122 research outputs found
On the topological classification of binary trees using the Horton-Strahler index
The Horton-Strahler (HS) index has been shown to
be relevant to a number of physical (such at diffusion limited aggregation)
geological (river networks), biological (pulmonary arteries, blood vessels,
various species of trees) and computational (use of registers) applications.
Here we revisit the enumeration problem of the HS index on the rooted,
unlabeled, plane binary set of trees, and enumerate the same index on the
ambilateral set of rooted, plane binary set of trees of leaves. The
ambilateral set is a set of trees whose elements cannot be obtained from each
other via an arbitrary number of reflections with respect to vertical axes
passing through any of the nodes on the tree. For the unlabeled set we give an
alternate derivation to the existing exact solution. Extending this technique
for the ambilateral set, which is described by an infinite series of non-linear
functional equations, we are able to give a double-exponentially converging
approximant to the generating functions in a neighborhood of their convergence
circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos
correcte
Topological self-similarity on the random binary-tree model
Asymptotic analysis on some statistical properties of the random binary-tree
model is developed. We quantify a hierarchical structure of branching patterns
based on the Horton-Strahler analysis. We introduce a transformation of a
binary tree, and derive a recursive equation about branch orders. As an
application of the analysis, topological self-similarity and its generalization
is proved in an asymptotic sense. Also, some important examples are presented
Self-similar community structure in organisations
The formal chart of an organisation is designed to handle routine and easily
anticipated problems, but unexpected situations arise which require the
formation of new ties so that the corresponding extra tasks can be properly
accomplished. The characterisation of the structure of such informal networks
behind the formal chart is a key element for successful management. We analyse
the complex e-mail network of a real organisation with about 1,700 employees
and determine its community structure. Our results reveal the emergence of
self-similar properties that suggest that some universal mechanism could be the
underlying driving force in the formation and evolution of informal networks in
organisations, as happens in other self-organised complex systems
Effects of watershed land use on nitrogen concentrations and δ15 Nitrogen in groundwater
Author Posting. © The Authors, 2005. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Biogeochemistry 77 (2006): 199-215, doi:10.1007/s10533-005-1036-2.Eutrophication is a major agent of change affecting freshwater, estuarine, and marine
systems. It is largely driven by transportation of nitrogen from natural and anthropogenic
sources. Research is needed to quantify this nitrogen delivery and to link the delivery to
specific land-derived sources. In this study we measured nitrogen concentrations and δ15N
values in seepage water entering three freshwater ponds and six estuaries on Cape Cod,
Massachusetts and assessed how they varied with different types of land use. Nitrate
concentrations and δ15N values in groundwater reflected land use in developed and pristine
watersheds. In particular, watersheds with larger populations delivered larger nitrate loads with
higher δ15N values to receiving waters. The enriched δ15N values confirmed nitrogen loading
model results identifying wastewater contributions from septic tanks as the major N source.
Furthermore, it was apparent that N coastal sources had a relatively larger impact on the N
loads and isotopic signatures than did inland N sources further upstream in the watersheds.
This finding suggests that management priorities could focus on coastal sources as a first
course of action. This would require management constraints on a much smaller population.This work was supported
by funds from the Woods Hole Oceanographic Institution Sea Grant Program, from the
Cooperative Institute for Coastal and Estuarine Environmental Technology, from
Massachusetts Department of Environmental Protection to Applied Science Associates,
Narragansett, RI, as well as from Palmer/McLeod and NOAA National Estuarine Research
Reserve Fellowships to Kevin Kroeger. This work is the result of research sponsored by NOAA
National Sea Grant College Program Office, Department of Commerce, under Grant No.
NA86RG0075, Woods Hole Oceanographic Institution Sea Grant Project No. R/M-40
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