A Graph Theoretic Analysis of Double Base Number Systems

2007 ◽  
pp. 152-166 ◽  
Author(s):  
Pradeep Kumar Mishra ◽  
Vassil Dimitrov
Keyword(s):  
Base Number ◽  
Theoretic Analysis ◽  
Graph Theoretic ◽  
Number Systems ◽  
Double Base

Bounds and trade-offs for Double-Base Number Systems

2011 ◽  
Vol 111 (10) ◽  
pp. 488-493 ◽  
Author(s):  
Tiancheng Lou ◽  
Xiaoming Sun ◽  
Christophe Tartary
Keyword(s):  
Base Number ◽  
Number Systems ◽  
Trade Offs ◽  
Double Base

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

scholarly journals Graph Theoretic Analysis Reveals Intranasal Oxytocin Induced Network Changes Over Frontal Regions

Neuroscience ◽  
2021 ◽  
Author(s):  
Shuhan Zheng ◽  
Diksha Punia ◽  
Haiyan Wu ◽  
Quanying Liu
Keyword(s):  
Theoretic Analysis ◽  
Graph Theoretic

Graph-Theoretic Analysis of Power Grid Robustness

2021 ◽  
pp. 175-194
Author(s):  
Dorcas Ofori-Boateng ◽  
Asim Kumer Dey ◽  
R. Gel Yulia ◽  
H. Vincent Poor
Keyword(s):  
Power Grid ◽  
Theoretic Analysis ◽  
Graph Theoretic

scholarly journals Integrative statistical analyses of multiple liquid biopsy analytes in metastatic breast cancer

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Corinna Keup ◽  
Vinay Suryaprakash ◽  
Siegfried Hauch ◽  
Markus Storbeck ◽  
Peter Hahn ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Overall Survival ◽  
Metastatic Breast Cancer ◽  
Mutual Information ◽  
Hierarchical Clustering ◽  
Liquid Biopsy ◽  
Metastatic Breast ◽  
The Other ◽  
Theoretic Analysis ◽  
Graph Theoretic

Abstract Background Single liquid biopsy analytes (LBAs) have been utilized for therapy selection in metastatic breast cancer (MBC). We performed integrative statistical analyses to examine the clinical relevance of using multiple LBAs: matched circulating tumor cell (CTC) mRNA, CTC genomic DNA (gDNA), extracellular vesicle (EV) mRNA, and cell-free DNA (cfDNA). Methods Blood was drawn from 26 hormone receptor-positive, HER2-negative MBC patients. CTC mRNA and EV mRNA were analyzed using a multi-marker qPCR. Plasma from CTC-depleted blood was utilized for cfDNA isolation. gDNA from CTCs was isolated from mRNA-depleted CTC lysates. CTC gDNA and cfDNA were analyzed by targeted sequencing. Hierarchical clustering was performed within each analyte, and its results were combined into a score termed Evaluation of multiple Liquid biopsy analytes In Metastatic breast cancer patients All from one blood sample (ELIMA.score), which calculates the contribution of each analyte to the overall survival prediction. Singular value decomposition (SVD), mutual information calculation, k-means clustering, and graph-theoretic analysis were conducted to elucidate the dependence between individual analytes. Results A combination of two/three/four LBAs increased the prevalence of patients with actionable signals. Aggregating the results of hierarchical clustering of individual LBAs into the ELIMA.score resulted in a highly significant correlation with overall survival, thereby bolstering evidence for the additive value of using multiple LBAs. Computation of mutual information indicated that none of the LBAs is independent of the others, but the ability of a single LBA to describe the others is rather limited—only CTC gDNA could partially describe the other three LBAs. SVD revealed that the strongest singular vectors originate from all four LBAs, but a majority originated from CTC gDNA. After k-means clustering of patients based on parameters of all four LBAs, the graph-theoretic analysis revealed CTC ERBB2 variants only in patients belonging to one particular cluster. Conclusions The additional benefits of using all four LBAs were objectively demonstrated in this pilot study, which also indicated a relative dominance of CTC gDNA over the other LBAs. Consequently, a multi-parametric liquid biopsy approach deconvolutes the genomic and transcriptomic complexity and should be considered in clinical practice.

scholarly journals Accurate airway centerline extraction based on topological thinning using graph-theoretic analysis

2014 ◽  
Vol 24 (6) ◽  
pp. 3239-3249 ◽  
Author(s):  
Zijian Bian ◽  
Wenjun Tan ◽  
Jinzhu Yang ◽  
Jiren Liu ◽  
Dazhe Zhao
Keyword(s):  
Theoretic Analysis ◽  
Graph Theoretic ◽  
Centerline Extraction
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