@article{vazquez2006modeling,
  abstract = { 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 P(τw)∼τw−α with α=3∕2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by α=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 α=1, the surface mail based communication belongs to the α=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.},
  author = {Vázquez, Alexei and Gama Oliveira, João and Dezsö, Zoltán and Goh, Kwang-Il and Kondor, Imre and Barabási, Albert-László},
  doi = {10.1103/PhysRevE.73.036127},
  interhash = {679487e36d59d3d8262632b9a05f9f45},
  intrahash = {f15dafcb20d0c9857acf1324c5c2279c},
  journal = {Physical Review E},
  month = mar,
  number = 3,
  numpages = {19},
  pages = 036127,
  publisher = {American Physical Society},
  title = {Modeling bursts and heavy tails in human dynamics},
  url = {http://link.aps.org/doi/10.1103/PhysRevE.73.036127},
  volume = 73,
  year = 2006
}

@misc{Vazquez2008,
  abstract = {  Data clustering, including problems such as finding network communities, can
be put into a systematic framework by means of a Bayesian approach. The
application of Bayesian approaches to real problems can be, however, quite
challenging. In most cases the solution is explored via Monte Carlo sampling or
variational methods. Here we work further on the application of variational
methods to clustering problems. We introduce generative models based on a
hidden group structure and prior distributions. We extend previous attends by
Jaynes, and derive the prior distributions based on symmetry arguments. As a
case study we address the problems of two-sides clustering real value data and
clustering data represented by a hypergraph or bipartite graph. From the
variational calculations, and depending on the starting statistical model for
the data, we derive a variational Bayes algorithm, a generalized version of the
expectation maximization algorithm with a built in penalization for model
complexity or bias. We demonstrate the good performance of the variational
Bayes algorithm using test examples.
},
  author = {Vazquez, Alexei},
  interhash = {ee1f9455db7046612d0baf0360e0f428},
  intrahash = {887ae82953a03602e0a135d303950b80},
  note = {cite arxiv:0805.2689
Comment: 12 pages, 5 figures. New sections added},
  title = {Bayesian approach to clustering real value, categorical and network
  data: solution via variational methods},
  url = {http://arxiv.org/abs/0805.2689},
  year = 2008
}