A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Non-uniform data distribution for communication-efficient parallel clustering

Global communicationrequirements andloadimbalanceof someparalleldataminingalgorithms arethe major obstacles to exploitthe computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication costin parallel data mining algorithms and, in particular, in the k-means algorithm for cluster analysis. In the straightforward parallel formulation of the k-means algorithm, data and computation loads are uniformly distributed over the processing nodes. This approach has excellent load balancing characteristics that may suggest it could scale up to large and extreme-scale parallel computing systems. However, at each iteration step the algorithm requires a global reduction operationwhichhinders thescalabilityoftheapproach.Thisworkstudiesadifferentparallelformulation of the algorithm where the requirement of global communication is removed, while maintaining the same deterministic nature ofthe centralised algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real-world distributed applications or can be induced by means ofmulti-dimensional binary searchtrees. The approachcanalso be extended to accommodate an approximation error which allows a further reduction ofthe communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing element

Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

The response of a uniform horizontal temperature gradient to heating

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

Finite element approximation of a sixth order nonlinear degenerate parabolic equation

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)? 2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

Quantitative proteomics using uniform 15N-labeling, mascot and the trans-proteomic pipeline

Stable isotope labeling combined with MS is a powerful method for measuring relative protein abundances, for instance, by differential metabolic labeling of some or all amino acids with 14N and 15N in cell culture or hydroponic media. These and most other types of quantitative proteomics experiments using high-throughput technologies, such as LC-MS/MS, generate large amounts of raw MS data. This data needs to be processed efficiently and automatically, from the mass spectrometer to statistically evaluated protein identifications and abundance ratios. This paper describes in detail an approach to the automated analysis of uniformly 14N/15N-labeled proteins using MASCOT peptide identification in conjunction with the trans-proteomic pipeline (TPP) and a few scripts to integrate the analysis workflow. Two large proteomic datasets from uniformly labeled Arabidopsis thaliana were used to illustrate the analysis pipeline. The pipeline can be fully automated and uses only common or freely available software.

Infrared intensities of furan, pyrrole and thiophene: beyond the double harmonic approximation

Infrared intensities of the fundamental, overtone and combination transitions in furan, pyrrole and thiophene have been calculated using the variational normal coordinate code MULTIMODE. We use pure vibrational wavefunctions, and quartic force fields and cubic dipole moment vector surfaces, generated by density functional theory. The results are compared graphically with second-order perturbation calculations and with relative intensities from experiment for furan and pyrrole.

Two new mu-(1,3-azido)-bridged polymers: alternating single and double bridges in a 1D nickel(II) complex and uniform bridge in a 2D copper(II) complex: Syntheses, single-crystal structures and magnetic studies

Two polymeric azido bridged complexes [Ni2L2(N-3)(3)](n)(ClO4). (1) and [Cu(bpdS)(2)(N-3)],(ClO4),(H2O)(2.5n) (2) [L = Schiff base, obtained from the condensation of pyridine-2-aldehyde with N,N,2,2-tetramethyl-1,3-propanediamine; bpds = 4,4'-bipyridyl disulfide] have been synthesized and their crystal structures have been determined. Complex 1, C26H42ClN15Ni2O4, crystallizes in a triclinic system, space group P1 with a 8.089(13), b = 9.392(14), c = 12.267(18) angstrom, a = 107.28(l), b 95.95(1), gamma = 96.92(1)degrees and Z = 2; complex 2, C20H21ClCuN7O6.5S4, crystallizes in an orthorhombic system, space group Pnna with a = 10.839(14), b = 13.208(17), c = 19.75(2) angstrom and Z = 4. The crystal structure of I consists of 1D polymers of nickel(L) units, alternatively connected by single and double bridging mu-(1,3-N-3) ligand with isolated perchlorate anions. Variable temperature magnetic susceptibility data of the complex have been measured and the fitting,of magnetic data was carried out applying the Borris-Almenar formula for such types of alternating one-dimensional S = 1 systems, based on the Hamiltonian H = -J Sigma(S2iS2i-1 + aS(2i)S(2i+1)). The best-fit parameters obtained are J = -106.7 +/- 2 cm(-1); a = 0.82 +/- 0.02; g = 2.21 +/- 0.02. Complex 2 is a 2D network of 4,4 topology with the nodes occupied by the Cu-II ions, and the edges formed by single azide and double bpds connectors. The perchlorate anions are located between pairs of bpds. The magnetic data have been fitted considering the complex as a pseudo-one-dimensional system, with all copper((II)) atoms linked by [mu(1,3-azido) bridging ligands at axial positions (long Cu...N-3 distances) since the coupling through long bpds is almost nil. The best-fit parameters obtained with this model are J = -1.21 +/- 0.2 cm(-1), g 2.14 +/- 0.02. (c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005).

Quantitative proteomics using uniform N-15-labeling, MASCOT, and the trans-proteomic pipeline

Stable isotope labeling combined with MS is a powerful method for measuring relative protein abundances, for instance, by differential metabolic labeling of some or all amino acids with N-14 and N-15 in cell culture or hydroponic media. These and most other types of quantitative proteomics experiments using high-throughput technologies, such as LC-MS/MS, generate large amounts of raw MS data. This data needs to be processed efficiently and automatically, from the mass spectrometer to statistically evaluated protein identifications and abundance ratios. This paper describes in detail an approach to the automated analysis of Uniformly N-14/N-15-labeled proteins using MASCOT peptide identification in conjunction with the trans-proteomic pipeline (TPP) and a few scripts to integrate the analysis workflow. Two large proteomic datasets from uniformly labeled Arabidopsis thaliana were used to illustrate the analysis pipeline. The pipeline can be fully automated and uses only common or freely available software.

A relative path attenuation approximation algorithm for DVB-T systems

In the United Kingdom and in fact throughout Europe, the chosen standard for digital terrestrial television is the European Telecommunications Standards Institute (ETSI) ETN 300 744 also known as Digital Video Broadcasting - Terrestrial (DVB-T). The modulation method under this standard was chosen to be Orthogonal Frequency Division Multiplex (0FD4 because of the apparent inherent capability for withstanding the effects of multipath. Within the DVB-T standard, the addition of pilot tones was included that can be used for many applications such as channel impulse response estimation or local oscillator phase and frequency offset estimation. This paper demonstrates a technique for an estimation of the relative path attenuation of a single multipath signal that can be used as a simple firmware update for a commercial set-top box. This technique can be used to help eliminate the effects of multipath(1).