Decomposing information into copying versus transformation

Public Versus Personal Information for Mate Copying in an Invertebrate

Organisms require information to make decisions about fitness-affecting resources, such as mates. Animals may extract "personal information" about potential mates by observing their physical characteristics or extract additional "public information" by observing their mating performance [1]. Mate copying by females [2-6] is a form of public information use that may reduce uncertainty about male...

Decomposing Matrices into Blocks

In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called bordered block diagonal form. More precisely, given some matrix A, we try to assign as many rows as possible to some number β of blocks of size κ such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirab...

Decomposing Graphs into Long Paths

It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...

Decomposing triples into cyclic designs

Decomposing complete graphs into cubes

This talk concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n ≡ 1 (mod d) and n ≡ 0 (mod 2). These are known to be sufficient for d equal to 3 or 5, but for larger values of d a decomposition has been proven to exist for only sparce sets of n. We prove that f...