Amortised resource analysis with separation logic

Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

The detection of extragalactic 15^{15}N: Consequences for nitrogen nucleosynthesis and chemical evolution

Detections of extragalactic $^{15}$N are reported from observations of the rare hydrogen cyanide isotope HC$^{15}$N toward the Large Magellanic Cloud (LMC) and the core of the (post-) starburst galaxy NGC 4945. Accounting for optical depth effects, the LMC data from the massive star-forming region N113 infer a $^{14}N/^{15}$N ratio of 111 $\pm$ 17, about twice the $^{12}C/^{13}$C value. For the LMC star-forming region N159HW and for the central region of NGC 4945, $^{14}N/^{15}$N ratios are also $\approx$ 100. The $^{14}N/^{15}$N ratios are smaller than all interstellar nitrogen isotope ratios measured in the disk and center of the Milky Way, strongly supporting the idea that $^{15}$N is predominantly of `primary' nature, with massive stars being its dominant source. Although this appears to be in contradiction with standard stellar evolution and nucleosynthesis calculations, it supports recent findings of abundant $^{15}$N production due to rotationally induced mixing of protons into the helium-burning shells of massive stars.Comment: 15 pages including one postscript figure, accepted for publication by ApJ Letter, further comments: please contact Yi-nan Chi

Memory usage verification using Hip/Sleek.

Embedded systems often come with constrained memory footprints. It is therefore essential to ensure that software running on such platforms fulfils memory usage specifications at compile-time, to prevent memory-related software failure after deployment. Previous proposals on memory usage verification are not satisfactory as they usually can only handle restricted subsets of programs, especially when shared mutable data structures are involved. In this paper, we propose a simple but novel solution. We instrument programs with explicit memory operations so that memory usage verification can be done along with the verification of other properties, using an automated verification system Hip/Sleek developed recently by Chin et al.[10,19]. The instrumentation can be done automatically and is proven sound with respect to an underlying semantics. One immediate benefit is that we do not need to develop from scratch a specific system for memory usage verification. Another benefit is that we can verify more programs, especially those involving shared mutable data structures, which previous systems failed to handle, as evidenced by our experimental results

Abundances and Isotope Ratios in the Magellanic Clouds: The Star Forming Environment of N113

With the goal of deriving the physical and chemical conditions of star forming regions in the Large Magellanic Cloud (LMC), a spectral line survey of the prominent star forming region N113 is presented. The observations cover parts of the frequency range from 85 GHz to 357 GHz and include 63 molecular transitions from a total of 16 species, among them spectra of rare isotopologues. Maps of selected molecular lines as well as the 1.2 mm continuum distribution are also presented. Molecular abundances in the core of the complex are found to be consistent with a photon dominated region (PDR) that is nitrogen deficient, with the potential exception of N2H+. Densities range from 5x10^3 cm-3 for CO to almost 10^6 for CS and HCN, indicating that only the densest regions provide sufficient shielding even for some of the most common species. An ortho- to para-H_2CO ratio of ~3 hints at H_2CO formation in a warm (>=40 K) environment. Isotope ratios are 12C/13C ~ 49+-5, 16O/18O ~ 2000+-250, 18O/17O ~ 1.7+-0.2 and 32S/34S ~ 15. Agreement with data from other star forming clouds shows that the gas is well mixed in the LMC . The isotope ratios do not only differ from those seen in the Galaxy. They also do not form a continuation of the trends observed with decreasing metallicity from the inner to the outer Galaxy. This implies that the outer Galaxy, is not providing a transition zone between the inner Galaxy and the metal poor environment of the Magellanic Clouds. A part of this discrepancy is likely caused by differences in the age of the stellar populations in the outer Galaxy and the LMC.Comment: 50 pages, 13 figures, accepted for publication in Ap

Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities

Since the kinetic and the potential energy term of the real time nonlinear Schr\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where $k_{max}=\pi/\Delta x$.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

The Multi-Phase Medium in the Interstellar Complex N44

We have obtained high-resolution HI observations of N44, one of the largest HII complexes in the Large Magellanic Cloud. The distribution and internal motions of the HI gas show dynamic effects of fast stellar winds and supernova blasts. Numerous HI holes are detected, with the most prominent two corresponding to the optically identified superbubbles Shell 1 and Shell 2. The HI gas associated with Shell 1 shows an expansion pattern similar to that of the ionized gas shell, but the mass and kinetic energy of the HI shell are 3--7 times those of the ionized gas shell. The total kinetic energy of the neutral and ionized gas of Shell 1 is still more than a factor of 5 lower than expected in a pressure-driven superbubble. It is possible that the central OB association was formed in a molecular cloud and a visible superbubble was not fully developed until the ambient molecular gas had been dissociated and cleared away. This hypothesis is supported by the existence of a molecular cloud toward N44 and the fact that the apparent dynamic age of the superbubble Shell 1 is much shorter than the age of its OB association LH47. Accelerated HI gas is detected at the supernova remnant 0523-679. The mass and kinetic energy in the associated HI gas are also much higher than those in the ionized gas of 0523-679. Studies of interstellar gas dynamics using ionized gas alone are clearly inadequate; neutral gas components must be included.Comment: 18 pages,5 figures; for "figures", see at "http://www.astro.uiuc.edu/~sek/N44.html" (4.9 MB postscript.gz) ; Appear to ApJ, 503, 729 (Aug 20