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

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

Dust masses of disks around 8 Brown Dwarfs and Very Low-Mass Stars in Upper Sco OB1 and Ophiuchus

We present the results of ALMA band 7 observations of dust and CO gas in the disks around 7 objects with spectral types ranging between M5.5 and M7.5 in Upper Scorpius OB1, and one M3 star in Ophiuchus. We detect unresolved continuum emission in all but one source, and the $^{12}$CO J=3-2 line in two sources. We constrain the dust and gas content of these systems using a grid of models calculated with the radiative transfer code MCFOST, and find disk dust masses between 0.1 and 1 M$_\oplus$, suggesting that the stellar mass / disk mass correlation can be extrapolated for brown dwarfs with masses as low as 0.05 M$_\odot$. The one disk in Upper Sco in which we detect CO emission, 2MASS J15555600, is also the disk with warmest inner disk as traced by its H - [4.5] photometric color. Using our radiative transfer grid, we extend the correlation between stellar luminosity and mass-averaged disk dust temperature originally derived for stellar mass objects to the brown dwarf regime to $\langle T_{dust} \rangle \approx 22 (L_{*} /L_{\odot})^{0.16} K$, applicable to spectral types of M5 and later. This is slightly shallower than the relation for earlier spectral type objects and yields warmer low-mass disks. The two prescriptions cross at 0.27 L$_\odot$, corresponding to masses between 0.1 and 0.2 M$_\odot$ depending on age.Comment: 9 pages,6 figures, accepted to ApJ on 26/01/201

Precipitation scavenging models: Sensitivities, tests, and applications

``Multiphase`` atmospheric-chemistry models can be described as atmospheric-pollutant simulations that explicitly differentiate between physical phases in the atmosphere (.e.g., gas, cloud water, rain water, snow,...), and directly compute chemical transport and transformation behavior between and within each of these individual phases. Initially formulated for specific application to precipitation-scavenging analysis, many attributes of these models have become incorporated into the more general atmospheric-chemisty codes as well. During the past few years, several of these multiphase precipitation-scavenging models have been developed to the point where they can be applied, in a moderately straightforward fashion, by members of the extended atmospheric sciences community. This presentation provides a brief overview of several aspects of a number of these models, including their structure, their application, their sensitivities and uncertainty levels, their evaluation against field measurements, and their availability

Genome-Wide Association Study and Subsequent Exclusion of ATCAY as a Candidate Gene Involved in Equine Neuroaxonal Dystrophy Using Two Animal Models.

Equine neuroaxonal dystrophy/equine degenerative myeloencephalopathy (eNAD/EDM) is an inherited neurodegenerative disorder of unknown etiology. Clinical signs of neurological deficits develop within the first year of life in vitamin E (vitE) deficient horses. A genome-wide association study (GWAS) was carried out using 670,000 SNP markers in 27 case and 42 control Quarter Horses. Two markers, encompassing a 2.5 Mb region on ECA7, were associated with the phenotype (p = 2.05 × 10-7 and 4.72 × 10-6). Within this region, caytaxin (ATCAY) was identified as a candidate gene due to its known role in Cayman Ataxia and ataxic/dystonic phenotypes in mouse models. Whole-genome sequence data in four eNAD/EDM and five unaffected horses identified 199 associated variants within the ECA7 region. MassARRAY® genotyping was performed on these variants within the GWAS population. The three variants within ATCAY were not concordant with the disease phenotype. No difference in expression or alternative splicing was identified using qRT-PCR in brainstem across the ATCAY transcript. Atcayji-hes mice were then used to conduct functional analysis in a second animal model. Histologic lesions were not identified in the central nervous system of Atcayji-hes mice. Additionally, supplementation of homozygous Atcayji-hes mice with 600 IU/day of dl-α-tocopheryl acetate (vitE) during gestation, lactation, and adulthood did not improve the phenotype. ATCAY has therefore been excluded as a candidate gene for eNAD/EDM

Stimulus-evoked high frequency oscillations are present in neuronal networks on microelectrode arrays

Pathological high frequency oscillations (250–600 Hz) are present in the brains of epileptic animals and humans. The etiology of these oscillations and how they contribute to the diseased state remains unclear. This work identifies the presence of microstimulation-evoked high frequency oscillations (250–400 Hz) in dissociated neuronal networks cultured on microelectrode arrays (MEAs). Oscillations are more apparent with higher stimulus voltages. As with in vivo studies, activity is isolated to a single electrode, however, the MEA provides improved spatial resolution with no spread of the oscillation to adjacent electrodes 200 μm away. Oscillations develop across four weeks in vitro. Oscillations still occur in the presence of tetrodotoxin and synaptic blockers, and they cause no apparent disruption in the ability of oscillation-presenting electrodes to elicit directly evoked action potentials (dAPs) or promote the spread of synaptic activity throughout the culture. Chelating calcium with ethylene glycol tetraacetic acid (EGTA) causes a temporal prolongation of the oscillation. Finally, carbenoxolone significantly reduces or eliminates the high frequency oscillations. Gap junctions may play a significant role in maintaining the oscillation given the inhibitory effect of carbenoxolone, the propagating effect of reduced calcium conditions and the isolated nature of the activity as demonstrated in previous studies. This is the first demonstration of stimulus-evoked high frequency oscillations in dissociated cultures. Unlike current models that rely on complex in vivo recording conditions, this work presents a simple controllable model in neuronal cultures on MEAs to further investigate how the oscillations occur at the molecular level and how they may contribute to the pathophysiology of disease

Is there really a debris disc around ζ2 Reticuli\zeta^2\,\mathrm{Reticuli} ?

The presence of a debris disc around the Gyr-old solar-type star $\zeta^2\,\mathrm{Reticuli}$ was suggested by the $\mathit{Spitzer}$ infrared excess detection. Follow-up observations with $\mathit{Herschel}$/PACS revealed a double-lobed feature, that displayed asymmetries both in brightness and position. Therefore, the disc was thought to be edge-on and significantly eccentric. Here we present ALMA/ACA observations in Band 6 and 7 which unambiguously reveal that these lobes show no common proper motion with $\zeta^2\,\mathrm{Reticuli}$. In these observations, no flux has been detected around $\zeta^2\,\mathrm{Reticuli}$ that exceeds the $3\sigma$ levels. We conclude that surface brightness upper limits of a debris disc around $\zeta^2\,\mathrm{Reticuli}$ are $5.7\,\mathrm{\mu Jy/arcsec^2}$ at 1.3 mm, and $26\,\mathrm{\mu Jy/arcsec^2}$ at 870 microns. Our results overall demonstrate the capability of the ALMA/ACA to follow-up $\mathit{Herschel}$ observations of debris discs and clarify the effects of background confusion.Comment: 6 pages, 2 figures, 2 table