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Discussion On Ph.D. Thesis Proposals in Computing Science
We first provide new constructions that prove that the "open" Hierarchical Piecewise Constant Derivative (HPCD) subclass is closer to the decidability and undecidability frontiers than was previously understood. After concluding that the HPCD-like classes are unsuitable for modeling chemical reactions, our quest for semi-decidable subclasses leads us to define the "semi-algebraic" subclass. This is the most expressive hybrid automaton subclass amenable to rigorous symbolic temporal reasoning. We begin with the bounded reachability problem, and then show how the dense-time temporal logic Timed Computation Tree Logic (TCTL) can be model-checked by exploiting techniques from real algebraic geometry, primarily real quantifier elimination. We also prove the undecidability of reachability in the Blum-Shub-Smale Turing Machine formalism. We then develop efficient approximation strategies by extending bisimulation partitioning, rectangular grid-based approximation, polytopal approximation and time discretization. We then develop a uniform algebraic framework for modeling biochemical and metabolic networks, also extending flux balance analysis. We present some preliminary results using a prototypical tool Tolque. It is a symbolic algebraic dense time model-checker for semi-algebraic hybrid automata, which uses Qepcad for quantifier elimination.
Thesis research in computer science
In recent years, the increase in the amounts of available genomic as well as gene expression data has provided researchers with the necessary information to train and test various models of gene origin, evolution, function and regulation. In this thesis, we present novel solutions to key problems in computational biology that deal with nucleotide sequences (horizontal gene transfer detection), amino-acid sequences (protein sub-cellular localization prediction), and gene expression data (transcription factor - binding site pair discovery). Different pattern discovery techniques are utilized, such as maximal sequence motif discovery and maximal itemset discovery, and combined with support vector machines in order to achieve significant improvements against previously proposed methods.