Fluctuation scaling in complex systems: Taylor's law and beyond

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form "$fluctuations \approx const.\times average^\alpha$", where the exponent $\alpha$ is predominantly in the range $[1/2, 1]$. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names \emph{Taylor's law} or \emph{fluctuation scaling}. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic

Correlated dynamics in egocentric communication networks

We investigate the communication sequences of millions of people through two different channels and analyze the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbors thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constrains (for short messages) and partly to the human behavioral features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.Comment: 7 pages, 6 figure

The origin of bursts and heavy tails in human dynamics

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. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. Here 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 experience very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. These findings have important implications from resource management to service allocation in both communications and retail.Comment: Supplementary Material available at http://www.nd.edu/~network

Multi-Product Firms and Product Switching

This paper examines the frequency, pervasiveness and determinants of product switching among U.S. manufacturing firms. We find that two-thirds of firms alter their mix of five-digit SIC products every five years, that one-third of the increase in real U.S. manufacturing shipments between 1972 and 1997 is due to the net adding and dropping of products by survivors, and that firms are more likely to drop products which are younger and have smaller production volumes relative to other firms producing the same product. The product-switching behavior we observe is consistent with an extended model of industry dynamics emphasizing firm heterogeneity and self-selection into individual product markets. Our findings suggest that product switching contributes towards a reallocation of economic activity within firms towards more productive uses.

Multi-Product Firms and Product Switching

This paper examines the frequency, pervasiveness and determinants of product switching among U.S. manufacturing firms. We find that two-thirds of firms alter their mix of five-digit SIC products every five years, that one-third of the increase in real U.S. manufacturing shipments between 1972 and 1997 is due to the net adding and dropping of products by survivors, and that firms are more likely to drop products which are younger and have smaller production volumes relative to other firms producing the same product. The product-switching behavior we observe is consistent with an extended model of industry dynamics emphasizing firm heterogeneity and self-selection into individual product markets. Our findings suggest that product switching contributes towards a reallocation of economic activity within firms towards more productive uses.Heterogeneous firms, Product differentiation, Product market entry and exit

Guns, germs, and stealing: exploring the link between infectious disease and crime.

Can variation in crime rates be traced to the threat of infectious disease? Pathogens pose an ongoing challenge to survival, leading humans to adapt defenses to manage this threat. In addition to the biological immune system, humans have psychological and behavioral responses designed to protect against disease. Under persistent disease threat, xenophobia increases and people constrict social interactions to known in-group members. Though these responses reduce disease transmission, they can generate favorable crime conditions in two ways. First, xenophobia reduces inhibitions against harming and exploiting out-group members. Second, segregation into in-group factions erodes people's concern for the welfare of their community and weakens the collective ability to prevent crime. The present study examined the effects of infection incidence on crime rates across the United States. Infection rates predicted violent and property crime more strongly than other crime covariates. Infections also predicted homicides against strangers but not family or acquaintances, supporting the hypothesis that in-group-out-group discrimination was responsible for the infections-crime link. Overall, the results add to evidence that disease threat shapes interpersonal behavior and structural characteristics of groups

Characterization of Sleep Stages by Correlations of Heartbeat Increments

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and REM sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the signs series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte