Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Array-based iterative measurements of SmKS travel times and their constraints on outermost core structure

Vigorous convection in Earth's outer core led to the suggestion that it is chemically homogeneous. However, there is increasing seismic evidence for structural complexities close to the outer core's upper and lower boundaries. Both body waves and normal mode data have been used to estimate a P wave velocity, V_p, at the top of the outer core (the E’ layer), which is lower than that in the Preliminary Reference Earth Model. However, these low V_p models do not agree on the form of this velocity anomaly. One reason for this is the difficulty in retrieving and measuring SmKS arrival times. To address this issue, we propose a novel approach using data from seismic arrays to iteratively measure SmKS-SKKS-differential travel times. This approach extracts individual SmKS signal from mixed waveforms of the SmKS series, allowing us to reliably measure differential travel times. We successfully use this method to measure SmKS time delays from earthquakes in the Fiji‐Tonga and Vanuatu subduction zones. SmKS time delays are measured by waveform cross correlation between SmKS and SKKS, and the cross‐correlation coefficient allows us to access measurement quality. We also apply this iterative scheme to synthetic SmKS seismograms to investigate the 3‐D mantle structure's effects. The mantle structure corrections are not negligible for our data, and neglecting them could bias the V_p estimation of uppermost outer core. After mantle structure corrections, we can still see substantial time delays of S3KS, S4KS, and S5KS, supporting a low V_p at the top of Earth's outer core

Atomic Gas in Debris Discs

We have conducted a search for optical circumstellar absorption lines in the spectra of 16 debris disc host stars. None of the stars in our sample showed signs of emission line activity in either H$_{\alpha}$, Ca II or Na I, confirming their more evolved nature. Four stars were found to exhibit narrow absorption features near the cores of the photospheric Ca II and Na I D lines (when Na I D data were available). We analyse the characteristics of these spectral features to determine whether they are of circumstellar or interstellar origins. The strongest evidence for circumstellar gas is seen in the spectrum of HD110058, which is known to host a debris disc observed close to edge-on. This is consistent with a recent ALMA detection of molecular gas in this debris disc, which shows many similarities to the $\beta$ Pictoris system.Comment: Accepted 13/12/2016. Received 2/12/2016; Deposited on 22/11/2016. - 13 Pages, 9 Figures - MNRAS Advance Access published December 15, 201

Detecting the Rise and Fall of 21 cm Fluctuations with the Murchison Widefield Array

We forecast the sensitivity with which the Murchison Widefield Array (MWA) can measure the 21 cm power spectrum of cosmic hydrogen, using radiative transfer simulations to model reionization and the 21 cm signal. The MWA is sensitive to roughly a decade in scale (wavenumbers of k ~ 0.1 - 1 h Mpc^{-1}), with foreground contamination precluding measurements on larger scales, and thermal detector noise limiting the small scale sensitivity. This amounts primarily to constraints on two numbers: the amplitude and slope of the 21 cm power spectrum on the scales probed. We find, however, that the redshift evolution in these quantities can yield important information about reionization. Although the power spectrum differs substantially across plausible models, a generic prediction is that the amplitude of the 21 cm power spectrum on MWA scales peaks near the epoch when the intergalactic medium (IGM) is ~ 50% ionized. Moreover, the slope of the 21 cm power spectrum on MWA scales flattens as the ionization fraction increases and the sizes of the HII regions grow. Considering detection sensitivity, we show that the optimal MWA antenna configuration for power spectrum measurements would pack all 500 antenna tiles as close as possible in a compact core. The MWA is sensitive enough in its optimal configuration to measure redshift evolution in the slope and amplitude of the 21 cm power spectrum. Detecting the characteristic redshift evolution of our models will confirm that observed 21 cm fluctuations originate from the IGM, and not from foregrounds, and provide an indirect constraint on the volume-filling factor of HII regions during reionization. After two years of observations under favorable conditions, the MWA can constrain the filling factor at an epoch when ~ 0.5 to within roughly +/- 0.1 at 2-sigma.Comment: 14 pages, 9 figures, submitted to Ap

Friction-Stir-Welded and Spin-Formed End Domes for Cryogenic Tanks

Manufacturing of single-piece end domes for cryogenic tanks employing spin forming of tailored, friction-stir-welded blanks of Al-Li alloy 2195 plate offers cost and reliability benefits. The introduction of plastic deformation into a friction stir weld is a unique feature of the proposed manufacturing route. This investigation addressed abnormal grain growth [AGG] within the friction stir weldments during postfabrication processing of a prototype dome. The phenomenon of AGG was observed during the solution heat treatment [SHT] phase of T8 tempering and is a major concern for meeting specifications. Such abrupt microstructural transitions can be detrimental to notch-sensitive mechanical properties, such as ductility and/or fracture toughness. If the issue of AGG cannot be resolved, then the acceptance of this approach as a viable manufacturing route may be in jeopardy. The innovative approach adopted in this investigation was the insertion of a stand-alone, Intermediate Annealing Treatment [IAT] between the spin forming and T8 processing operations. A simple, recovery annealing step was deemed to be the most readily-scalable solution when fabricating thin-walled, ellipsoidal domes. The research effort culminated in the development of an effective IAT, which resulted in a significant decrease in AGG following SHT. The processing philosophy adopted in designing the IAT is outlined and the microstructural reasons for success are discussed. The analytical results presented are consistent with promoting continuous grain growth during the IAT, thereby suppressing AGG during the SHT

Dense Packings of Superdisks and the Role of Symmetry

We construct the densest known two-dimensional packings of superdisks in the plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and concave-shaped particles (0 < p < 0.5). The packings of the convex cases with p 1 generated by a recently developed event-driven molecular dynamics (MD) simulation algorithm [Donev, Torquato and Stillinger, J. Comput. Phys. 202 (2005) 737] suggest exact constructions of the densest known packings. We find that the packing density (covering fraction of the particles) increases dramatically as the particle shape moves away from the "circular-disk" point (p = 1). In particular, we find that the maximal packing densities of superdisks for certain p 6 = 1 are achieved by one of the two families of Bravais lattice packings, which provides additional numerical evidence for Minkowski's conjecture concerning the critical determinant of the region occupied by a superdisk. Moreover, our analysis on the generated packings reveals that the broken rotational symmetry of superdisks influences the packing characteristics in a non-trivial way. We also propose an analytical method to construct dense packings of concave superdisks based on our observations of the structural properties of packings of convex superdisks.Comment: 15 pages, 8 figure

Diffusion Modelling Reveals the Decision Making Processes Underlying Negative Judgement Bias in Rats:Modelling Decision Making during Negative Affect

Human decision making is modified by emotional state. Rodents exhibit similar biases during interpretation of ambiguous cues that can be altered by affective state manipulations. In this study, the impact of negative affective state on judgement bias in rats was measured using an ambiguous-cue interpretation task. Acute treatment with an anxiogenic drug (FG7142), and chronic restraint stress and social isolation both induced a bias towards more negative interpretation of the ambiguous cue. The diffusion model was fit to behavioural data to allow further analysis of the underlying decision making processes. To uncover the way in which parameters vary together in relation to affective state manipulations, independent component analysis was conducted on rate of information accumulation and distances to decision threshold parameters for control data. Results from this analysis were applied to parameters from negative affective state manipulations. These projected components were compared to control components to reveal the changes in decision making processes that are due to affective state manipulations. Negative affective bias in rodents induced by either FG7142 or chronic stress is due to a combination of more negative interpretation of the ambiguous cue, reduced anticipation of the high reward and increased anticipation of the low reward

Helical Tubes in Crowded Environments

When placed in a crowded environment, a semi-flexible tube is forced to fold so as to make a more compact shape. One compact shape that often arises in nature is the tight helix, especially when the tube thickness is of comparable size to the tube length. In this paper we use an excluded volume effect to model the effects of crowding. This gives us a measure of compactness for configurations of the tube, which we use to look at structures of the semi-flexible tube that minimize the excluded volume. We focus most of our attention on the helix and which helical geometries are most compact. We found that helices of specific pitch to radius ratio 2.512 to be optimally compact. This is the same geometry that minimizes the global curvature of the curve defining the tube. We further investigate the effects of adding a bending energy or multiple tubes to begin to explore the more complete space of possible geometries a tube could form.Comment: 10 page

Prevalence of adult asthma symptoms in relation to climate in New Zealand.

We conducted an ecological study linking prevalence of adult asthma symptoms with climate in the 93 New Zealand general electorates. For each electorate, the 12-month period prevalence of self-reported asthma symptoms was determined using a random sample of adults aged 20-44 on the 1991 New Zealand electoral roll. Long-term average climate was estimated using a national climate database and a geographic information system. Asthma prevalence was calculated within quartiles of the exposure variables. Independent effects of climate variables were assessed using linear regression models, with adjustment for confounding by climate, social deprivation, and geographic variables. There was a statistically significant association between asthma prevalence and mean temperature, with the lowest quartile of mean temperature having an approximately 2% lower asthma prevalence. After adjusting for confounding, there was a monotonic increase in asthma prevalence within quartiles of temperature. The results of this study are in agreement with other research suggesting a lower prevalence of asthma at low temperatures. Although on short (day-to-day) time scales, low temperatures may have a direct effect resulting in acute exacerbations of asthma symptoms, warmer average temperatures are associated with increased asthma prevalence. The reasons for this are unclear, although it is possible that on longer term (annual) time scales, higher temperatures are associated with higher levels of allergen exposure