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     

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.     

Theory of a Pair of Quantum Bits

In this paper we present a thorough study of the theory of a pair of qubits, whose Hilbert space can be identified with ^{2 2}. Given an hermitian operator of trace 1 in ^{2 2} we focus on the following Problems: Problem 1: Find conditions that guarantee that is a state, that is, positive semidefinite. Problem 2: Find conditions that guarantee that a given state is separable, or that is a convex combination of products of one-particle states. The language we develop for our investigation makes use of the observation that ^{2 2} carries representations of the special unitary group SU(2) in two dimensions and of the direct product of this group by itself. We introduce a new type of observable called Bell observable (section 5) and a new measure of entanglement called concurrence, which is closely related to the concurrence introduced by Wootters (Physical Review Letters (1998) 80, 2245–2248) (section 8). The work has been inspired by the works of Wootters (Physical Review Letters (1997) 78, 5022–5025; Physical Review Letters (1998) 80, 2245–2248) and members of the Horodecki family (cf Horodecki and Horodecki, Physical Review A (1996) 54, 1838–1843; Horodecki et al., Physics Letters A (1996a) 223, 1–8; Physics Letters A (1996b) 222, 21–25) and reproduces some of their results.     

Neuronal expression of muskelin in the rodent central nervous system

Background  

The kelch repeat protein muskelin mediates cytoskeletal responses to the extracellular matrix protein thrombospondin 1, (TSP1), that is known to promote synaptogenesis in the central nervous system (CNS). Muskelin displays intracellular localization and affects cytoskeletal organization in adherent cells. Muskelin is expressed in adult brain and has been reported to bind the Cdk5 activator p39, which also facilitates the formation of functional synapses. Since little is known about muskelin in neuronal tissues, we here analysed the tissue distribution of muskelin in rodent brain and analysed its subcellular localization using cultured neurons from multiple life stages.