Convergence of nonconforming multigrid methods without full elliptic regularity

We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound () for the contraction number of the -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable -cycle algorithm is an optimal preconditioner.

     

Nucleic acid based biosensors: the desires of the user

The need for nucleic acid based diagnostic tests has increased enormously in the last few years. On the one hand, this has been stimulated by the discovery of new hereditary genetic disease loci following the completion of the Human Genome Project, but also by the presence of new rapidly spreading viral threats, such as that of the SARS epidemic, or even micro-organisms released for the purpose of biological warfare. As in many instances rapid diagnoses of specific target genetic loci is required, new strategies have to be developed, which will allow this to be achieved directly at the point-of-care setting. One of these avenues being explored is that of biosensors. In this review, we provide an overview of the current state of the art concerning the high-throughput analysis of nucleic acids, and address future requirements, which will hopefully be met by new biosensor-based developments.     

Empirical modeling of human face kinematics during speech using motion clustering

In this paper we present an algorithm for building an empirical model of facial biomechanics from a set of displacement records of markers located on the face of a subject producing speech. Markers are grouped into clusters, which have a unique primary marker and a number of secondary markers with an associated weight. Motion of the secondary markers is computed as the weighted sum of the primary markers of the clusters to which they belong. This model may be used to produce facial animations, by driving the primary markers with measured kinematic signals.     

Entanglement interferometry for precision measurement of atomic scattering properties

We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.     

High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip

We show that a concentration of light at a metal tip allows near-field optical imaging of single fluorescent dye molecules at very high resolution, despite strong quenching effects. Details as small as 10 nm were observed in the fluorescence patterns of single Cy-3 dyes bound to the termini of DNA. Data evaluation by model fitting determines the positions of the dyes to an accuracy even better than 1 nm and also yields their 3D orientation. The metal tip simultaneously provides high-resolution topographic imaging complementing the optical signal for a detailed surface examination.     

Korn's inequalities for piecewise vector fields

Korn's inequalities for piecewise vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

     

Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15