Robust calculation of effective atomic numbers: the Auto-Z(eff) software.

PURPOSE: The most appropriate method of evaluating the effective atomic number necessitates consideration of energy-dependent behavior. Previously, this required quite laborious calculation, which is why many scientists revert to over-simplistic power-law methods. The purpose of this work is to develop user-friendly software for the robust, energy-dependent computation of effective atomic numbers relevant within the context of medical physics, superseding the commonly employed simplistic power law approaches. METHOD: Visual Basic was used to develop a GUI allowing the straightforward calculation of effective atomic numbers. Photon interaction cross section matrices are constructed for energies spanning 10 keV to 10 GeV and elements Z = 1-100. Coefficients for composite media are constructed via linear additivity of the fractional constituents and contrasted against the precalculated matrices at each energy, thereby associating an effective atomic number through interpolation of adjacent cross section data. Uncertainties are of the order of 1-2%. RESULTS: Auto-Z(eff) allows rapid (∼0.6 s) calculation of effective atomic numbers for a range of predefined or user-specified media, allowing estimation of radiological properties and comparison of different media (for instance assessment of water equivalence). The accuracy of Auto-Z(eff) has been validated against numerous published theoretical and experimental predictions, demonstrating good agreement. The results also show that commonly employed power-law approaches are inaccurate, even in their intended regime of applicability (i.e., photoelectric regime). Furthermore, comparing the effective atomic numbers of composite materials using power-law approaches even in a relative fashion is shown to be inappropriate. CONCLUSION: Auto-Z(eff) facilitates easy computation of effective atomic numbers as a function of energy, as well as average and spectral-weighted means. The results are significantly more accurate than normal power-law predictions. The software is freely available to interested readers, who are encouraged to contact the authors.

Registered Replication Report: Rand, Greene, and Nowak (2012).

In an anonymous 4-person economic game, participants contributed more money to a common project (i.e., cooperated) when required to decide quickly than when forced to delay their decision (Rand, Greene & Nowak, 2012), a pattern consistent with the social heuristics hypothesis proposed by Rand and colleagues. The results of studies using time pressure have been mixed, with some replication attempts observing similar patterns (e.g., Rand et al., 2014) and others observing null effects (e.g., Tinghög et al., 2013; Verkoeijen & Bouwmeester, 2014). This Registered Replication Report (RRR) assessed the size and variability of the effect of time pressure on cooperative decisions by combining 21 separate, preregistered replications of the critical conditions from Study 7 of the original article (Rand et al., 2012). The primary planned analysis used data from all participants who were randomly assigned to conditions and who met the protocol inclusion criteria (an intent-to-treat approach that included the 65.9% of participants in the time-pressure condition and 7.5% in the forced-delay condition who did not adhere to the time constraints), and we observed a difference in contributions of -0.37 percentage points compared with an 8.6 percentage point difference calculated from the original data. Analyzing the data as the original article did, including data only for participants who complied with the time constraints, the RRR observed a 10.37 percentage point difference in contributions compared with a 15.31 percentage point difference in the original study. In combination, the results of the intent-to-treat analysis and the compliant-only analysis are consistent with the presence of selection biases and the absence of a causal effect of time pressure on cooperation.