ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution and any function that satisfies the boundary condition and is admissible with respect to the obstacle condition (i.e., it is valid for any approximation regardless of the method by which it was found). Computation of the estimates does not require knowledge of the exact solution and uses only the problem data and an approximation. The estimates provide guaranteed upper bounds of the error (error majorants) and vanish if and only if the approximation coincides with the exact solution. In the last section, the efficiency of error majorants is confirmed by an example, where the exact solution is known.
In the literature one often finds the claim that there is no such thing as an energy-momentum tensor for the gravitational field, and consequently, that the total energy-momentum conservation can only be defined in terms of a gravitational energy-momentum pseudo-tensor. Nevertheless, by relaxing the assumption that gravitational energy-momentum tensor should only depend on first derivatives of the metric, the Einstein equation leads to a trivial result that gravitational energy-momentum tensor is essentially the Einstein tensor. We discuss various peculiarities of such a definition of energy-momentum are argue that all these peculiarities have a sensible physical interpretation.
We study the analogue of Poisson ensembles of Markov loops ('loop soups') in the setting of one-dimensional diffusions. We give a detailed description of the corresponding intensity measure. The properties of this measure on loops lead us to an extension of Vervaat's bridge-to-excursion transformation that relates the bridges conditioned by their minimum and the excursions of all the diffusion we consider and not just the Brownian motion. Further we describe the Poisson point process of loops, their occupation fields and explain how to sample these Poisson ensembles of loops using two-dimensional Markov processes. Finally we introduce a couple of interwoven determinantal point processes on the line which is a dual through Wilson's algorithm of Poisson ensembles of loops and study the properties of these determinantal point processes.
A new scheme was recently proposed in which the usual SU(3) quadrupole-quadrupole interaction was replaced by an O(6) cubic interaction in the Interacting Boson Model, and also successfully applied to the description of $^{152}$Sm for the N = 90 rare earth isotones with X(5) symmetry. By using this new scheme, in the present work, we further explore the properties of another candidate of $^{150}$Nd for the N=90 with X(5) symmetry. The low-lying energy levels and E2 transition rates are calculated and compared with the experimental data. The results show that the new scheme can also reasonably describe the experimental low-lying spectrum and the intraband and the interband E2 transitions for $^{150}$Nd. However, for the low-lying spectrum, the O(6) cubic interaction seems better in describing the energy levels, especially in higher excited states and $\gamma$ band, yet the $0^{+}_{2}$ level within the $\beta$ band is lower than the corresponding experimental value and, the U(5)-SU(3) scheme seems better to describe the low-lying levels of $\beta$ band; and for the B(E2) transition, for the intraband transitions within the ground band and some interband transitions between the $\beta$ band and the ground band, the results from O(6) cubic interaction are better than those from SU(3) quadrupole-quadrupole interaction, yet of which seems better to describe the intraband E2 transitions within $\beta$ band. The present work is very meaningful in helping us to deeply understand the new characteristics of symmetry by the higher order O(6) cubic interaction.
2MASS J07024146-0235017 = GDS J0702414-023501 was included in the "Catalogue enriched with R CrB stars" on grounds of its near- and mid-infrared colours. The object, which corresponds to the carbon star IRAS 07001-0230 = CGCS 6197, has been found to exhibit large amplitude variability in its Bochum Galactic Disk Survey light curve. Taking into account all available data, GDS J0702414-023501 is here proposed as a new candidate Mira star.
Understanding traffic density from large-scale web camera (webcam) videos is a challenging problem because such videos have low spatial and temporal resolution, high occlusion and large perspective. To deeply understand traffic density, we explore both deep learning based and optimization based methods. To avoid individual vehicle detection and tracking, both methods map the image into vehicle density map, one based on rank constrained regression and the other one based on fully convolution networks (FCN). The regression based method learns different weights for different blocks in the image to increase freedom degrees of weights and embed perspective information. The FCN based method jointly estimates vehicle density map and vehicle count with a residual learning framework to perform end-to-end dense prediction, allowing arbitrary image resolution, and adapting to different vehicle scales and perspectives. We analyze and compare both methods, and get insights from optimization based method to improve deep model. Since existing datasets do not cover all the challenges in our work, we collected and labelled a large-scale traffic video dataset, containing 60 million frames from 212 webcams. Both methods are extensively evaluated and compared on different counting tasks and datasets. FCN based method significantly reduces the mean absolute error from 10.99 to 5.31 on the public dataset TRANCOS compared with the state-of-the-art baseline.
In this paper, we study the occurrence of patterns in the cycle structures of permutations.
We present the first extensive and detailed theoretical scenario for the interpretation of Cepheid properties observed in the SDSS filters. Three sets of nonlinear convective pulsation models, corresponding to the chemical compositions of Cepheids in the Milky Way, the Large Magellanic Cloud and the Small Magellanic Cloud respectively, are transformed into the SDSS bands by relying on updated model atmospheres. The resulting observables, namely the instability strip boundaries and the light curves, as well as the Period-Luminosity, the Wesenheit and the Period-Luminosity-Colour relations, are discussed as a function of the metal content, for both the fundamental and the first overtone mode. The fundamental PL relations are found to deviate from linear relations when computed over the whole observed Cepheid period range, especially at the shorter wavelenghts, confirming previous findings in the Johnson-Cousins bands. The obtained slopes are found to be mildly steeper than the ones of the semiempirical and the empirical relations available in the literature and covering roughly the same period range, with the discrepancy ranging from about 13% in u-band to about 3% in z.
We consider different types of external color sources that move through a strongly-coupled thermal N=4 super-Yang-Mills plasma, and calculate, via the AdS/CFT correspondence, the dissipative force (or equivalently, the rate of energy loss) they experience. A bound state of k quarks in the totally antisymmetric representation is found to feel a force with a nontrivial k-dependence. Our result for k=1 (or k=N-1) agrees at large N with the one obtained recently by Herzog et al. and Gubser, but contains in addition an infinite series of 1/N corrections. The baryon (k=N) is seen to experience no drag. Finally, a heavy gluon is found to be subject to a force which at large N is twice as large as the one experienced by a heavy quark, in accordance with gauge theory expectations.
LS~5039 is a powerful gamma-ray binary that probably hosts a non-accreting pulsar. Despite the wealth of data available, the power source of the non-thermal emitter is still unknown. We use a dynamical-radiative numerical model and multiwavelength data to constrain the properties of a pulsar wind that may power the non-thermal emitter in LS~5039. We ran simulations of an ultrarelativistic (low-$B$) cold $e^\pm$-wind that Compton scatters stellar photons and that dynamically interacts with the stellar wind. The effects of energy losses on the unshocked $e^\pm$-wind dynamics, and the geometry of the two-wind contact discontinuity, are computed for different wind models. The predicted unshocked $e^\pm$-wind radiation at periastron, when expected to be highest, is compared to LS~5039 data. The minimum possible radiation from an isotropic cold $e^\pm$-wind overpredicts the X-ray to gamma-ray fluxes at periastron by a factor of $\sim 3$. In the anisotropic wind case X-ray and $\gtrsim 100$ MeV data are not violated by wind radiation if the wind axis is at $\lesssim 20-40^\circ$ from the line of sight (probability of $\lesssim 6-24$\%), depending on the anisotropic wind model, or if the wind Lorentz factor $\in 10^2-10^3$, in which case the wind power can be higher, but it requires $e^\pm$-multiplicities of $\sim 10^6$ and $10^9$ for a $10^{-2}$~s and 10~s pulsar period, respectively. The studied model predicts that a low-$B$ cold pulsar $e^\pm$-wind in LS~5039 should be strongly anisotropic, with either a wind Lorentz factor $\in 10^2-10^3$ and very high multiplicities or with a fine-tuned wind orientation. A low-$B$, cold baryon-dominated wind would be possible, but then the multiplicities should be rather low, while the baryon-to-$e^\pm$ energy transfer should be very efficient at wind termination. A strongly magnetized cold wind seems to be the most favorable (least constrained) option.
We consider a system arising from a nonrelativistic Chern-Simon-Higgs model, in which a charged field is coupled with a gauge field. We prove an existence result for small coupling constants.
We employ triplet loss as a feature embedding regularizer to boost classification performance. Standard architectures, like ResNet and Inception, are extended to support both losses with minimal hyper-parameter tuning. This promotes generality while fine-tuning pretrained networks. Triplet loss is a powerful surrogate for recently proposed embedding regularizers. Yet, it is avoided due to large batch-size requirement and high computational cost. Through our experiments, we re-assess these assumptions.   During inference, our network supports both classification and embedding tasks without any computational overhead. Quantitative evaluation highlights a steady improvement on five fine-grained recognition datasets. Further evaluation on an imbalanced video dataset achieves significant improvement. Triplet loss brings feature embedding characteristics like nearest neighbor to classification models. Code available at \url{http://bit.ly/2LNYEqL}.
State-of-the-art methods for 3D reconstruction of faces from a single image require 2D-3D pairs of ground-truth data for supervision. Such data is costly to acquire, and most datasets available in the literature are restricted to pairs for which the input 2D images depict faces in a near fronto-parallel pose. Therefore, many data-driven methods for single-image 3D facial reconstruction perform poorly on profile and near-profile faces. We propose a method to improve the performance of single-image 3D facial reconstruction networks by utilizing the network to synthesize its own training data for fine-tuning, comprising: (i) single-image 3D reconstruction of faces in near-frontal images without ground-truth 3D shape; (ii) application of a rigid-body transformation to the reconstructed face model; (iii) rendering of the face model from new viewpoints; and (iv) use of the rendered image and corresponding 3D reconstruction as additional data for supervised fine-tuning. The new 2D-3D pairs thus produced have the same high-quality observed for near fronto-parallel reconstructions, thereby nudging the network towards more uniform performance as a function of the viewing angle of input faces. Application of the proposed technique to the fine-tuning of a state-of-the-art single-image 3D-reconstruction network for faces demonstrates the usefulness of the method, with particularly significant gains for profile or near-profile views.
Let $\Gamma$ be a finite rank subgroup of $\overline{\mathbb{Q}}^*$. We prove that the multiplicative group of the field generated by all elements in the divisible hull of $\Gamma$, is free abelian modulo this divisible hull. This proves that a necessary condition for R\'emond's generalized Lehmer conjecture is satisfied.
A global equilibrium state of a spin polarized fluid that undergoes constant acceleration along the stream lines is described as a solution of recently introduced perfect-fluid hydrodynamic equations with spin 1/2.
We present elemental abundances and stellar population ages for 68 massive quiescent galaxies at $0.59\leq z\leq0.75$ from the LEGA-C survey. The abundance patterns and ages, derived from full-spectrum modeling, are examined as a function of stellar mass ($M_*$) and size (i.e., half-light radius; $R_e$). We find that both [Mg/H] and [Fe/H] do not vary with stellar mass but are correlated with $M_*/R_e$ for quiescent galaxies with $M_*>10^{10.5} M_\odot$. Thus, at fixed mass, compact quiescent galaxies are on average more metal rich. This result reinforces the picture that supernova feedback and gravitational potential regulate chemical enrichment. [Mg/Fe] does not vary with $M_*$ or $M_*/R_e$, but there is a marginal positive relation between age and mass. Our results support low-redshift findings that more massive galaxies form their stars at earlier times. However, in contrast to low-redshift studies, star formation timescale does not appear to depend on mass or size. We also compare the mass-[Fe/H] and mass-[Mg/H] relations to stacks of quiescent galaxies at $z\sim0$ and find that both relations increase by $\sim0.2$ dex over the past 7 Gyr. Furthermore, at $z\sim0.7$ we find a clear trend with age, such that older quiescent galaxies have lower metallicities. Both results can be explained by a chemical evolution model in which galaxies quench via gas removal. Future work, in particular with JWST/NIRSpec, will extend this analysis to higher redshifts, allowing us to fully exploit abundance patterns to study the formation histories of quiescent galaxies.
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite amount of time depending upon the initial data. In the target problem, some $p$-th or $q$-th order perturbation term may work to blow up within this period. The problem arises from the conflict between the diffusion and the blow up, in the bulk and on the boundary. Firstly, the local existence and uniqueness of the solution are obtained. Finally, a result of finite time extinction for some small initial data is presented.
Recently, emergent symmetry is one of fast-growing intriguing issues in many-body systems. Its roles and consequential physics have not been well understood in quantum phase transitions. Emergent symmetry of degenerate groundstates is discussed in possible connection to spontaneous symmetry breaking within the Landau theory. For a clear discussion, a quantum spin-$1/2$ plaquette chain system is shown to have rich emergent symmetry phenomena in its groundstates. A covering symmetry group over all emergent symmetries responsible for degenerate groundstates in the plaquette chain system is found to correspond to a largest common symmetry group of constituent Hamiltonians describing the plaquette system. Consequently, this result suggests that, as a guiding symmetry principle in quantum phase transitions, {\it degenerate groundstates are induced by a spontaneous breaking of symmetries belonging to a largest common symmetry group of continent Hamiltonians describing a given system but can have more symmetries than the largest common symmetry}.
Lots of information on solar-like oscillations in red giants has been obtained thanks to observations with CoRoT and Kepler space telescopes. Data on dipolar modes appear most interesting. We study properties of dipolar oscillations in luminous red giants to explain mechanism of mode trapping in the convective envelope and to assess what may be learned from the new data. Equations for adiabatic oscillations are solved by numerical integration down to the bottom of convective envelope, where the boundary condition is applied. The condition is based on asymptotic decomposition of the fourth order system into components describing a running wave and a uniform shift of radiative core. If the luminosity of a red giant is sufficiently high, for instance at M = 2 Msun greater than about 100 Lsun, the dipolar modes become effectively trapped in the acoustic cavity, which covers the outer part of convective envelope. Energy loss caused by gravity wave emission at the envelope base is a secondary or negligible source of damping. Frequencies are insensitive to structure of the deep interior.
Two blue compact dwarf galaxies Mkn 104 and I Zw 97 are studied photometrically and spectroscopically. Mkn 104 is found to contain three distinct bright star forming regions, whereas I Zw 97 is found to contain three bright and two faint star forming regions. Medium resolution spectra of three bright HII regions in the two galaxies were obtained. Estimation of oxygen abundance in these regions yields a value equal to log(O/H)+12 = 8.5 (Z=Z_sun/2.7). Star formation rates in these star forming regions are estimated. The highest star formation rate for I Zw 97 is found to be 0.04 M_sun/yr and for Mkn 104, it is 0.02 M_sun/yr. A U-B vs V-I colour-colour mixed population model is created using the Starburst99 evolutionary model curves. The spectrum of the bright star forming knot of I Zw 97 does not show any strong signature of an underlying relatively older stellar population, but the U-B vs V-I two colour diagram indicates a strong contribution of a ~500 Myr population. The age of the underlying population of Mkn 104 using the U-B vs V-I two colour diagram is estimated to be ~500 Myr. The surface brightness profile of both the galaxies can be represented well by a two-component Sersic profile consisting of a near exponential distribution and a Gaussian nuclear starburst. I Zw 97 is a cometary blue compact dwarf galaxy where the underlying low surface brightness (LSB) galaxy is a dwarf irregular observed during a major stochastic enhancement of its otherwise moderate star formation activity. Both these galaxies are very similar in their stellar content, showing an older 4 Gyr population, an intermediate 500 Myr population and the current burst of star formation of age 5-13 Myr.
Almost all existing methods for image restoration are based on optimizing the mean squared error (MSE), even though it is known that the best estimate in terms of MSE may yield a highly atypical image due to the fact that there are many plausible restorations for a given noisy image. In this paper, we show how to combine explicit priors on patches of natural images in order to sample from the posterior probability of a full image given a degraded image. We prove that our algorithm generates correct samples from the distribution $p(x|y) \propto \exp(-E(x|y))$ where $E(x|y)$ is the cost function minimized in previous patch-based approaches that compute a single restoration. Unlike previous approaches that computed a single restoration using MAP or MMSE, our method makes explicit the uncertainty in the restored images and guarantees that all patches in the restored images will be typical given the patch prior. Unlike previous approaches that used implicit priors on fixed-size images, our approach can be used with images of any size. Our experimental results show that posterior sampling using patch priors yields images of high perceptual quality and high PSNR on a range of challenging image restoration problems.
Near-infrared (NIR) integral-field spectroscopy (IFS) of violent starburst environments at high spatial (and spectral) resolution has the potential to revolutionise our ideas regarding the local interactions between the newly-formed massive stars and the interstellar medium (ISM) of their host galaxies. To illustrate this point, I present NIR IFS analysis of the central starburst region of NGC 1140, obtained with CIRPASS on Gemini-South. While strong [FeII] emission is found throughout the galaxy, higher-order Brackett emission is predominantly associated with the northern starburst region. Based on the spatial distributions of the [FeII] versus Brackett line emission, I conclude that a galaxy-wide starburst was induced several x 10^7 yr ago, with more recent starburst activity concentrated around the northern starburst region. I look forward and discuss the exciting prospects that IFS at higher spatial (and spectral) resolution will allow us trace (i) the massive outflows ("superwinds") expected to originate in the dense, young massive star clusters commonly found in intense starburst environments, and (ii) their impact on the galaxy's ISM.
We report the discovery of a very young high-mass X-ray binary (HMXB) system associated with the supernova remnant (SNR) MCSNRJ0513-6724 in the Large Magellanic Cloud (LMC), using XMM-Newton X-ray observations. The HMXB is located at the geometrical centre of extended soft X-ray emission, which we confirm as an SNR. The HMXB spectrum is consistent with an absorbed power law with spectral index ~1.6 and a luminosity of 7x10^{33} ergs/s (0.2--12 keV). Tentative X-ray pulsations are observed with a periodicity of 4.4 s and the OGLE I-band light curve of the optical counterpart from more than 17.5 years reveals a period of 2.2324\pm0.0003 d, which we interpret as the orbital period of the binary system. The X-ray spectrum of the SNR is consistent with non-equilibrium shock models as expected for young/less evolved SNRs. From the derived ionisation time scale we estimate the age of the SNR to be <6 kyr. The association of the HMXB with the SNR makes it the youngest HMXB, in the earliest evolutionary stage known to date. A HMXB as young as this can switch on as an accreting pulsar only when the spin period has reached a critical value. Under this assumption, we obtain an upper limit to the magnetic field of < 5x10^{11} G. This implies several interesting possibilities including magnetic field burial, possibly by an episode of post-supernova hyper-critical accretion. Since these fields are expected to diffuse out on a timescale of 10^{3}-10^{4} years, the discovery of a very young HMXB can provide us the unique opportunity to observe the evolution of the observable magnetic field for the first time in X-ray binaries.
In this paper we generalize the martingale of Kella and Whitt to the setting of L\'{e}vy-type processes and show that the (local) martingales obtained are in fact square integrable martingales which upon dividing by the time index converge to zero a.s. and in $L^2$. The reflected L\'{e}vy-type process is considered as an example.
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group (DMRG) simulation, we identify a metal-insulator transition around $U_c/t=2.5\sim3$. In the vicinity of $U_c$, we find strong spin/orbital density wave fluctuations at commensurate wavevectors, accompanied by weaker incommensurate charge density wave (CDW) fluctuations. The spin/orbital density wave fluctuations are enhanced with increasing system sizes, suggesting the possible emergence of long-range order in the two dimensional limit. At larger $U$, our calculations indicate a possible nonmagnetic Mott insulator phase without spin or orbital polarization. Our findings offer new insights into correlated electron phenomena in twisted bilayer graphene and other multi-orbital honeycomb materials.