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In this paper, we extend some usual techniques of classification resulting from a large-scale data-mining and network approach. This new technology, which in particular is designed to be suitable to big data, is used to construct an open consolidated database from raw data on 4 million patents taken from the US patent office from 1976 onward. To build the pattern network, not only do we look at each patent title, but we also examine their full abstract and extract the relevant keywords accordingly. We refer to this classification as semantic approach in contrast with the more common technological approach which consists in taking the topology when considering US Patent office technological classes. Moreover, we document that both approaches have highly different topological measures and strong statistical evidence that they feature a different model. This suggests that our method is a useful tool to extract endogenous information., Comment: 28 pages ; 9 figures ; 5 Supplementary Materials

The Static User Equilibrium is a powerful framework for the theoretical study of traffic. Despite the restricting assumption of stationary flows that intuitively limit its application to real traffic systems, many operational models implementing it are still used without an empirical validation of the existence of the equilibrium. We investigate its existence on a traffic dataset of three months for the region of Paris, FR. The implementation of an application for interactive spatio-temporal data exploration allows to hypothesize a high spatial and temporal heterogeneity, and to guide further quantitative work. The assumption of locally stationary flows is invalidated in a first approximation by empirical results, as shown by a strong spatial and temporal variability in shortest paths and in network topological measures such as betweenness centrality. Furthermore, the behavior of spatial autocorrelation index of congestion patterns at different spatial ranges suggest a chaotic evolution at the local scale, especially during peak hours. We finally discuss the implications of these empirical findings and describe further possible developments based on the estimation of Lyapunov dynamical stability of traffic flows., Comment: 9 pages, 5 figures. Forthcoming in Transportation Research Procedia, EWGT2016, 5-7 September 2016, Istanbul

Multi-objective evaluation is a necessary aspect when managing complex systems, as the intrinsic complexity of a system is generally closely linked to the potential number of optimization objectives. However, an evaluation makes no sense without its robustness being given (in the sense of its reliability). Statistical robustness computation methods are highly dependent of underlying statistical models. We propose a formulation of a model-independent framework in the case of integrated aggregated indicators (multi-attribute evaluation), that allows to define a relative measure of robustness taking into account data structure and indicator values. We implement and apply it to a synthetic case of urban systems based on Paris districts geography, and to real data for evaluation of income segregation for Greater Paris metropolitan area. First numerical results show the potentialities of this new method. Furthermore, its relative independence to system type and model may position it as an alternative to classical statistical robustness methods., Comment: 14 pages, 2 figures, 1 table. Forthcoming in Proceedings of Complex Systems Design and Management, Paris 13-14 December 2016

Bike-sharing transportation systems have been well studied from a top-down viewpoint, either for an optimal conception of the system, or for a better statistical understanding of their working mechanisms in the aim of the optimization of the management strategy. Yet bottom-up approaches that could include behavior of users have not been well studied so far. We propose an agent-based model for the short time evolution of a bike-sharing system, with a focus on two strategical parameters that are the role of the quantity of information users have on the all system and the propensity of user to walk after having dropped their bike. We implement the model in a general way so it is applicable to every system as soon as data are available in a certain format. The model of simulation is parametrized and calibrated on processed real time-series of bike movements for the system of Paris. After showing the robustness of the simulations by validating internally and externally the model, we are able to test different user-based strategies for an increase of the level of service. In particular, we show that an increase of user information can have significant impact on the homogeneity of repartition of bikes in docking stations, and, what is important for a future implementation of the strategy, that an action on only 30% of regular users is enough to obtain most of the possible amelioration., Comment: 14 pages, 6 figures. in Proceedings of Complex Systems Design & Management, Paris, December 2014

A broad bibliographical study suggests a scarcity of quantitative models of simulation integrating both network and urban growth. This absence may be due to diverging interests of concerned disciplines, resulting in a lack of communication. We propose to proceed to an algorithmic systematic review to give quantitative elements of answer to this question. A formal iterative algorithm to retrieve corpuses of references from initial keywords, based on text-mining, is developed and implemented. We study its convergence properties and do a sensitivity analysis. We then apply it on queries representative of the specific question, for which results tend to confirm the assumption of disciplines compartmentalisation., Comment: 8 pages, 2 figures, 1 table. Forthcoming in Proceedings of European Colloquium on Theoretical and Quantitative Geography, Bari, September 2015

In this paper we prove that for a fixed neat principal congruence subgroup of a Bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated to the m-th symmetric power of the standard representation of SL_2(C) grows exponentially in m^2. We give upper and lower bounds for the growth rate. Our result extends a result of Mueller and Marshall, who proved the corresponding statement for closed arithmetic 3-manifolds, to the finite-volume case. We also prove a limit multiplicity formula for twisted combinatorial Reidemeister torsion on higher dimensional hyperbolic manifolds., Comment: Second version : 35 pages, we made minor corrections and added a cheap but substantial improvement of the main result

Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric point of view from Bowditch's paper. In particular, we discuss fundamental groups of flat and hyperbolic manifolds. The appendix settles an open question by providing an example of a group which is diffuse but not left-orderable., Comment: 37 pages, main text by Kionke and Raimbault, appendix by Dunfield. v2 : updated ancillary files and added url to the references

This paper is mostly a survey of recent work on sequences of locally symmetric spaces whose Riemannian volume goes to infinity. We also work out some applications to random surfaces., Comment: Mostly a survey (in French) by the second author; the appendix A is a translated and shortened version of arXiv:1411.0561

We study the ends of a generic manifold, with respect to a unimodular measure on the space of pointed Riemannian manifolds with bounded curvatures. We apply our general result to the case of surfaces and obtain as corollaries a very precise description of generic leaves for foliations with invariant measures and of quotients of the hyperbolic plane by invariant random subgroups of the isometry group., Comment: Short note, two figures. Major rewrite from v1: extended the scope and added remarks on foliations

We discuss the geometry of some arithmetic orbifolds locally isometric to a product of real hyperbolic spaces of dimension two and three, and prove that certain sequences of non-uniform orbifolds are convergent to this space in a geometric ("Benjamini--Schramm") sense for hyperbolic three--space and a product of hyperbolic planes. We also deal with arbitrary sequences of maximal arithmetic three--dimensional hyperbolic lattices defined over a quadratic or cubic field. A motivating application is the study of Betti numbers of Bianchi groups., Comment: Final version, 51 pages (journal layout). Minor correction to the main theorem from the first version

Starting from the results in math.DG:1212.3161 we prove that for a given Bianchi group, certain natural coefficent modules and a lot of sequences of congruence subgroups of the size of the torsion subgroup of the first homology grows exponentially with the index (we give an explicit rate). We also prove limit multiplicity results for the irreducible components of the space of cuspidal forms., Comment: Overdue update, the main result has been much weakened due to a gap in the last step of the proof (we get only an upper bound on the limsup instead of a limit). We include a conditional statement of the previous version, however checking the condition seems hard

We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficient systems the regularized analytic torsion approximates the $L^2$-torsion of the universal cover under an additional hypothesis. We also prove an asymptotic equality between the former and some Reidemeister torsion of the truncated manifolds., Comment: Final version, 55 pages (minor corrections and details from the previous version). To appear in Commentarii Mathematici Helvetici

We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge--Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini--Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the possible limits. We show that BS-convergence of locally symmetric spaces implies convergence, in an appropriate sense, of the associated normalized relative Plancherel measures. This then yields convergence of normalized multiplicities of unitary representations, Betti numbers and other spectral invariants. On the other hand, when the corresponding Lie group $G$ is simple and of real rank at least two, we prove that there is only one possible BS-limit, i.e. when the volume tends to infinity, locally symmetric spaces always BS-converge to their universal cover $G/K$. This leads to various general uniform results. When restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of BS-convergence which in turn implies upper estimates on the rate of convergence of normalized Betti numbers in the spirit of Sarnak--Xue. An important role in our approach is played by the notion of Invariant Random Subgroups. For higher rank simple Lie groups $G$, we exploit rigidity theory, and in particular the Nevo--St\"{u}ck--Zimmer theorem and Kazhdan's property (T), to obtain a complete understanding of the space of IRSs of $G$., Comment: The first version of this paper has been split into two papers. This is the first part. It is 64 pages long. To appear in Annals of Mathematics

We show that the number of noncommensurable lattices, hence also that of maximal lattices in SO(1,n) is at least exponential. To do so we construct large families of noncommensurable hybrid hyperbolic (Gromov/Piatetski-Shapiro) manifolds., Comment: 6 pages

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem \cite{luck}, which is much stronger than the linear upper bounds on Betti numbers given by Gromov in \cite{BGS}. The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamimi and Schramm, to sequences of Riemannian manifolds. Using rigidity theory we are able to show that when the volume tends to infinity, the manifolds locally converge to the universal cover in a sufficiently strong manner that allows us to derive the convergence of the normalized Betti numbers., Comment: Announcement

We study the growth of the order of torsion subgroups of the homology in a tower of finite abelian coverings. In particular, we prove that it is exponential for when the tower converges to the maximal free abelian cover of a link complement when the first nonzero Alexander polynomial has positive logarithmic Mahler measure., Comment: 42 pages, to appear in AGT. Various minor mistakes corrected and exposition changed

On doping polar dielectrics, such as the cuprates or liquid ammonia, the long range polarization leads to the formation of bound states (polarons or solvated electrons). However, the exact role of such entities in the metal-insulator transition (MIT) still remains unclear. We suggest that the driving mechanism of the MIT is a polarization catastrophe that occurs due to their unscreened Coulomb interaction. This phenomenon is associated to a negative static dielectric constant, which could be the origin of both the superconducting transition in the cuprates -- where the doping ions are frozen in the lattice structure -- and the phase separation observed in liquid metal-ammonia solutions -- where the counter-ions are mobile., Comment: 4 pages, 2 figures, proceedings of ECRYS-2002, to be published in Journal de Physique IV

In his Comment (cond-mat/0104060) to [Phys. Rev. E 60, 6530 (1999)], Mateescu shows that while the effective interactions remain repulsive when the specific size of the micro-ions is taken into account via a Modified Poisson-Boltzmann equation, a similar conclusion cannot be reached for the situation of complete lateral confinement. This point is correct but has already been considered in a more general study [Phys. Rev. E 62, R1465 (2000), where repulsion is generically obtained]; moreover, we argue that it illustrates the irrelevancy of the notion of pair potential in completely confined configurations, as shown on a simple example.

We present an exact field theoretical representation of the statistical mechanics of classical hard-core Coulomb systems. This approach generalizes the usual sine-Gordon theory valid for point-like charges or lattice systems to continuous Coulomb fluids with additional short-range interactions. This formalism is applied to derive the equation of state of the restricted primitive model of electrolytes in the low fugacity regime up to order $\rho^{5/2}$ ($\rho$ number density). We recover the results obtained by Haga by means of Mayer graphs expansions.

We perform a high-temperature expansion of the grand potential of the restrictive primitive model of electrolytes in the frame of the extended sine-Gordon theory exposed in the companion paper. We recover a result already obtained by Stell an Lebowitz (J. Chem. Phys., 49, 3706 (1968)) by means of diagrammatic expansions.

Within the framework of a Modified Poisson-Boltzmann theory accounting for steric effects of microions, we prove analytically that the effective pair interactions between like-charge colloids immersed in a confined electrolyte are repulsive. Our approach encompasses and extends previously known results to the case of complete confinement, and further incorporates the finite size of the microions which is absent in the standard Poisson-Boltzmann theory., Comment: 5 pages, 1 figure, to appear in Physical Review E