Ιδρυματικό Αποθετήριο
Πολυτεχνείο Κρήτης
Πολυτεχνείο Κρήτης
EN
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| URI | http://purl.tuc.gr/dl/dias/F4FC4C25-B05A-4074-9397-2D7A154486E5 | - |
| Αναγνωριστικό | https://doi.org/10.1090/tpms/1180 | - |
| Αναγνωριστικό | https://www.ams.org/journals/tpms/2022-107-00/S0094-9000-2022-01180-8/ | - |
| Γλώσσα | en | - |
| Μέγεθος | 24 pages | en |
| Τίτλος | Boltzmann–Gibbs random fields with mesh-free precision operators based on smoothed particle hydrodynamics | en |
| Δημιουργός | Christopoulos Dionysios | en |
| Δημιουργός | Χριστοπουλος Διονυσιος | el |
| Εκδότης | Taras Shevchenko National University of Kyiv | en |
| Περίληψη | Boltzmann–Gibbs random fields are defined in terms of the exponential expression, where is a suitably defined energy functional of the field states. This paper presents a new Boltzmann–Gibbs model which features local interactions in the energy functional. The interactions are embodied in a spatial coupling function which uses smoothed kernel-function approximations of spatial derivatives inspired from the theory of smoothed particle hydrodynamics. A specific model for the interactions based on a second-degree polynomial of the Laplace operator is studied. An explicit, mesh-free expression of the spatial coupling function (precision function) is derived for the case of the squared exponential (Gaussian) smoothing kernel. This coupling function allows the model to seamlessly extend from discrete data vectors to continuum fields. Connections with Gaussian Markov random fields and the Matérn field with are established. | en |
| Τύπος | Peer-Reviewed Journal Publication | en |
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | el |
| Άδεια Χρήσης | http://creativecommons.org/licenses/by/4.0/ | en |
| Ημερομηνία | 2024-02-08 | - |
| Ημερομηνία Δημοσίευσης | 2022 | - |
| Θεματική Κατηγορία | Random fields | en |
| Θεματική Κατηγορία | Kernel functions | en |
| Θεματική Κατηγορία | Precision matrix | en |
| Θεματική Κατηγορία | Smoothed particle hydrodynamics | en |
| Βιβλιογραφική Αναφορά | D. T. Hristopulos, “Boltzmann–Gibbs random fields with mesh-free precision operators based on smoothed particle hydrodynamics,” Theor. Probability and Math. Statist., vol. 107, pp. 37-60, 2022, doi: 10.1090/tpms/1180. | en |
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