ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a vector bundle $\mathcal{E}$ of rank $n+1$ over a smooth projective curve $C$ of genus $g$, let $X=\P_C (\mathcal{E})$ with projection map $\pi:X\to C$. In this paper we investigate the minimal free resolution of homogeneous coordinate rings of $X$.   We first clarify the relations between higher syzygies of very ample line bundles on $X$ and higher syzygies of Veronese embedding of fibres of $\pi$ by the same line bundle. More precisely, letting $H = \mathcal{O}_{\P_C (\mathcal{E})} (1)$ be the tautological line bundle, we prove that if $(\P^n,\mathcal{O}_{\P^n} (a))$ satisfies Property $N_p$, then $(X,aH+\pi^*B)$ satisfies Property $N_p$ for all $B \in {Pic}C$ having sufficiently large degree(Theorem \ref{thm:positive}). And also the effective bound of ${deg}(B)$ for Property $N_p$ is obtained(Theorem \ref{thm:1}, \ref{thm:2}, \ref{thm:3} and \ref{thm:4}). For the converse, we get some partial answer(Corollary \ref{cor:negative}). Secondly, by using these results we prove some Mukai-type statements. In particular, Mukai's conjecture is true for $X$ when ${rank}(\mathcal{E}) \geq g$ and $\mu^- (\mathcal{E})$ is an integer(Corollary \ref{cor:Mukai}). Finally for all $n$, we construct an $n$-dimensional ruled variety $X$ and an ample line bundle $A \in {Pic}X$ which shows that the condition of Mukai's conjecture is optimal for every $p \geq 0$.
The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied mathematics literature in the 1950s through the work of R. Dautray and collaborators, [7, 8, 19]. The NTE also has a probabilistic representation through the semigroup of the underlying physical process when envisaged as a stochastic process; cf. [7, 17, 18, 20]. More recently, [6] and [16] have continued the probabilistic analysis of the NTE, introducing more recent ideas from the theory of spatial branching processes and quasi-stationary distributions. In this paper, we continue in the same vein and look at a fundamental description of stochastic growth in the supercritical regime. Our main result provides a significant improvement on the last known contribution to growth properties of the physical process in [20], bringing neutron transport theory in line with modern branching process theory such as [14, 12].
Context. The study of the oldest and most metal-poor stars in our Galaxy promotes our understanding of the Galactic chemical evolution and the beginning of Galaxy and star formation. However, they are notoriously difficult to find, with only five stars at $\mathrm{[Fe/H]<-5.0}$ having been detected to date. Thus, the spectrophotometric data of 219 million sources which became available in the third Gaia Data Release comprise a very promising dataset for the identification of metal-poor stars. Aims. We want to use the low-resolution Gaia Blue Photometer / Red Photometer (BP/RP) spectra to identify metal-poor stars. Our primary aspiration is to help populate the poorly constrained tail of the metallicity distribution function of the stellar halo of the Galaxy. Methods. We developed a metal-poor candidate selection method based on flux ratios from the BP/RP Gaia spectra, using simulated synthetic spectra. Results. We found a relation between the relative iron abundance and the flux ratio of the Ca H \& K region to that of the $\mathrm{H\beta}$ line. This relation is temperature and surface gravity dependent, and it holds for stars with $\mathrm{4800\,K \leq T_{eff}\leq6300\,K}$. We applied it to noisy simulated synthetic spectra and inferred $\mathrm{[Fe/H]}$ with an uncertainty of $\sigma_{\mathrm{[Fe/H]}}\lessapprox0.65$ dex for $\mathrm{-3\leq[Fe/H]}\leq 0.5$ and G=15-17mag, which is sufficient to identify stars at $\mathrm{[Fe/H]<-2.0 }$ reliably. We predict that by selecting stars with inferred $\mathrm{[Fe/H]}\leq-2.5$ dex, we can retrieve 80% of the stars with $\mathrm{[Fe/H]}\leq-3$ and have a success rate of about 50%, that is one in two stars we select would have $\mathrm{[Fe/H]}\leq-3$. We do not take into account the effect of reddening, so our method should only be applied to stars which are located in regions of low extinction.
Erbium (Er) doped GaN has been studied extensively for optoelectronic applications, yet its defect physics is still not well understood. In this work, we report a first-principles hybrid density functional study of the structure, energetics, and thermodynamic transition levels of Er-related defect complexes in GaN. We discover for the first time that Er$_{\rm Ga}$-C$_{\rm N}$-$V_{\rm N}$, a defect complex of Er, a C impurity, and an N vacancy, and Er$_{\rm Ga}$-O$_{\rm N}$-$V_{\rm N}$, a complex of Er, an O impurity, and an N vacancy, form defect levels at 0.18 and 0.46 eV below the conduction band, respectively. Together with Er$_{\rm Ga}$-$V_{\rm N}$, a defect complex of Er and an N vacancy which has recently been found to produce a donor level at 0.61 eV, these defect complexes provide explanation for the Er-related defect levels observed in experiments. The role of these defects in optical excitation of the luminescent Er center is also discussed.
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans(1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of side L as L tends to infinity. Under appropriate conditions (and on a suitable timescale), we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).
For integer $m, p,$ we study tangent power sum $\sum^m_{k=1}\tan^{2p}\frac{\pi k}{2m+1}.$ We prove that, for every $m, p,$ it is integer, and, for a fixed p, it is a polynomial in $m$ of degree $2p.$ We give recurrent, asymptotical and explicit formulas for these polynomials and indicate their connections with Newman's digit sums in base $2m.$
In this work we revisit the definition of Matter Trapping Surfaces (MTS) introduced in previous investigations and show how it can be expressed in the so-called dual null formalism developed for Trapping Horizons (TH). With the aim of unifying both approaches, we construct a 2+2 threading from the 1+3 flow, and thus isolate one prefered spatial direction, that allows straightforward translation into a dual nul subbasis, and to deduce the geometric apparatus that follows. We remain as general as possible, reverting to spherical symmetry only when needed, and express the MTS conditions in terms of 2-expansion of the flow, then in purely geometric form of the dual null expansions. The Raychadhuri equations that describe both MTS and TH are written and interpreted using the previously defined gTOV (generalized Tolman-Oppenheimer-Volkov) functional introduced in previous work. Further using the Misner-Sharp mass and its previous perfect fluid definition, we relate the spatial 2-expansion to the fluid pressure, density and acceleration. The Raychaudhuri equations also allows us to define the MTS dynamic condition with first order differentials so the MTS conditions are now shown to be all first order differentials. This unified formalism allows one to realise that the MTS can only exist in normal regions, and so it can exist only between black hole horizons and cosmological horizons. Finally we obtain a relation yielding the sign, on a TH, of the non-vanishing null expansion which determines the nature of the TH from fluid content, and flow characteristics. The 2+2 unified formalism here investigated thus proves a powerful tool to reveal, in the future extensions, more of the very rich and subtle relations between MTS and TH.
We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an ADE quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with ADE global symmetry. This equivalence suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories.
As part of the survey component of the Megamaser Cosmology Project, we have discovered a disk megamaser system in the galaxy CGCG 074-064. Using the GBT and the VLA, we have obtained spectral monitoring observations of this maser system at a monthly cadence over the course of two years. We find that the systemic maser features display line-of-sight accelerations of ~4.4 km s$^{-1}$ yr$^{-1}$ that are nearly constant with velocity, while the high-velocity maser features show accelerations that are consistent with zero. We have also used the HSA to make a high-sensitivity VLBI map of the maser system in CGCG 074-064, which reveals that the masers reside in a thin, edge-on disk with a diameter of ~1.5 mas (0.6 pc). Fitting a three-dimensional warped disk model to the data, we measure a black hole mass of $2.42^{+0.22}_{-0.20} \times 10^7$ M$_{\odot}$ and a geometric distance to the system of $87.6^{+7.9}_{-7.2}$ Mpc. Assuming a CMB-frame recession velocity of $7308 \pm 150$ km s$^{-1}$, we constrain the Hubble constant to $H_0 = 81.0^{+7.4}_{-6.9}$ (stat.) $\pm 1.4$ (sys.) km s$^{-1}$ Mpc$^{-1}$.
We identify 814 discrete HI clouds in 40 dwarf irregular galaxies from the LITTLE THINGS survey using an automated cloud-finding algorithm. The cloud masses range from ~10^3 to 10^7 Msolar, have a surface density averaged over all of the clouds of ~9.65 Msolar/pc^2, and constitute 2-53% of the total HI mass of the host galaxy. For individual clouds, the mass including He varies with cloud radius as log M_{gas} = (2.11\pm0.04)x log R_{cl}+(0.78\pm0.08) and the internal velocity dispersion varies as log V_{disp} = 0.5xlog R_{cl}-0.57\pm0.21. The HI clouds tend to be in the outer regions of the galaxies, with 72% of the galaxies having more than 70% of their clouds outside one disk scale length, and 32% of the galaxies having more than 50% of their clouds outside the radius encircling the HII emission. 36% of the clouds are essentially non-self-gravitating from HI alone, with a virial parameter that exceeds alpha_{vir}~10, and 5% have alpha_{vir}\le2. We estimate the missing molecular mass, based on the total star formation rate and a typical molecular consumption time of 2 Gyr, as observed in CO-rich galaxies. The resulting molecular fraction has a value averaged over the galaxies of 0.23 and correlates with both the surface density of star formation and the fraction of HI clouds in the outer regions. We conclude that a significant fraction of the inner parts of these dwarf galaxy disks is in the form of dark molecular gas, and that this fraction could be high enough to make the inner disks mildly gravitationally unstable as a precursor to star formation.
Indirect excitons (IXs), also known as interlayer excitons, can form the medium for excitonic devices whose operation is based on controlled propagation of excitons. A proof of principle for excitonic devices was demonstrated in GaAs heterostructures where the operation of excitonic devices is limited to low temperatures. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by high binding energies making IXs robust at room temperature and offering an opportunity to create excitonic devices operating at high temperatures suitable for applications. However, a characteristic feature of TMD heterostructures is the presence of moir\'e superlattice potentials, which are predicted to cause modulations of IX energy reaching tens of meV. These in-plane energy landscapes can lead to IX localization, making IX propagation fundamentally different in TMD and GaAs heterostructures and making uncertain if long-range IX propagation can be realized in TMD heterostructures. In this work, we realize long-range IX propagation with the $1/e$ IX luminescence decay distances reaching 13 microns in a MoSe$_2$/WSe$_2$ heterostructure. We trace the IX luminescence along the IX propagation path. We also realize control of the long-range IX propagation: the IX luminescence signal in the drain of an excitonic transistor is controlled within 40 times by gate voltage. These data show that the long-range IX propagation is possible in TMD heterostructures with the predicted moir\'e superlattice potentials.
In this paper, we address the question as to whether or not measurable sources for gravitational waves could possibly be made in the laboratory. Based on an analogy of the dynamical Casimir effect with the stimulated emission of radiation in the laser, our answer to this question is in the affirmative, provided that superconducting radio-frequency cavities in fact possess high quality factors for both electromagnetic and gravitational microwave radiation, as one would expect due to a quantum-mechanical gravitational Meissner-like effect. In order to characterize the response of matter to tensor gravitational fields, we introduce a prefactor to the source term of the gravitational wave equation, which we call the "relative gravitational permeativity" analogous to the "relative electric permittivity" and "relative magnetic permeability" that characterize the vector response of matter to applied fields in electromagnetism. This allows for a possibly large quantum mechanical enhancement of the response of a superconductor to an incident tensor gravitational wave field. Finally, we describe our experimental work with high-Q superconducting radio-frequency cavities, and propose a design for a coupled-cavity system with a flexible superconducting membrane in its middle as its amplifying element. This will then allow us to test for a Meissner-like expulsion, and therefore reflection, of incident tensor gravitational wave fields, and, above a certain threshold, to generate coherent gravitational radiation via the dynamical Casimir effect.
The s-lecture hall polytopes P_s are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-M\'elou. We define a half-open parallelopiped Par_s associated with P_s and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the \delta-vector (or h^*-vector) and to obtain the connections to s-ascents and s-descents, as well as some generalizations of these results.
The stellar velocity dispersion, $\sigma$, is a quantity of crucial importance for spiral galaxies, where it enters fundamental dynamical processes such as gravitational instability and disc heating. Here we analyse a sample of 34 nearby spirals from the Calar Alto Legacy Integral Field Area (CALIFA) spectroscopic survey, deproject the line-of-sight $\sigma$ to $\sigma_{R}$ and present reliable radial profiles of $\sigma_{R}$ as well as accurate measurements of $\langle\sigma_{R}\rangle$, the radial average of $\sigma_{R}$ over one effective (half-light) radius. We show that there is a trend for $\sigma_{R}$ to increase with decreasing $R$, that $\langle\sigma_{R}\rangle$ correlates with stellar mass ($M_{\star}$) and tested correlations with other galaxy properties. The most significant and strongest correlation is the one with $M_{\star}$: $\langle\sigma_{R}\rangle \propto M_{\star}^{0.5}$. This tight scaling relation is applicable to spiral galaxies of type Sa $\mbox{--}$ Sd and stellar mass $M_{\star}\approx10^{9.5}\mbox{--}10^{11.5}\ \mbox{M}_{\odot}$. Simple models that relate $\sigma_{R}$ to the stellar surface density and disc scale length roughly reproduce that scaling, but overestimate $\langle\sigma_{R}\rangle$ significantly.
Temporal action detection (TAD) aims to determine the semantic label and the temporal interval of every action instance in an untrimmed video. It is a fundamental and challenging task in video understanding. Previous methods tackle this task with complicated pipelines. They often need to train multiple networks and involve hand-designed operations, such as non-maximal suppression and anchor generation, which limit the flexibility and prevent end-to-end learning. In this paper, we propose an end-to-end Transformer-based method for TAD, termed TadTR. Given a small set of learnable embeddings called action queries, TadTR adaptively extracts temporal context information from the video for each query and directly predicts action instances with the context. To adapt Transformer to TAD, we propose three improvements to enhance its locality awareness. The core is a temporal deformable attention module that selectively attends to a sparse set of key snippets in a video. A segment refinement mechanism and an actionness regression head are designed to refine the boundaries and confidence of the predicted instances, respectively. With such a simple pipeline, TadTR requires lower computation cost than previous detectors, while preserving remarkable performance. As a self-contained detector, it achieves state-of-the-art performance on THUMOS14 (56.7% mAP) and HACS Segments (32.09% mAP). Combined with an extra action classifier, it obtains 36.75% mAP on ActivityNet-1.3. Code is available at https://github.com/xlliu7/TadTR.
We extend the velocity channel analysis (VCA), introduced by Lazarian & Pogosyan, of the intensity fluctuations in the velocity slices of position-position-velocity (PPV) spectroscopic data from Doppler broadened lines to study statistical anisotropy of the underlying velocity and density that arises in a turbulent medium from the presence of magnetic field. In particular, we study analytically how the anisotropy of the intensity correlation in the channel maps changes with the thickness of velocity channels. In agreement with the earlier VCA studies we find that the anisotropy in the thick channels reflects the anisotropy of the density field, while the relative contribution of density and velocity fluctuations to the thin velocity channels depends on the density spectral slope. We show that the anisotropies arising from Alfven, slow and fast magnetohydrodynamical modes are different, in particular, the anisotropy in PPV created by fast modes is opposite to that created by Alfven and slow modes, and this can be used to separate their contributions. We successfully compare our results with the recent numerical study of the PPV anisotropies measured with synthetic observations. We also extend our study to the medium with self-absorption as well as to the case of absorption lines. In addition, we demonstrate how the studies of anisotropy can be performed using interferometers.
Families of boxes in $\mathbb R^d$ are considered. In the paper an upper bound on the size of a minimum transversal in terms of the space dimension and the independence number of the given family was improved.
The effect of the spatially varying spin current on a skyrmion is numerically investigated. It is shown that an inhomogeneous current density induces an elongation of the skyrmion. This elongation can be controlled using current pulses of different strength and duration. Long current pulses lead to a splitting that forms two replicas of the initial skyrmion while for short pulses the elongated skyrmion relaxes back to its initial circular state through rotation in the MHz-GHz frequency range. The frequency is dependent on the strength of the damping coefficient.
We perform molecular dynamics (MD) simulations with phonon spectral analysis aiming at understanding the two dimensional (2D) thermal transport in suspended and supported graphene. Within the framework of equilibrium MD simulations, we perform spectral energy density (SED) analysis to obtain the lifetime of individual phonon modes. The per-mode contribution to thermal conductivity is then calculated to obtain the lattice thermal conductivity in the temperature range 300-650 K. In contrast to prior studies, our results suggest that the contribution from out-of-plane acoustic (or ZA) branch to thermal conductivity is around 25-30% in suspended single-layer graphene (SLG) at room temperature. The thermal conductivity is found to reduce when SLG is put on amorphous SiO2 substrate. Such reduction is attributed to the strengthened scattering in all phonon modes in the presence of the substrate. Among them, ZA modes are mostly affected with their contribution to thermal conductivity reduced to around 15%. As a result, thermal transport is dominated by in-plane acoustic phonon modes in supported SLG.
We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conserved charges. The Kahler-space formulation of the theory has a natural supersymmetric extension in 4-D space-time. It contains a conserved current, but also a number of additional fields complicating the interpretation. Nevertheless, we show that an infinite set of conserved currents emerges in the vacuum sector of the additional fields. This sector can therefore be identified with a regime of supersymmetric fluid mechanics. Explicit expressions for the current and the density are obtained.
[Abridged] [...] AIMS: We aim to establish the stellar parameters and mass-loss rates of the Galactic WC stars. These data provide the empirical basis of studies of (i) the role of WC stars in the evolution of massive stars, (ii) the wind-driving mechanisms, and (iii) the feedback of WC stars as input to models of the chemical and dynamical evolution of galaxies. Methods: We analyze the nearly complete sample of un-obscured Galactic WC stars, using optical spectra as well as ultraviolet spectra when available. The observations are fitted with theoretical spectra, using the Potsdam Wolf-Rayet (PoWR) model atmosphere code. A large grid of line-blanked models has been established for the range of WC subtypes WC4 - WC8, and smaller grids for the WC9 parameter domain. Both WO stars and WN/WC transit types are also analyzed using special models. Results: Stellar and atmospheric parameters are derived for more than 50 GalacticWC and two WO stars, covering almost the whole GalacticWC population as far as the stars are single, and un-obscured in the visual. In the Hertzsprung-Russell diagram, theWC stars reside between the hydrogen and the helium zero-age main sequences, having luminosities L from 10^4.9 to 10^5.6 Lsun. The mass-loss rates scale very tightly with L^0.8. The two WO stars in our sample turn out to be outstandingly hot (\approx200 kK) and do not fit into the WC scheme. Conclusions: By comparing the empirical WC positions in the Hertzsprung-Russell diagram with evolutionary models, and from recent supernova statistics, we conclude that WC stars have evolved from initial masses between 20 solar masses and 45 Msun. In contrast to previous assumptions, it seems that WC stars in general do not descend from the most massive stars. Only the WO stars might stem from progenitors that have been initially more massive than 45 Msun.