122,827 research outputs found
On modular decompositions of system signatures
Considering a semicoherent system made up of components having i.i.d.
continuous lifetimes, Samaniego defined its structural signature as the
-tuple whose -th coordinate is the probability that the -th component
failure causes the system to fail. This -tuple, which depends only on the
structure of the system and not on the distribution of the component lifetimes,
is a very useful tool in the theoretical analysis of coherent systems.
It was shown in two independent recent papers how the structural signature of
a system partitioned into two disjoint modules can be computed from the
signatures of these modules. In this work we consider the general case of a
system partitioned into an arbitrary number of disjoint modules organized in an
arbitrary way and we provide a general formula for the signature of the system
in terms of the signatures of the modules.
The concept of signature was recently extended to the general case of
semicoherent systems whose components may have dependent lifetimes. The same
definition for the -tuple gives rise to the probability signature, which may
depend on both the structure of the system and the probability distribution of
the component lifetimes. In this general setting, we show how under a natural
condition on the distribution of the lifetimes, the probability signature of
the system can be expressed in terms of the probability signatures of the
modules. We finally discuss a few situations where this condition holds in the
non-i.i.d. and nonexchangeable cases and provide some applications of the main
results
Coleman-Gross height pairings and the -adic sigma function
We give a direct proof that the Mazur-Tate and Coleman-Gross heights on
elliptic curves coincide. The main ingredient is to extend the Coleman-Gross
height to the case of divisors with non-disjoint support and, doing some
-adic analysis, show that, in particular, its component above gives, in
the special case of an ordinary elliptic curve, the -adic sigma function.
We use this result to give a short proof of a theorem of Kim characterizing
integral points on elliptic curves in some cases under weaker assumptions. As a
further application, we give new formulas to compute double Coleman integrals
from tangential basepoints.Comment: AMS-LaTeX 17 page
Geographic Distribution of Environmental Relative Moldiness Index Molds in USA Homes
Objective. The objective of this study was to quantify and describe the distribution of the 36 molds that make up the Environmental Relative Moldiness Index (ERMI).
Materials and Methods. As part of the 2006 American Healthy Homes Survey, settled dust samples were analyzed by mold-specific quantitative PCR (MSQPCR) for the 36 ERMI molds. Each species' geographical distribution pattern was examined individually, followed by partitioning analysis in order to identify spatially meaningful patterns. For mapping, the 36 mold populations were divided into disjoint clusters on the basis of their standardized concentrations, and First Principal Component (FPC) scores were computed.
Results and Conclusions. The partitioning analyses failed to uncover a valid partitioning that yielded compact, well-separated partitions with systematic spatial distributions, either on global or local criteria. Disjoint variable clustering resulted in seven mold clusters. The 36 molds and ERMI values themselves were found to be heterogeneously distributed across the United States of America (USA)
Distributed Connectivity Decomposition
We present time-efficient distributed algorithms for decomposing graphs with
large edge or vertex connectivity into multiple spanning or dominating trees,
respectively. As their primary applications, these decompositions allow us to
achieve information flow with size close to the connectivity by parallelizing
it along the trees. More specifically, our distributed decomposition algorithms
are as follows:
(I) A decomposition of each undirected graph with vertex-connectivity
into (fractionally) vertex-disjoint weighted dominating trees with total weight
, in rounds.
(II) A decomposition of each undirected graph with edge-connectivity
into (fractionally) edge-disjoint weighted spanning trees with total
weight , in
rounds.
We also show round complexity lower bounds of
and
for the above two decompositions,
using techniques of [Das Sarma et al., STOC'11]. Moreover, our
vertex-connectivity decomposition extends to centralized algorithms and
improves the time complexity of [Censor-Hillel et al., SODA'14] from
to near-optimal .
As corollaries, we also get distributed oblivious routing broadcast with
-competitive edge-congestion and -competitive
vertex-congestion. Furthermore, the vertex connectivity decomposition leads to
near-time-optimal -approximation of vertex connectivity: centralized
and distributed . The former moves
toward the 1974 conjecture of Aho, Hopcroft, and Ullman postulating an
centralized exact algorithm while the latter is the first distributed vertex
connectivity approximation
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