On the Commutative Equivalence of Context-Free Languages

The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

Investigating fragmentation of gas structures in OB cluster-forming molecular clump G33.92+0.11 with 1000 AU resolution observations of ALMA

We report new, $\sim$1000 AU spatial resolution observations of 225 GHz dust continuum emission towards the OB cluster-forming molecular clump G33.92+0.11. On parsec scales, this molecular clump presents a morphology with several arm-like dense gas structures surrounding the two central massive ($\gtrsim$100 $M_{\odot}$) cores. From the new, higher resolution observations, we identified 28 localized, spatially compact dust continuum emission sources, which may be candidates of young stellar objects. Only one of them is not embedded within known arm-like (or elongated) dense gas structures. The spatial separations of these compact sources can be very well explained by Jeans lengths. We found that G33.92+0.11 may be consistently described by a marginally centrifugally supported, Toomre unstable accretion flow which is approximately in a face-on projection. The arm-like overdensities are natural consequence of the Toomre instability, which can fragment to form young stellar objects in shorter time scales than the timescale of the global clump contraction. On our resolved spatial scales, there is not yet evidence that the fragmentation is halted by turbulence, magnetic field, or stellar feedback.Comment: 24 pages, 18 figures. Accepted to publish on December 04, 2018; updated to arXiv on December 05, 201

Hypervelocity Stars III. The Space Density and Ejection History of Main Sequence Stars from the Galactic Center

We report the discovery of 3 new unbound hypervelocity stars (HVSs), stars traveling with such extreme velocities that dynamical ejection from a massive black hole (MBH) is their only suggested origin. We also detect a population of possibly bound HVSs. The significant asymmetry we observe in the velocity distribution -- we find 26 stars with v_rf > 275 km/s and 1 star with v_rf < -275 km/s -- shows that the HVSs must be short-lived, probably 3 - 4 Msun main sequence stars. Any population of hypervelocity post-main sequence stars should contain stars falling back onto the Galaxy, contrary to the observations. The spatial distribution of HVSs also supports the main sequence interpretation: longer-lived 3 Msun HVSs fill our survey volume; shorter-lived 4 Msun HVSs are missing at faint magnitudes. We infer that there are 96 +- 10 HVSs of mass 3 - 4 Msun within R < 100 kpc, possibly enough HVSs to constrain ejection mechanisms and potential models. Depending on the mass function of HVSs, we predict that SEGUE may find up to 5 - 15 new HVSs. The travel times of our HVSs favor a continuous ejection process, although a ~120 Myr-old burst of HVSs is also allowed.Comment: 10 pages, 8 figures, accepted to ApJ, minor revision

The Bolocam Galactic Plane Survey. XIV. Physical Properties of Massive Starless and Star Forming Clumps

We sort $4683$ molecular clouds between $10^\circ< \ell <65^\circ$ from the Bolocam Galactic Plane Survey based on observational diagnostics of star formation activity: compact $70$ $\mu{\rm m}$ sources, mid-IR color-selected YSOs, ${\rm H_2O}$ and ${\rm CH_3OH}$ masers, and UCHII regions. We also present a combined ${\rm NH_3}$-derived gas kinetic temperature and ${\rm H_2O}$ maser catalog for $1788$ clumps from our own GBT 100m observations and from the literature. We identify a subsample of $2223$ ($47.5\%$) starless clump candidates, the largest and most robust sample identified from a blind survey to date. Distributions of flux density, flux concentration, solid angle, kinetic temperature, column density, radius, and mass show strong ($>1$ dex) progressions when sorted by star formation indicator. The median starless clump candidate is marginally sub-virial ($\alpha \sim 0.7$) with $>75\%$ of clumps with known distance being gravitationally bound ($\alpha < 2$). These samples show a statistically significant increase in the median clump mass of $\Delta M \sim 170-370$ M$_\odot$ from the starless candidates to clumps associated with protostars. This trend could be due to (i) mass growth of the clumps at $\dot{M}\sim200-440$ Msun Myr$^{-1}$ for an average free-fall $0.8$ Myr time-scale, (ii) a systematic factor of two increase in dust opacity from starless to protostellar phases, (iii) and/or a variation in the ratio of starless to protostellar clump lifetime that scales as $\sim M^{-0.4}$. By comparing to the observed number of ${\rm CH_3OH}$ maser containing clumps we estimate the phase-lifetime of massive ($M>10^3$ M$_\odot$) starless clumps to be $0.37 \pm 0.08 \ {\rm Myr} \ (M/10^3 \ {\rm M}_\odot)^{-1}$; the majority ($M<450$ M$_\odot$) have phase-lifetimes longer than their average free-fall time.Comment: Accepted for publication in ApJ; 33 pages; 22 figures; 7 table

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards

Interprocedural Reachability for Flat Integer Programs

We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ... wd* over program statements is decidable in Nexptime. To achieve this upper bound, we combine a program transformation into the same class of programs but without procedures, with an Np-completeness result for the reachability problem of procedure-less programs. Besides the program, the expression w1* ... wd* is also mapped onto an expression of a similar form but this time over the transformed program statements. Several arguments involving context-free grammars and their generative process enable us to give tight bounds on the size of the resulting expression. The currently existing gap between Np-hard and Nexptime can be closed to Np-complete when a certain parameter of the analysis is assumed to be constant.Comment: 38 pages, 1 figur

Outflows and Massive Stars in the protocluster IRAS 05358+3543

We present new near-IR H2, CO J=2-1, and CO J = 3-2 observations to study outflows in the massive star forming region IRAS 05358+3543. The Canada-France-Hawaii Telescope H2 images and James Clerk Maxwell Telescope CO data cubes of the IRAS 05358 region reveal several new outflows, most of which emerge from the dense cluster of sub-mm cores associated with the Sh 2-233IR NE cluster to the northeast of IRAS 05358. We used Apache Point Observatory (APO) JHK spectra to determine line of sight velocities of the outflowing material. Analysis of archival VLA cm continuum data and previously published VLBI observations reveal a massive star binary as a probable source of one or two of the outflows. We have identified probable sources for 6 outflows and candidate counterflows for 7 out of a total of 11 seen to be originating from the IRAS 05358 clusters. We classify the clumps within Sh 2-233IR NE as an early protocluster and Sh 2-233IR SW as a young cluster, and conclude that the outflow energy injection rate approximately matches the turbulent decay rate in Sh 2-233IR NE.Comment: 15 figures, 42 pages, accepted for publication in the Astrophysical Journal. Full size figures are included at http://casa.colorado.edu/~ginsbura/iras05358.htm. Data can be accessed from figshare: http://figshare.com/articles/IRAS_05358_3543_Data_Cubes/80631

Mass fractionation of noble gases in synthetic methane hydrate : implications for naturally occurring gas hydrate dissociation

This paper is not subject to U.S. copyright. The definitive version was published in Chemical Geology 339 (2013): 242-250, doi:10.1016/j.chemgeo.2012.09.033.As a consequence of contemporary or longer term (since 15 ka) climate warming, gas hydrates in some settings may presently be dissociating and releasing methane and other gases to the ocean–atmosphere system. A key challenge in assessing the impact of dissociating gas hydrates on global atmospheric methane is the lack of a technique able to distinguish between methane recently released from gas hydrates and methane emitted from leaky thermogenic reservoirs, shallow sediments (some newly thawed), coal beds, and other sources. Carbon and deuterium stable isotopic fractionation during methane formation provides a first-order constraint on the processes (microbial or thermogenic) of methane generation. However, because gas hydrate formation and dissociation do not cause significant isotopic fractionation, a stable isotope-based hydrate-source determination is not possible. Here, we investigate patterns of mass-dependent noble gas fractionation within the gas hydrate lattice to fingerprint methane released from gas hydrates. Starting with synthetic gas hydrate formed under laboratory conditions, we document complex noble gas fractionation patterns in the gases liberated during dissociation and explore the effects of aging and storage (e.g., in liquid nitrogen), as well as sampling and preservation procedures. The laboratory results confirm a unique noble gas fractionation pattern for gas hydrates, one that shows promise in evaluating modern natural gas seeps for a signature associated with gas hydrate dissociation.Partial support for this research was provided by Interagency Agreements DE-FE0002911 and DE-NT0006147 between the U.S. Geological Survey Gas Hydrates Project and the U.S. Department of Energy's Methane Hydrates Research and Development Program

Antichain cutsets of strongly connected posets

Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we get such a characterization for semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We also consider a generalization to strongly connected hypergraphs having finite edges.Comment: 12 pages; v2 contains minor fixes for publicatio

Hypervelocity Stars from the Andromeda Galaxy

Hypervelocity stars (HVSs) discovered in the Milky Way (MW) halo are thought to be ejected from near the massive black hole (MBH) at the galactic centre. In this paper we investigate the spatial and velocity distributions of the HVSs which are expected to be similarly produced in the Andromeda galaxy (M31). We consider three different HVS production mechanisms: (i) the disruption of stellar binaries by the galactocentric MBH; (ii) the ejection of stars by an in-spiraling intermediate mass black hole; and (iii) the scattering of stars off a cluster of stellar-mass black holes orbiting around the MBH. While the first two mechanisms would produce large numbers of HVSs in M31, we show that the third mechanism would not be effective in M31. We numerically calculate 1.2*10^6 trajectories of HVSs from M31 within a simple model of the Local Group and hence infer the current distribution of these stars. Gravitational focusing of the HVSs by the MW and the diffuse Local Group medium leads to high densities of low mass (~ solar mass) M31 HVSs near the MW. Within the virialized MW halo, we expect there to be of order 1000 HVSs for the first mechanism and a few hundred HVSs for the second mechanism; many of these stars should have distinctively large approach velocities (< -500 km/s). In addition, we predict ~5 hypervelocity RGB stars within the M31 halo which could be identified observationally. Future MW astrometric surveys or searches for distant giants could thus find HVSs from M31.Comment: 14 pages, 6 figures, changed to match version accepted by MNRA