Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking
The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using the renormalization group from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to provide a complementary point of view on standard m...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-02-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/3/486 |
| _version_ | 1797441634375303168 |
|---|---|
| author | Vincent Lahoche Dine Ousmane Samary Mohamed Tamaazousti |
| author_facet | Vincent Lahoche Dine Ousmane Samary Mohamed Tamaazousti |
| author_sort | Vincent Lahoche |
| collection | DOAJ |
| description | The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using the renormalization group from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to provide a complementary point of view on standard methods used in data science, especially for open issues. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in Entropy, 23(9), 1132 to reproduce experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></semantics></math></inline-formula>-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes. |
| first_indexed | 2024-03-09T12:25:58Z |
| format | Article |
| id | doaj.art-9a639ef5bfd94361a9ff0ddb43c4aea2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:25:58Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9a639ef5bfd94361a9ff0ddb43c4aea22023-11-30T22:35:18ZengMDPI AGSymmetry2073-89942022-02-0114348610.3390/sym14030486Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry BreakingVincent Lahoche0Dine Ousmane Samary1Mohamed Tamaazousti2Université Paris-Saclay, CEA, List, F-91120 Palaiseau, FranceUniversité Paris-Saclay, CEA, List, F-91120 Palaiseau, FranceUniversité Paris-Saclay, CEA, List, F-91120 Palaiseau, FranceThe large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using the renormalization group from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to provide a complementary point of view on standard methods used in data science, especially for open issues. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in Entropy, 23(9), 1132 to reproduce experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></semantics></math></inline-formula>-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes.https://www.mdpi.com/2073-8994/14/3/486renormalization groupfield theorysymmetry breakingdata analysissignal detection |
| spellingShingle | Vincent Lahoche Dine Ousmane Samary Mohamed Tamaazousti Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking Symmetry renormalization group field theory symmetry breaking data analysis signal detection |
| title | Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking |
| title_full | Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking |
| title_fullStr | Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking |
| title_full_unstemmed | Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking |
| title_short | Signal Detection in Nearly Continuous Spectra and ℤ<sub>2</sub>-Symmetry Breaking |
| title_sort | signal detection in nearly continuous spectra and z sub 2 sub symmetry breaking |
| topic | renormalization group field theory symmetry breaking data analysis signal detection |
| url | https://www.mdpi.com/2073-8994/14/3/486 |
| work_keys_str_mv | AT vincentlahoche signaldetectioninnearlycontinuousspectraandzsub2subsymmetrybreaking AT dineousmanesamary signaldetectioninnearlycontinuousspectraandzsub2subsymmetrybreaking AT mohamedtamaazousti signaldetectioninnearlycontinuousspectraandzsub2subsymmetrybreaking |