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.     

Estimation of level set trees using adaptive partitions

We present methods for the estimation of level sets, a level set tree, and a volume function of a multivariate density function. The methods are such that the computation is feasible and estimation is statistically efficient in moderate dimensional cases (\(d\approx 8\)) and for moderate sample sizes (\(n\approx \) 50,000). We apply kernel estimation together with an adaptive partition of the sample space. We illustrate how level set trees can be applied in cluster analysis and in flow cytometry.     

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.     

Management of legacy nutrient stores through nitrogen and phosphorus fertilization,catch crops,and gypsum treatment

We develop a modeling framework, based on discrete-time dynamic optimization, to study the effect of legacy nutrient stores and soil nutrient dynamics on optimal nutrient management and agri-environmental policy in crop production. Three alternative measures are studied to reduce nutrient loss: reduced fertilization, nonlegume catch crop cultivation and gypsum amendment. According to our results, landowner can bring down excessively high phosphorus stocks causing environmental damage within decades, by simultaneous optimization of the nitrogen and phosphorus fertilizers on the economic basis of profit maximization. Our results suggest that nitrogen loss abatement with catch crops is socially optimal, whereas the use of gypsum is well justified as a temporary measure on soils with high soil phosphorus levels. A dynamic tax-subsidy-scheme, which takes into account the current soil nutrient levels and field attributes such as soil texture, can enforce the socially optimal outcome. The welfare losses of the static steady-state-based tax-subsidy-schemes are increasing functions of the legacy nutrient stores and soil's ability to hold nutrients. Recommendations for Resource Managers

• We develop a modeling framework to study the effect of the legacy nutrient stores and the soil nutrient dynamics on the optimal nutrient management and agri-environmental policy in crop production.
• Nonlegume catch crop cultivation is a socially optimal long-term measure for nitrogen loss abatement, whereas phosphorus loss abatement with gypsum is socially optimal on soils with high soil phosphorus levels.
• A dynamic tax-subsidy-scheme, which is adjusted annually according to the soil nutrient stocks, leads to social optimum. Although this can be difficult to implement in practice, it can be useful in the derivation of the simpler, static tax-subsidy-schemes.
• If a gypsum subsidy is paid for those years, where the soil P level is above the threshold level for the gypsum application, the welfare loss of the static steady-state-based tax-subsidy-schemes is almost zero.
• Simultaneous adjustment of the N and P fertilizer rates enables the use of simple, static and soil-texture-ignorant tax-subsidy schemes, without a notable social welfare loss

     

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.     

Correlated adiabatic and isocurvature cosmic microwave background fluctuations in the wake of the results from the wilkinson microwave anisotropy probe

In general correlated models, in addition to the usual adiabatic component with a spectral index n(ad1) there is another adiabatic component with a spectral index n(ad2) generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature cosmic microwave background fluctuations of the Wilkinson Microwave Anisotropy Probe (WMAP) group, who set the two adiabatic spectral indices equal. Allowing n(ad1) and n(ad2) to vary independently we find that the WMAP data favor models where the two adiabatic components have opposite spectral tilts. Using the WMAP data only, the 2sigma upper bound for the isocurvature fraction f(iso) of the initial power spectrum at k(0)=0.05 Mpc(-1) increases somewhat, e.g., from 0.76 of n(ad2)=n(ad1) models to 0.84 with a prior n(iso)<1.84 for the isocurvature spectral index.