On the complexity of submodular function minimisation on diamonds

Let (L;?,?) be a finite lattice and let n be a positive integer. A function f:Lⁿ→R is said to be submodular if for all . In this article we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding such that as efficiently as possible. We establish

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  a min–max theorem, which states that the minimum of the submodular function is equal to the maximum of a certain function defined over a certain polyhedron; and

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  a good characterisation of the minimisation problem, i.e., we show that given an oracle for computing a submodular f:Ln→Z and an integer m such that , there is a proof of this fact which can be verified in time polynomial in n and ; and

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  a pseudopolynomial-time algorithm for the minimisation problem, i.e., given an oracle for computing a submodular f:Ln→Z one can find in time bounded by a polynomial in n and .

     

Extracting the invariant model from the feedback paths of digital hearing aids

Feedback whistling is a severe problem with hearing aids. A typical acoustical feedback path represents a wave propagation path from the receiver to the microphone and includes many complicated effects among which some are invariant or nearly invariant for all users and in all acoustical environments given a specific type of hearing aids. Based on this observation, a feedback path model that consists of an invariant model and a variant model is proposed. A common-acoustical-pole and zero model-based approach and an iterative least-square search-based approach are used to extract the invariant model from a set of impulse responses of the feedback paths. A hybrid approach combining the two methods is also proposed. The general properties of the three methods are studied using artificial datasets, and the methods are cross-validated using the measured feedback paths. The results show that the proposed hybrid method gives the best overall performance, and the extracted invariant model is effective in modeling the feedback path.     

Potential solutions to improved sound performance of volume based lightweight multi-storey timber buildings

Lightweight building systems in general suffer from poor sound insulation, especially in the low frequency region. Since no reliable mathematical models that can predict the impact sound pressure level exists, the lightweight building design is to a high extent based upon previous experience and upon measurements. A special difficulty is related to experimental measurements since the variation among identical units must not be neglected. A modern volume based lightweight wooden building concept has here been tested by numerous well controlled measurements, in laboratory as well as in more field like conditions. The volume construction technique offers new possibilities and challenges to improve sound insulation in light weight timber construction. The main purpose was to investigate how different constructional solutions in the floor, like plaster board, mineral wool, elastic glue, dividing board, floating floor etc., affect the sound insulation. Many of the tested modifications resulted in only marginally changed impact sound pressure level but parameters that substantially can improve the sound insulation were found in using elastic glue to mount the floor boards, to install extra board layers and to use floating floors.     

Vocal Fold Vibration and Phonation Start in Aspirated, Unaspirated, and Staccato Onset

Objectives/Hypotheses

Singers learn to produce well-controlled tone onsets by accurate synchronization of glottal adduction and buildup of subglottal pressure. Spectrographic analyses have shown that the higher spectrum partials are present also at the vowel onset in classically trained singers’ performances. Such partials are produced by a sharp discontinuity in the waveform of the transglottal airflow, presumably produced by vocal fold collision.

Study Design

After hearing a prompt series of a triad pattern, six singer subjects sang the same triad pattern on the vowel /i/ (1) preceded by an aspirated /p/, (2) preceded by an unaspirated /p/, and (3) without any preceding consonant in staccato.

Methods

Using high-speed imaging we examined the initiation of vocal fold vibration in aspirated and unaspirated productions of the consonant /p/ as well as in the staccato tones.

Results

The number vibrations failing to produce vocal fold collision were significantly higher in the aspirated /p/ than in the unaspirated /p/ and in the staccato tones. High frequency ripple in the audio waveform was significantly delayed in the aspirated /p/.

Conclusions

Initiation of vocal fold collision and the appearance of high-frequency ripple in the vowel /i/ are slightly delayed in aspirated productions of a preceding consonant /p/.     

New methods for calculating \alpha BB-type underestimators

Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $ BB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existing approaches. The new methods are based on classical eigenvalue bounds from linear algebra and a more recent result on interval matrices. We show how parameters can be optimized with respect to the average underestimation error, in addition to the maximum error commonly used in $\alpha $ BB methods. Numerical comparisons are made, based on test functions and a set of randomly generated interval Hessians. The paper shows the relative strengths of the methods, and proves exact results where one method dominates another.     

Solutions for the storage and handling of SPINE standard pucks

Currently there is no rack system for the long‐term storage of SPINE pucks in spite of their commercial availability and heavy usage at the ESRF. The only way to store pucks is in transport dewar canisters which presents a number of limitations and drawbacks. Here a simple affordable rack for storing SPINE pucks is described, which we believe is accessible to not only synchrotrons but also both academic and industrial research laboratories.     

Plasma brominated polymer particles as grafting substrate for thiol‐terminated telomers

A combined surface activation and “grafting to” strategy was developed to convert divinylbenzene particles into weak cation exchangers suitable for protein separation. The initial activation step was based on plasma modification with bromoform, which rendered the particles amenable to further reaction with nucleophiles by introducing Br to a surface content of 11.2 atom‐%, as determined by X‐ray photoelectron spectroscopy. Grafting of thiol‐terminated glydicyl methacrylate telomers to freshly plasma activated surfaces was accomplished without the use of added initiator, and the grafting was verified both by reduction in bromine content and the appearance of sulfur‐carbon linkages, showing that the surface grafts were covalently bonded. Following grafting the attached glydicyl methacrylate telomer tentacles were further modified by a two‐step procedure involving hydrolysis to 2,3‐hydroxypropyl groups and conversion of hydroxyl groups to carboxylate functionality by succinic anhydride. The final material was capable of baseline separating four model proteins in 3 min by gradient cation exchange chromatography in a fully aqueous eluent.     

A note on the efficiency of the conjugate gradient method for a class of time‐dependent problems

We discuss the efficiency of the conjugate gradient (CG) method for solving a sequence of linear systems; Auⁿ⁺¹ = uⁿ, where A is assumed to be sparse, symmetric, and positive definite. We show that under certain conditions the Krylov subspace, which is generated when solving the first linear system Au¹ = u⁰, contains the solutions {uⁿ} for subsequent time steps. The solutions of these equations can therefore be computed by a straightforward projection of the right‐hand side onto the already computed Krylov subspace. Our theoretical considerations are illustrated by numerical experiments that compare this method with the order‐optimal scheme obtained by applying the multigrid method as a preconditioner for the CG‐method at each time step. Copyright © 2007 John Wiley & Sons, Ltd.     

Determination of mercury in natural samples at the sub-nanogram level using inductively coupled plasma/mass spectrometry after reduction to elemental mercury

Inductively coupled plasma/mass spectrometry was used to determine mercury. Sodium borohydride was used to reduce the mercury to its elemental form, which was purged directly to the plasma using the nebulizer gas. Applications to natural waters and reference sediment are demonstrated. The detection limit, defined as three times the standard deviation of the blank, is 8 pg. The precision at the 100-pg level is 3%. The ability to make isotope dilution measurements is demonstrated.