How Errors in Component Reliability Affect System Reliability

This paper studies how sampling variation in component reliability estimates affects the computation of system reliability that uses these estimates as input. Results show that relative bias in system reliability grows quadratically with the number of components for which each component reliability estimate is used, whereas the corresponding coefficient of variation grows linearly with this number of components. If these components are in parallel they lead to an understatement of system reliability. In series, they lead to an overstatement. The paper describes resampling schemes that eliminate bias without increasing the dominant variance term

A Monte Carlo Sampling Plan for Estimating Network Reliability

Consider an acyclic undirected network G = (V,E) with node set V and arc set E whose arcs are subject to random failure. Let s be a node in V and T a set of nodes in V such that s ⊄ T. This paper presents a relatively complete and comprehensive description of a general class of Monte Carlo sampling plans for estimating g = g(s,T), the probability that s is connected to all nodes in T. The paper also provides procedures for implementing these plans. Each plan uses known lower and upper bounds [B,A] on g to produce an estimator of g that has a smaller variance (A-g)(g-B)/K than one obtains for crude Monte Carlo sampling (B-O, A-1) on K independent replications. The paper describes worst case bounds on sample sizes K, in terms of B and A, for meeting absolute and relative error criteria. It also gives the worst case bound on the amount of variance reduction that can be expected when compared with crude Monte Carlo sampling. Two plans are studied in detail for the case T - {t}. An example illustrates the variance reductions achievable with these plans. The paper next shows how to assess the credibility that a specified error criterion for g is met as the Monte Carlo experiment progresses and then shows how confidence intervals can be computed for g. Lastly, the paper summarizes the steps needed toimplement the proposed technique

Estimating critical path and arc probabilities in stochastic activity networks

This paper describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset H of the network to produce an upper bound of O((log K)N-IHI+l/K) on the absolute error of approximation where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of I/K1/2 that one obtains for the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K . The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of H=7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean-square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large

Do Gamma-Ray Burst Sources Repeat?

The demonstration of repeated gamma-ray bursts from an individual source would severely constrain burst source models. Recent reports (Quashnock and Lamb 1993; Wang and Lingenfelter 1993) of evidence for repetition in the first BATSE burst catalog have generated renewed interest in this issue. Here, we analyze the angular distribution of 585 bursts of the second BATSE catalog (Meegan et al. 1994). We search for evidence of burst recurrence using the nearest and farthest neighbor statistic and the two-point angular correlation function. We find the data to be consistent with the hypothesis that burst sources do not repeat; however, a repeater fraction of up to about 20% of the observed bursts cannot be excluded.Comment: ApJ Letters, in press, 13 pages, including three embedded figures. uuencoded Unix-compressed PostScrip

Endocytotic formation of vesicles and other membranous structures induced by Ca2+ and axolemmal injury

Vesicles and/or other membranous structures that form after axolemmal damage have recently been shown to repair (seal) the axolemma of various nerve axons. To determine the origin of such membranous structures, (1) we internally dialyzed isolated intact squid giant axons (GAs) and showed that elevation of intracellular Ca21 .100 uM produced membranous structures similar to those in axons transected in Ca21-containing physiological saline; (2) we exposed GA axoplasm to Ca21- containing salines and observed that membranous structures did not form after removing the axolemma and glial sheath but did form in severed GAs after .99% of their axoplasm was removed by internal perfusion; (3) we examined transected GAs and crayfish medial giant axons (MGAs) with time-lapse confocal fluorescence microscopy and showed that many injuryinduced vesicles formed by endocytosis of the axolemma; (4) we examined the cut ends of GAs and MGAs with electron microscopy and showed that most membranous structures were single-walled at short (5–15 min) post-transection times, whereas more were double- and multi-walled and of probable glial origin after longer (30–150 min) post-transection times; and (5) we examined differential interference contrast and confocal images and showed that large and small lesions evoked similar injury responses in which barriers to dye diffusion formed amid an accumulation of vesicles and other membranous structures. These and other data suggest that Ca21 inflow at large or small axolemmal lesions induces various membranous structures (including endocytotic vesicles) of glial or axonal origin to form, accumulate, and interact with each other, preformed vesicles, and/or the axolemma to repair the axolemmal damage.This work was supported by grants from National Institutes of Health (NIH; NS31256) and the State of Texas (Advanced Technology 3658-446).Neuroscienc

The Fermi GBM Gamma-Ray Burst Spectral Catalog: Four Years Of Data

In this catalog we present the updated set of spectral analyses of GRBs detected by the Fermi Gamma-Ray Burst Monitor (GBM) during its first four years of operation. It contains two types of spectra, time-integrated spectral fits and spectral fits at the brightest time bin, from 943 triggered GRBs. Four different spectral models were fitted to the data, resulting in a compendium of more than 7500 spectra. The analysis was performed similarly, but not identically to Goldstein et al. 2012. All 487 GRBs from the first two years have been re-fitted using the same methodology as that of the 456 GRBs in years three and four. We describe, in detail, our procedure and criteria for the analysis, and present the results in the form of parameter distributions both for the observer-frame and rest-frame quantities. The data files containing the complete results are available from the High-Energy Astrophysics Science Archive Research Center (HEASARC).Comment: Accepted for publication in ApJ

Quantum Breaking Time Scaling in the Superdiffusive Dynamics

We show that the breaking time of quantum-classical correspondence depends on the type of kinetics and the dominant origin of stickiness. For sticky dynamics of quantum kicked rotor, when the hierarchical set of islands corresponds to the accelerator mode, we demonstrate by simulation that the breaking time scales as $\tau_{\hbar} \sim (1/\hbar)^{1/\mu}$ with the transport exponent $\mu > 1$ that corresponds to superdiffusive dynamics. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one $\tau_{\hbar} \sim \ln(1/\hbar)$ with respect to $\hbar$

Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201

Systematic sensitivity analysis of the full economic impacts of sea level rise

The potential impacts of sea level rise (SLR) due to climate change have been widely studied in the literature. However, the uncertainty and robustness of these estimates has seldom been explored. Here we assess the model input uncertainty regarding the wide effects of SLR on marine navigation from a global economic perspective. We systematically assess the robustness of computable general equilibrium (CGE) estimates to model’s inputs uncertainty. Monte Carlo (MC) and Gaussian quadrature (GQ) methods are used for conducting a Systematic sensitivity analysis (SSA). This design allows to both explore the sensitivity of the CGE model and to compare the MC and GQ methods. Results show that, regardless whether triangular or piecewise linear Probability distributions are used, the welfare losses are higher in the MC SSA than in the original deterministic simulation. This indicates that the CGE economic literature has potentially underestimated the total economic effects of SLR, thus stressing the necessity of SSA when simulating the general equilibrium effects of SLR. The uncertainty decomposition shows that land losses have a smaller effect compared to capital and seaport productivity losses. Capital losses seem to affect the developed regions GDP more than the productivity losses do. Moreover, we show the uncertainty decomposition of the MC results and discuss the convergence of the MC results for a decomposed version of the CGE model. This paper aims to provide standardised guidelines for stochastic simulation in the context of CGE modelling that could be useful for researchers in similar settings