ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let X=Gamma\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Gamma-equivariant deformation retractions of D=G/K onto a set D_0. We prove that D_0 is a spine, having dimension equal to the virtual cohomological dimension of Gamma. In fact, there is a (k-1)-parameter family of such deformations retractions, where k is the number of Gamma-conjugacy classes of rational parabolic subgroups of G. The construction of the spine also gives a way to construct an exact fundamental domain for Gamma.
In this letter the explicit form of general two-point functions in affine SL(N) current algebra is provided for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately read off.
Accurate nuclear reaction rates are needed for primordial nucleosynthesis and hydrostatic burning in stars. The relevant reactions are extremely difficult to measure directly in the laboratory at the small astrophysical energies. In recent years direct reactions have been developed and applied to extract low-energy astrophysical S-factors. These methods require a combination of new experimental techniques and theoretical efforts, which are the subject of this presentation.
The lamp-post geometry is often used to model X-ray data of accreting black holes. Despite its simple assumptions, it has proven to be powerful in inferring fundamental black hole properties such as the spin. Early results of X-ray reverberations showed support for such a simple picture, though wind-reverberation models have also been shown to explain the observed delays. Here, we analyze new and old XMM-Newton observations of the variable Seyfert-1 galaxy NGC 5506 to test these models. The source shows an emission line feature around 6.7 keV that is delayed relative to harder and softer energy bands. The spectral feature can be modeled with either a weakly relativistic disk line or by scattering in distant material. By modeling both the spectral and timing signatures, we find that the reflection fraction needed to explain the lags is larger than observed in the time-averaged spectrum, ruling out both a static lamp-post and simple wind reverberation models.
The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.
In this paper, we present a multi-object 6D detection and tracking pipeline for potentially similar and non-textured objects. The combination of a convolutional neural network for object classification and rough pose estimation with a local pose refinement and an automatic mismatch detection enables direct application in real-time AR scenarios. A new network architecture, trained solely with synthetic images, allows simultaneous pose estimation of multiple objects with reduced GPU memory consumption and enhanced performance. In addition, the pose estimates are further improved by a local edge-based refinement step that explicitly exploits known object geometry information. For continuous movements, the sole use of local refinement reduces pose mismatches due to geometric ambiguities or occlusions. We showcase the entire tracking pipeline and demonstrate the benefits of the combined approach. Experiments on a challenging set of non-textured similar objects demonstrate the enhanced quality compared to the baseline method. Finally, we illustrate how the system can be used in a real AR assistance application within the field of construction.
Colors of Type Ia supernovae in the first few days after explosion provide a potential discriminant between different models. In this paper, we present $g-r$ colors of 65 Type Ia supernovae discovered within 5 days from first light by the Zwicky Transient Facility in 2018, a sample that is about three times larger than that in the literature. We find that $g-r$ colors are intrinsically rather homogeneous at early phases, with about half of the dispersion attributable to photometric uncertainties ($\sigma_\mathrm{noise}\sim\sigma_\mathrm{int}\sim$ 0.18 mag). Colors are nearly constant starting from 6 days after first light ($g-r\sim-0.15$ mag), while the time evolution at earlier epochs is characterized by a continuous range of slopes, from events rapidly transitioning from redder to bluer colors (slope of $\sim-0.25$ mag day$^{-1}$) to events with a flatter evolution. The continuum in the slope distribution is in good agreement both with models requiring some amount of $^{56}$Ni mixed in the outermost regions of the ejecta and with "double-detonation" models having thin helium layers ($M_\mathrm{He}=0.01\,M_\odot$) and varying carbon-oxygen core masses. At the same time, six events show evidence for a distinctive "red bump" signature predicted by "double-detonation" models with larger helium masses. We finally identify a significant correlation between the early-time $g-r$ slopes and supernova brightness, with brighter events associated to flatter color evolution (p-value=0.006). The distribution of slopes, however, is consistent with being drawn from a single population, with no evidence for two components as claimed in the literature based on $B-V$ colors.
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle quantities for real and Matsubara frequencies and verify results through comparison to existing data on the Matsubara axis. With low order expansions at weak-coupling we observe a number of outcomes expected at higher orders: the opening of a gap, pseudogap behavior, and Fermi-surface reconstruction. Based on low-order perturbations we consider the phase diagram that arises from truncated expansions of the self-energy and Green's function and their relation via the Dyson equation. From Matsubara axis data we observe insulating behavior in direct expansions of the Green's function, while the same order of truncation of the self-energy produces metallic behavior. This observation is supported by additional calculations for real frequencies. We attribute this difference to the order in which diagrams are implicitly summed in the Dyson series. By separating the reducible and irreducible contributions at each order we show that the reducible diagrams implicitly summed in the Dyson equation lead to incorrect physics in the half-filled Hubbard model. Our observations for this particular case lead us to question the utility of the Dyson equation for any problem that shows a disparity between reducible and irreducible contributions to the expansion of the Green's function.
Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as single particles. The earliest and latest applications are conducting polymers and spin-Peierls chains. After a history introduction, we shall discuss the topological aspects of elementary excitations, especially the confinement and the dimensional D crossover. At the 1D level we exploit results of different exact and approximate techniques in theory of solitons, for both quantum and semiclassical models, and the related knowledge on anomalous charges and currents. At higher D the topological requirements for the combined symmetry originate the spin- or charge- roton like excitations with charge- or spin- kinks localized in the core. In quasi 1D world they can be viewed as resulting from a spin-charge recombination due to the 3D confinement.
We present results of a 3D model of optical to gamma-ray emission from the slot gap accelerator of a rotation-powered pulsar. Primary electrons accelerating to high-altitudes in the unscreened electric field of the slot gap reach radiation-reaction limited Lorentz factors of 2 x 10^7, while electron-positron pairs from lower-altitude cascades flow along field lines interior to the slot gap. The curvature, synchrotron and inverse Compton radiation of both primary electrons and pairs produce a broad spectrum of emission from infra-red to GeV energies. Both primaries and pairs undergo cyclotron resonant absorption of radio photons, allowing them to maintain significant pitch angles. Synchrotron radiation from pairs with a power-law energy spectrum with Lorentz factors 10^2 - 10^5, dominate the spectrum up to 10 MeV. Synchrotron and curvature radiation of primaries dominates from 10 MeV up to a few GeV. We examine the energy-dependent pulse profiles and phase-resolved spectra for parameters of the Crab pulsar as a function of magnetic inclination and viewing angle, comparing to broad-band data. In most cases, the pulse profiles are dominated by caustics on trailing field lines. We also explore the relation of the high-energy and the radio profiles, as well as the possibility of caustic formation in the radio cone emission. We find that the Crab pulsar profiles and spectrum can be reasonably well reproduced by a model with viewing angle 45 degrees and inclination angle 100 or 80 degrees. This model predicts that the slot gap emission below 200 MeV will exhibit correlations in time and phase with the radio emission.
We present theoretical study of morphology of Fe islands grown at Mo(110) surface in sub-monolayer MBE mode. We utilize atomistic SOS model with bond counting, and interactions of Fe adatom up to third nearest neighbors. We performed KMC simulations for different values of adatom interactions and varying temperatures. We have found that, while for the low temperature islands are fat fractals, for the temperature 500K islands have faceted rhombic-like shape. For the higher temperature, islands acquire a rounded shape. In order to evaluated qualitatively morphological changes, we measured averaged aspect ration of islands. We calculated dependence of the average aspect ratio on the temperature, and on the strength of interactions of an adatom with neighbors.
We propose a method to determine the power spectrum of \HI column density fluctuations using radio-interferometric observations of 21-cm emission from the ISM of galaxies. We have used this to estimate the power spectra of six nearly face on nearby spiral galaxies. Earlier work has shown that these power spectra are well fitted by power laws with slopes around -1.6 across length-scales $\sim 1 \, {\rm kpc}$ to $\sim 10 \, {\rm kpc}$, the amplitude however was undetermined. In the present work we have determined the amplitude of the \HI column density power spectrum. We find that the \HI column density $N_{\rm HI}$ expressed in units of $10^{20} \, {\rm cm}^{-2}$ has mean square fluctuations in the range $\sim 0.03$ to $\sim 20$. The amplitude of the power spectrum is found to be tightly correlated with the \HI mass fraction of the galaxies. The physical process responsible for these scale-invariant fluctuations is, however, at present not known.
To facilitate the design and optimization of nanomaterials for a given application it is necessary to understand the relationship between structure and physical properties. For large nanomaterials, there is imprecise structural information so the full structure is only resolved at the level of partial representations. Here we show how to reconcile partial structural representations using constraints from structural characterization measurements and theory to maximally exploit the limited amount of data available from experiment. We determine a range of parameter space where predictive theory can be used to design and optimize the structure. Using an example of variation of chemical composition profile across the interface of two nanomaterials, we demonstrate how, given experimental and theoretical constraints, to find a region of structure-parameter space within which computationally explored partial representations of the full structure will have observable real-world counterparts.
We review the current status of |V(cb)|, |V(ub)| and |V(tb)|, the absolute values of the matrix elements in the CKM third column.
A compelling feature of relativistic mean-field phenomenology has been the reproduction of spin-orbit splittings in finite nuclei after fitting only to equilibrium properties of infinite nuclear matter. This successful result occurs when the velocity dependence of the equivalent central potential that leads to saturation arises primarily because of a reduced nucleon effective mass. The spin-orbit interaction is then also specified when one works in a four-component Dirac framework. Here the nature of the spin-orbit force in more general chiral effective field theories of nuclei is examined, with an emphasis on the role of the tensor coupling of the isoscalar vector meson (omega) to the nucleon.
We present FEROS--Lick/SDSS, an empirical database of Lick/SDSS spectral indices of FGK stars to be used in population synthesis projects for discriminating different stellar populations within the integrated light of galaxies and globular clusters. From about 2500 FEROS stellar spectra obtained from the ESO Science Archive Facility we computed line--strength indices for 1085 non--supergiant stars with atmospheric parameter estimates from the AMBRE project.   Two samples of 312 {\it dwarfs} and of 83 {\it subgiants} with solar chemical composition and no significant $\alpha$--element abundance enhancement are used to compare their observational indices with the predictions of the Lick/SDSS library of synthetic indices. In general, the synthetic library reproduces very well the behaviour of observational indices as a function of temperature, but in the case of low temperature ($T_{\rm eff}$ $\lesssim $5000\,K) dwarfs; low temperature subgiants are not numerous enough to derive any conclusion. Several possible causes of the disagreement are discussed and promising theoretical improvements are presented.
We prove that among all flag triangulations of manifolds of odd dimension 2r-1 with sufficiently many vertices the unique maximizer of the entries of the f-, h-, g- and gamma-vector is the balanced join of r cycles. Our proof uses methods from extremal graph theory.
We calculate the integrated trace anomaly for a real spin-0 scalar field in six dimensions in a torsionless curved space without a boundary. We use a path integral approach for a corresponding supersymmetric quantum mechanical model. Weyl ordering the corresponding Hamiltonian in phase space, an extra two-loop counterterm ${1/8}\bigg(R + g^{ij} \Gamma^{l}_{k i} \Gamma^{k}_{l j} \bigg)$ is produced in the action. Applying a recursive method we evaluate the components of the metric tensor in Riemann normal coordinates in six dimensions and construct the interaction Langrangian density by employing the background field method.   The calculation of the anomaly is based on the end-point scalar propagator and not on the string inspired center-of-mass propagator which gives incorrect results for the local trace anomaly. The manipulation of the Feynman diagrams is partly relied on the factorization of four dimensional subdiagrams and partly on a brute force computer algebra program developed to serve this specific purpose. The computer program enables one to perform index contractions of twelve quantum fields (10395 in the present case) a task which cannot be accomplished otherwise. We observe that the contribution of the disconnected diagrams is no longer proportional to the two dimensional trace anomaly (which vanishes in four dimensions). The integrated trace anomaly is finally expressed in terms of the 17 linearly independent scalar monomials constructed out of covariant derivatives and Riemann tensors.
Despite their cosmological utility, the progenitors of Type Ia supernovae (SNe Ia) are still unknown, with many efforts focused on whether accretion from a nondegenerate companion can grow a carbon-oxygen white dwarf to near the Chandrasekhar mass. The association of SNe Ia resembling SN 1991T ("91T-like") with circumstellar interaction may be evidence for this "single-degenerate" channel. However, the observed circumstellar medium (CSM) in these interacting systems is unlike a stellar wind -- of particular interest, it is sometimes detached from the stellar surface, residing at $\sim 10^{16}~{\rm cm}$. A Hubble Space Telescope (HST) program to discover detached CSM around 91T-like SNe Ia successfully discovered interaction nearly two years after explosion in SN 2015cp (Graham et al., 2018). In this work, we present radio and X-ray follow-up observations of SN 2015cp and analyze them in the framework of Harris, Nugent, & Kasen (2016) to limit the properties of a constant-density CSM shell in this system. Assuming the HST detection was shortly after the shock crossed the CSM, we constrain the total CSM mass in this system to be $< 0.5~{\rm M_\odot}$. This limit is comparable to the CSM mass of supernova PTF11kx, but does not rule out lower masses predicted for recurrent novae. From lessons learned modeling PTF11kx and SN 2015cp, we suggest a strategy for future observations of these events to increase the sample of known interacting SNe Ia.
I study the buckling transition under compression of a two-dimensional, hexagonal, regular elastic honeycomb. Under isotropic compression, the system buckles to a configuration consisting of a unit cell containing four of the original hexagons. This buckling pattern preserves the sixfold rotational symmetry of the original lattice but is chiral, and can be described as a combination of three different elemental distortions in directions rotated 2pi/3 from each other. Non-isotropic compression may induce patterns consisting in a single elemental distortion or a superposition of two of them. The numerical results compare very well with the outcome of a Landau theory of second order phase transitions.
This paper presents results from wide-field imaging of the globular cluster (GC) systems of five intermediate-luminosity (M_V ~-21 to -22) early-type galaxies. The aim is to accurately quantify the global properties of the GC systems by measuring them out to large radii. We obtained BVR imaging of four lenticular galaxies (NGC 5866, NGC 4762, NGC 4754, NGC 3384) and one elliptical galaxy (NGC 5813) using the KPNO 4m telescope and MOSAIC imager and traced the GC population to projected galactocentric radii ranging from ~20 kpc to 120 kpc. We combine our imaging with Hubble Space Telescope data to measure the GC surface density close to the galaxy center. We calculate the total number of GCs (N_GC) from the integrated radial profile and find N_GC = 340 +/- 80 for NGC 5866, N_GC = 2900 +/- 400 for NGC 5813, N_GC = 270 +/- 30 for NGC 4762, N_GC = 115 +/- 15$ for NGC 4754, and N_GC = 120 +/- 30 for NGC 3384. The measured GC specific frequencies are S_N between 0.6 and 3.6 and T in the range 0.9 to 4.2. These values are consistent with the mean specific frequencies for the galaxies' morphological types found by our survey and other published data. Three galaxies (NGC 5866, NGC 5813, NGC 4762) had sufficient numbers of GC candidates to investigate color bimodality and color gradients in the GC systems. NGC 5813 shows strong evidence (>3 sigma) for bimodality and a B-R color gradient resulting from a more centrally concentrated red (metal-rich) GC subpopulation. We find no evidence for statistically significant color gradients in the other two galaxies.
We present new methods for the study of a class of generating functions introduced by the second author which carry some formal similarities with the Hurwitz zeta function. We prove functional identities which establish an explicit connection with certain deformations of the Carlitz logarithm introduced by M. Papanikolas and involve the Anderson-Thakur function and the Carlitz exponential function. They collect certain functional identities in families for a new class of L-functions introduced by the first author. This paper also deals with specializations at roots of unity of these generating functions, producing a link with Gauss-Thakur sums.
We have found for the first time a Balmer edge feature in the polarized flux spectrum of a quasar (Ton 202). The edge feature is seen as a discontinuity in the slope, rather than as a discontinuity in the absolute flux. Since the polarized flux contains essentially no broad emission lines, it is considered to arise interior to the broad emission line region, showing the spectrum with all the emissions outside the nucleus scraped off and removed. Therefore, the polarized flux spectrum is likely to reveal features intrinsic to the Big Blue Bump emission. In this case, the existence of the Balmer edge feature, seen in absorption in the shorter wavelength side, indicates that the Big Blue Bump is indeed thermal and optically thick.
The effect of nuclear deformation on the isoscalar toroidal and compression dipole modes in prolate $^{170}$Yb is studied in the framework of the random-phase-approximation method with a representative set of Skyrme forces (SV-bas, SLy6, SkM$^*$ and SkI3). It is shown that the deformation crucially redistributes the strength of both modes. The compression mode has the same sequence of $\mu$=0 and 1 branches as the isovector giant dipole resonance where for prolate nuclei the $\mu=0$ mode is lower in energy ($\mu$ being the projection of the axial momentum of the mode). Instead, the toroidal mode exhibits an anomalous (opposite) sequence where the $\mu$=1 branch precedes the $\mu$=0 one.
Objects and their relationships are critical contents for image understanding. A scene graph provides a structured description that captures these properties of an image. However, reasoning about the relationships between objects is very challenging and only a few recent works have attempted to solve the problem of generating a scene graph from an image. In this paper, we present a method that improves scene graph generation by explicitly modeling inter-dependency among the entire object instances. We design a simple and effective relational embedding module that enables our model to jointly represent connections among all related objects, rather than focus on an object in isolation. Our method significantly benefits the main part of the scene graph generation task: relationship classification. Using it on top of a basic Faster R-CNN, our model achieves state-of-the-art results on the Visual Genome benchmark. We further push the performance by introducing global context encoding module and geometrical layout encoding module. We validate our final model, LinkNet, through extensive ablation studies, demonstrating its efficacy in scene graph generation.
We tackle the essential task of finding dense visual correspondences between a pair of images. This is a challenging problem due to various factors such as poor texture, repetitive patterns, illumination variation, and motion blur in practical scenarios. In contrast to methods that use dense correspondence ground-truths as direct supervision for local feature matching training, we train 3DG-STFM: a multi-modal matching model (Teacher) to enforce the depth consistency under 3D dense correspondence supervision and transfer the knowledge to 2D unimodal matching model (Student). Both teacher and student models consist of two transformer-based matching modules that obtain dense correspondences in a coarse-to-fine manner. The teacher model guides the student model to learn RGB-induced depth information for the matching purpose on both coarse and fine branches. We also evaluate 3DG-STFM on a model compression task. To the best of our knowledge, 3DG-STFM is the first student-teacher learning method for the local feature matching task. The experiments show that our method outperforms state-of-the-art methods on indoor and outdoor camera pose estimations, and homography estimation problems. Code is available at: https://github.com/Ryan-prime/3DG-STFM.