A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

The influence of landscape characteristics and home-range size on the quantification of landscape-genetics relationships

A common approach used to estimate landscape resistance involves comparing correlations of ecological and genetic distances calculated among individuals of a species. However, the location of sampled individuals may contain some degree of spatial uncertainty due to the natural variation of animals moving through their home range or measurement error in plant or animal locations. In this study, we evaluate the ways that spatial uncertainty, landscape characteristics, and genetic stochasticity interact to influence the strength and variability of conclusions about landscape-genetics relationships. We used a neutral landscape model to generate 45 landscapes composed of habitat and non-habitat, varying in percent habitat, aggregation, and structural connectivity (patch cohesion). We created true and alternate locations for 500 individuals, calculated ecological distances (least-cost paths), and simulated genetic distances among individuals. We compared correlations between ecological distances for true and alternate locations. We then simulated genotypes at 15 neutral loci and investigated whether the same influences could be detected in simple Mantel tests and while controlling for the effects of isolation-by distance using the partial Mantel test. Spatial uncertainty interacted with the percentage of habitat in the landscape, but led to only small reductions in correlations. Furthermore, the strongest correlations occurred with low percent habitat, high aggregation, and low to intermediate levels of cohesion. Overall genetic stochasticity was relatively low and was influenced by landscape characteristics.

Constrained optimization model for the design of an adaptive (X)over-bar chart

An economic-statistical model is developed for variable parameters (VP) (X) over bar charts in which all design parameters vary adaptively, that is, each of the design parameters (sample size, sampling interval and control-limit width) vary as a function of the most recent process information. The cost function due to controlling the process quality through a VP (X) over bar chart is derived. During the optimization of the cost function, constraints are imposed on the expected times to signal when the process is in and out of control. In this way, required statistical properties can be assured. Through a numerical example, the proposed economic-statistical design approach for VP (X) over bar charts is compared to the economic design for VP (X) over bar charts and to the economic-statistical and economic designs for fixed parameters (FP) (X) over bar charts in terms of the operating cost and the expected times to signal. From this example, it is possible to assess the benefits provided by the proposed model. Varying some input parameters, their effect on the optimal cost and on the optimal values of the design parameters was analysed.

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Adaptive control charts for attributes

We develop a general model for adaptive c, np, u and p control charts in which one, two or three design parameters (sample size, sampling interval and control limit width) switch between two values, according to the most recent process information. For a given in-control average sampling rate and a given false alarm rate, the adaptive chart detects changes in the process much faster than a chart with fixed parameters. Moreover, this study also offers general guidance on how to choose an effective design.

Body size and allometric shape variation in the molly Poecilia vivipara along a gradient of salinity and predation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Emotional engagement and orienting: the effects of picture size on affective response

For their survival, humans and animals can rely on motivational systems which are specialized in assessing the valence and imminence of dangers and appetitive cues. The Orienting Response (OR) is a fundamental response pattern that an organism executes whenever a novel or significant stimulus is detected, and has been shown to be consistently modulated by the affective value of a stimulus. However, detecting threatening stimuli and appetitive affordances while they are far away compared to when they are within reach constitutes an obvious evolutionary advantage. Building on the linear relationship between stimulus distance and retinal size, the present research was aimed at investigating the extent to which emotional modulation of distinct processes (action preparation, attentional capture, and subjective emotional state) is affected when reducing the retinal size of a picture. Studies 1-3 examined the effects of picture size on emotional response. Subjective feeling of engagement, as well as sympathetic activation, were modulated by picture size, suggesting that action preparation and subjective experience reflect the combined effects of detecting an arousing stimulus and assessing its imminence. On the other hand, physiological responses which are thought to reflect the amount of attentional resources invested in stimulus processing did not vary with picture size. Studies 4-6 were conducted to substantiate and extend the results of studies 1-3. In particular, it was noted that a decrease in picture size is associated with a loss in the low spatial frequencies of a picture, which might confound the interpretation of the results of studies 1-3. Therefore, emotional and neutral images which were either low-pass filtered or reduced in size were presented, and affective responses were measured. Most effects which were observed when manipulating image size were replicated by blurring pictures. However, pictures depicting highly arousing unpleasant contents were associated with a more pronounced decrease in affective modulation when pictures were reduced in size compared to when they were blurred. The present results provide important information for the study of processes involved in picture perception and in the genesis and expression of an emotional response. In particular, the availability of high spatial frequencies might affect the degree of activation of an internal representation of an affectively charged scene, and might modulate subjective emotional state and preparation for action. Moreover, the manipulation of stimulus imminence revealed important effects of stimulus engagement on specific components of the emotional response, and the implications of the present data for some models of emotions have been discussed. In particular, within the framework of a staged model of emotional response, the tactic and strategic role of response preparation and attention allocation to stimuli varying in engaging power has been discussed, considering the adaptive advantages that each might represent in an evolutionary view. Finally, the identification of perceptual parameters that allow affective processing to be carried out has important methodological applications in future studies examining emotional response in basic research or clinical contexts.

Early bursts of body size and shape evolution are rare in comparative data

George Gaylord Simpson famously postulated that much of life's diversity originated as adaptive radiations-more or less simultaneous divergences of numerous lines from a single ancestral adaptive type. However, identifying adaptive radiations has proven difficult due to a lack of broad-scale comparative datasets. Here, we use phylogenetic comparative data on body size and shape in a diversity of animal clades to test a key model of adaptive radiation, in which initially rapid morphological evolution is followed by relative stasis. We compared the fit of this model to both single selective peak and random walk models. We found little support for the early-burst model of adaptive radiation, whereas both other models, particularly that of selective peaks, were commonly supported. In addition, we found that the net rate of morphological evolution varied inversely with clade age. The youngest clades appear to evolve most rapidly because long-term change typically does not attain the amount of divergence predicted from rates measured over short time scales. Across our entire analysis, the dominant pattern was one of constraints shaping evolution continually through time rather than rapid evolution followed by stasis. We suggest that the classical model of adaptive radiation, where morphological evolution is initially rapid and slows through time, may be rare in comparative data.

Generation of custom modes in a Nd:YAG laser with a semipassive bimorph adaptive mirror

Custom modes at a wavelength of 1064 nm were generated with a deformable mirror. The required surface deformations of the adaptive mirror were calculated with the Collins integral written in a matrix formalism. The appropriate size and shape of the actuators as well as the needed stroke were determined to ensure that the surface of the controllable mirror matches the phase front of the custom modes. A semipassive bimorph adaptive mirror with five concentric ring-shaped actuators and one defocus actuator was manufactured and characterised. The surface deformation was modelled with the response functions of the adaptive mirror in terms of an expansion with Zernike polynomials. In the experiments the Nd:YAG laser crystal was quasi-CW pumped to avoid thermally induced distortions of the phase front. The adaptive mirror allows to switch between a super-Gaussian mode, a doughnut mode, a Hermite-Gaussian fundamental beam, multi-mode operation or no oscillation in real time during laser operation.

Mothers adjust egg size to helper number in a cooperatively breeding cichlid

Mothers should adjust the size of propagules to the selective forces to which these offspring will be exposed. Usually, a larger propagule size is favored when young are exposed to high mortality risk or conspecific competition. Here we test 2 predictions on how egg size should vary with these selective agents. When offspring are cared for by parents and/or alloparents, protection may reduce the predation risk to young, which may allow mothers to invest less per single offspring. In the cooperatively breeding cichlid Neolamprologus pulcher, brood care helpers protect group offspring and reduce the latters' mortality rate. Therefore, females are expected to reduce their investment per egg when more helpers are present. In a first experiment, we tested this prediction by manipulating the helper number. In N. pulcher, helpers compete for dispersal opportunities with similar-sized individuals of neighboring groups. If the expected future competition pressure on young is high, females should increase their investment per offspring to give them a head start. In a second experiment, we tested whether females produce larger eggs when perceived neighbor density is high. Females indeed reduced egg size with increasing helper number. However, we did not detect an effect of local density on egg size, although females took longer to produce the next clutch when local density was high. We argue that females can use the energy saved by adjusting egg size to reduced predation risk to enhance future reproductive output. Adaptive adjustment of offspring size to helper number may be an important, as yet unrecognized, strategy of cooperative breeders.

Experimental evidence for trait utility of gill raker number in adaptive radiation of a north temperate fish

North temperate fish in post-glacial lakes are textbook examples for rapid parallel adaptive radiation into multiple trophic specialists within individual lakes. Speciation repeatedly proceeded along the benthic – limnetic habitat axis, and benthic – limnetic sister species diverge in the number of gill rakers. Yet, the utility of different numbers of gill rakers for consuming benthic vs. limnetic food has only very rarely been experimentally demonstrated. We bred and raised families of a benthic – limnetic species pair of whitefish under common garden conditions to test whether these species (i) show heritable differentiation in feeding efficiency on zooplankton, and (ii) whether varia- tion in feeding efficiency is predicted by variation in gill raker numbers. We used zooplankton of three different size classes to investigate prey size dependency of divergence in feeding efficiency and to investigate the effect strength of variation in the number of gill rakers. Our results show strong interspecific differences in feeding efficiency. These differences are largest when fish were tested with the smallest zooplankton. Importantly, feeding efficiency is significantly positively correlated with the number of gill rakers when using small zooplankton, also when species identity is statistically controlled for. Our results support the hypothesis that a larger number of gill rakers are of adaptive significance for feeding on zooplankton and pro- vide one of the first experimental demonstrations of trait utility of gill raker number when fish feed on zooplankton. These results are consistent with the suggested importance of divergent selection driven feeding adaptation during adaptive radiation of fish in post-glacial lakes.

Cichlid species-area relationships are shaped by adaptive radiations that scale with area

A positive relationship between species richness and island size is thought to emerge from an equilibrium between immigration and extinction rates, but the influence of species diversification on the form of this relationship is poorly understood. Here, we show that within-lake adaptive radiation strongly modifies the species-area relationship for African cichlid fishes. The total number of species derived from in situ speciation increases with lake size, resulting in faunas orders of magnitude higher in species richness than faunas assembled by immigration alone. Multivariate models provide evidence for added influence of lake depth on the species-area relationship. Diversity of clades representing within-lake radiations show responses to lake area, depth and energy consistent with limitation by these factors, suggesting that ecological factors influence the species richness of radiating clades within these ecosystems. Together, these processes produce lake fish faunas with highly variable composition, but with diversities that are well predicted by environmental variables.

Adaptive, convergent origins of the pygmy phenotype in African rainforest hunter-gatherers

Tropical rainforest hunter-gatherer populations worldwide share the pygmy phenotype, or small human body size. The evolutionary history of this phenotype is largely unknown. Here we studied DNA from the Batwa, a rainforest hunter-gatherer population from east central Africa, to identify regions of the Batwa genome that underlie the pygmy phenotype. We then performed population genomic analyses to study the evolution of these regions, including comparisons with the Baka, a west central African rainforest hunter-gatherer population. We conclude that the pygmy phenotype likely arose due to positive natural selection and that it arose possibly multiple times within Africa. These results support longstanding anthropological hypotheses that small body size confers an important selective advantage for human rainforest hunter-gatherers.

Performance evaluation in Bayesian adaptive randomization

Bayesian adaptive randomization (BAR) is an attractive approach to allocate more patients to the putatively superior arm based on the interim data while maintains good statistical properties attributed to randomization. Under this approach, patients are adaptively assigned to a treatment group based on the probability that the treatment is better. The basic randomization scheme can be modified by introducing a tuning parameter, replacing the posterior estimated response probability, setting a boundary to randomization probabilities. Under randomization settings comprised of the above modifications, operating characteristics, including type I error, power, sample size, imbalance of sample size, interim success rate, and overall success rate, were evaluated through simulation. All randomization settings have low and comparable type I errors. Increasing tuning parameter decreases power, but increases imbalance of sample size and interim success rate. Compared with settings using the posterior probability, settings using the estimated response rates have higher power and overall success rate, but less imbalance of sample size and lower interim success rate. Bounded settings have higher power but less imbalance of sample size than unbounded settings. All settings have better performance in the Bayesian design than in the frequentist design. This simulation study provided practical guidance on the choice of how to implement the adaptive design. ^

Apply response adaptive randomization to group sequential with early stopping

Group sequential methods and response adaptive randomization (RAR) procedures have been applied in clinical trials due to economical and ethical considerations. Group sequential methods are able to reduce the average sample size by inducing early stopping, but patients are equally allocated with half of chance to inferior arm. RAR procedures incline to allocate more patients to better arm; however it requires more sample size to obtain a certain power. This study intended to combine these two procedures. We applied the Bayesian decision theory approach to define our group sequential stopping rules and evaluated the operating characteristics under RAR setting. The results showed that Bayesian decision theory method was able to preserve the type I error rate as well as achieve a favorable power; further by comparing with the error spending function method, we concluded that Bayesian decision theory approach was more effective on reducing average sample size.^