scholarly journals Tight independent set neighborhood union condition for fractional critical deleted graphs and ID deleted graphs

2019 ◽  
Vol 12 (4-5) ◽  
pp. 711-721 ◽  
Author(s):  
Darko Dimitrov ◽  
◽  
Hosam Abdo ◽  
Keyword(s):  
Independent Set ◽  
Union Condition ◽  
Neighborhood Union Condition ◽  
Neighborhood Union

scholarly journals A note on the transmission feasibility problem in networks

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 889-895
Author(s):  
Wei Gao ◽  
Yunqing Zhang ◽  
Yaojun Chen
Keyword(s):  
Data Transmission ◽  
Independent Set ◽  
Feasibility Problem ◽  
Network Graph ◽  
Graph Problems ◽  
Union Condition ◽  
Neighborhood Union Condition ◽  
Entire Network ◽  
Neighborhood Union ◽  
The Ideal

Abstract In the networking designing phase, the network needs to be built according to certain indicators to ensure that the network has the ideal functions and can work smoothly. From a modeling perspective, each site in the network is represented by a vertex, channels between sites are represented by edges, and thus the entire network can be denoted as a graph. Problems in the network can be transformed into corresponding graph problems. In particular, the feasibility of data transmission can be transformed into the existence of fractional factors in network graph. This note gives an independent set neighborhood union condition for the existence of fractional factors in a special setting, and shows that the neighborhood union condition is sharp.

scholarly journals Color Neighborhood Union Conditions for Long Heterochromatic Paths in Edge-Colored Graphs

10.37236/995 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
He Chen ◽  
Xueliang Li
Keyword(s):  
Lower Bound ◽  
Colored Graph ◽  
Colored Graphs ◽  
Union Condition ◽  
Neighborhood Union Condition ◽  
Color Neighborhood ◽  
Neighborhood Union

Let $G$ be an edge-colored graph. A heterochromatic (rainbow, or multicolored) path of $G$ is such a path in which no two edges have the same color. Let $CN(v)$ denote the color neighborhood of a vertex $v$ of $G$. In a previous paper, we showed that if $|CN(u)\cup CN(v)|\geq s$ (color neighborhood union condition) for every pair of vertices $u$ and $v$ of $G$, then $G$ has a heterochromatic path of length at least $\lfloor{2s+4\over5}\rfloor$. In the present paper, we prove that $G$ has a heterochromatic path of length at least $\lceil{s+1\over2}\rceil$, and give examples to show that the lower bound is best possible in some sense.

Prediction of K562 Cells Functional Inhibitors Based on Machine Learning Approaches

2020 ◽  
Vol 25 (40) ◽  
pp. 4296-4302 ◽  
Author(s):  
Yuan Zhang ◽  
Zhenyan Han ◽  
Qian Gao ◽  
Xiaoyi Bai ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Inclusion Bodies ◽  
Cross Validation ◽  
Independent Set ◽  
K562 Cells ◽  
Machine Learning Algorithms ◽  
Learning Approaches ◽  
Validation Test ◽  
Excess Number ◽  
Fold Cross Validation

Background: β thalassemia is a common monogenic genetic disease that is very harmful to human health. The disease arises is due to the deletion of or defects in β-globin, which reduces synthesis of the β-globin chain, resulting in a relatively excess number of α-chains. The formation of inclusion bodies deposited on the cell membrane causes a decrease in the ability of red blood cells to deform and a group of hereditary haemolytic diseases caused by massive destruction in the spleen. Methods: In this work, machine learning algorithms were employed to build a prediction model for inhibitors against K562 based on 117 inhibitors and 190 non-inhibitors. Results: The overall accuracy (ACC) of a 10-fold cross-validation test and an independent set test using Adaboost were 83.1% and 78.0%, respectively, surpassing Bayes Net, Random Forest, Random Tree, C4.5, SVM, KNN and Bagging. Conclusion: This study indicated that Adaboost could be applied to build a learning model in the prediction of inhibitors against K526 cells.

Predicting Hub Genes of Glioblastomas Based on Support Vector Machine Combined with CFS algorithms

2020 ◽  
Vol 15 ◽  
Author(s):  
Chun Qiu ◽  
Sai Li ◽  
Shenghui Yang ◽  
Lin Wang ◽  
Aihui Zeng ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Expression Profiles ◽  
Independent Set ◽  
Classification Model ◽  
Support Vector ◽  
Feature Subset ◽  
Hub Genes ◽  
Effective Prevention ◽  
Key Genes ◽  
Control Samples

Aim: To search the genes related to the mechanisms of the occurrence of glioma and to try to build a prediction model for glioblastomas. Background: The morbidity and mortality of glioblastomas are very high, which seriously endangers human health. At present, the goals of many investigations on gliomas are mainly to understand the cause and mechanism of these tumors at the molecular level and to explore clinical diagnosis and treatment methods. However, there is no effective early diagnosis method for this disease, and there are no effective prevention, diagnosis or treatment measures. Methods: First, the gene expression profiles derived from GEO were downloaded. Then, differentially expressed genes (DEGs) in the disease samples and the control samples were identified. After that, GO and KEGG enrichment analyses of DEGs were performed by DAVID. Furthermore, the correlation-based feature subset (CFS) method was applied to the selection of key DEGs. In addition, the classification model between the glioblastoma samples and the controls was built by an Support Vector Machine (SVM) based on selected key genes. Results and Discussion: Thirty-six DEGs, including 17 upregulated and 19 downregulated genes, were selected as the feature genes to build the classification model between the glioma samples and the control samples by the CFS method. The accuracy of the classification model by using a 10-fold cross-validation test and independent set test was 76.25% and 70.3%, respectively. In addition, PPP2R2B and CYBB can also be found in the top 5 hub genes screened by the protein– protein interaction (PPI) network. Conclusions: This study indicated that the CFS method is a useful tool to identify key genes in glioblastomas. In addition, we also predicted that genes such as PPP2R2B and CYBB might be potential biomarkers for the diagnosis of glioblastomas.

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