In , , we proposed a new shift operator for graph signals, enforcing that our operator is isometric. Doing so, we ensure that as many properties of the time shift as possible get carried over. Finally, we show that our operator behaves reasonably for graph signals.

We extended the concept of stationary temporal signals to stationary graph signals . We introduced the concept of strict sense stationary and wide sense stationary graph signals as a statistical invariance through an isometric graph translation. Using these definitions, we proposed a spectral characterisation of WSS graph signals allowing to study stationarity using only the spectral components of a graph signal. Finally, we applied this characterisation to a synthetic graph in order to study a few important stochastic graph signals. Also, using geographic data, we analysed data from a graph set of weather stations and showed evidence of stationarity in the temperature signal .

Communities are an important type of structure in networks. Graph filters, such as wavelet filter-banks, have been used to detect such communities as groups of nodes more densely connected together than with the outsiders. When dealing with times series, it is possible to build a relational network based on the correlation matrix. However, in such a network, weights assigned to each edge have different properties than those of usual adjacency matrices. As a result, classical community detection methods based on modularity optimisation are not consistent and the modularity needs to be redefined to take into account the structure of the correlation from random matrix theory. In our contribution , we addressed how to detect communities from correlation matrices, by filtering global modes and random parts using properties that are specific to the distribution of correlation eigenvalues. Based on a Louvain approach, an algorithm to detect multiscale communities was also developed, which yields a weighted hierarchy of communities. The implementation of the method using graph filters was also discussed.

In , we showed that a characteristic function which can be approximated at 0 by any polynomial of order n is actually n-times differentiable at 0. This fact is exploited to strengthen a tauberian-type result by Lukacs and provides the theoretical basis for a wavelet based non-parametric estimator of the tail index of a distribution. This work is a technical improvement of our previous contribution .

The fetal heart rate (FHR) is commonly monitored during labor to detect early fetal acidosis. FHR variability is traditionally investigated using Fourier transform, often with adult predefined frequency band powers and the corresponding LF/HF ratio. However, fetal conditions differ from adults and modify spectrum repartition along frequencies. The study we reported in questioned the arbitrariness definition and relevance of the frequency band splitting procedure, and thus of the calculation of the underlying LF/HF ratio, as efficient tools for characterising intrapartum FHR variability. Then, we showed that the intrapartum FHR is characterised by fractal temporal dynamics and promotes the Hurst parameter as a potential marker of fetal acidosis. This parameter preserves the intuition of a power frequency balance, while avoiding the frequency band splitting procedure and thus the arbitrary choice of a frequency separating bands. The study also shows that extending the frequency range covered by the adult-based bands to higher and lower frequencies permits the Hurst parameter to achieve better performance for identifying fetal acidosis.

The PetaFlow application aims to contribute to the use of high performance computational resources for the benefit of society. To this goal the emergence of adequate information and communication technologies with respect to high performance computing-networking-visualisation and their mutual awareness is required. In the work published in , we present the developed technology and the algorithms that we applied to a real global peta-scale data intensive scientific problem with social and medical importance, i.e. human upper airflow modeling.

Multi-hop wireless networks are often regarded as a promising means to extend the limited coverage area offered by WLANs. However, they are usually associated with poor and uncertain performance in terms of available bandwidth and packet losses, which clearly stands as a limitation to their use. In , we consider the performance evaluation of a multi-hop path (also called chain), based on the IEEE 802.11 DCF. The proposed modeling framework is constructive and versatile, so that it can handle various types of multi-hop wireless paths, including scenarios with two flows in opposite directions, and topologies where nodes are exposed to the well-known hidden node problem. The models derived from our framework are conceptually simple, easy to implement and produce generally accurate results for the attained goodput of flows, as well as the datagram loss probability. Typical relative errors for these two quantities are below a few percent. Also, fundamental phenomena occurring in multi-hop wireless networks such as performance collapse and starvation, are well captured by the models.

Emerging architectures for computer networks such as SDN aim at offering a better handling of flows with stringent requirements of QoS. On the one hand, operators would benefit from a detailed description of common network performance (e.g., end-to-end delay and end-to end loss ratio) including their first two moments, namely mean and standard deviation. Indeed, for many applications, the variability in the end-to-end delay (e.g., jitter) deeply affects the actual QoS experienced by a flow. On the other hand, the cost and nuisance associated with the instrumentation, the measurements, and the computations must be kept as low as possible. This typically prevents the availability of end-to-end measurements. In , we propose an algorithm to estimate the second moment of the end-to-end delay experienced by the packets of a flow based only on delay measurements locally collected by the network nodes. Our solution estimates the standard deviation of the end-to-end delay in an easy and computationally efficient way. Based on thousands of simulations using a real-life trace, our solution is found to be accurate, typically differing by only a few percent from the actual value of the standard deviation of the end-to-end delay.

Vespa velutina, also known as the Asian hornet, is considered as an invasive species out of its native zone. In particular, since it preys on honey bees, its recent progression in Europe could soon pose a significant risk to the local apiculture activity. European beekeepers are therefore investigating adapted control strategies, including V. velutina nest destruction. Unfortunately, nest location pinpointing generally follows a manual process which can prove tedious, time-consuming and inaccurate. In , we propose the use of a network of micro aerial vehicles featuring autonomous and cooperative flight capabilities. We describe an adapted controlled mobility strategy and detail the design of our Virtual Force Protocol (VFP) which allows a swarm of vehicles to track and follow hornets to their nests, while maintaining connectivity through a wireless multi-hop communication route with a remote ground station used to store applicative data such as hornet trajectory and vehicle telemetry. In order to achieve the mission objectives with a minimum of vehicles, we identify through simulations appropriate value for the key parameters of VFP and discuss the obtained network performance.

A substitution network is a rapidly deployable wireless network that provides a backup solution to quickly react to failures on an existing network. We assume that the substitution network uses Wi-Fi technology and that wireless routers are equipped with several Wi-Fi cards. The problem, addressed in this work, deals with the channel assignment to these wireless interfaces. In this particular context, there is only one source-destination pair for which paths are known in advance. It is then possible to derive an objective function, function of the channel assignment, that very precisely reflects the overall throughput that can be achieved in this network. This problemis formulated through a linear optimization problem for which we propose different heuristics. Simulation results, performed with ns-3, consider several scenarios, and compare our heuristics to the optimum. Simulations show that, with only a few wireless cards, the throughput is signifficantly increased. Also, we show that the objective function fits to the throughput measured with ns-3.

Vehicular Ad-Hoc Network (VANET) is becoming a promising technology for improving the efficiency and the safety of Intelligent Transportation Systems (ITS). Smart vehicles are expected to continuously exchange a huge amount of data either through safety or non-safety messages dedicated for road safety or infotainment and passenger comfort applications, respectively. In this context we proposed two contributions: the estimation of the capacity offered by the wireless network  in order to dimension the applications, and the proposal of an efficient message dissemination protocol .

Cloud providers need to size their systems to determine the right amount of resources to allocate as a function of customer’s needs so as to meet their SLAs (Service Level Agreement), while at the same time minimizing their costs and energy use. Queueing theory based tools are a natural choice when dealing with performance aspects of the QoS (Quality of Service) part of the SLA and forecasting resource utilization. The characteristics of a cloud center lead to a queueing system with multiple servers (nodes) in which there is potentially a very large number of servers and both the arrival and service process can exhibit high variability. We propose to use a G/G/c-like model to represent a cloud system and assess expected performance indices. Given the potentially high number of servers in a cloud system, we present an efficient, fast and easy-to-implement approximate solution. We have extensively validated our approximation against discrete-event simulation for several QoS performance metrics such as task response time and blocking probability with excellent results. We apply our approach to examples of system sizing and our examples clearly demonstrate the importance of taking into account the variability of the tasks arrivals and thus expose the risk of under- or over-provisioning if one relies on a model with Poisson assumptions .

In this paper we consider the problem of combining calibrated performance models of system components in order to predict overall system performance. We focus on open workload system models, in which, under certain conditions, obtaining and validating the overall system performance measures can be a simple application of Little's law. We discuss the conditions of applicability of such a simple validation methodology, including examples of successful application, as well as examples where this approach fails. Additionally, we propose to analyze the deviations between the model predictions and system measurements, so as to decide if they correspond to “measurement noise” or if an important system component has not been correctly represented. This approach can be used as an aid in the design of validated system performance models .

Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets $(u,v,t)$ where $u$ and $v$ are two nodes having a link between them at time $t$. A great number of studies on these objects start by aggregating the data on disjoint time windows of length $\Delta$ in order to obtain a series of graphs on which are made all subsequent analyses. Here we are concerned with the impact of the chosen $\Delta$ on the obtained graph series. We address the fundamental question of knowing whether a series of graphs formed using a given $\Delta$ faithfully describes the original link stream. We answer the question by showing that such dynamic networks exhibit a threshold for $\Delta$, which we call the saturation scale, beyond which the properties of propagation of the link stream are altered, while they are mostly preserved before. We design an automatic method to determine the saturation scale of any link stream, which we apply and validate on several real-world datasets.

The clean-factor operator is a multipartite graph operator that has been introduced in the context of complex network modelling. Here, we consider a less constrained variation of the clean-factor operator, named strong-factor operator, and we prove that, as for the clean-factor operator, the iteration of the strong-factor operator always terminates, independently of the graph given as input. Obtaining termination for all graphs using minimal constraints on the definition of the operator is crucial for the modelling purposes for which the clean-factor operator has been introduced. Moreover we show that the relaxation of constraints we operate not only preserves termination but also preserves the termination time, in the sense that the strong-factor series always terminates before the clean-factor series.

We define a new graph operator, called the weak-factor graph, which comes from the context of complex network modelling. The weak-factor operator is close to the well-known clique-graph operator but it rather operates in terms of bicliques in a multipartite graph. We address the problem of the termination of the series of graphs obtained by iteratively applying the weak-factor operator starting from a given input graph. As for the clique-graph operator, it turns out that some graphs give rise to series that do not terminate. Therefore, we design a slight variation of the weak-factor operator, called clean-factor, and prove that its associated series terminates for all input graphs. In addition, we show that the multipartite graph on which the series terminates has a very nice combinatorial structure: we exhibit a bijection between its vertices and the chains of the inclusion order on the intersections of the maximal cliques of the input graph.

In this paper, we design an algorithm that, given a directed graph $G$ and the Cartesian-product decomposition of its underlying undirected graph $\tilde{G}$, produces the directed Cartesian-product decomposition of $G$ in linear time. This is the first time that the linear complexity is achieved for this problem, which has two major consequences. Firstly, it shows that the directed and undirected versions of the Cartesian-product decomposition of graphs are linear-time equivalent problems. And secondly, as there already exists a linear-time algorithm for solving the undirected version of the problem, combined together, it provides the first linear-time algorithm for computing the directed Cartesian-product decomposition of a directed graph.

We provide an $O\left(n^2\right)$ time algorithm computing a minimal permutation completion of an arbitrary graph $G=(V,E)$, i.e., a permutation graph $H=(V,F)$ on the same vertex set, such that $E\subseteq F$ and $F$ is inclusion-minimal among all possibilities.

Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalisation of contiguity in the sense that every encoding achieving contiguity $k$ induces an encoding achieving linearity $k$, both encoding having size $\Theta (k.n)$, where $n$ is the number of vertices of $G$. In this paper, we prove that linearity is a strictly more powerful encoding than contiguity, i.e. there exists some graph family such that the linearity is asymptotically negligible in front of the contiguity. We prove this by answering an open question asking for the worst case linearity of a cograph on $n$ vertices: we provide an $O(logn/loglogn)$ upper bound which matches the previously known lower bound.

In this work we study the socioeconomic structure of a communication network by combining mobile communication records and bank credit informations of a large number of individuals living in Mexico. We provide empirical evidences about present economic unbalances suggesting not only the distribution of wealth but also the distribution of debts to follow the Pareto principle. Further we study the internal and interconnected structure of socioeconomic groups. Through a weighted core analysis we signal assortative correlations between people regarding their economic capacities, and show the existence of "rich-clubs" indicating present social stratification in the social structure. This project is ongoing with final results expected in 2016.

The identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different graph regions. However, we argue here that this measure is not adapted for that task, as it gives equal weight to "local" centers (i.e. nodes of high degree central to a single region) and to "global" bridges, which connect different communities. This distinction is important as the roles of such nodes are different in terms of the local and global organisation of the network structure. In this paper we propose a decomposition of betweenness centrality into two terms, one highlighting the local contributions and the other the global ones. We call the latter bridgeness centrality and show that it is capable to specifically spot out global bridges. In addition, we introduce an effective algorithmic implementation of this measure and demonstrate its capability to identify global bridges in air transportation and scientific collaboration networks.

We study, on a sample of 2.3 million individuals, how Facebook users consumed different information at the edge of political discussion and news during the last Italian electoral competition. Pages are categorized, according to their topics and the communities of interests they pertain to, in a) alternative information sources (diffusing topics that are neglected by science and main stream media); b) online political activism; and c) main stream media. We show that attention patterns are similar despite the different qualitative nature of the information, meaning that unsubstantiated claims (mainly conspiracy theories) reverberate for as long as other information. Finally, we categorize users according to their interaction patterns among the different topics and measure how a sample of this social ecosystem (1279 users) responded to the injection of 2788 false information posts. Our analysis reveals that users which are prominently interacting with alternative information sources (i.e. more exposed to unsubstantiated claims) are more prone to interact with false claims.

We present new empirical evidence, based on millions of interactions on Twitter, confirming that human contacts scale with population sizes. We integrate such observations into a reaction-diffusion metapopulation framework providing an analytical expression for the global invasion threshold of a contagion process. Remarkably, the scaling of human contacts is found to facilitate the spreading dynamics. 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, and ideas.

Social interactions vary in time and appear to be driven by intrinsic mechanisms, which in turn shape the emerging structure of the social network. Large-scale empirical observations of social interaction structure have become possible only recently, and modelling their dynamics is an actual challenge. Here we propose a temporal network model which builds on the framework of activity-driven time-varying networks with memory. The model also integrates key mechanisms that drive the formation of social ties - social reinforcement, focal closure and cyclic closure, which have been shown to give rise to community structure and the global connectedness of the network. We compare the proposed model with a real-world time-varying network of mobile phone communication and show that they share several characteristics from heterogeneous degrees and weights to rich community structure. Further, the strong and weak ties that emerge from the model follow similar weight-topology correlations as real-world social networks, including the role of weak ties.

Diffusion of information, behavioural patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of media. Here we study analytically and by simulations a general model that incorporates threshold mechanism capturing sensitivity to peer pressure, the effect of `immune' nodes who never adopt, and a perpetual flow of external information. While any constant, non-zero rate of dynamically-introduced innovators leads to global spreading, the kinetics by which the asymptotic state is approached show rich behaviour. In particular we find that, as a function of the density of immune nodes, there is a transition from fast to slow spreading governed by entirely different mechanisms. This transition happens below the percolation threshold of fragmentation of the network, and has its origin in the competition between cascading behaviour induced by innovators and blocking of adoption due to immune nodes. This change is accompanied by a percolation transition of the induced clusters.