Atom-specific persistent homology and its application to protein flexibility analysis

An application of topological data analysis in predicting sumoylation sites

Sumoylation is a reversible post-translational modification that regulates certain significant biochemical functions in proteins. The protein alterations caused by sumoylation are associated with the incidence of some human diseases. Therefore, identifying the sites of sumoylation in proteins may provide a direction for mechanistic research and drug development. Here, we propose a new computational approach for identifying sumoylation sites using an encoding method based on topological data analysis. The features of our model captured the key physical and biological properties of proteins at multiple scales. In a 10-fold cross validation, the outcomes of our model showed 96.45% of sensitivity (Sn), 94.65% of accuracy (Acc), 0.8946 of Matthew's correlation coefficient (MCC), and 0.99 of area under curve (AUC). The proposed predictor with only topological features achieves the best MCC and AUC in comparison to the other released methods. Our results suggest that topological information is an additional parameter that can assist in the prediction of sumoylation sites and provide a novel perspective for further research in protein sumoylation.

Persistent Homology for RNA Data Analysis

Molecular representations are of great importance for machine learning models in RNA data analysis. Essentially, efficient molecular descriptors or fingerprints that characterize the intrinsic structural and interactional information of RNAs can significantly boost the performance of all learning modeling. In this paper, we introduce two persistent models, including persistent homology and persistent spectral, for RNA structure and interaction representations and their applications in RNA data analysis. Different from traditional geometric and graph representations, persistent homology is built on simplicial complex, which is a generalization of graph models to higher-dimensional situations. Hypergraph is a further generalization of simplicial complexes and hypergraph-based embedded persistent homology has been proposed recently. Moreover, persistent spectral models, which combine filtration process with spectral models, including spectral graph, spectral simplicial complex, and spectral hypergraph, are proposed for molecular representation. The persistent attributes for RNAs can be obtained from these two persistent models and further combined with machine learning models for RNA structure, flexibility, dynamics, and function analysis.

Construction of Mathematics Teaching Environment Based on Big Data on the Wisdom Cloud Platform of Higher Vocational Education

As a public basic course in the system of higher vocational colleges, mathematics has received more and more attention from education administrators. However, there are still problems in higher education that mathematics teaching resources are scatter and data are difficult to integrate. Big data (DT) and smart clouds are the burgeon of intelligent technology, which has provided support for teaching informatization and teaching data integration in colleges and universities. This article aims to solve the problems of mathematics teaching in higher vocational education, such as more content and less class hours, difficult, higher vocational education due to the expansion of enrollment, and the decline in mathematics teaching quality, and build a smart cloud platform based on big data mathematics instructing environment system and mathematics wisdom instructing. The reconstruction of the environment is the deep integration of information technology and mathematics instructing, which can promote the deep integration of information technology with teaching, management, and environment. The experiments in this article show that the application of the smart cloud platform to mathematics teaching can greatly increase students' enthusiasm for learning and improve the school's mathematics teaching level, and the improvement rate of students' performance can reach 99.89%. The research in this article is of great significance to the adjustment of mathematics teaching environment in higher professional education.

Topological data analysis in biomedicine: A review

Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.

Persistent homology and application on residues 1 to 28 of amyloid beta peptide

This article combines the principal component analysis (PCA) with persistent homology for applications in biomolecular data analysis. We extend the technique of persistent homology to localized weighted persistent homology to fit the properties of molecules. We introduce this novel PCA in the study of the folding process of residues 1 to 28 of amyloid beta peptide in solution. We are able to determine seven metastable states of amyloid beta 1 to 28 using homology of dimension 2, corresponding to seven local minimums in the free energy landscape. We also give the transition information between the seven types and the disconnectivity graph. Our result is very robust under change of parameters. Furthermore persistent homology of dimension 1 also give consistent results. This method can be applied to different peptides and molecules.