scholarly journals Recognition Problems for Connectivity Functions

2021 ◽  
Author(s):  
◽  
Susan Jowett
Keyword(s):  
Connectivity Function ◽  
Submodular Set Function ◽  
Set Function ◽  
Function Connectivity

<p>A connectivity function is a symmetric, submodular set function. Connectivity functions arise naturally from graphs, matroids and other structures. This thesis focuses mainly on recognition problems for connectivity functions, that is when a connectivity function comes from a particular type of structure. In particular we give a method for identifying when a connectivity function comes from a graph, which uses no more than a polynomial number of evaluations of the connectivity function. We also give a proof that no such method can exist for matroids.</p>

scholarly journals Recognition Problems for Connectivity Functions

2021 ◽  
Author(s):  
◽  
Susan Jowett
Keyword(s):  
Connectivity Function ◽  
Submodular Set Function ◽  
Set Function ◽  
Function Connectivity

<p>A connectivity function is a symmetric, submodular set function. Connectivity functions arise naturally from graphs, matroids and other structures. This thesis focuses mainly on recognition problems for connectivity functions, that is when a connectivity function comes from a particular type of structure. In particular we give a method for identifying when a connectivity function comes from a graph, which uses no more than a polynomial number of evaluations of the connectivity function. We also give a proof that no such method can exist for matroids.</p>

Multi-level facility location as the maximization of a submodular set function

2015 ◽  
Vol 247 (3) ◽  
pp. 1013-1016 ◽  
Author(s):  
Camilo Ortiz-Astorquiza ◽  
Ivan Contreras ◽  
Gilbert Laporte
Keyword(s):  
Facility Location ◽  
Multi Level ◽  
Submodular Set Function ◽  
Set Function

scholarly journals Potpourri: An Epistasis Test Prioritization Algorithm via Diverse SNP Selection

2019 ◽  
Author(s):  
Gizem Caylak ◽  
Oznur Tastan ◽  
A. Ercument Cicek
Keyword(s):  
Association Studies ◽  
Genetic Diseases ◽  
Genome Wide Association Studies ◽  
Coding Regions ◽  
Genome Wide ◽  
Genomic Location ◽  
Test Prioritization ◽  
Genomic Regions ◽  
Submodular Set Function ◽  
Set Function

AbstractGenome-wide association studies explain a fraction of the underlying heritability of genetic diseases. Investigating epistatic interactions between two or more loci help closing this gap. Unfortunately, sheer number of loci combinations to process and hypotheses to test prohibit the process both computationally and statistically. Epistasis test prioritization algorithms rank likely-epistatic SNP pairs to limit the number of tests. Yet, they still suffer from very low precision. It was shown in the literature that selecting SNPs that are individually correlated with the phenotype and also diverse with respect to genomic location, leads to better phenotype prediction due to genetic complementation. Here, we propose that an algorithm that pairs SNPs from such diverse regions and ranks them can improve prediction power. We propose an epistasis test prioritization algorithm which optimizes a submodular set function to select a diverse and complementary set of genomic regions that span the underlying genome. SNP pairs from these regions are then further ranked w.r.t. their co-coverage of the case cohort. We compare our algorithm with the state-of-the-art on three GWAS and show that (i) we substantially improve precision (from 0.003 to 0.652) while maintaining the significance of selected pairs, (ii) decrease the number of tests by 25 folds, and (iii) decrease the runtime by 4 folds. We also show that promoting SNPs from regulatory/coding regions improves the performance (up to 0.8). Potpourri is available at http:/ciceklab.cs.bilkent.edu.tr/potpourri.

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