ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a new finite volume method for computing numerical approximations of a system of nonlocal transport equation modeling interacting species. This method is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet, Convergence analysis of upwind type schemes for the aggregation equation with pointy potential, Ann. Henri. Lebesgue 2019], where the nonlocal continuity equations are 10 treated as conservative transport equations with a nonlocal, nonlinear, rough velocity field. We analyze some properties of the method, and illustrate the results with numerical simulations.
We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of the same type for the associated maximal operators. As an application, we obtain a wide variety of mixed inequalities for Schr\"odinger type singular integrals.   As far as we know, these results are a first approach of mixed inequalities in the Schr\"odinger setting.
NGC 3311 is the central galaxy of the Hydra I galaxy cluster. It has a hot interstellar medium and hosts a central dust lane with emission lines. These dust lanes are frequent in elliptical galaxies, but the case of NGC 3311 might be particularly interesting for problems of dust lifetime and the role of cool gas in the central parts. We aim to use archival HST images and MUSE data to investigate the central dust structure of NGC 3311. We used the tool PyParadise to model the stellar population and extract the emission lines. The HST/ACS colour map reveals the known dust structures, but also blue spots, which are places of strong line emission. A dusty 'mini-jet' emanates from the centre. The distribution of the emission line gas matches the dust silhouette almost exactly. Close to the brightest Halpha emission, the ratio [NII]/Halpha resembles that of HII-regions; in the outer parts, [NII] gets stronger and is similar to LINER-like spectra. The gas kinematics is consistent with that of a rotating disc. The Doppler shifts of the strongest line emissions, which indicate the areas of highest star formation activity, smoothly fit into the disc symmetry. The metallicity is supersolar. The presence of neutral gas is indicated by the fit residuals of the stellar NaI D absorption line, which we interpret as interstellar absorption. We estimate the mass of the neutral gas to be of the order of the X-ray mass. The dynamical mass infers a stellar population of intermediate age, whose globular clusters have already been identified. Our findings can be harmonised in a scenario in which the star formation is triggered by the accretion of cold gas onto a pre-existing gas/dust disc or ring. Newly produced dust then contributes to the longevity of the dust.
We prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions, i.e., locally they are merely measurable in one direction and have small mean oscillations in the other directions. Using this result, we establish the unique solvability in Muckenhoupt type weighted Sobolev spaces for the system with partially BMO coefficients on a Reifenberg flat domain. We also present weighted a priori $L_q$-estimates for the system when the domain is the whole Euclidean space or a half space.
Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a freely-specifiable variable, but rather is determined as a solution to the field equations. The new set of freely-specifiable variables includes only time-derivatives of metric quantities, which makes this decomposition very attractive for the construction of quasiequilibrium solutions. To date, this new formalism has only been used for binary neutron stars. Applications involving black holes require new boundary conditions for the conformal metric on the domain boundaries. In this paper we demonstrate how these boundary conditions follow naturally from the conformal geometry of the boundary surfaces and the inherent gauge freedom of the conformal metric.
We examine the question of whether quantum mechanics places limitations on the ability of small quantum devices to learn. We specifically examine the question in the context of Bayesian inference, wherein the prior and posterior distributions are encoded in the quantum state vector. We conclude based on lower bounds from Grover's search that an efficient blackbox method for updating the distribution is impossible. We then address this by providing a new adaptive form of approximate quantum Bayesian inference that is polynomially faster than its classical analogue and tractable if the quantum system is augmented with classical memory or if the low-order moments of the distribution are protected using a repetition code. This work suggests that there may be a connection between fault tolerance and the capacity of a quantum system to learn from its surroundings.
We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical bounds found for qubits. We define simulation cost by the number of terms that require Gaussian elimination of a $t \times t$ matrix and so capture the cost of simulation methods that proceed by computing stabilizer inner products or evaluating quadratic Gauss sums. Prior numerical searchs for qubits were unable to converge beyond $t=7$. We effectively increase the space searched for these non-trivial reductions by $>10^{10^4}$ and extend the bounds to $t=14$ for qutrits. This is accomplished by using the Wigner-Weyl-Moyal formalism to algebraically find bounds instead of relying on numerics. We find a new reduction in the upper bound from the $12$-qutrit magic state of ${3^{\sim 0.469t}}$, which improves on the bound obtained from the $6$-qutrit magic state of ${3^{\sim 0.482t}}$.
Although the theoretical study of very low metallicity (Z) and metal-free stars is not new, their importance has recently greatly increased since two related fields have been developing rapidly. The first is cosmological simulations of the formation of the first stars and of the reionisation period. The second is the observations of extremely metal poor stars. In this paper, we present pre-supernova evolution models of massive rotating stars at very low Z (Z=1e-8) and at Z=0. Rotation has a strong impact on mass loss and nucleosynthesis. Models reaching break-up velocities lose up to ten percents of their initial mass. In very low Z models, rotational and convective mixing enhances significantly the surface content in carbon, nitrogen and oxygen (CNO) when the star becomes a red supergiant. This induces a strong mass loss for stars more massive than about 60 solar masses. Our models predict type Ib,c supernovae and gamma-ray bursts at very low Z. Rotational mixing also induces a large production of CNO elements, in particular of primary nitrogen. The stellar wind chemical composition is compatible with the most metal-poor star know to date, HE 1327-2326, for CNO elements. Our models reproduce the early evolution of nitrogen in the Milky Way.
We try to explain quasar-galaxy associations by gravitational lensing by globular clusters, located in the halos of foreground galaxies. We propose observational test for verification of this hypothesis. We processed SUPERCOSMOS sky survey and found overdensities of star-like sources with zero proper motions in the vicinities of foreground galaxies from CfA3 catalog. We show mean effect for galaxies with different redshifts. Two effects can explain observational data - these are lensing by globular clusters and lensing by dwarf galaxies. We made CCD 3-color photometry with 2.0-1.2 meter telescopes to select extremely lensed objects around several galaxies for spectroscopic observations.
We analyze the density field of galaxies observed by the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) included in the SDSS Data Release Nine (DR9). DR9 includes spectroscopic redshifts for over 400,000 galaxies spread over a footprint of 3,275 deg^2. We identify, characterize, and mitigate the impact of sources of systematic uncertainty on large-scale clustering measurements, both for angular moments of the redshift-space correlation function and the spherically averaged power spectrum, P(k), in order to ensure that robust cosmological constraints will be obtained from these data. A correlation between the projected density of stars and the higher redshift (0.43 < z < 0.7) galaxy sample (the `CMASS' sample) due to imaging systematics imparts a systematic error that is larger than the statistical error of the clustering measurements at scales s > 120h^-1Mpc or k < 0.01hMpc^-1. We find that these errors can be ameliorated by weighting galaxies based on their surface brightness and the local stellar density. We use mock galaxy catalogs that simulate the CMASS selection function to determine that randomly selecting galaxy redshifts in order to simulate the radial selection function of a random sample imparts the least systematic error on correlation function measurements and that this systematic error is negligible for the spherically averaged correlation function. The methods we recommend for the calculation of clustering measurements using the CMASS sample are adopted in companion papers that locate the position of the baryon acoustic oscillation feature (Anderson et al. 2012), constrain cosmological models using the full shape of the correlation function (Sanchez et al. 2012), and measure the rate of structure growth (Reid et al. 2012). (abridged)
The radial profiles of the Hb, Mg, and Fe line-strength indices are presented for a sample of eight spiral galaxies with a low surface-brightness stellar disc and a bulge. The correlations between the central values of the line-strength indices and velocity dispersion are consistent to those known for early-type galaxies and bulges of high surface-brightness galaxies. The age, metallicity, and alpha/Fe enhancement of the stellar populations in the bulge-dominated region are obtained using stellar population models with variable element abundance ratios. Almost all the sample bulges are characterized by a young stellar population, on-going star formation, and a solar alpha/Fe enhancement. Their metallicity spans from high to sub-solar values. No significant gradient in age and alpha/Fe enhancement is measured, whereas only in a few cases a negative metallicity gradient is found. These properties suggest that a pure dissipative collapse is not able to explain formation of all the sample bulges and that other phenomena, like mergers or acquisition events, need to be invoked. Such a picture is also supported by the lack of a correlation between the central value and gradient of the metallicity in bulges with very low metallicity. The stellar populations of the bulges hosted by low surface-brightness discs share many properties with those of high surface-brightness galaxies. Therefore, they are likely to have common formation scenarios and evolution histories. A strong interplay between bulges and discs is ruled out by the fact that in spite of being hosted by discs with extremely different properties, the bulges of low and high surface-brightness discs are remarkably similar.
We study the sensitivity of the High-Luminosity LHC to a light baryonic dark photon B, primarily coupled to quarks, as a constituent of the proton. This is achieved by allowing for a dark photon parton distribution function (PDF) in the PDF evolution equations. Depending on the mass and coupling of the dark photon, the evolution of standard quark and gluon PDFs is distorted to varying degrees. By analysing the effect of the dark photon on the tails of Drell-Yan invariant mass distributions, we demonstrate the potential of the LHC in determining competitive bounds on dark photon parameter space.
In this paper we proof that any cactus graph satisfies graph complement conjecture by finding a orthogonal representation of its complement in $\mathbb{R}^5$.
We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of "homogenization" for Dyson Brownian Motion, this yields the universality of quantities which depend on the behavior of single eigenvalues of Wigner matrices and $\beta$-ensembles. Among the results we obtain are the Gaussian fluctuations of single eigenvalues for Wigner matrices (without an assumption of 4 matching moments) and classical $\beta$-ensembles ($\beta=1, 2, 4$), Gaussian fluctuations of the eigenvalue counting function, and an asymptotic expansion up to order $o(N^{-1})$ for the expected value of eigenvalues in the bulk of the spectrum. The latter result solves a conjecture of Tao and Vu.
Motivated by two identities published with Ramanujan's lost notebook and connected, respectively, with the Gauss circle problem and the Dirichlet divisor problem, in an earlier paper, three of the present authors derived representations for certain sums of products of trigonometric functions as double series of Bessel functions. These series are generalized in the present paper by introducing the novel notion of balanced derivatives, leading to further theorems. As we will see below, the regions of convergence in the unbalanced case are entirely different than those in the balanced case. From this viewpoint, it is remarkable that Ramanujan had the intuition to formulate entries that are, in our new terminology, "balanced". If $x$ denotes the number of products of the trigonometric functions appearing in our sums, in addition to proving the identities mentioned above, theorems and conjectures for upper and lower bounds for the sums as $x\to\infty$ are established.
We derive a new set of field equations within the framework of the Palatini formalism.These equations are a natural generalization of the Einstein-Maxwell equations which arise by adding a function $\mathcal{F}(\mathcal{Q})$, with $\mathcal{Q}\equiv F^{\alpha\beta}F_{\alpha\beta}$ to the Palatini Lagrangian $f(R,Q)$.The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field.In addition,a new method is introduced to solve the algebraic equation associated to the Ricci tensor.
We show the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0. As a corollary, we generalise many recent results to low characteristics including: $W\mathcal{O}$-rationality of klt singularities, inversion of adjunction, and normality of divisorial centres up to a universal homeomorphism.
Semantic segmentation research has recently witnessed rapid progress, but many leading methods are unable to identify object instances. In this paper, we present Multi-task Network Cascades for instance-aware semantic segmentation. Our model consists of three networks, respectively differentiating instances, estimating masks, and categorizing objects. These networks form a cascaded structure, and are designed to share their convolutional features. We develop an algorithm for the nontrivial end-to-end training of this causal, cascaded structure. Our solution is a clean, single-step training framework and can be generalized to cascades that have more stages. We demonstrate state-of-the-art instance-aware semantic segmentation accuracy on PASCAL VOC. Meanwhile, our method takes only 360ms testing an image using VGG-16, which is two orders of magnitude faster than previous systems for this challenging problem. As a by product, our method also achieves compelling object detection results which surpass the competitive Fast/Faster R-CNN systems.   The method described in this paper is the foundation of our submissions to the MS COCO 2015 segmentation competition, where we won the 1st place.
This is a review of recent developments regarding the Skyrmion sector of higher representation QCD. Ordinary QCD is a SU(n) gauge theory with n_f Dirac quarks in the fundamental representation. Changing the representation of quarks leads to different and interesting theories, which are not as well studied as ordinary QCD. In order to be able to have a consistent asymptotically free large n limit, we must limit ourselves to three cases: two-index representation (symmetric or anti-symmetric) and adjoint representation. Skyrmions of the low-energy effective Lagrangian shall be the main subject of this review. There are puzzling aspects, both in orientifold and adjoint QCD, regarding the identification of the Skyrmion and its quantum stability, that have not yet been understood. We shall explain these problems and the solution we proposed for them. The first part is dedicated to the two-index representation. Here the challenge is to identify the correct particle in the spectrum that has to be identified with the Skyrmion. It turns out not to be the simplest baryon (as in ordinary QCD) but a baryonic state with higher charge, precisely composed by n(n\pm 1)/2 quarks. Although not the simplest among the baryons, it is the one that minimizes the mass per unit of baryonic charge and thus is the most stable among them. The second part is devoted to the quarks in the adjoint representation. The task here assume a different perspective. We do not have a baryon charge, like in ordinary QCD. An important role is now played by a massive fermion that must be considered in the low-energy effective Lagrangian. Through this fermion, the Skyrmion acquires an anomalous fermionic number (-1)^F and, as a consequence, an odd relationship between the latter and its spin/statistic. This implies a Z_2 stability of the Skyrmion.
We rigorously show a large friction limit of hydrodynamic models with alignment, attractive, and repulsive effects. More precisely, we consider pressureless Euler equations with nonlocal forces and provide a quantitative estimate of large friction limit to a continuity equation with nonlocal velocity fields, which is often called an aggregation equation. Our main strategy relies on the relative entropy argument combined with the estimate of $p$-Wasserstein distance between densities.
To enable functional skyrmion based spintronic devices, the controllable generation and manipulation of skyrmions is essential. While the generation of skyrmions by using a magnetic geometrical constriction has already been demonstrated, this approach is difficult to combine with a subsequent controlled manipulation of skyrmions. The high efficiency of skyrmion generation from magnetic constrictions limits the useful current density, resulting in stochastic skyrmion motion, which may obscure topological phenomena such as the skyrmion Hall effect. In order to address this issue, we designed a nonmagnetic conducting Ti/Au point contact in devices made of Ta/CoFeB/TaOx trilayer films. By applying high voltage pulses, we experimentally demonstrated that skyrmions can be dynamically generated. Moreover, the accompanied spin topology dependent skyrmion dynamics, the skyrmion Hall effect is also experimentally observed in the same devices. The creation process has been numerically reproduced through micromagnetic simulations in which the important role of skyrmion-antiskyrmion pair generation is identified. The motion and Hall effect of the skyrmions, immediately after their creation is described using a modified Thiele equation after taking into account the contribution from spatially inhomogeneous spin-orbit torques and the Magnus force. The simultaneous generation and manipulation of skyrmions using a nonmagnetic point contact could provide a useful pathway for designing novel skyrmion based devices.
This survey article is a much extended version of a lecture given at a Clay Institute workshop in October 2006. It describes all known results on the existence of stable coherent systems on algebraic curves.
We use Monte Carlo simulations to study multicritical properties of an Ising metamagnet in an external field. According to the mean field theory predictions, a three-dimensional layered metamagnet is expected to display a tricritical point decomposition to a critical endpoint and a bicritical endpoint, when a ratio between intralayer ferromagnetic and interlayer antiferromagnetic couplings becomes sufficiently small. Our simulations show no evidence of such a decomposition and produce a tricritical behaviour even for a coupling ratio as small as R=0.01.
Place recognition is a core component of Simultaneous Localization and Mapping (SLAM) algorithms. Particularly in visual SLAM systems, previously-visited places are recognized by measuring the appearance similarity between images representing these locations. However, such approaches are sensitive to visual appearance change and also can be computationally expensive. In this paper, we propose an alternative approach adapting LiDAR descriptors for 3D points obtained from stereo-visual odometry for place recognition. 3D points are potentially more reliable than 2D visual cues (e.g., 2D features) against environmental changes (e.g., variable illumination) and this may benefit visual SLAM systems in long-term deployment scenarios. Stereo-visual odometry generates 3D points with an absolute scale, which enables us to use LiDAR descriptors for place recognition with high computational efficiency. Through extensive evaluations on standard benchmark datasets, we demonstrate the accuracy, efficiency, and robustness of using 3D points for place recognition over 2D methods.
I give a taste of recent progress in using chiral perturbation theory to understand nucleon and deuteron structure.
We provide, on the Birch and Swinnerton-Dyer conjecture, an explicit upper bound for the rank of the Mordell-Weil group of the Jacobian of the modular curve X_0(q) for q prime large enough, namely rank J_0(q)< 6.5 dim J_0(q).   The file j0q-pari.dvi contains the .dvi version of the commented listing of the Pari/GP program used for the computations of the paper ``Explicit Upper Bound for the rank of J_0(q)''.
It has been claimed that cosmic censorship conjecture can be violated by quantum tunnelling of neutrinos, though it is strongly supported by classical arguments. We consider the classical interaction of an extremal Kerr black hole with a test massless Dirac field, i.e. a "neutrino field". Evaluating the flux integrals imposed by the energy momentum tensor for fermionic fields and the Killing vectors of the space-time, we prove that this interaction can indeed destroy the event horizon of the black hole and convert it to a naked singularity. The classical process leads to a more generic violation of cosmic censorship conjecture compared to quantum tunnelling processes which occur with a low probability. The range of frequencies of the test neutrino field that can be used to destroy the black hole turns out to be the superradiant range for bosonic fields. We comment on back reaction and quantum effects. We argue that the destruction of black holes by neutrino fields cannot be fixed by self-force effects unlike similar attempts involving test bodies and bosonic fields.