Quasihyperbolic geodesics in convex domains

We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesies are quasiconvex in the norm metric in convex domains in all normed spaces.     

Algorithms for manipulation of level sets of nonparametric density estimates

Summary  We present algorithms for finding the level set tree of a multivariate density estimate. That is, we find the separated components of level sets of the estimate for a series of levels, gather information on the separated components, such as volume and barycenter, and present the information together with the tree structure of the separated components. The algorithm proceeds by first building a binary tree which partitions the support of the density estimate, followed by bottom-up travels of this tree during which we join those parts of the level sets which touch each other. As a byproduct we present an algorithm for evaluating a kernel estimate on a large multidimensional grid. Since we find the barycenters of the separated components of the level sets also for high levels, our method finds the locations of local extremes of the estimate. Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/8-1.     

Optimality with telecommunications network

This paper studies a telecommunications company's optimal networkinvestment strategies. The objective of the company is to maximizethe value of the network. According to our numerical exampleswe are not able to consider a single point-to-point connectionseparately from the network, because the network demands andcapacities affect each other. Therefore, the whole network structurehas to be considered in the point-to-point investments.     

Low temperature nanoparticle sintering with continuous wave and pulse lasers

New manufacturing methods are being sought for electronics production. Printable electronics is a promising method for producing low cost and large-scale electronics. In printable electronics nanoparticle inks printed on the surface of substrate contain additives, such as dispersing agent and carrier fluids that provide good printing properties by changing the viscosity and separating the nanoparticles of the ink. In the sintering process ink particles are heated to a certain, ink-specific temperature. During the sintering process the carrier fluid and dispersing agents are evaporated from the ink. Additional heating after evaporation causes the nanoparticles to start to agglomerate. A small particle size allows the use of a considerably lower sintering temperature than with bulk silver, for example 220 °C. The sintering process is usually utilized with a convection oven, with a long sintering time, and the thermal load on the surrounding material can become too great as components and patterns are formed from layers of different type inks. Hence, alternative sintering methods are sought. This paper describes tests done with two different types of laser; pulsed and continuous wave lasers. Laser sintering enables short sintering times and selective sintering, making it possible for printed structures to contain fragile active components produced with other technologies.     

An Inverse Problem of Calderón Type with Partial Data

A generalized variant of the Calderón problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension n ≥ 2. The following two results are shown: (i) The selfadjoint Dirichlet operator associated with an elliptic differential expression on a bounded Lipschitz domain is determined uniquely up to unitary equivalence by the knowledge of the Dirichlet-to-Neumann map on an open subset of the boundary, and (ii) the Dirichlet operator can be reconstructed from the residuals of the Dirichlet-to-Neumann map on this subset.     

Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions

We prove, that a Hamiltonian with infinitely many δ-point interactions in the plane can be approximated in the norm resolvent sense by a family of Schrödinger operators with regular, local scaled short-range potentials. Similar well known results from the 1D and the 3D case are complemented thereby. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automatic statistical shape analysis of cerebral asymmetry in 3D T1-weighted magnetic resonance images at vertex-level: Application to neuroleptic-naïve schizophrenia

The study of the structural asymmetries in the human brain can assist the early diagnosis and progression of various neuropsychiatric disorders, and give insights into the biological bases of several cognitive deficits. The high inter-subject variability in cortical morphology complicates the detection of abnormal asymmetries especially if only small samples are available. This work introduces a novel automatic method for the local (vertex-level) statistical shape analysis of gross cerebral hemispheric surface asymmetries which is robust to the individual cortical variations. After segmentation of the cerebral hemispheric volumes from three-dimensional (3D) T1-weighted magnetic resonance images (MRI) and their spatial normalization to a common space, the right hemispheric masks were reflected to match with the left ones. Cerebral hemispheric surfaces were extracted using a deformable model-based algorithm which extracted the salient morphological features while establishing the point correspondence between the surfaces. The interhemispheric asymmetry, quantified by customized measures of asymmetry, was evaluated in a few thousands of corresponding surface vertices and tested for statistical significance.     

Preoperative localization of the sensorimotor area using independent component analysis of resting-state fMRI

Analysis of resting-state functional magnetic resonance imaging (fMRI) data is based on detecting low-frequency signal fluctuations in functionally connected brain areas. These synchronous fluctuations in resting-state networks have been observed in several studies with healthy subjects. In this study, we explored if independent component analysis (ICA) can be used to localize the sensorimotor area from resting-state fMRI data in patients with brain tumors. Finger-tapping activation task and resting-state blood-oxygenation-level-dependent fMRI data were acquired from 8 patients with brain tumors and 10 healthy volunteers. Sensorimotor task independent components (IC_task) were used to verify resting-state independent components (IC_rest) individually. In addition, sensorimotor IC_rests were compared between the groups and no significant differences were detected in volume, spatial correlation or temporal correlation. These results show that it is possible to localize a sensorimotor area from resting-state data using ICA in patients with brain tumors. This offers a complementary method for assessing the sensorimotor area in subjects with brain tumors who have difficulties in performing motor paradigms.     

Lattice Boltzmann Simulation of Flow-Induced Wall Shear Stress in Porous Media

The lattice Boltzmann method is increasingly utilized in the simulation of flow-induced wall shear stress needed in various applications. In image-based flow simulations, the simulation geometry is usually based on a three-dimensional reconstruction of the true structure of the pore space obtained, for example, by X-ray tomography. The geometry is then given in a voxel-based representation, which complicates an accurate determination of the surface-normal vectors that are necessary in the computation of the wall shear stress. To avoid this problem, we introduce here a method for the determination of surface-normal vectors directly from a greyscale image instead of its segmented binary image version. The proposed method is fast and automatic, and it can be used for an arbitrary pore space geometry provided in a greyscale form by any imaging modality. We show that this method can produce accurate surface-normal vectors even for binary images and that their accuracy is further increased when the original greyscale images are used instead. We compute wall shear stresses for generated benchmark geometries and then demonstrate the utility of the method for soil samples with ‘random’ pores imaged by X-ray tomography.     

BRUTUS: optimization of a grid-based similarity function for rigid-body molecular superposition. II. Description and characterization

Finding novel lead molecules is one of the primary goals in early phases of drug discovery projects. However, structurally dissimilar compounds may exhibit similar biological activity, and finding new and structurally diverse lead compounds is difficult for computer algorithms. Molecular energy fields are appropriate for finding structurally novel molecules, but they are demanding to calculate and this limits their usefulness in virtual screening of large chemical databases. In our approach, energy fields are computed only once per superposition and a simple interpolation scheme is devised to allow coarse energy field lattices having fewer grid points to be used without any significant loss of accuracy. The resulting processing speed of about 0.25 s per conformation on a 2.4 GHz Intel Pentium processor allows the method to be used for virtual screening on commonly available desktop machines. Moreover, the results indicate that grid-based superposition methods could be efficiently used for the virtual screening of compound libraries.