ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the long time behavior of bounded, integrable solutions to a nonlocal diffusion equation, $\partial _t u=J*u-u$, where $J$ is a smooth, radially symmetric kernel with support $B_d(0)\subset\mathbb{R}^2$. The problem is set in an exterior two-dimensional domain which excludes a hole $\mathcal{H}$, and with zero Dirichlet data on $\mathcal{H}$. In the far field scale, $\xi_1\le |x|t^{-1/2}\le \xi_2$ with $\xi_1,\xi_2>0$, the scaled function $\log t\, u(x,t)$ behaves as a multiple of the fundamental solution for the local heat equation with a certain diffusivity determined by $J$. The proportionality constant, which characterizes the first non-trivial term in the asymptotic behavior of the mass, is given by means of the asymptotic \lq logarithmic momentum' of the solution, $\lim_{t\to\infty}\int_{\mathbb{R}^2}u(x,t)\log|x|\,dx$. This asymptotic quantity can be easily computed in terms of the initial data. In the near field scale, $|x|\le t^{1/2}h(t)$ with $\lim_{t\to\infty} h(t)=0$, the scaled function $t(\log t)^2u(x,t)/\log |x|$ converges to a multiple of $\phi(x)/\log |x|$, where $\phi$ is the unique stationary solution of the problem that behaves as $\log|x|$ when $|x|\to\infty$. The proportionality constant is obtained through a matching procedure with the far field limit. Finally, in the very far field, $|x|\ge t^{1/2} g(t)$ with $g(t)\to\infty$, the solution is proved to be of order $o((t\log t)^{-1})$.
Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kaehler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji's numerically trivial fibration and the Iitaka fibration. Using almost positive singular hermitian metrics with analytic singularities on a pseudo-effective line bundle, a foliation is constructed refining the nef fibration. If the singularities of the foliation are isolated points, the codimension of the leaves is an upper bound to the numerical dimension of the line bundle, and the foliation can be interpreted as a geometric reason for the deviation of nef and Kodaira-Iitaka dimension. Several surface examples are studied in more details, $\mathbb{P}^2$ blown up in 9 points giving a counter example to equality of numerical dimension and codimension of the leaves.
In 1959 Buchdahl \cite{Bu} obtained the inequality $2M/R\leq 8/9$ under the assumptions that the energy density is non-increasing outwards and that the pressure is isotropic. Here $M$ is the ADM mass and $R$ the area radius of the boundary of the static body. The assumptions used to derive the Buchdahl inequality are very restrictive and e.g. neither of them hold in a simple soap bubble. In this work we remove both of these assumptions and consider \textit{any} static solution of the spherically symmetric Einstein equations for which the energy density $\rho\geq 0,$ and the radial- and tangential pressures $p\geq 0$ and $p_T,$ satisfy $p+2p_T\leq\Omega\rho, \Omega>0,$ and we show that $$\sup_{r>0}\frac{2m(r)}{r}\leq \frac{(1+2\Omega)^2-1}{(1+2\Omega)^2},$$ where $m$ is the quasi-local mass, so that in particular $M=m(R).$ We also show that the inequality is sharp. Note that when $\Omega=1$ the original bound by Buchdahl is recovered. The assumptions on the matter model are very general and in particular any model with $p\geq 0$ which satisfies the dominant energy condition satisfies the hypotheses with $\Omega=3.$
In this paper we consider sandpile models and modify the drive mechanisms to control the size of avalanches. The modification to the drive mechanism is local. We have studied the scaling behavior of the BTW and Manna models. We have found that the BTW model is more sensitive to the modification than the Manna model. Furthermore we have assigned a cost function to each avalanche and have found an optimum value for the modification to arrive at the lowest cost.
The corrections of two-photon exchange on deuteron electromagnetic form factors are estimated based on an effective Lagrangian approach. Numerical results for the form factors $G_{C,M,Q}$ of the deuteron with the corrections are compared to its empirical ones. Moreover, the two new form factors, due to the two-photon exchange, are analyzed. Possible way to test the two-photon exchange corrections to the deuteron form factors is discussed.
One of the main goals and challenges of materials discovery is to find the best candidates for each interest property or application. Machine learning rises in this context to efficiently optimize this search, exploring the immense materials space, consisting of simultaneously the atomic, compositional, and structural spaces. Topological insulators, presenting symmetry-protected metallic edge states, are a promising class of materials for different applications. However, further, development is limited by the scarcity of viable candidates. Here we present and discuss machine learning-accelerated strategies for searching the materials space for two-dimensional topological materials. We show the importance of detailed investigations of each machine learning component, leading to different results. Using recently created databases containing thousands of ab initio calculations of 2D materials, we train machine learning models capable of determining the electronic topology of materials, with an accuracy of over 90%. We can then generate and screen thousands of novel materials, efficiently predicting their topological character without the need for a priori structural knowledge. We discover 56 non-trivial materials, of which 17 novel insulating candidates for further investigation, for which we corroborate their topological properties with density functional theory calculations. This strategy is 10$\times$ more efficient than the trial-and-error approach while few orders of magnitude faster and is a proof of concept for guiding improved materials discovery search strategies.
The Magellanic Clouds, especially the Large Magellanic Cloud, are places where multiple distance indicators can be compared with each other in a straight-forward manner at considerable precision. We here review the distances derived from Cepheids, Red Variables, RR Lyraes, Red Clump Stars and Eclipsing Binaries, and show that the results from these distance indicators generally agree to within their errors, and the distance modulus to the Large Magellanic Cloud appears to be defined to 3% with a mean value of 18.48 mag, corresponding to 49.7 Kpc. The utility of the Magellanic Clouds in constructing and testing the distance scale will remain as we move into the era of Gaia.
Low-temperature Hall measurements have been performed on two-dimensional electron gases (2DEGs) induced by deposition of Cs or Na on in situ cleaved surfaces of p-type InAs. The surface donor level, at which the Fermi energy of the 2DEG is pinned, is calculated from the observed saturation surface electron density using a surface potential determined self-consistently. The results are compared to those of previous photoelectron spectroscopy measurements.
The mean alpha-to-iron abundance ratio ([$\alpha$/Fe]) of galaxies is sensitive to the chemical evolution processes at early time, and it is an indicator of star formation timescale ($\tau_{{\rm SF}}$). Although the physical reason remains ambiguous, there is a tight relation between [$\alpha$/Fe] and stellar velocity dispersion ($\sigma$) among massive early-type galaxies (ETGs). However, no work has shown convincing results as to how this relation behaves at low masses. We assemble 15 data sets from the literature and build a large sample that includes 192 nearby low-mass ($18<\sigma<80$~\kms) ETGs. We find that the [$\alpha$/Fe]-$\sigma$ relation generally holds for low-mass ETGs, except in extreme environments. Specifically, in normal galaxy cluster environments, the [$\alpha$/Fe]-$\sigma$ relation and its intrinsic scatter are, within uncertainties, similar for low-mass and high-mass ETGs. However, in the most massive relaxed galaxy cluster in our sample, the zero point of the relation is higher and the intrinsic scatter is significantly larger. By contrast, in galaxy groups the zero point of the relation offsets in the opposite direction, again with substantial intrinsic scatter. The elevated [$\alpha$/Fe] of low-mass ETGs in the densest environments suggests that their star formation was quenched earlier than in high-mass ETGs. For the low-mass ETGs in the lowest density environments, we suggest that their more extended star formation histories suppressed their average [$\alpha$/Fe]. The large scatter in [$\alpha$/Fe] may reflect stochasticity in the chemical evolution of low-mass galaxies.
Gravitational perturbations which are present in any realistic stellar collapse to a black hole, die off in the exterior of the hole, but experience an infinite blueshift in the interior. This is believed to lead to a slowly contracting lightlike scalar curvature singularity, characterized by a divergence of the hole's (quasi-local) mass function along the inner horizon.   The region near the inner horizon is described to great accuracy by a plane wave spacetime. While Einstein's equations for this metric are still too complicated to be solved in closed form it is relatively simple to integrate them numerically.   We find for generic regular initial data the predicted mass inflation type null singularity, rather than a spacelike singularity. It thus seems that mass inflation indeed represents a generic self-consistent picture of the black hole interior.
The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the Weyl arrangement and their parallel translations. It was introduced by J.-Y. Shi in the study of the Kazhdan-Lusztig representation of the affine Weyl groups. M. Yoshinaga showed that the cone over every Shi arrangement is free. In this paper, we construct an explicit basis for the derivation module of the cone over the Shi arrangements of the type $B_{\ell}$ or $C_{\ell}$.
We have performed a systematic study of the electronic structures of BiMeO3 (Me = Sc, Cr, Mn, Fe, Co, Ni) series by soft X-ray emission (XES) and absorption (XAS) spectroscopy. The band gap values were estimated for all compounds in the series. For BiFeO3 a band gap of ~0.9 eV was obtained from the alignment of the O Ka XES and O 1s XAS. The O 1s XAS spectrum of BiNiO3 indicates that the formation of holes is due to a Ni2+ valency rather than a Ni3+ valency. We have found that the O Ka XES and O 1s XAS of BiMeO3 probing partially occupied and vacant O 2p states, respectively, are in agreement with the O 2p densities of states obtained from spin-polarized band structure calculations. The O Ka XES spectra show the same degree of Bi 6s--O 2p hybridization for all compounds in the series. We argue herein that the stereochemical activity of Bi 6s lone pairs must be supplemented with inversion symmetry breaking to allow electric polarization. For BiMnO3 and BiFeO3, two cases of multiferroic materials in this series, the former breaks the inversion symmetry due to the antiferromagnetic order induced by particular orbital ordering in the highly distorted perovskite structure and the latter has rhombohedral crystal structure without inversion symmetry.
We present the general properties of the far-ultraviolet (FUV; 1370-1720A) continuum background over most of the sky, obtained with the Spectroscopy of Plasma Evolution from Astrophysical Radiation instrument (SPEAR, also known as FIMS), flown aboard the STSAT-1 satellite mission. We find that the diffuse FUV continuum intensity is well correlated with N_{HI}, 100 $\mu$m, and H-alpha intensities but anti-correlated with soft X-ray. The correlation of the diffuse background with the direct stellar flux is weaker than the correlation with other parameters. The continuum spectra are relatively flat. However, a weak softening of the FUV spectra toward some sight lines, mostly at high Galactic latitudes, is found not only in direct-stellar but also in diffuse background spectra. The diffuse background is relatively softer that the direct stellar spectrum. We also find that the diffuse FUV background averaged over the sky has about the same level as the direct-stellar radiation field in the statistical sense and a bit softer spectrum compared to direct stellar radiation. A map of the ratio of 1400-1510A to 1560-1660A shows that the sky is divided into roughly two parts. However, this map shows a lot of patchy structures on small scales. The spatial variation of the hardness ratio seems to be largely determined by the longitudinal distribution of spectral types of stars in the Galactic plane. A correlation of the hardness ratio with the FUV intensity at high intensities is found but an anti-correlation at low intensities. We also find evidence that the FUV intensity distribution is log-normal in nature.
We present analyses of the physical conditions in the z=0.22496 and z=0.22638 multi-phase O VI absorption systems detected in the ultraviolet HST/STIS and FUSE spectra of the quasar H1821+643. Both absorbers are likely associated with the extended halo of a ~2L* Sbc-Sc galaxy situated at a projected distance of ~116 kpc from the sight line. The z=0.22496 absorber is detected in C II, C III, C IV, O III, O VI, Si II, Si III and H I at > 3 sigma significance. The low and intermediate ions in this absorber are consistent with an origin in photoionized gas with [Si/H] and [C/H] of -0.6 dex. In contrast, the broader O VI absorption is likely produced in collisionally ionized plasma under nonequilibrium conditions. The z=0.22638 system has broad-Lya (BLA) and C III absorption offset by v = -53 km/s from O VI. The H I and C III line widths for the BLA imply T = 1.1 x 10^5 K. For non-equilibrium cooling we obtain [C/H] of -1.5 dex and a total hydrogen column of N(H) = 3.2 x 10^{18} cm^-2 in the BLA. The O VI, offset from the BLA with no detected H I or C III, is likely collisionally ionized at T ~ 3 x 10^5 K. From the observed multiphase properties and the proximity to a luminous galaxy, we propose that the z=0.22496 absorber is an extragalactic analog of a highly ionized Galactic HVC, in which the O VI is produced in transition temperature plasma (T ~ 10^5 K) at the interface layers between the warm HVC gas phase and the hot coronal halo of the galaxy. The z=0.22638 O VI - BLA absorber could be tracing a cooling condensing fragment in the nearby galaxy's hot gaseous halo.
Hercules X-1 is one of the best studied highly magnetised neutron star X-ray binaries with a wealth of archival data. We present the discovery of an ionised wind in its X-ray spectrum when the source is in the high state. The wind detection is statistically significant in most of the XMM-Newton observations, with velocities ranging from 200 to 1000 km/s. Observed features in the iron K band can be explained by both wind absorption or by a forest of iron emission lines. However, we also detect nitrogen, oxygen and neon absorption lines at the same systematic velocity in the high-resolution RGS grating spectra. The wind must be launched from the accretion disc, and could be the progenitor of the UV absorption features observed at comparable velocities, but the latter likely originate at significantly larger distances from the compact object. We find strong correlations between the ionisation level of the outflowing material and the ionising luminosity as well as the super-orbital phase. If the luminosity is driving the correlation, the wind could be launched by a combination of Compton heating and radiation pressure. If instead the super-orbital phase is the driver for the variations, the observations are likely scanning the wind at different heights above the warped accretion disc. If this is the case, we can estimate the wind mass outflow rate, corrected for the limited launching solid angle, to be roughly 70% of the mass accretion rate.
Current logo retrieval research focuses on closed set scenarios. We argue that the logo domain is too large for this strategy and requires an open set approach. To foster research in this direction, a large-scale logo dataset, called Logos in the Wild, is collected and released to the public. A typical open set logo retrieval application is, for example, assessing the effectiveness of advertisement in sports event broadcasts. Given a query sample in shape of a logo image, the task is to find all further occurrences of this logo in a set of images or videos. Currently, common logo retrieval approaches are unsuitable for this task because of their closed world assumption. Thus, an open set logo retrieval method is proposed in this work which allows searching for previously unseen logos by a single query sample. A two stage concept with separate logo detection and comparison is proposed where both modules are based on task specific CNNs. If trained with the Logos in the Wild data, significant performance improvements are observed, especially compared with state-of-the-art closed set approaches.
We find the constraints on various non-standard interactions (NSI) of neutrinos from monojet+MET searches at the Large Hadron Collider (LHC). Also, we show that the measurement of neutrino-nucleon cross-section from the observation of high energy astrophysical neutrino events at IceCube facilitates strong constraints on NSI as well. To this end, we pursue a comparative study of the prospects of LHC and IceCube in detecting NSI, also mentioning the role of low-energy experiments. We discuss the case of NSI with a new vector boson $Z'$ and it is found that for some range of $m_{Z'}$ LHC puts more stringent bound, whereas IceCube supersedes elsewhere. We also pay special attention to the case of $Z'$ of mass of a few GeVs, pointing out that the IceCube constraints can surpass those from LHC and low-energy experiments. Although, for contact-type effective interactions with two neutrinos and two partons, constraints from LHC are superior.
We explore the deformation properties of the newly postulated BCP energy density functional (EDF). The results obtained for three isotope chains of Mg, Dy and Ra are compared to the available experimental data as well as to the results of the Gogny-D1S force. Results for the fission barrier of $^{240}$Pu are also discussed.
We present a formalism well adapted to the numerical study of the encounter of an ordinary main sequence star with a massive black hole. Symmetry considerations, the use of a well adapted moving grid and a well adapted moving frame along with integration of the partial differential equations by means of pseudo-spectral methods result in a very powerful and accurate tool. The hydrodynamical equations are written in a moving frame which mimics the bulk of the movement of the fluid, resulting in very small relative velocities and a well suited spatial resolution throughout the calculations. Therefore, the numerical calculations are considerably simplified, smoothing in particular the Courant condition. Typical runs are performed within a few hours on a workstation with the high accuracy linked to the spectral methods. Predictions of the so-called affine are tested against this full numerical simulation.
We prove the linear and nonlinear instability of the water line solitary waves with respect to transverse perturbations.
Considering the corrected Unruh temperature as well as the entropic force perspective of gravity, we are able to derive the modification of the Newton's law of gravity. In addition, we also investigate the effects of the highest achievable acceleration correction to the Unruh temperature on the Poisson equation. Moreover, we address modifications to the Newtonian cosmology as well as the Friedmann equations corresponding to the upper bound for acceleration.
The temporal evolutions of coherent resonances corresponding to electromagnetically induced transparency (EIT) and absorption (EIA) were observed in a Hanle absorption experiment carried on the $D_{2}$ lines of $% ^{87}$Rb vapor by suddenly turning the magnetic field on or off. The main features of the experimental observations are well reproduced by a theoretical model based on Bloch equation where the atomic level degeneracy has been fully accounted for. Similar (opposite phase) evolutions were observed at low optical field intensities for Hanle/EIT or Hanle/EIA resonances. Unlike the Hanle/EIA\ transients which are increasingly shorter for driving field intensities approaching saturation, the $B\neq 0$ transient of the Hanle/EIT signal at large driving field intensities present a long decay time approaching the atomic transit time. Such counterintuitive behavior is interpreted as a consequence of the Zeno effect.
Foreseeing the era of high spatial resolution measurements of the Sunyaev-Zel'dovich effect (SZE) in clusters of galaxies, we present a prototype analysis of this sort combined with Chandra X-ray data. It is applied specifically to RX J1347-1145 at z=0.451, the most X-ray-luminous galaxy cluster known, for which the highest resolution SZE and X-ray images are currently available. We demonstrate that the combined analysis yields a unique probe of complex structures in the intracluster medium, offering determinations of their temperature, density, and line-of-sight extent. For a subclump in RX J1347-1145, previously discovered in our SZE map, the temperature inferred after removing the foreground and background components is well in excess of 20 keV, indicating that the cluster has recently undergone a violent merger. Excluding the region around this subclump, the SZE signals in submillimeter to centimeter bands (350, 150, and 21 GHz) are all consistent with those expected from Chandra X-ray observations. We further present a temperature deprojection technique based on the SZE and X-ray images, without any knowledge of spatially resolved X-ray spectroscopy. The methodology presented here will be applicable to a statistical sample of clusters available in the future SZE surveys.
We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field $O(k)$ and the regularization .
This article presents a unified bijective scheme between planar maps and blossoming trees, where a blossoming tree is defined as a spanning tree of the map decorated with some dangling half-edges that enable to reconstruct its faces. Our method generalizes a previous construction of Bernardi by loosening its conditions of applications so as to include annular maps, that is maps embedded in the plane with a root face different from the outer face.   The bijective construction presented here relies deeply on the theory of \alpha-orientations introduced by Felsner, and in particular on the existence of minimal and accessible orientations. Since most of the families of maps can be characterized by such orientations, our generic bijective method is proved to capture as special cases all previously known bijections involving blossoming trees: for example Eulerian maps, m-Eulerian maps, non separable maps and simple triangulations and quadrangulations of a k-gon. Moreover, it also permits to obtain new bijective constructions for bipolar orientations and d-angulations of girth d of a k-gon.   As for applications, each specialization of the construction translates into enumerative by-products, either via a closed formula or via a recursive computational scheme. Besides, for every family of maps described in the paper, the construction can be implemented in linear time. It yields thus an effective way to encode and generate planar maps.   In a recent work, Bernardi and Fusy introduced another unified bijective scheme, we adopt here a different strategy which allows us to capture different bijections. These two approaches should be seen as two complementary ways of unifying bijections between planar maps and decorated trees.