Functions of random walks on hyperplane arrangements

Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only selected features of the chains are of interest, then the mixing times may change. We study the behavior of hyperplane walks, viewed on a subarrangement of a hyperplane arrangement. These include many new examples, for instance a random walk on the set of acyclic orientations of a graph. All such walks can be treated in a uniform fashion, yielding diagonalizable matrices with known eigenvalues, stationary distribution and good rates of convergence to stationarity.Comment: Final version; Section 4 has been split into two section

Fastest mixing Markov chain on graphs with symmetries

We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition probability matrix). Exploiting symmetry can lead to significant reduction in both the number of variables and the size of matrices in the corresponding semidefinite program, thus enable numerical solution of large-scale instances that are otherwise computationally infeasible. We obtain analytic or semi-analytic results for particular classes of graphs, such as edge-transitive and distance-transitive graphs. We describe two general approaches for symmetry exploitation, based on orbit theory and block-diagonalization, respectively. We also establish the connection between these two approaches.Comment: 39 pages, 15 figure

The XMM Newton and INTEGRAL observations of the supergiant fast X-ray transient IGR J16328-4726

The accretion mechanism producing the short flares observed from the Supergiant Fast X-ray Transients (SFXT) is still highly debated and forms a major part in our attempts to place these X-ray binaries in the wider context of the High Mass X-ray Binaries. We report on a 216 ks INTEGRAL observation of the SFXT IGR J16328-4726 (August 24-27, 2014) simultaneous with two fixed-time observations with XMM Newton (33ks and 20ks) performed around the putative periastron passage, in order to investigate the accretion regime and the wind properties during this orbital phase. During these observations, the source has shown luminosity variations, from 4x10^{34} erg/s to 10^{36} erg/s, linked to spectral properties changes. The soft X-ray continuum is well modeled by a power law with a photon index varying from 1.2 up to 1.7 and with high values of the column density in the range 2-4x10^{23}/cm^2. We report on the presence of iron lines at 6.8-7.1 keV suggesting that the X-ray flux is produced by accretion of matter from the companion wind characterized by density and temperature inhomogeneities

A mid-IR survey of the L 1641-N region with ISOCAM

We present an analysis of the L 1641 outflow region using broad-band and narrow-band imaging data at mid-infrared wavelengths from ISOCAM. We detect a total of 34 sources in the $7.65^{\prime}$ x $8.40^{\prime}$ region covered by the broad-band filters. Four of these sources have no reported detection in previous studies of the region. We find that the source previously identified as the near-IR counter-part to the IRAS detected point-source (IRAS 05338-0624) is not the brightest source in the wavelength region of the IRAS 12 \micron\ filter. We find instead that a nearby object (within the beam of IRAS and not detected at near-IR wavelengths) outshines all others sources in the area by a factor of $\sim$2. We submit that this source is likely to be the IRAS detected point source. A comparison of the near-IR (J-H vs H-K) and mid-IR (J-K vs [6.7 um]-[14 um]) color-color plots shows only four sources with excess emission at near-IR wavelengths, but atleast 85% of all sources show excess emission at mid-IR wavelengths. The CVF spectra suggest a range of evolutionary status in the program stars ranging from embedded YSOs to the young disks. When combined with optical and near-IR age estimates, these results show active current star-formation in the region that has been on-going for at least 2 Myr.Comment: Submitted to ApJ. Abstracted edited for arXiv submission Replaced by version accepted by Ap

High-spatial-resolution observations of NH3 and CH3OH towards the massive twin cores NGC6334 I & I(N)

Molecular line observations of NH3 (J,K)=(1,1), (2,2) and CH3OH at 24.93GHz taken with the Australian Telescope Compact Array (ATCA) toward the massive twin cores NGC6334 I & I(N) reveal significant variations in the line emission between the two massive cores. The UCHII region/hot core NGC6334 I exhibits strong thermal NH3 and CH3OH emission adjacent to the UCHII region and coincident with two mm continuum peaks observed by Hunter et al. (in prep.). In contrast, we find neither compact NH3 nor thermal CH3OH line emission toward NGC6334 I(N). There, the NH3 emission is distributed over a broad region (>1') without a clear peak, and we find Class I CH3OH maser emission with peak brightness temperatures up to 7000K. The maser emission peaks appear to be spatially associated with the interfaces between the molecular outflows and the ambient dense gas. Peak NH3(1,1) line brightness temperatures >= 70K in both regions indicate gas temperatures of the same order. NH3 emission is also detected toward the outflow in NGC6334 I resulting in an estimated rotational temperature of Trot~19K. Furthermore, we observe CH3OH and NH3 absorption toward the UCHII region, the velocity structure is consistent with expanding molecular gas around the UCHII region. Thermal and kinematic effects possibly imposed from the UCHII region on the molecular core are also discussed.Comment: Accepted for the Astrophysical Journa

The true nature of the alleged planetary nebula W16-185

We report the discovery of a small cluster of massive stars embedded in a NIR nebula in the direction of the IRAS15411-5352 point source, which is related to the alleged planetary nebula W16-185. The majority of the stars present large NIR excess characteristic of young stellar objects and have bright counterparts in the Spitzer IRAC images; the most luminous star (IRS1) is the NIR counterpart of the IRAS source. We found very strong unresolved Brgamma emission at the IRS1 position and more diluted and extended emission across the continuum nebula. From the sizes and electron volume densities we concluded that they represent ultra-compact and compact HII regions, respectively. Comparing the Brgamma emission with the 7 mm free-free emission, we estimated that the visual extinction ranges between 14 and 20 mag. We found that only one star (IRS1) can provide the number of UV photons necessary to ionize the nebula.Comment: 30 pages, 15 figures, 2 tables V3: minor grammatical changes. Figure 4 is available in pdf file. Accepted for publication in AJ, April / 200

Quiescent H2 Emission From Pre-Main Sequence Stars in Chamaeleon I

We report the discovery of quiescent emission from molecular hydrogen gas located in the circumstellar disks of six pre-main sequence stars, including two weak-line T Tauri stars (TTS), and one Herbig AeBe star, in the Chamaeleon I star forming region. For two of these stars, we also place upper limits on the 2->1 S(1)/1->0 S(1) line ratios of 0.4 and 0.5. Of the 11 pre-main sequence sources now known to be sources of quiescent near-infrared hydrogen emission, four possess transitional disks, which suggests that detectable levels of H$_2$ emission and the presence of inner disk holes are correlated. These H$_2$ detections demonstrate that these inner holes are not completely devoid of gas, in agreement with the presence of observable accretion signatures for all four of these stars and the recent detections of [Ne II] emission from three of them. The overlap in [Ne II] and H$_2$ detections hints at a possible correlation between these two features and suggests a shared excitation mechanism of high energy photons. Our models, combined with the kinematic information from the H$_2$ lines, locate the bulk of the emitting gas at a few tens of AU from the stars. We also find a correlation between H$_2$ detections and those targets which possess the largest H$\alpha$ equivalent widths, suggesting a link between accretion activity and quiescent H$_2$ emission. We conclude that quiescent H$_2$ emission from relatively hot gas within the disks of TTS is most likely related to on-going accretion activity, the production of UV photons and/or X-rays, and the evolutionary status of the dust grain populations in the inner disks.Comment: 12 pages, emulateapj, Accepted by Ap

A multi-wavelength census of star formation activity in the young embedded cluster around Serpens/G3-G6

Aims. The aim of this paper is to characterise the star formation activity in the poorly studied embedded cluster Serpens/G3-G6, located ~ 45' (3 pc) to the south of the Serpens Cloud Core, and to determine the luminosity and mass functions of its population of Young Stellar Objects (YSOs). Methods. Multi-wavelength broadband photometry was obtained to sample the near and mid-IR spectral energy distributions to separate YSOs from field stars and classify the YSO evolutionary stage. ISOCAM mapping in the two filters LW2 (5-8.5 um) and LW3 (12-18 um) of a 19' x 16' field was combined with JHKs data from 2MASS, Ks data from Arnica/NOT, and L' data from SIRCA/NOT. Continuum emission at 1.3 mm (IRAM) and 3.6 cm (VLA) was mapped to study the cloud structure and the coldest/youngest sources. Deep narrow band imaging at the 2.12 um S(1) line of H2 from NOTCam/NOT was obtained to search for signs of bipolar outflows. Results. We have strong evidence for a stellar population of 31 Class II sources, 5 flat-spectrum sources, 5 Class I sources, and two Class 0 sources. Our method does not sample the Class III sources. The cloud is composed of two main dense clumps aligned along a ridge over ~ 0.5 pc plus a starless core coinciding with absorption features seen in the ISOCAM maps. We find two S-shaped bipolar collimated flows embedded in the NE clump, and propose the two driving sources to be a Class 0 candidate (MMS3) and a double Class I (MMS2). For the Class II population we find a best age of ~ 2 Myr and compatibility with recent Initial Mass Functions (IMFs) by comparing the observed Class II luminosity function (LF), which is complete to 0.08 L_sun, to various model LFs with different star formation scenarios and input IMFs.Comment: 18 pages, 16 figures, 3 online tables, accepted by A&