Humans clapping together in unison is a familiar and robust example of emergent synchrony. We find that in experiments, such groups (from two to a few hundred) always increase clapping frequency, and larger groups increase more quickly. Based on single-person experiments and modeling, an individual tendency to rush is ruled out as an explanation. Instead, an asymmetric sensitivity in aural interactions explains the frequency increase, whereby individuals correct more strongly to match neighbour claps that precede their own clap, than those that follow it. A simple conceptual coupled oscillator model based on this interaction recovers the main features observed in experiments, and shows that the collective frequency increase is driven by the small timing errors in individuals, and the resulting inter-individual interactions that occur to maintain unison.
Numerical modeling methods and hyperthermia treatment temperature measurements have been used together to reconstruct steady-state tumor temperature distributions. However, model errors will exist which may in turn produce errors in the reconstructed temperature distributions. A series of computer experiments was conducted to study the sensitivity of reconstructed two-dimensional temperature distributions to perfusion distribution modeling errors. Temperature distributions were simulated using a finite element approximation of Pennes' bioheat transfer equation. Relevant variables such as tumor shape, perfusion distribution, and power deposition were modeled. An optimization method and the temperatures "measured" from the simulated temperature distributions were used to reconstruct the tumor temperature distribution. Using this procedure, the sensitivity of the reconstructed tumor temperature distribution to model-related errors, such as the perfusion function, was studied. It was found that: 1) if the problem is conduction dominated, large errors in the perfusion distribution produce only small errors in the reconstructed temperature distribution (maximum error < 1.0 degrees C), and 2) when the actual perfusion distribution contains a small random variation (+/- 15%) which is neglected by the model, the reconstructed temperature distribution will be in good agreement with the actual temperature distribution (maximum error < or = 0.3 degrees.
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