A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At first, we show the existence and the uniqueness of a viscosity solution to this problem. Then we propose a numerical scheme for solving the nonlinear level set equation on unstructured triangulations adapted to the data sample. We show the consistency of this scheme. In addition, we show how to compute nodewise first and second order derivatives. Some application examples of curve or surface construction are provided to illustrate the potential and to demonstrate the accuracy of this method.     

Addendum to the paper "Dead-time free measurement of dipole-dipole interactions between electron spins" by M. Pannier, S. Veit, A. Godt, G. Jeschke, and H.W. Spiess [J. Magn. Reson. 142 (2000) 331-340

The development of four-pulse DEER as described, which has been published in the Journal of Magnetic Resonance more than 10 years ago. The corresponding paper is an example where a slight advance, such as adding a refocusing pulse, which in retrospect looks so simple, can have a remarkable impact on an entire field of science. In our case it offered a simple way to exact measurements of distances between defined species in the nanometer range. The current applications are mainly in determining structures of proteins and nucleic acids.     

TLD measurements and Monte Carlo simulations for glandular dose and scatter fraction assessment in mammography: A comparative study

The main purpose of this study was to validate and compare Mean Glandular Dose (MGD) values obtained using Monte Carlo simulations with experimental values obtained from Entrance Surface Dose (ESD) and depth dose measurements performed in a Hospital mammography unit. ESD and depth dose were measured using ThermoLuminescent Dosimeters (TLDs), and a tissue equivalent mammography phantom recommended by the American College of Radiology (ACR). Measurements and Monte Carlo simulations were also compared with the MGD calculated using the Automatic Exposure Control (AEC) system of the mammographic unit. In the simulations the Doppler energy broadening effect was also taken into account. The simulated ESD are about 5%–10% higher than the measured ESD values. The deviation between the measured and simulated MGD values in the phantom is of about 15%. The MGD evaluated using the AEC system is smaller both with respect to the Monte Carlo simulation and experimental result by a factor of about 15% and 25% respectively. Moreover the BackScatter Factor (BSF) estimated by Monte Carlo simulations was used for the MGD calculation according to the Wu’s method. Finally the inclusion of the energy broadening effect on MGD calculation produces negligible variations on the simulated results.     

An interplay between static potential and Reggeon trajectory for QCD string

I consider two cases where QCD string is described by an effective theory of long strings: the static potential and meson scattering amplitudes in the Regge regime. I show how they can be solved in the mean-field approximation, justified by the large number of space–time dimensions, and argue that it turns out to be exact. I compare contributions from QCD string and perturbative QCD and discuss experimental consequences for the scattering amplitudes.     

Escape process and stochastic resonance under noise intensity fluctuation

We study the effects of noise intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions, mean-first passage time (MFPT) and the spectral amplification factor using a complete set expansion (CSE) technique. We found resonant activation (RA) and stochastic resonance (SR) phenomena in the system under investigation. Moreover, the strength of RA and SR phenomena exhibit non-monotonic behavior and their trade-off relation as a function of the squared variation coefficient of the noise intensity process. The reliability of CSE is verified with Monte Carlo simulations.     

A transportation problem with fuzzy-stochastic cost

In this paper, we consider some transportation problems (TPs) with different types of fuzzy-stochastic unit transportation costs and budget constraints. These fuzzy stochastic costs are reduced to corresponding crisp ones in two different ways. For the first method, using the definition of α$\alpha$-cut of the fuzzy numbers, expectation is taken separately on both lower and upper α$\alpha$-cuts and then mean expectation is calculated with the help of signed distance. In the second procedure, we realize fuzzy random events (ξ?r)$(\xi ?r)$ and (ξ?r)$(\xi ?r)$ for the fuzzy random variable (ξ)$(\xi )$. Using credibility measure of these events, mean chances for the above fuzzy random events are calculated and then expectation is taken to get the crisp expressions. The reduced deterministic problems of the fuzzy stochastic TP are solved using a real coded genetic algorithm with Roulette wheel selection, arithmetic crossover and random mutation. Few numerical examples are demonstrated to find the optimal solutions of the proposed models.     

Mean–variance portfolio selection under a constant elasticity of variance model

This paper discusses a mean–variance portfolio selection problem under a constant elasticity of variance model. A backward stochastic Riccati equation is first considered. Then we relate the solution of the associated stochastic control problem to that of the backward stochastic Riccati equation. Finally, explicit expressions of the optimal portfolio strategy, the value function and the efficient frontier of the mean–variance problem are expressed in terms of the solution of the backward stochastic Riccati equation.     

Arithmetic returns for investment performance measurement

This paper introduces new money-weighted metrics for investment performance analysis, based on arithmetic means of holding period rates weighted by the investment’s market values. This approach generates rates of return which measure a fund’s or portfolio’s performance and a fund manager’s performance. It also enables to show that the Internal Rate of Return (IRR) is a weighted mean of holding period rates associated with interim values which differ from market values, so that value additivity is violated. The manager’s Arithmetic Internal Rate of Return (AIRR) is shown to be the true period equivalent of the cumulative Time Weighted Rate of Return (TWRR), whereas the period TWRR (a geometric return) provides a different ranking. The method is easily generalized for coping with varying benchmark rates. We also cope with the practical problem of estimating interim values whenever they are not available.     

Maximum integrated likelihood estimator of the interest parameter when the nuisance parameter is location or scale

The problem of estimation of an interest parameter in the presence of a nuisance parameter, which is either location or scale, is studied. Two estimators are considered: the usual maximum likelihood estimator and the estimator based on maximization of the integrated likelihood function. The estimators are compared, asymptotically, with respect to the bias and with respect to the mean squared error. The examples are given.