Barabasi

S. Grauwin, M. Szell, S. Sobolevsky, P. Hovel, F. Simini, M. Vanhoof, Z. Smoreda, A.-L. Barabasi, C. Ratti

Identifying and modeling the structural discontinuities of human interactions

Scientific Reports 7: 46677 (2017)

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The idea of a hierarchical spatial organization of society lies at the core of seminal theories in human geography that have strongly influenced our understanding of social organization. Along the same line, the recent availability of large-scale human mobility and communication data has offered novel quantitative insights hinting at a strong geographical confinement of human interactions within neighboring regions, extending to local levels within countries. However, models of human interaction largely ignore this effect. Here, we analyze several country-wide networks of telephone calls - both, mobile and landline - and in either case uncover a systematic decrease of communication induced by borders which we identify as the missing variable in state-of-the-art models. Using this empirical evidence, we propose an alternative modeling framework that naturally stylizes the damping effect of borders. We show that this new notion substantially improves the predictive power of widely used interaction models. This increases our ability to understand, model and predict social activities and to plan the development of infrastructures across multiple scales.
Barabasi

Barabasi, A.-L.

Bordering Fiction

Science 343: 6169 (2014)

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Eggers portrays a world---in which an omnipotent social networking company encourages everyone to monitor everybody everywhere---that feels eerily everyday. Photo Credit: Courtesy of Knopf
Barabasi

R. Sinatra, D. Wang, P. Deville, C. Song, A.-L. Barabasi

Quantifying the Evolution of Individual Scientific Impact

Science 4: 354, 6312 (November 2016) - http://barabasilab.com/scienceofsuccess/

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Despite the frequent use of numerous quantitative indicators to gauge the professional impact of a scientist, little is known about how scientific impact emerges and evolves in time. Here, we quantify the changes in impact and productivity throughout a career in science, finding that impact, as measured by influential publications, is distributed randomly within a scientist’s sequence of publications. This random-impact rule allows us to formulate a stochastic model that uncouples the effects of productivity, individual ability, and luck and unveils the existence of universal patterns governing the emergence of scientific success. The model assigns a unique individual parameter Q to each scientist, which is stable during a career, and it accurately predicts the evolution of a scientist’s impact, from the h-index to cumulative citations, and independent recognitions, such as prizes.
Barabasi

P. Deville, C. Song, N. Eagle, V. D. Blondel, A.-L. Barabasi, D. Wang

Scaling Identity Connects Human Mobility and Social Interactions

PNAS 113: 26, 7047-7052 (2016)

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Both our mobility and communication patterns obey spatial constraints: Most of the time, our trips or communications occur over a short distance, and occasionally, we take longer trips or call a friend who lives far away. These spatial dependencies, best described as power laws, play a consequential role in broad areas ranging from how an epidemic spreads to diffusion of ideas and information. Here we established the first formal link, to our knowledge, between mobility and communication patterns by deriving a scaling relationship connecting them. The uncovered scaling theory not only allows us to derive human movements from communication volumes, or vice versa, but it also documents a new degree of regularity that helps deepen our quantitative understanding of human behavior. Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality.
Barabasi

B. Yucesoy, A.-L. Barabási

Untangling performance from success

EPJ Data Science 5:17 (2016)

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Fame, popularity and celebrity status, frequently used tokens of success, are often loosely related to, or even divorced from professional performance. This dichotomy is partly rooted in the difficulty to distinguish performance, an individual measure that captures the actions of a performer, from success, a collective measure that captures a community’s reactions to these actions. Yet, finding the relationship between the two measures is essential for all areas that aim to objectively reward excellence, from science to business. Here we quantify the relationship between performance and success by focusing on tennis, an individual sport where the two quantities can be independently measured. We show that a predictive model, relying only on a tennis player’s performance in tournaments, can accurately predict an athlete’s popularity, both during a player’s active years and after retirement. Hence the model establishes a direct link between performance and momentary popularity. The agreement between the performance-driven and observed popularity suggests that in most areas of human achievement exceptional visibility may be rooted in detectable performance measures.
Barabasi

L. Pappalardo, F. Simini, S. Rinzivillo, D. Pedreschi, F. Giannotti, A.-L. Barabási

Returners and explorers dichotomy in human mobility

Nature Communications 6:8166, 1-8 (2015)

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The availability of massive digital traces of human whereabouts has offered a series of novel insights on the quantitative patterns characterizing human mobility. In particular, numerous recent studies have lead to an unexpected consensus: the considerable variability in the characteristic travelled distance of individuals coexists with a high degree of predictability of their future locations. Here we shed light on this surprising coexistence by systematically investigating the impact of recurrent mobility on the characteristic distance travelled by individuals. Using both mobile phone and GPS data, we discover the existence of two distinct classes of individuals: returners and explorers. As existing models of human mobility cannot explain the existence of these two classes, we develop more realistic models able to capture the empirical findings. Finally, we show that returners and explorers play a distinct quantifiable role in spreading phenomena and that a correlation exists between their mobility patterns and social interactions.
Barabasi

B. Barzel, Y.-Y. Liu, A.-L. Barabási

Constructing minimal models for complex system dynamics

Nature Communications 6:7186, 1-8 (2015)

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One of the strengths of statistical physics is the ability to reduce macroscopic observations into microscopic models, offering a mechanistic description of a system’s dynamics. This paradigm, rooted in Boltzmann’s gas theory, has found applications from magnetic phenomena to subcellular processes and epidemic spreading. Yet, each of these advances were the result of decades of meticulous model building and validation, which are impossible to replicate in most complex biological, social or technological systems that lack accurate microscopic models. Here we develop a method to infer the microscopic dynamics of a complex system from observations of its response to external perturbations, allowing us to construct the most general class of nonlinear pairwise dynamics that are guaranteed to recover the observed behavior. The result, which we test against both numerical and empirical data, is an effective dynamic model that can predict the system’s behavior and provide crucial insights into its inner workings.
Barabasi

H.-W. Shen, A.-L. Barabasi

Collective credit allocation in science

Proceedings of the National Academy of Sciences 10.1073/pnas.1401992111, 1-6 (2014)

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Collaboration among researchers is an essential component of the modern scientific enterprise, playing a particularly important role in multidisciplinary research. However, we _continue to wrestle with allocating credit to the coauthors of publications with multiple authors, because the relative contribution of each author is difficult to determine. At the same time, the scientific community runs an informal field-dependent credit allocation process that assigns credit in a collective fashion to each work. Here we develop a credit allocation algorithm that captures the coauthors’ contribution to a publication as perceived by the scientific community, reproducing the informal collective credit allocation of science. We validate the method by identifying the authors of Nobel-winning papers that are credited for the discovery, independent of their positions in the author list. The method can also compare the relative impact of researchers working in the same field, even if they did not publish together. The ability to accurately measure the relative credit of researchers could affect many aspects of credit allocation in science, potentially impacting hiring, funding, and promotion decisions.
Barabasi

H. Shen, D. Wang, C. Song, A.-L. Barabási

Modeling and predicting popularity dynamics via reinforced poisson processes

Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence , 291-297 (2014)

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An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforced Poisson process to explicitly model the process through which individual items gain their popularity. This model distinguishes itself from existing models via its capability of modeling the arrival process of popularity and its remarkable power at predicting the popularity of individual items. It possesses the flexibility of applying Bayesian treatment to further improve the predictive power using a conjugate prior. Extensive experiments on a longitudinal citation dataset demonstrate that this model consistently outperforms existing popularity prediction methods.
Barabasi

S. Gil, A. Kott, A.-L. Barabási

A genetic epidemiology approach to cyber-security

Scientific Reports 4:5659, 1-7 (2014)

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While much attention has been paid to the vulnerability of computer networks to node and link failure, there is limited systematic understanding of the factors that determine the likelihood that a node (computer) is compromised. We therefore collect threat log data in a university network to study the patterns of threat activity for individual hosts. We relate this information to the properties of each host as observed through network-wide scans, establishing associations between the network services a host is running and the kinds of threats to which it is susceptible. We propose a methodology to associate services to threats inspired by the tools used in genetics to identify statistical associations between mutations and diseases. The proposed approach allows us to determine probabilities of infection directly from observation, offering an automated high-throughput strategy to develop comprehensive metrics for cyber-security.
Barabasi

P. Deville, D. Wang, R. Sinatra, C. Song, V. Blondel, A.-L. Barabási

Career on the move: Geography, stratification, and scientific impact

Scientific Reports 4, 1-7 (2014)

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Changing institutions is an integral part of an academic life. Yet little is known about the mobility patterns of scientists at an institutional level and how these career choices affect scientific outcomes. Here, we examine over 420,000 papers, to track the affiliation information of individual scientists, allowing us to reconstruct their career trajectories over decades. We find that career movements are not only temporally and spatially localized, but also characterized by a high degree of stratification in institutional ranking. When cross-group movement occurs, we find that while going from elite to lower-rank institutions on average associates with modest decrease in scientific performance, transitioning into elite institutions does not result in subsequent performance gain. These results offer empirical evidence on institutional level career choices and movements and have potential implications for science policy.
Barabasi

L. Gao, C. Song, Z. Gao, A.-L. Barabasi, J. P. Bagrow, D. Wang

Quantifying information flow during emergencies

Scientific Reports 4, 1-6 (2014)

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Recent advances on human dynamics have focused on the normal patterns of human activities, with the quantitative understanding of human behavior under extreme events remaining a crucial missing chapter. This has a wide array of potential applications, ranging from emergency response and detection to traffic control and management. Previous studies have shown that human communications are both temporally and spatially localized following the onset of emergencies, indicating that social propagation is a primary means to propagate situational awareness. We study real anomalous events using country-wide mobile phone data, finding that information flow during emergencies is dominated by repeated communications. We further demonstrate that the observed communication patterns cannot be explained by inherent reciprocity in social networks, and are universal across different demographics.
Barabasi

D. Wang, C. Song, A.-L. Barabási

Quantifying Long-Term Scientific Impact

Science 342, 127-131 (2013)

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The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a mechanistic model for the citation dynamics of individual papers, allowing us to collapse the citation histories of papers from different journals and disciplines into a single curve, indicating that all papers tend to follow the same universal temporal pattern. The observed patterns not only help us uncover basic mechanisms that govern scientific impact but also offer reliable measures of influence that may have potential policy implications.
Barabasi

N. Blumm, G. Ghoshal, Z. Forro, M. Schich, G. Bianconi, J.-P. Bouchard, A.-L. Barabasi

Dynamics of ranking processes in complex systems

Physical Review Letters 109, 128701:1-5 (2012)

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The world is addicted to ranking: everything, from the reputation of scientists, journals, and universities to purchasing decisions is driven by measured or perceived differences between them. Here, we analyze empirical data capturing real time ranking in a number of systems, helping to identify the universal characteristics of ranking dynamics. We develop a continuum theory that not only predicts the stability of the ranking process, but shows that a noise-induced phase transition is at the heart of the observed differences in ranking regimes. The key parameters of the continuum theory can be explicitly measured from data, allowing us to predict and experimentally document the existence of three phases that govern ranking stability.
Barabasi

Albert-László Barabási

Network science: Luck or reason

Nature 489, 1-2 (2012)

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The concept of preferential attachment is behind the hubs and power laws seen in many networks. New results fuel an old debate about its origin, and beg the question of whether it is based on randomness or optimization.
Barabasi

V. Palchykov, K. Kaski, J. Kertesz, A.-L. Barabási, R. Dunbar

Sex differences in intimate relationships

Scientific Reports 2:370, 105 (2012)

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Social networks based on dyadic relationships are fundamentally important for understanding of human sociality. However, we have little understanding of the dynamics of close relationships and how these change over time. Evolutionary theory suggests that, even in monogamous mating systems, the pattern of investment in close relationships should vary across the lifespan when post-weaning investment plays an important role in maximizing fitness. Mobile phone data sets provide a unique window into the structure and dynamics of relationships. We here use data from a large mobile phone dataset to demonstrate striking sex differences in the gender-bias of preferred relationships that reflect the way the reproductive investment strategies of both sexes change across the lifespan, i.e. women’s shifting patterns of investment in reproduction and parental care. These results suggest that human social strategies may have more complex dynamics than previously assumed and a life-history perspective is crucial for understanding them.
Barabasi

F. Simini, M. González, A. Maritan, A.-L. Barabási

A universal model for mobility and migration patterns

Nature 484, 96-100 (2012)

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Introduced in its contemporary form in 1946, but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes.
Barabasi

Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási

Few inputs can reprogram biological networks (reply by Liu et al.)

Nature 473, 167-173 (2011)

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Reply to Franz-Josef Muller and Andreas Schuppert (Nature 478, Pg. E4, Oct. 2011)
Barabasi

Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási

Controllability of complex networks

Nature 473, 167-173 (2011)

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The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.
Barabasi

J. P. Bagrow, D. Wang, A.-L. Barabasi

Collective response of human populations to large-scale emergencies

PLoS One 6:3, 1-8 (2011)

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Despite recent advances in uncovering the quantitative features of stationary human activity patterns, many applications,from pandemic prediction to emergency response, require an understanding of how these patterns change when thepopulation encounters unfamiliar conditions. To explore societal response to external perturbations we identified real-timechanges in communication and mobility patterns in the vicinity of eight emergencies, such as bomb attacks andearthquakes, comparing these with eight non-emergencies, like concerts and sporting events. We find that communicationspikes accompanying emergencies are both spatially and temporally localized, but information about emergencies spreadsglobally, resulting in communication avalanches that engage in a significant manner the social network of eyewitnesses.These results offer a quantitative view of behavioral changes in human activity under extreme conditions, with potentiallong-term impact on emergency detection and response.
Barabasi

C. Song, T. Koren, P. Wang, A.-L. Barabási

Modelling the scaling properties of human mobility

Nature Physics 7, 713- (2010)

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Individual human trajectories are characterized by fat-tailed distributions of jump sizes and waiting times, suggesting the relevance of continuous-time random-walk (CTRW) models for human mobility. However, human traces are barely random. Given the importance of human mobility, from epidemic modelling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile-phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model accounts for the empirically observed scaling laws, but also allows us to analytically predict most of the pertinent scaling exponents.
Barabasi

C. Song, Z. Qu, N. Blumm, A.-L. Barabási

Limits of Predictability in Human Mobility

Science 327, 1018-1021 (2010)

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A range of applications, from predicting the spread of human and electronic viruses to city planning and resource management in mobile communications, depend on our ability to foresee the whereabouts and mobility of individuals, raising a fundamental question: To what degree is human behavior predictable? Here we explore the limits of predictability in human dynamics by studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of each individual’s trajectory, we find a 93% potential predictability in user mobility across the whole user base. Despite the significant differences in the travel patterns, we find a remarkable lack of variability in predictability, which is largely independent of the distance users cover on a regular basis.
Barabasi

D. A. Davis, N. V. Chawla, N. A. Christakis, A.-L. Barabasi

Time to CARE: a collaborative engine for practical disease prediction

Data Mining and Knowledge Discovery 30:3, 388-41 (2009)

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The monumental cost of health care, especially for chronic disease treatment, is quickly becoming unmanageable. This crisis has motivated the drive towards preventative medicine, where the primary concern is recognizing disease risk and taking action at the earliest signs. However, universal testing is neither time nor cost efficient. We propose CARE, a Collaborative Assessment and Recommendation Engine, which relies only on patient’s medical history using ICD-9-CM codes in order to predict future disease risks. CARE uses collaborative filtering methods to predict each patient’s greatest disease risks based on their own medical history and that of similar patients. We also describe an Iterative version, ICARE, which incorporates ensemble concepts for improved performance. Also, we apply time-sensitive modifications which make the CARE framework practical for realistic long-term use. These novel systems require no specialized information and provide predictions for medical conditions of all kinds in a single run. We present experimental results on a larg Medicare dataset, demonstrating that CARE and ICARE perform well at capturing future disease risks.
Barabasi

P. Wang, M. Gonzalez, C. A. Hidalgo, A.-L. Barabási

Understanding the spreading patterns of mobile phone viruses

Science 324, 1071-1076 (2009)

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We modeled the mobility of mobile phone users in order to study the fundamental spreading patterns that characterize a mobile virus outbreak. We find that although Bluetooth viruses can reach all susceptible handsets with time, they spread slowly because of human mobility, offering ample opportunities to deploy antiviral software. In contrast, viruses using multimedia messaging services could infect all users in hours, but currently a phase transition on the underlying call graph limits them to only a small fraction of the susceptible users. These results explain the lack of a major mobile virus breakout so far and predict that once a mobile operating system’s market share reaches the phase transition point, viruses will pose a serious threat to mobile communications.
Barabasi

D. Lazer, A. Pentland, L. Adamic, S. Aral, A.-L. Barabási, D. Brewer, N. Christakis, N. Contractor, J. Fowler, M. Gutmann, T. Jebara, G. King, M. Macy, D. Roy, M. Van Alstyne

Computation Social Science

Science 323, 721-724 (2009)

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We live life in the network. We check our e-mails regularly, make mobile phone calls from almost any location, swipe transit cards to use public transportation, and make purchases with credit cards. Our movements in public places may be captured by video cameras, and our medical records stored as digital files. We may post blog entries accessible to anyone, or maintain friendships through online social networks. Each of these transactions leaves digital traces that can be compiled into comprehensive pictures of both individual and group behavior, with the potential to transform our understanding of ourlives, organizations, and societies.
Barabasi

M. C. González, C. A. Hidalgo, A.-L. Barabási

Understanding individual human mobility patterns

Nature 453, 779-782 (2008)

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Despite their importance for urban planning, traffic forecasting and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modeling.
Barabasi

J. Candia, M. C. Gonzalez, P. Wang, T. Schoenharl, G. Madey, A.-L. Barabási

Uncovering individual and collective human dynamics from mobile phone records

Journal of Physics A: Mathematical and Theoretical 41, 1-11 (2008)

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Novel aspects of human dynamics and social interactions are investigated by means of mobile phone data. Using extensive phone records resolved in both time and space, we study the mean collective behavior at large scales and focus on the occurrence of anomalous events. We discuss how these spatiotemporal anomalies can be described using standard percolation theory tools. We also investigate patterns of calling activity at the individual level and show that the interevent time of consecutive calls is heavy-tailed. This finding, which has implications for dynamics of spreading phenomena in social networks, agrees with results previously reported on other human activities.
Barabasi

K.-L. Goh, A.-L. Barabási

Burstiness and memory in complex systems

Europhysics Letters 81, 48002 (2008)

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The dynamics of a wide range of real systems, from email patterns to earthquakes,display a bursty, intermittent nature, characterized by short timeframes of intense activity followed by long times of no or reduced activity. The understanding of the origin of such bursty patterns is hindered by the lack of tools to compare different systems using a common framework. Here we propose to characterize the bursty nature of real signals using orthogonal measures quantifying two distinct mechanisms leading to burstiness: the interevent time distribution and the memory. We find that while the burstiness of natural phenomena is rooted in both the interevent time distribution and memory, for human dynamics memory is weak, and the bursty character is due to the changes in the interevent time distribution. Finally, we show that current models lack in their ability to reproduce the activity pattern observed in real systems, opening up avenues for future work.
Barabasi

A.-L. Barabási

The architecture of complexity

IEEE Control Systems Magazine 27:4, 33-42 (2007)

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We are surrounded by complex systems, from cells made of thousands of molecules to society, a collection of billions of interacting individuals. These systems display signatures of order and self-organization. Understanding and quantifying this complexity is a grand challenge for science. Kinetic theory, developed at the end of the 19th century, shows that the measurable properties of gases, from pressure to temperature, can be reduced to the random motion of atoms and molecules. In the 1960s and 1970s, researchers developed systematic approaches to quantifying the transition from disorder to order in material systems such as magnets and liquids. Chaos theory dominated the quest to understand complex behavior in the 1980s with the message that unpredictable behavior can emerge from the nonlinear interactions of a few components. The 1990s was the decade of fractals, quantifying the geometry of patterns emerging in self-organized systems, from leaves to snowflakes.
Barabasi

J.-P. Onnela, J. Saramäki, J. Hyvönen, G. Szabó, M A. de Menezes, K. Kaski, A.-L. Barabási, J. Kertész

Analysis of a large-scale weighted network of one-to-one human communication

New Journal of Physics 9, 1-27 (2007)

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We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities.We give an account of motif intensity and coherence distributions and compare them to a randomized reference system.We also use the concept of link overlap to measure the number of common neighbours any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing strong quantitative evidence for the weak ties hypothesis, a central concept in social network analysis. The percolation properties of the network are found to depend on the type and order of removed links, and they can help understand how the local structure of the network manifests itself at the global level.We hope that our results will contribute to modelling weighted large-scale social networks, and believe that the systematic approach followed here can be adopted to study other weighted networks.
Barabasi

A. Vazquez, B. Rácz, A. Lukács, A.-L. Barabási

Impact of non-Poissonian activity patterns on spreading processes

Physical Review Letters 98:15, 158702 (2007)

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Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicates that the intercontact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer viruses, which, according to virus bulletins, show a decay time close to a year, in contrast with the 1 day decay predicted by the standard Poisson process based models.
Barabasi

G. Palla, A.-L. Barabási, T. Vicsek

Quantifying social group evolution

Nature 446:7136, 664-667 (2007)

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Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist for longer if they are capable of dynamically altering their membership, suggesting that an ability to change the group composition results in better adaptability. The behaviour of small groups displays the opposite tendency—the condition for stability is that their composition remains unchanged. We also show that knowledge of the time commitment of members to a given community can be used for estimating the community’s lifetime. These findings offer insight into the fundamental differences between the dynamics of small groups and large institutions.
Barabasi

M. C. Gonzalez, A.-L. Barabási

Complex networks - From data to models

Nature Physics 3, 224-225 (2007)

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Data on the movement of people becomes ever more detailed, but robust models explaining the observed patterns are still needed. Mapping the problem onto a 'network of networks' could be a promising approach.
Barabasi

Z. Dezso, E. Almaas, A. Lukacs, B. Racz, I. Szakadat, A.-L. Barabási

Dynamics of information access on the web

Physical Review E 73, 066132 (2006)

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While current studies on complex networks focus on systems that change relatively slowly in time, the structure of the most visited regions of the web is altered at the time scale from hours to days. Here we investigate the dynamics of visitation of a major news portal, representing the prototype for such a rapidly evolving network. The nodes of the network can be classified into stable nodes, which form the timeindependent skeleton of the portal, and news documents. The visitations of the two node classes are markedly different, the skeleton acquiring visits at a constant rate, while a news document’s visitation peaks after a few hours. We find that the visitation pattern of a news document decays as a power law, in contrast with the exponential prediction provided by simple models of site visitation. This is rooted in the inhomogeneous nature of the browsing pattern characterizing individual users: the time interval between consecutive visits by the same user to the site follows a power-law distribution, in contrast to the exponential expected for Poisson processes. We show that the exponent characterizing the individual user’s browsing patterns determines the power-law decay in a document’s visitation. Finally, our results document the fleeting quality of news and events: while fifteen minutes of fame is still an exaggeration in the online media, we find that access to most news items significantly decays after 36 hours of posting.
Barabasi

A. Vazquez, J.G. Oliveira, Z. Dezso, K.I. Goh, I. Kondor, A.-L. Barabási

Modeling bursts and heavy tails in human dynamics

Physical Review E 73, 036127 (2006)

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The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution Pww− with =3/2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by =1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display =1, the surface mail based communication belongs to the =3/2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.
Barabasi

J. G. Oliveira, A.-L. Barabási

Darwin and Einstein correspondence patterns

Nature 437, 1251 (2005)

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These scientists prioritized their replies to letters in the same way that people rate their e-mails today.
Barabasi

A.-L. Barabási

The origin of bursts and heavy tails in humans dynamics

Nature 435, 207 (2005)

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Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.