ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a new type of obstacle problem in the cylindrical domain $\Omega=D\times (0,1)$ arising from minimization of the functional $$ \int_\Omega \frac{1}{2}|\nabla u|^2+\chi_{\{v>0\}}udx, $$ where $v(x')=\int_0^1 u(x', t) dt $. We prove several existence and regularity results and show that the comparison principle does not hold for minimizers.   This problem is derived from a classical optimal rearrangement problem in a cylindrical domain, under the constraint that the force function does not depend on the $x_n$ variable of the cylindrical axis.   A mistake in the Theorem 4.2 of the previous version has been found. The statement remains an open problem.
We study the positivity of the first Chern class of a rank r Ulrich vector bundle E on a smooth n-dimensional variety $X \subseteq \mathbb P^N$. We prove that $c_1(E)$ is very positive on every subvariety not contained in the union of lines in X. In particular if X is not covered by lines, then E is big and $c_1(E)^n \ge r^n$. Moreover we classify rank r Ulrich vector bundles E with $c_1(E)^2=0$ on surfaces and with $c_1(E)^2=0$ or $c_1(E)^3=0$ on threefolds (with some exceptions).
We present a study of the dynamic magnetic properties of TiN-buffered epitaxial thin films of the Heusler alloy Fe$_{1.5}$CoGe. Thickness series annealed at different temperatures are prepared and the magnetic damping is measured, a lowest value of $\alpha=2.18\times 10^{-3}$ is obtained. The perpendicular magnetic anisotropy properties in Fe$_{1.5}$CoGe/MgO are also characterized. The evolution of the interfacial perpendicular anisotropy constant $K^{\perp}_{\rm S}$ with the annealing temperature is shown and compared with the widely used CoFeB/MgO interface. A large volume contribution to the perpendicular anisotropy of $(4.3\pm0.5)\times 10^{5}$ $\rm J/m^3$ is also found, in contrast with vanishing bulk contribution in common Co- and Fe-based Heusler alloys.
We prove a version of Rao decomposition for quasi-martingales indexed by a linearly ordered set.
Spectral population synthesis (PS) is a fundamental tool in extragalactic research that aims to decipher the assembly history of galaxies from their SED. However, until recently all PS codes were restricted to purely stellar fits, neglecting the essential contribution of nebular emission (NE). With the advent of FADO, the now possible self-consistent modelling of stellar and NE opens new routes to the exploration of galaxy SFHs. The main goal of this study is to quantitatively explore the accuracy to which FADO can recover physical and evolutionary properties of galaxies and compare its output with that from purely stellar PS codes. With this in mind, FADO and STARLIGHT were applied to synthetic SEDs that track the spectral evolution of stars and gas in extinction-free mock galaxies that form their stellar mass ($M_\star$) according to different parametric SFHs. Spectral fits were computed for two different set-ups that approximate the spectral range of SDSS and CALIFA data. Our analysis indicates that FADO can recover the key physical and evolutionary properties of galaxies, such as $M_\star$ and mass- and light-weighted mean age and metallicity, with an accuracy better than 0.2 dex. This is the case even in phases of strongly elevated sSFR and thus with considerable NE contamination. As for STARLIGHT, our analysis documents a moderately good agreement with theoretical values only for evolutionary phases for which NE drops to low levels. Indeed, fits with STARLIGHT during phases of high sSFR severely overestimate both $M_\star$ and the mass-weighted stellar age, whereas strongly underestimate the light-weighted age and metallicity. The insights from this study suggest that the neglect of nebular continuum emission in STARLIGHT and similar purely stellar PS codes could systematically impact $M_\star$ and SFH estimates for star-forming galaxies.
The observed relation between the X-ray and radio properties of low-luminosity accreting black holes has enabled the identification of multiple candidate black hole X-ray binaries (BHXBs) in globular clusters. Here we report an identification of the radio source VLA J213002.08+120904 (aka M15 S2), recently reported in Kirsten et al. 2014, as a BHXB candidate. They showed that the parallax of this flat-spectrum variable radio source indicates a 2.2$^{+0.5}_{-0.3}$ kpc distance, which identifies it as lying in the foreground of the globular cluster M15. We determine the radio characteristics of this source, and place a deep limit on the X-ray luminosity of $\sim4\times10^{29}$ erg s$^{-1}$. Furthermore, we astrometrically identify a faint red stellar counterpart in archival Hubble images, with colors consistent with a foreground star; at 2.2 kpc its inferred mass is 0.1-0.2 $M_{\odot}$. We rule out that this object is a pulsar, neutron star X-ray binary, cataclysmic variable, or planetary nebula, concluding that VLA J213002.08+120904 is the first accreting black hole X-ray binary candidate discovered in quiescence outside a globular cluster. Given the relatively small area over which parallax studies of radio sources have been performed, this discovery suggests a much larger population of quiescent BHXBs in our Galaxy, $2.6\times10^4-1.7\times10^8$ BHXBs at $3\sigma$ confidence, than has been previously estimated ($\sim10^2-10^4$) through population synthesis.
We present new H and K bands spectroscopy of 15 high luminosity active galactic nuclei (AGNs) at redshifts 2.3-3.4 obtained on Gemini South. We combined the data with spectra of additional 29 high-luminosity sources to obtain a sample with 10^{45.2}<\lambda L_{\lambda}(5100A)<10^{47.3} ergs/sec and black hole (BH) mass range, using reverberation mapping relationships based on the H_beta method, of 10^{8.8}-10^{10.7} M_sun. We do not find a correlation of L/L_Edd with M_BH but find a correlation with \lambda L_{\lambda}(5100A) which might be due to selection effects. The L/L_Edd distribution is broad and covers the range ~0.07-1.6, similar to what is observed in lower redshift, lower luminosity AGNs. We suggest that this consistently measured and calibrated sample gives the best representation of L/L_Edd at those redshifts and note potential discrepancies with recent theoretical and observational studies. The lower accretion rates are not in accord with growth scenarios for BHs at such redshifts and the growth times of many of the sources are longer than the age of the universe at the corresponding epochs. This suggests earlier episodes of faster growth at z>~3 for those sources. The use of the C IV method gives considerably different results and a larger scatter; this method seems to be a poor M_BH and L/L_Edd estimator at very high luminosity.
Quantitative characterization of galaxy morphology is vital in enabling comparison of observations to predictions from galaxy formation theory. However, without significant overlap between the observational footprints of deep and shallow galaxy surveys, the extent to which structural measurements for large galaxy samples are robust to image quality (e.g., depth, spatial resolution) cannot be established. Deep images from the Sloan Digital Sky Survey (SDSS) Stripe 82 co-adds provide a unique solution to this problem - offering $1.6-1.8$ magnitudes improvement in depth with respect to SDSS Legacy images. Having similar spatial resolution to Legacy, the co-adds make it possible to examine the sensitivity of parametric morphologies to depth alone. Using the Gim2D surface-brightness decomposition software, we provide public morphology catalogs for 16,908 galaxies in the Stripe 82 $ugriz$ co-adds. Our methods and selection are completely consistent with the Simard et al. (2011) and Mendel et al. (2014) photometric decompositions. We rigorously compare measurements in the deep and shallow images. We find no systematics in total magnitudes and sizes except for faint galaxies in the $u$-band and the brightest galaxies in each band. However, characterization of bulge-to-total fractions is significantly improved in the deep images. Furthermore, statistics used to determine whether single-S\'ersic or two-component (e.g., bulge+disc) models are required become more bimodal in the deep images. Lastly, we show that asymmetries are enhanced in the deep images and that the enhancement is positively correlated with the asymmetries measured in Legacy images.
Visual dialog is a challenging task that requires the comprehension of the semantic dependencies among implicit visual and textual contexts. This task can refer to the relation inference in a graphical model with sparse contexts and unknown graph structure (relation descriptor), and how to model the underlying context-aware relation inference is critical. To this end, we propose a novel Context-Aware Graph (CAG) neural network. Each node in the graph corresponds to a joint semantic feature, including both object-based (visual) and history-related (textual) context representations. The graph structure (relations in dialog) is iteratively updated using an adaptive top-$K$ message passing mechanism. Specifically, in every message passing step, each node selects the most $K$ relevant nodes, and only receives messages from them. Then, after the update, we impose graph attention on all the nodes to get the final graph embedding and infer the answer. In CAG, each node has dynamic relations in the graph (different related $K$ neighbor nodes), and only the most relevant nodes are attributive to the context-aware relational graph inference. Experimental results on VisDial v0.9 and v1.0 datasets show that CAG outperforms comparative methods. Visualization results further validate the interpretability of our method.
We consider non-negative solutions of the fast diffusion equation $u_t=\Delta u^m$ with $m \in (0,1)$, in the Euclidean space R^d, d?3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to $t\to\infty$ for $m\ge m_c=(d-2)/d$, or as t approaches the extinction time when m < mc. For a class of initial data we prove that the solution converges with a polynomial rate to a self-similar solution, for t large enough if $m\ge m_c$, or close enough to the extinction time if m < mc. Such results are new in the range $m\le m_c$ where previous approaches fail. In the range mc < m < 1 we improve on known results.
In a typical exclusive quarkonium production process, when the center-of-mass energy, $\sqrt{s}$, is much greater than the heavy quark mass $m$, large kinematic logarithms of $s/m^2$ will unavoidably arise at each order of perturbative expansion in the short-distance coefficients of the nonrelativistic QCD (NRQCD) factorization formalism, which may potentially harm the perturbative expansion. This symptom reflects that the hard regime in NRQCD factorization is too coarse and should be further factorized. We suggest that this regime can be further separated into "hard" and "collinear" degrees of freedom, so that the familiar light-cone approach can be employed to reproduce the NRQCD matching coefficients at the zeroth order of $m^2/s$ and order by order in $\alpha_s$. Taking two simple processes, exclusive $\eta_b+\gamma$ production in $e^+ e^-$ annihilation and Higgs boson radiative decay into $\Upsilon$, as examples, we illustrate how the leading logarithms of $s/m^2$ in the NRQCD matching coefficients are identified and summed to all orders in $\alpha_s$ with the aid of Brodsky-Lepage evolution equation.
We show that temperature of a current (I = 20 mA) carrying manganite (Nd0.5Ca0.5Mn0.93Ni0.07O3) in presence of a magnetic field (H) decreases abruptly as much as deltaT = 45 K (7 K) accompanied by a step like decrease in magnetoresistance at a critical value of H when the base temperature is 40 K (100 K). The magnitude of deltaT and the position of magnetoresistance step decrease towards lower H with decreasing amplitude of the current. We discuss possible origins of the current and magnetic- field driven temperature change which may find applications in magnetothermal refrigeration besides magnetocaloric effect.
In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. We will adopt the weak convergence approach. Because of the appearance of jumps, this result is significantly different from that in Gaussian case.
We study the orbital stablity and instability of solitary wave solutions for nonlinear Schr\"odinger equations of derivative type.
This is the first in a series of articles on the moduli spaces of Burniat surfaces. We prove that Burniat surfaces are Inoue surfaces and we calculate their fundamental groups. As a main result of this paper we prove that every smooth projective surface which is homotopically equivalent to a primary Burniat surface (i.e., a Burniat surface with K^2 = 6) is indeed a primary Burniat surface.
We study the radio--FIR correlation between the nonthermal (synchrotron) radio continuum emission at \lambda 90 cm (333 MHz) and the far infrared emission due to cool (~20 K) dust at \lambda 70\mu m in spatially resolved normal galaxies at scales of ~1 kpc. The slope of the radio--FIR correlation significantly differs between the arm and interarm regions. However, this change is not evident at a lower wavelength of \lambda 20 cm (1.4 GHz). We find the slope of the correlation in the arm to be 0.8 \pm 0.12 and we use this to determine the coupling between equipartition magnetic field (B_{eq}) and gas density (\rho_{gas}) as B_{eq} \propto \rho_{gas}^{0.51 \pm 0.12}. This is close to what is predicted by MHD simulations of turbulent ISM, provided the same region produces both the radio and far infrared emission. We argue that at 1 kpc scales this condition is satisfied for radio emission at 1.4 GHz and may not be satisfied at 333 MHz. Change of slope observed in the interarm region could be caused by propagation of low energy (~1.5 GeV) and long lived (~ 10^8 yr) cosmic ray electrons at 333 MHz.
In this work, we describe the Cohen-Macaulay space CM of twisted cubics parameterizing curves $C$ together with a finite map $i: C \to \mathbb{P}^3$ that is generically a closed immersion and such that $C$ has Hilbert polynomial $p(t)=3t+1$ with respect to $i$. We show that CM is irreducible, smooth and birational to one component of the Hilbert scheme of twisted cubics.
We give a procedure for reconstructing a magnetic field and electric potential from boundary measurements related to the magnetic Schroedinger operator in three and higher dimensions.
Based on density functional calculations, we present a detailed theoretical study of the electronic structure and the magnetic properties of the quasi-one dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we find alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical point at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study in detail the influence of structural peculiarities such as the reported Li disorder and the non-planar chain geometry on the magnetic interactions combining the results of LDA based tight-binding models with LDA+U derived exchange parameters. Our investigation is complemented by an exact diagonalization study of a multi-band Hubbard model for finite clusters predicting a strong temperature dependence of the optical conductivity for Li_2ZrCuO_4.
In order to understand the formation and evolution of galaxies fully, it is important to study their three-dimensional gravitational potential for a large sample of galaxies. Since polar-ring galaxies (PRGs) provide useful laboratories for this investigation, we have started our detailed study of a sample of known PRGs by using the data set obtained by the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). During the course of this study, we have discovered a new PRG, identified as SDSS J095351.58+012036.1. Its photometric redshift is estimated as z ~ 0.2. The polar ring structure in this PRG appears to be almost perpendicular to the disk of its host galaxy without any disturbed features. Therefore, this PRG will provide us with useful information on the formation of such an undisturbed polar structure. We discuss its photometric properties in detail.
Transformations of coherent states of the free particle by bounded and semibounded symmetry operators are considered. Resolution of the identity operator in terms of the transformed states is analyzed. A generalized identity resolution is formulated. Darboux transformation operators are analyzed as operators defined in a Hilbert space. Coherent states of multisoliton potentials are studied.
A detailed analysis has been made by R.Zavin and N.Moiseyev(2004 J. Phys. A: Math, Gen, \textbf{37} 4619) for the change of bound states into resonance states via coalescence of virtual states in a one-dimensional symmetric rectangular attractive potential as it becomes shallow, with convergent wave functions of virtual and resonance states by the complex scaling method. As a complement to such an analysis, we discuss some global features of the pole spectrum of the S-matrix by using a complex extension of the real potential $V^{(\mathrm{real})}$ to $e^{i\alpha}V^{(\mathrm{real})}$ with a real phase $\alpha$. We show the structures of trajectories of poles developed for the change of $\alpha$ in the complex momentum plane, which is useful to understand the mutual transformation among the bound, virtual and resonance states.
Roughly 10% of quasars are "radio-loud", producing copious radio emission in large jets. The origin of the low-level radio emission seen from the remaining 90% of quasars is unclear. Observing a sample of eight radio-quiet quasars with the Very Long Baseline Array, we discovered that their radio properties depend strongly on their Eddington ratio (r_Edd=L_AGN/L_Edd). At lower Eddington ratios (r_Edd < 0.3), the total radio emission of the AGN predominately originates from an extremely compact region, possibly as small as the accretion disk. At higher Eddington ratios (r_Edd > 0.3), the relative contribution of this compact region decreases significantly, and though the total radio power remains about the same, the emission now originates from regions >100 pc large. The change in the physical origin of the radio-emitting plasma region with r_Edd is unexpected, as the properties of radio-loud quasars show no dependence with Eddington ratio. Our results suggest that at lower Eddington ratios the magnetised plasma is likely confined by the accretion disk corona, and only at higher Eddington ratios escapes to larger scales. Stellar-mass black holes show a similar dependence of their radio properties on the accretion rate, supporting the paradigm which unifies the accretion onto black holes across the mass range.
We present angle-resolved photoemission spectra of the $\gamma$-phase of manganese as well as a theoretical analysis using a recently developed approach that combines density functional and dynamical mean field methods (LDA+DMFT). The comparison of experimental data and theoretical predictions allows us to identify effects of the Coulomb correlations, namely the presence of broad and undispersive Hubbard bands in this system.
We propose a cost volume-based neural network for depth inference from multi-view images. We demonstrate that building a cost volume pyramid in a coarse-to-fine manner instead of constructing a cost volume at a fixed resolution leads to a compact, lightweight network and allows us inferring high resolution depth maps to achieve better reconstruction results. To this end, we first build a cost volume based on uniform sampling of fronto-parallel planes across the entire depth range at the coarsest resolution of an image. Then, given current depth estimate, we construct new cost volumes iteratively on the pixelwise depth residual to perform depth map refinement. While sharing similar insight with Point-MVSNet as predicting and refining depth iteratively, we show that working on cost volume pyramid can lead to a more compact, yet efficient network structure compared with the Point-MVSNet on 3D points. We further provide detailed analyses of the relation between (residual) depth sampling and image resolution, which serves as a principle for building compact cost volume pyramid. Experimental results on benchmark datasets show that our model can perform 6x faster and has similar performance as state-of-the-art methods. Code is available at https://github.com/JiayuYANG/CVP-MVSNet
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a complex network extended by the additional transition, called hereafter the gate. The random skips through the gate, driven by the external constant force, violate the detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge, regardless of the network topology, to the normal distribution. This result, combined with the stationary fluctuation theorem, permits to show that its standard deviation depends directly on the square root of the average flux. In turn, the central result of our paper relates this quantity to the external constant force and the two parameters that entirely characterize the normal distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of the computer simulations are widely discussed in terms of the rigorous theoretical predictions.
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a source for these wave equations. We demonstrate that this splitting method allows for the accurate simulation of compact objects, with gravitational field strengths less than or equal to those of neutron stars. This method could thus provide a straightforward path for general relativistic effects to be added to astrophysics simulations, such as in core collapse, accretion disks, and extreme mass ratio systems.
With recent Chandra observations, at least 60% of the 2-10 keV background is now resolved into discrete sources. Here we present deep optical, NIR, submm, and 20 cm (radio) images, as well as high-quality optical spectra, of a complete sample of 20 hard X-ray sources in a deep Chandra observation of the SSA13 field. The thirteen I<23.5 galaxies have redshifts in the range 0.1 to 2.6. Two are quasars, five show AGN signatures, and six are z<1.5 luminous bulge-dominated galaxies whose spectra show no obvious optical AGN signatures. The seven spectroscopically unidentified sources have colors that are consistent with evolved early galaxies at z=1.5-3. Only one hard X-ray source is significantly detected in an ultradeep submm map; its millimetric redshift is in the range z=1.2-2.4. None of the remaining 19 sources is detected in the submm. These results probably reflect the fact that the 850-micron flux limits obtainable with SCUBA are quite close to the expected fluxes from obscured AGN. The hard X-ray sources have an average L(FIR)/L(2-10 keV)~60, similar to that of local obscured AGN. The same ratio for a sample of submm selected sources is in excess of 1100, suggesting that their FIR light is primarily produced by star formation. Our data show that luminous hard X-ray sources are common in bulge-dominated optically luminous galaxies. We use our measured bolometric corrections with the 2-10 keV EBL to infer the growth of supermassive black holes. Even with a high radiative efficiency of accretion (e=0.1), the black hole mass density required to account for the observed light is comparable to the local black hole mass density. (Abridged)