Approximation Schemes for Independent Set and Sparse Subsets of Polygons

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.

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

Current Bioinformatics ◽

10.2174/1574893615999200819162140 ◽

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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Improvement Dependability of Offshore Horizontal-Axis Wind Turbines by Applying New Mathematical Methods for Calculation the Excess Speed in Case of Wind Gusts

Energies ◽

10.3390/en14113085 ◽

2021 ◽

Vol 14 (11) ◽

pp. 3085

Author(s):

Konstantin Osintsev ◽

Seregei Aliukov ◽

Alexander Shishkov

Keyword(s):

Computer Simulation ◽

Wind Turbines ◽

Experimental Studies ◽

Offshore Wind ◽

Approximation Schemes ◽

Calculation Error ◽

Strong Wind ◽

Mathematical Methods ◽

Wind Gusts ◽

Gas Dynamic

The problem of increasing the reliability of wind turbines exists in the development of new offshore oil and natural gas fields. Reducing emergency situations is necessary due to the autonomous operation of drilling rigs and bulk seaports in the subarctic and Arctic climate. The relevance of the topic is linked with the development of a methodology for theoretical and practical studies of gas dynamics when gas flows in a pipe, based on a mathematical model using new mathematical methods for calculation of excess speeds in case of wind gusts. Problems in the operation of offshore wind turbines arise with storm gusts of wind, which is comparable to the wave movement of the gas flow. Thus, the scientific problem of increasing the reliability of wind turbines in conditions of strong wind gusts is solved. The authors indicate a gross error in the calculations when approximating through the use of the Fourier series. The obtained results will allow us to solve one of the essential problems of modeling at this stage of its development, namely: to reduce the calculation time and the adequacy of the model built for similar installations and devices. Experimental studies of gas-dynamic flows are carried out on the example of a physical model of a wind turbine. In addition, a computer simulation of the gas-dynamic flow process was carried out. The use of new approximation schemes in processing the results of experiments and computer simulation can reduce the calculation error by 1.2 percent.

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ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

Nagoya Mathematical Journal ◽

10.1017/nmj.2021.6 ◽

2021 ◽

pp. 1-40

Author(s):

NICK GILL ◽

BIANCA LODÀ ◽

PABLO SPIGA

Keyword(s):

Permutation Group ◽

Model Theory ◽

Independent Set ◽

Maximum Size ◽

Proper Subset ◽

Permutation Groups ◽

Finite Permutation Group ◽

Pointwise Stabilizer ◽

Relational Complexity

Abstract Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ . We define the height of G to be the maximum size of an independent set, and we denote this quantity $\textrm{H}(G)$ . In this paper, we study $\textrm{H}(G)$ for the case when G is primitive. Our main result asserts that either $\textrm{H}(G)< 9\log t$ or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study $\textrm{I}(G)$ , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either $\textrm{I}(G)<7\log t$ or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).

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