Schema mappings have been extensively studied in database research over the past decade – notably in the areas of data exchange and data integration. Recently, the notion of an information transfer order on schema mappings has been introduced to compare the amount of source information that is actually transferred by two mappings. In this paper, we present two new operators: the union and inter...

Many families of pattern-avoiding permutations can be described by a generating tree in which each node carries one integer label, computed recursively via a rewriting rule. A typical example is that of 123-avoiding permutations. The rewriting rule automatically gives a functional equation satisfied by the bivariate generating function that counts the permutations by their length and the label ...

We show that if a Legendrian knot in standard contact R3 possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology is isomorphic to singular homology groups arising from the generating family. We discuss the relationship between normal rulings, augmentations, and generating families. In particular, we provid...

New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addit...

The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition of a family of graphs that are colourable according to certain rules. In this thesis, we study additive induced-hereditary families, and some generalisations, from a colour...

Domains of unknown function (DUFs) are a large set of uncharacterized protein families that are found in the Pfam database. Here, the scale and growth of functionally uncharacterized families in biological databases are surveyed and the prospects for discovering their function are examined. In particular, the important role that structural genomics can play in identifying potential function is ...

We use the Rosetta de novo structure prediction method to produce three-dimensional structure models for all Pfam-A sequence families with average length under 150 residues and no link to any protein of known structure. To estimate the reliability of the predictions, the method was calibrated on 131 proteins of known structure. For approximately 60% of the proteins one of the top five models wa...

The first part of the talk will be a quick survey on the homotopy type of the group of Diffeomorphisms of a 3-manifold. Pioneering work was done by Hatcher and Ivanov in the late 70s and early 80s, computing this for Haken 3-manifolds and famously the Smale conjecture. Following Thurston, the natural question is whether Diff is homotopy equivalent to the group of isometries, for geometric 3-man...