The robustness of the weak selection approximation for the evolution of altruism against strong selection.

The weak selection approximation of population genetics has made possible the analysis of social evolution under a considerable variety of biological scenarios. Despite its extensive usage, the accuracy of weak selection in predicting the emergence of altruism under limited dispersal when selection intensity increases remains unclear. Here, we derive the condition for the spread of an altruistic mutant in the infinite island model of dispersal under a Moran reproductive process and arbitrary strength of selection. The simplicity of the model allows us to compare weak and strong selection regimes analytically. Our results demonstrate that the weak selection approximation is robust to moderate increases in selection intensity and therefore provides a good approximation to understand the invasion of altruism in spatially structured population. In particular, we find that the weak selection approximation is excellent even if selection is very strong, when either migration is much stronger than selection or when patches are large. Importantly, we emphasize that the weak selection approximation provides the ideal condition for the invasion of altruism, and increasing selection intensity will impede the emergence of altruism. We discuss that this should also hold for more complicated life cycles and for culturally transmitted altruism. Using the weak selection approximation is therefore unlikely to miss out on any demographic scenario that lead to the evolution of altruism under limited dispersal.

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Validity of the acoustic approximation in full-waveform seismic crosshole tomography

Acoustic waveform inversions are an increasingly popular tool for extracting subsurface information from seismic data. They are computationally much more efficient than elastic inversions. Naturally, an inherent disadvantage is that any elastic effects present in the recorded data are ignored in acoustic inversions. We investigate the extent to which elastic effects influence seismic crosshole data. Our numerical modeling studies reveal that in the presence of high contrast interfaces, at which P-to-S conversions occur, elastic effects can dominate the seismic sections, even for experiments involving pressure sources and pressure receivers. Comparisons of waveform inversion results using a purely acoustic algorithm on synthetic data that is either acoustic or elastic, show that subsurface models comprising small low-to-medium contrast (?30%) structures can be successfully resolved in the acoustic approximation. However, in the presence of extended high-contrast anomalous bodies, P-to-S-conversions may substantially degrade the quality of the tomographic images. In particular, extended low-velocity zones are difficult to image. Likewise, relatively small low-velocity features are unresolved, even when advanced a priori information is included. One option for mitigating elastic effects is data windowing, which suppresses later arriving seismic arrivals, such as shear waves. Our tests of this approach found it to be inappropriate because elastic effects are also included in earlier arriving wavetrains. Furthermore, data windowing removes later arriving P-wave phases that may provide critical constraints on the tomograms. Finally, we investigated the extent to which acoustic inversions of elastic data are useful for time-lapse analyses of high contrast engineered structures, for which accurate reconstruction of the subsurface structure is not as critical as imaging differential changes between sequential experiments. Based on a realistic scenario for monitoring a radioactive waste repository, we demonstrated that acoustic inversions of elastic data yield substantial distortions of the tomograms and also unreliable information on trends in the velocity changes.