scholarly journals Random Models for Geometric Graphs (Abstract)

2007 ◽  
pp. 37-37
Author(s):  
Maria Serna
Keyword(s):  
Geometric Graphs ◽  
Random Models

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

scholarly journals Geometric graphs from data to aid classification tasks with Graph Convolutional Networks

Patterns ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 100237
Author(s):  
Yifan Qian ◽  
Paul Expert ◽  
Pietro Panzarasa ◽  
Mauricio Barahona
Keyword(s):  
Geometric Graphs ◽  
Convolutional Networks ◽  
Classification Tasks

scholarly journals Connectivity in one-dimensional soft random geometric graphs

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Michael Wilsher ◽  
Carl P. Dettmann ◽  
Ayalvadi Ganesh
Keyword(s):  
Geometric Graphs ◽  
Random Geometric Graphs ◽  
One Dimensional

Latitudinal gradients in diversity: real patterns and random models

Ecography ◽  
2001 ◽  
Vol 24 (3) ◽  
pp. 341-351 ◽  
Author(s):  
Patricia Koleff ◽  
Kevin J. Gaston
Keyword(s):  
Latitudinal Gradients ◽  
Random Models

Differential Equations on Networks (Geometric Graphs)

2004 ◽  
Vol 119 (6) ◽  
pp. 691-718 ◽  
Author(s):  
Yu. V. Pokornyi ◽  
A. V. Borovskikh
Keyword(s):  
Differential Equations ◽  
Geometric Graphs

scholarly journals On local transformations in plane geometric graphs embedded on small grids

2008 ◽  
Vol 39 (2) ◽  
pp. 65-77 ◽  
Author(s):  
Manuel Abellanas ◽  
Prosenjit Bose ◽  
Alfredo García ◽  
Ferran Hurtado ◽  
Pedro Ramos ◽  
...  
Keyword(s):  
Geometric Graphs

scholarly journals Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

2000 ◽  
Vol 9 (6) ◽  
pp. 489-511 ◽  
Author(s):  
JOSEP DÍAZ ◽  
MATHEW D. PENROSE ◽  
JORDI PETIT ◽  
MARÍA SERNA
Keyword(s):  
Constant Factor ◽  
Geometric Graphs ◽  
Convergence Theorems ◽  
Linear Arrangement ◽  
Random Lattice ◽  
Random Geometric Graphs ◽  
Unit Square ◽  
Subcritical Regime ◽  
Probabilistic Setting ◽  
Lattice Graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant factor. We apply percolation theory to the study of lattice graphs in a probabilistic setting. In particular, we deal with the subcritical regime that this class of graphs exhibits and characterize the behaviour of several layout measures in this space of probability. We extend the results on random lattice graphs to random geometric graphs, which are graphs whose nodes are spread at random in the unit square and whose edges connect pairs of points which are within a given distance. We also characterize the behaviour of several layout measures on random geometric graphs in their subcritical regime. Our main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

Abstract W P26: Meta-analysis Of Studies Using Solitaire And Trevo Pro Stent Retriever Devices For Mechanical Thromboembolectomy In Acute Cerebral Ischemia

Stroke ◽  
2014 ◽  
Vol 45 (suppl_1) ◽  
Author(s):  
Vikram Jadhav ◽  
Mushtaq H Qureshi ◽  
Malik M Adil ◽  
Amna Zarar ◽  
Nidaullah Mian ◽  
...  
Keyword(s):  
Cerebral Ischemia ◽  
Publication Bias ◽  
Mechanical Thrombectomy ◽  
Meta Analysis ◽  
Analysis Software ◽  
Symptomatic Intracerebral Hemorrhage ◽  
Acute Cerebral Ischemia ◽  
Random Models ◽  
Log Odds ◽  
Event Rates

Objective: To report rates of recanalization and symptomatic intracerebral hemorrhage (SICH) after mechanical thromboembolectomy using Solitaire and Trevo Pro devices in acute cerebral ischemia using meta-analysis of published studies. Methods: We identified all studies that used Solitaire or Trevo devices for mechanical thromboembolectomy in treatment of acute cerebral ischemia using a search on PubMed and Cochrane libraries, stroke trials database, proceedings of neurology and neurosurgery related conferences, and supplemented by a review of bibliographies of selected publications. Recanalization was assessed using TICI >2a and rates of SICH were recorded. For the meta-analysis, forest plots and statistical analysis including event rates [ER] with 95% confidence intervals [CI] based on both fixed and random models were performed using Comprehensive Meta-Analysis Software. The presence of publication bias was interrogated by funnel plot of Standard Error by log odds ratio. Results: Eighteen studies with Solitaire device and five with Trevo device were identified and included in the meta-analysis. There were a total of 433/505 (85%, ER 0.85 [CI] 0.80-0.88, P<0.001) successful recanalizations with Solitaire device whereas 196/243 (80%, ER 0.80 [CI] 0.74-0.85, P<0.001) successful recanalizations were noted with Trevo device. The incidence of SICH was 45/505 (9%, ER 0.09 [CI] 0.06-0.14, P<0.001) with Solitaire device and 17/243 (6%, ER 0.06 [CI] 0.049-0129, P<0.001) with Trevo device after mechanical thrombectomy. There was no publication bias. Conclusions: Meta-analysis of studies reveals similar rates for recanalization and SICH after mechanical thromboembolectomy using Solitaire or Trevo Pro devices.

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