Item Open AccessClustering protein-protein interactions based on conversed domain similarities(Bilkent University, 2004) Ayaz, AslıProtein interactions govern most cellular processes, including signal transduction, transcriptional regulation and metabolism. Saccharomyces ceravisae is estimated to have 16,000 protein interactions. Appereantly only a small number of these interactions were formed ab initio (invention), rest of them were formed through gene duplications and exon shuffling (birth). Domains form functional units of a protein and are responsible for most of the interaction births, since they can be recombined and rearranged much more easily compared to innovation. Therefore groups of functionally similar, homologous interactions that evolved through births are expected to have a certain domain signature. Several high throughput techniques can detect interacting protein pairs, resulting in a rapidly growing corpus of protein interactions. Although there are several efforts for computationally integrating this data with literature and other high throughput data such as gene expression, annotation of this corpus is inadaquate for deriving interaction mechanism and outcome. Finding interaction homologies would allow us to annotate an unannotated interaction based on already annotated known interactions, or predict new ones. In this study we propose a probabilistic model for assigning interactions to homologous groups, according to their conserved domain similarities. Based on this model we have developed and implemented an Expectation-Maximization algorithm for finding the most likely grouping of an interaction set. We tested our algorithm with synthetic and real data, and showed that our initial results are very promising. Finally we propose several directions to improve this work Item Open AccessSolving equations in the universe of hypersets(Bilkent University, 1993) Pakkan, MüjdatHyperset Theory (a.k.a. ZFC~/AFA) of Peter Aczel is an enrichment of the classical ZFC set theory and uses a graphical representation for sets. By allowing non-well-founded sets, the theory provides an appropriate framework for modeling various phenomena involving circularity. Z F C /A F A has an important consequence that guarantees a solution to a set of equations in the universe of hypersets, viz. the Solution Lemma. This lemma asserts that a system of equations defined in the universe of hypersets has a unique solution, and has applications in areas like artificial intelligence, database theory, and situation theory. In this thesis, a program called HYPERSOLVER, which can solve systems of equations to which the Solution Lemma is applicable and which has built-in procedures to display the graphs depicting the solutions, is presented.