Perfect codes in direct graph bundles

2015 ◽  
Vol 115 (9) ◽  
pp. 707-711 ◽  
Author(s):  
Irena Hrastnik Ladinek ◽  
Janez Žerovnik
Keyword(s):  
2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Giselle Strey ◽  
João E. Strapasson ◽  
Sueli I. R. Costa

2009 ◽  
Vol 57 (4) ◽  
pp. 873-878 ◽  
Author(s):  
Haider Al-Lawati ◽  
Fady Alajaji
Keyword(s):  

2019 ◽  
Vol 223 (3) ◽  
pp. 931-947 ◽  
Author(s):  
Sanming Zhou
Keyword(s):  

2017 ◽  
Vol 63 (7) ◽  
pp. 4325-4331 ◽  
Author(s):  
Tao Zhang ◽  
Gennian Ge
Keyword(s):  

Author(s):  
Levon Arsalanyan ◽  
Hayk Danoyan

The Nearest Neighbor search algorithm considered in this paper is well known (Elias algorithm). It uses error-correcting codes and constructs appropriate hash-coding schemas. These schemas preprocess the data in the form of lists. Each list is contained in some sphere, centered at a code-word. The algorithm is considered for the cases of perfect codes, so the spheres and, consequently, the lists do not intersect. As such codes exist for the limited set of parameters, the algorithm is considered for some other generalizations of perfect codes, and then the same data point may be contained in different lists. A formula of time complexity of the algorithm is obtained for these cases, using coset weight structures of the mentioned codes


EP Europace ◽  
2021 ◽  
Vol 23 (Supplement_3) ◽  
Author(s):  
L Lowie ◽  
E Van Nieuwenhuyse ◽  
J Sanchez ◽  
A Panfilov ◽  
S Knecht ◽  
...  

Abstract Funding Acknowledgements Type of funding sources: None. Background Entrainment mapping (EM) is an important tool to determine the mechanism of complex reentrant atrial tachycardias (ATs), mostly to distinguish dominant from bystander reentrant loops. However, entrainment maneuvers are challenging, time consuming and risk to end the tachycardia.  Purpose Recently, we developed a novel method Directed Graph Mapping (DGM), using concepts of network theory, allowing to automatically determine AT reentry loops from the local activation times (LAT) of any clinical mapping system. DGM showed good performance: it correctly finds ablation target (100 % success rate) on simple AT cases and could automatically determine reentry loops confirmed by the expert electrophysiologist with EM in complex AT cases. Out of 32 single loop cases, 62.5 % was identified correctly with automated DGM and out of 6 true double loop cases, 83.3 %. Lower performance for single reentry complex cases compared to EM was mainly because DGM could not distinguish the dominant loop from additional bystander loops found by DGM. Hence, the purpose of this work was to develop additional algorithms which in case of multiple found DGM loops could automatically find the dominant loop and compare it with the results of EM. Methods We performed multiple  simulations of various types of double loop reentry on a patient specific model of the left atrium. Based on a clinical case, double loops were simulated around a scar at the anterior wall (localized reentry) and the mitral valve (MV). LAT maps were determined similar as in the clinic. By varying the size of the scar in multiple steps, we obtained a transition from a regime of a dominant loop around the scar (small scar), to a true double loop and further to a regime of a dominant loop around the MV (large scar). We developed a novel DGM algorithm to determine the dominant loop from the region of collision (ROC) found from the vector field of the wavefront graph.   The developed method was also tested on 8 clinical cases of double loop ATs with EM measurements. Results Our algorithm found the location of the ROC and determined the correct dominant loop in 100% of the simulated data.  We tested this on 8 clinical cases of AT, and accuracy of the method was 75 %. Conclusions Determining the ROC in case of multiple loops in AT could correctly determine the dominant versus bystander loop, leading to the correct ablation target, without the need for further EM.


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