scholarly journals The partial duplication random graph with edge deletion

Author(s):  
Felix Hermann ◽  
Peter Pfaffelhuber
2009 ◽  
Vol 46 (4) ◽  
pp. 1213-1220 ◽  
Author(s):  
Xian-Yuan Wu ◽  
Zhao Dong ◽  
Ke Liu ◽  
Kai-Yuan Cai

In this paper we focus on the problem of the degree sequence for a random graph process with edge deletion. We prove that, while a specific parameter varies, the limit degree distribution of the model exhibits critical phenomenon.


2009 ◽  
Vol 46 (04) ◽  
pp. 1213-1220
Author(s):  
Xian-Yuan Wu ◽  
Zhao Dong ◽  
Ke Liu ◽  
Kai-Yuan Cai

In this paper we focus on the problem of the degree sequence for a random graph process with edge deletion. We prove that, while a specific parameter varies, the limit degree distribution of the model exhibits critical phenomenon.


Author(s):  
Mark Newman

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Philip A. I. Guthrie ◽  
Mohammad R. Abdollahi ◽  
Tom Gaunt ◽  
Debbie A. Lawlor ◽  
Yoav Ben-Shlomo ◽  
...  

Background. Haptoglobin acts as an antioxidant by limiting peroxidative tissue damage by free hemoglobin. The haptoglobin gene allele Hp2 comprises a 1.7 kb partial duplication. Relative to allele Hp1, Hp2 carriers form protein multimers, suboptimal for hemoglobin scavenging.Objective. To examine the association of haptoglobin genotype with a range of phenotypes, with emphasis on vitamin C and hemoglobin levels.Methods. We applied a quantitative PCR assay for the duplication junction to two population cohorts including 2747 British women and 1198 British men. We examined the association of haptoglobin duplicon copy number with hemoglobin and vitamin C and used the copy number to complete a phenome scan.Results.Hemoglobin concentrations were greater in those with Hp2,2 genotype, in women only (Hp1,1 13.45 g/dL, Hp1,2 13.49 g/dL, Hp2,2 13.61 g/dL;P=0.002), though statistically there was no evidence of a difference between the sexes (zvalue = 1.2,P=0.24). Haptoglobin genotype was not associated with vitamin C or any other phenotype in either cohort.Conclusions. Our results do not support association of haptoglobin genotype with vitamin C or with other phenotypes measured in two population cohorts. The apparent association between haptoglobin genotype and hemoglobin in the women’s cohort merits further investigation.


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