Superselection sectors and the structure of fusion rule algebras

1993 ◽  
pp. 45-101
Author(s):  
Jürg Fröhlich ◽  
Thomas Kerler
Keyword(s):  
Fusion Rule

Censoring Based Mixed Fusion Rule

2011 ◽  
Vol 30 (1) ◽  
pp. 159-162 ◽  
Author(s):  
Xiang-yang Liu ◽  
Ying-ning Peng
Keyword(s):  
Fusion Rule

ON ROBERTS’ PROOF OF THE TURAEV-WALKER THEOREM

1996 ◽  
Vol 05 (04) ◽  
pp. 427-439 ◽  
Author(s):  
RICCARDO BENEDETTI ◽  
CARLO PETRONIO
Keyword(s):  
Euler Characteristic ◽  
A Priori ◽  
Algebraic Approach ◽  
Fusion Rule ◽  
Point Of View ◽  
Witten Invariant ◽  
Manifolds With Boundary ◽  
3 Dimensional ◽  
Skein Theory ◽  
Natural Way

In this paper we discuss the beautiful idea of Justin Roberts [7] (see also [8]) to re-obtain the Turaev-Viro invariants [11] via skein theory, and re-prove elementarily the Turaev-Walker theorem [9], [10], [13]. We do this by exploiting the presentation of 3-manifolds introduced in [1], [4]. Our presentation supports in a very natural way a formal implementation of Roberts’ idea. More specifically, what we show is how to explicitly extract from an o-graph (the object by which we represent a manifold, see below), one of the framed links in S3 which Roberts uses in the construction of his invariant, and a planar diagrammatic representation of such a link. This implies that the proofs of invariance and equality with the Turaev-Viro invariant can be carried out in a completely “algebraic” way, in terms of a planar diagrammatic calculus which does not require any interpretation of 3-dimensional figures. In particular, when proving the “term-by-term” equality of the expansion of the Roberts invariant with the state sum which gives the Turaev-Viro invariant, we simultaneously apply several times the “fusion rule” (which is formally defined, strictly speaking, only in diagrammatic terms), showing that the “braiding and twisting” which a priori may exist on tetrahedra is globally dispensable. In our point of view the success of this formal “algebraic” approach witnesses a certain efficiency of our presentation of 3-manifolds via o-graphs. In this work we will widely use recoupling theory which was very clearly exposed in [2], and therefore we will avoid recalling notations. Actually, for the purpose of stating and proving our results we will need to slightly extend the class of trivalent ribbon diagrams on which the bracket can be computed. We also address the reader to the references quoted in [2], in particular for the fundamental contributions of Lickorish to this area. In our approach it is more natural to consider invariants of compact 3-manifolds with non-empty boundary. The case of closed 3-manifolds is included by introducing a correction factor corresponding to boundary spheres, as explained in §2. Our main result is actually an extension to manifolds with boundary of the Turaev-Walker theorem: we show that the Turaev-Viro invariant of such a manifold coincides (up to a factor which depends on the Euler characteristic) with the Reshetikhin-Turaev-Witten invariant of the manifold mirrored in its boundary.

scholarly journals Interpretable Detection and Location of Myocardial Infarction Based on Ventricular Fusion Rule Features

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Wenzhi Zhang ◽  
Runchuan Li ◽  
Shengya Shen ◽  
Jinliang Yao ◽  
Yan Peng ◽  
...  
Keyword(s):  
Myocardial Infarction ◽  
Clinical Decision Making ◽  
Human Life ◽  
Principal Component ◽  
Fusion Rule ◽  
Clinical Decision ◽  
Gradient Boosting ◽  
Discrete Wavelet ◽  
Extreme Gradient Boosting ◽  
Ventricular Activity

Myocardial infarction (MI) is one of the most common cardiovascular diseases threatening human life. In order to accurately distinguish myocardial infarction and have a good interpretability, the classification method that combines rule features and ventricular activity features is proposed in this paper. Specifically, according to the clinical diagnosis rule and the pathological changes of myocardial infarction on the electrocardiogram, the local information extracted from the Q wave, ST segment, and T wave is computed as the rule feature. All samples of the QT segment are extracted as ventricular activity features. Then, in order to reduce the computational complexity of the ventricular activity features, the effects of Discrete Wavelet Transform (DWT), Principal Component Analysis (PCA), and Locality Preserving Projections (LPP) on the extracted ventricular activity features are compared. Combining rule features and ventricular activity features, all the 12 leads features are fused as the ultimate feature vector. Finally, eXtreme Gradient Boosting (XGBoost) is used to identify myocardial infarction, and the overall accuracy rate of 99.86% is obtained on the Physikalisch-Technische Bundesanstalt (PTB) database. This method has a good medical diagnosis basis while improving the accuracy, which is very important for clinical decision-making.

scholarly journals An Efficient PET-MRI Medical Image Fusion based on IHS-NSCT-PCA Integrated Method

2019 ◽  
Vol 9 (2) ◽  
pp. 2073-2079
Keyword(s):  
Structural Data ◽  
Fusion Rule ◽  
Integrated Approach ◽  
Disease Diagnosis ◽  
Weighted Averaging ◽  
Fusion Algorithm ◽  
Integrated Method ◽  
Histogram Matching ◽  
Multiple Imaging ◽  
Fused Image

Merging of multiple imaging modalities leads to a single image that acquire high information content. These find useful applications in disease diagnosis and treatment planning. IHS-PCA method is a spatial domain approach for fusion that offersfinestvisibility but demands vast memory and it lacks steering information. We propose an integrated approach that incorporates NSCT combined with PCA utilizing IHS space and histogram matching. The fusion algorithm is applied on MRI with PET image and improved functional property was obtained. The IHS transform is a sharpening technique that converts multispectral image from RGB channels to Intensity Hue and Saturation independent values. Histogram matching is performed with intensity values of the two input images. Pathological details in images can be emphasized in multi-scale and multi-directions by using PCA withNSCT. Fusion rule applied is weighted averaging andprincipal components are used for dimensionality reduction. Inverse NSCT and Inverse IHS are performed so as to obtain the fused image in new RGB space. Visual and subjective investigation is compared with existing methods which demonstrate that our proposed technique gives high structural data content with high spatial and spectral resolution compared withearlier methods.

Design of a decision fusion rule for power system security assessment

1993 ◽  
Vol 8 (3) ◽  
pp. 858-864 ◽  
Author(s):  
J.-C. Chow ◽  
Q. Zhu ◽  
R. Fischl ◽  
M. Kam
Keyword(s):  
Power System ◽  
System Security ◽  
Fusion Rule ◽  
Decision Fusion ◽  
Security Assessment ◽  
Power System Security
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