81,599 research outputs found
How proofs are prepared at Camelot
We study a design framework for robust, independently verifiable, and
workload-balanced distributed algorithms working on a common input. An
algorithm based on the framework is essentially a distributed encoding
procedure for a Reed--Solomon code, which enables (a) robustness against
byzantine failures with intrinsic error-correction and identification of failed
nodes, and (b) independent randomized verification to check the entire
computation for correctness, which takes essentially no more resources than
each node individually contributes to the computation. The framework builds on
recent Merlin--Arthur proofs of batch evaluation of Williams~[{\em Electron.\
Colloq.\ Comput.\ Complexity}, Report TR16-002, January 2016] with the
observation that {\em Merlin's magic is not needed} for batch evaluation---mere
Knights can prepare the proof, in parallel, and with intrinsic
error-correction.
The contribution of this paper is to show that in many cases the verifiable
batch evaluation framework admits algorithms that match in total resource
consumption the best known sequential algorithm for solving the problem. As our
main result, we show that the -cliques in an -vertex graph can be counted
{\em and} verified in per-node time and space on
compute nodes, for any constant and
positive integer divisible by , where is the
exponent of matrix multiplication. This matches in total running time the best
known sequential algorithm, due to Ne{\v{s}}et{\v{r}}il and Poljak [{\em
Comment.~Math.~Univ.~Carolin.}~26 (1985) 415--419], and considerably improves
its space usage and parallelizability. Further results include novel algorithms
for counting triangles in sparse graphs, computing the chromatic polynomial of
a graph, and computing the Tutte polynomial of a graph.Comment: 42 p
On sets of irreducible polynomials closed by composition
Let be a set of monic degree polynomials over a finite field
and let be the compositional semigroup generated by . In this
paper we establish a necessary and sufficient condition for to be
consisting entirely of irreducible polynomials. The condition we deduce depends
on the finite data encoded in a certain graph uniquely determined by the
generating set . Using this machinery we are able both to show
examples of semigroups of irreducible polynomials generated by two degree
polynomials and to give some non-existence results for some of these sets in
infinitely many prime fields satisfying certain arithmetic conditions
Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation
An extremely fast time-harmonic finite element solver developed for the
transmission analysis of photonic crystals was applied to mask simulation
problems. The applicability was proven by examining a set of typical problems
and by a benchmarking against two established methods (FDTD and a differential
method) and an analytical example. The new finite element approach was up to
100 times faster than the competing approaches for moderate target accuracies,
and it was the only method which allowed to reach high target accuracies.Comment: 12 pages, 8 figures (see original publication for images with a
better resolution
Molecular gas in extreme star-forming environments: the starbursts Arp220 and NGC6240 as case studies
We report single-dish multi-transition measurements of the 12^CO, HCN, and
HCO^+ molecular line emission as well as HNC J=1-0 and HNCO in the two
ultraluminous infra-red galaxies Arp220 and NGC6240. Using this new molecular
line inventory, in conjunction with existing data in the literature, we
compiled the most extensive molecular line data sets to date for such galaxies.
The many rotational transitions, with their different excitation requirements,
allow the study of the molecular gas over a wide range of different densities
and temperatures with significant redundancy, and thus allow good constraints
on the properties of the dense gas in these two systems. The mass (~(1-2) x
10^10 Msun) of dense gas (>10^5-6 cm^-3) found accounts for the bulk of their
molecular gas mass, and is consistent with most of their IR luminosities
powered by intense star bursts while self-regulated by O,B star cluster
radiative pressure onto the star-forming dense molecular gas. The highly
excited HCN transitions trace a gas phase ~(10-100)x denser than that of the
sub-thermally excited HCO^+ lines (for both galaxies). These two phases are
consistent with an underlying density-size power law found for Galactic GMCs
(but with a steeper exponent), with HCN lines tracing denser and more compact
regions than HCO^+. Whether this is true in IR-luminous, star forming galaxies
in general remains to be seen, and underlines the need for observations of
molecular transitions with high critical densities for a sample of bright
(U)LIRGs in the local Universe -- a task for which the HI-FI instrument on
board Herschel is ideally suited to do.Comment: 38 pages (preprint ApJ style), 3 figures, accepted for Ap
Close Pairs as Proxies for Galaxy Cluster Mergers
Galaxy cluster merger statistics are an important component in understanding
the formation of large-scale structure. Unfortunately, it is difficult to study
merger properties and evolution directly because the identification of cluster
mergers in observations is problematic. We use large N-body simulations to
study the statistical properties of massive halo mergers, specifically
investigating the utility of close halo pairs as proxies for mergers. We
examine the relationship between pairs and mergers for a wide range of merger
timescales, halo masses, and redshifts (0<z<1). We also quantify the utility of
pairs in measuring merger bias. While pairs at very small separations will
reliably merge, these constitute a small fraction of the total merger
population. Thus, pairs do not provide a reliable direct proxy to the total
merger population. We do find an intriguing universality in the relation
between close pairs and mergers, which in principle could allow for an estimate
of the statistical merger rate from the pair fraction within a scaled
separation, but including the effects of redshift space distortions strongly
degrades this relation. We find similar behavior for galaxy-mass halos, making
our results applicable to field galaxy mergers at high redshift. We investigate
how the halo merger rate can be statistically described by the halo mass
function via the merger kernel (coagulation), finding an interesting
environmental dependence of merging: halos within the mass resolution of our
simulations merge less efficiently in overdense environments. Specifically,
halo pairs with separations less than a few Mpc/h are more likely to merge in
underdense environments; at larger separations, pairs are more likely to merge
in overdense environments.Comment: 12 pages, 9 figures; Accepted for publication in ApJ. Significant
additions to text and two figures changed. Added new findings on the
universality of pair mergers and added analysis of the effect of FoF linking
length on halo merger
On the Triality Theory for a Quartic Polynomial Optimization Problem
This paper presents a detailed proof of the triality theorem for a class of
fourth-order polynomial optimization problems. The method is based on linear
algebra but it solves an open problem on the double-min duality left in 2003.
Results show that the triality theory holds strongly in a tri-duality form if
the primal problem and its canonical dual have the same dimension; otherwise,
both the canonical min-max duality and the double-max duality still hold
strongly, but the double-min duality holds weakly in a symmetrical form. Four
numerical examples are presented to illustrate that this theory can be used to
identify not only the global minimum, but also the largest local minimum and
local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011.
arXiv admin note: substantial text overlap with arXiv:1104.297
Covariant entropy conjecture and concordance cosmological models
Recently a covariant entropy conjecture has been proposed for dynamical
horizons. We apply this conjecture to concordance cosmological models, namely,
those cosmological models filled with perfect fluids, in the presence of a
positive cosmological constant. As a result, we find this conjecture has a
severe constraint power. Not only does this conjecture rule out those
cosmological models disfavored by the anthropic principle, but also it imposes
an upper bound on the cosmological constant for our own universe,
which thus provides an alternative macroscopic perspective for understanding
the long-standing cosmological constant problem.Comment: 10 pages, 1 figure, JHEP style, references added, published versio
Water-soluble SOA from Alkene ozonolysis: composition and droplet activation kinetics inferences from analysis of CCN activity
Cloud formation characteristics of the water-soluble organic fraction (WSOC) of secondary organic aerosol (SOA) formed from the ozonolysis of alkene hydrocarbons (terpinolene, 1-methlycycloheptene and cycloheptene) are studied. Based on size-resolved measurements of CCN activity (of the pure and salted WSOC samples) we estimate the average molar volume and surface tension depression associated with the WSOC using Köhler Theory Analysis (KTA). Consistent with known speciation, the results suggest that the WSOC are composed of low molecular weight species, with an effective molar mass below 200 g mol^(−1). The water-soluble carbon is also surface-active, depressing surface tension 10–15% from that of pure water (at CCN-relevant concentrations). The inherent hygroscopicity parameter, κ, of the WSOC ranges between 0.17 and 0.25; if surface tension depression and molar volume effects are considered in κ, a remarkably constant "apparent" hygroscopicity ~0.3 emerges for all samples considered. This implies that the volume fraction of soluble material in the parent aerosol is the key composition parameter required for prediction of the SOA hygroscopicity, as shifts in molar volume across samples are compensated by changes in surface tension. Finally, using "threshold droplet growth analysis", the water-soluble organics in all samples considered do not affect CCN activation kinetics
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