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It is known from the work of Koch that the two-dimensional incompressible Euler equations propagate Dini modulus of continuity for the vorticity. In this work, we consider the two-dimensional Euler equations with a modulus of continuity for vorticity rougher than Dini continuous. We first show that the two-dimensional Euler equations propagate an explicit family of moduli of continuity for the vorticity that are rougher than Dini continuity. The main goal of this work is to address the following question: Given a modulus of continuity for the 2D Euler equations, can we always propagate it? The answer to this question is \textit{No}. We construct a family of moduli of continuity for the 2D Euler equations that are \textit{not} propagated.

We explore the potential of the Gaussian Mixture Model (GMM), an unsupervised machine learning method, to identify coherent physical structures in the ISM. The implementation we present can be used on any kind of spatially and spectrally resolved data set. We provide a step-by-step guide to use these models on different sources and data sets. Following the guide, we run the models on NGC 1977, RCW 120 and RCW 49 using the [CII] 158 $\mu$m mapping observations from the SOFIA telescope. We find that the models identified 6, 4 and 5 velocity coherent physical structures in NGC 1977, RCW 120 and RCW 49, respectively, which are validated by analysing the observed spectra towards these structures and by comparison to earlier findings. In this work we demonstrate that GMM is a powerful tool that can better automate the process of spatial and spectral analysis to interpret mapping observations., Comment: 19 pages, 14 figures

We quantified the effects of stellar feedback in RCW 49 by determining the physical conditions in different regions using the [CII] 158 $\mu$m and [OI] 63 $\mu$m observations from SOFIA, the $^{12}$CO (3-2) observations from APEX and the H$_2$ line observations from Spitzer telescopes. Large maps of RCW 49 were observed with the SOFIA and APEX telescopes, while the Spitzer observations were only available towards three small areas. From our qualitative analysis, we found that the H$_2$ 0-0 S(2) emission line probes denser gas compared to the H$_2$ 0-0 S(1) line. In four regions ("northern cloud", "pillar", "ridge", and "shell"), we compared our observations with the updated PDR Toolbox models and derived the integrated far-ultraviolet flux between 6-13.6 eV ($G_{\rm 0}$), H nucleus density ($n$), temperatures and pressures. We found the ridge to have the highest $G_{\rm 0}$ (2.4 $\times$ 10$^3$ Habing units), while the northern cloud has the lowest $G_{\rm 0}$ (5 $\times$ 10$^2$ Habing units). This is a direct consequence of the location of these regions with respect to the Wd2 cluster. The ridge also has a high density (6.4 $\times$ 10$^3$ cm$^{-3}$), which is consistent with its ongoing star formation. Among the Spitzer positions, we found the one closest to the Wd2 cluster to be the densest, suggesting an early phase of star formation. Furthermore, the Spitzer position that overlaps with the shell was found to have the highest $G_{\rm 0}$ and we expect this to be a result of its proximity to an O9V star., Comment: 18 pages, 12 figures

We present [CII] 158 $\mu$m and [OI] 63 $\mu$m observations of the bipolar HII region RCW 36 in the Vela C molecular cloud, obtained within the SOFIA legacy project FEEDBACK, which is complemented with APEX $^{12/13}$CO(3-2) and Chandra X-ray (0.5-7 keV) data. This shows that the molecular ring, forming the waist of the bipolar nebula, expands with a velocity of 1 - 1.9 km s$^{-1}$. We also observe an increased linewidth in the ring indicating that turbulence is driven by energy injection from the stellar feedback. The bipolar cavity hosts blue-shifted expanding [CII] shells at 5.2$\pm$0.5$\pm$0.5 km s$^{-1}$ (statistical and systematic uncertainty) which indicates that expansion out of the dense gas happens non-uniformly and that the observed bipolar phase might be relatively short ($\sim$0.2 Myr). The X-ray observations show diffuse emission that traces a hot plasma, created by stellar winds, in and around RCW 36. At least 50 \% of the stellar wind energy is missing in RCW 36. This is likely due to leakage which is clearing even larger cavities around the bipolar RCW 36 region. Lastly, the cavities host high-velocity wings in [CII] which indicates relatively high mass ejection rates ($\sim$5$\times$10$^{-4}$ M$_{\odot}$ yr$^{-1}$). This could be driven by stellar winds and/or radiation pressure, but remains difficult to constrain. This local mass ejection, which can remove all mass within 1 pc of RCW 36 in 1-2 Myr, and the large-scale clearing of ambient gas in the Vela C cloud indicates that stellar feedback plays a significant role in suppressing the star formation efficiency (SFE)., Comment: 38 pages, 27 figures, 8 tables, accepted in ApJ

We prove strong ill-posedness in $L^{\infty}$ for linear perturbations of the 2d Euler equations of the form: \[\partial_t \omega + u\cdot\nabla\omega = R(\omega),\] where $R$ is any non-trivial second order Riesz transform. Namely, we prove that there exist smooth solutions that are initially small in $L^{\infty}$ but become arbitrarily large in short time. Previous works in this direction relied on the strong ill-posedness of the linear problem, viewing the transport term perturbatively, which only led to mild growth. In this work we derive a nonlinear model taking all of the leading order effects into account to determine the precise pointwise growth of solutions for short time. Interestingly, the Euler transport term does counteract the linear growth so that the full nonlinear equation grows an order of magnitude less than the linear one. In particular, the (sharp) growth rate we establish is consistent with the global regularity of smooth solutions., Comment: 24 pages

Ionized gas probes the influence of massive stars on their environment. The Cygnus X region (d~1.5 kpc) is one of the most massive star forming complexes in our Galaxy, in which the Cyg OB2 association (age of 3-5 Myr and stellar mass $2 \times 10^{4}$ M$_{\odot}$) has a dominant influence. We observe the Cygnus X region at 148 MHz using the Low Frequency Array (LOFAR) and take into account short-spacing information during image deconvolution. Together with data from the Canadian Galactic Plane Survey, we investigate the morphology, distribution, and physical conditions of low-density ionized gas in a $4^{\circ} \times 4^{\circ}$ (100 pc $\times$ 100 pc) region at a resolution of 2' (0.9 pc). The Galactic radio emission in the region analyzed is almost entirely thermal (free-free) at 148 MHz, with emission measures of $10^3 < EM~{\rm[pc~cm^{-6}]} < 10^6$. As filamentary structure is a prominent feature of the emission, we use DisPerSE and FilChap to identify filamentary ridges and characterize their radial ($EM$) profiles. The distribution of radial profiles has a characteristic width of 4.3 pc and a power-law distribution ($\beta = -1.8 \pm 0.1$) in peak $EM$ down to our completeness limit of 4200 pc cm$^{-6}$. The electron densities of the filamentary structure range from $10 < n_e~{\rm[cm^{-3}]} < 400$ with a median value of 35 cm$^{-3}$, remarkably similar to [N II] surveys of ionized gas. Cyg OB2 may ionize at most two-thirds of the total ionized gas and the ionized gas in filaments. More than half of the filamentary structures are likely photoevaporating surfaces flowing into a surrounding diffuse (~5 cm$^{-3}$) medium. However, this is likely not the case for all ionized gas ridges. A characteristic width in the distribution of ionized gas points to the stellar winds of Cyg OB2 creating a fraction of the ionized filaments through swept-up ionized gas or dissipated turbulence., Comment: 19 pages, 14 figures, 1 table; accepted for publication in A&A

Data is fundamental to machine learning-based products and services and is considered strategic due to its externalities for businesses, governments, non-profits, and more generally for society. It is renowned that the value of organizations (businesses, government agencies and programs, and even industries) scales with the volume of available data. What is often less appreciated is that the data value in making useful organizational predictions will range widely and is prominently a function of data characteristics and underlying algorithms. In this research, our goal is to study how the value of data changes over time and how this change varies across contexts and business areas (e.g. next word prediction in the context of history, sports, politics). We focus on data from Reddit.com and compare the value's time-dependency across various Reddit topics (Subreddits). We make this comparison by measuring the rate at which user-generated text data loses its relevance to the algorithmic prediction of conversations. We show that different subreddits have different rates of relevance decline over time. Relating the text topics to various business areas of interest, we argue that competing in a business area in which data value decays rapidly alters strategies to acquire competitive advantage. When data value decays rapidly, access to a continuous flow of data will be more valuable than access to a fixed stock of data. In this kind of setting, improving user engagement and increasing user-base help creating and maintaining a competitive advantage., Comment: 24 Pages

Extensive research has documented the immediate impacts of the COVID-19 pandemic on scientists, yet it remains unclear if and how such impacts have shifted over time. Here we compare results from two surveys of principal investigators, conducted between April 2020 and January 2021, along with analyses of large-scale publication data. We find that there has been a clear sign of recovery in some regards, as scientists' time spent on their work has almost returned to pre-pandemic levels. However, the latest data also reveals a new dimension in which the pandemic is affecting the scientific workforce: the rate of initiating new research projects. Except for the small fraction of scientists who directly engaged in COVID-related research, most scientists started significantly fewer new research projects in 2020. This decline is most pronounced amongst the same demographic groups of scientists who reported the largest initial disruptions: female scientists and those with young children. Yet in sharp contrast to the earlier phase of the pandemic, when there were large disparities across scientific fields, this loss of new projects appears remarkably homogeneous across fields. Analyses of large-scale publication data reveal a global decline in the rate of new collaborations, especially in non-COVID-related preprints, which is consistent with the reported decline in new projects. Overall, these findings highlight that, while the end of the pandemic may appear in sight in some countries, its large and unequal impact on the scientific workforce may be enduring, which may have broad implications for inequality and the long-term vitality of science., Comment: 14 pages, 2 figures, with supplementary information

We unveil the stellar wind driven shell of the luminous massive star-forming region of RCW 49 using SOFIA FEEDBACK observations of the [CII] 158 $\mu$m line. The complementary dataset of the $^{12}$CO and $^{13}$CO J = 3 - 2 transitions is observed by the APEX telescope and probes the dense gas toward RCW 49. Using the spatial and spectral resolution provided by the SOFIA and APEX telescopes, we disentangle the shell from a complex set of individual components of gas centered around RCW 49. We find that the shell of radius ~ 6 pc is expanding at a velocity of 13 km s$^{-1}$ toward the observer. Comparing our observed data with the ancillary data at X-Ray, infrared, sub-millimeter and radio wavelengths, we investigate the morphology of the region. The shell has a well defined eastern arc, while the western side is blown open and is venting plasma further into the west. Though the stellar cluster, which is ~ 2 Myr old gave rise to the shell, it only gained momentum relatively recently as we calculate the shell's expansion lifetime ~ 0.27 Myr, making the Wolf-Rayet star WR20a a likely candidate responsible for the shell's re-acceleration., Comment: 31 pages, 17 figures

FEEDBACK is a SOFIA legacy program dedicated to study the interaction of massive stars with their environment. It performs a survey of 11 galactic high mass star forming regions in the 158 $\mu$m (1.9 THz) line of CII and the 63 $\mu$m (4.7 THz) line of OI. We employ the 14 pixel LFA and 7 pixel HFA upGREAT instrument to spectrally resolve (0.24 MHz) these FIR structure lines. With an observing time of 96h, we will cover $\sim$6700 arcmin$^2$ at 14.1$''$ angular resolution for the CII line and 6.3$''$ for the OI line. The observations started in spring 2019 (Cycle 7). Our aim is to understand the dynamics in regions dominated by different feedback processes from massive stars such as stellar winds, thermal expansion, and radiation pressure, and to quantify the mechanical energy injection and radiative heating efficiency. The CII line provides the kinematics of the gas and is one of the dominant cooling lines of gas for low to moderate densities and UV fields. The OI line traces warm and high-density gas, excited in photodissociations regions with a strong UV field or by shocks. The source sample spans a broad range in stellar characteristics from single OB stars, to small groups of O stars, to rich young stellar clusters, to ministarburst complexes. It contains well-known targets such as Aquila, the Cygnus X region, M16, M17, NGC7538, NGC6334, Vela, and W43 as well as a selection of HII region bubbles, namely RCW49, RCW79, and RCW120. These CII maps, together with the less explored OI 63 $\mu$m line, provide an outstanding database for the community. They will be made publically available and will trigger further studies and follow-up observations.

The COVID-19 pandemic has undoubtedly disrupted the scientific enterprise, but we lack empirical evidence on the nature and magnitude of these disruptions. Here we report the results of a survey of approximately 4,500 Principal Investigators (PIs) at U.S.- and Europe-based research institutions. Distributed in mid-April 2020, the survey solicited information about how scientists' work changed from the onset of the pandemic, how their research output might be affected in the near future, and a wide range of individuals' characteristics. Scientists report a sharp decline in time spent on research on average, but there is substantial heterogeneity with a significant share reporting no change or even increases. Some of this heterogeneity is due to field-specific differences, with laboratory-based fields being the most negatively affected, and some is due to gender, with female scientists reporting larger declines. However, among the individuals' characteristics examined, the largest disruptions are connected to a usually unobserved dimension: childcare. Reporting a young dependent is associated with declines similar in magnitude to those reported by the laboratory-based fields and can account for a significant fraction of gender differences. Amidst scarce evidence about the role of parenting in scientists' work, these results highlight the fundamental and heterogeneous ways this pandemic is affecting the scientific workforce, and may have broad relevance for shaping responses to the pandemic's effect on science and beyond.

Researchers cite works for a variety of reasons, including some having nothing to do with acknowledging influence. The distribution of different citation types in the literature, and which papers attract which types, is poorly understood. We investigate high-influence and low-influence citations and the mechanisms producing them using 17,154 ground-truth citation types provided via survey by 9,380 authors systematically sampled across academic fields. Overall, 54% of citations denote little-to-no influence and these citations are concentrated among low status (lightly cited) papers. In contrast, high-influence citations are concentrated among high status (highly cited) papers through a number of steps that resemble a pipeline. Authors discover highly cited papers earlier in their projects, more often through social contacts, and read them more closely. Papers' status, above and beyond any quality differences, directly helps determine their pipeline: experimentally revealing or hiding citation counts during the survey shows that low counts cause lowered perceptions of quality. Accounting for citation types thus reveals a "double status effect": in addition to affecting how often a work is cited, status affects how meaningfully it is cited. Consequently, highly cited papers are even more influential than their raw citation counts suggest., Comment: Heavily revised narrative in this version including new title, figures, abstract, and narrative structure. Central empirical findings unchanged

We report the findings of a month-long online competition in which participants developed algorithms for augmenting the digital version of patent documents published by the United States Patent and Trademark Office (USPTO). The goal was to detect figures and part labels in U.S. patent drawing pages. The challenge drew 232 teams of two, of which 70 teams (30%) submitted solutions. Collectively, teams submitted 1,797 solutions that were compiled on the competition servers. Participants reported spending an average of 63 hours developing their solutions, resulting in a total of 5,591 hours of development time. A manually labeled dataset of 306 patents was used for training, online system tests, and evaluation. The design and performance of the top-5 systems are presented, along with a system developed after the competition which illustrates that winning teams produced near state-of-the-art results under strict time and computation constraints. For the 1st place system, the harmonic mean of recall and precision (f-measure) was 88.57% for figure region detection, 78.81% for figure regions with correctly recognized figure titles, and 70.98% for part label detection and character recognition. Data and software from the competition are available through the online UCI Machine Learning repository to inspire follow-on work by the image processing community.