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- Title
- Algebraic topology and machine learning for biomolecular modeling
- Creator
- Cang, Zixuan
- Date
- 2018
- Collection
- Electronic Theses & Dissertations
- Description
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Data is expanding in an unprecedented speed in both quantity and size. Topological data analysis provides excellent tools for analyzing high dimensional and highly complex data. Inspired by the topological data analysis's ability of robust and multiscale characterization of data and motivated by the demand of practical predictive tools in computational biology and biomedical researches, this dissertation extends the capability of persistent homology toward quantitative and predictive data...
Show moreData is expanding in an unprecedented speed in both quantity and size. Topological data analysis provides excellent tools for analyzing high dimensional and highly complex data. Inspired by the topological data analysis's ability of robust and multiscale characterization of data and motivated by the demand of practical predictive tools in computational biology and biomedical researches, this dissertation extends the capability of persistent homology toward quantitative and predictive data analysis tools with an emphasis in biomolecular systems. Although persistent homology is almost parameter free, careful treatment is still needed toward practically useful prediction models for realistic systems. This dissertation carefully assesses the representability of persistent homology for biomolecular systems and introduces a collection of characterization tools for both macromolecules and small molecules focusing on intra- and inter-molecular interactions, chemical complexities, electrostatics, and geometry. The representations are then coupled with deep learning and machine learning methods for several problems in drug design and biophysical research. In real-world applications, data often come with heterogeneous dimensions and components. For example, in addition to location, atoms of biomolecules can also be labeled with chemical types, partial charges, and atomic radii. While persistent homology is powerful in analyzing geometry of data, it lacks the ability of handling the non-geometric information. Based on cohomology, we introduce a method that attaches the non-geometric information to the topological invariants in persistent homology analysis. This method is not only useful to handle biomolecules but also can be applied to general situations where the data carries both geometric and non-geometric information. In addition to describing biomolecular systems as a static frame, we are often interested in the dynamics of the systems. An efficient way is to assign an oscillator to each atom and study the coupled dynamical system induced by atomic interactions. To this end, we propose a persistent homology based method for the analysis of the resulting trajectories from the coupled dynamical system. The methods developed in this dissertation have been applied to several problems, namely, prediction of protein stability change upon mutations, protein-ligand binding affinity prediction, virtual screening, and protein flexibility analysis. The tools have shown top performance in both commonly used validation benchmarks and community-wide blind prediction challenges in drug design.
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- Title
- Dynamic augmentation of dissipative algebraic loops
- Creator
- Graf, Peter Leo
- Date
- 1981
- Collection
- Electronic Theses & Dissertations
- Title
- Equivariant algebraic cobordism and double point relations
- Creator
- Liu, Chun Lung
- Date
- 2012
- Collection
- Electronic Theses & Dissertations
- Description
-
For a reductive connected group or a finite group over a field of characteristic zero, we define an equivariant algebraic cobordism theory by a generalized version of the double point relation of Levine-Pandharipande. We prove basic properties and the well-definedness of a canonical fixed point map. We also find explicit generators of the algebraic cobordism ring of the point when the group is finite abelian.
- Title
- Graphs and their associated line-graphs
- Creator
- Chartrand, Gary
- Date
- 1964
- Collection
- Electronic Theses & Dissertations
- Title
- Images of certain manifolds under mappings of degree one
- Creator
- Spence, Lawrence Edward, 1946-
- Date
- 1970
- Collection
- Electronic Theses & Dissertations
- Title
- Integration of topological data analysis and machine learning for small molecule property predictions
- Creator
- Wu, Kedi
- Date
- 2018
- Collection
- Electronic Theses & Dissertations
- Description
-
Accurate prediction of small molecule properties is of paramount importance to drug design and discovery. A variety of quantitative properties of small molecules has been studied in this thesis. These properties include solvation free energy, partition coefficient, aqueous solubility, and toxicity endpoints. The highlight of this thesis is to introduce an algebraic topology based method, called element specific persistent homology (ESPH), to predict small molecule properties. Essentially ESPH...
Show moreAccurate prediction of small molecule properties is of paramount importance to drug design and discovery. A variety of quantitative properties of small molecules has been studied in this thesis. These properties include solvation free energy, partition coefficient, aqueous solubility, and toxicity endpoints. The highlight of this thesis is to introduce an algebraic topology based method, called element specific persistent homology (ESPH), to predict small molecule properties. Essentially ESPH describes molecular properties in terms of multiscale and multicomponent topological invariants and is different from conventional chemical and physical representations. Based on ESPH and its modified version, element-specific topological descriptors (ESTDs) are constructed. The advantage of ESTDs is that they are systematical, comprehensive, and scalable with respect to molecular size and composition variations, and are readily suitable for machine learning methods, rendering topological learning algorithms. Due to the inherent correlation between different small molecule properties, multi-task frameworks are further employed to simultaneously predict related properties. Deep neural networks, along with ensemble methods such as random forest and gradient boosting trees, are used to develop quantitative predictive models. Physical based molecular descriptors and auxiliary descriptors are also used in addition to ESTDs. As a result, we obtain state-of-the-art results for various benchmark data sets of small molecule properties. We have also developed two online servers for predicting properties of small molecules, TopP-S and TopTox. TopP-S is a software for topological learning predictions of partition coefficient and aqueous solubility, and TopTox is a software for computing element-specific tological descriptors (ESTDs) for toxicity endpoint predictions. They are available at http://weilab.math.msu.edu/TopP-S/ and http://weilab.math.msu.edu/TopTox/, respectively.
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- Title
- Manifolds which are homology doubles
- Creator
- Downing, John Scott
- Date
- 1969
- Collection
- Electronic Theses & Dissertations
- Title
- Relative bounded cohomology and relative ℓ₁ homology
- Creator
- Park, HeeSook
- Date
- 2001
- Collection
- Electronic Theses & Dissertations