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 $k$-cliques in an $n$-vertex graph can be counted {\em and} verified in per-node $O(n^{(\omega+\epsilon)k/6})$ time and space on $O(n^{(\omega+\epsilon)k/6})$ compute nodes, for any constant $\epsilon>0$ and positive integer $k$ divisible by $6$, where $2\leq\omega<2.3728639$ 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

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-KK isomers in the proton-rich A∼80A\sim80 mass region

Configuration-constrained potential-energy-surface calculations have been performed to investigate the $K$ isomerism in the proton-rich $A\sim80$ mass region. An abundance of high-$K$ states are predicted. These high-$K$ states arise from two and four-quasi-particle excitations, with $K^{\pi}=8^{+}$ and $K^{\pi}=16^{+}$, 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-$K$ states may indicate a combination of $K$ 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 $S$ under the constraint that the total number of particles is fixed. We show that extrema of $S$ 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 $1.1\times 10^{18}$ 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