Vincent D. Blondel

Fast unfolding of communities in large networks

We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.

Convergence in Multiagent Coordination, Consensus, and Flocking

We discuss an old distributed algorithm for reaching consensus that has received a fair amount of recent attention. In this algorithm, a number of agents exchange their values asynchronously and form weighted averages with (possibly outdated) values possessed by their neighbors. We overview existing convergence results, and establish some new ones, for the case of unbounded intercommunication intervals.

Survey A survey of computational complexity results in systems and control

The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial-time algorithms, NP-completeness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, time-varying linear systems, nonlinear and hybrid systems, and stochastic optimal control.

Unique in the Crowd: The privacy bounds of human mobility

We study fifteen months of human mobility data for one and a half million individuals and find that human mobility traces are highly unique. In fact, in a dataset where the location of an individual is specified hourly, and with a spatial resolution equal to that given by the carriers antennas, four spatio-temporal points are enough to uniquely identify 95% of the individuals. We coarsen the data spatially and temporally to find a formula for the uniqueness of human mobility traces given their resolution and the available outside information. This formula shows that the uniqueness of mobility traces decays approximately as the 1/10 power of their resolution. Hence, even coarse datasets provide little anonymity. These findings represent fundamental constraints to an individuals privacy and have important implications for the design of frameworks and institutions dedicated to protect the privacy of individuals.

NP-Hardness of Some Linear Control Design Problems

We show that some basic linear control design problems are NP-hard, implying that, unless P=NP, they cannot be solved by polynomial time algorithms. The problems that we consider include simultaneous stabilization by output feedback, stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix, and decentralized control. These results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is NP-hard.

Geographical dispersal of mobile communication networks

In this paper, we analyze statistical properties of a communication network constructed from the records of a mobile phone company. The network consists of 2.5 million customers that have placed 810 million communications (phone calls and text messages) over a period of 6 months and for whom we have geographical home localization information. It is shown that the degree distribution in this network has a power-law degree distribution k−5 and that the probability that two customers are connected by a link follows a gravity model, i.e. decreases as d−2, where d is the distance between the customers. We also consider the geographical extension of communication triangles and we show that communication triangles are not only composed of geographically adjacent nodes but that they may extend over large distances. This last property is not captured by the existing models of geographical networks and in a last section we propose a new model that reproduces the observed property. Our model, which is based on the migration and on the local adaptation of agents, is then studied analytically and the resulting predictions are confirmed by computer simulations.

The Lyapunov exponent and joint spectral radius of pairs of matrices are hard—when not impossible—to compute and to approximate

We analyze the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities—the lower spectral radius and the largest Lyapunov exponent—are not algorithmically approximable.

Dynamic population mapping using mobile phone data

Significance Knowing where people are is critical for accurate impact assessments and intervention planning, particularly those focused on population health, food security, climate change, conflicts, and natural disasters. This study demonstrates how data collected by mobile phone network operators can cost-effectively provide accurate and detailed maps of population distribution over national scales and any time period while guaranteeing phone users’ privacy. The methods outlined may be applied to estimate human population densities in low-income countries where data on population distributions may be scarce, outdated, and unreliable, or to estimate temporal variations in population density. The work highlights how facilitating access to anonymized mobile phone data might enable fast and cheap production of population maps in emergency and data-scarce situations. During the past few decades, technologies such as remote sensing, geographical information systems, and global positioning systems have transformed the way the distribution of human population is studied and modeled in space and time. However, the mapping of populations remains constrained by the logistics of censuses and surveys. Consequently, spatially detailed changes across scales of days, weeks, or months, or even year to year, are difficult to assess and limit the application of human population maps in situations in which timely information is required, such as disasters, conflicts, or epidemics. Mobile phones (MPs) now have an extremely high penetration rate across the globe, and analyzing the spatiotemporal distribution of MP calls geolocated to the tower level may overcome many limitations of census-based approaches, provided that the use of MP data is properly assessed and calibrated. Using datasets of more than 1 billion MP call records from Portugal and France, we show how spatially and temporarily explicit estimations of population densities can be produced at national scales, and how these estimates compare with outputs produced using alternative human population mapping methods. We also demonstrate how maps of human population changes can be produced over multiple timescales while preserving the anonymity of MP users. With similar data being collected every day by MP network providers across the world, the prospect of being able to map contemporary and changing human population distributions over relatively short intervals exists, paving the way for new applications and a near real-time understanding of patterns and processes in human geography.

Complexity of stability and controllability of elementary hybrid systems

In this paper, we consider simple classes of nonlinear systems and prove that basic questions related to their stability and controllability are either undecidable or computationally intractable (NP-hard). As a special case, we consider a class of hybrid systems in which the state space is partitioned into two halfspaces, and the dynamics in each halfspace correspond to a different linear system.

Unsolved problems in mathematical systems and control theory

Among the signs of developing maturity in a field of research is willingness to share research problems and encourage collaborative efforts toward resolving them. There are now two important examples of this trend in control theory. In Liège, Belgium, in 1997, a workshop put together 53 expositions of open problems in our field which appeared in print as [1]; a web site [2] keeps track of comments and attempts at solutions of these problems. The book under review presents 63 new and stimulating papers, some with several distinct questions; see [3] to keep in touch with their progress. Some of these papers were presented at Open Problem sessions organized for Oberwohlfach Control Theory Days, February 2002, and for MTNS, Notre Dame, August 2002. Editors V. D. Blondel and A. Megretski were assisted by Associate Editors R. W. Brockett, J. M. Coron, R. Hildebrand, M. Krstic, A. Rantzer, J. Rosenthal, E. D. Sontag, M. Vidyasagar, and J. Willems. These editors, with over 100 authors from four continents, have produced an attractive volume, modestly priced, that will remain interesting for a long time; even the dust-jacket is admirable. My only complaint about the book is the absence of an index. The book has ten parts, a list of which follows: 1) Linear Systems: 13 problems, 60 pages; 2) Stochastic Systems: four problems, 20 pages; 3) Nonlinear Systems: nine problems, 38 pages; 4) Discrete-Event, Hybrid Systems: four problems, 20 pages; 5) Distributed Parameter Systems: six problems, 33 pages; 6) Stability, Stabilization: ten problems, 55 pages; 7) Controllability, Observability: 4 problems, 17 pages; 8) Robustness, Robust Control: four problems, 16 pages; 9) Identification, Signal Processing: two problems, ten pages; 10) Algorithms, Computation: seven problems, 21 pages.