52,502 research outputs found
Convergence of the Abelian sandpile
The Abelian sandpile growth model is a diffusion process for configurations
of chips placed on vertices of the integer lattice , in which
sites with at least 2d chips {\em topple}, distributing 1 chip to each of their
neighbors in the lattice, until no more topplings are possible. From an initial
configuration consisting of chips placed at a single vertex, the rescaled
stable configuration seems to converge to a particular fractal pattern as . However, little has been proved about the appearance of the stable
configurations. We use PDE techniques to prove that the rescaled stable
configurations do indeed converge to a unique limit as . We
characterize the limit as the Laplacian of the solution to an elliptic obstacle
problem.Comment: 12 pages, 2 figures, acroread recommended for figure displa
Dairy Product Manufacturing Costs at Cooperative Plants
Cost data are summarized for 14 plants manufacturing cheese, butter, and powder and average costs are presented for each product. Average cost curves are estimated for each plant. The scale of plant for least-cost operations is identified for plants of each product type. Plant capacity utilization and seasonal volume variation and their impacts on manufacturing cost are delineated.Cooperatives, dairy, average cost curve, productivity, capacity utilization, seasonal variation, economies of scale, Agribusiness,
Identifying Keystone Species in the Human Gut Microbiome from Metagenomic Timeseries using Sparse Linear Regression
Human associated microbial communities exert tremendous influence over human
health and disease. With modern metagenomic sequencing methods it is possible
to follow the relative abundance of microbes in a community over time. These
microbial communities exhibit rich ecological dynamics and an important goal of
microbial ecology is to infer the interactions between species from sequence
data. Any algorithm for inferring species interactions must overcome three
obstacles: 1) a correlation between the abundances of two species does not
imply that those species are interacting, 2) the sum constraint on the relative
abundances obtained from metagenomic studies makes it difficult to infer the
parameters in timeseries models, and 3) errors due to experimental uncertainty,
or mis-assignment of sequencing reads into operational taxonomic units, bias
inferences of species interactions. Here we introduce an approach, Learning
Interactions from MIcrobial Time Series (LIMITS), that overcomes these
obstacles. LIMITS uses sparse linear regression with boostrap aggregation to
infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested
LIMITS on synthetic data and showed that it could reliably infer the topology
of the inter-species ecological interactions. We then used LIMITS to
characterize the species interactions in the gut microbiomes of two individuals
and found that the interaction networks varied significantly between
individuals. Furthermore, we found that the interaction networks of the two
individuals are dominated by distinct "keystone species", Bacteroides fragilis
and Bacteroided stercosis, that have a disproportionate influence on the
structure of the gut microbiome even though they are only found in moderate
abundance. Based on our results, we hypothesize that the abundances of certain
keystone species may be responsible for individuality in the human gut
microbiome
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