Immutable glycine-based perfect alignment of protein families

Perfect Triangle Families

The Dual Theorem of Lucchesi and Younger [3] states that in every (finite) planar directed graph, there is a minimum feedback set (an edge set containing at least one edge of each directed circuit) whose cardinality is equal to the maximum number of mutually edge-disjoint directed circuits. In this note we prove that an analogue of this classical result remains valid when 3-circuits (that is, t...

Probabilistic Modeling and Alignment of Protein Structure Families

ABSTRACT Motivation: Multiple protein structure alignment is an important tool in bioinformatics. Although several algorithms exist for this purpose, recent publications highlight inconsistencies among alignments from different algorithms and, increasingly, the recognition that alignments by a single algorithm may be highly unstable under small fluctuations of the input protein structures arisi...

Mad families constructed from perfect almost disjoint families

We prove the consistency of b > א1 together with the existence of a Π11definable mad family, answering a question posed by Friedman and Zdomskyy in [7, Question 16]. For the proof we construct a mad family in L which is an א1-union of perfect a.d. sets, such that this union remains mad in the iterated Hechler extension. The construction also leads us to isolate a new cardinal invariant, the Bor...

Perfect hash families from transversal designs

Some Recursive Constructions for Perfect Hash Families

An (n; m; w)-perfect hash family is a set of functions F such that there exists at least one f 2 F such that fj X is one-to-one. Perfect hash families have been extensively studied by computer scientists for over 15 years, mainly from the point of view of constructing eecient algorithms. In this paper, we study perfect hash families from a com-binatorial viewpoint, and describe some new recursi...