Poissonian bursts in e-mail correspondence

Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend the analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data depart from the known correlations of Poissonian statistics. The analysis shows that the higher-order statistics from the empirical data is indistinguishable from that of randomly reordered time series, thus demonstrating that e-mail correspondence is no more bursty or correlated than a Poisson process. Furthermore synthetic data sets generated by a cascading Poisson process replicate the burstiness and correlations observed in the empirical data. Finally, a simple rescaling analysis using the best-estimate rate of activity, confirms that the empirically observed correlations arise from a non-homogeneus Poisson process

Weblog patterns and human dynamics with decreasing interest

Weblog is the fourth way of network exchange after Email, BBS and MSN. Most bloggers begin to write blogs with great interest, and then their interests gradually achieve a balance with the passage of time. In order to describe the phenomenon that people's interest in something gradually decreases until it reaches a balance, we first propose the model that describes the attenuation of interest and reflects the fact that people's interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, that is, it is a power law with an exponential cutoff. Second, we collect blogs in ScienceNet.cn and carry on empirical studies on the interarrival time distribution. The empirical results agree well with the analytical result, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model, providing an evidence for a new class of phenomena in human dynamics. In human dynamics there are other distributions, besides power-law distributions. These findings demonstrate the variety of human behavior dynamics.Comment: 8 pages, 1 figure

Differential loss of effector genes in three recently expanded pandemic clonal lineages of the rice blast fungus

BACKGROUND: Understanding the mechanisms and timescales of plant pathogen outbreaks requires a detailed genome-scale analysis of their population history. The fungus Magnaporthe (Syn. Pyricularia) oryzae-the causal agent of blast disease of cereals- is among the most destructive plant pathogens to world agriculture and a major threat to the production of rice, wheat, and other cereals. Although M. oryzae is a multihost pathogen that infects more than 50 species of cereals and grasses, all rice-infecting isolates belong to a single genetically defined lineage. Here, we combined the two largest genomic datasets to reconstruct the genetic history of the rice-infecting lineage of M. oryzae based on 131 isolates from 21 countries. RESULTS: The global population of the rice blast fungus consists mainly of three well-defined genetic groups and a diverse set of individuals. Multiple population genetic tests revealed that the rice-infecting lineage of the blast fungus probably originated from a recombining diverse group in Southeast Asia followed by three independent clonal expansions that took place over the last ~ 200 years. Patterns of allele sharing identified a subpopulation from the recombining diverse group that introgressed with one of the clonal lineages before its global expansion. Remarkably, the four genetic lineages of the rice blast fungus vary in the number and patterns of presence and absence of candidate effector genes. These genes encode secreted proteins that modulate plant defense and allow pathogen colonization. In particular, clonal lineages carry a reduced repertoire of effector genes compared with the diverse group, and specific combinations of presence and absence of effector genes define each of the pandemic clonal lineages. CONCLUSIONS: Our analyses reconstruct the genetic history of the rice-infecting lineage of M. oryzae revealing three clonal lineages associated with rice blast pandemics. Each of these lineages displays a specific pattern of presence and absence of effector genes that may have shaped their adaptation to the rice host and their evolutionary history

Timing interactions in social simulations: The voter model

The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.Comment: Book Chapter, 23 pages, 9 figures, 5 table

Statistical mixing and aggregation in Feller diffusion

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.Comment: 16 pages, 3 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen