Construction of C 2 Pythagorean-hodograph interpolating splines by the homotopy method

The complex representation of polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic “spline” that interpolates a given sequence of points p 0 , p 1 ,..., p N and end-derivatives d 0 and d N to be reduced to solving a “tridiagonal” system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 N +1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable “looping” behavior (which may be quantified in terms of the elastic bending energy , i.e., the integral of the square of the curvature with respect to arc length). The remaining “good” interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding “ordinary” C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a polynomial function of the curve parameter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41719/1/10444_2005_Article_BF02124754.pd

Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

Absence of lattice strain anomalies at the electronic topological transition in zinc at high pressure

High pressure structural distortions of the hexagonal close packed (hcp) element zinc have been a subject of controversy. Earlier experimental results and theory showed a large anomaly in lattice strain with compression in zinc at about 10 GPa which was explained theoretically by a change in Fermi surface topology. Later hydrostatic experiments showed no such anomaly, resulting in a discrepancy between theory and experiment. We have computed the compression and lattice strain of hcp zinc over a wide range of compressions using the linearized augmented plane wave (LAPW) method paying special attention to k-point convergence. We find that the behavior of the lattice strain is strongly dependent on k-point sampling, and with large k-point sets the previously computed anomaly in lattice parameters under compression disappears, in agreement with recent experiments.Comment: 9 pages, 6 figures, Phys. Rev. B (in press

Hall-conductivity sign change and fluctuations in amorphous Nbx_{x}Ge1−x_{1-x} films

The sign change in the Hall conductivity has been studied in thin amorphous Nb$_{1-x}$Ge$_x (x\approx$0.3) films. By changing the film thickness it is shown that the field at which the sign reversal occurs shifts to lower values (from above to below the mean-field transition field $H_{c2}$) with increasing film thickness. This effect can be understood in terms of a competition between a positive normal and a negative fluctuation contribution to the Hall conductivity.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Tomato: a crop species amenable to improvement by cellular and molecular methods

Tomato is a crop plant with a relatively small DNA content per haploid genome and a well developed genetics. Plant regeneration from explants and protoplasts is feasable which led to the development of efficient transformation procedures. In view of the current data, the isolation of useful mutants at the cellular level probably will be of limited value in the genetic improvement of tomato. Protoplast fusion may lead to novel combinations of organelle and nuclear DNA (cybrids), whereas this technique also provides a means of introducing genetic information from alien species into tomato. Important developments have come from molecular approaches. Following the construction of an RFLP map, these RFLP markers can be used in tomato to tag quantitative traits bred in from related species. Both RFLP's and transposons are in the process of being used to clone desired genes for which no gene products are known. Cloned genes can be introduced and potentially improve specific properties of tomato especially those controlled by single genes. Recent results suggest that, in principle, phenotypic mutants can be created for cloned and characterized genes and will prove their value in further improving the cultivated tomato.

Height Systems and Vertical Datums: a Review in the Australian Context

This paper reviews (without equations) the various definitions of height systems and vertical geodetic datum surfaces, together with their practical realisation for users in Australia. Excluding geopotential numbers, a height system is a one-dimensional coordinate system used to express the metric distance (height) of a point from some reference surface. Its definition varies according to the reference surface chosen and the path along which the height is measured. A vertical geodetic datum is the practical realisation of a height system and its reference surface for users, nominally tied to mean sea level. In Australia, the normal-orthometric height system is used, which is embedded in the Australian Height Datum (AHD). The AHD was realised by the adjustment of ~195,000 km of spirit-levelling observations fixed to limited-term observations of mean sea level at multiple tide-gauges. The paper ends by giving some explanation of the problems with the AHD and of the differences between the AHD and the national geoid model, pointing out that it is preferable to recompute the AHD

Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure

Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies

Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020

We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe