Ron C The C Theory Rarest
arXiv:1903.07418 [pdf, ps, other]
The Norms of Graph Spanners
Abstract: A $t$-spanner of a graph $G$ is a subgraph $H$ in which all distances are preserved up to a multiplicative $t$ factor. A classical result of Althöfer et al. is that for every integer $k$ and every graph $G$, there is a $(2k-1)$-spanner of $G$ with at most $O(n^{1+1/k})$ edges. But for some settings the more interesting notion is not the number of edges, but the degrees of the nodes. This spurred i… ▽ More A $t$-spanner of a graph $G$ is a subgraph $H$ in which all distances are preserved up to a multiplicative $t$ factor. A classical result of Althöfer et al. is that for every integer $k$ and every graph $G$, there is a $(2k-1)$-spanner of $G$ with at most $O(n^{1+1/k})$ edges. But for some settings the more interesting notion is not the number of edges, but the degrees of the nodes. This spurred interest in and study of spanners with small maximum degree. However, this is not necessarily a robust enough objective: we would like spanners that not only have small maximum degree, but also have 'few' nodes of 'large' degree. To interpolate between these two extremes, in this paper we initiate the study of graph spanners with respect to the $ell_p$-norm of their degree vector, thus simultaneously modeling the number of edges (the $ell_1$-norm) and the maximum degree (the $ell_{infty}$-norm). We give precise upper bounds for all ranges of $p$ and stretch $t$: we prove that the greedy $(2k-1)$-spanner has $ell_p$ norm of at most $max(O(n), O(n^{(k+p)/(kp)}))$, and that this bound is tight (assuming the Erdős girth conjecture). We also study universal lower bounds, allowing us to give 'generic' guarantees on the approximation ratio of the greedy algorithm which generalize and interpolate between the known approximations for the $ell_1$ and $ell_{infty}$ norm. Finally, we show that at least in some situations, the $ell_p$ norm behaves fundamentally differently from $ell_1$ or $ell_{infty}$: there are regimes ($p=2$ and stretch $3$ in particular) where the greedy spanner has a provably superior approximation to the generic guarantee. △ Less
Submitted 18 March, 2019; originally announced March 2019.
arXiv:1903.04751 [pdf, other]
Star formation in IRDC G31.97+0.07
Abstract: We utilize multiple-waveband continuum and molecular-line data of CO isotopes, to study the dynamical structure and physical properties of the IRDC G31.97+0.07. We derive the dust temperature and H$_2$ column density maps of the whole structure by SED fitting. The total mass is about $2.5times10^5,M_{odot}$ for the whole filamentary structure and about $7.8times10^4,M_{odot}$ for the IRDC. C… ▽ More We utilize multiple-waveband continuum and molecular-line data of CO isotopes, to study the dynamical structure and physical properties of the IRDC G31.97+0.07. We derive the dust temperature and H$_2$ column density maps of the whole structure by SED fitting. The total mass is about $2.5times10^5,M_{odot}$ for the whole filamentary structure and about $7.8times10^4,M_{odot}$ for the IRDC. Column density PDFs produced from the column density map are generally in the power-law form suggesting that this part is mainly gravity-dominant. The flatter slope of the PDF of the IRDC implies that it might be compressed by an adjacent, larger HII region. There are 27 clumps identified from the 850,micron continuum located in this filamentary structure. Based on the average spacing of the fragments in the IRDC, we estimate the age of the IRDC. The age is about $6.4,$Myr assuming inclination angle $i = 30^circ$. For 18 clumps with relatively strong CO and $^{13}$CO (3-2) emission, we study their line profiles and stabilities. We find 5 clumps with blue profiles which indicate gas infall motion and 2 clumps with red profiles which indicate outflows or expansion. Only one clump has $α_mathrm{vir} > 2$, suggesting that most clumps are gravitationally bound and tend to collapse. In the Mass-$R_mathrm{eq}$ diagram, 23 of 27 clumps are above the threshold for high-mass star formation, suggesting that this region can be a good place for studying high-mass star-forming. △ Less
Submitted 12 March, 2019; originally announced March 2019.
Comments:19 pages, 13 figures
arXiv:1902.10180 [pdf, ps, other]
SCOPE: SCUBA-2 Continuum Observations of Pre-protostellar Evolution - Survey Description and Compact Source Catalogue
Abstract: We present the first release of the data and compact-source catalogue for the JCMT Large Program SCUBA-2 Continuum Observations of Pre-protostellar Evolution (SCOPE). SCOPE consists of 850-um continuum observations of 1235 Planck Galactic Cold Clumps (PGCCs) made with the Submillimetre Common-User Bolometer Array 2 on the James Clerk Maxwell Telescope. These data are at an angular resolution of 14… ▽ More We present the first release of the data and compact-source catalogue for the JCMT Large Program SCUBA-2 Continuum Observations of Pre-protostellar Evolution (SCOPE). SCOPE consists of 850-um continuum observations of 1235 Planck Galactic Cold Clumps (PGCCs) made with the Submillimetre Common-User Bolometer Array 2 on the James Clerk Maxwell Telescope. These data are at an angular resolution of 14.4 arcsec, significantly improving upon the 353-GHz resolution of Planck at 5 arcmin, and allowing for a catalogue of 3528 compact sources in 558 PGCCs. We find that the detected PGCCs have significant sub-structure, with 61 per cent of detected PGCCs having 3 or more compact sources, with filamentary structure also prevalent within the sample. A detection rate of 45 per cent is found across the survey, which is 95 per cent complete to Planck column densities of $N_{H_{2}}$ $>$ 5 $times$ 10$^{21}$ cm$^{-2}$. By positionally associating the SCOPE compact sources with YSOs, the star formation efficiency, as measured by the ratio of luminosity to mass, in nearby clouds is found to be similar to that in the more distant Galactic Plane, with the column density distributions also indistinguishable from each other. △ Less
Submitted 26 February, 2019; originally announced February 2019.
Comments:16 pages, 13 figures, 1 table. Accepted for publication in MNRAS
arXiv:1902.08086 [pdf, ps, other]
The Arboricity Captures the Complexity of Sampling Edges
Abstract: In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $α$, we design an algorithm that performs… ▽ More In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $α$, we design an algorithm that performs $O!left(fracα{d} cdot frac{log^3 n}{varepsilon}right)$ queries in expectation and returns an edge in the graph such that every edge $e in E$ is sampled with probability $(1 pm varepsilon)/m$. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in $varepsilon$), as $Ω!left(fracα{d} right)$ queries are necessary for the easier task of sampling edges from any distribution over $E$ that is close to uniform in total variational distance. We also prove that even if $G$ is a tree (i.e., $α= 1$ so that $fracα{d}=Θ(1)$), $Ωleft(frac{log n}{loglog n}right)$ queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a $mathrm{poly}(log n)$ factor is necessary for constant $α$. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019). △ Less
Submitted 21 February, 2019; originally announced February 2019.
arXiv:1812.10503 [pdf, ps, other]
Marvel analysis of the measured high-resolution rovibrational spectra of H2S
Abstract: 44325 measured and assigned transitions of H$_2^{32}$S, the parent isotopologue of the hydrogen sulfide molecule, are collated from 33 publications into a single database and reviewed critically. Based on this information, rotation-vibration energy levels are determined for the ground electronic state using the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The ortho and… ▽ More 44325 measured and assigned transitions of H$_2^{32}$S, the parent isotopologue of the hydrogen sulfide molecule, are collated from 33 publications into a single database and reviewed critically. Based on this information, rotation-vibration energy levels are determined for the ground electronic state using the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The ortho and para principal components of the measured spectroscopic network of H$_2^{32}$S are considered separately. The verified set of 25293 ortho- and 18778 para- H$_2^{32}$S transitions determine 3969 ortho and 3467 para energy levels. The Marvel results are compared with alternative data compilations, including a theoretical variational linelist. △ Less
Submitted 26 December, 2018; originally announced December 2018.
Comments:39 pages, 3 figures, JQSRT, 2018
Journal ref: JQSRT, 218, (2018), 178-186
arXiv:1811.04425 [pdf, ps, other]
Faster sublinear approximations of $k$-cliques for low arboricity graphs
Abstract: Given query access to an undirected graph $G$, we consider the problem of computing a $(1pmε)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor queries, and pair queries. Let $n$ be the number of vertices, $m$ be the number of edges, and $n_k$ be the number of $k$-cliques. Previous work by Eden, Ron and Seshadhri (S… ▽ More Given query access to an undirected graph $G$, we consider the problem of computing a $(1pmε)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor queries, and pair queries. Let $n$ be the number of vertices, $m$ be the number of edges, and $n_k$ be the number of $k$-cliques. Previous work by Eden, Ron and Seshadhri (STOC 2018) gives an $O^*(frac{n}{n^{1/k}_k} + frac{m^{k/2}}{n_k})$-time algorithm for this problem (we use $O^*(cdot)$ to suppress $poly(log n, 1/ε, k^k)$ dependencies). Moreover, this bound is nearly optimal when the expression is sublinear in the size of the graph. Our motivation is to circumvent this lower bound, by parameterizing the complexity in terms of emph{graph arboricity}. The arboricity of $G$ is a measure for the graph density 'everywhere'. We design an algorithm for the class of graphs with arboricity at most $α$, whose running time is $O^*(min{frac{nα^{k-1}}{n_k},, frac{n}{n_k^{1/k}}+frac{m α^{k-2}}{n_k} })$. We also prove a nearly matching lower bound. For all graphs, the arboricity is $O(sqrt m)$, so this bound subsumes all previous results on sublinear clique approximation. As a special case of interest, consider minor-closed families of graphs, which have constant arboricity. Our result implies that for any minor-closed family of graphs, there is a $(1pmε)$-approximation algorithm for $n_k$ that has running time $O^*(frac{n}{n_k})$. Such a bound was not known even for the special (classic) case of triangle counting in planar graphs. △ Less
Submitted 11 November, 2018; originally announced November 2018.
The RMS Survey: Ammonia mapping of the environment of young massive stellar objects II
Abstract: We present the results from NH$_{3}$ mapping observations towards 34 regions identified by the Red MSX Source (RMS) survey. We have used the Australia Telescope Compact Array to map ammonia (1,1) and (2,2) inversion emission spectra at a resolution of 10' with velocity channel resolution of 0.4$,$km$,$s$^{-1}$ towards the positions of embedded massive star formation. Complementary data have bee… ▽ More We present the results from NH$_{3}$ mapping observations towards 34 regions identified by the Red MSX Source (RMS) survey. We have used the Australia Telescope Compact Array to map ammonia (1,1) and (2,2) inversion emission spectra at a resolution of 10' with velocity channel resolution of 0.4$,$km$,$s$^{-1}$ towards the positions of embedded massive star formation. Complementary data have been used from the ATLASGAL and GLIMPSE Legacy Surveys in order to improve the understanding of the regions and to estimate physical parameters for the environments. The fields have typical masses of ~1000$,$M$odot$, radii of ~0.15$,$pc and distances of ~3.5$,$kpc. Luminosities range between ~10$^{3}$ to ~10$^{6}$$,$L$odot$ and kinetic temperatures between 10 and 40$,$K. We classify each field into one of two subsets in order to construct an evolutionary system for massive star formation in these regions based on the morphology and relative positions of the NH$_{3}$ emission, RMS sources and ATLASGAL thermal dust emission. Differences in morphology between NH$_{3}$ emission and ATLASGAL clumps are shown to correspond to evolutionary stages of ongoing massive star formation in these regions. The study has been further refined by including the positions of known methanol and water masers in the regions to gain insight into possible protostellar regions and triggered star formation. △ Less
Submitted 7 November, 2018; originally announced November 2018.
Comments:22 pages, 16 figures, 7 tables
arXiv:1809.00864 [pdf, other]
Dust spectrum and polarisation at 850 um in the massive IRDC G035.39-00.33
Abstract: The dust sub-millimetre polarisation of star-forming clouds carries information on dust and the role of magnetic fields in cloud evolution. With observations of a dense filamentary cloud G035.39-00.33, we aim to characterise the dust emission properties and the variations of the polarisation fraction. JCMT SCUBA-2/POL-2 data at 850um are combined with Planck 850um (353GHz) data to map polarisation… ▽ More The dust sub-millimetre polarisation of star-forming clouds carries information on dust and the role of magnetic fields in cloud evolution. With observations of a dense filamentary cloud G035.39-00.33, we aim to characterise the dust emission properties and the variations of the polarisation fraction. JCMT SCUBA-2/POL-2 data at 850um are combined with Planck 850um (353GHz) data to map polarisation fractions. With previous SCUBA-2 observations (450um and 850um) and Herschel data, the column densities are determined via modified blackbody fits and via radiative transfer modelling. Models are constructed to examine how the polarisation angles and fractions depend on potential magnetic field geometries and grain alignment. POL-2 data show clear changes in the magnetic field orientation. The filament has a peak column density of N(H2)~7 10^22 cm-2, a minimum dust temperature of T~12 K, and a mass of some 4300Msun for the area N(H2)> 5 10^21 cm-2. The estimated average value of the dust opacity spectral index is beta ~ 1.9. The ratio of sub-millimetre and J band optical depths is tau(250 um)/tau(J) ~ 2.5 10^-3, more than four times the typical values for diffuse medium. The polarisation fraction decreases as a function of column density to p ~ 1% in the central filament. Because of noise, the observed decrease of p(N) is significant only at N(H2)>2 10^22 cm-2. The observations suggest that the grain alignment is not constant. Although the data can be explained with a complete loss of alignment at densities above ~ 10^4 cm-3 or using the predictions of radiative torques alignment, the uncertainty of the field geometry and the spatial filtering of the SCUBA-2 data prevent strong conclusions. G035.39-00.33 shows strong signs of dust evolution and the low polarisation fraction is suggestive of a loss of polarised emission from its densest parts. △ Less
Submitted 6 September, 2018; v1 submitted 4 September, 2018; originally announced September 2018.
Comments:accepted for publication in Astronomy and Astrophysics
Journal ref: A&A 620, A26 (2018)
arXiv:1808.05921 [pdf, other]
Electromagnetically Induced Transparency of On-demand Single Photons in a Hybrid Quantum Network
Abstract: Long range quantum communication and quantum information processing require the development of light-matter interfaces for distributed quantum networks. Even though photons are ideal candidates for network links to transfer quantum information, the system of choice for the realization of quantum nodes has not been identified yet. Ideally, one strives for a hybrid network architecture, which will c… ▽ More Long range quantum communication and quantum information processing require the development of light-matter interfaces for distributed quantum networks. Even though photons are ideal candidates for network links to transfer quantum information, the system of choice for the realization of quantum nodes has not been identified yet. Ideally, one strives for a hybrid network architecture, which will consist of different quantum systems, combining the strengths of each system. However, interfacing different quantum systems via photonic channels remains a major challenge because a detailed understanding of the underlying light-matter interaction is missing. Here, we show the coherent manipulation of single photons generated on-demand from a semiconductor quantum dot using a rubidium vapor quantum memory, forming a hybrid quantum network. We demonstrate the engineering of the photons' temporal wave function using four-level atoms and the creation of a new type of electromagnetic induced transparency for quantum dot photons on resonance with rubidium transitions. Given the short lifetime of our quantum dot transition the observed dynamics cannot be explained in the established steady-state picture. Our results play a pivotal role in understanding quantum light-matter interactions at short time scales. These findings demonstrate a fundamental active node to construct future large-scale hybrid quantum networks. △ Less
Submitted 17 August, 2018; originally announced August 2018.
Comments:16 pages, 5 figures
arXiv:1806.08276 [pdf, other]
The role of spiral arms in Milky Way star formation
Abstract: What role does Galactic structure play in star formation? We have used the Herschel Hi-GAL compact-clump catalogue to examine trends in evolutionary stage over large spatial scales in the inner Galaxy. We examine the relationship between the fraction of clumps with embedded star formation (the star-forming fraction, or SFF) and other measures of star-formation activity. Based on a positive correla… ▽ More What role does Galactic structure play in star formation? We have used the Herschel Hi-GAL compact-clump catalogue to examine trends in evolutionary stage over large spatial scales in the inner Galaxy. We examine the relationship between the fraction of clumps with embedded star formation (the star-forming fraction, or SFF) and other measures of star-formation activity. Based on a positive correlation between SFF and evolutionary indicators such as the luminosity-to-mass ratio, we assert that the SFF principally traces the average evolutionary state of a sample and must depend on the local fraction of rapidly-evolving, high-mass young stellar objects. The spiral-arm tangent point longitudes show small excesses in the SFF, though these can be accounted for by a small number of the most massive clusters, just 7.6% of the total number of clumps in the catalogue. This suggests that while the arms tend to be home to the Galaxy's massive clusters, the remaining 92.4% of Hi-GAL clumps in our catalogue do not show an enhancement of star formation within arms. Globally, the SFF is highest at the Galactic midplane and inner longitudes. We find no significant trend in evolutionary stage as a function of position across spiral arms at the tangent-point longitudes. This indicates that the angular offset observed between gas and stars, if coordinated by a density wave, is not evident at the clump phase; alternatively, the onset of star formation is not triggered by the spiral density wave. △ Less
Submitted 21 June, 2018; originally announced June 2018.
Comments:14 pages, accepted for publication in Monthly Notices of the Royal Astronomical Society
arXiv:1806.06051 [pdf, other]
Positivity of hexagon perturbation theory
Abstract: The hexagon-form-factor program was proposed as a way to compute three- and higher-point correlation functions in $mathcal{N}=4$ super-symmetric Yang-Mills theory and in the dual AdS$_5times$S$^5$ superstring theory, by exploiting the integrability of the theory in the 't Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it applies to a large-volume expansion. Fini… ▽ More The hexagon-form-factor program was proposed as a way to compute three- and higher-point correlation functions in $mathcal{N}=4$ super-symmetric Yang-Mills theory and in the dual AdS$_5times$S$^5$ superstring theory, by exploiting the integrability of the theory in the 't Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it applies to a large-volume expansion. Finite-volume corrections can be incorporated through Lüscher-like formulae, though the systematics of this expansion is largely unexplored so far. Strikingly, finite-volume corrections may feature negative powers of the 't Hooft coupling $g$ in the small-$g$ expansion, potentially leading to a breakdown of the formalism. In this work we show that the finite-volume perturbation theory for the hexagon is positive and thereby compatible with the weak-coupling expansion for arbitrary $n$-point functions. △ Less
Submitted 30 June, 2018; v1 submitted 15 June, 2018; originally announced June 2018.
Comments:v2: misprints corrected, further details on physical magnons added
Report number: HU-EP-18/18, HU-MATH 2018-05, TCDMATH~18-08
arXiv:1805.06349 [pdf]
Automatic segmentation of the spinal cord and intramedullary multiple sclerosis lesions with convolutional neural networks
Abstract: The spinal cord is frequently affected by atrophy and/or lesions in multiple sclerosis (MS) patients. Segmentation of the spinal cord and lesions from MRI data provides measures of damage, which are key criteria for the diagnosis, prognosis, and longitudinal monitoring in MS. Automating this operation eliminates inter-rater variability and increases the efficiency of large-throughput analysis pipe… ▽ More The spinal cord is frequently affected by atrophy and/or lesions in multiple sclerosis (MS) patients. Segmentation of the spinal cord and lesions from MRI data provides measures of damage, which are key criteria for the diagnosis, prognosis, and longitudinal monitoring in MS. Automating this operation eliminates inter-rater variability and increases the efficiency of large-throughput analysis pipelines. Robust and reliable segmentation across multi-site spinal cord data is challenging because of the large variability related to acquisition parameters and image artifacts. The goal of this study was to develop a fully-automatic framework, robust to variability in both image parameters and clinical condition, for segmentation of the spinal cord and intramedullary MS lesions from conventional MRI data. Scans of 1,042 subjects (459 healthy controls, 471 MS patients, and 112 with other spinal pathologies) were included in this multi-site study (n=30). Data spanned three contrasts (T1-, T2-, and T2*-weighted) for a total of 1,943 volumes. The proposed cord and lesion automatic segmentation approach is based on a sequence of two Convolutional Neural Networks (CNNs). To deal with the very small proportion of spinal cord and/or lesion voxels compared to the rest of the volume, a first CNN with 2D dilated convolutions detects the spinal cord centerline, followed by a second CNN with 3D convolutions that segments the spinal cord and/or lesions. When compared against manual segmentation, our CNN-based approach showed a median Dice of 95% vs. 88% for PropSeg, a state-of-the-art spinal cord segmentation method. Regarding lesion segmentation on MS data, our framework provided a Dice of 60%, a relative volume difference of -15%, and a lesion-wise detection sensitivity and precision of 83% and 77%, respectively. The proposed framework is open-source and readily available in the Spinal Cord Toolbox. △ Less
Submitted 11 September, 2018; v1 submitted 16 May, 2018; originally announced May 2018.
Comments:38 pages, 7 figures, 2 tables
arXiv:1805.05738 [pdf, other]
Planck Cold Clumps in the $λ$ Orionis complex. II. Environmental effects on core formation
Abstract: Based on the 850 $μ$m dust continuum data from SCUBA-2 at James Clerk Maxwell Telescope (JCMT), we compare overall properties of Planck Galactic Cold Clumps (PGCCs) in the $λ$ Orionis cloud to those of PGCCs in the Orion A and B clouds. The Orion A and B clouds are well known active star-forming regions, while the $λ$ Orionis cloud has a different environment as a consequence of the interaction wi… ▽ More Based on the 850 $μ$m dust continuum data from SCUBA-2 at James Clerk Maxwell Telescope (JCMT), we compare overall properties of Planck Galactic Cold Clumps (PGCCs) in the $λ$ Orionis cloud to those of PGCCs in the Orion A and B clouds. The Orion A and B clouds are well known active star-forming regions, while the $λ$ Orionis cloud has a different environment as a consequence of the interaction with a prominent OB association and a giant Hii region. PGCCs in the $λ$ Orionis cloud have higher dust temperatures ($Td=16.13pm0.15$ K) and lower values of dust emissivity spectral index ($ β=1.65pm0.02$) than PGCCs in the Orion A (Td=13.79$pm 0.21$K, $β=2.07pm0.03$) and Orion B ($Td=13.82pm0.19$K, $β=1.96pm0.02$) clouds. We find 119 sub-structures within the 40 detected PGCCs and identify them as cores. Of total 119 cores, 15 cores are discovered in the $λ$ Orionis cloud, while 74 and 30 cores are found in the Orion A and B clouds, respectively. The cores in the $λ$ Orionis cloud show much lower mean values of size R=0.08 pc, column density N(H2)=$(9.5pm1.2) times 10^{22}$ cm$^{-2}$, number density n(H2)=$(2.9 pm 0.4)times10^{5}$ cm$^{-3}$, and mass $M_{core}$=$1.0pm0.3$ M$_{odot}$ compared to the cores in the Orion A (R=0.11pc, $N(H2)=(2.3pm0.3) times 10^{23}$ cm$^{-2}$, n(H2)=$(3.8pm0.5) times 10^{5}$cm$^{-3}$, and $M_{core}$=$2.4 pm 0.3$ M$_{odot}$) and Orion B (R=0.16pc, N(H2)=$(3.8 pm 0.4) times 10^{23}$cm$^{-2}$, n(H2)=$(15.6pm1.8)times10^{5}$ cm$^{-3}$, and $M_{core}$= $2.7pm0.3$ M$_{odot}$) clouds. These core properties in the $λ$ Orionis cloud can be attributed to the photodissociation and external heating by the nearby Hii region, which may prevent the PGCCs from forming gravitationally bound structures and eventually disperse them. These results support the idea of negative stellar feedback on core formation. △ Less
Submitted 15 May, 2018; originally announced May 2018.
arXiv:1805.05619 [pdf, ps, other]
The MALATANG Survey: the L_gas-L_IR correlation on sub-kiloparsec scale in six nearby star-forming galaxies as traced by HCN J=4-3 and HCO^+ J=4-3
Abstract: We present HCN J=4-3 and HCO^+ J=4-3 maps of six nearby star-forming galaxies, NGC 253, NGC 1068, IC 342, M82, M83, and NGC 6946, obtained with the James Clerk Maxwell Telescope as part of the MALATANG survey. All galaxies were mapped in the central 2 arcmin $times$ 2 arcmin region at 14 arcsec (FWHM) resolution (corresponding to linear scales of ~ 0.2-1.0 kpc). The L_IR-L'_dense relation, where… ▽ More We present HCN J=4-3 and HCO^+ J=4-3 maps of six nearby star-forming galaxies, NGC 253, NGC 1068, IC 342, M82, M83, and NGC 6946, obtained with the James Clerk Maxwell Telescope as part of the MALATANG survey. All galaxies were mapped in the central 2 arcmin $times$ 2 arcmin region at 14 arcsec (FWHM) resolution (corresponding to linear scales of ~ 0.2-1.0 kpc). The L_IR-L'_dense relation, where the dense gas is traced by the HCN J=4-3 and the HCO^+ J=4-3 emission, measured in our sample of spatially-resolved galaxies is found to follow the linear correlation established globally in galaxies within the scatter. We find that the luminosity ratio, L_IR/L'_dense, shows systematic variations with L_IR within individual spatially resolved galaxies, whereas the galaxy-integrated ratios vary little. A rising trend is also found between L_IR/L'_dense ratio and the warm-dust temperature gauged by the 70 μm/100 μm flux ratio. We find the luminosity ratios of IR/HCN(4-3) and IR/HCO^+(4-3), which can be taken as a proxy for the efficiency of star formation in the dense molecular gas (SFE_dense), appears to be nearly independent of the dense-gas fraction (f_dense) for our sample of galaxies. The SFE of the total molecular gas (SFE_mol) is found to increase substantially with f_dense when combining our data with that on local (ultra)luminous infrared galaxies and high-z quasars. The mean L'_HCN(4-3)/L'_HCO^+(4-3) line ratio measured for the six targeted galaxies is 0.9+/-0.6. No significant correlation is found for the L'_HCN(4-3)/L'_HCO^+(4-3) ratio with the SFR as traced by L_IR, nor with the warm-dust temperature, for the different populations of galaxies. △ Less
Submitted 15 May, 2018; originally announced May 2018.
Comments:29 pages, 12 figures, accepted for publication in ApJ
arXiv:1805.03883 [pdf, ps, other]
The TOP-SCOPE survey of PGCCs: PMO and SCUBA-2 observations of 64 PGCCs in the 2nd Galactic Quadrant
Abstract: In order to understand the initial conditions and early evolution of star formation in a wide range of Galactic environments, we carried out an investigation of 64 textit{Planck} Galactic Cold Clumps (PGCCs) in the second quadrant of the Milky Way. Using the $^{13}$CO and C$^{18}$O $J = 1 - 0$ lines, and 850,$μ$m continuum observations, we investigated cloud fragmentation and evolution associate… ▽ More In order to understand the initial conditions and early evolution of star formation in a wide range of Galactic environments, we carried out an investigation of 64 textit{Planck} Galactic Cold Clumps (PGCCs) in the second quadrant of the Milky Way. Using the $^{13}$CO and C$^{18}$O $J = 1 - 0$ lines, and 850,$μ$m continuum observations, we investigated cloud fragmentation and evolution associated with star formation. We extracted 468 clumps and 117 cores from the $^{13}$CO line and 850,$μ$m continuum maps, respectively. We make use of the Bayesian Distance Calculator and derived the distances of all 64 PGCCs. We found that in general, the mass-size plane follows a relation of $msim r^{1.67}$. At a given scale, the masses of our objects are around 1/10 of that of typical Galactic massive star-forming regions. Analysis of the clump and core masses, virial parameters, densities, and mass-size relation suggests that the PGCCs in our sample have a low core formation efficiency ($sim$3.0%), and most PGCCs are likely low-mass star-forming candidates. Statistical study indicates that the 850,$μ$m cores are more turbulent, more optically thick, and denser than the $^{13}$CO clumps for star formation candidates, suggesting that the 850,$μ$m cores are likely more appropriate future star-formation candidates than the $^{13}$CO clumps. △ Less
Submitted 10 May, 2018; originally announced May 2018.
Comments:51 pages, 13 figures, 5 tables; Accepted for publication in ApJS; Supplementary figures can be downloaded in https://zcp521.github.io/pub/Figs.zip
arXiv:1804.03244 [pdf, other]
Prompt Scheduling for Selfish Agents
Abstract: We give a prompt online mechanism for minimizing the sum of [weighted] completion times. This is the first prompt online algorithm for the problem. When such jobs are strategic agents, delaying scheduling decisions makes little sense. Moreover, the mechanism has a particularly simple form of an anonymous menu of options. We give a prompt online mechanism for minimizing the sum of [weighted] completion times. This is the first prompt online algorithm for the problem. When such jobs are strategic agents, delaying scheduling decisions makes little sense. Moreover, the mechanism has a particularly simple form of an anonymous menu of options. △ Less
Submitted 9 April, 2018; originally announced April 2018.
arXiv:1803.09457 [pdf, other]
A holistic perspective on the dynamics of G035.39-00.33: the interplay between gas and magnetic fields
Abstract: Magnetic field is one of the key agents that play a crucial role in shaping molecular clouds and regulating star formation, yet the complete information on the magnetic field is not well constrained due to the limitations in observations. We study the magnetic field in the massive infrared dark cloud G035.39-00.33 from dust continuum polarization observations at 850 $micron$ with SCUBA-2/POL-2 at… ▽ More Magnetic field is one of the key agents that play a crucial role in shaping molecular clouds and regulating star formation, yet the complete information on the magnetic field is not well constrained due to the limitations in observations. We study the magnetic field in the massive infrared dark cloud G035.39-00.33 from dust continuum polarization observations at 850 $micron$ with SCUBA-2/POL-2 at JCMT. The magnetic field tends to be perpendicular to the densest part of the main filament (F$_{M}$), whereas it has a less defined relative orientation in the rest of the structure, where it tends to be parallel to some diffuse regions. A mean plane-of-the-sky magnetic field strength of $sim$50 $μ$G for F$_{M}$ is obtained using Davis-Chandrasekhar-Fermi method. Based on $^{13}$CO (1-0) line observations, we suggest a formation scenario of F$_{M}$ due to large-scale ($sim$10 pc) cloud-cloud collision. Using additional NH$_3$ line data, we estimate that F$_{M}$ will be gravitationally unstable if it is only supported by thermal pressure and turbulence. The northern part of F$_{M}$, however, can be stabilized by a modest additional support from the local magnetic field. The middle and southern parts of F$_{M}$ are likely unstable even if the magnetic field support is taken into account. We claim that the clumps in F$_{M}$ may be supported by turbulence and magnetic fields against gravitational collapse. Finally, we identified for the first time a massive ($sim$200 M$_{sun}$), collapsing starless clump candidate, 'c8', in G035.39-00.33. The magnetic field surrounding 'c8' is likely pinched, hinting at an accretion flow along the filament. △ Less
Submitted 18 June, 2018; v1 submitted 26 March, 2018; originally announced March 2018.
Comments:Published on ApJ, 27 pages
Journal ref: Liu, T., Li, P. S., Juvela M., et al., 2018, ApJ, 859 ,151
arXiv:1803.00475 [pdf, ps, other]
Extreme star formation in the Milky Way: Luminosity distributions of young stellar objects in W49A and W51
Abstract: We have compared the star-formation properties of the W49A and W51 regions by using far-infrared data from the Herschel infrared Galactic Plane Survey (Hi-GAL) and 850-um observations from the James Clerk Maxwell Telescope (JCMT) to obtain luminosities and masses, respectively, of associated compact sources. The former are infrared luminosities from the catalogue of Elia et al. (2017), while the l… ▽ More We have compared the star-formation properties of the W49A and W51 regions by using far-infrared data from the Herschel infrared Galactic Plane Survey (Hi-GAL) and 850-um observations from the James Clerk Maxwell Telescope (JCMT) to obtain luminosities and masses, respectively, of associated compact sources. The former are infrared luminosities from the catalogue of Elia et al. (2017), while the latter are from the JCMT Plane survey source catalogue as well as measurements from new data. The clump-mass distributions of the two regions are found to be consistent with each other, as are the clump-formation efficiency and star-formation efficiency analogues. However, the frequency distributions of the luminosities of the young stellar objects are significantly different. While the luminosity distribution in W51 is consistent with Galaxy-wide samples, that of W49A is top-heavy. The differences are not dramatic, and are concentrated in the central regions of W49A. However, they suggest that physical conditions there, which are comparable in part to those in extragalactic starbursts, are significantly affecting the star-formation properties or evolution of the dense clumps in the region. △ Less
Submitted 1 March, 2018; originally announced March 2018.
Comments:14 pages, 11 figures, accepted for publication in MNRAS
arXiv:1802.05378 [pdf, ps, other]
Great escape lake george. The properties of Planck Galactic cold clumps in the L1495 dark cloud
Abstract: Planck Galactic Cold Clumps (PGCCs) possibly represent the early stages of star formation. To understand better the properties of PGCCs, we studied 16 PGCCs in the L1495 cloud with molecular lines and continuum data from Herschel, JCMT/SCUBA-2 and the PMO 13.7 m telescope. Thirty dense cores were identified in 16 PGCCs from 2-D Gaussian fitting. The dense cores have dust temperatures of… ▽ More Planck Galactic Cold Clumps (PGCCs) possibly represent the early stages of star formation. To understand better the properties of PGCCs, we studied 16 PGCCs in the L1495 cloud with molecular lines and continuum data from Herschel, JCMT/SCUBA-2 and the PMO 13.7 m telescope. Thirty dense cores were identified in 16 PGCCs from 2-D Gaussian fitting. The dense cores have dust temperatures of $T_{rm d}$ = 11-14 K, and H$_{2}$ column densities of $N_{rm H_{2}}$ = 0.36-2.5$times10^{22}$ cm$^{-2}$. We found that not all PGCCs contain prestellar objects. In general, the dense cores in PGCCs are usually at their earliest evolutionary stages. All the dense cores have non-thermal velocity dispersions larger than the thermal velocity dispersions from molecular line data, suggesting that the dense cores may be turbulence-dominated. We have calculated the virial parameter $α$ and found that 14 of the dense cores have $α$ $<$ 2, while 16 of the dense cores have $α$ $>$ 2. This suggests that some of the dense cores are not bound in the absence of external pressure and magnetic fields. The column density profiles of dense cores were fitted. The sizes of the flat regions and core radii decrease with the evolution of dense cores. CO depletion was found to occur in all the dense cores, but is more significant in prestellar core candidates than in protostellar or starless cores. The protostellar cores inside the PGCCs are still at a very early evolutionary stage, sharing similar physical and chemical properties with the prestellar core candidates. △ Less
Submitted 14 February, 2018; originally announced February 2018.
arXiv:1711.09425 [pdf, other]
Herschel and SCUBA-2 observations of dust emission in a sample of Planck cold clumps
Abstract: Analysis of all-sky Planck submillimetre observations and the IRAS 100um data has led to the detection of a population of Galactic cold clumps. The clumps can be used to study star formation and dust properties in a wide range of Galactic environments. Our aim is to measure dust spectral energy distribution (SED) variations as a function of the spatial scale and the wavelength. We examine the SEDs… ▽ More Analysis of all-sky Planck submillimetre observations and the IRAS 100um data has led to the detection of a population of Galactic cold clumps. The clumps can be used to study star formation and dust properties in a wide range of Galactic environments. Our aim is to measure dust spectral energy distribution (SED) variations as a function of the spatial scale and the wavelength. We examine the SEDs at large scales using IRAS, Planck, and Herschel data. At smaller scales, we compare with JCMT/SCUBA-2 850um maps with Herschel data that are filtered using the SCUBA-2 pipeline. Clumps are extracted using the Fellwalker method and their spectra are modelled as modified blackbody functions. According to IRAS and Planck data, most fields have dust colour temperatures T_C ~ 14-18K and opacity spectral index values of beta=1.5-1.9. The clumps/cores identified in SCUBA-2 maps have T~ 13K and similar beta values. There are some indications of the dust emission spectrum becoming flatter at wavelengths longer than 500um. In fits involving Planck data, the significance is limited by the uncertainty of the corrections for CO line contamination. The fits to the SPIRE data give a median beta value slightly above 1.8. In the joint SPIRE and SCUBA-2 850um fits the value decreases to beta ~1.6. Most of the observed T-beta anticorrelation can be explained by noise. The typical submillimetre opacity spectral index beta of cold clumps is found to be ~1.7. This is above the values of diffuse clouds but lower than in some previous studies of dense clumps. There is only tentative evidence of T-beta anticorrelation and beta decreasing at millimetre wavelengths. △ Less
Submitted 27 December, 2017; v1 submitted 26 November, 2017; originally announced November 2017.
Comments:37 pages, accepted to A&A, final version with language corrections
Journal ref: A&A 612, A71 (2018)
arXiv:1711.04382 [pdf, other]
The TOP-SCOPE survey of Planck Galactic Cold Clumps: Survey overview and results of an exemplar source, PGCC G26.53+0.17
Abstract: The low dust temperatures (<14 K) of Planck Galactic Cold Clumps (PGCCs) make them ideal targets to probe the initial conditions and very early phase of star formation. TOP-SCOPE is a joint survey program targeting ~2000 PGCCs in J=1-0 transitions of CO isotopologues and ~1000 PGCCs in 850 micron continuum emisison. The objective of the TOP-SCOPE survey and the joint surveys (SMT 10-m, KVN 21-m an… ▽ More The low dust temperatures (<14 K) of Planck Galactic Cold Clumps (PGCCs) make them ideal targets to probe the initial conditions and very early phase of star formation. TOP-SCOPE is a joint survey program targeting ~2000 PGCCs in J=1-0 transitions of CO isotopologues and ~1000 PGCCs in 850 micron continuum emisison. The objective of the TOP-SCOPE survey and the joint surveys (SMT 10-m, KVN 21-m and NRO 45-m) is to statistically study the initial conditions occurring during star formation and the evolution of molecular clouds, across a wide range of environments. The observations, data analysis and example science cases for these surveys are introduced with an exemplar source, PGCC G26.53+0.17 (G26), which is a filamentary infrared dark cloud (IRDC). The total mass, the length and the mean line-mass (M/L) of the G26 filament are ~6200 Msun, ~12 pc and ~500 Msun/pc, respectively. Ten massive clumps including eight starless ones are found along the filament. The most massive Clump as a whole may be still in global collapse while its denser part seems to be undergoing expansion due to outflow feedback. The fragmentation in G26 filament from cloud scale to clump scale is in agreement with gravitational fragmentation of an isothermal, non-magnetized, and turbulent supported cylinder. A bimodal behavior in dust emissivity spectral index ($β$) distribution is found in G26, suggesting grain growth along the filament. The G26 filament may be formed due to large-scale compression flows evidenced by the temperature and velocity gradients across its natal cloud. △ Less
Submitted 19 December, 2017; v1 submitted 12 November, 2017; originally announced November 2017.
Comments:Accepted for publication in the ApJS
arXiv:1710.08607 [pdf, other]
Provable and practical approximations for the degree distribution using sublinear graph samples
Abstract: The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a large graph through a small, random sample. The degree distribution estimation poses a significant challenge, due to its heavy-tailed nature and the large variance… ▽ More The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a large graph through a small, random sample. The degree distribution estimation poses a significant challenge, due to its heavy-tailed nature and the large variance in degrees. We design a new algorithm, SADDLES, for this problem, using recent mathematical techniques from the field of sublinear algorithms. The SADDLES algorithm gives provably accurate outputs for all values of the degree distribution. For the analysis, we define two fatness measures of the degree distribution, called the $h$-index and the $z$-index. We prove that SADDLES is sublinear in the graph size when these indices are large. A corollary of this result is a provably sublinear algorithm for any degree distribution bounded below by a power law. We deploy our new algorithm on a variety of real datasets and demonstrate its excellent empirical behavior. In all instances, we get extremely accurate approximations for all values in the degree distribution by observing at most $1%$ of the vertices. This is a major improvement over the state-of-the-art sampling algorithms, which typically sample more than $10%$ of the vertices to give comparable results. We also observe that the $h$ and $z$-indices of real graphs are large, validating our theoretical analysis. △ Less
Submitted 28 August, 2018; v1 submitted 24 October, 2017; originally announced October 2017.
Comments:Longer version of the WWW 2018 submission
Lower Bounds for Approximating Graph Parameters via Communication Complexity
Abstract: In a celebrated work, Blais, Brody, and Matulef developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower bounds as well as simplified analyses of known lower bounds. Here, we take a further step in generalizing the methodology of Blais et al. to analyze the query comple… ▽ More In a celebrated work, Blais, Brody, and Matulef developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower bounds as well as simplified analyses of known lower bounds. Here, we take a further step in generalizing the methodology of Blais et al. to analyze the query complexity of graph parameter estimation problems. In particular, our technique decouples the lower bound arguments from the representation of the graph, allowing it to work with any query type. We illustrate our technique by providing new simpler proofs of previously known tight lower bounds for the query complexity of several graph problems: estimating the number of edges in a graph, sampling edges from an almost-uniform distribution, estimating the number of triangles (and more generally, $r$-cliques) in a graph, and estimating the moments of the degree distribution of a graph. We also prove new lower bounds for estimating the edge connectivity of a graph and estimating the number of instances of any fixed subgraph in a graph. We show that the lower bounds for estimating the number of triangles and edge connectivity also hold in a strictly stronger computational model that allows access to uniformly random edge samples. △ Less
Submitted 25 January, 2018; v1 submitted 13 September, 2017; originally announced September 2017.
Comments:Current version includes new section on graph connectivity, as well as various improvements throughout
arXiv:1709.00392 [pdf, other]
ATLASGAL --- properties of a complete sample of Galactic clumps
Abstract: Abridged: ATLASGAL is an unbiased 870 micron submillimetre survey of the inner Galactic plane. It provides a large and systematic inventory of all massive, dense clumps in the Galaxy (>1000 Msun) and includes representative samples of all embedded stages of high-mass star formation. Here we present the first detailed census of the properties (velocities, distances, luminosities and masses) and spa… ▽ More Abridged: ATLASGAL is an unbiased 870 micron submillimetre survey of the inner Galactic plane. It provides a large and systematic inventory of all massive, dense clumps in the Galaxy (>1000 Msun) and includes representative samples of all embedded stages of high-mass star formation. Here we present the first detailed census of the properties (velocities, distances, luminosities and masses) and spatial distribution of a complete sample of ~8000 dense clumps located in the Galactic disk. We derive highly reliable velocities and distances to ~97% of the sample and use mid- and far-infrared survey data to develop an evolutionary classification scheme that we apply to the whole sample. Comparing the evolutionary subsamples reveals trends for increasing dust temperatures, luminosities and line-widths as a function of evolution indicating that the feedback from the embedded proto-clusters is having a significant impact on the structure and dynamics of their natal clumps. We find 88,per,cent are already associated with star formation at some level. We also find the clump mass to be independent of evolution suggesting that the clumps form with the majority of their mass in-situ. We estimate the statistical lifetime of the quiescent stage to be ~5 x 10^4 yr for clump masses ~1000 Msun decreasing to ~1 x 10^4 yr for clump masses >10000 Msun. We find a strong correlation between the fraction of clumps associated with massive stars and peak column density. The fraction is initially small at low column densities but reaching 100,per,cent for column densities above 10^{23} cm^{-2}; there are no clumps with column density clumps above this value that are not already associated with massive star formation. All of the evidence is consistent with a dynamic view of star formation wherein the clumps form rapidly and are initially very unstable so that star formation quickly ensues. △ Less
Submitted 5 September, 2017; v1 submitted 1 September, 2017; originally announced September 2017.
Comments:Accepted for publication in MNRAS. Consists of 45 pages, including 10 pages of appendices. Full versions of Tables 2, 5, 8 and A2 will be made available via CDS once the paper has been published as will full versions of Figures 6, 8 and A1. The quality of the images has been reduced but a high-resolution version is available on request. V2: some minor corrections made
arXiv:1707.04864 [pdf, ps, other]
Testing bounded arboricity
Abstract: In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs with bounded treewidth) and randomly generated preferential attachment graphs. Graphs with bounded arboricity have been studied extensively in the past, in part… ▽ More In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs with bounded treewidth) and randomly generated preferential attachment graphs. Graphs with bounded arboricity have been studied extensively in the past, in particular since for many problems they allow for much more efficient algorithms and/or better approximation ratios. We present a tolerant tester in the sparse-graphs model. The sparse-graphs model allows access to degree queries and neighbor queries, and the distance is defined with respect to the actual number of edges. More specifically, our algorithm distinguishes between graphs that are $ε$-close to having arboricity $α$ and graphs that $c cdot ε$-far from having arboricity $3α$, where $c$ is an absolute small constant. The query complexity and running time of the algorithm are $tilde{O}left(frac{n}{sqrt{m}}cdot frac{log(1/ε)}ε + frac{ncdot α}{m} cdot left(frac{1}εright)^{O(log(1/ε))}right)$ where $n$ denotes the number of vertices and $m$ denotes the number of edges. In terms of the dependence on $n$ and $m$ this bound is optimal up to poly-logarithmic factors since $Ω(n/sqrt{m})$ queries are necessary (and $α= O(sqrt{m}))$. We leave it as an open question whether the dependence on $1/ε$ can be improved from quasi-polynomial to polynomial. Our techniques include an efficient local simulation for approximating the outcome of a global (almost) forest-decomposition algorithm as well as a tailored procedure of edge sampling. △ Less
Submitted 16 July, 2017; originally announced July 2017.
On Approximating the Number of $k$-cliques in Sublinear Time
Abstract: We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let $n$ denote the number of vertices in the graph, $m$ the number of edges, and $C_k$ the number of $k$-cliques. We design an algorithm that outputs a… ▽ More We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let $n$ denote the number of vertices in the graph, $m$ the number of edges, and $C_k$ the number of $k$-cliques. We design an algorithm that outputs a $(1+varepsilon)$-approximation (with high probability) for $C_k$, whose expected query complexity and running time are $Oleft(frac{n}{C_k^{1/k}}+frac{m^{k/2}}{C_k}right)poly(log n,1/varepsilon,k)$. Hence, the complexity of the algorithm is sublinear in the size of the graph for $C_k = ω(m^{k/2-1})$. Furthermore, we prove a lower bound showing that the query complexity of our algorithm is essentially optimal (up to the dependence on $log n$, $1/varepsilon$ and $k$). The previous results in this vein are by Feige (SICOMP 06) and by Goldreich and Ron (RSA 08) for edge counting ($k=2$) and by Eden et al. (FOCS 2015) for triangle counting ($k=3$). Our result matches the complexities of these results. The previous result by Eden et al. hinges on a certain amortization technique that works only for triangle counting, and does not generalize for larger cliques. We obtain a general algorithm that works for any $kgeq 3$ by designing a procedure that samples each $k$-clique incident to a given set $S$ of vertices with approximately equal probability. The primary difficulty is in finding cliques incident to purely high-degree vertices, since random sampling within neighbors has a low success probability. This is achieved by an algorithm that samples uniform random high degree vertices and a careful tradeoff between estimating cliques incident purely to high-degree vertices and those that include a low-degree vertex. △ Less
Submitted 12 March, 2018; v1 submitted 16 July, 2017; originally announced July 2017.
arXiv:1706.10009 [pdf, other]
Pricing Social Goods
Abstract: Social goods are goods that grant value not only to their owners but also to the owners' surroundings, be it their families, friends or office mates. The benefit a non-owner derives from the good is affected by many factors, including the type of the good, its availability, and the social status of the non-owner. Depending on the magnitude of the benefit and on the price of the good, a potential b… ▽ More Social goods are goods that grant value not only to their owners but also to the owners' surroundings, be it their families, friends or office mates. The benefit a non-owner derives from the good is affected by many factors, including the type of the good, its availability, and the social status of the non-owner. Depending on the magnitude of the benefit and on the price of the good, a potential buyer might stay away from purchasing the good, hoping to free ride on others' purchases. A revenue-maximizing seller who sells social goods must take these considerations into account when setting prices for the good. The literature on optimal pricing has advanced considerably over the last decade, but little is known about optimal pricing schemes for selling social goods. In this paper, we conduct a systematic study of revenue-maximizing pricing schemes for social goods: we introduce a Bayesian model for this scenario, and devise nearly-optimal pricing schemes for various types of externalities, both for simultaneous sales and for sequential sales. △ Less
Submitted 3 July, 2017; v1 submitted 29 June, 2017; originally announced June 2017.
On Sampling Edges Almost Uniformly
Abstract: We consider the problem of sampling an edge almost uniformly from an unknown graph, $G = (V, E)$. Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe an algorithm that returns a random edge $e in E$ using $tilde{O}(n / sqrt{varepsilon m})$ queries in expectation, where $n = V $ is the number… ▽ More We consider the problem of sampling an edge almost uniformly from an unknown graph, $G = (V, E)$. Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe an algorithm that returns a random edge $e in E$ using $tilde{O}(n / sqrt{varepsilon m})$ queries in expectation, where $n = V $ is the number of vertices, and $m = E $ is the number of edges, such that each edge $e$ is sampled with probability $(1 pm varepsilon)/m$. We prove that our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform $Ω(n / sqrt{m})$ queries. △ Less
Submitted 29 June, 2017; originally announced June 2017.
arXiv:1706.01046 [pdf, other]
Properties of Hi-GAL clumps in the inner Galaxy]{The Hi-GAL compact source catalogue. I. The physical properties of the clumps in the inner Galaxy ($-71.0^{circ}< ell < 67.0^{circ}$)
Abstract: Hi-GAL is a large-scale survey of the Galactic plane, performed with Herschel in five infrared continuum bands between 70 and 500 $μ$m. We present a band-merged catalogue of spatially matched sources and their properties derived from fits to the spectral energy distributions (SEDs) and heliocentric distances, based on the photometric catalogs presented in Molinari et al. (2016a), covering the port… ▽ More Hi-GAL is a large-scale survey of the Galactic plane, performed with Herschel in five infrared continuum bands between 70 and 500 $μ$m. We present a band-merged catalogue of spatially matched sources and their properties derived from fits to the spectral energy distributions (SEDs) and heliocentric distances, based on the photometric catalogs presented in Molinari et al. (2016a), covering the portion of Galactic plane $-71.0^{circ}< ell < 67.0^{circ}$. The band-merged catalogue contains 100922 sources with a regular SED, 24584 of which show a 70 $μ$m counterpart and are thus considered proto-stellar, while the remainder are considered starless. Thanks to this huge number of sources, we are able to carry out a preliminary analysis of early stages of star formation, identifying the conditions that characterise different evolutionary phases on a statistically significant basis. We calculate surface densities to investigate the gravitational stability of clumps and their potential to form massive stars. We also explore evolutionary status metrics such as the dust temperature, luminosity and bolometric temperature, finding that these are higher in proto-stellar sources compared to pre-stellar ones. The surface density of sources follows an increasing trend as they evolve from pre-stellar to proto-stellar, but then it is found to decrease again in the majority of the most evolved clumps. Finally, we study the physical parameters of sources with respect to Galactic longitude and the association with spiral arms, finding only minor or no differences between the average evolutionary status of sources in the fourth and first Galactic quadrants, or between 'on-arm' and 'inter-arm' positions. △ Less
Submitted 4 June, 2017; originally announced June 2017.
Comments:Accepted by MNRAS
arXiv:1705.09877 [pdf, other]
Spatial distribution of star formation related to ionized regions throughout the inner Galactic plane
Abstract: We present a comprehensive statistical analysis of star-forming objects located in the vicinities of 1 360 bubble structures throughout the Galactic Plane and their local environments. The compilation of ~70 000 star-forming sources, found in the proximity of the ionized (Hii) regions and detected in both Hi-GAL and GLIMPSE surveys, provided a broad overview of the different evolutionary stages of… ▽ More We present a comprehensive statistical analysis of star-forming objects located in the vicinities of 1 360 bubble structures throughout the Galactic Plane and their local environments. The compilation of ~70 000 star-forming sources, found in the proximity of the ionized (Hii) regions and detected in both Hi-GAL and GLIMPSE surveys, provided a broad overview of the different evolutionary stages of star-formation in bubbles, from prestellar objects to more evolved young stellar objects (YSOs). Surface density maps of star-forming objects clearly reveal an evolutionary trend where more evolved star-forming objects are found spatially located near the center, while younger star-forming objects are found at the edge of the bubbles. We derived dynamic ages for a subsample of 182 Hii regions for which kinematic distances and radio continuum flux measurements were available. We detect ~80% more star-forming sources per unit area in the direction of bubbles than in the surrounding fields. We estimate ~10% clump formation efficiency (CFE) of Hi-GAL clumps in bubbles, twice the CFE in fields not affected by feedback. We find higher CFE of protostellar clumps in younger bubbles, whose density of the bubble shells is higher. We argue that the formation rate from prestellar to protostellar phase is probably higher during the early stages of the bubble expansion. Evaluation of the fragmentation time inside the shell of bubbles advocates the preexistence of clumps in the medium before the bubble, as supported by numerical simulations. Approximately 23% of the Hi-GAL clumps are found located in the direction of a bubble, with 15% for prestellar clumps and 41% for protostellar clumps. We argue that the high fraction of protostellar clumps may be due to the acceleration of the star-formation process cause by the feedback of the (Hii) bubbles. △ Less
Submitted 27 May, 2017; originally announced May 2017.
Comments:15 pages, 12 figures. Accepted for publication by Astronomy and Astrophysics
Journal ref: A&A 605, A35 (2017)
arXiv:1705.05970 [pdf]
Changes in Ugandan Climate Rainfall at the Village and Forest Level
Abstract: In 2013, the US National Oceanographic and Atmospheric Agency refined the historical rainfall estimates over the African Continent and produced the African Rainfall Climate version 2.0 (ARC2) estimator. ARC2 offers a nearly complete record of daily rainfall estimates since 1983 at 0.1 x 0.1 degree resolution. Despite short-term anomalies in twice-yearly rainy season intensities in Uganda, we ident… ▽ More In 2013, the US National Oceanographic and Atmospheric Agency refined the historical rainfall estimates over the African Continent and produced the African Rainfall Climate version 2.0 (ARC2) estimator. ARC2 offers a nearly complete record of daily rainfall estimates since 1983 at 0.1 x 0.1 degree resolution. Despite short-term anomalies in twice-yearly rainy season intensities in Uganda, we identify an overall decrease in average rainfall of about 12% during the past 34 years. Spatiotemporally, these decreases are greatest in agricultural regions of central and western Uganda, but are also reflective of rainfall decreases in the gorilla habitat within the Bwindi Forest in Southwest Uganda. The findings carry significant implications for agriculture, food security, and wildlife habitat. △ Less
Submitted 18 May, 2017; v1 submitted 16 May, 2017; originally announced May 2017.
Comments:19 pages, 5 figures
arXiv:1704.02982 [pdf, other]
The JCMT Plane Survey: First complete data release - emission maps and compact source catalogue
Abstract: We present the first data release of the James Clerk Maxwell Telescope (JCMT) Plane Survey (JPS), the JPS Public Release 1 (JPSPR1). JPS is an 850-um continuum survey of six fields in the northern inner Galactic Plane in a longitude range of l=7-63, made with the Sub-millimetre Common-User Bolometer Array 2 (SCUBA-2). This first data release consists of emission maps of the six JPS regions with an… ▽ More We present the first data release of the James Clerk Maxwell Telescope (JCMT) Plane Survey (JPS), the JPS Public Release 1 (JPSPR1). JPS is an 850-um continuum survey of six fields in the northern inner Galactic Plane in a longitude range of l=7-63, made with the Sub-millimetre Common-User Bolometer Array 2 (SCUBA-2). This first data release consists of emission maps of the six JPS regions with an average pixel-to-pixel noise of 7.19 mJy beam^-1, when smoothed over the beam, and a compact-source catalogue containing 7,813 sources. The 95 per cent completeness limits of the catalogue are estimated at 0.04 Jy beam^-1 and 0.3 Jy for the peak and integrated flux densities, respectively. The emission contained in the compact-source catalogue is 42 +- 5 per cent of the total and, apart from the large-scale (greater than 8') emission, there is excellent correspondence with features in the 500-um Herschel maps. We find that, with two-dimensional matching, 98 +- 2 per cent of sources within the fields centred at l=20, 30, 40 and 50 are associated with molecular clouds, with 91 +- 3 per cent of the l=30 and 40 sources associated with dense molecular clumps. Matching the JPS catalogue to Herschel 70-um sources, we find that 38 +- 1 per cent of sources show evidence of ongoing star formation. The images and catalogue will be a valuable resource for studies of star formation in the Galaxy and the role of environment and spiral arms in the star formation process. △ Less
Submitted 10 April, 2017; originally announced April 2017.
Comments:22 pages, 18 figures, 4 tables. Full version of Table 3 available from http://www.canfar.phys.uvic.ca/vosui/#/JPSPR1 Accepted for publication in Monthly Notices of the Royal Astronomical Society
arXiv:1607.07626 [pdf, other]
The prevalence of star formation as a function of Galactocentric radius
Abstract: We present large-scale trends in the distribution of star-forming objects revealed by the Hi-GAL survey. As a simple metric probing the prevalence of star formation in Hi-GAL sources, we define the fraction of the total number of Hi-GAL sources with a 70-micron counterpart as the 'star-forming fraction' or SFF. The mean SFF in the inner galactic disc (3.1 kpc < R_GC < 8.6 kpc) is 25%. Despite an a… ▽ More We present large-scale trends in the distribution of star-forming objects revealed by the Hi-GAL survey. As a simple metric probing the prevalence of star formation in Hi-GAL sources, we define the fraction of the total number of Hi-GAL sources with a 70-micron counterpart as the 'star-forming fraction' or SFF. The mean SFF in the inner galactic disc (3.1 kpc < R_GC < 8.6 kpc) is 25%. Despite an apparent pile-up of source numbers at radii associated with spiral arms, the SFF shows no significant deviations at these radii, indicating that the arms do not affect the star-forming productivity of dense clumps either via physical triggering processes or through the statistical effects of larger source samples associated with the arms. Within this range of Galactocentric radii, we find that the SFF declines with R_GC at a rate of -0.026 +/- 0.002 per kiloparsec, despite the dense gas mass fraction having been observed to be constant in the inner Galaxy. This suggests that the SFF may be weakly dependent on one or more large-scale physical properties of the Galaxy, such as metallicity, radiation field, pressure or shear, such that the dense sub-structures of molecular clouds acquire some internal properties inherited from their environment. △ Less
Submitted 26 July, 2016; originally announced July 2016.
Comments:accepted for publication in MNRAS, 8 pages, 6 figures
arXiv:1607.03938 [pdf, ps, other] Jual camera tembus pandang.
Tolerant Junta Testing and the Connection to Submodular Optimization and Function Isomorphism
Abstract: A function $fcolon {-1,1}^n to {-1,1}$ is a $k$-junta if it depends on at most $k$ of its variables. We consider the problem of tolerant testing of $k$-juntas, where the testing algorithm must accept any function that is $ε$-close to some $k$-junta and reject any function that is $ε'$-far from every $k'$-junta for some $ε'= O(ε)$ and $k' = O(k)$. Our first result is an algorithm that solve… ▽ More A function $fcolon {-1,1}^n to {-1,1}$ is a $k$-junta if it depends on at most $k$ of its variables. We consider the problem of tolerant testing of $k$-juntas, where the testing algorithm must accept any function that is $ε$-close to some $k$-junta and reject any function that is $ε'$-far from every $k'$-junta for some $ε'= O(ε)$ and $k' = O(k)$. Our first result is an algorithm that solves this problem with query complexity polynomial in $k$ and $1/ε$. This result is obtained via a new polynomial-time approximation algorithm for submodular function minimization (SFM) under large cardinality constraints, which holds even when only given an approximate oracle access to the function. Our second result considers the case where $k'=k$. We show how to obtain a smooth tradeoff between the amount of tolerance and the query complexity in this setting. Specifically, we design an algorithm that given $ρin(0,1/2)$ accepts any function that is $frac{ερ}{16}$-close to some $k$-junta and rejects any function that is $ε$-far from every $k$-junta. The query complexity of the algorithm is $Obig( frac{klog k}{ερ(1-ρ)^k} big)$. Finally, we show how to apply the second result to the problem of tolerant isomorphism testing between two unknown Boolean functions $f$ and $g$. We give an algorithm for this problem whose query complexity only depends on the (unknown) smallest $k$ such that either $f$ or $g$ is close to being a $k$-junta. △ Less
Submitted 3 November, 2016; v1 submitted 13 July, 2016; originally announced July 2016.
Comments:Polished the writing, corrected typos, and fixed an issue in the proof of Theorem 1.2
arXiv:1604.05911 [pdf, other]
Hi-GAL, the Herschel infrared Galactic Plane Survey: photometric maps and compact source catalogues. First data release for Inner Milky Way: +68°> l > -70°
Abstract: (Abridged) We present the first public release of high-quality data products (DR1) from Hi-GAL, the {em Herschel} infrared Galactic Plane Survey. Hi-GAL is the keystone of a suite of continuum Galactic Plane surveys from the near-IR to the radio, and covers five wavebands at 70, 160, 250, 350 and 500 micron, encompassing the peak of the spectral energy distribution of cold dust for 8 < T < 50K. T… ▽ More (Abridged) We present the first public release of high-quality data products (DR1) from Hi-GAL, the {em Herschel} infrared Galactic Plane Survey. Hi-GAL is the keystone of a suite of continuum Galactic Plane surveys from the near-IR to the radio, and covers five wavebands at 70, 160, 250, 350 and 500 micron, encompassing the peak of the spectral energy distribution of cold dust for 8 < T < 50K. This first Hi-GAL data release covers the inner Milky Way in the longitude range 68° > l > -70° in a b <1° latitude strip. Photometric maps have been produced with the ROMAGAL pipeline, that optimally capitalizes on the excellent sensitivity and stability of the bolometer arrays of the {em Herschel} PACS and SPIRE photometric cameras, to deliver images of exquisite quality and dynamical range, absolutely calibrated with {em Planck} and {em IRAS}, and recovering extended emission at all wavelengths and all spatial scales. The compact source catalogues have been generated with the CuTEx algorithm, specifically developed to optimize source detection and extraction in the extreme conditions of intense and spatially varying background that are found in the Galactic Plane in the thermal infrared. Hi-GAL DR1 images will be accessible via a dedicated web-based image cutout service. The DR1 Compact Source Catalogues are delivered as single-band photometric lists containing, in addition to source position, peak and integrated flux and source sizes, a variety of parameters useful to assess the quality and reliability of the extracted sources, caveats and hints to help this assessment are provided. Flux completeness limits in all bands are determined from extensive synthetic source experiments and depend on the specific line of sight along the Galactic Plane. Hi-GAL DR1 catalogues contain 123210, 308509, 280685, 160972 and 85460 compact sources in the five bands, respectively. △ Less
Submitted 20 April, 2016; originally announced April 2016.
Comments:Astronomy & Astrophysics, accepted
arXiv:1604.03661 [pdf, ps, other]
Sublinear Time Estimation of Degree Distribution Moments: The Degeneracy Connection
Abstract: We revisit the classic problem of estimating the degree distribution moments of an undirected graph. Consider an undirected graph $G=(V,E)$ with $n$ vertices, and define (for $s > 0$) $μ_s = frac{1}{n}cdotsum_{v in V} d^s_v$. Our aim is to estimate $μ_s$ within a multiplicative error of $(1+ε)$ (for a given approximation parameter $ε>0$) in sublinear time. We consider the sparse graph model th… ▽ More We revisit the classic problem of estimating the degree distribution moments of an undirected graph. Consider an undirected graph $G=(V,E)$ with $n$ vertices, and define (for $s > 0$) $μ_s = frac{1}{n}cdotsum_{v in V} d^s_v$. Our aim is to estimate $μ_s$ within a multiplicative error of $(1+ε)$ (for a given approximation parameter $ε>0$) in sublinear time. We consider the sparse graph model that allows access to: uniform random vertices, queries for the degree of any vertex, and queries for a neighbor of any vertex. For the case of $s=1$ (the average degree), $widetilde{O}(sqrt{n})$ queries suffice for any constant $ε$ (Feige, SICOMP 06 and Goldreich-Ron, RSA 08). Gonen-Ron-Shavitt (SIDMA 11) extended this result to all integral $s > 0$, by designing an algorithms that performs $widetilde{O}(n^{1-1/(s+1)})$ queries. We design a new, significantly simpler algorithm for this problem. In the worst-case, it exactly matches the bounds of Gonen-Ron-Shavitt, and has a much simpler proof. More importantly, the running time of this algorithm is connected to the degeneracy of $G$. This is (essentially) the maximum density of an induced subgraph. For the family of graphs with degeneracy at most $α$, it has a query complexity of $widetilde{O}left(frac{n^{1-1/s}}{μ^{1/s}_s} Big(α^{1/s} + min{α,μ^{1/s}_s}Big)right) = widetilde{O}(n^{1-1/s}α/μ^{1/s}_s)$. Thus, for the class of bounded degeneracy graphs (which includes all minor closed families and preferential attachment graphs), we can estimate the average degree in $widetilde{O}(1)$ queries, and can estimate the variance of the degree distribution in $widetilde{O}(sqrt{n})$ queries. This is a major improvement over the previous worst-case bounds. Our key insight is in designing an estimator for $μ_s$ that has low variance when $G$ does not have large dense subgraphs. △ Less
Submitted 16 February, 2017; v1 submitted 13 April, 2016; originally announced April 2016.
arXiv:1512.08235 [pdf, other]
CHIMPS: the $^{13}$CO/C$^{18}$O (J=3-2) Heterodyne Inner Milky Way Plane Survey
Abstract: We present the $^{13}$CO/C$^{18}$O (J=3-2) Heterodyne Inner Milky Way Plane Survey (CHIMPS) which has been carried out using the Heterodyne Array Receiver Program on the 15 m James Clerk Maxwell Telescope (JCMT) in Hawaii. The high-resolution spectral survey currently covers b < 0.5 deg and 28 < l < 46 deg, with an angular resolution of 15 arcsec in 0.5 km/s velocity channels. The spectra have a… ▽ More We present the $^{13}$CO/C$^{18}$O (J=3-2) Heterodyne Inner Milky Way Plane Survey (CHIMPS) which has been carried out using the Heterodyne Array Receiver Program on the 15 m James Clerk Maxwell Telescope (JCMT) in Hawaii. The high-resolution spectral survey currently covers b < 0.5 deg and 28 < l < 46 deg, with an angular resolution of 15 arcsec in 0.5 km/s velocity channels. The spectra have a median rms of $sim$ 0.6 K at this resolution, and for optically thin gas at an excitation temperature of 10 K, this sensitivity corresponds to column densities of $N_{mathrm{H}_{2}} sim 3 times 10^{20},$cm$^{-2}$ and $N_{mathrm{H}_{2}} sim 4 times 10^{21},$cm$^{-2}$ for $^{13}$CO and C$^{18}$O, respectively. The molecular gas that CHIMPS traces is at higher column densities and is also more optically thin than in other publicly available CO surveys due to its rarer isotopologues, and thus more representative of the three-dimensional structure of the clouds. The critical density of the J=3-2 transition of CO is $gtrsim 10^{4}$ cm$^{-3}$ at temperatures of $leq 20$ K, and so the higher density gas associated with star formation is well traced. These data complement other existing Galactic plane surveys, especially the JCMT Galactic Plane Survey which has similar spatial resolution and column density sensitivity, and the Herschel infrared Galactic Plane Survey. In this paper, we discuss the observations, data reduction and characteristics of the survey, presenting integrated emission maps for the region covered. Position-velocity diagrams allow comparison with Galactic structure models of the Milky Way, and while we find good agreement with a particular four arm model, there are some significant deviations. △ Less
Submitted 27 December, 2015; originally announced December 2015.
Comments:Accepted by MNRAS, 15 pages, 9 figures
arXiv:1509.00318 [pdf, other]
The JCMT Plane Survey: early results from the l = 30 degree field
Abstract: We present early results from the JCMT Plane Survey (JPS), which has surveyed the northern inner Galactic plane between longitudes l=7 and l=63 degrees in the 850-μm continuum with SCUBA-2, as part of the James Clerk Maxwell Telescope Legacy Survey programme. Data from the l=30 degree survey region, which contains the massive star-forming regions W43 and G29.96, are analysed after approximately 40… ▽ More We present early results from the JCMT Plane Survey (JPS), which has surveyed the northern inner Galactic plane between longitudes l=7 and l=63 degrees in the 850-μm continuum with SCUBA-2, as part of the James Clerk Maxwell Telescope Legacy Survey programme. Data from the l=30 degree survey region, which contains the massive star-forming regions W43 and G29.96, are analysed after approximately 40% of the observations had been completed. The pixel-to-pixel noise is found to be 19 mJy/beam, after a smooth over the beam area, and the projected equivalent noise levels in the final survey are expected to be around 10 mJy/beam. An initial extraction of compact sources was performed using the FellWalker method resulting in the detection of 1029 sources above a 5-σ surface-brightness threshold. The completeness limits in these data are estimated to be around 0.2 Jy/beam (peak flux density) and 0.8 Jy (integrated flux density) and are therefore probably already dominated by source confusion in this relatively crowded section of the survey. The flux densities of extracted compact sources are consistent with those of matching detections in the shallower ATLASGAL survey. We analyse the virial and evolutionary state of the detected clumps in the W43 star-forming complex and find that they appear younger than the Galactic-plane average. △ Less
Submitted 1 September, 2015; originally announced September 2015.
Comments:Accepted by MNRAS
arXiv:1507.02187 [pdf, ps, other]
The RMS Survey: Ammonia mapping of the environment of massive young stellar objects
Abstract: We present the results of ammonia observations towards 66 massive star forming regions identified by the Red MSX source survey. We have used the Green Bank Telescope and the K-band focal plane array to map the ammonia NH3 (1,1) and (2,2) inversion emission at a resolution of 30 arcsec in 8 arcmin regions towards the positions of embedded massive star formation. We have identified a total of 115 di… ▽ More We present the results of ammonia observations towards 66 massive star forming regions identified by the Red MSX source survey. We have used the Green Bank Telescope and the K-band focal plane array to map the ammonia NH3 (1,1) and (2,2) inversion emission at a resolution of 30 arcsec in 8 arcmin regions towards the positions of embedded massive star formation. We have identified a total of 115 distinct clumps, approximately two-thirds of which are associated with an embedded massive young stellar object or compact HII region, while the others are classified as quiescent. There is a strong spatial correlation between the peak NH3 emission and the presence of embedded objects. We derive the spatial distribution of the kinetic gas temperatures, line widths, and NH$_3$ column densities from these maps, and by combining these data with dust emission maps we estimate clump masses, H$_2$ column densities and ammonia abundances. The clumps have typical masses of ~1000 Msun and radii ~0.5 pc, line widths of ~2 km/s and kinetic temperatures of ~16-20 K. We find no significant difference between the sizes and masses of the star forming and quiescent subsamples; however, the distribution maps reveal the presence of temperature and line width gradients peaking towards the centre for the star forming clumps while the quiescent clumps show relatively uniform temperatures and line widths throughout. Virial analysis suggests that the vast majority of clumps are gravitationally bound and are likely to be in a state of global free fall in the absence of strong magnetic fields. The similarities between the properties of the two subsamples suggest that the quiescent clumps are also likely to form massive stars in the future, and therefore provide a excellent opportunity to study the initial conditions of massive pre-stellar and protostellar clumps. △ Less
Submitted 8 July, 2015; originally announced July 2015.
Comments:Accepted for publication by MNRAS. 25 pages, 21 figures and 6 tables. This paper also contains 100 pages of additional online images and tables that are not included here. A full resolution version of the paper including all of the online material can be found here http://rms.leeds.ac.uk/cgi-bin/public/RMS_PUBLICATIONS.cgi
arXiv:1506.04552 [pdf, ps, other]
Star formation scales and efficiency in Galactic spiral arms
Abstract: We positionally match a sample of infrared-selected young stellar objects (YSOs), identified by combining the Spitzer GLIMPSE, WISE and Herschel Space Observatory Hi-GAL surveys, to the dense clumps identified in the millimetre continuum by the Bolocam Galactic Plane Survey in two Galactic lines of sight centred towards l = 30deg and l = 40deg. We calculate the ratio of infrared luminosity, L_IR,… ▽ More We positionally match a sample of infrared-selected young stellar objects (YSOs), identified by combining the Spitzer GLIMPSE, WISE and Herschel Space Observatory Hi-GAL surveys, to the dense clumps identified in the millimetre continuum by the Bolocam Galactic Plane Survey in two Galactic lines of sight centred towards l = 30deg and l = 40deg. We calculate the ratio of infrared luminosity, L_IR, to the mass of the clump, M_clump, in a variety of Galactic environments and find it to be somewhat enhanced in spiral arms compared to the interarm regions when averaged over kiloparsec scales. We find no compelling evidence that these changes are due to the mechanical influence of the spiral arm on the star-formation efficiency rather than, e.g., different gradients in the star-formation rate due to patchy or intermittent star formation, or local variations that are not averaged out due to small source samples. The largest variation in L_IR/M_clump is found in individual clump values, which follow a log-normal distribution and have a range of over three orders of magnitude. This spread is intrinsic as no dependence of L_IR/M_clump with M_clump was found. No difference was found in the luminosity distribution of sources in the arm and interarm samples and a strong linear correlation was found between L_IR and M_clump. △ Less
Submitted 15 June, 2015; originally announced June 2015.
Comments:13 pages, 12 figures, accepted for publication in MNRAS
arXiv:1504.00954 [pdf, ps, other]
Approximately Counting Triangles in Sublinear Time
Abstract: We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a {em sublinear-time/} algorithm for approximating the number of triangles in a graph, where the algorithm is given query access to the graph. The allowed queries are degree queri… ▽ More We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a {em sublinear-time/} algorithm for approximating the number of triangles in a graph, where the algorithm is given query access to the graph. The allowed queries are degree queries, vertex-pair queries and neighbor queries. We show that for any given approximation parameter $0<ε<1$, the algorithm provides an estimate $widehat{t}$ such that with high constant probability, $(1-ε)cdot t< widehat{t}<(1+ε)cdot t$, where $t$ is the number of triangles in the graph $G$. The expected query complexity of the algorithm is $!left(frac{n}{t^{1/3}} + minleft{m, frac{m^{3/2}}{t}right}right)cdot {rm poly}(log n, 1/ε)$, where $n$ is the number of vertices in the graph and $m$ is the number of edges, and the expected running time is $!left(frac{n}{t^{1/3}} + frac{m^{3/2}}{t}right)cdot {rm poly}(log n, 1/ε)$. We also prove that $Ω!left(frac{n}{t^{1/3}} + minleft{m, frac{m^{3/2}}{t}right}right)$ queries are necessary, thus establishing that the query complexity of this algorithm is optimal up to polylogarithmic factors in $n$ (and the dependence on $1/ε$). △ Less
Submitted 22 September, 2015; v1 submitted 3 April, 2015; originally announced April 2015.
Comments:To appear in the 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2015)
arXiv:1503.03028 [pdf, other]
Cascading Quantum Light-Matter Interfaces
Abstract: The ability to interface multiple optical quantum devices is a key milestone towards the development of future quantum networks that are capable of sharing and processing quantum information encoded in light. One of the requirements for any node of these quantum networks will be cascadability, i.e. the ability to drive the input of a node using the output of another node. Here, we report the casca… ▽ More The ability to interface multiple optical quantum devices is a key milestone towards the development of future quantum networks that are capable of sharing and processing quantum information encoded in light. One of the requirements for any node of these quantum networks will be cascadability, i.e. the ability to drive the input of a node using the output of another node. Here, we report the cascading of quantum light-matter interfaces by storing few-photon level pulses of light in warm vapor followed by the subsequent storage of the retrieved field onto a second ensemble. We demonstrate that even after the sequential storage, the final signal-to-background ratio can remain greater than 1 for weak pulses containing 8 input photons on average. △ Less
Submitted 10 March, 2015; originally announced March 2015.
Comments:5 pages, 5 figures
Journal ref: Phys. Rev. A 92, 033846 (2015)
arXiv:1412.5140 [pdf, ps, other]
Separated Response Functions in Exclusive, Forward $π^{pm}$ Electroproduction on Deuterium
Abstract: Background: Measurements of forward exclusive meson production at different squared four-momenta of the exchanged virtual photon, $Q^2$, and at different four-momentum transfer, t, can be used to probe QCD's transition from meson-nucleon degrees of freedom at long distances to quark-gluon degrees of freedom at short scales. Ratios of separated response functions in $π^-$ and $π^+$ electroproductio… ▽ More Background: Measurements of forward exclusive meson production at different squared four-momenta of the exchanged virtual photon, $Q^2$, and at different four-momentum transfer, t, can be used to probe QCD's transition from meson-nucleon degrees of freedom at long distances to quark-gluon degrees of freedom at short scales. Ratios of separated response functions in $π^-$ and $π^+$ electroproduction are particularly informative. The ratio for transverse photons may allow this transition to be more easily observed, while the ratio for longitudinal photons provides a crucial verification of the assumed pole dominance, needed for reliable extraction of the pion form factor from electroproduction data. Method: Data were acquired with 2.6-5.2 GeV electron beams and the HMS+SOS spectrometers in Jefferson Lab Hall C, at central $Q^2$ values of 0.6, 1.0, 1.6 GeV$^2$ at W=1.95 GeV, and $Q^2$=2.45 GeV$^2$ at W=2.22 GeV. There was significant coverage in $φ$ and $ε$, which allowed separation of $σ_{L,T,LT,TT}$. Results: $σ_L$ shows a clear signature of the pion pole, with a sharp rise at small -t. In contrast, $σ_T$ is much flatter versus t. The longitudinal/transverse ratios evolve with $Q^2$ and t, and at the highest $Q^2$=2.45 GeV$^2$ show a slight enhancement for $π^-$ production compared to $π^+$. The $π^-/π^+$ ratio for transverse photons exhibits only a small $Q^2$-dependence, following a nearly universal curve with t, with a steep transition to a value of about 0.25, consistent with s-channel quark knockout. The $σ_{TT}/σ_T$ ratio also drops rapidly with $Q^2$, qualitatively consistent with s-channel helicity conservation. The $π^-/π^+$ ratio for longitudinal photons indicates a small isoscalar contamination at W=1.95 GeV, consistent with what was observed in our earlier determination of the pion form factor at these kinematics. △ Less
Submitted 16 December, 2014; originally announced December 2014.
Comments:25 pages, 16 figures, 6 tables
Journal ref: Physical Review C 91 (2015) 015202
arXiv:1410.6322 [pdf, ps, other]
The almost ubiquitous association of 6.7 GHz methanol masers with dust
Abstract: We report the results of 870-$μ$m continuum observations, using the Large APEX Bolometer Camera (LABOCA), towards 77 class-II, 6.7-GHz methanol masers identified by the Methanol Multibeam (MMB) survey to map the thermal emission from cool dust towards these objects. These data complement a study of 630 methanol masers associated with compact dense clumps identified from the ATLASGAL survey. Compac… ▽ More We report the results of 870-$μ$m continuum observations, using the Large APEX Bolometer Camera (LABOCA), towards 77 class-II, 6.7-GHz methanol masers identified by the Methanol Multibeam (MMB) survey to map the thermal emission from cool dust towards these objects. These data complement a study of 630 methanol masers associated with compact dense clumps identified from the ATLASGAL survey. Compact dust emission is detected towards 70 sources, which implies a dust-association rate of 99% for the full MMB catalogue. Evaluation of the derived dust and maser properties leads us to conclude that the combined sample represents a single population tracing the same phenomenon. We find median clump masses of a few 10$^3$ M$odot$ and that all but a handful of sources satisfy the mass-size criterion required for massive star formation. This study provides the strongest evidence of the almost ubiquitous association of methanol masers with massive, star-forming clumps. The fraction of methanol-maser associated clumps is a factor of ~2 lower in the outer Galaxy than the inner Galaxy, possibly a result of the lower metallicity environment of the former. We find no difference in the clump-mass and maser-luminosity distributions of the inner and outer Galaxy. The maser-pumping and clump-formation mechanisms are therefore likely to be relatively invariant to Galactic location. Finally, we use the ratio of maser luminosity and clump mass to investigate the hypothesis that the maser luminosity is a good indicator of the evolutionary stage of the embedded source, however, we find no evidence to support this. △ Less
Submitted 23 October, 2014; originally announced October 2014.
Comments:Accepted by MNRAS. 17 pages, 17 figures and 5 tables. The full version of Figs. 3 and 5 are only available in electronic form of the journal while the full versions of Tables 1, 2 and 4 will only be available through CDS. A complete version of the paper is available on request
arXiv:1405.6117 [pdf, other]
Room-Temperature Quantum Memory for Polarization States
Abstract: An optical quantum memory is a stationary device that is capable of storing and recreating photonic qubits with a higher fidelity than any classical device. Thus far, these two requirements have been fulfilled in systems based on cold atoms and cryogenically cooled crystals. Here, we report a room-temperature quantum memory capable of storing arbitrary polarization qubits with a signal-to-backgrou… ▽ More An optical quantum memory is a stationary device that is capable of storing and recreating photonic qubits with a higher fidelity than any classical device. Thus far, these two requirements have been fulfilled in systems based on cold atoms and cryogenically cooled crystals. Here, we report a room-temperature quantum memory capable of storing arbitrary polarization qubits with a signal-to-background ratio higher than 1 and an average fidelity clearly surpassing the classical limit for weak laser pulses containing 1.6 photons on average. Our results prove that a common vapor cell can reach the low background noise levels necessary for quantum memory operation, and propels atomic-vapor systems to a level of quantum functionality akin to other quantum information processing architectures. △ Less
Submitted 23 May, 2014; originally announced May 2014.
arXiv:1404.3985 [pdf, ps, other]
Separated Response Function Ratios in Exclusive, Forward pi^{+/-} Electroproduction
Abstract: The study of exclusive $π^{pm}$ electroproduction on the nucleon, including separation of the various structure functions, is of interest for a number of reasons. The ratio $R_L=σ_L^{π^-}/σ_L^{π^+}$ is sensitive to isoscalar contamination to the dominant isovector pion exchange amplitude, which is the basis for the determination of the charged pion form factor from electroproduction data. A chang… ▽ More The study of exclusive $π^{pm}$ electroproduction on the nucleon, including separation of the various structure functions, is of interest for a number of reasons. The ratio $R_L=σ_L^{π^-}/σ_L^{π^+}$ is sensitive to isoscalar contamination to the dominant isovector pion exchange amplitude, which is the basis for the determination of the charged pion form factor from electroproduction data. A change in the value of $R_T=σ_T^{π^-}/σ_T^{π^+}$ from unity at small $-t$, to 1/4 at large $-t$, would suggest a transition from coupling to a (virtual) pion to coupling to individual quarks. Furthermore, the mentioned ratios may show an earlier approach to pQCD than the individual cross sections. We have performed the first complete separation of the four unpolarized electromagnetic structure functions above the dominant resonances in forward, exclusive $π^{pm}$ electroproduction on the deuteron at central $Q^2$ values of 0.6, 1.0, 1.6 GeV$^2$ at $W$=1.95 GeV, and $Q^2=2.45$ GeV$^2$ at $W$=2.22 GeV. Here, we present the $L$ and $T$ cross sections, with emphasis on $R_L$ and $R_T$, and compare them with theoretical calculations. Results for the separated ratio $R_L$ indicate dominance of the pion-pole diagram at low $-t$, while results for $R_T$ are consistent with a transition between pion knockout and quark knockout mechanisms. △ Less
Submitted 15 April, 2014; originally announced April 2014.
Comments:6 pages, 3 figures
Journal ref: Physical Review Letters 112, 182501 (2014)
arXiv:1312.1163 [pdf, other]
Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
Abstract: Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article… ▽ More Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article we extend this analysis to seven loops and use it to construct the full integrand of the five-point amplitude up to five loops, and in the parity even sector to six loops. All results, both parity even and parity odd, are obtained in a concise local form in dual momentum space and can be displayed efficiently through graphs. We have verified agreement with other local formulae both in terms of supertwistors and scalar momentum integrals as well as BCJ forms where those exist in the literature, i.e. up to three loops. Finally we note that the four-point correlation function can be extracted directly from the four-point amplitude and so this uncovers a direct link from four- to five-point amplitudes. △ Less
Submitted 4 December, 2013; originally announced December 2013.
Comments:29 pages LaTeX, 8 figures
Report number: HU-Mathematik: 2013-23, HU-EP-13/75, DCPT-13/49
arXiv:1307.4105 [pdf, ps, other]
ATLASGAL --- properties of compact HII regions and their natal clumps
Abstract: We present a complete sample of molecular clumps containing compact and ultra-compact (UC) HII regions between ell=10degr and 60degr and $ b <1degr, identified by combining the the ATLASGAL submm and CORNISH radio continuum surveys with visual examination of archival infrared data. Our sample is complete to optically thin, compact and UCHII regions driven by a zero age main sequence star of s… ▽ More We present a complete sample of molecular clumps containing compact and ultra-compact (UC) HII regions between ell=10degr and 60degr and $ b <1degr, identified by combining the the ATLASGAL submm and CORNISH radio continuum surveys with visual examination of archival infrared data. Our sample is complete to optically thin, compact and UCHII regions driven by a zero age main sequence star of spectral type B0 or earlier embedded within a 1,000 Msun clump. In total we identify 213 compact and UCHII regions, associated with 170 clumps. Unambiguous kinematic distances are derived for these clumps and used to estimate their masses and physical sizes, as well as the Lyman continuum fluxes and sizes of their embedded HII regions. We find a clear lower envelope for the surface density of molecular clumps hosting massive star formation of 0.05 g cm^{-2}, which is consistent with a similar sample of clumps associated with 6.7 GHz masers. The mass of the most massive embedded stars is closely correlated with the mass of their natal clump. Young B stars appear to be significantly more luminous in the ultraviolet than predicted by current stellar atmosphere models. The properties of clumps associated with compact and UCHII regions are very similar to those associated with 6.7 GHz methanol masers and we speculate that there is little evolution in the structure of the molecular clumps between these two phases. Finally, we identify a significant peak in the surface density of compact and UCHII regions associated with the W49A star-forming complex, noting that this complex is truly one of the most massive and intense regions of star formation in the Galaxy. △ Less
Submitted 15 July, 2013; originally announced July 2013.
Comments:Accepted for publication in MNRAS. Paper consists of 29 pages, 26 figures and 4 tables. The resolution of Figures 21 and 25 has been reduced to comply with file size restrictions. Full versions of Figures 11 and 12 and Tables 3 and 4 will only be available in the electronic version of the journal and through CDS
arXiv:1302.2874 [pdf, ps, other]
Star formation in Galactic spiral arms and the inter-arm regions
Abstract: The line of sight through the Galactic Plane between longitudes l = 37.83 degr and l = 42.50 degr allows for the separation of Galactic Ring Survey molecular clouds into those that fall within the spiral arms and those located in the inter-arm regions. By matching these clouds in both position and velocity with dense clumps detected in the mm continuum by the Bolocam Galactic Plane Survey, we are… ▽ More The line of sight through the Galactic Plane between longitudes l = 37.83 degr and l = 42.50 degr allows for the separation of Galactic Ring Survey molecular clouds into those that fall within the spiral arms and those located in the inter-arm regions. By matching these clouds in both position and velocity with dense clumps detected in the mm continuum by the Bolocam Galactic Plane Survey, we are able to look for changes in the clump formation efficiency (CFE), the ratio of clump-to-cloud mass, with Galactic environment. We find no evidence of any difference in the CFE between the inter-arm and spiral-arm regions along this line of sight. This is further evidence that, outside the Galactic Centre region, the large-scale structures of the Galaxy play little part in changing the dense, potentially star-forming structures within molecular clouds. △ Less
Submitted 12 February, 2013; originally announced February 2013.
Comments:Accepted for publication in MNRAS. arXiv admin note: text overlap with arXiv:1203.0295
arXiv:1212.1429 [pdf, ps, other]
The Correlation of Dust and Gas Emission in Star-Forming Environments
Abstract: We present ammonia maps of portions of the W3 and Perseus molecular clouds in order to compare gas emission with submillimetre continuum thermal emission which are commonly used to trace the same mass component in star-forming regions, often under the assumption of LTE. The Perseus and W3 star-forming regions are found to have significantly different physical characteristics consistent with the… ▽ More We present ammonia maps of portions of the W3 and Perseus molecular clouds in order to compare gas emission with submillimetre continuum thermal emission which are commonly used to trace the same mass component in star-forming regions, often under the assumption of LTE. The Perseus and W3 star-forming regions are found to have significantly different physical characteristics consistent with the difference in size scales traced by our observations. Accounting for the distance of the W3 region does not fully reconcile these differences, suggesting that there may be an underlying difference in the structure of the two regions. Peak positions of submillimetre and ammonia emission do not correlate strongly. Also, the extent of diffuse emission is only moderately matched between ammonia and thermal emission. Source sizes measured from our observations are consistent between regions, although there is a noticeable difference between the submillimetre source sizes with sources in Perseus being significantly smaller than those in W3. Fractional abundances of ammonia are determined for our sources which indicate a dip in the measured ammonia abundance at the positions of peak submillimetre column density. Virial ratios are determined which show that our sources are generally bound in both regions, although there is considerable scatter in both samples. We conclude that sources in Perseus are bound on smaller scales than in W3 in a way that may reflect their previous identification as low- and high-mass, respectively. Our results indicate that assumptions of local thermal equilibrium and/or the coupling of the dust and gas phases in star-forming regions may not be as robust as commonly assumed. △ Less
Submitted 1 April, 2014; v1 submitted 6 December, 2012; originally announced December 2012.
Comments:38 pages, 16 Figures
Journal ref: Monthly Notices of the Royal Astronomical Society 2014
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