20,822 research outputs found
A New Expansion for Nucleon-Nucleon Interactions
We introduce a new and well defined power counting for the effective field
theory describing nucleon-nucleon interactions. Because of the large NN
scattering lengths it differs from other applications of chiral perturbation
theory and is facilitated by introducing an unusual subtraction scheme and
renormalization group analysis. Calculation to subleading order in the
expansion can be done analytically, and we present the results for both the 1S0
and 3S1-3D1 channels.Comment: 10 pages, 3 figures, latex. Corrected typo, small change to tex
Network Kriging
Network service providers and customers are often concerned with aggregate
performance measures that span multiple network paths. Unfortunately, forming
such network-wide measures can be difficult, due to the issues of scale
involved. In particular, the number of paths grows too rapidly with the number
of endpoints to make exhaustive measurement practical. As a result, it is of
interest to explore the feasibility of methods that dramatically reduce the
number of paths measured in such situations while maintaining acceptable
accuracy.
We cast the problem as one of statistical prediction--in the spirit of the
so-called `kriging' problem in spatial statistics--and show that end-to-end
network properties may be accurately predicted in many cases using a
surprisingly small set of carefully chosen paths. More precisely, we formulate
a general framework for the prediction problem, propose a class of linear
predictors for standard quantities of interest (e.g., averages, totals,
differences) and show that linear algebraic methods of subset selection may be
used to effectively choose which paths to measure. We characterize the
performance of the resulting methods, both analytically and numerically. The
success of our methods derives from the low effective rank of routing matrices
as encountered in practice, which appears to be a new observation in its own
right with potentially broad implications on network measurement generally.Comment: 16 pages, 9 figures, single-space
Fast Computation of Smith Forms of Sparse Matrices Over Local Rings
We present algorithms to compute the Smith Normal Form of matrices over two
families of local rings.
The algorithms use the \emph{black-box} model which is suitable for sparse
and structured matrices. The algorithms depend on a number of tools, such as
matrix rank computation over finite fields, for which the best-known time- and
memory-efficient algorithms are probabilistic.
For an \nxn matrix over the ring \Fzfe, where is a power of an
irreducible polynomial f \in \Fz of degree , our algorithm requires
\bigO(\eta de^2n) operations in \F, where our black-box is assumed to
require \bigO(\eta) operations in \F to compute a matrix-vector product by
a vector over \Fzfe (and is assumed greater than \Pden). The
algorithm only requires additional storage for \bigO(\Pden) elements of \F.
In particular, if \eta=\softO(\Pden), then our algorithm requires only
\softO(n^2d^2e^3) operations in \F, which is an improvement on known dense
methods for small and .
For the ring \ZZ/p^e\ZZ, where is a prime, we give an algorithm which
is time- and memory-efficient when the number of nontrivial invariant factors
is small. We describe a method for dimension reduction while preserving the
invariant factors. The time complexity is essentially linear in where is the number of operations in \ZZ/p\ZZ to evaluate the
black-box (assumed greater than ) and is the total number of non-zero
invariant factors.
To avoid the practical cost of conditioning, we give a Monte Carlo
certificate, which at low cost, provides either a high probability of success
or a proof of failure. The quest for a time- and memory-efficient solution
without restrictions on the number of nontrivial invariant factors remains
open. We offer a conjecture which may contribute toward that end.Comment: Preliminary version to appear at ISSAC 201
Screen Barriers for Reducing Interplot Movement of Three Adult Plant Bug (Hemiptera: Miridae) Species in Small Plot Experiments
Fiberglass screen barriers 1.2 m high were erected around small (7.3 x 3.7 m) plots of birdsfoot trefoil, Lotus corniculatus, to study the effectiveness of screen barriers in reducing adult plant bug migration into small field plots. Screened and unscreened (control) plots were sprayed with an insecticide at the onset of the experiment, and subsequent adult mirid migration into these trefoil plots was measured by sweep net samples during the following 24 day period. Combined adult Adelphocoris lineolatus, Lygus lineolaris, and Plagiognathus chrysanthemi densities were significantly lower in screened versus unscreened plots with 37070, 28010, and 23070 fewer adults at 7, 17, and 24 days, respectively, following insecticide application. Although these barriers were inexpensive and simple to construct, we conclude that they were not practical and effective enough for reducing adult mirid migration in small plot experiments of this type
Positive-measure self-similar sets without interior
We recall the problem posed by Peres and Solomyak in Problems on self-similar and self-affine sets; an update. Progr. Prob. 46 (2000), 95â106: can one find examples of self-similar sets with positive Lebesgue measure, but with no interior? The method in Properties of measures supported on fat Sierpinski carpets, this issue, leads to families of examples of such sets
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