Recovery of sums of sparse and dense signals by incorporating graphical structure among predictors

2021 ◽  
Author(s):  
Yiyun Luo ◽  
Yufeng Liu ◽  
Keyword(s):  
Graphical Structure

Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mudasir Younis ◽  
Deepak Singh ◽  
Ishak Altun ◽  
Varsha Chauhan
Keyword(s):  
Metric Spaces ◽  
Fixed Point Theory ◽  
Directed Graphs ◽  
Point Theory ◽  
Graph Structure ◽  
Open Ball ◽  
Open Problems ◽  
Graphical Structure ◽  
State Of Art ◽  
Transverse Oscillations

Abstract The purpose of this article is to present the notion of graphical extended b-metric spaces, blending the concepts of graph theory and metric fixed point theory. We discuss the structure of an open ball of the new proposed space and elaborate on the newly introduced ideas in a novel way by portraying suitably directed graphs. We also provide some examples in graph structure to show that our results are sharp as compared to the results in the existing state-of-art. Furthermore, an application to the transverse oscillations of a homogeneous bar is entrusted to affirm the applicability of the established results. Additionally, we evoke some open problems for enthusiastic readers for the future aspects of the study.

Weaving the Rainbow (Odd I)

2021 ◽  
Vol 114 (10) ◽  
pp. 812
Author(s):  
Lucy Rycroft-Smith
Keyword(s):  
Flow Pattern ◽  
Central Importance ◽  
Odd Degree ◽  
Graphical Structure

This piece is a rumination on flow, pattern, and edges/transitions, focusing on polynomials of odd degree and overlaying/underlaying the flow of the graphical structure with a rainbow to suggest the central importance of queer visibility in mathematics.

Golden Ratio Butterflies

2021 ◽  
Vol 114 (11) ◽  
pp. 908
Author(s):  
Clarissa Grandi
Keyword(s):  
Flow Pattern ◽  
Golden Ratio ◽  
Central Importance ◽  
Odd Degree ◽  
Graphical Structure

This piece is a rumination on flow, pattern, and edges/transitions, focusing on polynomials of odd degree and overlaying/underlaying the flow of the graphical structure with a rainbow to suggest the central importance of queer visibility in mathematics.

The Beauty of the Graphical Structure Graph

1991 ◽  
pp. 225-231
Author(s):  
T. Cieplak
Keyword(s):  
Graphical Structure ◽  
Structure Graph

Graphical Structure-Oriented Search in a Hypertext System

1992 ◽  
pp. 179-184
Author(s):  
M. Hofmann ◽  
S. Schmezko
Keyword(s):  
Graphical Structure

Probability on Graphical Structure: A Knowledge-Based Agricultural Case

2020 ◽  
Author(s):  
Paula Ianishi ◽  
Oilson Alberto Gonzatto Junior ◽  
Marcos Jardel Henriques ◽  
Diego Carvalho do Nascimento ◽  
Gabriel Kamada Mattar ◽  
...  
Keyword(s):  
Knowledge Based ◽  
Graphical Structure

Incorporating Graphical Structure of Predictors in Sparse Quantile Regression

2020 ◽  
pp. 1-10
Author(s):  
Zhanfeng Wang ◽  
Xianhui Liu ◽  
Wenlu Tang ◽  
Yuanyuan Lin
Keyword(s):  
Quantile Regression ◽  
Graphical Structure

DSRIG: Incorporating graphical structure in the regularized modeling of SNP data

2019 ◽  
Vol 17 (03) ◽  
pp. 1950017 ◽  
Author(s):  
Matthew Stephenson ◽  
Gerarda A. Darlington ◽  
Flavio S. Schenkel ◽  
E. James Squires ◽  
R. Ayesha Ali
Keyword(s):  
Cross Validation ◽  
Genetic Selection ◽  
Boar Taint ◽  
Farm Animals ◽  
Candidate Snps ◽  
Snp Data ◽  
Validation Procedure ◽  
Improvement Programs ◽  
Graphical Structure ◽  
Selection Of

Genetic selection of farm animals plays an important role in genetic improvement programs. Regularized regression methods on single nucleotide polymorphism (SNP) data from a set of candidate genes can help to identify genes that are associated with the trait of interest. This complex task must also consider the relative effect sizes on the desired trait and account for the relationships among the candidate SNPs so that selection of a SNP does not promote other undesirable traits through breeding. We present the Doubly Sparse Regression Incorporating Graphical structure (DSRIG), a novel regularized method for genetic selection that exploits the relationships among candidate SNPs to improve prediction. DSRIG was applied in the prediction of skatole and androstenone levels, two compounds known to be associated with boar taint. DSRIG was shown to provide a predictive benefit when compared to ordinary least squares (OLS) and the least absolute shrinkage and selection operator (LASSO) in a cross-validation procedure. The relative sizes of the coefficient estimates over the cross-validation procedure were compared to determine which SNPs may have the greatest impact on expression of the boar taint compounds and a consensus graph was used to infer the relationships among SNPs.

Bayesian sparse covariance decomposition with a graphical structure

2014 ◽  
Vol 26 (1-2) ◽  
pp. 493-510 ◽  
Author(s):  
Lin Zhang ◽  
Abhra Sarkar ◽  
Bani K. Mallick
Keyword(s):  
Covariance Decomposition ◽  
Graphical Structure
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