Heavy-tailed Patterns Research Articles

Sector, industry and inter-organizational movement statistics in the Stockholm Region: informing organizational growth models

Organizational growth processes exhibit interesting statistical regularities, chiefly the heavy-tailed pattern of the size and growth-rate (i.e. yearly change in size) distributions. In spite of its ubiquity, empirical studies of growth are often limited to private activities and specific sectors, and generative models on the other hand are built on simplified assumptions and only aim at reproducing stylized facts. In this study, we use a unique Swedish longitudinal database on employment in the Stockholm Region, to analyze the interplay between organizational growth statistics by ownership sector, industrial activity and inter-organizational employee movements during a period of 14 years. We fit distributions for organizational size and growth rates. We find that the body of the aggregate growth-rate distribution is dominated by public sector growth, while the private sector dominates the tails. Industries with mostly public organizations tend to have a lognormal size distribution, while privately-owned industries are better fitted by a truncated power law. Growth-rate distributions are fitted to an exponential power (Subbotin) distribution. We decompose the change in size into incoming and outgoing employee movements, and find that the distribution of aggregated movements is well approximated by a lognormal distribution. Most organizations that do not grow have however in- and outgoing movements, but these mostly cancel each other out.

Modeling Tree Diameter Distributions in Natural Forests: An Evaluation of 10 Statistical Models

In forestry, the description of tree sizes is commonly performed by fitting statistical models to diameter distributions. However, there is little agreement on which models are more flexible to this end, especially in tropical forests. Here we provide the simultaneous evaluation at species and subplot levels of 10 models using large data sets from four representative forest types in Brazil. We aimed to detect which models provide best fits and under which sample properties (size, median, variance, skewness, and kurtosis). We show that the combination of the logit-logistic, odd Weibull, Weibull, and Johnson’s special bounded models provided reasonable descriptions for nearly all species (94.8%) and subplots (99.6%). However, there was little overlap between these four models, meaning that single models were rarely appropriate to describe the majority of cases. This complementarity was evident between the odd Weibull (better performance for more symmetrical, bimodal, or rotated-sigmoid patterns) and logit-logistic models (typical right-skewed and heavy-tailed patterns). The performance of all models was significantly related to forest type or sample properties. Models with more than three parameters had more problems related to optimization convergence, confidence interval estimation, and unrealistic fits. Finally, we discuss some theoretical issues related to the choice of appropriate models.

Statistical analysis on the evolution of OpenStreetMap road networks in Beijing

In recent years, extensive efforts have been paid on the investigation of OpenStreetMap (OSM) in developed countries, but little attention has been given to the cities in developing countries. This paper presents the results regarding the evolution of OSM road networks in Beijing, China, from four aspects. First, findings from general analysis indicate that (1) the overall growth pattern could be mainly explained by the increasing number of volunteers and their mapping contributions. Second, findings from geometric analysis suggest: (2) mapping intensity exhibits heavy-tailed pattern both for a certain time period and across time; (3) mapping direction moves from outskirts to downtown distinguished from other regions; and (4) mapping behaviors are mainly constrained by the underlying structure of road networks. Third, results of topological analysis indicate that (5) OSM road networks resemble the growth of real road networks and are undergoing an evolution process depicted by exploration and densification. Last, from the perspective of centrality analysis, (6) two kinds of nodes are identified with the ones accounting for the exploration and the other ones for the densification, which further hints the evolution process of continuous strong exploration accompanied by weak densification.

Power-law distributions in binned empirical data

Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for correctly understanding and modeling complex systems. However, statistical evidence for or against the power-law hypothesis is complicated by large fluctuations in the empirical distribution’s tail, and these are worsened when information is lost from binning the data. We adapt the statistically principled framework for testing the power-law hypothesis, developed by Clauset, Shalizi and Newman, to the case of binned data. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov–Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. We evaluate the effectiveness of these methods on synthetic binned data with known structure, quantify the loss of statistical power due to binning, and apply the methods to twelve real-world binned data sets with heavy-tailed patterns.

A study of design approach of spreading schemes for viral marketing based on human dynamics

Before launching a real viral marketing campaign, it is needed to design a spreading scheme by simulations. Based on a categorization of spreading patterns in real world and models, we point out that the existing research (especially Yang et al. (2010) Ref. [16]) implicitly assume that if a user decides to post a received message (is activated), he/she will take the reposting action promptly (Prompt Action After Activation, or PAAA). After a careful analysis on a real dataset however, it is found that the observed time differences between action and activation exhibit a heavy-tailed distribution. A simulation model for heavy-tailed pattern is then proposed and performed. Similarities and differences of spreading processes between the heavy-tailed and PAAA patterns are analyzed. Consequently, a more practical design approach of spreading scheme for viral marketing on QQ platform is proposed. The design approach can be extended and applied to the contexts of non-heavy-tailed pattern, and viral marketing on other instant messaging platforms.

The impact of human activity patterns on asymptomatic infectious processes in complex networks

The study of the impact of human activity patterns on network dynamics has attracted a lot of attention in recent years. However, individuals’ knowledge of their own physical states has rarely been incorporated into modeling processes. In real life, for certain infectious processes, infected agents may not have any visible or physical signs and symptoms; therefore, they may believe that they are uninfected even when they have been infected asymptomatically. This infection awareness factor is covered neither in the classical epidemic models such as SIS nor in network propagation studies. In this article, we propose a novel infectious process model that differentiates between the infection awareness states and the physical states of individuals and extend the SIS model to deal with both asymptomatic infection characteristics and human activity patterns. With regards to the latter, we focus particularly on individuals’ testing action, which is to determine whether an individual is infected by an epidemic. The simulation results show that less effort is required in controlling the disease when the transmission probability is either very small or large enough and that Poisson activity patterns are more effective than heavy-tailed patterns in controlling and eliminating asymptomatic infectious diseases due to the long-tail characteristic.

Analysis of burstiness monitoring and detection in an adaptive Web system

Due to the heavy tailed pattern of Internet traffic, it is crucial to monitor the incoming arrival rate in a Web system to preserve its performance. In this study, we focus on the arrival rate processing mechanism as part of the design of an adaptive load balancing Web algorithm. The arrival rate is one of the most important metrics to be monitored in a Web site to avoid the possible congestion of Web servers. Six methods are analysed to detect the burstiness of incoming traffic in a Web system. We define six burstiness factors to be individually included in an adaptive load balancing algorithm, which also needs to monitor some Web servers' parameters continuously, such as the arrival rate at the server or its CPU utilization in order to avoid an unexpected overload situation. We also define adaptive time slot scheduling based on the burstiness factor, which reduces considerably the overhead of the monitoring process by increasing the monitoring frequency when bursty traffic arrives at the system and by decreasing the frequency when no bursts are detected in the arrival rate. Simulation results of the behaviour of the six burstiness factors and adaptive time slot scheduling when sudden changes are detected in the arrival rate are presented and discussed. We have considered a scenario made up of a locally distributed cluster-based Web information system for simulations.