83,806 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
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Thermal performance and energy savings of white and sedum-tray garden roof: A case study in a Chongqing office building
This study presents the experimental measurement of the energy consumption of three top-floor air-conditioned rooms in a typical office building in Chongqing, which is a mountainous city in the hot-summer and cold-winter zone of China, to examine the energy performance of white and sedum-tray garden roofs. The energy consumption of the three rooms was measured from September 2014 to September 2015 by monitoring the energy performance (temperature distributions of the roofs, evaporation, heat fluxes, and energy consumption) and indoor air temperature. The rooms had the same construction and appliances, except that one roof top was black, one was white, and one had a sedum-tray garden roof. This study references the International Performance Measurement and Verification Protocol (IPMVP) to calculate and compare the energy savings of the three kinds of roofs. The results indicate that the energy savings ratios of the rooms with the sedum-tray garden roof and with the white roof were 25.0% and 20.5%, respectively, as compared with the black-roofed room, in the summer; by contrast, the energy savings ratios were −9.9% and −2.7%, respectively, in the winter. Furthermore, Annual conditioning energy savings of white roof (3.9 kWh/m2) were 1.6 times the energy savings for the sedum-tray garden roof. It is evident that white roof is a preferable choice for office buildings in Chongqing. Additionally, The white roof had a reflectance of 0.58 after natural aging owing to the serious air pollution worsened its thermal performance, and the energy savings reduced by 0.033 kWh/m2·d. Evaporation was also identified to have a significant effect on the energy savings of the sedum-tray garden roof
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
Structure of polydisperse inverse ferrofluids: Theory and computer simulation
By using theoretical analysis and molecular dynamics simulations, we
investigate the structure of colloidal crystals formed by nonmagnetic
microparticles (or magnetic holes) suspended in ferrofluids (called inverse
ferrofluids), by taking into account the effect of polydispersity in size of
the nonmagnetic microparticles. Such polydispersity often exists in real
situations. We obtain an analytical expression for the interaction energy of
monodisperse, bidisperse, and polydisperse inverse ferrofluids. Body-centered
tetragonal (bct) lattices are shown to possess the lowest energy when compared
with other sorts of lattices and thus serve as the ground state of the systems.
Also, the effect of microparticle size distributions (namely, polydispersity in
size) plays an important role in the formation of various kinds of structural
configurations. Thus, it seems possible to fabricate colloidal crystals by
choosing appropriate polydispersity in size.Comment: 22 pages, 8 figure
Quasiparticle relaxation in optically excited high-Q superconducting resonators
The quasiparticle relaxation time in superconducting films has been measured
as a function of temperature using the response of the complex conductivity to
photon flux. For tantalum and aluminium, chosen for their difference in
electron-phonon coupling strength, we find that at high temperatures the
relaxation time increases with decreasing temperature, as expected for
electron-phonon interaction. At low temperatures we find in both
superconducting materials a saturation of the relaxation time, suggesting the
presence of a second relaxation channel not due to electron-phonon interaction.Comment: 4 pages, 3 figure
Searching for high- isomers in the proton-rich mass region
Configuration-constrained potential-energy-surface calculations have been
performed to investigate the isomerism in the proton-rich mass
region. An abundance of high- states are predicted. These high- states
arise from two and four-quasi-particle excitations, with and
, respectively. Their excitation energies are comparatively
low, making them good candidates for long-lived isomers. Since most nuclei
under studies are prolate spheroids in their ground states, the oblate shapes
of the predicted high- states may indicate a combination of isomerism
and shape isomerism
A general maximum entropy principle for self-gravitating perfect fluid
We consider a self-gravitating system consisting of perfect fluid with
spherical symmetry. Using the general expression of entropy density, we
extremize the total entropy under the constraint that the total number of
particles is fixed. We show that extrema of coincides precisely with the
relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic
equilibrium. Furthermore, we apply the maximum entropy principle to a charged
perfect fluid and derive the generalized TOV equation. Our work provides a
strong evidence for the fundamental relationship between general relativity and
ordinary thermodynamics.Comment: 13 pages, no figure. The arguments have been improved so that the
assumption p=p(\rho) is no longer neede
Effective potentials for atom-atom interaction at low temperatures
We discuss the concept and design of effective atom-atom potentials that
accurately describe any physical processes involving only states around the
threshold. The existence of such potentials gives hope to a quantitative, and
systematic, understanding of quantum few-atom and quantum many-atom systems at
relatively low temperatures.Comment: 4 pages, 4 figure
A laser-driven target of high-density nuclear polarized hydrogen gas
We report the best figure-of-merit achieved for an internal nuclear polarized
hydrogen gas target and a Monte Carlo simulation of spin-exchange optical
pumping. The dimensions of the apparatus were optimized using the simulation
and the experimental results were in good agreement with the simulation. The
best result achieved for this target was 50.5% polarization with 58.2% degree
of dissociation of the sample beam exiting the storage cell at a hydrogen flow
rate of atoms/s.Comment: Accepted as a Rapid Communication article in Phys. Rev.
Enhancement of quasiparticle recombination in Ta and Al superconductors by implantation of magnetic and nonmagnetic atoms
The quasiparticle recombination time in superconducting films, consisting of
the standard electron-phonon interaction and a yet to be identified low
temperature process, is studied for different densities of magnetic and
nonmagnetic atoms. For both Ta and Al, implanted with Mn, Ta and Al, we observe
an increase of the recombination rate. We conclude that the enhancement of
recombination is not due to the magnetic moment, but arises from an enhancement
of disorder.Comment: 4 pages, 4 figure
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