Talbot quadratures and rational approximations

Many computational problems can be solved with the aid of contour integrals containing $e^z$ in the the integrand: examples include inverse Laplace transforms, special functions, functions of matrices and operators, parabolic PDEs, and reaction-diffusion equations. One approach to the numerical quadrature of such integrals is to apply the trapezoid rule on a Hankel contour defined by a suitable change of variables. Optimal parameters for three classes of such contours have recently been derived: (a) parabolas, (b) hyperbolas, and (c) cotangent contours, following Talbot in 1979. The convergence rates for these optimized quadrature formulas are very fast: roughly $O(3^{-N})$, where $N$ is the number of sample points or function evaluations. On the other hand, convergence at a rate apparently about twice as fast, $O(9.28903^{-N})$, can be achieved by using a different approach: best supremum-norm rational approximants to $e^z$ for $z\in (-\infty,0]$, following Cody, Meinardus and Varga in 1969. (All these rates are doubled in the case of self-adjoint operators or real integrands.) It is shown that the quadrature formulas can be interpreted as rational approximations and the rational approximations as quadrature formulas, and the strengths and weaknesses of the different approaches are discussed in the light of these connections. A MATLAB function is provided for computing Cody--Meinardus--Varga approximants by the method of Carathèodory-Fejèr approximation

Association between genetic variants in the Coenzyme Q10 metabolism and Coenzyme Q10 status in humans

<p>Abstract</p> <p>Background</p> <p>Coenzyme Q₁₀(CoQ₁₀) is essential for mitochondrial energy production and serves as an antioxidants in extra mitochondrial membranes. The genetics of primary CoQ₁₀deficiency has been described in several studies, whereas the influence of common genetic variants on CoQ₁₀status is largely unknown. Here we tested for non-synonymous single-nucleotidepolymorphisms (SNP) in genes involved in the biosynthesis (CoQ3^G272S, CoQ6^M406V, CoQ7^M103T), reduction (NQO1^P187S, NQO2^L47F) and metabolism (apoE3/4) of CoQ₁₀and their association with CoQ₁₀status. For this purpose, CoQ₁₀serum levels of 54 healthy male volunteers were determined before (T₀) and after a 14 days supplementation (T₁₄) with 150 mg/d of the reduced form of CoQ₁₀.</p> <p>Findings</p> <p>At T₀, the CoQ₁₀level of heterozygous NQO1^P187Scarriers were significantly lower than homozygous S/S carriers (0.93 ± 0.25 μM versus 1.34 ± 0.42 μM, p = 0.044). For this polymorphism a structure homology-based method (PolyPhen) revealed a possibly damaging effect on NQO1 protein activity. Furthermore, CoQ₁₀plasma levels were significantly increased in apoE4/E4 genotype after supplementation in comparison to apoE2/E3 genotype (5.93 ± 0.151 μM versus 4.38 ± 0.792 μM, p = 0.034). Likewise heterozygous CoQ3^G272Scarriers had higher CoQ₁₀plasma levels at T₁₄compared to G/G carriers but this difference did not reach significance (5.30 ± 0.96 μM versus 4.42 ± 1.67 μM, p = 0.082).</p> <p>Conclusions</p> <p>In conclusion, our pilot study provides evidence that NQO1^P187Sand apoE polymorphisms influence CoQ₁₀status in humans.</p

Effects of food on bacterial community composition associated with the copepod Acartia tonsa Dana

The estuarine copepod Acartia tonsa naturally carried diverse strains of bacteria on its body. The bacterial community composition (BCC) remained very conservative even when the copepod was fed different axenic algal species, indicating that the food per se did not much affect BCC associated with the copepod. In xenic algal treatments, however, copepod-associated BCC differed with each alga fed, even though the same bacterial source was used to inoculate the algae. In addition, starved copepods taken at the same location but at different times significantly differed in their BCC. Algal species composition and copepod life history therefore serve to regulate BCC associated with copepods, and spatial and temporal variations in algal species composition and copepod origin would alter bacteria-copepod interactions

Homogeneous crystal nucleation in polymers

© 2017 IOP Publishing Ltd. The pathway of crystal nucleation significantly influences the structure and properties of semi-crystalline polymers. Crystal nucleation is normally heterogeneous at low supercooling, and homogeneous at high supercooling, of the polymer melt. Homogeneous nucleation in bulk polymers has been, so far, hardly accessible experimentally, and was even doubted to occur at all. This topical review summarizes experimental findings on homogeneous crystal nucleation in polymers. Recently developed fast scanning calorimetry, with cooling and heating rates up to 10 6 K s -1 , allows for detailed investigations of nucleation near and even below the glass transition temperature, including analysis of nuclei stability. As for other materials, the maximum homogeneous nucleation rate for polymers is located close to the glass transition temperature. In the experiments discussed here, it is shown that polymer nucleation is homogeneous at such temperatures. Homogeneous nucleation in polymers is discussed in the framework of the classical nucleation theory. The majority of our observations are consistent with the theory. The discrepancies may guide further research, particularly experiments to progress theoretical development. Progress in the understanding of homogeneous nucleation is much needed, since most of the modelling approaches dealing with polymer crystallization exclusively consider homogeneous nucleation. This is also the basis for advancing theoretical approaches to the much more complex phenomena governing heterogeneous nucleation

Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general non-equilibrium thermodynamic description of the system when it is out of equilibrium. We then apply it to study the structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.Comment: 20 pages, 1 figur

Narrow Field of View Zenith Radiometer (NFOV) Handbook

The two-channel narrow field-of-view radiometer (NFOV2) is a ground-based radiometer that looks straight up and measures radiance directly above the instrument at wavelengths of 673 and 870 nm. The field-of-view of the instrument is 1.2 degrees, and the sampling time resolution is one second. Measurements of the NFOV2 have been used to retrieve optical properties for overhead clouds that range from patchy to overcast. With a one-second sampling rate of the NFOV2, faster than almost any other ARM Climate Research Facility (ACRF) instrument, we are able, for the first time, to capture changes in cloud optical properties at the natural time scale of cloud evolution

A condensed matter interpretation of SM fermions and gauge fields

We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio

Biosynthesis of Mitochondrial Porin and Insertion into the Outer Mitochondrial Membrane of Neuruspora crassa

Mitochondrial porin, the major protein of the outer mitochondrial membrane is synthesized by free cytoplasmic polysomes. The apparent molecular weight of the porin synthesized in homologous or heterologous cell-free systems is the same as that of the mature porin. Transfer in vitro of mitochondrial porin from the cytosolic fraction into the outer membrane of mitochondria could be demonstrated. Before membrane insertion, mitochondrial porin is highly sensitive to added proteinase; afterwards it is strongly protected. Binding of the precursor form to mitochondria occurs at 4°C and appears to precede insertion into the membrane. Unlike transfer of many precursor proteins into or across the inner mitochondrial membrane, assembly of the porin is not dependent on an electrical potential across the inner membrane

The Simplicial Ricci Tensor

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension.Comment: 19 pages, 2 figure