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Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture
Monte Carlo (MC) simulations allowing to describe photons propagation in statistical mixtures represent an interest that goes way beyond the domain of optics, and can cover, e.g., nuclear reactor physics, image analysis or life science just to name a few. MC simulations are considered a “gold standa...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10279715/ https://www.ncbi.nlm.nih.gov/pubmed/37336902 http://dx.doi.org/10.1038/s41598-023-36919-2 |
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author | Binzoni, Tiziano Mazzolo, Alain |
author_facet | Binzoni, Tiziano Mazzolo, Alain |
author_sort | Binzoni, Tiziano |
collection | PubMed |
description | Monte Carlo (MC) simulations allowing to describe photons propagation in statistical mixtures represent an interest that goes way beyond the domain of optics, and can cover, e.g., nuclear reactor physics, image analysis or life science just to name a few. MC simulations are considered a “gold standard” because they give exact solutions (in the statistical sense), however, in the case of statistical mixtures their implementation is often extremely complex. For this reason, the aim of the present contribution is to propose a new approach that should allow us in the future to simplify the MC approach. This is done through an explanatory example, i.e.; by deriving the ‘exact’ analytical expression for the probability density function of photons’ random steps (single step function, SSF) propagating in a medium represented as a binary (isotropic-Poisson) statistical mixture. The use of the SSF reduces the problem to an ‘equivalent’ homogeneous medium behaving exactly as the original binary statistical mixture. This will reduce hundreds MC simulations, allowing to obtain one set of wanted parameters, to only one equivalent simple MC simulation. To the best of our knowledge the analytically ‘exact’ SSF for a binary (isotropic-Poisson) statistical mixture has never been derived before. |
format | Online Article Text |
id | pubmed-10279715 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-102797152023-06-21 Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture Binzoni, Tiziano Mazzolo, Alain Sci Rep Article Monte Carlo (MC) simulations allowing to describe photons propagation in statistical mixtures represent an interest that goes way beyond the domain of optics, and can cover, e.g., nuclear reactor physics, image analysis or life science just to name a few. MC simulations are considered a “gold standard” because they give exact solutions (in the statistical sense), however, in the case of statistical mixtures their implementation is often extremely complex. For this reason, the aim of the present contribution is to propose a new approach that should allow us in the future to simplify the MC approach. This is done through an explanatory example, i.e.; by deriving the ‘exact’ analytical expression for the probability density function of photons’ random steps (single step function, SSF) propagating in a medium represented as a binary (isotropic-Poisson) statistical mixture. The use of the SSF reduces the problem to an ‘equivalent’ homogeneous medium behaving exactly as the original binary statistical mixture. This will reduce hundreds MC simulations, allowing to obtain one set of wanted parameters, to only one equivalent simple MC simulation. To the best of our knowledge the analytically ‘exact’ SSF for a binary (isotropic-Poisson) statistical mixture has never been derived before. Nature Publishing Group UK 2023-06-19 /pmc/articles/PMC10279715/ /pubmed/37336902 http://dx.doi.org/10.1038/s41598-023-36919-2 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Binzoni, Tiziano Mazzolo, Alain Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture |
title | Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture |
title_full | Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture |
title_fullStr | Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture |
title_full_unstemmed | Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture |
title_short | Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture |
title_sort | probability density function for random photon steps in a binary (isotropic-poisson) statistical mixture |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10279715/ https://www.ncbi.nlm.nih.gov/pubmed/37336902 http://dx.doi.org/10.1038/s41598-023-36919-2 |
work_keys_str_mv | AT binzonitiziano probabilitydensityfunctionforrandomphotonstepsinabinaryisotropicpoissonstatisticalmixture AT mazzoloalain probabilitydensityfunctionforrandomphotonstepsinabinaryisotropicpoissonstatisticalmixture |