Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations

We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric and magnetic field. Special emphasis is placed on an efficient implementation which is achieved by taking advantage of recurrence properties and the tensor-product structure of the chosen shape functions. These recurrences have been derived symbolically with computer algebra methods reminiscent of the holonomic systems approach.Comment: 16 pages, 1 figure, 1 table; Springer Wien, ISBN 978-3-7091-0793-

Order preserving pattern matching on trees and DAGs

The order preserving pattern matching (OPPM) problem is, given a pattern string $p$ and a text string $t$, find all substrings of $t$ which have the same relative orders as $p$. In this paper, we consider two variants of the OPPM problem where a set of text strings is given as a tree or a DAG. We show that the OPPM problem for a single pattern $p$ of length $m$ and a text tree $T$ of size $N$ can be solved in $O(m+N)$ time if the characters of $p$ are drawn from an integer alphabet of polynomial size. The time complexity becomes $O(m \log m + N)$ if the pattern $p$ is over a general ordered alphabet. We then show that the OPPM problem for a single pattern and a text DAG is NP-complete

Fast Locality-Sensitive Hashing Frameworks for Approximate Near Neighbor Search

The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a general technique for constructing a data structure to answer approximate near neighbor queries by using a distribution $\mathcal{H}$ over locality-sensitive hash functions that partition space. For a collection of $n$ points, after preprocessing, the query time is dominated by $O(n^{\rho} \log n)$ evaluations of hash functions from $\mathcal{H}$ and $O(n^{\rho})$ hash table lookups and distance computations where $\rho \in (0,1)$ is determined by the locality-sensitivity properties of $\mathcal{H}$. It follows from a recent result by Dahlgaard et al. (FOCS 2017) that the number of locality-sensitive hash functions can be reduced to $O(\log^2 n)$, leaving the query time to be dominated by $O(n^{\rho})$ distance computations and $O(n^{\rho} \log n)$ additional word-RAM operations. We state this result as a general framework and provide a simpler analysis showing that the number of lookups and distance computations closely match the Indyk-Motwani framework, making it a viable replacement in practice. Using ideas from another locality-sensitive hashing framework by Andoni and Indyk (SODA 2006) we are able to reduce the number of additional word-RAM operations to $O(n^\rho)$.Comment: 15 pages, 3 figure

Association of severity of primary open-angle glaucoma with serum vitamin D levels in patients of African descent.

PurposeTo study the relationship between primary open-angle glaucoma (POAG) in a cohort of patients of African descent (AD) and serum vitamin D levels.MethodsA subset of the AD and glaucoma evaluation study III (ADAGES III) cohort, consisting of 357 patients with a diagnosis of POAG and 178 normal controls of self-reported AD, were included in this analysis. Demographic information, family history, and blood samples were collected from all the participants. All the subjects underwent clinical evaluation, including visual field (VF) mean deviation (MD), central cornea thickness (CCT), intraocular pressure (IOP), and height and weight measurements. POAG patients were classified into early and advanced phenotypes based on the severity of their visual field damage, and they were matched for age, gender, and history of hypertension and diabetes. Serum 25-Hydroxy (25-OH) vitamin D levels were measured by enzyme-linked immunosorbent assay (ELISA). The association of serum vitamin D levels with the development and severity of POAG was tested by analysis of variance (ANOVA) and the paired t-test.ResultsThe 178 early POAG subjects had a visual field MD of better than -4.0 dB, and the 179 advanced glaucoma subjects had a visual field MD of worse than -10 dB. The mean (95% confidence interval [CI]) levels of vitamin D of the subjects in the control (8.02 ± 6.19 pg/ml) and early phenotype (7.56 ± 5.74 pg/ml) groups were significantly or marginally significantly different from the levels observed in subjects with the advanced phenotype (6.35 ± 4.76 pg/ml; p = 0.0117 and 0.0543, respectively). In contrast, the mean serum vitamin D level in controls was not significantly different from that of the subjects with the early glaucoma phenotype (p = 0.8508).ConclusionsIn this AD cohort, patients with advanced glaucoma had lower serum levels of vitamin D compared with early glaucoma and normal subjects

Detecting Discontinuities Over Triangular Meshes Using Multiwavelets

It is well known that solutions to nonlinear hyperbolic PDEs develop discontinuities in time. The generation of spurious oscillations in such regions can be prevented by applying a limiter in the troubled zones. In earlier work, we constructed a multiwavelet troubled-cell indicator for one and (tensor-product) two dimensions (SIAM J. Sci. Comput. 38(1):A84–A104, 2016). In this paper, we investigate multiwavelet troubled-cell indicators on structured triangular meshes. One indicator uses a problem-dependent parameter; the other indicator is combined with outlier detection

A global analysis of field body temperatures of active squamates in relation to climate and behaviour

Aim Squamate fitness is affected by body temperature, which in turn is influenced by environmental temperatures and, in many species, by exposure to solar radiation. The biophysical drivers of body temperature have been widely studied, but we lack an integrative synthesis of actual body temperatures experienced in the field, and their relationships to environmental temperatures, across phylogeny, behaviour and climate. Location Global (25 countries on six continents). Taxa Squamates (210 species, representing 25 families). Methods We measured the body temperatures of 20,231 individuals of squamates in the field while they were active. We examined how body temperatures vary with substrate and air temperatures across taxa, climates and behaviours (basking and diel activity). Results Heliothermic lizards had the highest body temperatures. Their body temperatures were the most weakly correlated with substrate and air temperatures. Body temperatures of non-heliothermic diurnal lizards were similar to heliotherms in relation to air temperature, but similar to nocturnal species in relation to substrate temperatures. The correlation of body temperature with air and substrate temperatures was stronger in diurnal snakes and non-heliothermic lizards than in heliotherms. Body-substrate and body-air temperature correlations varied with mean annual temperatures in all diurnal squamates, especially in heliotherms. Thermal relations vary with behaviour (heliothermy, nocturnality) in cold climates but converge towards the same relation in warm climates. Non-heliotherms and nocturnal species body temperatures are better explained by substrate temperature than by air temperature. Body temperature distributions become left-skewed in warmer-bodied species, especially in colder climates. Main Conclusions Squamate body temperatures, their frequency distributions and their relation to environmental temperature, are globally influenced by behavioural and climatic factors. For all temperatures and climates, heliothermic species' body temperatures are consistently higher and more stable than in other species, but in regions with warmer climate these differences become less pronounced. A comparable variation was found in non-heliotherms, but in not nocturnal species whose body temperatures were similar to air and substrate irrespective of the macroclimatic context

Severity of cardiomyopathy associated with adenine nucleotide translocator-1 deficiency correlates with mtDNA haplogroup

Mutations of both nuclear and mitochondrial DNA (mtDNA)-encoded mitochondrial proteins can cause cardiomyopathy associated with mitochondrial dysfunction. Hence, the cardiac phenotype of nuclear DNA mitochondrial mutations might be modulated by mtDNA variation. We studied a 13-generation Mennonite pedigree with autosomal recessive myopathy and cardiomyopathy due to an SLC25A4 frameshift null mutation (c.523delC, p.Q175RfsX38), which codes for the heart-muscle isoform of the adenine nucleotide translocator-1. Ten homozygous null (adenine nucleotide translocator-1(-/-)) patients monitored over a median of 6 years had a phenotype of progressive myocardial thickening, hyperalaninemia, lactic acidosis, exercise intolerance, and persistent adrenergic activation. Electrocardiography and echocardiography with velocity vector imaging revealed abnormal contractile mechanics, myocardial repolarization abnormalities, and impaired left ventricular relaxation. End-stage heart disease was characterized by massive, symmetric, concentric cardiac hypertrophy; widespread cardiomyocyte degeneration; overabundant and structurally abnormal mitochondria; extensive subendocardial interstitial fibrosis; and marked hypertrophy of arteriolar smooth muscle. Substantial variability in the progression and severity of heart disease segregated with maternal lineage, and sequencing of mtDNA from five maternal lineages revealed two major European haplogroups, U and H. Patients with the haplogroup U mtDNAs had more rapid and severe cardiomyopathy than those with haplogroup H

High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: application to cardiac electrophysiology

We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hp elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac electrophysiology where sharp gradients in the solution benefit from the high-order discretisation, while the compu- tational cost of anatomically-realistic models can be reduced through the surface representation. We describe and validate our discretisation and provide a demonstration of its application to modeling electrochemical propagation across a human left atrium

Comparative study of the stability of bimatoprost 0.03% and latanoprost 0.005%: A patient-use study

<p>Abstract</p> <p>Background</p> <p>The stability of ophthalmic preparations in multidose containers is influenced by the preservative as well as the stability of the active ingredient. Unstable drugs may require refrigeration to preserve their active ingredient level and they are more likely to degrade over time, therefore becoming more susceptible to degradation based on patient mishandling. The purpose of this study was to determine the degree of molecular degradation that occurs in bimatoprost and latanoprost in a patient-use setting.</p> <p>Methods</p> <p>This was an open-label, laboratory evaluation of the relative stability of bimatoprost and latanoprost. Patients presently using bimatoprost (n = 31) or latanoprost (n = 34) were identified at 2 clinical sites in Brazil. Patients were instructed to use and store their drops as usual and return all used medication bottles between day 28 and day 34 after opening.</p> <p>Results</p> <p>Bimatoprost demonstrated no degradation, but latanoprost degraded at various levels. The mean age of bimatoprost was 43.0 ± 3.4 days and the mean age of latanoprost was 43.9 ± 2.8 days (P = .072). The mean percentage of labeled concentration was 103.7% in the bimatoprost bottles and 88.1% in the latanoprost bottles (P < 001).</p> <p>Conclusion</p> <p>This study showed that bimatoprost maintained ≥100% concentration throughout the study period while latanoprost did not.</p