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homology
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Applications of Algebraic Topology in Data Analysis
, M.Sc. Thesis Sharif University of Technology ; Jafari, Amir (Supervisor) ; Parsa, Salman (Co-Supervisor)
Abstract
The goal of this thesis is to represent some application of algebraic topology specially homology and simplicial structures in data analysis and image processing. First the notion of topological persistence will be introduced and next for computing that several efficient algorithms will be proposed. Also complexity of the algorithms base on the topological spaces and by some algebraic topology tools. And it will be tried to test this theorical algorithms on real data and represent some application of topology in real data analysis. To do that, at the begining the tools of algebraic topology will be reviewed and the notions like singular complexes and singular homology and some related...
Improvement on Deep Learning based Methods of Protein Structure Prediction
, M.Sc. Thesis Sharif University of Technology ; Koohi, Somayye (Supervisor)
Abstract
Proteins are natural polymers composed of amino acids, which, according to their structure, can interact with other molecules and play a wide range of roles. Predicting the tertiary structure of proteins is fundamental for explaining their function and for applications such as drug design. Considering the time-consuming and expensive laboratory methods on one hand and the rapid growth and large volume of protein data on the other hand, a faster solution for finding protein structure in large scales is needed. With the increasing progress of artificial intelligence and neural networks, the use of this approach to predict the three-dimensional structure of proteins using their amino acid...