Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

Activity of microemulsion-based nanoparticles at the human bio-nano interface: concentration-dependent effects on thrombosis and hemolysis in whole blood

Background: Although microemulsion-based nanoparticles (MEs) may be useful for drug delivery or scavenging, these benefits must be balanced against potential nanotoxicological effects in biological tissue (bio-nano interface). We investigated the actions of assembled MEs and their individual components at the bio-nano interface of thrombosis and hemolysis in human blood. Methods: Oil-in-water MEs were synthesized using ethylbutyrate, sodium caprylate, and pluronic F-68 (ME4) or F-127 (ME6) in 0.9% NaCl_w/v. The effects of MEs or components on thrombosis were determined using thrombo-elastography, platelet contractile force, clot elastic modulus, and platelet counting. For hemolysis, ME or components were incubated with erythrocytes, centrifuged, and washed for measurement of free hemoglobin by spectroscopy. Results and conclusions: The mean particle diameters (polydispersity index) for ME6 and ME4 were 23.6 ± 2.5 nm (0.362) and 14.0 ± 1.0 nm (0.008), respectively. MEs (0, 0.03, 0.3, 3 mM) markedly reduced the thromboelastograph maximal amplitude in a concentration-dependent manner (49.0 ± 4.2, 39.0 ± 5.6, 15.0 ± 8.7, 3.8 ± 1.3 mm, respectively), an effect highly correlated (r2 = 0.94) with similar changes caused by pluronic surfactants (48.7 ± 10.9, 30.7 ± 15.8, 20.0 ± 11.3, 2.0 ± 0.5) alone. Neither oil nor sodium caprylate alone affected the thromboelastograph. The clot contractile force was reduced by ME (27.3 ± 11.1–6.7 ± 3.4 kdynes/cm², P = 0.02, n = 5) whereas the platelet population not affected (175 ± 28–182 ± 23 10⁶/ml, P = 0.12, n = 6). This data suggests that MEs reduced platelet activity due to associated pluronic surfactants, but caused minimal changes in protein function necessary for coagulation. Although pharmacological concentrations of sodium caprylate caused hemolysis (EC₅₀ = 213 mM), MEs and pluronic surfactants did not disrupt erythrocytes. Knowledge of nanoparticle activity and potential associated nanotoxicity at this bio-nano interface enables rational ME design for in vivo applications.     

Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x _s ] which predicts a stronger than linear time dependence of Var[x _s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS: 05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics     

Derivations in Commutative Regular Algebras

Mathematical Notes -     

Electronic transport properties of bismuth nanobridges through silicon-nitride membranes

The electronic transport through nanostructured bismuth nanobridges has been investigated at low temperatures (T<2 K) and in magnetic fields B up to 8.5 T. The samples show reproducible resistance fluctuations as a function of B, superimposed on a large magnetoresistance of up to 50%. In addition, time-dependent resistance fluctuations in zero magnetic field demonstrate the presence of bistable scatterers in the constriction region of our samples, which are described by two-level systems. Their dynamics are shown to be sensitive to subtle modifications of the static scatterer configuration in their vicinity, which cannot be detected in the sample magnetofingerprint.     

A representation of the Belavkin equation via Feynman path integrals

 The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the complex Cameron-Martin space is given. Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002 Mathematics Subject Classification (2000): 81, 81S40, 60H15 Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals     

Beryllium (boron) clustering quest in relativistic multifragmentation (BECQUEREL Project)

A physical program of irradiation of emulsions in beams of relativistic nuclei named the BECQUEREL Project is reviewed. It is destined to study in detail the processes of relativistic fragmentation of light radioactive and stable nuclei. The expected results would make it possible to answer some topical questions concerning the cluster structure of light nuclei. Owing to the best spatial resolution, the nuclear emulsions would enable one to obtain unique and evident results. The most important irradiations will be performed in the secondary beams of He, Be, B, C, and N radioactive nuclei formed on the basis of JINR Nuclotron beams of stable nuclei. We present results on the charged state topology of relativistic fragmentation of the ¹⁰B nucleus at low energy-momentum transfers as the first step of the research.     

Crystallographic report: A new polymorph for bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The title compound is a centrosymmetric dimer with each cadmium in a distorted CdS₅ square pyramidal geometry. The Cd–S bond distances range from 2.5626(11) to 2.8459(11) Å. Copyright © 2004 John Wiley & Sons, Ltd.