How intermittent breaks in interaction improve collective intelligence.

People influence each other when they interact to solve problems. Such social influence introduces both benefits (higher average solution quality due to exploitation of existing answers through social learning) and costs (lower maximum solution quality due to a reduction in individual exploration for novel answers) relative to independent problem solving. In contrast to prior work, which has focused on how the presence and network structure of social influence affect performance, here we investigate the effects of time. We show that when social influence is intermittent it provides the benefits of constant social influence without the costs. Human subjects solved the canonical traveling salesperson problem in groups of three, randomized into treatments with constant social influence, intermittent social influence, or no social influence. Groups in the intermittent social-influence treatment found the optimum solution frequently (like groups without influence) but had a high mean performance (like groups with constant influence); they learned from each other, while maintaining a high level of exploration. Solutions improved most on rounds with social influence after a period of separation. We also show that storing subjects' best solutions so that they could be reloaded and possibly modified in subsequent rounds-a ubiquitous feature of personal productivity software-is similar to constant social influence: It increases mean performance but decreases exploration.

Power laws and fragility in flow networks.

What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence.

Power law versus exponential state transition dynamics: application to sleep-wake architecture.

BACKGROUND: Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. METHODOLOGY/PRINCIPAL FINDINGS: To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. CONCLUSIONS/SIGNIFICANCE: Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.