Studying the Σ-reducibility of families introduced by [Kalimullin and Puzarenko 2009] we show that for every set X T ∅′ there is a family of sets F which is the Σ-least countable family whose Σ-jump is Σ-equivalent to X ⊕X. This fact will be generalized for the class of n-families (families of families of . . . of sets).

................................................................................ ...... CHAPTER I: INTRODUCTION.......................................................... ... OVERVIEW................................................................................... . Brief account of Drosophila embryonic development.................................. Maternal Genes in Development. . .

Protein functional annotation consists in associating proteins with textual descriptors elucidating their biological roles. The bulk of annotation is done via automated procedures that ultimately rely on annotation transfer. Despite a large number of existing protein annotation procedures the ever growing protein space is never completely annotated. One of the facets of annotation incompletenes...

Systematic analysis of the statistical and dynamical properties of proteins is critical to understanding cellular events. Extraction of biologically relevant information from a set of high-resolution structures is important because it can provide mechanistic details behind the functional properties of protein families, enabling rational comparison between families. Most of the current structura...

BACKGROUND Biological sequences, such as proteins, have been provided with annotations that assign functional information. These functional annotations are associations of proteins (or other biological sequences) with descriptors characterizing their biological roles. However, not all proteins are fully (or even at all) annotated. This annotation incompleteness limits our ability to make sound ...