scholarly journals Cycle lengths in sparse random graphs

2021 ◽  
Author(s):  
Yahav Alon ◽  
Michael Krivelevich ◽  
Eyal Lubetzky
Keyword(s):  
Random Graphs ◽  
Cycle Lengths

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

Asymptotics with remainder term for moments of the total cycle number of random A-permutation

2021 ◽  
Vol 31 (1) ◽  
pp. 51-60
Author(s):  
Arsen L. Yakymiv
Keyword(s):  
Remainder Term ◽  
Random Permutation ◽  
Natural Numbers ◽  
Cycle Number ◽  
Fixed Set ◽  
Cycle Lengths

Abstract Dedicated to the memory of Alexander Ivanovich Pavlov. We consider the set of n-permutations with cycle lengths belonging to some fixed set A of natural numbers (so-called A-permutations). Let random permutation τ n be uniformly distributed on this set. For some class of sets A we find the asymptotics with remainder term for moments of total cycle number of τ n .

scholarly journals Time-to-event analysis in economic evaluations: a comparison of modelling methods to assess the cost-effectiveness of transplanting a marginal quality kidney

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sameera Senanayake ◽  
Nicholas Graves ◽  
Helen Healy ◽  
Keshwar Baboolal ◽  
Adrian Barnett ◽  
...  
Keyword(s):  
Cost Effectiveness ◽  
Time Horizon ◽  
Transition Probabilities ◽  
Discrete Event ◽  
Economic Evaluations ◽  
Event Analysis ◽  
Time To Event ◽  
Modelling Method ◽  
Cycle Lengths ◽  
Modelling Methods

Abstract Background Economic-evaluations using decision analytic models such as Markov-models (MM), and discrete-event-simulations (DES) are high value adds in allocating resources. The choice of modelling method is critical because an inappropriate model yields results that could lead to flawed decision making. The aim of this study was to compare cost-effectiveness when MM and DES were used to model results of transplanting a lower-quality kidney versus remaining waitlisted for a kidney. Methods Cost-effectiveness was assessed using MM and DES. We used parametric survival models to estimate the time-dependent transition probabilities of MM and distribution of time-to-event in DES. MMs were simulated in 12 and 6 monthly cycles, out to five and 20-year time horizon. Results DES model output had a close fit to the actual data. Irrespective of the modelling method, the cycle length of MM or the time horizon, transplanting a low-quality kidney as compared to remaining waitlisted was the dominant strategy. However, there were discrepancies in costs, effectiveness and net monetary benefit (NMB) among different modelling methods. The incremental NMB of the MM in the 6-months cycle lengths was a closer fit to the incremental NMB of the DES. The gap in the fit of the two cycle lengths to DES output reduced as the time horizon increased. Conclusion Different modelling methods were unlikely to influence the decision to accept a lower quality kidney transplant or remain waitlisted on dialysis. Both models produced similar results when time-dependant transition probabilities are used, most notable with shorter cycle lengths and longer time-horizons.

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