A direct solver with O(N) complexity for variable coefficient elliptic PDEs discretized via a high-order composite spectral collocation method

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The resulting system of linear equations is solved using a direct (as opposed to iterative) solver that has optimal O(N) complexity for all stages of the computation when applied to problems with non-oscillatory solutions such as the Laplace and the Stokes equations. Numerical examples demonstrate that the scheme is capable of computing solutions with relative accuracy of $10^{-10}$ or better, even for challenging problems such as highly oscillatory Helmholtz problems and convection-dominated convection diffusion equations. In terms of speed, it is demonstrated that a problem with a non-oscillatory solution that was discretized using $10^{8}$ nodes was solved in 115 minutes on a personal work-station with two quad-core 3.3GHz CPUs. Since the solver is direct, and the "solution operator" fits in RAM, any solves beyond the first are very fast. In the example with $10^{8}$ unknowns, solves require only 30 seconds.Comment: arXiv admin note: text overlap with arXiv:1302.599

Neural Substrates of Contingency Learning and Executive Control: Dissociating Physical, Valuative, and Behavioral Changes

Contingency learning is fundamental to cognition. Knowledge about environmental contingencies allows behavioral flexibility, as executive control processes accommodate the demands of novel or changing environments. Studies of experiential learning have focused on the relationship between actions and the values of associated outcomes. However, outcome values have often been confounded with the physical changes in the outcomes themselves. Here, we dissociated contingency learning into valuative and non-valuative forms, using a novel version of the two-alternative choice task, while measuring the neural effects of contingency changes using functional magnetic resonance imaging (fMRI). Changes in value-relevant contingencies evoked activation in the lateral prefrontal cortex (LPFC), posterior parietal cortex (PPC), and dorsomedial prefrontal cortex (DMPFC) consistent with prior results (e.g., reversal-learning paradigms). Changes in physical contingencies unrelated to value or to action produced similar activations within the LPFC, indicating that LPFC may engage in generalized contingency learning that is not specific to valuation. In contrast, contingency changes that required behavioral shifts evoked activation localized to the DMPFC, supplementary motor, and precentral cortices, suggesting that these regions play more specific roles within the executive control of behavior

A cross sectional study of the prevalence, risk factors and population attributable fractions for limb and body lesions in lactating sows on commercial farms in England

Background: Lesions on sows' limbs and bodies are an abnormality that might impact on their welfare. The prevalence of and risks for limb and body lesions on lactating sows on commercial English pig farms were investigated using direct observation of the sows and their housing. Results: The prevalence of lesions on the limbs and body were 93% (260/279) and 20% (57/288) respectively. The prevalence of limb and body lesions was significantly lower in outdoor-housed sows compared with indoor-housed sows. Indoor-housed sows had an increased risk of wounds (OR 6.8), calluses (OR 8.8) and capped hock (OR 3.8) on their limbs when housed on fully slatted floors compared with solid concrete floors. In addition, there was an increased risk of bursitis (OR 2.7), capped hock (OR 2.3) and shoulder lesions (OR 4.8) in sows that were unwilling to rise to their feet. There was a decreased risk of shoulder lesions (OR 0.3) and lesions elsewhere on the body (OR 0.2) in sows with more than 20 cm between their tail and the back of the crate compared with sows with less than 10 cm. Conclusion: The sample of outdoor housed sows in this study had the lowest prevalence of limb and body lesions. In lactating sows housed indoors there was a general trend for an increased risk of limb and body lesions in sows housed on slatted floors compared with those housed on solid concrete floors with bedding. Sows that were less responsive to human presence and sows that had the least space to move within their crates had an additional increased risk of lesions

Hybrid Pixel Detector Development for the Linear Collider Vertex Tracker

In order to fully exploit the physics potential of the future high energy e+e- linear collider, a Vertex Tracker able to provide particle track extrapolation with very high resolution is needed. Hybrid Si pixel sensors are an attractive technology due to their fast read-out capabilities and radiation hardness. A novel pixel detector layout with interleaved cells has been developed to improve the single point resolution. Results of the characterisation of the first processed prototypes by electrostatic measurements and charge collection studies are discussed.Comment: 5 pages, 1 figure, to appear in the Proceedings of the 9th Int. Workshop on Vertex Detectors, Lake Michigan MI (USA), September~200

MV3: A new word based stream cipher using rapid mixing and revolving buffers

MV3 is a new word based stream cipher for encrypting long streams of data. A direct adaptation of a byte based cipher such as RC4 into a 32- or 64-bit word version will obviously need vast amounts of memory. This scaling issue necessitates a look for new components and principles, as well as mathematical analysis to justify their use. Our approach, like RC4's, is based on rapidly mixing random walks on directed graphs (that is, walks which reach a random state quickly, from any starting point). We begin with some well understood walks, and then introduce nonlinearity in their steps in order to improve security and show long term statistical correlations are negligible. To minimize the short term correlations, as well as to deter attacks using equations involving successive outputs, we provide a method for sequencing the outputs derived from the walk using three revolving buffers. The cipher is fast -- it runs at a speed of less than 5 cycles per byte on a Pentium IV processor. A word based cipher needs to output more bits per step, which exposes more correlations for attacks. Moreover we seek simplicity of construction and transparent analysis. To meet these requirements, we use a larger state and claim security corresponding to only a fraction of it. Our design is for an adequately secure word-based cipher; our very preliminary estimate puts the security close to exhaustive search for keys of size < 256 bits.Comment: 27 pages, shortened version will appear in "Topics in Cryptology - CT-RSA 2007

An accelerated Poisson solver based on multidomain spectral discretization

This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The method works best for domains that can readily be mapped onto a rectangle, or a collection of nonoverlapping rectangles. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and higher have been tested and work well). Local mesh refinement results in highly accurate solutions even in the presence of local irregular behavior due to corner singularities, localized loads, etc. The system of linear equations attained upon discretization is solved using a direct (as opposed to iterative) solver with O(N1.5) complexity for the factorization stage and O(N log N) complexity for the solve. The scheme is ideally suited for executing the elliptic solve required when parabolic problems are discretized via time-implicit techniques. In situations where the geometry remains unchanged between time-steps, very fast execution speeds are obtained since the solution operator for each implicit solve can be pre-computed

Environment and Obesity in the National Children\u27s Study

Objective: In this review we describe the approach taken by the National Children’s Study (NCS), a 21-year prospective study of 100,000 American children, to understanding the role of environmental factors in the development of obesity. Data sources and extraction: We review the literature with regard to the two core hypotheses in the NCS that relate to environmental origins of obesity and describe strategies that will be used to test each hypothesis. Data synthesis: Although it is clear that obesity in an individual results from an imbalance between energy intake and expenditure, control of the obesity epidemic will require understanding of factors in the modern built environment and chemical exposures that may have the capacity to disrupt the link between energy intake and expenditure. The NCS is the largest prospective birth cohort study ever undertaken in the United States that is explicitly designed to seek information on the environmental causes of pediatric disease. Conclusions: Through its embrace of the life-course approach to epidemiology, the NCS will be able to study the origins of obesity from preconception through late adolescence, including factors ranging from genetic inheritance to individual behaviors to the social, built, and natural environment and chemical exposures. It will have sufficient statistical power to examine interactions among these multiple influences, including gene–environment and gene–obesity interactions. A major secondary benefit will derive from the banking of specimens for future analysis

Validation of self-reported weights and heights in the avoiding diabetes after pregnancy trial (ADAPT)

Background: Randomized controlled trials that test the effectiveness of mobile health-based weight loss programs are attractive to participants, funders, and researchers because of the low implementation cost, minimal participant burden, and the ability to recruit participants from longer distances. Collecting weight data from geographically dispersed participants is a challenge. Relying on participant self-report is one approach to data collection, but epidemiologic studies indicate that self-reported anthropometric data may be inaccurate. Methods: We provided women enrolled in a randomized controlled trial (RCT) of postpartum weight loss after gestational diabetes with a digital scale and training to collect and report weight via a web-based survey. To validate self-reported weights and heights, we visited 30 randomly selected women in their homes, with a reference scale and stadiometer, a mean of 34 days after the self-report. We ran linear regression models to identify characteristics that were associated with underreporting or overreporting of anthropometric measures. Results: Of the 30 women we visited, 11 women (37%) were assigned to the weight loss intervention group and 19 women (63%) were in the control group. Mean age was 38.5 years (SD 4.5). The overall mean difference between participants’ self-reported weights and the weights obtained at their home visit was 0.70 kg (+1.92). Women assigned to the intervention group underreported their weight in comparison with the control group by 1.29 kg (95% CI −2.52, −0.06). The overall difference in collected to self-reported height was −0.56 cm (±1.91). No characteristics were associated with underreporting or overreporting of height. Conclusions: Our research suggests that by providing a digital scale and developing a weight collection protocol, researchers can train women to collect and record their own study weights with reasonable validity. To achieve the level of validity required for clinical trials, researchers should consider additional strategies to assure the validity of the data. Trial registration NCT01923350

Artifacts with uneven sampling of red noise

The vast majority of sampling systems operate in a standard way: at each tick of a fixed-frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern that is either transmitted, stored, or processed right away. Thus signal sampling at evenly spaced time intervals is the rule: however this is not always the case, and uneven sampling is sometimes unavoidable. While periodic or quasi-periodic uneven sampling of a deterministic signal can reasonably be expected to produce artifacts, it is much less obvious that the same happens with noise: here I show that this is indeed the case only for long-memory noise processes, i.e., power-law noises $1/f^\alpha$ with $\alpha > 2$. The resulting artifacts are usually a nuisance although they can be eliminated with a proper processing of the signal samples, but they could also be turned to advantage and used to encode information.Comment: 5 figure