We address the problem of reconstructing a non-duplicated ancestor to a partially duplicated genome in a model where duplicated content is caused by several tandem duplications throughout its evolution and the only allowed rearrangement operations are DCJ. As a starting point, we consider a variant of the Genome Halving Problem, aiming at reconstructing a tandem duplicated genome instead of the...

General results on transformations on information production processes (IPPs), involving transformations of the h-index and related indices, are applied in concrete, simple cases: doubling the production per source, doubling the number of sources, doubling the number of sources but halving their production, halving the number of sources but doubling their production (fusion of sources) and, fin...

Article history: Received 12 December 2007 Available online 16 June 2009 Communicated by James W. P. Hirschfeld

In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.

We study the following Maker/Breaker game. Maker and Breaker take turns in choosing vertices from a given n-uniform hypergraph F , with Maker going first. Maker’s goal is to completely occupy a hyperedge and Breaker tries to avoid this. Beck conjectures that if the maximum neighborhood size of F is at most 2 then Breaker has a winning strategy. We disprove this conjecture by establishing an n-u...

A. For f , g ∈ ω let c∀f ,g be the minimal number of uniform g-splitting trees needed to cover the uniform f -splitting tree, i.e., for every branch ν of the f -tree, one of the g-trees contains ν. Let c∃f ,g be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that it is consistent that c∃fǫ ,gǫ = c ∀ fǫ ,gǫ = κǫ for continuum many pairwise d...

If a configuration of m triangles in the plane has only n points as vertices, then there must be a set of max { dm/(2n− 5)e Ω(m3/(n6 log n)) triangles having a common intersection. As a consequence the number of halving planes for a three-dimensional point set is O(n log n). For all m and n there exist configurations of triangles in which the largest common intersection involves max {dm/(2n− 5)...

We show that the number of halving sets of a set of n points in R is O ( n ) , improving the previous bound of [9] with a simpler (albeit similar) proof.

We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 in general position is O(n4−2/45). This improves the previous bound of O(n4−1/13 4 ). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.