Physics-related epistemic uncertainties in proton depth dose simulation

A set of physics models and parameters pertaining to the simulation of proton energy deposition in matter are evaluated in the energy range up to approximately 65 MeV, based on their implementations in the Geant4 toolkit. The analysis assesses several features of the models and the impact of their associated epistemic uncertainties, i.e. uncertainties due to lack of knowledge, on the simulation results. Possible systematic effects deriving from uncertainties of this kind are highlighted; their relevance in relation to the application environment and different experimental requirements are discussed, with emphasis on the simulation of radiotherapy set-ups. By documenting quantitatively the features of a wide set of simulation models and the related intrinsic uncertainties affecting the simulation results, this analysis provides guidance regarding the use of the concerned simulation tools in experimental applications; it also provides indications for further experimental measurements addressing the sources of such uncertainties.Comment: To be published in IEEE Trans. Nucl. Sc

Optimal quantization for the pricing of swing options

In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz algorithm.Comment: 27

Validation Test of Geant4 Simulation of Electron Backscattering

Backscattering is a sensitive probe of the accuracy of electron scattering algorithms implemented in Monte Carlo codes. The capability of the Geant4 toolkit to describe realistically the fraction of electrons backscattered from a target volume is extensively and quantitatively evaluated in comparison with experimental data retrieved from the literature. The validation test covers the energy range between approximately 100 eV and 20 MeV, and concerns a wide set of target elements. Multiple and single electron scattering models implemented in Geant4, as well as preassembled selections of physics models distributed within Geant4, are analyzed with statistical methods. The evaluations concern Geant4 versions from 9.1 to 10.1. Significant evolutions are observed over the range of Geant4 versions, not always in the direction of better compatibility with experiment. Goodness-of-fit tests complemented by categorical analysis tests identify a configuration based on Geant4 Urban multiple scattering model in Geant4 version 9.1 and a configuration based on single Coulomb scattering in Geant4 10.0 as the physics options best reproducing experimental data above a few tens of keV. At lower energies only single scattering demonstrates some capability to reproduce data down to a few keV. Recommended preassembled physics configurations appear incapable of describing electron backscattering compatible with experiment. With the support of statistical methods, a correlation is established between the validation of Geant4-based simulation of backscattering and of energy deposition

A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors

ROOT - A C++ Framework for Petabyte Data Storage, Statistical Analysis and Visualization

ROOT is an object-oriented C++ framework conceived in the high-energy physics (HEP) community, designed for storing and analyzing petabytes of data in an efficient way. Any instance of a C++ class can be stored into a ROOT file in a machine-independent compressed binary format. In ROOT the TTree object container is optimized for statistical data analysis over very large data sets by using vertical data storage techniques. These containers can span a large number of files on local disks, the web, or a number of different shared file systems. In order to analyze this data, the user can chose out of a wide set of mathematical and statistical functions, including linear algebra classes, numerical algorithms such as integration and minimization, and various methods for performing regression analysis (fitting). In particular, ROOT offers packages for complex data modeling and fitting, as well as multivariate classification based on machine learning techniques. A central piece in these analysis tools are the histogram classes which provide binning of one- and multi-dimensional data. Results can be saved in high-quality graphical formats like Postscript and PDF or in bitmap formats like JPG or GIF. The result can also be stored into ROOT macros that allow a full recreation and rework of the graphics. Users typically create their analysis macros step by step, making use of the interactive C++ interpreter CINT, while running over small data samples. Once the development is finished, they can run these macros at full compiled speed over large data sets, using on-the-fly compilation, or by creating a stand-alone batch program. Finally, if processing farms are available, the user can reduce the execution time of intrinsically parallel tasks - e.g. data mining in HEP - by using PROOF, which will take care of optimally distributing the work over the available resources in a transparent way