Graph Partitioning Induced Phase Transitions

We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any partitioning process (even if non-optimal) that partitions the graph into equal sized connected components (clusters), the system undergoes a percolation phase transition at $f=f_c=1-2/k$ where $f$ is the fraction of edges removed to partition the graph. For optimal partitioning, at the percolation threshold, we find $S \sim N^{0.4}$ where $S$ is the size of the clusters and $\ell\sim N^{0.25}$ where $\ell$ is their diameter. Additionally, we find that $S$ undergoes multiple non-percolation transitions for $f<f_c$

Biomass distribution among tropical tree species grown under\ud differing regional climates

In the Neotropics, there is a growing interest in establishing plantations of native tree species for commerce, local consumption, and to replant on abandoned agricultural lands. Although numerous trial plantations have been established, comparative information on the performance of native trees under different regional environments is generally lacking. In this study, we evaluated the accumulation and partitioning of above-ground biomass in 16 native and two exotic tree species growing in replicated species selection trials in Panama under humid and dry regional environments. Seven of the 18 species accumulated greater total biomass at the humid site than at the dry site over a two-year period. Species specific biomass partitioning among leaves, branches and trunks was observed. However, awide range of total biomass found among species (from 1.06 kg for Dipteryx panamensis to 29.84 kg for Acacia mangium at Soberania) justified the used of an Aitchison log ratio transformation to adjust for size. When biomass partitioning was adjusted for size, a majority of these differences proved to be a result of the ability of the tree to support biomass components rather than the result of differences in the regional environments at the two sites. These findings were confirmed by comparative ANCOVAs on Aitchison-transformed and non-Aitchison-transformed variables. In these comparisons, basal diameter, height and diameter at breast height were robust predictors of biomass for the pooled data from both sites, but Aitchison-transformed\ud variables had little predictive power

Spanners for Geometric Intersection Graphs

Efficient algorithms are presented for constructing spanners in geometric intersection graphs. For a unit ball graph in R^k, a (1+\epsilon)-spanner is obtained using efficient partitioning of the space into hypercubes and solving bichromatic closest pair problems. The spanner construction has almost equivalent complexity to the construction of Euclidean minimum spanning trees. The results are extended to arbitrary ball graphs with a sub-quadratic running time. For unit ball graphs, the spanners have a small separator decomposition which can be used to obtain efficient algorithms for approximating proximity problems like diameter and distance queries. The results on compressed quadtrees, geometric graph separators, and diameter approximation might be of independent interest.Comment: 16 pages, 5 figures, Late

Termite Resource Partitioning Related to Log Diameter

The termites Reticuliterines virginicus and R. flavipes are sympatric in forests along the eastern United States from Florida to Maryland. These congeners construct subterranean nests, forage on surface and buried wood, and appear to have very similar ecological requirements. In the present study, I examined host-wood selection by these species in a coastal forest over two years. Logs inhabited by R. virginicus had significantly greater diameters than those used by R. flavipes. It is not known whether this pattern resulted from species-specific differences in preference for host size or competition for preferred logs. Host-wood temperature did not differ for R. virginicus and R. flavipes

Fiedler Vectors and Elongation of Graphs: A Threshold Phenomenon on a Particular Class of Trees

Let $G$ be a graph. Its laplacian matrix $L(G)$ is positive and we consider eigenvectors of its first non-null eigenvalue that are called Fiedler vector. They have been intensively used in spectral partitioning problems due to their good empirical properties. More recently Fiedler vectors have been also popularized in the computer graphics community to describe elongation of shapes. In more technical terms, authors have conjectured that extrema of Fiedler vectors can yield the diameter of a graph. In this work we present (FED) property for a graph $G$, i.e. the fact that diameter of a graph can be obtain by Fiedler vectors. We study in detail a parametric family of trees that gives indeed a counter example for the previous conjecture but reveals a threshold phenomenon for (FED) property. We end by an exhaustive enumeration of trees with at most 20 vertices for which (FED) is true and some perspectives.Comment: 19 page

Non-close-packed breath figures via ion-partitioning-mediated self-assembly

We report a one-step method of forming non-close-packed (NCP) pore arrays of micro- and sub-micropores using chloroform-based solutions of polystyrene acidified with hydrogen bromide for breath figure (BF) patterning. As BF patterning takes place, water vapor condenses onto the polystyrene solution, forming water droplets on the solution surface. Concurrently, preferential ion partitioning of hydrogen bromide leads to positively charged water droplets, which experience interdroplet electrostatic repulsion. Self-organization of charged water droplets because of surface flow and subsequent evaporation of the droplet templates result in ordered BF arrays with pore separation/diameter (L/D) ratios of up to 16.5. Evidence from surface potential scans show proof for preferential ion partitioning of HBr. Radial distribution functions and Voronoi polygon analysis of pore arrays show that they possess a high degree of conformational order. Past fabrication methods of NCP structures typically require multi-step processes. In contrast, we have established a new route for facile self-assembly of previously inaccessible patterns, which comprises of only a single operational step