ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present the detection of RR Lyrae variable stars in the field of the Sagittarius II (Sgr II) ultra-faint dwarf (UFD) galaxy. Using B, V time-series photometry obtained with the Korea Microlensing Telescope Network (KMTNet) 1.6 m telescope at CTIO and G-band data from Gaia Data Release 2 (DR2), we identified and characterized two ab-type and four c-type RR Lyrae variables. Five out of the six stars are clustered within three half-light radii (~4.8') of the galaxy indicating their association with Sgr II, while the RRab star V4 is located ~22' from the galaxy center. By excluding V4, the high c-type fraction (0.8) and the period of the only RRab star V3 (P_V3 = 0.666 days) suggest an Oosterhoff II (Oo II) classification for Sgr II. Located close to the locus of Oo II clusters in the period-amplitude diagram, V3 is similar to RRab stars in other UFDs having Oosterhoff-intermediate and Oo II properties. Sgr II is, however, more compact than usual UFDs, placed in between star clusters and dwarf galaxies in the size-luminosity plane, and therefore spectroscopic studies are eventually required to ascertain the true nature of this stellar system. We derive the metallicity ([Fe/H]_RRab = -2.1 +- 0.3) and heliocentric distance (~64 +- 3 kpc) of Sgr II from the RR Lyrae stars, and estimate its age (~12 Gyr) based on our stellar population models. The Oosterhoff properties of UFDs can be explained with the evolution effect of RR Lyrae stars in the instability strip.
We present a detailed theoretical analysis of the Wigner crystal states in confined semiconducting carbon nanotubes. We show by robust scaling arguments as well as by detailed semi-microscopic calculations that the effective exchange interaction has an SU(4) symmetry, and can reach values even as large as $J\sim 100 {\rm \,K}$ in weakly screened, small diameter nanotubes, close to the Wigner crystal - electron liquid crossover. Modeling the nanotube carefully and analyzing the magnetic structure of the inhomogeneous electron crystal, we recover the experimentally observed 'phase boundaries' of Deshpande and Bockrath [V. V. Deshpande and M. Bockrath, Nature Physics $\mathbf 4$, 314 (2008)]. Spin-orbit coupling only slightly modifies these phase boundaries, but breaks the spin symmetry down to SU(2)$\times$SU(2), and in Wigner molecules it gives rise to interesting excitation spectra, reflecting the underlying SU(4) as well as the residual SU(2)$\times$SU(2) symmetries.
In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble Embedding, for which a single ordinary differential equation for the remaining velocity field can be derived. Using this equation, all solutions with transverse 2D Hubble embedding and power law ansatz for the remaining longitudinal velocity field will be found. Going beyond the power law ansatz, we further find a few solutions with transverse 2D Hubble embedding and nontrivial longitudinal velocity field. Finally we investigate general scaling flows with each component of the velocity fields scaling independently, for which we also find all possible solutions. Possible physical relevance of these solutions will be discussed.
Using a leading algorithmic implementation of the functional renormalization group (fRG) for interacting fermions on two-dimensional lattices, we provide a detailed analysis of its quantitative reliability for the Hubbard model. In particular, we show that the recently introduced multiloop extension of the fRG flow equations for the self-energy and two-particle vertex allows for a precise match with the parquet approximation also for two-dimensional lattice problems. The refinement with respect to previous fRG-based computation schemes relies on an accurate treatment of the frequency and momentum dependences of the two-particle vertex, which combines a proper inclusion of the high-frequency asymptotics with the so-called truncated unity fRG for the momentum dependence. The adoption of the latter scheme requires, as an essential step, a consistent modification of the flow equation of the self-energy. We quantitatively compare our fRG results for the self-energy and momentum-dependent susceptibilities and the corresponding solution of the parquet approximation to determinant quantum Monte Carlo data, demonstrating that the fRG is remarkably accurate up to moderate interaction strengths. The presented methodological improvements illustrate how fRG flows can be brought to a quantitative level for two-dimensional problems, providing a solid basis for the application to more general systems.
We calculate the ground, first intrinsic excited states and density distribution for neutron-rich thorium and uranium isotopes, within the framework of relativistic mean field(RMF) approach using axially deformed basis. The total nucleon densities are calculated, from which the cluster-structures inside the parent nuclei are determined. The possible modes of decay, like {\alpha}-decay and \b{eta} -decay are analyzed. We find the neutron-rich isotopes are stable against {\alpha}-decay, however they are very much unstable against \b{eta} -decay. The life time of these nuclei predicted to be tens of second against \b{eta} -decay.
We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry involves hypersurfaces in toric varieties (such as P^2 blown up at more than 3 points) presents a challenge for the brane picture. We also find a simple physical explanation of Batyrev's construction of mirror pairs of Calabi-Yau manifolds using T-duality.
Dalitz decay of baryon resonances is studied and expressions for the decay width are derived for resonances with arbitrary spin and parity. Contributions of the various terms in the transition matrix element are compared and relevance of spin-parity and the resonance mass is discussed. Explicite algebraic expressions are cited for spin$\le$5/2 resonances. The results can be used in models of dielectron production in elementary reactions and heavy ion collisions.
We discuss the results of computer model for the thermal emissivity of a three-dimensional photonic band gap (PBG) crystal, specifically an inverted opal structure. The thermal emittance for a range of frequencies and angles is calculated.
Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N >= 3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the 'Future', the 'Past' and the set of noncomparable states.
We expand on the recently reported detections of the gamma-ray resonant absorption along the line of sight toward gamma-ray bright quasars (QSOs), like 3C279. We propose to use this novel gamma-ray absorption method to study the Dark Matter distribution in the Milky Way, as well as in the Local Group. Properties of the absorber that was detected on the sight lines towards gamma-ray bright QSOs at zero redshift are discussed. We compare our results with the expected Dark Matter distributions in the halo of Milky Way, that were simulated in boundaries of different CDM models. Application of this new method to study evolution of CDM in the QSO host galaxies, and of baryons distribution in the halo of galaxies in the Local Universe is proposed.
Existence and a priori estimates for real-valued periodic solutions to the modified Korteweg-de Vries equation with initial data in $H^s$ are established for $s>0$. The short-time Fourier restriction norm method is employed to overcome the derivative loss. Further, non-existence of solutions below $L^2$ is proved conditional upon conjectured linear Strichartz estimates.
We briefly review the existing database of supernova spectropolarimetry, concentrating on recent data and on results from our group's research. Spectropolarimetry provides the only direct known probe of early-time supernova geometry. To obtain reliable conclusions, however, it is very important to correctly account for interstellar polarization. We find that Type IIn supernovae (SNe IIn) tend to be highly polarized, perhaps in part because of the interaction of the ejecta with an asymmetric circumstellar medium. In contrast, SNe II-P are not polarized much, at least shortly after the explosion. At later times, however, there is evidence for increasing polarization, as one views deeper into the expanding ejecta. Moreover, core-collapse SNe that have lost part (SN IIb) or all (SN Ib) of their hydrogen (or even helium; SN Ic) layers prior to the explosion tend to show substantial polarization; thus, the deeper we probe into core-collapse events, the greater the asphericity. There is now conclusive evidence that at least some SNe Ia are intrinsically polarized, although only by a small amount. Finally, SN spectropolarimetry provides the opportunity to study the fundamental properties of the interstellar dust in external galaxies. For example, we have found evidence for extremely high polarization efficiency for the dust along the line-of-sight to SN 1999gi in NGC 3184.
This paper elucidates the connection between stationary symmetric alpha-stable processes with 0<alpha<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that a necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.
Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic shear two-point statistics. We demonstrate how to use log-normal simulations of the convergence field and the corresponding shear field to carry out realistic tests of internal covariance estimators and find that most estimators such as jackknife or sub-sample covariance can reach a satisfactory compromise between bias and variance of the estimated covariance.   In a forecast for the complete, 5-year DES survey we show that internally estimated covariance matrices can provide a large fraction of the true uncertainties on cosmological parameters in a 2D cosmic shear analysis. The volume inside contours of constant likelihood in the $\Omega_m$-$\sigma_8$ plane as measured with internally estimated covariance matrices is on average $\gtrsim 85\%$ of the volume derived from the true covariance matrix. The uncertainty on the parameter combination $\Sigma_8 \sim \sigma_8 \Omega_m^{0.5}$ derived from internally estimated covariances is $\sim 90\%$ of the true uncertainty.
We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme-TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, $^{56}$Fe, the Skyrme-TQRPA approach is applied to analyze thermal effects on the strength function of GT$_+$ transitions which dominate electron capture at $E_e\le 30$~MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are compared with those of the other model calculations.
Two infinite sequences A and B of non-negative integers are called additive complements, if their sum contains all sufficiently large integers. Let $A(x)$ and $B(x)$ be the counting functions of A and B. In this paper, we extend the results of Liu and Fang in 2016 and obtain some results on additive complements. For example, we prove that there exist additive complements $A$ and $B$ such that $\limsup_{x\to+\infty} A(x)B(x)/x= 2$ and $A(x)B(x) - x = 1$ for infinitely positive integers $x$.
A new approach for the reduction of tensor integrals is described. The standard decomposition \`{a} la Davydychev is applied. Integrals with higher indices are then expressed in terms of scalar higher-dimensional integrals with generic indices. The approach allows to perform contractions with external momenta in a particularly efficient manner. This is due to the possibility to perform analytically the resulting sums over the indices of products of signed minors and scalar products of chords. Advantages of this approach for the calculation of cross sections are described. We are preparing the numerical package OLEC (\texttt{O}ne \texttt{L}oop \texttt{E}xternal \texttt{C}ontractions) with interfaces in Mathematica for algebraic and in C++ for numerical calculations. First numerical results are discussed.
We refine Catalan numbers and Fu{\ss}-Catalan numbers by introducing colour statistics for triangulations of polygons and $d$-dimensional generalisations there-of which we call Fu{\ss}-Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively Fu{\ss}-Catalan complexes, with a given colour distribution of its vertices is given by closed product formulae. The crucial ingredient in the proof is the Lagrange-Good inversion formula.
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season of lockdown, I modestly try to contribute to scientific interaction at a distance. Therefore all comments and exchange of information are most welcome.
While it is well known that mass transfer in binaries can pollute the surfaces of the accretors, it is still unclear whether this mechanism can reproduce the observed chemical inhomogeneities in globular clusters. We study the surface abundances of the accretors in low-mass binaries, as a first step towards understanding whether mass transfer in low-mass binaries is one of the potential origins of the aforementioned abundance anomalies in globular clusters. We use the Modules for Experiments in Stellar Astrophysics code to calculate binary evolutionary models with different initial donor masses between 0.9 and 1.9 $ \rm {M}_\odot$ for an initial metallicity of Z = 0.0034. The results show that in some low-mass binary systems, the accretors exhibit peculiar chemical patterns when they are still unevolved stars, e.g. C and O depletion; Na and N enhancement; constant Mg, Al and C+N+O. The abundance patterns of the accretors are significantly different from their initial abundances (or that of normal single stars), and can match the observed populations. These abundance patterns strongly depend not only on the initial parameters of binaries (donor mass, mass ratio, and orbital period), but also on the assumptions regarding mass-transfer efficiency and angular momentum loss. These results support the hypothesis that mass transfer in low-mass binaries is at least partly responsible for the unevolved anomalous stars in globular clusters. More work on binary evolutionary models and binary population synthesis is required to fully evaluate the contribution of this scenario.
We report the results of an expanded search for z~9-10 candidates over the ~883 arcmin^2 CANDELS+ERS fields. This study adds 147 arcmin^2 to the search area we consider over the CANDELS COSMOS, UDS, and EGS fields, while expanding our selection to include sources with bluer J_{125}-H_{160} colors than our previous J_{125}-H_{160}>0.5 mag selection. In searching for new z~9-10 candidates, we make full use of all available HST, Spitzer/IRAC, and ground-based imaging data. As a result of our expanded search and use of broader color criteria, 3 new candidate z~9-10 galaxies are identified. We also find again the z=8.683 source previously confirmed by Zitrin+2015. This brings our sample of probable z~9-11 galaxy candidates over the CANDELS+ERS fields to 19 sources in total, equivalent to 1 candidate per 47 arcmin^2 (1 per 10 WFC3/IR fields). To be comprehensive, we also discuss 28 mostly lower likelihood z~9-10 candidates, including some sources that seem to be reliably at z>8 using the HST+IRAC data alone, but which the ground-based data show are much more likely at z<4. One case example is a bright z~9.4 candidate COS910-8 which seems instead to be at z~2. Based on this expanded sample, we obtain a more robust LF at z~9 and improved constraints on the volume density of bright z~9 and z~10 galaxies. Our improved z~9-10 results again reinforce previous findings for strong evolution in the UV LF at z>8, with a factor of ~10 evolution seen in the luminosity density from z~10 to z~8.
Prompt gamma-ray burst (GRB) emission requires some mechanism to dissipate an ultrarelativistic jet. Internal shocks or some form of electromagnetic dissipation are candidate mechanisms. Any mechanism needs to answer basic questions, such as what is the origin of variability, what radius does dissipation occur at, and how does efficient prompt emission occur. These mechanisms also need to be consistent with how ultrarelativistic jets form and stay baryon pure despite turbulence and electromagnetic reconnection near the compact object and despite stellar entrainment within the collapsar model. We use the latest magnetohydrodynamical models of ultrarelativistic jets to explore some of these questions in the context of electromagnetic dissipation due to the slow collisional and fast collisionless reconnection mechanisms, as often associated with Sweet-Parker and Petschek reconnection, respectively. For a highly magnetized ultrarelativistic jet and typical collapsar parameters, we find that significant electromagnetic dissipation may be avoided until it proceeds catastrophically near the jet photosphere at large radii ($r\sim 10^{13}--10^{14}{\rm cm}$), by which the jet obtains a high Lorentz factor ($\gamma\sim 100--1000), has a luminosity of $L_j \sim 10^{50}--10^{51}\ergs$, has observer variability timescales of order 1s (ranging from 0.001-10s), achieves $\gamma\theta_j\sim 10--20 (for opening half-angle $\theta_j$) and so is able to produce jet breaks, and has comparable energy available for both prompt and afterglow emission. This reconnection switch mechanism allows for highly efficient conversion of electromagnetic energy into prompt emission and associates the observed prompt GRB pulse temporal structure with dissipation timescales of some number of reconnecting current sheets embedded in the jet.[abridged]
We formulate and prove an analogue of the non-commutative Iwasawa Main Conjecture for $\ell$-adic representations of the Galois group of a function field of characteristic $p$. We also prove a functional equation for the resulting non-commutative $L$-functions. As corollaries, we obtain non-commutative generalisations of the main conjecture for Picard-$1$-motives of Greither and Popescu and a main conjecture for abelian varieties over function fields in precise analogy to the $\operatorname{GL}_2$ main conjecture of Coates, Fukaya, Kato, Sujatha and Venjakob.
Temporal Action Detection (TAD) is an essential and challenging topic in video understanding, aiming to localize the temporal segments containing human action instances and predict the action categories. The previous works greatly rely upon dense candidates either by designing varying anchors or enumerating all the combinations of boundaries on video sequences; therefore, they are related to complicated pipelines and sensitive hand-crafted designs. Recently, with the resurgence of Transformer, query-based methods have tended to become the rising solutions for their simplicity and flexibility. However, there still exists a performance gap between query-based methods and well-established methods. In this paper, we identify the main challenge lies in the large variants of action duration and the ambiguous boundaries for short action instances; nevertheless, quadratic-computational global attention prevents query-based methods to build multi-scale feature maps. Towards high-quality temporal action detection, we introduce Sparse Proposals to interact with the hierarchical features. In our method, named SP-TAD, each proposal attends to a local segment feature in the temporal feature pyramid. The local interaction enables utilization of high-resolution features to preserve action instances details. Extensive experiments demonstrate the effectiveness of our method, especially under high tIoU thresholds. E.g., we achieve the state-of-the-art performance on THUMOS14 (45.7% on mAP@0.6, 33.4% on mAP@0.7 and 53.5% on mAP@Avg) and competitive results on ActivityNet-1.3 (32.99% on mAP@Avg). Code will be made available at https://github.com/wjn922/SP-TAD.
The statistical properties of three-level lasing are investigated theoretically. It is assumed that the three-level medium is coherently excited by another laser with an arbitrary photon statistics. It is proved that, under the specific conditions, the photon statistics of the three-level laser duplicate the photon statistics of the exciting laser. We call this phenomenon an induced photon statistics. We suggest to use this to analyze the statistical properties of a laser involved into a feedback process. Applying this laser for the coherent pump of a three-level laser, we can follow its photon statistics by means of direct following the three-level generation. In accordance with [H. M. Wiseman and G. J. Milburn, Phys. Rev. A, 49, 1350-1366 (1994)], we conclude that the feedback in itself is unable to generate the non-classical manifestation in the laser field.
Two additional reasons are suggested for the seeming lack of progress in producing quantum algorithms.
Layered materials with robust magnetic ordering have been attracting significant research interest. In recent experiments, a new layered material 1$T$-CrTe$_{2}$ has been synthesized and exhibits ferromagnetism above the room temperature. Here, based on first-principles calculations, we investigate the electronic, magnetic, and transport properties of 1$T$-CrTe$_{2}$, both in the bulk and in the two-dimensional (2D) limit. We show that 1$T$-CrTe$_{2}$ can be stable in the monolayer form, and has a low exfoliation energy. The monolayer structure is an intrinsic ferromagnetic metal, which maintains a high Curie temperature above the room temperature. Particularly, we reveal interesting features in the anomalous Hall transport. We show that in the ground state, both bulk and monolayer 1$T$-CrTe$_{2}$ possess vanishing anomalous Hall effect, because the magnetization preserves one vertical mirror symmetry. The anomalous Hall conductivity can be made sizable by tuning the magnetization direction or by uniaxial strains that break the mirror symmetry. The room-temperature 2D ferromagnetism and the tunable anomalous Hall effect make the material a promising platform for nanoscale device applications.
We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to the case of H-type groups, this algebra property is generalized to paraproduct estimates.