Functional renormalization group approach for signal detection
This review paper utilizes renormalization group techniques for signal detection in nearly continuous positive spectra. We emphasize the universal aspects of the analogue field-theory approach. The primary objective is to present an extended self-consistent construction of the analogue effective fie...
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| Format: | Article |
| Language: | English |
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SciPost
2024-12-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.7.4.077 |
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| _version_ | 1846143344982360064 |
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| author | Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti |
| author_facet | Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti |
| author_sort | Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti |
| collection | DOAJ |
| description | This review paper utilizes renormalization group techniques for signal detection in nearly continuous positive spectra. We emphasize the universal aspects of the analogue field-theory approach. The primary objective is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be interpreted as a maximum entropy model. In particular, we leverage universality arguments to justify the $\mathbb{Z}_2$ symmetry of the classical action, highlighting the existence of both a large-scale (local) regime and a small-scale (nonlocal) regime. Secondly, in relation to noise models, we observe the universal relationship between phase transitions and symmetry breaking near the detection threshold. Finally, we address the challenge of defining the covariance matrix for tensor-like data. Based on the cutting graph prescription, we note the superiority of definitions that rely on complete graphs of large size for data analysis. |
| format | Article |
| id | doaj-art-4be82f4c65fc41a6ac4dac64e68e0371 |
| institution | Kabale University |
| issn | 2666-9366 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj-art-4be82f4c65fc41a6ac4dac64e68e03712024-12-02T16:07:33ZengSciPostSciPost Physics Core2666-93662024-12-017407710.21468/SciPostPhysCore.7.4.077Functional renormalization group approach for signal detectionVincent Lahoche, Dine Ousmane Samary, Mohamed TamaazoustiThis review paper utilizes renormalization group techniques for signal detection in nearly continuous positive spectra. We emphasize the universal aspects of the analogue field-theory approach. The primary objective is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be interpreted as a maximum entropy model. In particular, we leverage universality arguments to justify the $\mathbb{Z}_2$ symmetry of the classical action, highlighting the existence of both a large-scale (local) regime and a small-scale (nonlocal) regime. Secondly, in relation to noise models, we observe the universal relationship between phase transitions and symmetry breaking near the detection threshold. Finally, we address the challenge of defining the covariance matrix for tensor-like data. Based on the cutting graph prescription, we note the superiority of definitions that rely on complete graphs of large size for data analysis.https://scipost.org/SciPostPhysCore.7.4.077 |
| spellingShingle | Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti Functional renormalization group approach for signal detection SciPost Physics Core |
| title | Functional renormalization group approach for signal detection |
| title_full | Functional renormalization group approach for signal detection |
| title_fullStr | Functional renormalization group approach for signal detection |
| title_full_unstemmed | Functional renormalization group approach for signal detection |
| title_short | Functional renormalization group approach for signal detection |
| title_sort | functional renormalization group approach for signal detection |
| url | https://scipost.org/SciPostPhysCore.7.4.077 |
| work_keys_str_mv | AT vincentlahochedineousmanesamarymohamedtamaazousti functionalrenormalizationgroupapproachforsignaldetection |