Another view of sequential sampling in the birth process with immigration.

We explore properties of the family sizes arising in a linear birth process with immigration (BI). In particular, we study the correlation of the number of families observed during consecutive disjoint intervals of time. Letting S(a, b) be the number of families observed in (a, b), we study the expected sample variance and its asymptotics for p consecutive sequential samples [Formula: see text], for [Formula: see text].

Genomic Distance with High Indel Costs.

We determine complexity of computing the DCJ-indel distance, when DCJ and indel operations have distinct constant costs, by showing an exact formula that can be computed in linear time for any choice of (constant) costs for DCJ and indel operations. We additionally consider the problem of triangular inequality disruption and propose an algorithmically efficient correction on each member of the family of DCJ-indel.

DCJ-indel and DCJ-substitution distances with distinct operation costs.

Background: Classical approaches to compute the genomic distance are usually limited to genomes with the same content and take into consideration only rearrangements that change the organization of the genome (i.e. positions and orientation of pieces of DNA, number and type of chromosomes, etc.

Restricted DCJ-indel model: sorting linear genomes with DCJ and indels.

Background: The double-cut-and-join (DCJ) is a model that is able to efficiently sort a genome into another, generalizing the typical mutations (inversions, fusions, fissions, translocations) to which genomes are subject, but allowing the existence of circular chromosomes at the intermediate steps. In the general model many circular chromosomes can coexist in some intermediate step. However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation.