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Attendance rate is an important indicator of students' study motivation, behavior and Psychological status; However, the heterogeneous nature of student attendance rates due to the course registration difference or the online/offline difference in a blended learning environment makes it challenging to compare attendance rates. In this paper, we propose a novel method called Relative Attendance Index (RAI) to measure attendance rates, which reflects students' efforts on attending courses. While traditional attendance focuses on the record of a single person or course, relative attendance emphasizes peer attendance information of relevant individuals or courses, making the comparisons of attendance more justified. Experimental results on real-life data show that RAI can indeed better reflect student engagement.

We have obtained sensitive dust continuum polarization observations at 850 $\mu$m in the B213 region of Taurus using POL-2 on SCUBA-2 at the James Clerk Maxwell Telescope (JCMT), as part of the BISTRO (B-fields in STar-forming Region Observations) survey. These observations allow us to probe magnetic field (B-field) at high spatial resolution ($\sim$2000 au or $\sim$0.01 pc at 140 pc) in two protostellar cores (K04166 and K04169) and one prestellar core (Miz-8b) that lie within the B213 filament. Using the Davis-Chandrasekhar-Fermi method, we estimate the B-field strengths in K04166, K04169, and Miz-8b to be 38$\pm$14 $\mu$G, 44$\pm$16 $\mu$G, and 12$\pm$5 $\mu$G, respectively. These cores show distinct mean B-field orientations. B-field in K04166 is well ordered and aligned parallel to the orientations of the core minor axis, outflows, core rotation axis, and large-scale uniform B-field, in accordance with magnetically regulated star formation via ambipolar diffusion taking place in K04166. B-field in K04169 is found to be ordered but oriented nearly perpendicular to the core minor axis and large-scale B-field, and not well-correlated with other axes. In contrast, Miz-8b exhibits disordered B-field which show no preferred alignment with the core minor axis or large-scale field. We found that only one core, K04166, retains a memory of the large-scale uniform B-field. The other two cores, K04169 and Miz-8b, are decoupled from the large-scale field. Such a complex B-field configuration could be caused by gas inflow onto the filament, even in the presence of a substantial magnetic flux., Comment: 20 pages (10 are main), 5 figures (3 are main), and 3 tables (2 are main); Accepted for its publication in ApJL

Prestellar cores are self-gravitating dense and cold structures within molecular clouds where future stars are born. They are expected, at the stage of transitioning to the protostellar phase, to harbor centrally concentrated dense (sub)structures that will seed the formation of a new star or the binary/multiple stellar systems. Characterizing this critical stage of evolution is key to our understanding of star formation. In this work, we report the detection of high density (sub)structures on the thousand-au scale in a sample of dense prestellar cores. Through our recent ALMA observations towards the Orion molecular cloud, we have found five extremely dense prestellar cores, which have centrally concentrated regions $\sim$ 2000 au in size, and several $10^7$ $cm^{-3}$ in average density. Masses of these centrally dense regions are in the range of 0.30 to 6.89 M$_\odot$. {\it For the first time}, our higher resolution observations (0.8$'' \sim $ 320 au) further reveal that one of the cores shows clear signatures of fragmentation; such individual substructures/fragments have sizes of 800 -1700 au, masses of 0.08 to 0.84 M$_\odot$, densities of $2 - 8\times 10^7$ $cm^{-3}$ and separations of $\sim 1200$ au. The substructures are massive enough ($\gtrsim 0.1~M_\odot$) to form young stellar objects and are likely examples of the earliest stage of stellar embryos which can lead to widely ($\sim$ 1200 au) separated multiple systems., Comment: Published in The Astrophysical Journal Letters (ApJL)

We report the first high spatial resolution measurement of magnetic fields surrounding LkH$\alpha$ 101, a part of the Auriga-California molecular cloud. The observations were taken with the POL-2 polarimeter on the James Clerk Maxwell Telescope within the framework of the B-fields In Star-forming Region Observations (BISTRO) survey. Observed polarization of thermal dust emission at 850 $\mu$m is found to be mostly associated with the red-shifted gas component of the cloud. The magnetic field displays a relatively complex morphology. Two variants of the Davis-Chandrasekhar-Fermi method, unsharp masking and structure function, are used to calculate the strength of magnetic fields in the plane of the sky, yielding a similar result of $B_{\rm POS}\sim 115$ $\mathrm{\mu}$G. The mass-to-magnetic-flux ratio in critical value units, $\lambda\sim0.3$, is the smallest among the values obtained for other regions surveyed by POL-2. This implies that the LkH$\alpha$ 101 region is sub-critical and the magnetic field is strong enough to prevent gravitational collapse. The inferred $\delta B/B_0\sim 0.3$ implies that the large scale component of the magnetic field dominates the turbulent one. The variation of the polarization fraction with total emission intensity can be fitted by a power-law with an index of $\alpha=0.82\pm0.03$, which lies in the range previously reported for molecular clouds. We find that the polarization fraction decreases rapidly with proximity to the only early B star (LkH$\alpha$ 101) in the region. The magnetic field tangling and the joint effect of grain alignment and rotational disruption by radiative torques are potential of explaining such a decreasing trend., Comment: 25 pages, 19 figures, Accepted for publication in The Astrophysical Journal

Aims. We investigate the role of selective dissociation in the process of star formation by comparing the physical parameters of protostellar-prestellar cores and the distinct regions with the CO isotope distributions in photodissociation regions. We seek to understand whether there is a better connection between the evolutionary age of star forming regions and the effect of selective dissociation Methods. Wide-field observations of the $\rm ^{12}CO$, $\rm ^{13}CO$, and $\rm C^{18}O$ ( J = 1 - 0) emission lines are used to study the ongoing star formation activity in the Aquila molecular region, and the 70 $\mu$m and 250 $\mu$m data are used to describe the heating of the surrounding material and as an indicator of the evolutionary age of the core. Results. The protostellar-prestellar cores are found at locations with the highest $\rm C^{18}O$ column densities and their increasing evolutionary age would relate to an increasing 70$\mu$m/250$\mu$m emission ratio at their location. An evolutionary age of the cores may also follow from the $\rm ^{13}CO$ versus $\rm C^{18}O$ abundance ratio, which decreases with increasing $\rm C^{18}O$ column densities. The original mass has been estimated for nine representative star formation regions and the original mass of the region correlated well with the integrated 70 $\mu$m flux density. Similarly, the $ X_{\rm ^{13}CO}$/$X_{\rm C^{18}O}$ implying the dissociation rate for these regions correlates with the 70$\mu$m/250$\mu$m flux density ratio and reflects the evolutionary age of the star formation activity., Comment: 10 pages

We surveyed the Aquila Rift complex including the Serpens South and W40 region in the NH$_3$(1,1) and (2,2) transitions making use of the Nanshan 26-m telescope. The kinetic temperatures of the dense gas in the Aquila Rift complex range from 8.9 to 35.0K with an average of 15.3$\pm$6.1K. Low gas temperatures associate with Serpens South ranging from 8.9 to 16.8K with an average 12.3$\pm$1.7K, while dense gas in the W40 region shows higher temperatures ranging from 17.7 to 35.0K with an average of 25.1$\pm$4.9 K. A comparison of kinetic temperatures against HiGal dust temperatures indicates that the gas and dust temperatures are in agreement in the low mass star formation region of Serpens South. In the high mass star formation region W40, the measured gas kinetic temperatures are higher than those of the dust. The turbulent component of the velocity dispersion of NH$_3$(1,1) is found to be positively correlated with the gas kinetic temperature, which indicates that the dense gas may be heated by dissipation of turbulent energy. For the fractional total-NH3 abundance obtained by a comparison with Herschel infrared continuum data representing dust emission we find values from 0.1 to 21$\times 10^{-8}$ with an average of 6.9$(\pm 4.5)\times 10^{-8}$. Serpens South also shows a fractional total-NH3 abundance ranging from 0.2 to 21$\times 10^{-8}$ with an average of 8.6($\pm 3.8)\times 10^{-8}$. In W40, values are lower, between 0.1 and 4.3$\times 10^{-8}$ with an average of 1.6($\pm 1.4)\times 10^{-8}$. Weak velocity gradients demonstrate that the rotational energy is a negligible fraction of the gravitational energy. In W40, gas and dust temperatures are not strongly dependent on the projected distance to the recently formed massive stars. Overall, the morphology of the mapped region is ring-like, with strong emission at lower and weak emission at higher Galactic longitudes.

In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic evolution equations in Hilbert spaces. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property., Comment: 50 pages. arXiv admin note: substantial text overlap with arXiv:2005.05309, arXiv:2007.04079; text overlap with arXiv:2004.02095

We mapped the kinetic temperature structure of Orion KL in a $\sim$20$''$ ($\sim$8000 AU) sized region with para-H$_{2}$CS $7_{07}-6_{06}$, $7_{26}-6_{25}$, and $7_{25}-6_{24}$ making use of ALMA Band 6 Science Verification data. The kinetic temperatures obtained with a resolution of $1\hbox{$\,.\!\!^{\prime\prime}$}65$$\times$$1\hbox{$\,.\!\!^{\prime\prime}$}14$ ($\sim$550 AU) are deduced by modeling the measured averaged velocity-integrated intensity ratios of para-H$_2$CS $7_{26}-6_{25}/7_{07}-6_{06}$ and $7_{25}-6_{24}/7_{07}-6_{06}$ with a RADEX non-LTE model. The kinetic temperatures of the dense gas, derived from the para-H$_2$CS line ratios at a spatial density of 10$^7$ cm$^{-3}$, are high, ranging from 43 to $>$500 K with an unweighted average of $\sim$170 K. There is no evidence for internal sources playing an important role in the heating of the various structures identified in previous work, namely the elongated ridge, the northwestern clump, and the eastern region of the compact ridge, while the high temperatures in the western region of the compact ridge may be dominated by internal massive star formation. Significant gradients of kinetic temperature along molecular filaments traced by H$_2$CS indicate that the dense gas is heated by the shocks induced by the enigmatic explosive event, which occurred several hundred years ago greatly affecting the energetics of the Orion KL region. Thus, with the notable exception of the western region of the compact ridge, the high temperatures of the dense gas in Orion KL are probably caused by shocks from the explosive event, leading to a dominant component of externally heated dense gas., Comment: Accepted for publication to ApJ

In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent evolution equations in Hilbert space. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property., Comment: 25 pages. arXiv admin note: substantial text overlap with arXiv:2005.05309, arXiv:2004.02095

We present new observations of the active star-formation region NGC 1333 in the Perseus molecular cloud complex from the James Clerk Maxwell Telescope B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. The BISTRO data cover the entire NGC 1333 complex (~1.5 pc x 2 pc) at 0.02 pc resolution and spatially resolve the polarized emission from individual filamentary structures for the first time. The inferred magnetic field structure is complex as a whole, with each individual filament aligned at different position angles relative to the local field orientation. We combine the BISTRO data with low- and high- resolution data derived from Planck and interferometers to study the multiscale magnetic field structure in this region. The magnetic field morphology drastically changes below a scale of ~1 pc and remains continuous from the scales of filaments (~0.1 pc) to that of protostellar envelopes (~0.005 pc or ~1000 au). Finally, we construct simple models in which we assume that the magnetic field is always perpendicular to the long axis of the filaments. We demonstrate that the observed variation of the relative orientation between the filament axes and the magnetic field angles are well reproduced by this model, taking into account the projection effects of the magnetic field and filaments relative to the plane of the sky. These projection effects may explain the apparent complexity of the magnetic field structure observed at the resolution of BISTRO data toward the filament network., Comment: 33 pages, 21 figures, accepted for publication in ApJ

In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property. Applications to backward stochastic Hamilton-Jacobi-Bellman equations are also given., Comment: 48 pages. arXiv admin note: text overlap with arXiv:2004.02095, arXiv:1611.05533

In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value functional of the optimal control problems as a unique viscosity solution to the associated HJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property., Comment: 25 pages

We selected 90 massive star-forming clumps with strong N2H+, HCO+, HCN, and HNC emission from the Millimetre Astronomy Legacy Team 90 GHz survey. We obtained Herschel data for all 90 sources and NRAO VLA Sky Survey data for 51 of them. We convolved and regridded all images to the same resolution and pixel size and derived the temperature, H2 column density, molecules' abundances and abundance, and ratios of each pixel. Our analysis yields three main conclusions. First, the abundances of N2H+, HCO+, HCN, and HNC increase when the column density decreases and the temperature increases, with spatial variations in their abundances dominated by changes in the H2 column density. Second, the abundance ratios between N2H+, HCO+, HCN, and HNC also display systemic variations as a function of the column density due to the chemical properties of these molecules. Third, the sources associated with the 20 cm continuum emission can be classified into four types based on the behavior of the abundances of the four molecules considered here as a function of this emission. The variations of the first three types could also be attributed to the variation of the H2 column density., Comment: 18 pictures, ApJS, Published

A total of 188 high-mass outflows have been identified from a sample of 694 clumps from the Millimetre Astronomy Legacy Team 90 GHz survey, representing a detection rate of approximately 27%. The detection rate of outflows increases from the protostellar stage to the H II stage, but decreases again at the photodissociation (PDR) stage suggesting that outflows are being switched off during the PDR stage. An intimate relationship is found between outflow action and the presence of masers, and water masers appear together with 6.7 GHz methanol masers. Comparing the infall detection rate of clumps with and without outflows, we find that outflow candidates have a lower infall detection rate. Finally, we find that outflow action has some influence on the local environment and the clump itself, and this influence decreases with increasing evolutionary time as the outflow action ceases., Comment: 10 pages, 11 figures, MNRAS, Accepted

A multi-wavelength analysis of the large Galactic infrared bubble N 24 is has been presented in this paper in order to investigate the molecular and star formation environment around expanding HII regions. Using archival data from Herschel and ATLASGAL, the distribution and physical properties of the dust over the entire bubble are studied. Twenty three dense clumps are identified using the Clumpfind2d algorithm with sizes and masses in the range 0.65-1.73 pc and 600-16300 Msun, respectively. To analyse the molecular environment in N 24, observations of NH3 (1,1) and (2,2) were carried out using the Nanshan 26m radio telescope. Analysis of the kinetic temperature and gravitational stability of these clumps suggests gravitational collapse in several of them. The mass-size distributions of the clumps and the presence of massive young protostars indicate that the shell of N 24 is a region of ongoing massive star formation. The compatibility of the dynamical and fragmentation time-scales and the overabundance of YSOs and clumps on the rim suggest that the collect and collapse mechanism is in play at the boundary of the bubble, but the existence of the IRDC at the edge of bubble indicates that radiation-driven implosion mechanism may also have played a role there., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society

We present the POL-2 850 $\mu$m linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations (BISTRO) survey at the James Clerk Maxwell Telescope. We find a trend of decreasing polarization fraction as a function of total intensity, which we link to depolarization effects towards higher density regions of the cloud. We then use the polarization data at 850 $\mu$m to infer the plane-of-sky orientation of the large-scale magnetic field in Barnard 1. This magnetic field runs North-South across most of the cloud, with the exception of B1-c where it turns more East-West. From the dispersion of polarization angles, we calculate a turbulence correlation length of $5.0 \pm 2.5$ arcsec ($1500$ au), and a turbulent-to-total magnetic energy ratio of $0.5 \pm 0.3$ inside the cloud. We combine this turbulent-to-total magnetic energy ratio with observations of NH$_3$ molecular lines from the Green Bank Ammonia Survey (GAS) to estimate the strength of the plane-of-sky component of the magnetic field through the Davis-Chandrasekhar-Fermi method. With a plane-of-sky amplitude of $120 \pm 60$ $\mu$G and a criticality criterion $\lambda_c = 3.0 \pm 1.5$, we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component., Comment: 22 pages, 7 figures, accepted in the Astrophysical Journal

The formaldehyde $\rm H_2CO(1_{10} - 1_{11})$ absorption line and H$110\alpha$ radio recombination line (RRL) have been observed toward the Aquila Molecular Cloud using the Nanshan 25 m telescope operated by the Xinjiang Astronomical Observatory CAS. These first observations of the $\rm H_2CO$ $(1_{10} - 1_{11})$ absorption line determine the extent of the molecular regions that are affected by the ongoing star formation in the Aquila molecular complex and show some of the dynamic properties. The distribution of the excitation temperature $T_{ex}$ for $\rm H_2CO$ identifies the two known star formation regions W40 and Serpens South as well as a smaller new region Serpens 3. The intensity and velocity distributions of $\rm H_2CO$ and $\rm ^{13}CO(1-0)$ do not agree well with each other, which confirms that the $\rm H_2CO$ absorption structure is mostly determined by the excitation of the molecules resulting from the star formation rather than by the availability of molecular material as represented by the distribution. Some velocity-coherent linear $\rm ^{13}CO(1-0)$ structures have been identified in velocity channel maps of $\rm H_2CO$ and it is found that the three star formation regions lie on the intersect points of filaments. The $\rm H110\alpha$ emission is found only at the location of the W40 H II region and spectral profile indicates a redshifted spherical outflow structure in the outskirts of the H II region. Sensitive mapping of $\rm H_2CO$ absorption of the Aquila Complex has correctly identified the locations of star-formation activity in complex molecular clouds and the spectral profiles reveal the dominant velocity components and may identify the presence of outflows., Comment: Accepted by ApJ

We report 850~$\mu$m dust polarization observations of a low-mass ($\sim$12 $M_{\odot}$) starless core in the $\rho$ Ophiuchus cloud, Ophiuchus C, made with the POL-2 instrument on the James Clerk Maxwell Telescope (JCMT) as part of the JCMT B-fields In STar-forming Region Observations (BISTRO) survey. We detect an ordered magnetic field projected on the plane of sky in the starless core. The magnetic field across the $\sim$0.1~pc core shows a predominant northeast-southwest orientation centering between $\sim$40$^\circ$ to $\sim$100$^\circ$, indicating that the field in the core is well aligned with the magnetic field in lower-density regions of the cloud probed by near-infrared observations and also the cloud-scale magnetic field traced by Planck observations. The polarization percentage ($P$) decreases with an increasing total intensity ($I$) with a power-law index of $-$1.03 $\pm$ 0.05. We estimate the plane-of-sky field strength ($B_{\mathrm{pos}}$) using modified Davis-Chandrasekhar-Fermi (DCF) methods based on structure function (SF), auto-correlation (ACF), and unsharp masking (UM) analyses. We find that the estimates from the SF, ACF, and UM methods yield strengths of 103 $\pm$ 46 $\mu$G, 136 $\pm$ 69 $\mu$G, and 213 $\pm$ 115 $\mu$G, respectively. Our calculations suggest that the Ophiuchus C core is near magnetically critical or slightly magnetically supercritical (i.e. unstable to collapse). The total magnetic energy calculated from the SF method is comparable to the turbulent energy in Ophiuchus C, while the ACF method and the UM method only set upper limits for the total magnetic energy because of large uncertainties., Comment: 22 pages, 12 figures

We present the 850 $\mu$m polarization observations toward the IC5146 filamentary cloud taken using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) and its associated polarimeter (POL-2), mounted on the James Clerk Maxwell Telescope (JCMT), as part of the B-fields In STar forming Regions Observations (BISTRO). This work is aimed at revealing the magnetic field morphology within a core-scale ($\lesssim 1.0$ pc) hub-filament structure (HFS) located at the end of a parsec-scale filament. To investigate whether or not the observed polarization traces the magnetic field in the HFS, we analyze the dependence between the observed polarization fraction and total intensity using a Bayesian approach with the polarization fraction described by the Rice likelihood function, which can correctly describe the probability density function (PDF) of the observed polarization fraction for low signal-to-noise ratio (SNR) data. We find a power-law dependence between the polarization fraction and total intensity with an index of 0.56 in $A_V\sim$ 20--300 mag regions, suggesting that the dust grains in these dense regions can still be aligned with magnetic fields in the IC5146 regions. Our polarization maps reveal a curved magnetic field, possibly dragged by the contraction along the parsec-scale filament. We further obtain a magnetic field strength of 0.5$\pm$0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermi method, corresponding to a mass-to-flux criticality of $\sim$ $1.3\pm0.4$ and an Alfv\'{e}nic Mach number of $<$0.6. These results suggest that gravity and magnetic field is currently of comparable importance in the HFS, and turbulence is less important., Comment: 24 pages, 15 figures, accepted for publication in ApJ

An unbiased search of molecular outflows within the region of the COHRS survey has identified 157 high-mass outflows from a sample of 770 ATLASGAL clumps with a detection rate of 20\%. The detection rate of outflows increases for clumps with higher M$_{clump}$, L$_{bol}$, L$_{bol}$/M$_{clump}$, N$_{H_{2}}$, and T$_{dust}$ compared to the clumps with no outflow. The detection rates of the outflow increases from protostellar (8\%) to YSO clump (17\%) and to MSF clump (29\%). The detection rate 26\% for quiescent clump is preliminary, because the sample of quiescent clumps is small. A statistical relation between the outflow and clump masses for our sample is $\log(M_{out}/M_{\bigodot}) = (-1.1\pm0.21) + (0.9\pm0.07)\log(M_{clump}/M_{\bigodot})$. The detection rate of outflows and the outflow mass-loss rate show an increase with increasing M$_{clump}$, L$_{bol}$, N$_{H_{2}}$, and T$_{dust}$, which indicates that clumps with outflow with higher parameter values are at a more advanced evolutionary stage. The outflow mechanical force increases with increasing bolometric luminosities. No clear evidence has yet been found that higher mass outflows have different launching conditions than low-mass outflows., Comment: 16 pages, 20 figures, accepted for publication in ApJ