arXiv subjects

Renaud Lambiotte

Publications and source records attributed to Renaud Lambiotte.

At least 127 records · Page 7Linked to original sources

arXiv2016

Input-output relationship in social communications characterized by spike train analysis

We study the dynamical properties of human communication through different channels, i.e., short messages, phone calls, and emails, adopting techniques from neuronal spike train analysis in order to characterize the temporal fluctuations of successive inter-event times. We first measure the so-called local variation (LV) of incoming and outgoing event sequences of users, and find that these in- and out- LV values are positively correlated for short messages, and uncorrelated for phone calls and emails. Second, we analyze the response-time distribution after receiving a message to focus on the input-output relationship in each of these channels. We find that the time scales and amplitudes of response are different between the three channels. To understand the impacts of the response-time distribution on the correlations between the LV values, we develop a point process model whose activity rate is modulated by incoming and outgoing events. Numerical simulations of the model indicate that a quick response to incoming events and a refractory effect after outgoing events are key factors to reproduce the positive LV correlations.

physics.soc-ph↗

arXiv2016

Graph partitions and cluster synchronization in networks of oscillators

Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators.

physics.soc-ph↗

arXiv2016

Stationarity of the inter-event power-law distributions

A number of human activities exhibit a bursty pattern, namely periods of very high activity that are followed by rest periods. Records of these processes generate time series of events whose inter-event times follow a probability distribution that displays a fat tail. The grounds for such phenomenon are not yet clearly understood. In the present work we use the freely available Wikipedia editing records to unravel some features of this phenomenon. We show that even though the probability to start editing is conditioned by the circadian 24 hour cycle, the conditional probability for the time interval between successive edits at a given time of the day is independent from the latter. We confirm our findings with the activity of posting on the social network Twitter. Our result suggests there is an intrinsic humankind scheduling pattern: after overcoming the encumbrance to start an activity, there is a robust distribution of new related actions, which does not depend on the time of day.

physics.soc-ph↗

arXiv2016

Imperfect spreading on temporal networks

We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where transmission is successful with a determined probability at each contact. We first derive an expression for the inter-success time distribution, determining the speed of the propagation, and then focus on a problem related to epidemic spreading, by estimating the epidemic threshold in a system where nodes remain infectious during a finite, random period of time. Finally, we discuss the implications of our work to design an efficient strategy to enhance spreading on temporal networks.

physics.soc-ph↗

arXiv2016

TiDeH: Time-Dependent Hawkes Process for Predicting Retweet Dynamics

Online social networking services allow their users to post content in the form of text, images or videos. The main mechanism driving content diffusion is the possibility for users to re-share the content posted by their social connections, which may then cascade across the system. A fundamental problem when studying information cascades is the possibility to develop sound mathematical models, whose parameters can be calibrated on empirical data, in order to predict the future course of a cascade after a window of observation. In this paper, we focus on Twitter and, in particular, on the temporal patterns of retweet activity for an original tweet. We model the system by Time-Dependent Hawkes process (TiDeH), which properly takes into account the circadian nature of the users and the aging of information. The input of the prediction model are observed retweet times and structural information about the underlying social network. We develop a procedure for parameter optimization and for predicting the future profiles of retweet activity at different time resolutions. We validate our methodology on a large corpus of Twitter data and demonstrate its systematic improvement over existing approaches in all the time regimes.

cs.SI↗

arXiv2016

The classical origin of modern mathematics

The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database includes a large number (N~200K) of advisor-student relationships, with affiliations and keywords on their research topic, over several centuries, from the 14th century until today. We focus on two different topics, the evolving importance of countries and of the research disciplines over time. Moreover we study the database at three levels, its global statistics, the mesoscale networks connecting countries and disciplines, and the genealogical level.

math.HO↗

arXiv2016

Burstiness and fractional diffusion on complex networks

Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on distributions whose average inter-event time diverges, and study its impact on the dynamics of random walkers on networks. The process can naturally be described, in the long time limit, in terms of Riemann-Liouville fractional derivatives. We show that all the dynamical modes possess, in the asymptotic regime, the same power law relaxation, which implies that the dynamics does not exhibit time-scale separation between modes, and that no mode can be neglected versus another one, even for long times. Our results are then confirmed by numerical simulations.

physics.soc-ph↗

arXiv2016

On the origin of burstiness in human behavior: The wikipedia edits case

A number of human activities exhibit a bursty pattern, namely periods of very high activity that are followed by rest periods. Records of this process generate time series of events whose inter-event times follow a probability distribution that displays a fat tail. The grounds for such phenomenon are not yet clearly understood. In the present work we use the freely available Wikipedia's editing records to tackle this question by measuring the level of burstiness, as well as the memory effect of the editing tasks performed by different editors in different pages. Our main finding is that, even though the editing activity is conditioned by the circadian 24 hour cycle, the conditional probability of an activity of a given duration at a given time of the day is independent from the latter. This suggests that the human activity seems to be related to the high "cost" of starting an action as opposed to the much lower "cost" of continuing that action.

physics.soc-ph↗

arXiv2015

Predicting links in ego-networks using temporal information

Link prediction appears as a central problem of network science, as it calls for unfolding the mechanisms that govern the micro-dynamics of the network. In this work, we are interested in ego-networks, that is the mere information of interactions of a node to its neighbors, in the context of social relationships. As the structural information is very poor, we rely on another source of information to predict links among egos' neighbors: the timing of interactions. We define several features to capture different kinds of temporal information and apply machine learning methods to combine these various features and improve the quality of the prediction. We demonstrate the efficiency of this temporal approach on a cellphone interaction dataset, pointing out features which prove themselves to perform well in this context, in particular the temporal profile of interactions and elapsed time between contacts.

cs.SI↗

arXiv2015

Temporal Pattern of Online Communication Spike Trains in Spreading a Scientific Rumor: How Often, Who Interacts with Whom?

We study complex time series (spike trains) of online user communication while spreading messages about the discovery of the Higgs boson in Twitter. We focus on online social interactions among users such as retweet, mention, and reply, and construct different types of active (performing an action) and passive (receiving an action) spike trains for each user. The spike trains are analyzed by means of local variation, to quantify the temporal behavior of active and passive users, as a function of their activity and popularity. We show that the active spike trains are bursty, independently of their activation frequency. For passive spike trains, in contrast, the local variation of popular users presents uncorrelated (Poisson random) dynamics. We further characterize the correlations of the local variation in different interactions. We obtain high values of correlation, and thus consistent temporal behavior, between retweets and mentions, but only for popular users, indicating that creating online attention suggests an alignment in the dynamics of the two interactions.

cs.SI↗

arXiv2015

Mining Open Datasets for Transparency in Taxi Transport in Metropolitan Environments

Uber has recently been introducing novel practices in urban taxi transport. Journey prices can change dynamically in almost real time and also vary geographically from one area to another in a city, a strategy known as surge pricing. In this paper, we explore the power of the new generation of open datasets towards understanding the impact of the new disruption technologies that emerge in the area of public transport. With our primary goal being a more transparent economic landscape for urban commuters, we provide a direct price comparison between Uber and the Yellow Cab company in New York. We discover that Uber, despite its lower standard pricing rates, effectively charges higher fares on average, especially during short in length, but frequent in occurrence, taxi journeys. Building on this insight, we develop a smartphone application, OpenStreetCab, that offers a personalized consultation to mobile users on which taxi provider is cheaper for their journey. Almost five months after its launch, the app has attracted more than three thousand users in a single city. Their journey queries have provided additional insights on the potential savings similar technologies can have for urban commuters, with a highlight being that on average, a user in New York saves 6 U.S. Dollars per taxi journey if they pick the cheapest taxi provider. We run extensive experiments to show how Uber's surge pricing is the driving factor of higher journey prices and therefore higher potential savings for our application's users. Finally, motivated by the observation that Uber's surge pricing is occurring more frequently that intuitively expected, we formulate a prediction task where the aim becomes to predict a geographic area's tendency to surge. Using exogenous to Uber datasets we show how it is possible to estimate customer demand within an area, and by extension surge pricing, with high accuracy.

cs.CY↗

arXiv2015

Diffusion on networked systems is a question of time or structure

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalised formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism --- network structure, burstiness or fat-tails of waiting times --- determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal-structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities.

physics.soc-ph↗

arXiv2015

Sufficient conditions of endemic threshold on metapopulation networks

In this paper, we focus on susceptible-infected-susceptible dynamics on metapopulation networks, where nodes represent subpopulations, and where agents diffuse and interact. Recent studies suggest that heterogeneous network structure between elements plays an important role in determining the threshold of infection rate at the onset of epidemics, a fundamental quantity governing the epidemic dynamics. We consider the general case in which the infection rate at each node depends on its population size, as shown in recent empirical observations. We first prove that a sufficient condition for the endemic threshold (i.e., its upper bound), previously derived based on a mean-field approximation of network structure, also holds true for arbitrary networks. We also derive an improved condition showing that networks with the rich-club property (i.e., high connectivity between nodes with a large number of links) are more prone to disease spreading. The dependency of infection rate on population size introduces a considerable difference between this upper bound and estimates based on mean-field approximations, even when degree-degree correlations are considered. We verify the theoretical results with numerical simulations.

physics.soc-ph↗

arXiv2015

The non-linear health consequences of living in larger cities

Urbanization promotes economy, mobility, access and availability of resources, but on the other hand, generates higher levels of pollution, violence, crime, and mental distress. The health consequences of the agglomeration of people living close together are not fully understood. Particularly, it remains unclear how variations in the population size across cities impact the health of the population. We analyze the deviations from linearity of the scaling of several health-related quantities, such as the incidence and mortality of diseases, external causes of death, wellbeing, and health-care availability, in respect to the population size of cities in Brazil, Sweden and the USA. We find that deaths by non-communicable diseases tend to be relatively less common in larger cities, whereas the per-capita incidence of infectious diseases is relatively larger for increasing population size. Healthier life style and availability of medical support are disproportionally higher in larger cities. The results are connected with the optimization of human and physical resources, and with the non-linear effects of social networks in larger populations. An urban advantage in terms of health is not evident and using rates as indicators to compare cities with different population sizes may be insufficient.

physics.soc-ph↗

arXiv2015

Local variation of hashtag spike trains and popularity in Twitter

We draw a parallel between hashtag time series and neuron spike trains. In each case, the process presents complex dynamic patterns including temporal correlations, burstiness, and all other types of nonstationarity. We propose the adoption of the so-called local variation in order to uncover salient dynamics, while properly detrending for the time-dependent features of a signal. The methodology is tested on both real and randomized hashtag spike trains, and identifies that popular hashtags present regular and so less bursty behavior, suggesting its potential use for predicting online popularity in social media.

cs.SI↗

arXiv2015

Local Variation of Collective Attention in Hashtag Spike Trains

In this paper, we propose a methodology quantifying temporal patterns of nonlinear hashtag time series. Our approach is based on an analogy between neuron spikes and hashtag diffusion. We adopt the local variation, originally developed to analyze local time delays in neuron spike trains. We show that the local variation successfully characterizes nonlinear features of hashtag spike trains such as burstiness and regularity. We apply this understanding in an extreme social event and are able to observe temporal evaluation of online collective attention of Twitter users to that event.

cs.SI↗

arXiv2015

Respondent-driven sampling bias induced by clustering and community structure in social networks

Sampling hidden populations is particularly challenging using standard sampling methods mainly because of the lack of a sampling frame. Respondent-driven sampling (RDS) is an alternative methodology that exploits the social contacts between peers to reach and weight individuals in these hard-to-reach populations. It is a snowball sampling procedure where the weight of the respondents is adjusted for the likelihood of being sampled due to differences in the number of contacts. In RDS, the structure of the social contacts thus defines the sampling process and affects its coverage, for instance by constraining the sampling within a sub-region of the network. In this paper we study the bias induced by network structures such as social triangles, community structure, and heterogeneities in the number of contacts, in the recruitment trees and in the RDS estimator. We simulate different scenarios of network structures and response-rates to study the potential biases one may expect in real settings. We find that the prevalence of the estimated variable is associated with the size of the network community to which the individual belongs. Furthermore, we observe that low-degree nodes may be under-sampled in certain situations if the sample and the network are of similar size. Finally, we also show that low response-rates lead to reasonably accurate average estimates of the prevalence but generate relatively large biases.

stat.AP↗

arXiv2015

Topological Properties and Temporal Dynamics of Place Networks in Urban Environments

Understanding the spatial networks formed by the trajectories of mobile users can be beneficial to applications ranging from epidemiology to local search. Despite the potential for impact in a number of fields, several aspects of human mobility networks remain largely unexplored due to the lack of large-scale data at a fine spatiotemporal resolution. Using a longitudinal dataset from the location-based service Foursquare, we perform an empirical analysis of the topological properties of place networks and note their resemblance to online social networks in terms of heavy-tailed degree distributions, triadic closure mechanisms and the small world property. Unlike social networks however, place networks present a mixture of connectivity trends in terms of assortativity that are surprisingly similar to those of the web graph. We take advantage of additional semantic information to interpret how nodes that take on functional roles such as `travel hub', or `food spot' behave in these networks. Finally, motivated by the large volume of new links appearing in place networks over time, we formulate the classic link prediction problem in this new domain. We propose a novel variant of gravity models that brings together three essential elements of inter-place connectivity in urban environments: network-level interactions, human mobility dynamics, and geographic distance. We evaluate this model and find it outperforms a number of baseline predictors and supervised learning algorithms on a task of predicting new links in a sample of one hundred popular cities.

cs.SI↗