Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization

We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update time of $\tilde O(mn/\epsilon)$ and constant query time by Roditty and Zwick [FOCS 2004]. The fastest deterministic algorithm is from a 1981 paper by Even and Shiloach [JACM 1981]; it has a total update time of $O(mn^2)$ and constant query time. We improve these results as follows: (1) We present an algorithm with a total update time of $\tilde O(n^{5/2}/\epsilon)$ and constant query time that has an additive error of $2$ in addition to the $1+\epsilon$ multiplicative error. This beats the previous $\tilde O(mn/\epsilon)$ time when $m=\Omega(n^{3/2})$. Note that the additive error is unavoidable since, even in the static case, an $O(n^{3-\delta})$-time (a so-called truly subcubic) combinatorial algorithm with $1+\epsilon$ multiplicative error cannot have an additive error less than $2-\epsilon$, unless we make a major breakthrough for Boolean matrix multiplication [Dor et al. FOCS 1996] and many other long-standing problems [Vassilevska Williams and Williams FOCS 2010]. The algorithm can also be turned into a $(2+\epsilon)$-approximation algorithm (without an additive error) with the same time guarantees, improving the recent $(3+\epsilon)$-approximation algorithm with $\tilde O(n^{5/2+O(\sqrt{\log{(1/\epsilon)}/\log n})})$ running time of Bernstein and Roditty [SODA 2011] in terms of both approximation and time guarantees. (2) We present a deterministic algorithm with a total update time of $\tilde O(mn/\epsilon)$ and a query time of $O(\log\log n)$. The algorithm has a multiplicative error of $1+\epsilon$ and gives the first improved deterministic algorithm since 1981. It also answers an open question raised by Bernstein [STOC 2013].Comment: A preliminary version was presented at the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS 2013

The Limit Behavior Of The Trajectories of Dissipative Quadratic Stochastic Operators on Finite Dimensional Simplex

The limit behavior of trajectories of dissipative quadratic stochastic operators on a finite-dimensional simplex is fully studied. It is shown that any dissipative quadratic stochastic operator has either unique or infinitely many fixed points. If dissipative quadratic stochastic operator has a unique point, it is proven that the operator is regular at this fixed point. If it has infinitely many fixed points, then it is shown that $\omega-$ limit set of the trajectory is contained in the set of fixed points.Comment: 14 pages, accepted in Difference Eq. App

Monitoring the Thermal Power of Nuclear Reactors with a Prototype Cubic Meter Antineutrino Detector

In this paper, we estimate how quickly and how precisely a reactor's operational status and thermal power can be monitored over hour to month time scales, using the antineutrino rate as measured by a cubic meter scale detector. Our results are obtained from a detector we have deployed and operated at 25 meter standoff from a reactor core. This prototype can detect a prompt reactor shutdown within five hours, and monitor relative thermal power to three percent within seven days. Monitoring of short-term power changes in this way may be useful in the context of International Atomic Energy Agency's (IAEA) Reactor Safeguards Regime, or other cooperative monitoring regimes.Comment: 10 pages, 9 figure

Reconstructing the direction of reactor antineutrinos via electron scattering in Gd-doped water Cherenkov detectors

The potential of elastic antineutrino-electron scattering in a Gd-doped water Cherenkov detector to determine the direction of a nuclear reactor antineutrino flux was investigated using the recently proposed WATCHMAN antineutrino experiment as a baseline model. The expected scattering rate was determined assuming a 13-km standoff from a 3.758-GWt light water nuclear reactor and the detector response was modeled using a Geant4-based simulation package. Background was estimated via independent simulations and by scaling published measurements from similar detectors. Background contributions were estimated for solar neutrinos, misidentified reactor-based inverse beta decay interactions, cosmogenic radionuclides, water-borne radon, and gamma rays from the photomultiplier tubes (PMTs), detector walls, and surrounding rock. We show that with the use of low background PMTs and sufficient fiducialization, water-borne radon and cosmogenic radionuclides pose the largest threats to sensitivity. Directional sensitivity was then analyzed as a function of radon contamination, detector depth, and detector size. The results provide a list of experimental conditions that, if satisfied in practice, would enable antineutrino directional reconstruction at 3$\sigma$ significance in large Gd-doped water Cherenkov detectors with greater than 10-km standoff from a nuclear reactor.Comment: 11 pages, 9 figure

The effect of hydrogen on the deformation behavior of a single crystal nickel-base superalloy

The effect of hydrogen on the tensile deformation behavior of PWA 1480 is presented. Tensile tests were interrupted at different plastic strain levels to observe the development of the dislocation structure. Transmission electron microscopy (TEM) foils were cut perpendicular to the tensile axis to allow the deformation of both phases to be simultaneously observed as well as parallel to zone axes (III) to show the superdislocations on their slip planes. Similar to other nickel-base superalloys, hydrogen was detrimental to the room temperature tensile properties of PWA 1480. There was little effect on strength, however the material was severely embrittled. Even without hydrogen, the elongation-to-failure was only approximately 3 percent. The tensile fracture surface was made up primarily of ductile voids with regions of cleavage fracture. These cleavage facets are the eutectic (gamma') in the microstructure. It was shown by quantitative fractography that hydrogen embrittles the eutectic (gamma') and causes the crack path to seek out and fracture through the eutectic (gamma'). There was two to three times the amount of cleavage on the fracture surface of the hydrogen-charged samples than on the surface of the uncharged samples. The effect of hydrogen can also be seen in the dislocation structure. There is a marked tendency for dislocation trapping in the gamma matrix with and without hydrogen at all plastic strain levels. Without hydrogen there is a high dislocation density in the gamma matrix leading to strain exhaustion in this region and failure through the matrix. The dislocation structure at failure with hydrogen is slightly different. The TEM foils cut parallel to zone axes (III) showed dislocations wrapping around gamma precipitates. Zone axes (001) foils show that there is a lower dislocation density in the gamma matrix which can be linked to the effects of hydrogen on the fracture behavior. The primary activity in the gamma precipitates is in the form of superlattice intrinsic stacking faults (SISFs). These faults have also been reported in other ordered alloys and superalloys

Observation of Neutrons with a Gadolinium Doped Water Cerenkov Detector

Spontaneous and induced fission in Special Nuclear Material (SNM) such as 235U and 239Pu results in the emission of neutrons and high energy gamma-rays. The multiplicities of and time correlations between these particles are both powerful indicators of the presence of fissile material. Detectors sensitive to these signatures are consequently useful for nuclear material monitoring, search, and characterization. In this article, we demonstrate sensitivity to both high energy gamma-rays and neutrons with a water Cerenkov based detector. Electrons in the detector medium, scattered by gamma-ray interactions, are detected by their Cerenkov light emission. Sensitivity to neutrons is enhanced by the addition of a gadolinium compound to the water in low concentrations. Cerenkov light is similarly produced by an 8 MeV gamma-ray cascade following neutron capture on the gadolinium. The large solid angle coverage and high intrinsic efficiency of this detection approach can provide robust and low cost neutron and gamma-ray detection with a single device.Comment: 7 pages, 4 figures. Submitted to Nuclear Instruments and Methods,

Energy Dependence of the Delta Resonance: Chiral Dynamics in Action

There is an important connection between the low energy theorems of QCD and the energy dependence of the Delta resonance in pi-N scattering, as well as the closely related gamma^{*} N -> pi N reaction. The resonance shape is due not only to the strong pi-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presentedComment: 11 pages, 6 figures, Festschrift for S.N. yan

Extending Feynman's Formalisms for Modelling Human Joint Action Coordination

The recently developed Life-Space-Foam approach to goal-directed human action deals with individual actor dynamics. This paper applies the model to characterize the dynamics of co-action by two or more actors. This dynamics is modelled by: (i) a two-term joint action (including cognitive/motivatonal potential and kinetic energy), and (ii) its associated adaptive path integral, representing an infinite--dimensional neural network. Its feedback adaptation loop has been derived from Bernstein's concepts of sensory corrections loop in human motor control and Brooks' subsumption architectures in robotics. Potential applications of the proposed model in human--robot interaction research are discussed. Keywords: Psycho--physics, human joint action, path integralsComment: 6 pages, Late