Total Acquisition in Graphs

Let G be a weighted graph in which each vertex initially has weight 1. A total acquisition move transfers all the weight from a vertex u to a neighboring vertex v, under the condition that before the move the weight on v is at least as large as the weight on u. The (total) acquisition number of G, written at(G), is the minimum size of the set of vertices with positive weight after a sequence of total acquisition moves. Among connected n-vertex graphs, at(G) is maximized by trees. The maximum is Θ(√(n lg n) for trees with diameter 4 or 5. It is⌊(n + 1)/3⌋ for trees with diameter between 6 and (2/3)(n + 1), and it is⌈(2n – 1 – D)/4⌉ for trees with diameter D when (2/3)(n + 1) ≤ D ≤ n - 1. We characterize trees with acquisition number 1, which permits testing at(G) ≤ k in time O(nk+2) on trees. If G ≠ C5, then min{at(G), at()} = 1. If G has diameter 2, then at(G) ≤ 32 ln n ln ln n; we conjecture a constant upper bound. Indeed, at(G) = 1 when G has diameter 2 and no 4-cycle, except for four graphs with acquisition number 2. Deleting one edge of an n-vertex graph cannot increase at by more than 6.84√n, but we construct an n-vertex tree with an edge whose deletion increases it by more than (1/2)√n. We also obtain multiplicative upper bounds under products

Responses of soil cellulolytic fungal communities to elevated atmospheric CO 2 are complex and variable across five ecosystems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86979/1/j.1462-2920.2011.02548.x.pd

Common bacterial responses in six ecosystems exposed to 10 years of elevated atmospheric carbon dioxide

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91149/1/j.1462-2920.2011.02695.x.pd

No jacket required – new fungal lineage defies dress code

Analyses of environmental DNAs have provided tantalizing evidence for “rozellida” or “cryptomycota”, a clade of mostly undescribed and deeply diverging aquatic fungi. Here, we put cryptomycota into perspective through consideration of Rozella , the only clade member growing in culture. This is timely on account of the publication in Nature of the first images of uncultured cryptomycota from environmental filtrates, where molecular probes revealed non‐motile cyst‐like structures and motile spores, all lacking typical fungal chitinous cell walls. Current studies of Rozella can complement these fragmentary observations from environmental samples. Rozella has a fungal‐specific chitin synthase and its resting sporangia have walls that appear to contain chitin. Cryptomycota, including Rozella , lack a cell wall when absorbing food but like some other fungi, they may have lost their “dinner jacket” through convergence. Rather than evolutionary intermediates, the cryptomycota may be strange, divergent fungi that evolved from an ancestor with a nearly complete suite of classical fungal‐specific characters.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90101/1/94_ftp.pd

The phylogenetic composition and structure of soil microbial communities shifts in response to elevated carbon dioxide

http://www.nature.com/ismej/journal/v6/n2/full/ismej201199a.htmlOne of the major factors associated with global change is the ever-increasing concentration of atmospheric CO2. Although the stimulating effects of elevated CO2 (eCO2) on plant growth and primary productivity have been established, its impacts on the diversity and function of soil microbial communities are poorly understood. In this study, phylogenetic microarrays (PhyloChip) were used to comprehensively survey the richness, composition and structure of soil microbial communities in a grassland experiment subjected to two CO2 conditions (ambient, 368 p.p.m., versus elevated, 560 p.p.m.) for 10 years. The richness based on the detected number of operational taxonomic units (OTUs) significantly decreased under eCO2. PhyloChip detected 2269 OTUs derived from 45 phyla (including two from Archaea), 55 classes, 99 orders, 164 families and 190 subfamilies. Also, the signal intensity of five phyla (Crenarchaeota, Chloroflexi, OP10, OP9/JS1, Verrucomicrobia) significantly decreased at eCO2, and such significant effects of eCO2 on microbial composition were also observed at the class or lower taxonomic levels for most abundant phyla, such as Proteobacteria, Firmicutes, Actinobacteria, Bacteroidetes and Acidobacteria, suggesting a shift in microbial community composition at eCO2. Additionally, statistical analyses showed that the overall taxonomic structure of soil microbial communities was altered at eCO2. Mantel tests indicated that such changes in species richness, composition and structure of soil microbial communities were closely correlated with soil and plant properties. This study provides insights into our understanding of shifts in the richness, composition and structure of soil microbial communities under eCO2 and environmental factors shaping the microbial community structure