Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure

Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk has to be taken into consideration. On the other hand the premium that the insured pays has to be fair. This fairness is measured by a function of the difference between the risk and the premium paid—we call this function a distance function. For a given small probability of insolvency, we find the premium for each class, such that the distance function is minimized. Next we formulate and solve the dual problem, which is minimizing the insolvency probability under the constraint that the distance function does not exceed a given level. This paper generalizes a previous paper [Zaks, Y., Frostig, E., Levikson, B., 2006. Optimal pricing of a heterogeneous portfolio for a given risk level. Astin Bull. 36 (1), 161–185] where only a square distance function was considered.     

Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in {\mathbb{R}^2}

We consider the linearization of the time-dependent Ginzburg-Landau system near the normal state. We assume that an electric current is applied through the sample, which captures the whole plane, inducing thereby, a magnetic field. We show that independently of the current, the normal state is always stable. Using Fourier analysis the detailed behaviour of solutions is obtained as well. Relying on semi-group theory we then obtain the spectral properties of the steady-state elliptic operator.     

Twist impeded self-diffusion in a cholesteric

Molecular self-diffusion along the pitch axis of a twisted nematic is measured by its motional averaging effect on the deuterium quadrupole interaction. The diffusion constant is found to decrease as the pitch length is decreased. This result is explained by simple phenomenological considerations and is consistent with published viscosity measurements.     

The effect of reverberation on the performance of cepstral mean subtraction in speaker verification

Speaker verification (SVR) performance is degraded under reverberation conditions. Cepstral mean subtraction (CMS) is often applied to the feature vectors in order to compensate for convolutive effects of transmission channels, which are considered to have a short-duration impulse response. The effect of reverberation on the performance of CMS applied to the feature vectors in SVR is investigated. Although CMS was found effective in reducing the effect of reverberation for short reverberation time (RT), in cases of long RT, it is shown that CMS may degrade SVR performance rather than improve it. Hence, CMS should not to be used in these cases. In addition, the effect of the room volume was tested and found less critical than the effect of long RT.     

A note on the variational formulation for quasi-linear initial-value problems

A variational formulation, equivalent to an initial-value problem for nonlinear systems, not necessarily self-adjoint, is derived with applications to linear and nonlinear wave problems and transonic aerodynamics.

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Résumé Nous présentons une formulation variationnelle pour les systèmes quasi-linéaires et leur applications aux ondes non-linéaires et l'écoulement transonique stationnaire.

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Work partially supported by Air-Force Grant No. AFOSR-73-2561.     

Variational multiple-tensor fitting of fiber-ambiguous diffusion-weighted magnetic resonance imaging voxels

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.     

Regularization of diffusion tensor MRI via local coordinates

We propose a novel framework for regularization of symmetric positive-definite (SPD) tensors (e.g., diffusion tensors). This framework is based on differential geometry. The space of SPD matrices, P_n, is described as a Riemannian manifold that is parameterized via the Iwasawa coordinate system. Then, distances on P_n are measured in terms of a natural GL (n)-invariant Riemannian metric. Using the Beltrami framework we construct a set of coupled geometric PDEs with respect to the Iwasawa coordinates. Then, by means of the gradient descent method these equations define the regularization flow over P_n. It appears to be that the local coordinate approach via that coordinate system results in very simple numerics that leads to fast convergence of the algorithm. We demonstrate the efficiency of this algorithm on real volumetric DTI datasets. Results of fibers tractography before and afterthe regularization process arepresented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of varying correlation lengths on Anomalous Transport

Conventional concepts for transport in porous media assume that the heterogeneous distribution of hydraulic conductivities is the source for the contaminant temporal and spatial heavy tail. This tailing, known as anomalous or non-Fickian transport, can be captured by the β parameter in the continuous-time random walk framework. This study shows that with the increase in spatial correlation length between these heterogeneous distributions of hydraulic conductivities, the transport’s anomaly reduces; yet, the β value is unchanged, suggesting a topological component of the conductivity field, captured by the β. This finding is verified by an analysis of the solute transport, showing that the changing conductivity values have a moderate effect on the transport shape.

     

Highly efficient bismuth telluride doped p‐type Pb0.13Ge0.87Te for thermoelectric applications

Bi₂Te₃ doped p‐type Pb_0.13Ge_0.87Te samples were prepared by hot pressing. We report on very high power factor values of ～30 μW/cm K² at 500 °C, as were determined from Seebeck coefficient and electrical resistivity measurements. From dilatometric characterization, the phase transition from the low temperature rhombohedral to the high temperature cubic NaCl structures, takes place at 373 °C. This transition is accompanied by a continuous and gradual change of the lattice parameters, as was observed by hot stage XRD, suggesting a good mechanical durability upon thermal cycling and operating in large thermal gradients.