena and briefly wrote about the theory of universality classes and critical exponents. Then I introduced the important statistical models which were examined later in the thesis and I gave a short description of disordered models. In the next chapter first, I pointed out the definitions of graph theory that I needed to introduce the applied geometrical structures and I reviewed the main properties of regular lattices and defined their general used boundary conditions. I closed this chapter with a short introduction to complex networks. The next chapter contains the applied numerical methods that I used in the course of numerical studies. I write a few words about Monte Carlo methods and introduce a combinatorial optimization algorithm and its mathematical background. As a last point I describe my own techniques to generate scale-free networks. Following this theoretical introduction the obtained scientific results were presented in the following way. My first investigated subject was a study of non-equilibrium phase transitions in weighted scale-free networks where I introduced edge weights and rescaled each of them by a power of the connectivities, thus a phase transition could be realized even in realistic networks having a degree exponent g <= 3. The investigated non-equilibrium system was the contact process which is a reaction-diffusion model belonging to the universality class of directed percolation. This epidemic spreading model presents a phase transition between an infected and a recovered state ordered by the ration of the recovering and infecting probability. The second problem I investigated was the ferromagnetic random bond Potts model with large values of q on evolving scale-free networks. This problem is equivalent to an optimal cooperation problem, where the agents try to find an optimal situation where the benefits of pair cooperation (here the Potts couplings) and total sum of the support, which is the same for all projects are maximized. A phase transition occurs in the system between a state when each agents are correlated and a high temperature disordered state. I examined this model using a combinatorial optimization algorithm on scale-free Barab si-Albert networks with homogeneous couplings and when the edge weights were a independent random values following a quasi-continuous distribution with different strength of disorder. The third examined problem was related to the large-q sate random bond Potts model also. Here I examined the critical density of clusters which touched a certain border of a perpendicular strip like geometry. Following from conformal prediction I expected the same density behavior as it was exactly derived for critical percolation in infinite strips. I calculated averages by the above mentioned effective combinatorial optimization algorithm and I compared the numerical means to the expected theoretical curves. The last investigated problem was the antiferromagnetic Ising model on two-dimensional triangular lattice at zero temperature in the absence of external field. This model was intensively studied during the last few decades, since it shows exotic features in equilibrium due to its geometrical frustration. However contradictory explanations were published in the literature about its non-equilibrium dynamical behaviour as it was characterized by a diffusive growth with logarithmic correction or by a sub-diffusive dynamics with effective exponents. My aim was to find independent evidences for one of the explanation and examine the dynamical behavior in the aging regime.GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

Un algorithme matriciel pour le calcul des composantes connectées d'un réseau complexe temporel

Temporal pairwise interactions of entities are depicted by temporal networks. Dynamical processes, such as epidemic spreading or information cascades, evolve on top of these networks. The largest outcome of these processes is directly linked the structure of the underlying network. Indeed, a node of the network cannot affect more nodes than it can reach. This set of nodes that are reachable from a source is called the out-component and its computation for any source is costly. In this paper, we propose an efficient matrix algorithm to tackle this issue and show that it outperforms the state-of-the-art method.Les interactions temporelles par paires d'entités peuvent être représentées par des réseaux temporels. Les processus dynamiques, tels que la propagation d'épidémies ou les cascades d'informations, qui évoluent sur ces réseaux, sont contraints à respecter sa structure. En effet, un noeud du réseau ne peut pas affecter plus de noeuds qu'il ne peut atteindre selon l'ordre des interactions. Cet ensemble de noeuds atteignables est appelé la composante sortante et son calcul est coûteux. Nous proposons un algorithme matriciel efficace pour résoudre ce problème et nous montrons qu'il est plus performant que l'état de l'art

Un algorithme matriciel pour le calcul des composantes connectées d'un réseau complexe temporel

Temporal pairwise interactions of entities are depicted by temporal networks. Dynamical processes, such as epidemic spreading or information cascades, evolve on top of these networks. The largest outcome of these processes is directly linked the structure of the underlying network. Indeed, a node of the network cannot affect more nodes than it can reach. This set of nodes that are reachable from a source is called the out-component and its computation for any source is costly. In this paper, we propose an efficient matrix algorithm to tackle this issue and show that it outperforms the state-of-the-art method.Les interactions temporelles par paires d'entités peuvent être représentées par des réseaux temporels. Les processus dynamiques, tels que la propagation d'épidémies ou les cascades d'informations, qui évoluent sur ces réseaux, sont contraints à respecter sa structure. En effet, un noeud du réseau ne peut pas affecter plus de noeuds qu'il ne peut atteindre selon l'ordre des interactions. Cet ensemble de noeuds atteignables est appelé la composante sortante et son calcul est coûteux. Nous proposons un algorithme matriciel efficace pour résoudre ce problème et nous montrons qu'il est plus performant que l'état de l'art

Randomized reference models for temporal networks

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may for example be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use non-trivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs) that sample networks with uniform probability. Focusing on temporal networks, we survey applications of MRRMs found in literature, and we use this framework to build a taxonomy of MRRMs that proposes a canonical naming convention, classifies them, and deduces their effects on a range of important network features. We furthermore show that certain classes of MRRMs may be applied in sequential composition to generate new MRRMs from the existing ones surveyed in this article. We finally provide a tutorial showing how to apply a series of MRRMs to analyze how different network features affect a dynamic process in an empirical temporal network. Our taxonomy provides a reference for the use of MRRMs, and the theoretical foundations laid here may further serve as a base for the development of a principled and automatized way to generate and apply randomized reference models for the study of networked systems