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

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

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

Experimental study of the jamming transition at zero temperature

We experimentally investigate jamming in a quasi-two-dimensional granular system of automatically swelling particles and show that a maximum in the height of the first peak of the pair correlation function is a structural signature of the jamming transition at zero temperature. The same signature is also found in the second peak of the pair correlation function, but not in the third peak, reflecting the underlying singularity of jamming transition. We also study the development of clusters in this system. A static length scale extracted from the cluster structure reaches the size of the system when the system approaches the jamming point. Finally, we show that in a highly inhomogeneous system, friction causes the system to jam in series of steps. In this case, jamming may be obtained through successive buckling of force chains.Comment: 15 pages, 17 figure

When Silence is Not Golden: Why Acknowledgement Matters Even When Being Excluded

Following ostracism, individuals are highly sensitive to social cues. Here we investigate whether and when minimal acknowledgment can improve need satisfaction following an ostracism experience. In four studies, participants were either ostracized during Cyberball (Studies 1 and 2) or through a novel apartment-application paradigm (Studies 3 and 4). To signal acknowledgement following ostracism, participants were either thrown a ball a few times at the end of the Cyberball game, or received a message that was either friendly, neutral, or hostile in the apartment-application paradigm. Both forms of acknowledgment increased need satisfaction, even when the acknowledgment was hostile (Study 4), emphasizing the beneficial effect of any kind of acknowledgment following ostracism. Reinclusion buffered threat immediately, whereas acknowledgment without reinclusion primarily aided recovery. Our results suggest that minimal acknowledgment such as a few ball throws or even an unfriendly message can reduce the sting of ostracism