ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of [12] and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.
Magneto-optical studies of Weyl semimetals have been proposed as a versatile tool for observing low-energy Weyl fermions in candidate materials including the chiral Landau level. However, previous theoretical results have been restricted to the linearized regime around the Weyl node and are at odds with experimental findings. Here, we derive a closed form expression for the magneto-optical conductivity of generic Weyl semimetals in the presence of an external magnetic field aligned with the tilt of the spectrum. The systems are taken to have linear dispersion in two directions, while the tilting direction can consist of any arbitrary continuously differentiable function. This general calculation is then used to analytically evaluate the magneto-optical conductivity of Weyl semimetals expanded to cubic order in momentum. In particular, systems with arbitrary tilt, as well as systems hosting trivial Fermi pockets are investigated. The higher-order terms in momentum close the Fermi pockets in the type-II regime, removing the need for unphysical cutoffs when evaluating the magneto-optical conductivity. Crucially, the ability to take into account closed over-tilted and additional trivial Fermi pockets allows us to treat model systems closer to actual materials and we propose a simple explanation why the presence of parasitic trivial Fermi pockets can mask the characteristic signature of Weyl fermions in magneto-optical conductivity measurements.
The low energy properties of different one-dimensional fermionic lattice models are investigated using the bosonization technique. We attach much importance to a proper consideration of the Klein factors which are neglected or inaccurately treated in the majority of the literature. In order to deal with the nonlinear terms, arising from the dimerization or similar scattering processes, we use the self-consistent harmonic approximation (SCHA), a variational method where the nonlinearities are replaced by a quadratic potential. We construct an extension of the SCHA in order to account for the existence of Klein factors in bosonized Hamiltonians. As prototypical models we consider one-dimensional dimerized spinless fermions and Hubbard models with periodic modulation of the hopping and of the chemical potential, respectively.   In an attempt to describe more realistic systems we also consider a model where one-dimensional electrons are coupled to a three-dimensional conduction band via a local interaction. In order to see how the one-dimensional electron system is modified in the presence of the three-dimensional environment, we calculate the charge and the spin susceptibility, and analyze the collective excitations within RPA. We find that the spin excitations remain unaffected while in the charge channel, the collective modes of the one-dimensional and three-dimensional subsystems are coupled.
In this paper we give an algorithm for computing equations of Brauer-Severi varieties over perfect fields of characteristic 0. As an example we show the equations of all Brauer-Severi surfaces defined over $\mathbb{Q}$.
In the impulse approximation regime the nuclear response to a weakly interacting probe can be written in terms of the measured nucleon structure fuctions and the target spectral function, yielding the energy and momentum distribution of the constituent nucleons. We discuss a calculation of charged current neutrino-oxygen interactions in the quasielastic channel, carried out within nuclear many body theory. The proposed approach, extensively and successfully employed in the analysys of electron-nucleus scattering data, allows for a parameter free prediction of the neutrino-nucleus cross section, whose quantitative understanding will be critical to the analysis of the next genaration of high precision neutrino oscillation experiments.
In this paper, we investigate two hydrogen-poor superluminous supernovae (SLSNe) iPTF15esb and iPTF13dcc whose light curves (LCs) show significant deviation from the smooth rise and fall. The LC of iPTF15esb exhibits two peaks and a post-peak plateau, and furthermore the late-time spectrum of iPTF15esb shows a strong, broad H$\alpha$ emission line. The early-time LC of iPTF13dcc shows a long duration bump followed by the second peak. Here we propose an ejecta-circumstellar medium (CSM) interaction model involving multiple shells/winds and use it to explain the LCs of iPTF15esb and iPTF13dcc. We find that the theoretical LCs reproduced by this model can well match the observations of iPTF15esb and iPTF13dcc. Based on our results, we infer that the progenitors have undergone multiple violent mass-loss processes before the SN explosion. In addition, we find that the variation trend of our inferred densities of the shells is consistent with that predicted by the stellar mass-loss history before an SN explosion. Further investigations for other bumpy SLSNe/SNe would shed light on their nature and provide a probe for the mass-loss history of their progenitors.
In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.
Extremely metal-poor (XMP) galaxies are low-mass, star-forming galaxies with gas-phase oxygen abundances below 12+log(O/H) = 7.35 (~1/20 Zsun). Galaxy evolution scenarios suggest three pathways to form an XMP: (1) secular evolution at low galaxy masses, (2) slow evolution in voids, or (3) dilution of measured abundances from infall of pristine gas. The recently discovered XMP galaxy Leoncino, with an oxygen abundance below 3% Zsun, provides an opportunity to explore these different scenarios. Using Hubble Space Telescope imaging of the resolved stellar populations of Leoncino, we measure the distance to the galaxy to be D=12.1 (+1.7/-3.4) Mpc and find that Leoncino is located in an under-dense environment. Leoncino has a compact morphology, hosts a population of young, massive stars, has a high gas-to-star mass ratio, and shows signs of interaction with a galaxy nearby on the sky, UGC 5186. Similar to nearly all XMP galaxies known in the nearby universe, Leoncino is offset from the Luminosity-Metallicity (LZ) relation. Yet, Leoncino is consistent with the stellar Mass-Metallicity (MZ) relation defined by Local Volume galaxies. Thus, our results suggest that the offset from the LZ relation is due to higher recent star formation, likely triggered by a minor interaction, while the low oxygen abundance is consistent with the expectation that low-mass galaxies will undergo secular evolution marked by inefficient star formation and metal-loss via galactic winds. This is in contrast to XMP galaxies that are outliers in both the LZ and MZ relations; in such cases, the low oxygen abundances are best explained by dilution due to the infall of pristine gas. We also discuss why quiescent XMP galaxies are underrepresented in current surveys.
We have developed a numerical galactic chemical evolution model. The model is constructed such that the effect of a wide range of parameters can be investigated. It takes into account results from stellar evolution models, a differentiation between diverse types of core collapse SNe and the contribution of AGB stars in the mass range 3-8 Msun. We consider the lifetime-dependent yield injection into the ISM by all sources as well as dust destruction due to SN shocks in the ISM. We ascertain the temporal progression of the dust mass, the dust-to-gas and dust-to-metal mass ratios as well as other physical properties of a galaxy and study their dependence on the mass of the galaxy, the IMF, dust production efficiencies and dust destruction in the ISM. The amount of dust and the physical properties of a galaxy strongly depend on the initial gas mass available. Overall, while the total amount of dust produced increases with galaxy mass, the detailed outcome depends on the SN dust production efficiency, the IMF and the strength of dust destruction in the ISM. Dust masses are higher for IMFs biased towards higher stellar masses, despite the fact that these IMFs are more strongly affected by dust destruction in the ISM. The sensitivity to the IMF increases as the mass of the galaxy decreases. SNe are primarily responsible for a significant enrichment with dust at early epochs (< 200 Myr). Dust production with a dominant contribution by AGB stars is found to be insufficient to account for dust masses in excess of 10^8 Msun within 400 Myr after starburst. We find that galaxies with initial gas masses between 1-5 x 10^11 Msun are sufficiently massive to enable production of dust masses >10^8 Msun. Our preferred scenario is dominated by SN dust production in combination with top-heavy IMFs and moderate dust destruction in the ISM.
Galaxy-galaxy mergers and close interactions have long been regarded as a viable mechanism for channeling gas toward the central supermassive black holes (SMBHs) of galaxies which are triggered as active galactic nuclei (AGNs). AGN pairs, in which the central SMBHs of a galaxy merger are both active, are expected to be common from such events. We conduct a systematic study of 1286 AGN pairs at z ~ 0.1 with line-of-sight velocity offsets dv < 600 km/s and projected separations r_p < 100 kpc, selected from the Seventh Data Release of the Sloan Digital Sky Survey (SDSS). This AGN pair sample was drawn from 138,070 AGNs optically identified based on diagnostic emission line ratios and/or line widths. The fraction of AGN pairs with 5 kpc ~< r_p < 100 kpc among all spectroscopically selected AGNs at 0.02 < z < 0.16 is 3.6% after correcting for SDSS spectroscopic incompleteness; ~ 30% of these pairs show morphological tidal features in their SDSS images, and the fraction becomes >~ 80% for pairs with the brightest nuclei. Our sample increases the number of known AGN pairs on these scales by more than an order of magnitude. We present their AGN and host-galaxy star formation properties in a companion paper.
Early-type dwarfs (ETDs) are the end points of the evolution of low-mass galaxies whose gas supply has been extinguished. The cessation of star-formation lays bare the ancient stellar populations. A wealth of information is stored in the colours, magnitudes, metallicities and abundances of resolved stars of the dwarf spheroidal and ultra-faint galaxies around the Milky Way, allowing their chemistry and stellar populations to be studied in great detail. Here, we summarize our current understanding, which has advanced rapidly over the last decade thanks to the flourishing of large-scale astrometric, photometric and spectroscopic surveys. We emphasise that the primeval stellar populations in the ETDs provide a unique laboratory to study the physical conditions on small scales at epochs beyond z=2. We highlight the observed diversity of star-formation and chemical enrichment histories in nearby dwarfs. These data can not yet be fully deciphered to reveal the key processes in the dwarf evolution but the first successful attempts have been made to pin down the sites of heavy element production.
We consider the mathematical model of photoacoustic and thermoacoustic tomography in media with a variable sound speed. When the sound speed is known, the explicit reconstruction formula by P. Stefanov and G. Uhlmann (Inverse Problems, 25(7):075011, 16, 2009) can be used. We study how a modelling error in the sound speed affects the reconstruction formula and quantify the effect in terms of a stability estimate.
For every $d \geq 2$, we present a generalization of the CHSH inequality with the property that maximal violation self-tests the maximally entangled state of local dimension $d$. This is the first example of a family of inequalities with this property. Moreover, we provide a conjecture for a family of inequalities generalizing the tilted CHSH inequalities, and we conjecture that for each pure bipartite entangled state there is an inequality in the family whose maximal violation self-tests it. All of these inequalities are inspired by the self-testing correlations of [Nat. Comm. 8, 15485 (2017)].
We compare existing high spectral resolution (R=40,000) CaII K observations towards 88 mainly B-type stars, and new observations at R=10,000 towards 3 stars, with 21-cm HI emission-line profiles, in order to search for optical absorption towards known intermediate and high velocity cloud complexes. Given certain assumptions, limits to the gas phase abundance of CaII are estimated for the cloud components. We use the data to derive the following distances from the Galactic plane (z); 1) Tentative lower z-height limits of 2800 pc and 4100 pc towards Complex C using lack of absorption in the spectra of HD 341617 and PG 0855+294. 2) A weak lower z-height of 1400 pc towards Complex WA-WB using lack of absorption in EC 09470-1433 and weak lower limit of 2470 pc with EC 09452-1403. 3) An upper z-height of 2470 pc towards a southern intermediate velocity cloud (IVC) with v_LSR=-55 km/s using PG 2351+198. 4) Detection of a possible IVC in CaK absorption at v_LSR=+52 km/s using EC 20104-2944. No associated HI in emission is detected. At this position, normal Galactic rotation predicts velocities of up to +25 km/s. The detection puts an upper z-height of 1860 pc to the cloud. 5) Tentative HI and CaK detections towards an IVC at +70 km/s in the direction of HVC Complex WE, sightline EC 06387-8045, indicating that the IVC may be at a z-height lower than 1770 pc. 6) Detection of CaK absorption in the spectrum of PG 0855+294 in the direction of IV20, indicating that this IVC has a z-height smaller than 4100 pc. 7) A weak lower z-height of 4300 pc towards a small HVC with v_LSR=+115 km/s at l,b=200,+52, using lack of absorption in the CaK spectrum of PG 0955+291.
The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises. We obtain sufficient conditions for stochastic ultimate boundedness, stochastic permanence, nonpersistence in the mean, strong persistence in the mean and extinction of the solution to the considered system.
Local windows are routinely used in computer vision and almost without exception the center of the window is aligned with the pixels being processed. We show that this conventional wisdom is not universally applicable. When a pixel is on an edge, placing the center of the window on the pixel is one of the fundamental reasons that cause many filtering algorithms to blur the edges. Based on this insight, we propose a new Side Window Filtering (SWF) technique which aligns the window's side or corner with the pixel being processed. The SWF technique is surprisingly simple yet theoretically rooted and very effective in practice. We show that many traditional linear and nonlinear filters can be easily implemented under the SWF framework. Extensive analysis and experiments show that implementing the SWF principle can significantly improve their edge preserving capabilities and achieve state of the art performances in applications such as image smoothing, denoising, enhancement, structure-preserving texture-removing, mutual-structure extraction, and HDR tone mapping. In addition to image filtering, we further show that the SWF principle can be extended to other applications involving the use of a local window. Using colorization by optimization as an example, we demonstrate that implementing the SWF principle can effectively prevent artifacts such as color leakage associated with the conventional implementation. Given the ubiquity of window based operations in computer vision, the new SWF technique is likely to benefit many more applications.
We present 75 near-infrared (NIR; 0.8$-$2.5 $\mu$m) spectra of 34 stripped-envelope core-collapse supernovae (SESNe) obtained by the Carnegie Supernova Project-II (CSP-II), encompassing optical spectroscopic Types IIb, Ib, Ic, and Ic-BL. The spectra range in phase from pre-maximum to 80 days past maximum. This unique data set constitutes the largest NIR spectroscopic sample of SESNe to date. NIR spectroscopy provides observables with additional information that is not available in the optical. Specifically, the NIR contains the resonance lines of He I and allows a more detailed look at whether Type Ic supernovae are completely stripped of their outer He layer. The NIR spectra of SESNe have broad similarities, but closer examination through statistical means reveals a strong dichotomy between NIR "He-rich" and "He-poor" SNe. These NIR subgroups correspond almost perfectly to the optical IIb/Ib and Ic/Ic-BL types, respectively. The largest difference between the two groups is observed in the 2 $\mu$m region, near the He I $\lambda$2.0581 $\mu$m line. The division between the two groups is not an arbitrary one along a continuous sequence. Early spectra of He-rich SESNe show much stronger He I $\lambda$2.0581 $\mu$m absorption compared to the He-poor group, but with a wide range of profile shapes. The same line also provides evidence for trace amounts of He in half of our SNe in the He-poor group.
Dusty starbursts were more numerous around z~1 than today and appear to be responsible for the majority of cosmic star formation over the Hubble time. We suggest that they represent a common phase within galaxies in general which is triggered by the growth of cosmic structure. We discuss the origin of the luminosity of luminous infrared galaxies at z~1. Are these galaxies dominated by star formation or nuclear activity ? What is triggering their strong activity ? Is it triggered by external interactions or did it happen naturally within isolated galaxies ? We present HST-ACS high resolution optical images of luminous infrared galaxies at z~0.7 showing the evolution of the morphology of these galaxies as a function of infrared luminosity, or star formation rate, and discuss the effect of the environment on their activity.
Inspired by the classic Sauvola local image thresholding approach, we systematically study it from the deep neural network (DNN) perspective and propose a new solution called SauvolaNet for degraded document binarization (DDB). It is composed of three explainable modules, namely, Multi-Window Sauvola (MWS), Pixelwise Window Attention (PWA), and Adaptive Sauolva Threshold (AST). The MWS module honestly reflects the classic Sauvola but with trainable parameters and multi-window settings. The PWA module estimates the preferred window sizes for each pixel location. The AST module further consolidates the outputs from MWS and PWA and predicts the final adaptive threshold for each pixel location. As a result, SauvolaNet becomes end-to-end trainable and significantly reduces the number of required network parameters to 40K -- it is only 1\% of MobileNetV2. In the meantime, it achieves the State-of-The-Art (SoTA) performance for the DDB task -- SauvolaNet is at least comparable to, if not better than, SoTA binarization solutions in our extensive studies on the 13 public document binarization datasets. Our source code is available at https://github.com/Leedeng/SauvolaNet.
Least common multiple ($lcm$) has been shown to posses the property of $D$-magic number, that is, its least significant digit $0$ does not change when the number is transferred into all other numbering systems with smaller bases. The number $lcm + 1$ preserves this property as well.
Let G be a finite subgroup of SL(n,C), then the quotient C^n/G has a Gorenstein canonical singularity. Bridgeland-King-Reid proved that the G-Hilbert scheme Hilb^G(C^3) gives a crepant resolution of the quotient C^3/G for any finite subgroup G of SL(3,C). However, in dimension 4, very few crepant resolutions are known. In this paper, we will show several examples of crepant resolutions in dimension 4 and show examples in which Hilb^G(C^4) is blow-up of certain crepant resolutions for C^4/G, or Hilb^G(C^4) has singularity.
We assess the effects of simulated active galactic nuclei (AGNs) on the colour and morphology measurements of their host galaxies. To test the morphology measurements, we select a sample of galaxies not known to host AGNs and add a series of point sources scaled to represent specified fractions of the observed V band light detected from the resulting systems; we then compare morphology measurements of the simulated systems to measurements of the original galaxies. AGN contributions >20 per cent bias most of the morphology measurements tested, though the extent of the apparent bias depends on the morphological characteristics of the original galaxies. We test colour measurements by adding to non-AGN galaxy spectra a quasar spectrum scaled to contribute specified fractions of the rest-frame B band light detected from the resulting systems. A quasar fraction of 5 per cent can move the NUV-r colour of an elliptical galaxy from the UV-optical red sequence to the green valley, and 20 per cent can move it into the blue cloud. Combining the colour and morphology results, we find that a galaxy/AGN system with an AGN contribution >20 per cent may appear bluer and more bulge-dominated than the underlying galaxy. We conclude that (1) bulge-dominated, E/S0/Sa, and early-type morphology classifications are accurate for red AGN host galaxies and may be accurate for blue host galaxies, unless the AGN manifests itself as a well-defined point source; and (2) although highly unobscured AGNs, such as the quasar used for our experiments, can significantly bias the measured colours of AGN host galaxies, it is possible to identify such systems by examining optical images of the hosts for the presence of a point source and/or measuring the level of nuclear obscuration.
The Einstein Telescope (ET), a wide-band, future third generation gravitational wave detector, is expected to have detection rates of $\sim 10^5 - 10^6$ binary black hole (BBH) detections and $\sim 7 \times 10^4$ binary neutron star (BNS) detections in one year. The coalescence of compact binaries with a total mass of 20 - 100 $M_{\odot}$, typical of BH-BH or BH-NS binaries, will be visible up to redshift $z\approx 20$ and even higher, thus facilitating the understanding of the dark era of the Universe preceding the birth of the first stars. The ET will therefore be a crucial instrument for population studies. We analysed the compact binaries originating in stars from (i) Population (Pop) I+II, (ii) Pop III, and (iii) globular clusters (GCs), with the single ET instrument, using the ET-D design sensitivity for the analysis. We estimated the constraints on the chirp mass, redshift, and merger rate as function of redshift for these classes of compact object binaries. We conclude that the ET as a single instrument is capable of detecting and distinguishing different compact binary populations separated in chirp mass - redshift space. While compact binaries originating in stars from Pop III are clearly distinguishable, owing to the separation in chirp mass - redshift space, the other two populations, Pop I+II, and GCs, can be distinguished with just 500 detections, corresponding to an observation time of $\sim 1$ hr. The mass distribution characteristics of such different compact binary populations can also be estimated with the single ET instrument.
We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 5D, N=1 M-theory and the 4D type II superstring. This theory is a complexification of the fundamental 5-brane theory that embeds the 4D, N=1 M-theory of the 3D type II string in a sense that we make explicit at the level of the Lagrangian and Hamiltonian formulations. We find three types of section condition: in spacetime, on the worldvolume, and one tying them together. The 5-brane theory is recovered from the new theory by a double dimensional reduction.