2,292,503 research outputs found
Waiwhakareke Restoration Plantings: Establishment of Monitoring Plots 2005-06
Waiwhakareke Natural Heritage Park is being developed to reconstruct native lowland and wetland ecosystems as were once widespread in the Waikato Region. The 60ha Natural Heritage Park is located on the north-west outskirts of Hamilton City and includes a peat lake (Horseshoe Lake) which is surrounded by introduced willow trees. There is some native marginal vegetation around the lake, including rushes and sedges, and an extensive area of gently sloping pasture completes the catchment. The restoration and recreation of the native plant and animal communities is being lead by the Hamilton City Council in partnership with The University of Waikato, Wintec, Nga Mana Toopu o Kirikiriroa Limited Resource Management and Cultural Consultants and Tui 2000 (McQueen 2005; McQueen & Clarkson 2003)
Improved Distributed Algorithms for Exact Shortest Paths
Computing shortest paths is one of the central problems in the theory of
distributed computing. For the last few years, substantial progress has been
made on the approximate single source shortest paths problem, culminating in an
algorithm of Becker et al. [DISC'17] which deterministically computes
-approximate shortest paths in time, where
is the hop-diameter of the graph. Up to logarithmic factors, this time
complexity is optimal, matching the lower bound of Elkin [STOC'04].
The question of exact shortest paths however saw no algorithmic progress for
decades, until the recent breakthrough of Elkin [STOC'17], which established a
sublinear-time algorithm for exact single source shortest paths on undirected
graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for
exact all pairs shortest paths problem on directed graphs.
In this paper, we present a new single-source shortest path algorithm with
complexity . For polylogarithmic , this improves
on Elkin's bound and gets closer to the
lower bound of Elkin [STOC'04]. For larger values of
, we present an improved variant of our algorithm which achieves complexity
, and
thus compares favorably with Elkin's bound of in essentially the entire range of parameters. This
algorithm provides also a qualitative improvement, because it works for the
more challenging case of directed graphs (i.e., graphs where the two directions
of an edge can have different weights), constituting the first sublinear-time
algorithm for directed graphs. Our algorithm also extends to the case of exact
-source shortest paths...Comment: 26 page
Nilpotent pairs, dual pairs, and sheets
Recently, V.Ginzburg introduced the notion of a principal nilpotent pair (=
pn-pair) in a semisimple Lie algebra {\frak g}. It is a double counterpart of
the notion of a regular nilpotent element. A pair (e_1,e_2) of commuting
nilpotent elements is called a pn-pair, if the dimension of their simultaneous
centralizer is equal to the rank of {\frak g} and some bi-homogeneity condition
is satisfied. Ginzburg proved that many familiar results of the `ordinary'
theory have analogues for pn-pairs. The aim of this article is to develop the
theory of nilpotent pairs a bit further and to present some applications of it
to dual pairs and sheets. It is shown that a large portion of Ginzburg's theory
can be extended to the pairs whose simultaneous centraliser is of dimension
rk{\frak g}+1. Such pairs are called almost pn-pairs. It is worth noting that
the very existence of almost pn-pairs is a purely "double" phenomenon, because
the dimension of "ordinary" orbits is always even. We prove that to any
principal or almost nilpotent pair one naturally associates a dual pair.
Moreover, this dual pair is reductive if and only if e_1 and e_2 can be
included in commuting sl_2-triples. We also study sheets containing members of
pn-pairs. Some cases are described, where these sheets are smooth and admit a
section.Comment: 27 pages, LaTeX 2.0
Ample Pairs
We show that the ample degree of a stable theory with trivial forking is
preserved when we consider the corresponding theory of belles paires, if it
exists. This result also applies to the theory of -structures of a trivial
theory of rank .Comment: Research partially supported by the program MTM2014-59178-P. The
second author conducted research with support of the programme
ANR-13-BS01-0006 Valcomo. The third author would like to thank the European
Research Council grant 33882
Cartan Pairs
A new notion of Cartan pairs as a substitute of notion of vector fields in
noncommutative geometry is proposed. The correspondence between Cartan pairs
and differential calculi is established.Comment: 7 pages in LaTeX, to be published in Czechoslovak Journal of Physics,
presented at the 5th Colloquium on Quantum Groups and Integrable Systems,
Prague, June 199
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