scholarly journals Degree distribution of large networks generated by the partial duplication model

2013 ◽  
Vol 476 ◽  
pp. 94-108 ◽  
Author(s):  
Si Li ◽  
Kwok Pui Choi ◽  
Taoyang Wu
Keyword(s):  
Degree Distribution ◽  
Large Networks ◽  
Partial Duplication

Comparing node degrees in probabilistic networks

2019 ◽  
Vol 7 (5) ◽  
pp. 749-763 ◽  
Author(s):  
Amin Kaveh ◽  
Matteo Magnani ◽  
Christian Rohner
Keyword(s):  
Computational Complexity ◽  
Degree Distribution ◽  
Fundamental Property ◽  
Experimental Results ◽  
Probabilistic Networks ◽  
Large Networks ◽  
Real Dataset ◽  
Reference Node ◽  
Accurate Probability

Abstract Degree is a fundamental property of nodes in networks. However, computing the degree distribution of nodes in probabilistic networks is an expensive task for large networks. To overcome this difficulty, expected degree is commonly utilized in the literature. However, in this article, we show that in some cases expected degree does not allow us to evaluate the probability of two nodes having the same degree or one node having higher degree than another. This suggests that expected degree in probabilistic networks does not completely play the same role as degree in deterministic networks. For each node, we define a reference node with the same expected degree but the least possible variance, corresponding to the least uncertain degree distribution. Then, we show how the probability of a node’s degree being higher or equal to the degree of its reference node can be approximated by using variance and skewness of the degree distribution in addition to expected degree. Experimental results on a real dataset show that our approximation functions produce accurate probability estimations in linear computational complexity, while computing exact probabilities is polynomial with order of 3.

Analysis of Oncogene Protein Structure Using Small World Network Concept

2020 ◽  
Vol 15 (7) ◽  
pp. 732-740
Author(s):  
Neetu Kumari ◽  
Anshul Verma
Keyword(s):  
Amino Acids ◽  
Protein Structure ◽  
Degree Distribution ◽  
Protein Structures ◽  
Small World ◽  
Extreme Condition ◽  
Centrality Measures ◽  
Small World Network ◽  
Network Concept ◽  
Oncogene Protein

Background: The basic building block of a body is protein which is a complex system whose structure plays a key role in activation, catalysis, messaging and disease states. Therefore, careful investigation of protein structure is necessary for the diagnosis of diseases and for the drug designing. Protein structures are described at their different levels of complexity: primary (chain), secondary (helical), tertiary (3D), and quaternary structure. Analyzing complex 3D structure of protein is a difficult task but it can be analyzed as a network of interconnection between its component, where amino acids are considered as nodes and interconnection between them are edges. Objective: Many literature works have proven that the small world network concept provides many new opportunities to investigate network of biological systems. The objective of this paper is analyzing the protein structure using small world concept. Methods: Protein is analyzed using small world network concept, specifically where extreme condition is having a degree distribution which follows power law. For the correct verification of the proposed approach, dataset of the Oncogene protein structure is analyzed using Python programming. Results: Protein structure is plotted as network of amino acids (Residue Interaction Graph (RIG)) using distance matrix of nodes with given threshold, then various centrality measures (i.e., degree distribution, Degree-Betweenness correlation, and Betweenness-Closeness correlation) are calculated for 1323 nodes and graphs are plotted. Conclusion: Ultimately, it is concluded that there exist hubs with higher centrality degree but less in number, and they are expected to be robust toward harmful effects of mutations with new functions.

Models of network formation

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Degree Distribution ◽  
Network Formation ◽  
Preferential Attachment ◽  
Network Size ◽  
Large Network ◽  
Citation Networks ◽  
Airline Networks ◽  
Attachment Model ◽  
Delivery Networks

This chapter describes models of the growth or formation of networks, with a particular focus on preferential attachment models. It starts with a discussion of the classic preferential attachment model for citation networks introduced by Price, including a complete derivation of the degree distribution in the limit of large network size. Subsequent sections introduce the Barabasi-Albert model and various generalized preferential attachment models, including models with addition or removal of extra nodes or edges and models with nonlinear preferential attachment. Also discussed are node copying models and models in which networks are formed by optimization processes, such as delivery networks or airline networks.

scholarly journals Haptoglobin Duplicon, Hemoglobin, and Vitamin C: Analyses in the British Women’s Heart and Health Study and Caerphilly Prospective Study

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Philip A. I. Guthrie ◽  
Mohammad R. Abdollahi ◽  
Tom Gaunt ◽  
Debbie A. Lawlor ◽  
Yoav Ben-Shlomo ◽  
...  
Keyword(s):  
Vitamin C ◽  
Copy Number ◽  
Health Study ◽  
Free Hemoglobin ◽  
Pcr Assay ◽  
Partial Duplication ◽  
Haptoglobin Genotype ◽  
Haptoglobin Gene ◽  
Apparent Association ◽  
Quantitative Pcr Assay

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.

scholarly journals Bayesian graphical models for modern biological applications

2021 ◽  
Author(s):  
Yang Ni ◽  
Veerabhadran Baladandayuthapani ◽  
Marina Vannucci ◽  
Francesco C. Stingo
Keyword(s):  
Graphical Models ◽  
Cancer Genomics ◽  
Graph Structure ◽  
Biological Processes ◽  
Limited Sample ◽  
Large Networks ◽  
Bayesian Approaches ◽  
Complex Sampling ◽  
Complex Dependence ◽  
Bayesian Graphical Models

AbstractGraphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the various biological processes, for intuitive and rigorous understanding and interpretations. In the context of large networks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. These features are particularly important in applications with limited sample size, including genomics and imaging studies. In this paper, we review several recently developed techniques for the analysis of large networks under non-standard settings, including but not limited to, multiple graphs for data observed from multiple related subgroups, graphical regression approaches used for the analysis of networks that change with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

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