scholarly journals Vertex Partitions into an Independent Set and a Forest with Each Component Small

2021 ◽  
Vol 35 (3) ◽  
pp. 1769-1791
Author(s):  
Daniel W. Cranston ◽  
Matthew P. Yancey
Keyword(s):  
Independent Set ◽  
Vertex Partitions

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.

scholarly journals ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

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).

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
Author(s):  
Yanfang Liu ◽  
Hong Zhao ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Independent Set ◽  
Approximation Operator ◽  
Approximation Number ◽  
Lower Approximation ◽  
The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

scholarly journals Assisting scalable diagnosis automatically via CT images in the combat against COVID-19

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bohan Liu ◽  
Pan Liu ◽  
Lutao Dai ◽  
Yanlin Yang ◽  
Peng Xie ◽  
...  
Keyword(s):  
Large Scale ◽  
Area Under The Curve ◽  
Independent Set ◽  
Reference Method ◽  
Ct Images ◽  
Loss Of Life ◽  
Case Identification ◽  
Reverse Transcription Pcr ◽  
Using Data

AbstractThe pandemic of Coronavirus Disease 2019 (COVID-19) is causing enormous loss of life globally. Prompt case identification is critical. The reference method is the real-time reverse transcription PCR (RT-PCR) assay, whose limitations may curb its prompt large-scale application. COVID-19 manifests with chest computed tomography (CT) abnormalities, some even before the onset of symptoms. We tested the hypothesis that the application of deep learning (DL) to 3D CT images could help identify COVID-19 infections. Using data from 920 COVID-19 and 1,073 non-COVID-19 pneumonia patients, we developed a modified DenseNet-264 model, COVIDNet, to classify CT images to either class. When tested on an independent set of 233 COVID-19 and 289 non-COVID-19 pneumonia patients, COVIDNet achieved an accuracy rate of 94.3% and an area under the curve of 0.98. As of March 23, 2020, the COVIDNet system had been used 11,966 times with a sensitivity of 91.12% and a specificity of 88.50% in six hospitals with PCR confirmation. Application of DL to CT images may improve both efficiency and capacity of case detection and long-term surveillance.

scholarly journals EPCO-25. AN IMMUNOMETHYLOMIC PLATFORM INTEGRATING SYSTEMIC IMMUNE PROFILES AND EPIGENETIC AGE IN NEURO-ONCOLOGY

2020 ◽  
Vol 22 (Supplement_2) ◽  
pp. ii74-ii74
Author(s):  
Annette Molinaro ◽  
John Wiencke ◽  
Gayathri Warrier ◽  
JiYoon Lee ◽  
Devin Koestler ◽  
...  
Keyword(s):  
Immune Cell ◽  
Independent Set ◽  
Survival Models ◽  
Brier Score ◽  
Biological Aging ◽  
Survival Times ◽  
Bootstrap Sampling ◽  
Final Model ◽  
Epigenetic Age ◽  
Cell Fractions

Abstract Lineage-specific DNA methylation marks differentiate leukocyte cell types while individual biological aging mechanisms impact other methylation alterations. Human glioma incidence and survival times have been shown to be associated with aberrant immune profiles and have a strong dependency on age. Here we developed a single epigenetic analysis framework to evaluate both immune cell fractions and epigenetic age in peripheral blood. We examined these measures in archived blood from 197 triple-negative glioma patients (TNG; IDH wildtype, 1p19q intact and TERT wildtype) and 312 frequency-matched controls from the SF Bay Area Adult Glioma Study (AGS). Significant differences were observed with TNG cases having lower CD4 and CD8 T cell, natural killer, and B cell fractions, and higher neutrophil fractions than controls. TNG cases were significantly older than controls in two of three epigenetic age estimates; however, there was no difference in epigenetic age acceleration once immune cell proportions were considered. For the TNG cases, we augmented results from several machine learning methods to delineate risk groups of TNG patients with significantly different overall survival. We compared survival models built by recursive partitioning, random forest, and elastic net methods. The final model was chosen by repeated bootstrap sampling via the Brier score loss function and validated in an independent set of 72 IDH-mutant only or TERT-mutant only glioma patients also from the AGS. The final model indicated important interactions between immune cell fractions (including CD4 and CD8 T cells and neutrophils) and treatment, age, and dexamethasone status when adjusted for the main effects of epigenetic age, glioblastoma status, and the neutrophil-to-lymphocyte ratio. The capacity of immunomethylomics to capture diverse, clinically relevant information and the simplicity of its implementation make this a powerful tool for personalized patient evaluation in the neuro-oncology clinic.

scholarly journals Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yaoxin Li ◽  
Jing Liu ◽  
Guozheng Lin ◽  
Yueyuan Hou ◽  
Muyun Mou ◽  
...  
Keyword(s):  
Objective Function ◽  
Statistical Physics ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Vertex Cover ◽  
Independent Set ◽  
Computational Social Science ◽  
Maximization Problem ◽  
Maximum Independent Set ◽  
Gradient Descent Algorithm

AbstractIn computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

scholarly journals Imaging Mass Spectrometry-Based Proteomic Analysis to Differentiate Melanocytic Nevi and Malignant Melanoma

Cancers ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 3197
Author(s):  
Rita Casadonte ◽  
Mark Kriegsmann ◽  
Katharina Kriegsmann ◽  
Isabella Hauk ◽  
Rolf R. Meliß ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Malignant Melanoma ◽  
Operating Characteristic ◽  
Characteristic Curve ◽  
Imaging Mass Spectrometry ◽  
Independent Set ◽  
Molecular Techniques ◽  
Charge Ratio ◽  
Linear Discriminant ◽  
Melanocytic Nevi

The discrimination of malignant melanoma from benign nevi may be difficult in some cases. For this reason, immunohistological and molecular techniques are included in the differential diagnostic toolbox for these lesions. These methods are time consuming when applied subsequently and, in some cases, no definitive diagnosis can be made. We studied both lesions by imaging mass spectrometry (IMS) in a large cohort (n = 203) to determine a different proteomic profile between cutaneous melanomas and melanocytic nevi. Sample preparation and instrument setting were tested to obtain optimal results in term of data quality and reproducibility. A proteomic signature was found by linear discriminant analysis to discern malignant melanoma from benign nevus (n = 113) with an overall accuracy of >98%. The prediction model was tested in an independent set (n = 90) reaching an overall accuracy of 93% in classifying melanoma from nevi. Statistical analysis of the IMS data revealed mass-to-charge ratio (m/z) peaks which varied significantly (Area under the receiver operating characteristic curve > 0.7) between the two tissue types. To our knowledge, this is the largest IMS study of cutaneous melanoma and nevi performed up to now. Our findings clearly show that discrimination of melanocytic nevi from melanoma is possible by IMS.

Sign in / Sign up

Export Citation Format

Share Document