ShantanuT01/DACTYL-Pretraining huggingface dataset:
Ricci collineations and Ricci inheritance collineations of Friedmann-Robertson-Walker spacetimes are considered. When the Ricci tensor is non-degenerate, it is shown that the spacetime always admits a fifteen parameter group of Ricci inheritance collineations; this is the maximal possible dimension for spacetime manifolds. The general form of the vector generating the symmetry is exhibited. It is also shown, in the generic case, that the group of Ricci collineations is six-dimensional and coincides with the isometry group. In special cases the spacetime may admit either one or four proper Ricci collineations in addition to the six isometries. These special cases are classified and the general form of the vector fields generating the Ricci collineations is exhibited. When the Ricci tensor is degenerate, the groups of Ricci inheritance collineations and Ricci collineations are infinite-dimensional. General forms for the generating vectors are obtained. Similar results are obtained for matter collineations and matter inheritance collineations.
Given two consecutive frames from a pair of stereo cameras, 3D scene flow methods simultaneously estimate the 3D geometry and motion of the observed scene. Many existing approaches use superpixels for regularization, but may predict inconsistent shapes and motions inside rigidly moving objects. We instead assume that scenes consist of foreground objects rigidly moving in front of a static background, and use semantic cues to produce pixel-accurate scene flow estimates. Our cascaded classification framework accurately models 3D scenes by iteratively refining semantic segmentation masks, stereo correspondences, 3D rigid motion estimates, and optical flow fields. We evaluate our method on the challenging KITTI autonomous driving benchmark, and show that accounting for the motion of segmented vehicles leads to state-of-the-art performance.
We develop a theory for energy and spatially resolved tunneling spectroscopy of topological quantum spin Hall helical states driven out of equilibrium. When a helical liquid is constrained between two superconducting reservoirs transport at the edge is governed by multiple Andreev reflections. The resulting quasiparticle distribution functions of the edge channels exhibit multiple discontinuities at subgap energies with the periodicity of an applied voltage. The combined effect of interactions, disorder, and normal scattering off the superconducting interface leads to the inelastic processes mixing different helicity modes, thus causing smearing of these singularities. If equilibration is strong, then the distribution functions of the edge channels tend to collapse into a Fermi-like function with an effective temperature determined by the superconducting gap, applied voltage, and intraedge interaction parameter. We conclude that mapping out nonequilibrium distribution functions may help to quantify the relative importance of various relevant perturbations that spoil ideally ballistic edge transport.
We present the results of a weak gravitational lensing analysis to determine whether the stellar mass or the velocity dispersion is more closely related to the amplitude of the lensing signal around galaxies - and hence to the projected distribution of dark matter. The lensing signal on scales smaller than the virial radius corresponds most closely to the lensing velocity dispersion in the case of a singular isothermal profile, but is on larger scales also sensitive to the clustering of the haloes. We select over 4000 lens galaxies at a redshift z<0.2 with concentrated (or bulge-dominated) surface brightness profiles from the ~300 square degree overlap between the Red-sequence Cluster Survey 2 (RCS2) and the data release 7 (DR7) of the Sloan Digital Sky Survey (SDSS). We consider both the spectroscopic velocity dispersion and a model velocity dispersion (a combination of the stellar mass, the size and the Sersic index of a galaxy). Comparing the model and spectroscopic velocity dispersion we find that they correlate well for galaxies with concentrated brightness profiles. We find that the stellar mass and the spectroscopic velocity dispersion trace the amplitude of the lensing signal on small scales equally well. The model velocity dispersion, however, does significantly worse. A possible explanation is that the halo properties that determine the small-scale lensing signal - mainly the total mass - also depend on the structural parameters of galaxies, such as the effective radius and Sersic index, but we lack data for a definitive conclusion.
Based on some elementary estimates for the space-time derivatives of the heat kernel, we use a bootstrapping approach to establish the optimal decay rates for the $L^q(\mathbb{R}^d)$ ($1\leq q\leq\infty$, $d\in\mathbb{N}$) norm of the space-time derivatives of solutions to the (modified) Patlak-Keller-Segel equations with initial data in $L^1(\mathbb{R}^d)$, which implies the joint space-time analyticity of solutions. When the $L^1(\mathbb{R}^d)$ norm of the initial datum is small, the upper bound for the decay estimates is global in time, which yields a lower bound on the growth rate of the radius of space-time analyticity in time. As a byproduct, the space analyticity is obtained for any initial data in $L^1(\mathbb{R}^d)$. The decay estimates and space-time analyticity are also established for solutions bounded in both space and time variables. The results can be extended to a more general class of equations, including the Navier-Stokes equations.
In this paper we localize some of Watanabe's results on fractional Wiener functionals, and use them to give a precise estimate of the difference between two Donsker's delta functionals even with fractional differentiability. As an application, the convergence rate of the density of the Euler scheme for non-Markovian stochastic differential equations is obtained.
We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with thermodynamic Bethe ansatz results.
We propose a model of the evolution of the tachyonic scalar field over two phases in the universe. The field components do not interact in phase I, while in the subsequent phase II, they change flavours due to relative suppression of the radiation contribution. In phase II, we allow them to interact mutually with time-independent perturbation in their equations of state, as Shifted Cosmological Parameter (SCP) and Shifted Dust Matter (SDM). We determine the solutions of their scaling with the cosmic redshift in both phases. We further suggest the normalized Hubble function diagnostic, which, together with the low- and high-redshift $H(z)$ data and the concordance values of the present density parameters from the CMBR, BAO statistics etc., constrains the strength of interaction, by imposing the viable conditions to break degeneracy in 3-parameter $(\gamma, \varepsilon, \dot{\phi}^2)$ space. The range of redshifts $(z=0.1$ to $z=1.75)$ is chosen to highlight the role of interaction during structure formation, and it may lead to a future analysis of power spectrum in this model \emph{vis a vis} Warm Dark Matter (WDM) or $\Lambda$CDM models. We further calculate the influence of interaction in determining the age of the universe at the present epoch, within the degeneracy space of model parameters.
Overcomplete families of states of the type of Barut-Girardello coherent states (BG CS) are constructed for noncompact algebras $u(p,q)$ and $sp(N,C)$ in quadratic bosonic representation. The $sp(N,C)$ BG CS are obtained in the form of multimode ordinary Schr\"odinger cat states. A set of such macroscopic superpositions is pointed out which is overcomplete in the whole $N$ mode Hilbert space (while the associated $sp(N,C)$ representation is reducible). The multimode squared amplitude Schr\"odinger cat states are introduced as macroscopic superpositions of the obtained $sp(N,C)$ BG CS.}
The development of scene text recognition (STR) in the era of deep learning has been mainly focused on novel architectures of STR models. However, training protocol (i.e., settings of the hyper-parameters involved in the training of STR models), which plays an equally important role in successfully training a good STR model, is under-explored for scene text recognition. In this work, we attempt to improve the accuracy of existing STR models by searching for optimal training protocol. Specifically, we develop a training protocol search algorithm, based on a newly designed search space and an efficient search algorithm using evolutionary optimization and proxy tasks. Experimental results show that our searched training protocol can improve the recognition accuracy of mainstream STR models by 2.7%~3.9%. In particular, with the searched training protocol, TRBA-Net achieves 2.1% higher accuracy than the state-of-the-art STR model (i.e., EFIFSTR), while the inference speed is 2.3x and 3.7x faster on CPU and GPU respectively. Extensive experiments are conducted to demonstrate the effectiveness of the proposed method and the generalization ability of the training protocol found by our search method. Code is available at https://github.com/VDIGPKU/STR_TPSearch.
We have used archival far-ultraviolet spectra from observations made by HST/STIS and FUSE to determine the column densities and rotational excitation temperatures for CO and H2, respectively, along the lines of sight to 23 Galactic O and B stars. The sightlines have reddening values in the range E(B-V)= 0.07-0.62, sampling the diffuse to translucent interstellar medium. We find that the H2 column densities range from 5x10^18-8x10^20 cm^-2 and the CO from upper limits around 2x10^12 cm^-2 to detections as high as 1.4x10^16 cm^-2. CO increases with increasing H2, roughly following a power law of factor \~2. The CO/H2 column density ratio is thus not constant, and ranges from 10^-7 - 10^-5, with a mean value of 3x10^-6. The sample segregates into "diffuse" and "translucent" regimes, the former having a molecular fraction less than ~0.25 and A_V/d<1 mag kpc^-1. The mean CO/H2 for these two regimes are 3.6x10^-7 and 9.3x10^-6, respectively, significantly lower than the canonical dark cloud value of 10^-4. In six of the sightlines, 13CO is observed, and the isotopic ratio we observe (~50-70) is consistent with, if perhaps a little below, the average 12C/13C for the ISM at large. The average H2 rotational excitation temperature is 74+/-24 K, in good agreement with previous studies, and the average CO temperature is 4.1 K, with some sightlines as high as 6.4 K. The higher excitation CO is observed with higher column densities, consistent with the effects of photon trapping in clouds with densities in the 20-100 cm^-3 range. We discuss the implications for the structure of the diffuse/translucent regimes of the interstellar medium and the estimation of molecular mass in galaxies.
We report gapless quantum spin liquid behavior in the layered triangular Sr$_{3}$CuSb$_{2}$O$_{9}$ (SCSO) system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well-separated by Sb planes. Muon spin relaxation ($\mu$SR) measurements show that the $S = \frac{1}{2}$ moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature $\theta_{\mathrm{cw}} \simeq $ -143 K as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat ($\mathit{C}$$_{\mathrm{m}}$) below 5 K reveals a $\mathit{C}$$_{\mathrm{m}}$ $=$ $\gamma T$ + $\alpha T$$^{2}$ behavior. The significant $T$$^{2}$ contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-$T$ specific heat data, we estimate the dominant exchange scale to be $\sim $ 36 K using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations ($\sim $ 45 K) as well as high-temperature susceptibility analysis ($\sim$ 70 K). The linear specific heat coefficient is about 18 mJ/mol-K$^2$ which is somewhat larger than for typical Fermi liquids.
We consider a scalar charge travelling in a curved background spacetime. We calculate the quasi-local contribution to the scalar self-force experienced by such a particle following a geodesic in a general spacetime. We also show that if we assume a massless field and a vacuum background spacetime, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analog are of immediate physical interest for the calculation of radiation reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results.
Pseudoscalar and charged Higgs bosons production in the processes $\mu^+ \mu^-\to P^0_i Z^0$, $\mu^+\mu^- \to H^{\pm}W^{\mp}$ within the models with several Higgs doublets and singlets is considered.
We obtain a differential equation for the enumeration of the path length of general increasing trees. By using differential operators and their combinatorial interpretation we give a bijective proof of a version of Fa\`a di Bruno formula, and model the generation of ballot and Dyck paths. We get formulas for its enumeration according with the height of their lattice points. Recursive formulas for the enumeration of enriched increasing trees and forests with respect to the height of their internal and external vertices are also obtained. Finally we present a generalized form of all those results using one-parameter groups in the general context of formal power series in an arbitrary number of variables.
In grid-based codes that provide the combined solution of the Einstein equations and of relativistic hydrodynamics, the history of the fluid is not simple to track, especially when compared with particle-based codes. The use of tracers, namely massless particles that are advected with the flow, represents a simple and effective way to solve this problem. Yet, the use of tracers in numerical relativity is far from being settled and several issues, such as the impact of different placements in time and space of the tracers, or the relation between the placement and the description of the underlying fluid, have not yet been addressed. In this paper we present the first detailed discussion of the use tracers in numerical-relativity simulations focussing on both unbound material -- such as the one leading to r-process nucleosynthesis in binary mergers of neutron stars -- and on bound material -- such as the one in the core of the object produced from the merger of two neutron stars. In particular, when interested in unbound matter, we have evaluated four different placement schemes that could be used to initially distribute the tracers and how well their predictions match those obtained when using information from the actual fluid flow. Countering our naive expectations, we found that the most effective method does not rely on the rest-mass density distribution nor on the fluid that is unbound, but simply distributes tracers uniformly in rest-mass density. This prescription leads to the closest matching with the information obtained from the hydrodynamical solution. When considering bound matter, we demonstrate that tracers can provide insight into the fine details of the fluid motion as they can be used to track the evolution of fluid elements or to calculate the variation of quantities that are conserved along streamlines of adiabatic flows.
SnTe hosts ferroelectricity that competes with its weak non-trivial band topology: in the high-symmetry rocksalt structure--in which its intrinsic electric dipole is quenched--this material develops metallic surface bands, but in its rhombic ground-state configuration--that hosts a non-zero spontaneous electric dipole--the crystalline symmetry is lowered and the presence of surface electronic bands is not guaranteed. Here, the type of ferroelectric coupling and the atomistic and electronic structure of SnTe films ranging from 2 to 40 ALs are examined on freestanding samples, to which atomic layers were gradually added. 4 AL SnTe films are antiferroelectrically-coupled, while thicker freestanding SnTe films are ferroelectrically-coupled. The electronic band gap reduces its magnitude in going from 2 ALs to 40 ALs but it does not close due to the rhombic nature of the structure. These results bridge the structure of SnTe films from the monolayer to the bulk.
We obtain sharp two-sided heat kernel estimates on spaces with varying dimension, in which two spaces of general dimension are connected at one point. On these spaces, if the dimensions of the two constituent parts are different, the volume doubling property fails with respect to the measure induced by the associated Lebesgue measures. Thus the parabolic Harnack inequalities fail and the heat kernels do not enjoy Aronson type estimates. Our estimates show that the on-diagonal estimates are independent of the dimensions of the two parts of the space for small time, whereas they depend on their transience or recurrence for large time. These are multidimensional version of a space considered by Z.-Q. Chen and S. Lou (Ann. Probab. 2019), in which a 1-dimensional space and a 2-dimensional space are connected at one point.
This paper improves the upper bound for the exceptional zeroes of Dirichlet L-functions with even characters. The result is obtained by improving on explicit estimate for $L'(\sigma;\chi)$ for $\sigma$ close to unity, using a result on the average of Dirichlet characters, and on the lower bound for $L(1;\chi)$, with computational aid.
Most hydrodynamical calculations used in heavy-ion physics ignore the effect of freeze-out matter carrying energy and momentum away from the expanding fluid. In a simple one-dimensional model we compare calculated energy density and velocity profiles, with and without interaction between fluid-like and freeze-out parts of the system, in order to estimate the importance of this effect.
We present a novel observation of the white-light flare (WLF) continuum, which was significantly enhanced during the X1 flare on March 29, 2014 (SOL2014-03-29T17:48). Data from the Interface Region Imaging Spectrograph (IRIS) in its NUV channel show that at the peak of the continuum enhancement, the contrast at the quasi-continuum window above 2813 \AA\ reached 100 - 200 % and can be even larger closer to the Mg II lines. This is fully consistent with the hydrogen recombination Balmer continuum emission, which follows an impulsive thermal and non-thermal ionization caused by the precipitation of electron beams through the chromosphere. However, a less probable photospheric continuum enhancement cannot be excluded. The light curves of the Balmer continuum have an impulsive character with a gradual fading, similar to those detected recently in the optical region on Hinode/SOT. This observation represents a first Balmer-continuum detection from space far beyond the Balmer limit (3646 \AA), eliminating seeing effects known to complicate the WLF detection. Moreover, we use a spectral window so far unexplored for flare studies, which provides the potential to study the Balmer continuum, as well as many metallic lines appearing in emission during flares. Combined with future ground-based observations of the continuum near the Balmer limit, we will be able to disentangle between various scenarios of the WLF origin. IRIS observations also provide a critical quantitative measure of the energy radiated in the Balmer continuum, which constrains various models of the energy transport and deposition during flares.
We have examined the luminosity-size relationship as a function of environment for 12150 SDSS galaxies with precise visual classifications from the catalog of Nair & Abraham (2010a). Our analysis is subdivided into investigations of early-type galaxies and late-type galaxies. Early-type galaxies reveal a surprisingly tight luminosity-size relation. The dispersion in luminosity about the fiducial relation is only ~0.14 dex (0.35 mag), even though the sample contains galaxies which differ by a factor of almost 100 in luminosity. The dispersion about the luminosity-size relation is comparable to the dispersion about the fundamental plane, even though the luminosity-size relation is fundamentally simpler and computed using purely photometric parameters. The key contributors to the dispersion about the luminosity-size relation are found to be color and central concentration. Expanding our analysis to the full range of morphological types, we show that the slope, zero point, and scatter about the luminosity-size relation is independent of environmental density. Our study thus indicates that whatever process is building galaxies is doing so in a way that preserves fundamental scaling laws even as the typical luminosity of galaxies changes with environment. However, the distribution of galaxies along the luminosity-size relation is found to be strongly dependent on galaxy environment. This variation is in the sense that, at a given morphology, larger and more luminous galaxies are rarer in sparser environments. Our analysis of late-type galaxy morphologies reveals that scatter increases towards later Hubble types. Taken together, these results place strong constraints on conventional hierarchical models in which galaxies are built up in an essentially stochastic way.
We investigate a new natural class $\mathcal{J}$ of probability distributions modeling large claim sizes, motivated by the `principle of one big jump'. Though significantly more general than the (sub-)class of subexponential distributions $\mathcal{S}$, many important and desirable structural properties can still be derived. We establish relations to many other important large claim distribution classes (such as $\mathcal{D}$, $\mathcal{S}$, $\mathcal{L}$, $\mathcal {K}$, $\mathcal{OS}$ and $\mathcal{OL}$), discuss the stability of $\mathcal{J}$ under tail-equivalence, convolution, convolution roots, random sums and mixture, and then apply these results to derive a partial analogue of the famous Pakes-Veraverbeke-Embrechts theorem from ruin theory for $\mathcal{J}$. Finally, we discuss the (weak) tail-equivalence of infinitely-divisible distributions in $\mathcal{J}$ with their L\'{e}vy measure.
We obtain new elliptic function identities, which are an elliptic analogue of Fukuhara's trigonometric identities. We show that the coefficients of Laurent expansions at $z=0$ of our elliptic identities give rise to some reciprocity laws for elliptic Dedekind sums.