Orientation-Constrained Rectangular Layouts

We construct partitions of rectangles into smaller rectangles from an input consisting of a planar dual graph of the layout together with restrictions on the orientations of edges and junctions of the layout. Such an orientation-constrained layout, if it exists, may be constructed in polynomial time, and all orientation-constrained layouts may be listed in polynomial time per layout.Comment: To appear at Algorithms and Data Structures Symposium, Banff, Canada, August 2009. 12 pages, 5 figure

Tracing the HIV-1 subtype B mobility in Europe: a phylogeographic approach

<p>Abstract</p> <p>Background</p> <p>The prevalence and the origin of HIV-1 subtype B, the most prevalent circulating clade among the long-term residents in Europe, have been studied extensively. However the spatial diffusion of the epidemic from the perspective of the virus has not previously been traced.</p> <p>Results</p> <p>In the current study we inferred the migration history of HIV-1 subtype B by way of a phylogeography of viral sequences sampled from 16 European countries and Israel. Migration events were inferred from viral phylogenies by character reconstruction using parsimony. With regard to the spatial dispersal of the HIV subtype B sequences across viral phylogenies, in most of the countries in Europe the epidemic was introduced by multiple sources and subsequently spread within local networks. Poland provides an exception where most of the infections were the result of a single point introduction. According to the significant migratory pathways, we show that there are considerable differences across Europe. Specifically, Greece, Portugal, Serbia and Spain, provide sources shedding HIV-1; Austria, Belgium and Luxembourg, on the other hand, are migratory targets, while for Denmark, Germany, Italy, Israel, Norway, the Netherlands, Sweden, Switzerland and the UK we inferred significant bidirectional migration. For Poland no significant migratory pathways were inferred.</p> <p>Conclusion</p> <p>Subtype B phylogeographies provide a new insight about the geographical distribution of viral lineages, as well as the significant pathways of virus dispersal across Europe, suggesting that intervention strategies should also address tourists, travellers and migrants.</p

Existence theorems for floorplans

The existence of floorplans with given areas and adjacencies for the rooms cannot always be guaranteed. Rectangular, isometric and convex floorplans are considered. For each, the areas of the rooms and a graph representing the required internal adjacencies between the rooms is given. This thesis gives existence theorems for a floorplan satisfying these conditions. If the graph is maximal outerplanar, only a convex floorplan can always be guaranteed. Floorplans of each type can be found if the graph is a tree. A branching index is defined for a tree, and used to give the minimum number of vertices of degree 2 in any maximal outerplanar graph, in which the tree can be embedded. If the graph of adjacencies is a tree, and each room in the plan is external, once again only convex floorplans can always be guaranteed. Rectangular floorplans can always be found in some cases, depending on the embedding index of the tree

Rectangular and orthogonal floorplans with required room areas and tree adjacency

A rectangular floorplan can always be found to satisfy area requirements for each room and adjacencies between rooms represented by a given tree, T . The branching index and embedding index of a tree are defined. If, further, each room is required to be external, then the existence of a rectangular floorplan is dependent upon the embedding index of T . Orthogonal floorplans in which each room is rectangular or L-shaped are always possible under the same conditions. Extensions to some other nonrectangular floorplans are given.

Orthogonal floorplans from maximal planar graphs

It is shown that it is always possible to construct an orthogonal floorplan satisfying the area and adjacency requirements of any vertex-weighted maximal planar graph which is its dual.

Probing the impact of chromatin conformation on genome editing tools

Therapeutic cell differentiatio