Perfect Hash Families: The Generalization to Higher Indices

Perfect hash families are often represented as combinatorial arrays encoding partitions of kitems into v classes, so that every t or fewer of the items are completely separated by at least a specified number of chosen partitions. This specified number is the index of the hash family. The case when each t-set must be separated at least once has been extensively researched; they arise in diverse applications, both directly and as fundamental ingredients in a column replacement strategy for a variety of combinatorial arrays. In this paper, construction techniques and algorithmic methods for constructing perfect hash families are surveyed, in order to explore extensions to the situation when each t-set must be separated by more than one partition.https://digitalcommons.usmalibrary.org/books/1029/thumbnail.jp

IgE binds asymmetrically to its B cell receptor CD23.

The antibody IgE plays a central role in allergic disease mechanisms. Its effector functions are controlled through interactions between the Fc region and two principal cell surface receptors FcεRI and CD23. The interaction with FcεRI is primarily responsible for allergic sensitization and the inflammatory response, while IgE binding to CD23 is involved in the regulation of IgE synthesis and allergen transcytosis. Here we present the crystal structure of a CD23/IgE-Fc complex and conduct isothermal titration calorimetric binding studies. Two lectin-like "head" domains of CD23 bind to IgE-Fc with affinities that differ by more than an order of magnitude, but the crystal structure reveals only one head bound to one of the two identical heavy-chains in the asymmetrically bent IgE-Fc. These results highlight the subtle interplay between receptor binding sites in IgE-Fc and their affinities, the understanding of which may be exploited for therapeutic intervention in allergic disease