A new criterion for almost controllable graphs being determined by their generalized spectra
Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Qiu, Lihong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations - Guo, Bangwei ELSEVIER, 2023, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:345 ; year:2022 ; number:11 ; pages:0 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.disc.2022.113060 |
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ELV058658017 |
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| 520 | |a Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. | ||
| 520 | |a Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. | ||
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10.1016/j.disc.2022.113060 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001874.pica (DE-627)ELV058658017 (ELSEVIER)S0012-365X(22)00266-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Qiu, Lihong verfasserin aut A new criterion for almost controllable graphs being determined by their generalized spectra 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Determined by spectrum Elsevier Generalized spectrum Elsevier Rational orthogonal matrix Elsevier Almost controllable graph Elsevier Wang, Wei oth Wang, Wei oth Zhang, Hao oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:345 year:2022 number:11 pages:0 https://doi.org/10.1016/j.disc.2022.113060 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 345 2022 11 0 |
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10.1016/j.disc.2022.113060 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001874.pica (DE-627)ELV058658017 (ELSEVIER)S0012-365X(22)00266-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Qiu, Lihong verfasserin aut A new criterion for almost controllable graphs being determined by their generalized spectra 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Determined by spectrum Elsevier Generalized spectrum Elsevier Rational orthogonal matrix Elsevier Almost controllable graph Elsevier Wang, Wei oth Wang, Wei oth Zhang, Hao oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:345 year:2022 number:11 pages:0 https://doi.org/10.1016/j.disc.2022.113060 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 345 2022 11 0 |
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10.1016/j.disc.2022.113060 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001874.pica (DE-627)ELV058658017 (ELSEVIER)S0012-365X(22)00266-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Qiu, Lihong verfasserin aut A new criterion for almost controllable graphs being determined by their generalized spectra 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Determined by spectrum Elsevier Generalized spectrum Elsevier Rational orthogonal matrix Elsevier Almost controllable graph Elsevier Wang, Wei oth Wang, Wei oth Zhang, Hao oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:345 year:2022 number:11 pages:0 https://doi.org/10.1016/j.disc.2022.113060 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 345 2022 11 0 |
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10.1016/j.disc.2022.113060 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001874.pica (DE-627)ELV058658017 (ELSEVIER)S0012-365X(22)00266-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Qiu, Lihong verfasserin aut A new criterion for almost controllable graphs being determined by their generalized spectra 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. Determined by spectrum Elsevier Generalized spectrum Elsevier Rational orthogonal matrix Elsevier Almost controllable graph Elsevier Wang, Wei oth Wang, Wei oth Zhang, Hao oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:345 year:2022 number:11 pages:0 https://doi.org/10.1016/j.disc.2022.113060 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 345 2022 11 0 |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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A new criterion for almost controllable graphs being determined by their generalized spectra |
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A new criterion for almost controllable graphs being determined by their generalized spectra |
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Qiu, Lihong |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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10.1016/j.disc.2022.113060 |
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a new criterion for almost controllable graphs being determined by their generalized spectra |
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A new criterion for almost controllable graphs being determined by their generalized spectra |
| abstract |
Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. |
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Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. |
| abstract_unstemmed |
Let G be a graph on n vertices with adjacency matrix A ( G ) and let e be the all-one vector. Then the walk-matrix of G is defined as W ( G ) = [ e , A ( G ) e , A 2 ( G ) e , … , A n − 1 ( G ) e ] . We call G controllable if W ( G ) is non-singular and almost controllable if the rank of W ( G ) is n − 1 . In Wang (2017) , the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. |
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A new criterion for almost controllable graphs being determined by their generalized spectra |
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https://doi.org/10.1016/j.disc.2022.113060 |
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Wang, Wei Zhang, Hao |
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