From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit

Assuming any site-potential dependent on two-point correlations, we rigorously derive a new model for an interlayer potential for incommensurate bilayer heterostructures such as twisted bilayer graphene. We use the ergodic property of the local configuration in incommensurate bilayer heterostructures to prove convergence of an atomistic model to its thermodynamic limit without a rate for minimal conditions on the lattice displacements. We provide an explicit error control with a rate of convergence for sufficiently smooth lattice displacements. For that, we introduce the notion of Diophantine 2D rotations, a two-dimensional analogue of Diophantine numbers, and give a quantitative ergodic theorem for Diophantine 2D rotations.Comment: 55 pages, 1 figur

System Engineering of Autonomous Space Vehicles

Human exploration of the solar system requires fully autonomous systems when travelling more than 5 light minutes from Earth. This autonomy is necessary to manage a large, complex spacecraft with limited crew members and skills available. The communication latency requires the vehicle to deal with events with only limited crew interaction in most cases. The engineering of these systems requires an extensive knowledge of the spacecraft systems, information theory, and autonomous algorithm characteristics. The characteristics of the spacecraft systems must be matched with the autonomous algorithm characteristics to reliably monitor and control the system. This presents a large system engineering problem. Recent work on product-focused, elegant system engineering will be applied to this application, looking at the full autonomy stack, the matching of autonomous systems to spacecraft systems, and the integration of different types of algorithms. Each of these areas will be outlined and a general approach defined for system engineering to provide the optimal solution to the given application context

Detection of Extended Hot Water in the Outflow from NGC 2071

We report the results of spectroscopic mapping observations carried out toward a ~1 min x 1 min region within the northern lobe of the outflow from NGC 2071 using the Infrared Spectrograph (IRS) of the Spitzer Space Telescope. These observations covered the 5.2-37 um spectral region and have led to the detection of a number of ionic, atomic, and molecular lines, including fine-structure emission of Si+, Fe+, S++, S, the S(0)-S(7) pure rotational lines of H2, the R(3) and R(4) transitions of HD, and at least 11 transitions of H2O. In addition, the 6.2, 7.4, 7.6, 7.9, 8.6 and 11.3 um PAH emission bands were also observed and several transitions of OH were tentatively detected. Most of the detected line transitions were strong enough to map including, for the first time, three transitions of hot H2O. We find that: (1) the water emission is extended; (2) the extended emission is aligned with the outflow; and, (3) the spatial distribution of the water emission generally follows that observed for H2. Based on the measured line intensities, we derive an HD abundance relative to H2 of 1.1-1.8 10^-5 and an H2O number density of 12-2 cm^3. The H2 density in the water-emitting region is not well constrained by our observations, but is likely between 3 10^4 and 10^6 cm^3, yielding an H2O abundance relative to H2 of between 2 10^-5 and 6 10^-4. Future observations planned for the Herschel Space Observatory should greatly improve the density estimate, and thus our knowledge of the H2O abundance, for the water-emitting regions reported here. Finally, we note a possible departure from the H2O ortho-to-para ratio of 3:1 expected for water formed in hot post-shocked gas, suggesting that a significant fraction of the water vapor we detect may arise from H2O sputtered from cold dust grains.Comment: 35 pages, 15 figures, 4 tables, accepted for publication in Ap

Algorithm XXX: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data

Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data

Longitudinal assessment of global and regional atrophy rates in Alzheimer's disease and dementia with Lewy bodies.

BACKGROUND & OBJECTIVE: Percent whole brain volume change (PBVC) measured from serial MRI scans is widely accepted as a sensitive marker of disease progression in Alzheimer's disease (AD). However, the utility of PBVC in the differential diagnosis of dementia remains to be established. We compared PBVC in AD and dementia with Lewy bodies (DLB), and investigated associations with clinical measures. METHODS: 72 participants (14 DLBs, 25 ADs, and 33 healthy controls (HCs)) underwent clinical assessment and 3 Tesla T1-weighted MRI at baseline and repeated at 12 months. We used FSL-SIENA to estimate PBVC for each subject. Voxelwise analyses and ANCOVA compared PBVC between DLB and AD, while correlational tests examined associations of PBVC with clinical measures. RESULTS: AD had significantly greater atrophy over 1 year (1.8%) compared to DLB (1.0%; p = 0.01) and HC (0.9%; p < 0.01) in widespread regions of the brain including periventricular areas. PBVC was not significantly different between DLB and HC (p = 0.95). There were no differences in cognitive decline between DLB and AD. In the combined dementia group (AD and DLB), younger age was associated with higher atrophy rates (r = 0.49, p < 0.01). CONCLUSIONS: AD showed a faster rate of global brain atrophy compared to DLB, which had similar rates of atrophy to HC. Among dementia subjects, younger age was associated with accelerated atrophy, reflecting more aggressive disease in younger people. PBVC could aid in differentiating between DLB and AD, however its utility as an outcome marker in DLB is limited.This work was supported by the Sir Jules Thorn Charitable Trust (grant number 05/JTA), the NIHR Biomedical Research Unit in Dementia and the Biomedical Research Centre awarded to Cambridge University Hospitals NHS Foundation Trust and the University of Cambridge, and the NIHR Biomedical Research Unit in Dementia and the Biomedical Research Centre awarded to Newcastle upon Tyne Hospitals NHS Foundation Trust and the Newcastle University. Elijah Mak was in receipt of a Gates Cambridge, PhD studentship.This is the final published version. It first appeared at http://www.sciencedirect.com/science/article/pii/S2213158215000182#

Monitoring rock freezing and thawing by novel geoelectrical and acoustic techniques

Automated monitoring of freeze-thaw cycles and fracture propagation in mountain rockwalls is 23 needed to provide early warning about rockfall hazards. Conventional geoelectrical methods 24 such as electrical resistivity tomography (ERT) are limited by large and variable ohmic contact 25 resistances, requiring galvanic coupling with metal electrodes inserted into holes drilled into 26 rock, and which can be loosened by rock weathering. We report a novel experimental 27 methodology that combined capacitive resistivity imaging (CRI), ERT and microseismic event 28 recording to monitor freeze-thaw of six blocks of hard and soft limestones under conditions 29 simulating an active layer above permafrost and seasonally frozen rock in a non-permafrost 30 environment. Our results demonstrate that the CRI method is highly sensitive to freeze-thaw 31 processes; it yields property information equivalent to that obtained with conventional ERT and 32 offers a viable route for non-galvanic long-term geoelectrical monitoring, extending the benefits 33 of the methodology to soft/hard rock environments. Contact impedances achieved with CRI are 34 less affected by seasonal temperature changes, the aggregate state of the pore water (liquid or 35 frozen), and the presence of low-porosity rock with high matrix resistivities than those achieved 36 with ERT. Microseismic monitoring has the advantage over acoustic emissions that events were 37 recorded in relevant field distances of meters to decameters from cracking events. For the first 38 time we recorded about 1000 microcracking events and clustered them in four groups according 39 to frequency and waveform. Compared to previous studies, mainly on ice-cracking in glaciers, 40 the groups are attributed to single- or multiple-stage cracking events such as crack coalescence

Progressive cortical thinning and subcortical atrophy in dementia with Lewy bodies and Alzheimer's disease.

Patterns of progressive cortical thinning in dementia with Lewy bodies (DLB) remain poorly understood. We examined spatiotemporal patterns of cortical thinning and subcortical atrophy over 12 months in DLB (n = 13), compared with Alzheimer's disease (AD) (n = 23) and healthy control subjects (HC) (n = 33). Rates of temporal thinning in DLB were relatively preserved compared with AD. Volumetric analyses subcortical changes revealed that the AD group demonstrated significantly increased hippocampal atrophy (-5.8%) relative to the HC (-1.7%; p < 0.001) and DLB groups (-2.5%, p = 0.006). Significant lateral ventricular expansion was also observed in AD (8.9%) compared with HC (4.3%; p < 0.001) and DLB (4.7%; p = 0.008) at trend level. There was no significant difference in subcortical atrophy and ventricular expansion between DLB and HC. In the DLB group, increased rates of cortical thinning in the frontal and parietal regions were significantly correlated with decline in global cognition (Mini-Mental State Examination) and motor deterioration (Unified Parkinson's Disease Rating Scale 3), respectively. Overall, AD and DLB are characterized by different spatiotemporal patterns of cortical thinning over time. Our findings warrant further consideration of longitudinal cortical thinning as a potential imaging marker to differentiate DLB from AD.This work was supported by the Sir Jules Thorn Charitable Trust (Grant number 05/JTA), the NIHR Biomedical Research Unit in Dementia and the Biomedical Research Centre awarded to Cambridge University Hospitals NHS Foundation Trust and the University of Cambridge, and the NIHR Biomedical Research Unit in Dementia and the Biomedical Research Centre awarded to Newcastle upon Tyne Hospitals NHS Foundation Trust and the Newcastle University. Elijah Mak was in receipt of a Gates Cambridge PhD studentship. Elijah Mak formulated the research question, performed the statistical analyses, interpreted the results, and wrote the article. Li Su and Guy Williams assisted with the interpretation of the results and provided comments and additional suggestions for revisions of the draft. Rosie Watson recruited and assessed study participants, assisted with the interpretation of the results, and reviewed the article. Michael Firbank designed the imaging protocol, assisted with the interpretation of the results, and reviewed the article. Andrew Blamire obtained funding for the project, designed the imaging protocol, undertook routine quality assurance on the MR system, assisted with the interpretation of the results, and reviewed the article. John O’Brien obtained funding for the project, designed the imaging protocol, assisted with recruitment of study participants, assisted with the interpretation of the results, and reviewed the article. All authors approved the final article.This is the accepted manuscript for a paper published in Neurobiology of Aging Volume 36, Issue 4, April 2015, Pages 1743–1750, DOI: 10.1016/j.neurobiolaging.2014.12.03