Abstract Interpretation of Stateful Networks

Modern networks achieve robustness and scalability by maintaining states on their nodes. These nodes are referred to as middleboxes and are essential for network functionality. However, the presence of middleboxes drastically complicates the task of network verification. Previous work showed that the problem is undecidable in general and EXPSPACE-complete when abstracting away the order of packet arrival. We describe a new algorithm for conservatively checking isolation properties of stateful networks. The asymptotic complexity of the algorithm is polynomial in the size of the network, albeit being exponential in the maximal number of queries of the local state that a middlebox can do, which is often small. Our algorithm is sound, i.e., it can never miss a violation of safety but may fail to verify some properties. The algorithm performs on-the fly abstract interpretation by (1) abstracting away the order of packet processing and the number of times each packet arrives, (2) abstracting away correlations between states of different middleboxes and channel contents, and (3) representing middlebox states by their effect on each packet separately, rather than taking into account the entire state space. We show that the abstractions do not lose precision when middleboxes may reset in any state. This is encouraging since many real middleboxes reset, e.g., after some session timeout is reached or due to hardware failure

Ionization Structure and the Reverse Shock in E0102-72

The young oxygen-rich supernova remnant E0102-72 in the Small Magellanic Cloud has been observed with the High Energy Transmission Grating Spectrometer of Chandra. The high resolution X-ray spectrum reveals images of the remnant in the light of individual emission lines of oxygen, neon, magnesium and silicon. The peak emission region for hydrogen-like ions lies at larger radial distance from the SNR center than the corresponding helium-like ions, suggesting passage of the ejecta through the "reverse shock". We examine models which test this interpretation, and we discuss the implications.Comment: 4 pages, 6 figures; To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Radion Potential and Brane Dynamics

We examine the cosmology of the Randall-Sundrum model in a dynamic setting where scalar fields are present in the bulk as well as the branes. This generates a mechanism similar to that of Goldberger-Wise for radion stabilization and the recovery of late-cosmology features in the branes. Due to the induced radion dynamics, the inflating branes roll towards the minimum of the radion potential, thereby exiting inflation and reheating the Universe. In the slow roll part of the potential, the 'TeV' branes have maximum inflation rate and energy as their coupling to the radion and bulk modes have minimum suppresion. Hence, when rolling down the steep end of the potential towards the stable point, the radion field (which appears as the inflaton of the effective 4D theory in the branes) decays very fast, reheats the Universe .This process results decayin a decrease of brane's canonical vacuum energy $\Lambda_4$. However, at the minimum of the potential $\Lambda_4$ is small but not neccessarily zero and the fine-tuning issue remains .Density perturbation constraints introduce an upper bound when the radion stabilizies. Due to the large radion mass and strong suppression to the bulk modes, moduli problems and bulk reheating do not occur. The reheat temperature and a sufficient number of e-folding constraints for the brane-universe are also satisfied. The model therefore recovers the radiation dominated FRW universe.Comment: 16 pages, 3 figures,extraneous sentences removed, 2 footnotes added, some typos correcte

Abstract Interpretation with Unfoldings

We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal dependence and interference between sequences of transformers. Our main contribution is an unfolding algorithm that uses a new notion of independence to avoid redundant transformer application, thread-local fixed points to reduce the size of the unfolding, and a novel cutoff criterion based on subsumption to guarantee termination of the analysis. Our experiments show that the abstract unfolding produces an order of magnitude fewer false alarms than a mature abstract interpreter, while being several orders of magnitude faster than solver-based tools that have the same precision.Comment: Extended version of the paper (with the same title and authors) to appear at CAV 201

Spectral Line Imaging Observations of 1E0102.2-7219

E0102-72 is the second brightest X-ray source in the Small Magellanic Cloud and the brightest supernova remnant in the SMC. We observed this SNR for ~140 ksec with the High Energy Transmission Gratings (HETG) aboard the Chandra X-ray Observatory. The small angular size and high surface brightness make this an excellent target for HETG and we resolve the remnant into individual lines. We observe fluxes from several lines which include O VIII Ly$\alpha$, Ly$\beta$, and O VII along with several lines from Ne X, Ne IX and Mg XII. These line ratios provide powerful constraints on the electron temperature and the ionization age of the remnant.Comment: To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Predicting the Starquakes in PSR J0537-6910

We report on more than 7 years of monitoring of PSR J0537-6910, the 16 ms pulsar in the Large Magellanic Cloud, using data acquired with the RXTE. During this campaign the pulsar experienced 23 sudden increases in frequency (``glitches'') amounting to a total gain of over six ppm of rotation frequency superposed on its gradual spindown of d(nu)/d(t) = -2e-10 Hz/s. The time interval from one glitch to the next obeys a strong linear correlation to the amplitude of the first glitch, with a mean slope of about 400 days ppm (6.5 days per uHz), such that these intervals can be predicted to within a few days, an accuracy which has never before been seen in any other pulsar. There appears to be an upper limit of ~40 uHz for the size of glitches in_all_ pulsars, with the 1999 April glitch of J0537 as the largest so far. The change in the spindown of J0537 across the glitches, Delta(d(nu)/d(t)), appears to have the same hard lower limit of -1.5e-13 Hz/s, as, again, that observed in all other pulsars. The spindown continues to increase in the long term, d(d(nu)/d(t))/d(t) = -1e-21 Hz/s/s, and thus the timing age of J0537 (-0.5 nu d(nu)/d(t)) continues to decrease at a rate of nearly one year every year, consistent with movement of its magnetic moment away from its rotational axis by one radian every 10,000 years, or about one meter per year. J0537 was likely to have been born as a nearly-aligned rotator spinning at 75-80 Hz, with a |d(nu)/d(t)| considerably smaller than its current value of 2e-10 Hz/s. The pulse profile of J0537 consists of a single pulse which is found to be flat at its peak for at least 0.02 cycles.Comment: 54 pages, 12 figures. Accepted for publication in The Astrophysical Journal. Cleaner figure 2. V4 -- in line with version accepted by Ap

Avalanche dynamics of radio pulsar glitches

We test statistically the hypothesis that radio pulsar glitches result from an avalanche process, in which angular momentum is transferred erratically from the flywheel-like superfluid in the star to the slowly decelerating, solid crust via spatially connected chains of local, impulsive, threshold-activated events, so that the system fluctuates around a self-organised critical state. Analysis of the glitch population (currently 285 events from 101 pulsars) demonstrates that the size distribution in individual pulsars is consistent with being scale invariant, as expected for an avalanche process. The waiting-time distribution is consistent with being exponential in seven out of nine pulsars where it can be measured reliably, after adjusting for observational limits on the minimum waiting time, as for a constant-rate Poisson process. PSR J0537$-$6910 and PSR J0835$-$4510 are the exceptions; their waiting-time distributions show evidence of quasiperiodicity. In each object, stationarity requires that the rate $\lambda$ equals $- \epsilon \dot{\nu} /$, where $\dot{\nu}$ is the angular acceleration of the crust, $$ is the mean glitch size, and $\epsilon\dot{\nu}$ is the relative angular acceleration of the crust and superfluid. There is no evidence that $\lambda$ changes monotonically with spin-down age. The rate distribution itself is fitted reasonably well by an exponential for $\lambda \geq 0.25 {\rm yr^{-1}}$. For $\lambda < 0.25 {\rm yr^{-1}}$, its exact form is unknown; the exponential overestimates the number of glitching pulsars observed at low $\lambda$, where the limited total observation time exercises a selection bias.Comment: Accepted for publication in the Astrophysical Journa

Bayesian Analysis of the Polarization of Distant Radio Sources: Limits on Cosmological Birefringence

A recent study of the rotation of the plane of polarization of light from 160 cosmological sources claims to find significant evidence for cosmological anisotropy. We point out methodological weaknesses of that study, and reanalyze the same data using Bayesian methods that overcome these problems. We find that the data always favor isotropic models for the distribution of observed polarizations over counterparts that have a cosmological anisotropy of the type advocated in the earlier study. Although anisotropic models are not completely ruled out, the data put strong lower limits on the length scale $\lambda$ (in units of the Hubble length) associated with the anisotropy; the lower limits of 95% credible regions for $\lambda$ lie between 0.43 and 0.62 in all anisotropic models we studied, values several times larger than the best-fit value of $\lambda \approx 0.1$ found in the earlier study. The length scale is not constrained from above. The vast majority of sources in the data are at distances closer than 0.4 Hubble lengths (corresponding to a redshift of $\approx$0.8); the results are thus consistent with there being no significant anisotropy on the length scale probed by these data.Comment: 8 pages, 3 figures; submitted to Phys. Rev.