Good Lattice Rules in Weighted Korobov Spaces with General Weights

We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found. These conditions are also necessary if the weights are such that the reproducing kernel of the weighted Korobov space is pointwise non-negative. The existence of a lattice rule which achieves the nearly optimal convergence order is proven. A component-by-component (CBC) algorithm that constructs good lattice rules is presented. The resulting lattice rules achieve tractability or strong tractability error bounds and achieve nearly optimal convergence order for suitably decaying weights. We also study special weights such as finite-order and order-dependent weights. For these special weights, the cost of the CBC algorithm is polynomial. Numerical computations show that the lattice rules constructed by the CBC algorithm give much smaller worst-case errors than the mean worst-case errors over all quasi-Monte Carlo rules or over all lattice rules, and generally smaller worst-case errors than the best Korobov lattice rules in dimensions up to hundreds. Numerical results are provided to illustrate the efficiency of CBC lattice rules and Korobov lattice rules (with suitably chosen weights), in particular for high-dimensional finance problems.     

Short universal generators via generalized ratio-of-uniforms method

We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions for a particular generator. The algorithms can be implemented in a few lines of high level language code.

     

PDF and scale uncertainties of various DY distributions in ADD and RS models at hadron colliders

In the extra dimension models of ADD and RS we study the dependence of the various parton distribution functions on observables of Drell–Yan processes to NLO in QCD at LHC and Tevatron energies. Uncertainties at LHC due to factorisation scales in going from leading to next-to-leading order in QCD for the various distributions get reduced by about 2.75 times for a μ_F range 0.5Q<μ_F<1.5Q. Further uncertainties arising from the error on the experimental data are estimated using the MRST parton distribution functions.     

Parametric harmonic-to-fundamental ratio contrast echocardiography: a novel approach to identification and accurate measurement of left ventricular area under variable levels of ultrasound signal attenuation

Objectives

We introduced a harmonic-to-fundamental ratio (HFR) of the radiofrequency (RF) signals that reduces confounding effects of attenuation. We studied whether HFR analysis of RF signals received from contrast microbubbles allows accurate measurement of the left ventricular (LV) cavity area under varying levels of attenuation.

Background

Attenuation is a fundamental problem in ultrasound imaging and limits the use of clinical echocardiography.

Methods

RF data from short axis systolic and diastolic scans were obtained from 14 open-chest dogs following left-atrial bolus of Optison. Attenuation was induced by interposed silicone pads calibrated to induce 7 dB or 14 dB reductions of the backscattered RF signal. RF images were reconstructed from the RF signals, HFR values calculated for each image pixel for 0 dB, 7 dB and 14 dB attenuation conditions, and LV area obtained by summation of “LV cavity pixels”. A reference LV cavity area was obtained from endocardial border tracings in enhanced scans by experts.

Results

Correlation of the HFR-defined and reference areas at systole was R = 0.95, R = 0.94, and R = 0.91 for 0 dB, 7 dB and 14 dB levels of attenuation, respectively, and at diastole was R = 0.95 for 0 dB, 7 dB and 14 dB levels of attenuation. The mean difference from both systolic and diastolic values was <1.45 cm² (i.e. negligible) in all attenuation settings.

Conclusion

Our novel HFR method supports precise measurement of the LV cavity area in contrast images with simulated high attenuation of ultrasound signals.     

Microporous Organically Pillared Layered Silicates (MOPS): A Versatile Class of Functional Porous Materials

The design of microporous hybrid materials, tailored for diverse applications, is a key to address our modern society's imperative of sustainable technologies. Prerequisites are flexible customization of host–guest interactions by incorporating various types of functionality and by adjusting the pore structure. On that score, metal–organic frameworks (MOFs) have been the reference in the past decades. More recently, a new class of microporous hybrid materials emerged, microporous organically pillared layered silicates (MOPS). MOPS are synthesized by simple ion exchange of organic or metal complex cations in synthetic layered silicates. MOFs and MOPSs share the features of “component modularity” and “functional porosity”. While both, MOFs and MOPS maintain the intrinsic characteristics of their building blocks, new distinctive properties arise from their assemblage. MOPS are unique since allowing for simultaneous and continuous tuning of micropores in the sub-Ångström range. Consequently, with MOPS the adsorbent recognition may be optimized without the need to explore different framework topologies. Similar to the third generation of MOFs (also termed soft porous crystals), MOPS are structurally ordered, permanently microporous solids that may also show a reversible structural flexibility above a distinct threshold pressure of certain adsorbents. This structural dynamism of MOPS can be utilized by meticulously adjusting the charge density of the silicate layers to the polarizability of the adsorbent leading to different gate opening mechanisms. The potential of MOPS is far from being fully explored. This Concept article highlights the main features of MOPS and illustrates promising directions for further research.     

Development and experimental validation of a continuum micromechanics model for the elasticity of wood

This contribution covers the development and validation of a microelastic model for wood, based on a four-step homogenization scheme. At a length scale of several tens of nanometers, hemicellulose, lignin, and water are intimately mixed, and build up a polymer (polycrystal-type) network. At a length scale of around one micron, fiberlike aggregates of crystalline and amorphous cellulose are embedded in an contiguous polymer matrix, constituting the so-called cell wall material. At a length scale of about one hundred microns, the material softwood is defined, comprising cylindrical pores (lumen) in the cell wall material of the preceding homogenization step. Finally, at a length scale of several millimeters, hardwood comprises larger cylindrical pores (vessels) embedded in the softwood-type material homogenized before. Model validation rests on statistically and physically independent experiments: The macroscopic stiffness values (of hardwood or softwood) predicted by the micromechanical model on the basis of tissue-independent (‘universal’) phase stiffness properties of hemicellulose, amorphous cellulose, crystalline cellulose, lignin, and water (experimental set I) for tissue-specific composition data (experimental set IIb) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIa).     

Vibrations and buckling of axially loaded stiffened cylindrical shells with elastic restraints

A theory is derived for calculation of the influence of elastic edge restraints on the vibrations and buckling of stiffened cylindrical shells. The stiffeners are considered “smeared” and the edge restraints can be axial, radial, circumferential or rotational. Extensive computations are performed for special kinds of stringer-stiffened shells, and the theoretical predictions are compared with experimental results. A method of definition of equivalent elastically restrained boundary conditions by use of vibration tests is discussed. Application of this technique to tests on 10 shells significantly reduces the scatter in the ratio of experimental to predicted buckling loads.