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Computer simulations are a powerful tool in many fields of research. This also applies to the broadly understood analysis of experimental data, which are frequently burdened with multiple imperfections. Often the underlying imprecision or vagueness can be suitably described in terms of fuzzy numbers which enable also the capture of subjectivity. On the other hand, due to the random nature of the experimental data, the tools for their description must take into account their statistical nature. In this way, we come to random fuzzy numbers that model fuzzy data and are also solidly formalized within the probabilistic setting. In this contribution, we introduce the so-called LR random fuzzy numbers that can be used in various Monte-Carlo simulations on fuzzy data. The proposed method of generating fuzzy numbers with membership functions given by probability densities is both simple and rich, well-grounded mathematically, and has a high application potential. [ABSTRACT FROM AUTHOR]

Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms. [ABSTRACT FROM AUTHOR]

Simulated annealing (SA) is a generic optimization method that is quite popular because of its ease of implementation and its global convergence properties. However, SA is widely reported to converge very slowly, and it is common practice to allow extra freedom in its design at the expense of losing global convergence guarantees. A natural way to increase the flexibility of SA is to allow the objective function and the communication mechanism to be temperature-dependent, the idea being to gradually reveal the complexity of the optimization problem and to increase the mixing rate at low temperatures. We call this general class of annealing processes stochastic continuation (SC). In the first part of this paper, we introduce SC starting from SA, and we derive simple sufficient conditions for the global convergence of SC. Our main result is interesting in two respects: first, the conditions for global convergence are surprisingly weak-in particular, they do not involve the variations of the objective function with temperature-and second, exponential cooling makes it possible to be arbitrarily close to the best possible convergence speed exponent of SA. The second part is devoted to the application of SC to the problem of producing aesthetically pleasing drawings of undirected graphs. We consider the objective function defined by Kamada and Kawai (Inf Process Lett 31(1):7-15, ), which measures the quality of a drawing as a weighted sum of squared differences between Euclidean and graph-theoretic inter-vertex distances. Our experiments show that SC outperforms SA with optimal communication setting both in terms of minimizing the objective function and in terms of standard aesthetic criteria. [ABSTRACT FROM AUTHOR]

One of the main limitations to the sensitivity of the infrared camera ISOCAM on-board the Infrared Space Observatory (ISO) comes from responsivity variations and glitches caused by the impacts of charged particles in photo-detectors. Glitch rate measurements, glitch properties and removal methods have already been addressed during the first ISO detector workshop(Madrid, 1998) and published in a special issue of Experimental Astronomy. It appeared that glitch rate and most of glitch properties could be reproduced by Monte-Carlo simulations. This is very interesting in order to predict before launch the effect of charged particles in photo-detectors operated in space. This paper presents results of Monte-Carlo simulations of radiation effects on ISOCAM detectors. Glitch rates, spatial and energetic properties of glitches have been computed and are compared with measured values. [ABSTRACT FROM AUTHOR]

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