On topological and geometrical distance matrices

1993 ◽  
Vol 13 (1) ◽  
pp. 145-151 ◽  
Author(s):  
Milan Kunz
Keyword(s):  
Distance Matrices ◽  
Geometrical Distance

scholarly journals Identities for minors of the Laplacian, resistance and distance matrices

2011 ◽  
Vol 435 (6) ◽  
pp. 1479-1489 ◽  
Author(s):  
R.B. Bapat ◽  
Sivaramakrishnan Sivasubramanian
Keyword(s):  
Distance Matrices

scholarly journals The triangles method to buildX-trees from incomplete distance matrices

2001 ◽  
Vol 35 (2) ◽  
pp. 283-300 ◽  
Author(s):  
Alain Guénoche ◽  
Bruno Leclerc
Keyword(s):  
Distance Matrices

Application of recurrence plot analysis to characterise whole chamber propagation of atrial fibrillation

EP Europace ◽  
2021 ◽  
Vol 23 (Supplement_3) ◽  
Author(s):  
M Pope ◽  
P Kuklik ◽  
A Briosa E Gala ◽  
M Leo ◽  
J Paisey ◽  
...  
Keyword(s):  
Atrial Fibrillation ◽  
Catheter Ablation ◽  
Charge Density ◽  
De Novo ◽  
Inverse Correlation ◽  
Right Atrial ◽  
Research Centre ◽  
Activation Patterns ◽  
Density Mapping ◽  
Distance Matrices

Abstract Funding Acknowledgements Type of funding sources: Public hospital(s). Main funding source(s): Oxford Biomedical Research Centre Introduction Non-contact charge density mapping allows visualisation of whole chamber propagation during atrial fibrillation (AF). The identification of regions with repetitive or, conversely, more complex patterns of wavefront propagation may provide clues to mechanisms responsible for AF maintenance and lead to improved outcomes from catheter ablation. Our novel mapping approach based on signal recurrence plots has never been applied to whole chamber, bi-atrial recording of atrial fibrillation. Purpose To apply recurrence analysis to characterise whole chamber bi-atrial AF propagation. Methods Non-contact dipole signals from left and right atrial maps were obtained during simultaneous bi-atrial charge density mapping of AF. Signals were converted to phase and mean phase coherence calculated for the generation of recurrence distance matrices for the whole chamber and each anatomical region (6x LA and 4x RA) over the 30-second recording duration, where a value of 1 (purple, see figure panel A) represents uniform repetitive conduction, and 0 (red), irregular, non-repetitive activity. Whole chamber and regional mean recurrence values were calculated and correlated with the frequency of wavefronts of localised irregular activation patterns. Results Maps were obtained prior to ablation in 21 patients (5 paroxysmal (pAF), 16 persistent AF (persAF)) undergoing de-novo catheter ablation procedures. Whole chamber recurrence was higher in patients with pAF (0.40 ± 0.08) than persAF (0.34 ± 0.05), p < 0.0005. There was an inverse correlation between regional recurrence values and the number of localised irregular activations detected (-0.7021, p < 0.0005, figure panel B) with the lateral LA and anterior RA demonstrating the highest recurrence values in each chamber (figure panel C). Conclusion Use of recurrence distance matrices characterises global AF propagation phenotypes. Regional values are inversely correlated with the frequency of localised irregular activation patterns identified demonstrating an anatomic dependence in the level of AF propagation complexity, greatest in the anterior LA and septal RA. Comparison of strategies targeting regions with maximal vs. minimal values during catheter ablation may define an optimal approach to treatment of persistent AF. Abstract Figure. Recurrence abstract figure

On the Eigenvalues of the Ordinary and Reciprocal Resistance-Distance Matrices

2009 ◽  
Author(s):  
Sonja Nikolić ◽  
Nenad Trinajstić ◽  
Bo Zhou ◽  
George Maroulis ◽  
Theodore E. Simos
Keyword(s):  
Resistance Distance ◽  
Distance Matrices

Maximal Accurate Forests from Distance Matrices

2006 ◽  
pp. 281-295 ◽  
Author(s):  
Constantinos Daskalakis ◽  
Cameron Hill ◽  
Alexandar Jaffe ◽  
Radu Mihaescu ◽  
Elehanan Mossel ◽  
...  
Keyword(s):  
Distance Matrices
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