arXiv subjects

R. Lambiotte

Publications and source records attributed to R. Lambiotte.

35 records · Page 2Linked to original sources

arXiv2007

Majority Model on a network with communities

We focus on the majority model in a topology consisting of two coupled fully-connected networks, thereby mimicking the existence of communities in social networks. We show that a transition takes place at a value of the inter-connectivity parameter. Above this value, only symmetric solutions prevail, where both communities agree with each other and reach consensus. Below this value, in contrast, the communities can reach opposite opinions and an asymmetric state is attained. The importance of the interface between the sub-networks is shown.

physics.soc-ph↗

arXiv2007

Growing network with j-redirection

A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when a new node enters the network, it either connects to a randomly selected node, or to the j -ancestor of this selected node. The j -ancestor is found by following j links from the randomly selected node. The system is shown to undergo a transition to a phase where condensates develop. We also find analytical predictions for the height statistics and show numerically the non-trivial behaviour of the degree distribution.

physics.soc-ph↗

arXiv2006

Clusters or networks of economies? A macroeconomy study through GDP fluctuation correlations

We follow up on the study of correlations between GDP's of rich countries. We analyze web-downloaded data on GDP that we use as individual wealth signatures of the country economical state. We calculate the yearly fluctuations of the GDP. We look for forward and backward correlations between such fluctuations. The system is represented by an evolving network, nodes being the GDP fluctuations (or countries) at different times. In order to extract structures from the network, we focus on filtering the time delayed correlations by removing the least correlated links. This percolation idea-based method reveals the emergence of connections, that are visualized by a branching representation. Note that the network is made of weighted and directed links when taking into account a delay time. Such a measure of collective habits does not fit the usual expectations defined by politicians or economists.

physics.soc-ph↗

arXiv2005

Collaborative tagging as a tripartite network

We describe online collaborative communities by tripartite networks, the nodes being persons, items and tags. We introduce projection methods in order to uncover the structures of the networks, i.e. communities of users, genre families... To do so, we focus on the correlations between the nodes, depending on their profiles, and use percolation techniques that consist in removing less correlated links and observing the shaping of disconnected islands. The structuring of the network is visualised by using a tree representation. The notion of diversity in the system is also discussed.

cs.DS↗

arXiv2005

Granular Matter: a wonderful world of clusters in far-from-equilibrium systems

In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline materials. The phase space available can be quite different. Unexpected features, with respect to standard or expected ones in classical fluids or solids, are observed, - like slow relaxation processes or anomalous electrical and thermoelectrical transport property dependences. The cases of various pile structures and the interplay between classical phase transitions and self-organized criticality for avalanches are also outlined.

cond-mat.mtrl-sci↗

arXiv2005

Endo- vs. Exo-genous shocks and relaxation rates in book and music "sales"

In this paper, we analyze the response of music and book sales to an external field and to buyer herding. We distinguish endogenous and exogenous shocks. We focus on some case studies, whose data have been collected from ranking on amazon.com. We show that an ensemble of equivalent systems quantitatively respond in a similar way to a similar ''external shock'', indicating roads to universality features. In contrast to Sornette et al. [Phys. Rev. Lett. {93}, 228701 (2004)] who seemed to find power law behaviors, in particular at long times, - a law interpreted in terms of an epidemic activity, we observe that the relaxation process can be as well seen as an exponential one that saturates toward an asymptotic state, itself different from the pre-shock state. By studying an ensemble of 111 shocks, on books or records, we show that exogenous and endogenous shocks are discriminated by their short-time behaviour: the relaxation time seems to be twice shorter in endogenous shocks than in exogenous ones. We interpret the finding through a simple thermodynamic model with a dissipative force.

physics.soc-ph↗

arXiv2005

Energy and number of collisions fluctuations in inelastic gases

We study by numerical simulations the two-dimensional Inelastic Maxwell Model (IMM), and show how the inelasticity of collisions together with the fluctuations of the number of collisions undergone by a particle lead to energy fluctuations that decay like a power-law. These fluctuations are associated to a shrinking of the available phase space. We find the asymptotic scaling of these energy fluctuations and show how they affect the tail of the velocity distribution during long time intervals.

cond-mat.stat-mech↗

arXiv2005

Uncovering collective listening habits and music genres in bipartite networks

In this paper, we analyze web-downloaded data on people sharing their music library, that we use as their individual musical signatures (IMS). The system is represented by a bipartite network, nodes being the music groups and the listeners. Music groups audience size behaves like a power law, but the individual music library size is an exponential with deviations at small values. In order to extract structures from the network, we focus on correlation matrices, that we filter by removing the least correlated links. This percolation idea-based method reveals the emergence of social communities and music genres, that are visualised by a branching representation. Evidence of collective listening habits that do not fit the neat usual genres defined by the music industry indicates an alternative way of classifying listeners/music groups. The structure of the network is also studied by a more refined method, based upon a random walk exploration of its properties. Finally, a personal identification - community imitation model (PICI) for growing bipartite networks is outlined, following Potts ingredients. Simulation results do reproduce quite well the empirical data.

physics.soc-ph↗

arXiv2005

On high energy tails in inelastic gases

We study the formation of high energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time- discretized version of the stochastic process, and show that continuous time implies larger fluctuations of the particles energies. This is due to a statistical relation between the number of inelastic collisions undergone by a particle and its average energy. This feature is responsible for the high energy tails in the model, as shown by computer simulations and by analytical calculations on a linear Lorentz model.

cond-mat.stat-mech↗

arXiv2005

From particle segregation to the granular clock

Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an overpopulation of particles in one side of the box. Here we study the segregation of a mixture of particles composed of inelastic hard spheres and fluidized by a vibrating wall. Our numerical simulations show a rich phenomenology: horizontal segregation and periodic behavior. We also propose an empirical system of ODEs representing the proportion of each type of particles and the segregation flux of particles. These equations reproduce the major features observed by the simulations.

cond-mat.stat-mech↗

arXiv2005

Truncated Levy distributions in an inelastic gas

We study a one-dimensional model for granular gases, the so-called Inelastic Maxwell Model. We show theoretically the existence of stationary solutions of the unforced case, that are characterized by an infinite average energy per particle. Moreover, we verify the quasi-stationarity of these states by performing numerical simulations with a finite number of particles, thereby highlighting truncated Lévy distributions for the velocities.

cond-mat.stat-mech↗

arXiv2005

N-body decomposition of bipartite networks

In this paper, we present a method to project co-authorship networks, that accounts in detail for the geometrical structure of scientists collaborations. By restricting the scope to 3-body interactions, we focus on the number of triangles in the system, and show the importance of multi-scientists (more than 2) collaborations in the social network. This motivates the introduction of generalized networks, where basic connections are not binary, but involve arbitrary number of components. We focus on the 3-body case, and study numerically the percolation transition.

physics.soc-ph↗

arXiv2005

A Brownian particle having a fluctuating mass

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By performing numerical simulations of the Langevin equation, we check the theoretical predictions derived in the adiabatic limit, and study deviations outside this limit. We compare the mass velocity distribution with truncated Tsallis distributions [J. Stat. Phys. 52 (1988) 479] and find excellent agreement if the masses are chi- squared distributed. We also consider the diffusion of the Brownian particle by studying a Bernoulli random walk with fluctuating walk length in one dimension. We observe the time dependence of the position distribution kurtosis and find interesting behaviours. We point out a few physical cases where the mass fluctuation problem could be encountered as a first approximation for agglomeration- fracture non equilibrium processes.

cond-mat.stat-mech↗

arXiv2005

On the genre-fication of Music: a percolation approach (long version)

In this paper, we analyze web-downloaded data on people sharing their music library. By attributing to each music group usual music genres (Rock, Pop...), and analysing correlations between music groups of different genres with percolation-idea based methods, we probe the reality of these subdivisions and construct a music genre cartography, with a tree representation. We also show the diversity of music genres with Shannon entropy arguments, and discuss an alternative objective way to classify music, that is based on the complex structure of the groups audience. Finally, a link is drawn with the theory of hidden variables in complex networks.

physics.soc-ph↗

arXiv2005

Time-evolving distribution of time lags between commercial airline disasters

We have studied the time lags between commercial line airplane disasters and their occurrence frequency till 2002, as obtained from a freely available website. We show that the time lags seem to be well described by Poisson random events, where the average events rate is itself a function of time, i.e. time-dependent Poisson events. This is likely due to the unsteady growth of the industry. The time lag distribution is compared with a truncated Tsallis distribution, thereby showing that the ''phenomenon'' has similarities with a Brownian particle with time dependent mass. We distinguish between ''other causes'' (or natural causes) and ''terrorism acts", the latter amounts to about 5 percents, but we find no drastic difference nor impact due to the latter on the overall distribution.

physics.soc-ph↗

arXiv2005

Energy non-equipartition in multicomponent granular mixtures

We study non-equipartition of energy in granular fluids composed by an arbitrarily large number of components. We focus on a simple mean field model, based upon a Maxwell collision operator kernel, and predict the temperature ratios for the species. Moreover, we perform Direct Monte Carlo simulations in order to verify the predictions.

cond-mat.stat-mech↗

arXiv2005

From sand to networks: a study of multi-disciplinarity

In this paper, we study empirically co-authorship networks of neighbouring scientific disciplines, and describe the system by two coupled networks. By considering a large time window, we focus on the properties of the interface between the disciplines. We also focus on the time evolution of the co-authorship network, and highlight a rich phenomenology including first order transition and cluster bouncing and merging. Finally, we present a ferro- electric-like model (CDIM), involving bond redistribution between the nodes, that reproduces qualitatively the structuring of the system in homogeneous phases

physics.soc-ph↗