ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the +/--Asai (aka tensor induction) representation that is critical in the sense of Deligne. For this we relate the oddness of the associated polarized Galois representations (in the sense of the Bella\"iche-Chenevier sign being +1) to the parity condition for criticality. Under an assumption similar to Vandiver's conjecture this also provides evidence for the Fontaine-Mazur conjecture for polarized Galois representations of any even dimension.
The self-affinity of growing systems with radial symmetry, from tumors to grain-grain displacement, has devoted increasing interest in the last decade. In this work, we analyzed features about the interface scaling of these clusters through large scale simulations (up to $3\times 10^7$ particles) of two-dimensional growth processes with special emphasis on the off-lattice Eden model. The central objective is to discuss an important pitfall associated to the evaluation of the growth exponent $\beta$ of these systems. We show that the $\beta$ value depends on the choice of the origin used to determine the interface width. We considered two strategies frequently used. When the width is evaluated in relation to the center of mass (CM) of the border, the exponent obtained for the Eden model was $\beta_{CM}=0.404\pm0.013$, in very good agreement with previous reported values. However, if the border CM is replaced by the initial seed position (a static origin), the exponent $\beta_0=0.333\pm 0.010$, in complete agreement with the KPZ value $\beta_{KPZ}=1/3$, was found. The difference between $\beta_{CM}$ and $\beta_{0}$ was explained through the border CM fluctuations that grow faster than the overall interface fluctuations. Indeed, we show that the exponents $\beta_0$ and $\beta_{CM}$ characterize large and small wavelength fluctuations of the interface, respectively. These finds were also observed in three distinct lattice models, in which the lattice-imposed anisotropy is absent.
We construct explicit embeddings of generalized Danielewski surfaves in affine spaces. The equations defining these embeddings are obtained from the 2x2 minors of a matrix attached to a labelled rooted tree. Then we describe more precisely those surfaces with a trivial Makar-Limanov invariant.
The stellar content of the intracluster light (ICL) provides unique insight into the hierarchical assembly process of galaxy clusters.However, the ICL is difficult to study due to its low surface brightness and large physical extent. We present optical spectra of three ICL regions in the Coma cluster, located between 100-180kpc from their nearest BCGs: NGC4889 and NGC4874. The mean surface brightness of the three ICL regions are {\mu}$_g$~25.3-26.2mag arcsec$^{-2}$. IFU spectroscopy with 13.5 hr on-source integration time were acquired as part of an ancillary program within the SDSS-IV MaNGA survey. We stacked the 127 individual fiber spectra in each IFU in order to achieve a 1{\sigma} limiting surface brightness of 27.9mag arcsec$^{-2}$, corresponding to a mean S/N in the optical of 21.6,9.6,and 11.6\AA$^{-1}$. We apply stellar population models to the stacked spectra, and measure the recession velocities, velocity dispersions ($\sigma$), stellar ages, and [Fe/H]. Our results show that the $\sigma$ of ICL regions are very high, indicating the stars are tracing the gravitational potential of the cluster, instead of any individual galaxy. The line-of-sight velocities of the three ICL regions are different from each other by ~700km/s, while the velocity of each region is similar to the closest BCG. This suggests that the ICL regions are associated with two distinct subclusters centered on NGC4889 and NGC4874.The stellar populations of these regions are old and metal poor, with ages of 7-12Gyr, and [Fe/H] of -0.8 to -0.6 dex. From the derived age and [Fe/H], the build-up of ICL in Coma is likely to be through the accretion of low mass galaxies or the tidal stripping of the outskirts of massive galaxies that have ended their star formation early on, instead of directly from major mergers of massive galaxies.
The 340-year old supernova remnant Cassiopeia A at 3.4 kpc distance is the best-studied young core-collapse supernova remnant. Nucleosynthesis yields in radioactive isotopes have been studied with different methods, in particular for production and ejection of $^{44}$Ti and $^{56}$Ni which originate from the innermost regions of the supernova. $^{44}$Ti was first discovered in this remnant, but is not seen consistently in other core-collapse sources. We analyse the observations accumulated with the SPI spectrometer on INTEGRAL, together with an improved instrumental background method, to achieve high spectroscopic resolution which enables interpretation towards a velocity constraint on $^{44}$Ti ejecta from the 1.157 MeV $\gamma$-ray line of the $^{44}$Sc decay. We observe both the hard X-ray line at 78 keV and the $\gamma$-ray line at 1157 keV from the $^{44}$Ti decay chain, at a combined significance of 3.8 $\sigma$. Measured fluxes are $(2.1\pm0.4)~10^{-5}~\mathrm{ph~cm^{-2}~s^{-1}}$ and $(3.5\pm1.2)~10^{-5}~\mathrm{ph~cm^{-2}~s^{-1}}$, which corresponds to $(1.5\pm0.4)~10^{-4}$ and $(2.4\pm0.9)~10^{-4}~\mathrm{M}_{\odot}$ of $^{44}$Ti, respectively. The measured Doppler broadening of the lines implies expansion velocities of $4300$ and $2200~\mathrm{km~s^{-1}}$, respectively. Combining our results with previous studies, we determine a more precise estimate of ejected $^{44}$Ti of $(1.37\pm0.19)~10^{-4}~\mathrm{M}_{\odot}$. The measurements of both lines are consistent with previous studies. The flux in the line originating from excited $^{44}$Ca is significantly higher than the flux determined in the lines from $^{44}$Sc. Cosmic ray acceleration within the supernova remnant may be responsible for an additional contribution to this line from nuclear de-excitation following energetic particle collisions in the remnant and swept-up material.
We get a new inequality on the Hodge number $h^{1,1}(S)$ of fibred algebraic complex surfaces $S$, which is a generalization of an inequality of Beauville. Our inequality implies the Arakelov type inequalities due to Arakelov, Faltings, Viehweg and Zuo, respectively.
We present a study of the magnetoresistance and Hall effect in the narrow-gap semiconductor FeSb2 at low temperatures. Both the electrical and Hall resistivities show unusual magnetic field dependence in the low-temperature range where a large Seebeck coefficient was observed. By applying a two-carrier model, we find that the carrier concentration decreases from 1 down to 10^-4 ppm/unit cell and the mobility increases from 2000 to 28000 cm2/Vs with decreasing temperature from 30 down to 4 K. At lower temperatures, the magnetoresistive behavior drastically changes and a negative magnetoresistance is observed at 3 K. These low-temperature behaviors are reminiscent of the low-temperature magnetotransport observed in doped semiconductors such as As-doped Ge, which is well described by a weak-localization picture. We argue a detailed electronic structure in FeSb2 inferred from our observations.
Precipitation nowcasting is a short-range forecast of rain/snow (up to 2 hours), often displayed on top of the geographical map by the weather service. Modern precipitation nowcasting algorithms rely on the extrapolation of observations by ground-based radars via optical flow techniques or neural network models. Dependent on these radars, typical nowcasting is limited to the regions around their locations. We have developed a method for precipitation nowcasting based on geostationary satellite imagery and incorporated the resulting data into the Yandex.Weather precipitation map (including an alerting service with push notifications for products in the Yandex ecosystem), thus expanding its coverage and paving the way to a truly global nowcasting service.
We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic (2002) prove an upper bound of the form $b/(b+\delta)$ for the speed on the $b$-ary tree, where $\delta$ is the reinforcement parameter. For $\delta>1$ we provide a lower bound of the form $\gamma^2 b/(b+\delta)$, where $\gamma$ is the survival probability of an associated branching process.
In this paper, we prove the existence of extremal functions for the best constant of embedding from anisotropic space, allowing some of the Sobolev exponents to be equal to $1$. We prove also that the extremal functions satisfy a partial differential equation involving the $1$ Laplacian.
Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.
We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n. Well-posedness of solutions reconstructing maximal parabolic regularity in nonlinear thermoelastic plates is established. In addition, exponential decay rates for strong solutions are also shown.
We present two large, nearby (0.013$\le$z$\le$0.06) samples of Early-Type Galaxies (ETGs): a visually classified sample of 220 ETGs, created using source-matched data from the Galaxy and Mass Assembly (GAMA) database with FIR/sub-mm detections from $Herschel$-ATLAS; and a visually classified sample of 551 ETGs which are undetected with $Herschel$-ATLAS. Active galactic nuclei (AGN) are removed from our samples using optical emission line diagnostics. These samples are scrutinised to determine characteristics of sub-mm detected versus undetected ETGs. We find similarities in the stellar mass distributions of the two ETG samples but testing other properties uncovers significant differences. The sub-mm detected sample is shown to have lower concentration and S\'ersic indices than those in the undetected sample - a result which may be linked to the presence of dust in the former. Optical and UV-optical colours are also shown to be much bluer, indicating that the dust is linked with recent star formation. The intrinsic effective radii are on average 1.5 times larger for the sub-mm detected ETGs. Surface densities and groups data from the GAMA database are examined for the two samples, leading to the conclusion that dusty ETGs inhabit sparser environments than non-dusty ETGs in the nearby universe, although environments of the brightest ETGs are shown to differ the least. Modified Planck functions are fit to the H-ATLAS detected PACS and SPIRE fluxes for ETGs with sub-mm flux densities of at least 3$\sigma$ in the 350$\mu$m SPIRE band, giving a resultant mean cold dust temperature of T$_{d}$=22.1K, with a range of 9-30K. The corresponding mean dust mass is 1.8$\times10^{7}$M$_{\odot}$, with a range of (0.08-35.0)$\times10^{7}$M$_{\odot}$. The dust masses calculated from these fits, normalised by stellar mass, are shown to increase with decreasing stellar mass and bluer colours.
We reviewed multi-wavelength blazars variability and detection of quasi-periodic oscillations on intra-day timescales. The variability timescale from few minutes to up to less than a days is commonly known as intra-day variability. These fast variations are extremely useful to constrain the size of emitting region, black hole mass estimation, etc. It is noticed that in general blazars show intra-day variability in the complete electromagnetic spectrum. But some class of blazars either do not show or show very little intra-day variability in a specific band of electromagnetic spectrum. Blazars show rarely quasi-periodic oscillations in time series data in optical and X-ray bands. Other properties and emission mechanism of blazars are also briefly discussed.
We consider an elliptic system with regular H{\"o}lderian weight and exponential nonlinearity or with weight and boundary singularity, and, Dirichlet condition. We prove the boundedness of the volume of the solutions to those systems on the annulus.
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split into two classes: a class of "astro-physically interesting" solutions describing "ordinary" matter with positive density and pressure, and a class of "phantom-like" solutions with positive density but negative active gravitational mass, which can also be of interest in several "very strong fields" regimes. Known results on linear-barotropic equations of state are recovered as particular cases.
The standard architecture of synthetic aperture radar (SAR) automatic target recognition (ATR) consists of three stages: detection, discrimination, and classification. In recent years, convolutional neural networks (CNNs) for SAR ATR have been proposed, but most of them classify target classes from a target chip extracted from SAR imagery, as a classification for the third stage of SAR ATR. In this report, we propose a novel CNN for end-to-end ATR from SAR imagery. The CNN named verification support network (VersNet) performs all three stages of SAR ATR end-to-end. VersNet inputs a SAR image of arbitrary sizes with multiple classes and multiple targets, and outputs a SAR ATR image representing the position, class, and pose of each detected target. This report describes the evaluation results of VersNet which trained to output scores of all 12 classes: 10 target classes, a target front class, and a background class, for each pixel using the moving and stationary target acquisition and recognition (MSTAR) public dataset.
We report the exact dimer phase, in which the ground states are described by product of singlet dimer, in the extended XYZ model by generalizing the isotropic Majumdar-Ghosh model to the fully anisotropic region. We demonstrate that this phase can be realized even in models when antiferromagnetic interaction along one of the three directions. This model also supports three different ferromagnetic (FM) phases, denoted as $x$-FM, $y$-FM and $z$-FM, polarized along the three directions. The boundaries between the exact dimer phase and FM phases are infinite-fold degenerate. The breaking of this infinite-fold degeneracy by either translational symmetry breaking or $\mathbb{Z}_2$ symmetry breaking leads to exact dimer phase and FM phases, respectively. Moreover, the boundaries between the three FM phases are critical with central charge $c=1$ for free fermions. We characterize the properties of these boundaries using entanglement entropy, excitation gap, and long-range spin-spin correlation functions. These results are relevant to a large number of one dimensional magnets, in which anisotropy is necessary to isolate a single chain out from the bulk material. We discuss the possible experimental signatures in realistic materials with magnetic field along different directions and show that the anisotropy may resolve the disagreement between theory and experiments based on isotropic spin-spin interactions.
Graphone is a half-hydrogenated graphene. The structure of graphone is illustrated as trigonal adsorption of hydrogen atoms on graphene at first. However, we found the trigonal adsorption is unstable. We present an illustration in detail to explain how a trigonal adsorption geometry evolves into a rectangular adsorption geometry. We check the change of magnetism during the evolution of geometry by evaluating the spin polarization of the intermediate geometries. We prove and clarify that the rectangular adsorption of hydrogen atoms on graphene is the most stable geometry of graphone and graphone is actually antiferromagnetic.
We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.
Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided $n < 1/2$, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for $n$ within this range, the obtained cosmological quantities are fully compatible with the Planck constraints, and that the "low curvature limit" comes as a viable approximation to calculate the power spectra of both scalar and tensor perturbations. Using reconstruction techniques for F(R) gravity with the Lagrange multiplier, the precise form of the effective F(R) gravity is found, from which one determines the power spectra of scalar and tensor perturbations in such bouncing scenario. Correspondingly, the spectral index for curvature perturbations and the tensor to scalar ratio are obtained, and these values are successfully confronted with the latest Planck observations. Further, it is shown that both the weak and the null energy conditions are satisfied, thanks to the holonomy corrections performed in the theory--which are then proven to be necessary for achieving this goal. In fact, when approaching the bouncing era, the holonomy corrections become significant and play a crucial role in order to restore the energy conditions. Summing up, a cosmological bouncing scenario with the scale factor above and fulfilling the energy conditions can be adequately described by the F(R) model with a Lagrange multiplier and holonomy corrections, which prove to be very important.
The double copy procedure relates gauge and gravity theories through color-kinematics replacements and holds for both scattering amplitudes and in classical contexts. Moreover, it has been shown that there is a web of theories whose scattering amplitudes are related through operations that exchange color and kinematic factors. In this paper, we generalize and extend this procedure by showing that the classical perturbative double copy of pions corresponds to special Galileons. We consider point-particles coupled to the relevant scalar fields, and find the leading and next to leading order radiation amplitudes. By considering couplings motivated by those that would arise from extracting the longitudinal modes of the gauge and gravity theories, we are able to map the non-linear sigma model radiation to that of the special Galileon. We also construct the single copy by mapping the bi-adjoint scalar radiation to the non-linear sigma model radiation through generalized color-kinematics replacements.
We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence (2009 Phys. Rev. D 80, 124008) in the appropriate limits. We also compute the Hawking temperature of the KN$AdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.
We present some new exact results for general four-dimensional superconformal field theories. We derive differential equations governing the coupling constant dependence of chiral primary correlators. For N=2 theories we show that the Zamolodchikov metric on the moduli space and the operator mixing of chiral primaries are quasi-topological quantities and constrained by holomorphy. The equations that we find are the four-dimensional analogue of the tt* equations in two-dimensions, discovered by the method of "topological anti-topological fusion" by Cecotti and Vafa. Our analysis relies on conformal perturbation theory and the superconformal Ward identities and does not use a topological twist.
Nucleon resonances are investigated through the electromagnetic production of K-mesons. We study the kaon photoproduction process at tree-level and compare to a recently developed unitary K-matrix approach. Employing hadronic form factors along with the proper gauge prescription yields suppression of the Born terms and leads a resonance dominated process for both K-Lambda and K-Sigma photoproduction. Using new SAPHIR data we find the K+-Lambda photoproduction to be dominated by the S11(1650) at threshold, with additional contributions from the P11(1710) and P13(1720) states. The K-Sigma channel couples to a cluster of Delta resonances around W = 1900 MeV. We briefly discuss some tantalizing evidence for a missing D13 resonance around 1900 MeV with a strong branching ratio into KLambda channel.
In 1969 Erdoes found a lower bound on the number of (r+1)-cliques sharing an edge in graphs with n vertices and t(r,n)+1 edges, where t(r,n) is the size of the Turan graph of order n and r color classes. We improve Erdoes's bound and prove a related stability result.
We give a pedagogical introduction to certain aspects of supersymmetric field theories in anti-de Sitter space. Among them are the presence of masslike terms in massless wave equations, irreducible unitary representations and the phenomenon of multiplet shortening.
The classical Kronecker limit formula gives the constant term of the non-holomorphic Eisenstein series E(z,s) for SL(2,Z) at s=1 in terms of the Dedekind eta function. Here we compute the analagous formula for an Eisenstein series twisted by modular symbols (periods of weight two holomorphic cusp forms) for general Fuchsian groups of the first kind.
Near threshold neutral pion electroproduction on the deuteron is studied in the framework of heavy baryon chiral perturbation theory. We include the next-to-leading order corrections to the three-body contributions. We find an improved description of the total and differential cross section data measured at MAMI. We also obtain more precise values for the threshold S-wave multipoles. We discuss in detail the theoretical uncertainties of the calculation.