ShantanuT01/DACTYL-Pretraining huggingface dataset:
M. Nori proved that on a projective smooth variety, a bundle is finite, (that is the ring it generates has dimension 0), if and only if it trivializes on a finite cover. In this note, we consider bundles of degree 0 on an elliptic curve. We prove that the dimension of the ring generated by such a bundle is the same as the dimension of a torsor trivializing the bundle (and is 1).
We define a Fourier-Mukai transform for Higgs bundles on smooth curves and study its properties. It is shown that the transform of a stable zero-degree Higgs bundle is an algebraic vector bundle on the cotangent bundle of the Jacobian of the curve. We show that this transformed bundle admits a natural extension to an algebraic vector bundle over a projective compactification of the base. The main result is that the original Higgs bundle can be reconstructed from this extension. We also compute certain invariants of the transformed bundle.
In this paper we study the conjectured dual operators to a near maximal giant graviton and their open string fluctuations in the large $N$ limit. Using matrix model estimates we show that the spectrum of states near the D-brane operator is consistent with a Fock space of open plus closed string states. We also give an argument that these operators, in spite of having large R charge of order N, are amenable to being studied with standard perturbative techniques, which organize themselves in a 1/N expansion. Also the spectrum of operators dual to massless fluctuations on the D-brane is shown to be protected from weak to strong coupling at leading order, so it is possible to read the shape of the dual operator by understanding how the spherical harmonics of the D-brane fluctuations appear.
By the Lefschetz hyperplane theorem, if X is a smooth quasi-projective variety and C a general curve section of X then the fundamental group of C surjects onto the fundamental group of X. Here we consider when this conclusion holds for a general member of an arbitrary family of curves that covers X. The most interesting case is families of rational curves.
The present work obtains the fundamental group of a toroidal compactification X' of a non-compact quotient X of a Hermitian symmetric space D of non-compact type by a lattice L in the isometry group G of D. As a consequence it derives the equality of the ranks of the first homology groups of X' and X with integral coefficients. The paper provides also a sufficient condition on a torsion free non-uniform lattice L, under which the fundamental group of X' is residually finite. Articles of Hummel-Schroeder, Hummel and Di Cerbo imply that the toroidal compactifications X' of generic non-compact torsion free quotients X of the complex balls satisfy this sufficient condition.
We present deep radio observations of the most distant complete quasar sample drawn from the Sloan Digital Sky Survey. Combining our new data with those from literature we obtain a sample which is ~100 per cent complete down to S_1.4GHz = 60 \mu Jy over the redshift range 3.8 < z < 5. The fraction of radio detections is relatively high (~43 per cent), similar to what observed locally in bright optical surveys. Even though the combined radio and optical properties of quasars remain overall unchanged from z ~ 5 to the local Universe, there is some evidence for a slight over-abundance of radio-loud sources at the highest redshifts when compared with the lower-z regime.   Exploiting the deep radio VLA observations we present the first attempt to directly derive the radio luminosity function of bright quasars at z ~ 4. The unique depth -- both in radio and optical -- allows us to thoroughly explore the population of optically bright FR~II quasars up to z ~ 5 and opens a window on the behaviour of the brightest FR~I sources. A close investigation of the space density of radio loud quasars also suggests a differential evolution, with the more luminous sources showing a less pronounced cut-off at high z when compared with the less luminous ones.
The entropy of the two-dimensional $t$-$J$ model is investigated using its 12th order high temperature series. A direct Pad\'{e} extrapolation of the entropy series doesn't converge well for temperatures below $T\sim J$. The series coefficients are exact polynomials so the series convergence can be improved by modifying the series that is extrapolated. By subtracting a scaled version of the series for the entropy of the Heisenberg antiferromagnet from the $t$-$J$ entropy series the low temperature convergence is greatly improved. Using this technique results are obtained for the full range of electron densities and temperatures. The electron density is an adjustable parameter in the series coefficients allowing the density dependence of the entropy and the density derivative at fixed temperature $\partial S/\partial n|_T$ to be determined accurately. The density derivative depends strongly on temperature, unlike noninteracting models. The density derivative is also an approximation to the experimentally measured thermopower.
We use the Eighth Data Release of Sloan Digital Sky Survey (SDSS DR8) catalog with its additional sky coverage of the southern Galactic hemisphere, to measure the extent and study the nature of the Virgo Overdensity (VOD; Juric et al. 2008). The data show that the VOD extends over no less than 2000 deg^2, with its true extent likely closer to 3000 deg^2. We test whether the VOD can be attributed to a tilt in the stellar halo ellipsoid with respect to the plane of the Galactic disk and find that the observed symmetry of the north-south Galactic hemisphere star counts excludes this possibility. We argue that the Virgo Overdensity, in spite of its wide area and cloud-like appearance, is still best explained by a minor merger. Its appearance and position is qualitatively similar to a near perigalacticon merger event and, assuming that the VOD and the Virgo Stellar Stream share the same progenitor, consistent with the VSS orbit determined by Casetti-Dinescu et al. (2009).
We present a detailed analysis of the behavior of the triaxial Schwarzschild orbit superposition method near the axisymmetric limit. Orbit superposition modeling is the primary method used to determine dynamical masses of supermassive black holes ($M_\mathrm{BH}$) in nearby galaxies; however, prior studies have reported conflicting results when comparing the outcome from axisymmetric orbit codes with that from a triaxial orbit code in the axisymmetric limit. We show that in order to achieve (oblate) axisymmetry in a triaxial code, care needs to be taken to axisymmetrize the short-axis tube orbits and to exclude both the long-axis tube and box orbits from the orbit library. Using up to 12 Gauss-Hermite moments of the line-of-sight velocity distributions as constraints, we demonstrate the effects of orbit types on the best-fit $M_\mathrm{BH}$ in orbit modeling of the massive elliptical galaxy NGC 1453 reported in Liepold et al. 2020. In addition, we verify the efficacy of our updated code on a mock galaxy dataset. We identify a subset of slowly precessing quasi-planar orbits for which the typical integration times can be insufficient to fully capture the equilibrium orbital behavior in both axisymmetric and triaxial systems with central black holes. Further investigation is needed for a more reliable treatment of these orbits.
The cosmic web contains filamentary structure on a wide range of scales. On the largest scales, superclustering aligns multiple galaxy clusters along inter-cluster bridges, visible through their thermal Sunyaev-Zel'dovich signal in the Cosmic Microwave Background. We demonstrate a new, flexible method to analyze the hot gas signal from multi-scale extended structures. We use a Compton-$y$ map from the Atacama Cosmology Telescope (ACT) stacked on redMaPPer cluster positions from the optical Dark Energy Survey (DES). Cutout images from the $y$ map are oriented with large-scale structure information from DES galaxy data such that the superclustering signal is aligned before being overlaid. We find evidence for an extended quadrupole moment of the stacked $y$ signal at the 3.5$\sigma$ level, demonstrating that the large-scale thermal energy surrounding galaxy clusters is anisotropically distributed. We compare our ACT$\times$DES results with the Buzzard simulations, finding broad agreement. Using simulations, we highlight the promise of this novel technique for constraining the evolution of anisotropic, non-Gaussian structure using future combinations of microwave and optical surveys.
While the unit cell volume of compounds belonging to the Mn$_3$Ga$_{1-x}$Sn$_x$C, (0 $ \le x \le $ 1) series shows a conformity with Vegard's law, their magnetic and magnetocaloric properties behave differently from those of parent compounds Mn$_3$GaC and Mn$_3$SnC. A correlation between the observed magnetic properties and underlying magnetic and local structure suggests that replacing Ga atoms by larger atoms of Sn results in the formation of Ga-rich and Sn-rich clusters. As a result, even though the long range structure appears to be cubic, Mn atoms find themselves in two different local environments. The packing of these two different local structures into a single global structure induces tensile/compressive strains on the Mn$_{6}$C functional unit and is responsible for the observed magnetic properties across the entire solid solution range.
Energy system information valuable for electricity access planning such as the locations and connectivity of electricity transmission and distribution towers, termed the power grid, is often incomplete, outdated, or altogether unavailable. Furthermore, conventional means for collecting this information is costly and limited. We propose to automatically map the grid in overhead remotely sensed imagery using deep learning. Towards this goal, we develop and publicly-release a large dataset ($263km^2$) of overhead imagery with ground truth for the power grid, to our knowledge this is the first dataset of its kind in the public domain. Additionally, we propose scoring metrics and baseline algorithms for two grid mapping tasks: (1) tower recognition and (2) power line interconnection (i.e., estimating a graph representation of the grid). We hope the availability of the training data, scoring metrics, and baselines will facilitate rapid progress on this important problem to help decision-makers address the energy needs of societies around the world.
We investigate the generation of the entanglement in a cavity magnomechanical system, which consists of three modes: a magnon mode, a microwave cavity mode and a mechanical vibration mode, the couplings of the magnon-photon and the magnon-phonon are achieved by the magnetic dipole interaction and the magnetostrictive interaction, respectively. By introducing a squeezing of the magnon mode, the magnon-photon and the magnon-phonon entanglements are significantly enhanced compared with the case without inserting the magnon squeezing. We find that an optimal parameter of the squeezing exists, which yields the maximum entanglement. This study provides a new idea for exploring the properties of quantum entanglement in the the cavity magnomechanical systems, and may have some potential applications in the quantum state engineering.
The NGT field equations with sources are expanded first about a flat Minkowski background and then about a GR background to first-order in the antisymmetric part of the fundamental tensor, $g_{\mu\nu}$. From the general, static spherically symmetric solution of the field equation in empty space, we establish that there are two conserved charges $m$ and $\ell^2$ corresponding to the two basic gauge invariances of NGT. There is no direct contribution to the flux of gravitational waves from the antisymmetric, $g_{[\mu\nu]}$, sector in the linearized, lowest order of approximation, nor in the non-linear theory. It is demonstrated that the flux of gravitational waves is finite in magnitude and positive definite for solutions of the field equations which satisfy the boundary condition of asymptotic flatness.
The measurement of the anomalous magnetic moment of the muon exhibits a long standing discrepancy compared to the Standard model prediction. In this paper, we concentrate on this issue in the framework of $R$-parity violating Minimal supersymmetric standard model. Such a scenario provides substantial contribution to the anomalous magnetic moment of the muon while satisfying constraints from low energy experimental observables as well as neutrino mass. In addition, we point out that the implication of such operators satisfying muon $g-2$ are immense from the perspective of the LHC experiment, leading to a spectacular four muon final state. We propose an analysis in this particular channel which might help to settle the debate of R-parity violation as a probable explanation for $(g-2)_{\mu}$.
It is well established that the properties of supermassive black holes and their host galaxies are correlated through scaling relations. While hydrodynamical cosmological simulations have begun to account for the co-evolution of BHs and galaxies, they typically have neglected the BH spin, even though it may play an important role in modulating the growth and feedback of BHs. Here we introduce a new sub-grid model for the BH spin evolution in the moving-mesh code {\small AREPO} in order to improve the physical faithfulness of the BH modelling in galaxy formation simulations. We account for several different channels of spin evolution, in particular gas accretion through a Shakura-Sunyaev $\alpha$-disc, chaotic accretion, and BH mergers. For BH feedback, we extend the IllustrisTNG model, which considers two different BH feedback modes, a thermal quasar mode for high accretion states and a kinetic mode for low Eddington ratios, with a self-consistent accounting of spin-dependent radiative efficiencies and thus feedback strength. We find that BHs with mass $M_{\rm{bh}}\lesssim 10^{8}\, {\rm M}_\odot$ reach high spin values as they typically evolve in the coherent gas accretion regime. On the other hand, BHs with mass $M_{\rm{bh}}\gtrsim 10^{8}\, {\rm M}_\odot$ have lower spins as BH mergers become more frequent, and their accretion discs fragment due to self-gravity, inducing chaotic accretion. We also explore the hypothesis that the transition between the quasar and kinetic feedback modes is mediated by the accretion mode of the BH disc itself, i.e.~the kinetic feedback mode is activated when the disc enters the self-gravity regime. We find excellent agreement between the galaxy and BH populations for this approach and the fiducial TNG model with no spin evolution. Furthermore, our new approach alleviates a tension in the galaxy morphology -- colour relation of the original TNG model.
The harmonic index of a graph $G$, is defined as the sum of weights $\frac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ is the degree of the vertex $u$ in $G$. In this paper we find the minimum harmonic index of bicyclic graph of order $n$ and diameter $d$. We also characterized all bicyclic graphs reaching the minimum bound.
In this paper, we present counterexamples showing that for any $p\in (1,\infty)$, $p\neq 2$, there is a non-divergence form uniformly elliptic operator with piecewise constant coefficients in $\mathbb{R}^2$ (constant on each quadrant in $\mathbb{R}^2$) for which there is no $W^2_p$ estimate. The corresponding examples in the divergence case are also discussed. One implication of these examples is that the ranges of $p$ are sharp in the recent results obtained in [4,5] for non-divergence type elliptic and parabolic equations in a half space with the Dirichlet or Neumann boundary condition when the coefficients do not have any regularity in a tangential direction.
We give a short survey of problems and results on (1) diameter graphs and hypergraphs, and (2) geometric Ramsey theory. We also make some modest contributions to both areas. Extending a well known theorem of Kahn and Kalai which disproved Borsuk's conjecture, we show that for any integer $r\ge 2$, there exist $\varepsilon=\varepsilon(r)>0$ and $d_0=d_0(r)$ with the following property. For every $d\ge d_0$, there is a finite point set $P\subset\mathbb{R}^d$ of diameter $1$ such that no matter how we color the elements of $P$ with fewer than $(1+\varepsilon)^{\sqrt{d}}$ colors, we can always find $r$ points of the same color, any two of which are at distance $1$.
In this paper we give a new proof of the fact that for all pairs of positive integers (d, m) with d/m < 117/37, the linear system of plane curves of degree d with ten general base points of multiplicity m is empty.
We present an intuitive theoretical description of the optical properties of complex metal nano-structure, consisting of two nano-shells connected by a nano-rod giving a dumb-bell like appearance. The simulations were done using Finite Element Method. The effect of the nano-rod length and radius as also the dimensions of the nano-shells were analyzed. The absorption spectra as in peak positions and intensities have been found to have a strong dependence on the geometrical parameters of the dumb-bell. This study provides evidence that the localized surface plasmon modes play a key role in the broadband light harvesting capabilities of these nanostructures and is promising for a wide range of practical applications, for example in surface-enhanced spectroscopies.
In a randomly oriented graph containing vertices $x$ and $y$, denote by $\{x\to y\}$ the event that there is a directed path from $x$ to $y$. We study the correlation between the events $\{x\to y\}$ and $\{y\to z\}$ for a (large) oriented complete bipartite graph with orientation chosen uniformly at random. We classify the cases of positive and negative correlation respectively in terms of the relative proportions of the sizes of the color classes of the graph.
We have constructed an analytic formula to treat the perpendicular magnetic anisotropy energy in ferromagnetic metals with low symmetry, such as C4V and C3V. We find that the anisotropy energy is proportional to a part of the expectation values of the orbital angular momentum and magnetic dipole operator. Although the result is similar to the model proposed by Laan [J. Phys.: Condens. Matter 10, 3239 (1998)], we have derived a concrete expression for the spin-flip virtual excitation process term, which can be dominant in atoms with small magnetic moments and/or small exchange splitting. Pt monatomic layer with proximity-induced spin polarization grown on Fe is an example of this. Other multilayer systems such as Co/Pd and Co/Ni and bilayer systems such as Fe(CoB)/MgO can be discussed similarly. Moreover, the relation between perpendicular magnetic anisotropy energy and measurable physical parameters is discussed based on X-ray magnetic circular dichroism spectroscopy.
We consider the problem of determining amplitudes from observables for the case of pseudoscalar meson photoproduction. We find a number of surprisingly simple constraints which give necessary conditions for a complete set of measurements. These results contradict one of the selection rules derived previously.
We have combined the wide-area Herschel-ATLAS far-IR survey with spectroscopic redshifts from GAMA and SDSS to define a sample of 21 low--redshift ($z_{\rm spec} < 0.5$) analogs of submm galaxies (SMGs). These have been selected because their dust temperatures and total IR luminosities are similar to those for the classical high-redshift SMG population. As well as presenting the sample, in this paper we report $^{12}$CO(2-1) and $^{12}$CO(1-0) observations of 16 low-redshift analogs of SMGs taken with the IRAM-30m telescope. We have obtained that low-redshift analogs of SMGs represent a very diverse population, similar to what has been found for high-redshift SMGs. A large variety in the molecular gas excitation or $^{12}$CO(2-1)/$^{12}$CO(1-0) line ratio is seen, meaning that extrapolations from $J \geq 2$ CO lines can result in very uncertain molecular gas mass determinations. Our sources with $^{12}$CO(1-0) detections follow the dust--gas correlation found in previous work at different redshifts and luminosities. The molecular gas mass of low-redshift SMGs has an average value of $M_{\rm H_2} \sim 1.6 \times 10^{10}\,M_\odot$ and will be consumed in $\sim 100 \, {\rm Myr}$ . We also find a wide range of molecular gas fractions, with the highest values being compatible with those found in high-redshift SMGs with $^{12}$CO(1-0) detections, which are only the most luminous. Low-redshift SMGs offer a unique opportunity to study the properties of extreme star formation in a detail not possible at higher redshifts.
We study the effects of noncommutative spaces on the horizon, the area spectrum and Hawking temperature of a Schwarzschild black hole. The results show deviations from the usual horizon, area spectrum and the Hawking temperature. The deviations depend on the parameter of space-space noncommutativity.
The role played by the intergalactic medium (IGM) in the X-ray absorption towards high-redshift sources has recently drawn more attention in spectral analysis studies. Here, we study the X-ray absorption towards 15 flat-spectrum radio quasars at $z>2$, relying on high counting statistic ($\gtrsim10\,000$ photons) provided by XMM-Newton, with additional NuSTAR (and simultaneous Swift-XRT) observations when available. Blazars can be confidently considered to have negligible X-ray absorption along the line of sight within the host galaxy, likely swept by the kpc-scale relativistic jet. This makes our sources ideal for testing the absorption component along the IGM. Our new approach is to revisit the origin of the soft X-ray spectral hardening observed in high-z blazars in terms of X-ray absorption occurring along the IGM, with the help of a low-z sample used as comparison. We verify that the presence of absorption in excess of the Galactic value is the preferred explanation to explain the observed hardening, while intrinsic energy breaks, predicted by blazars' emission models, can easily occur out of the observing energy band in most sources. First, we perform an indirect analysis comparing the inferred amount of absorption in excess of the Galactic value with a simulated IGM absorption contribution, that increases with redshift and includes both a minimum component from diffuse IGM metals, and the additional contribution of discrete denser intervening regions. Then, we directly investigate the warm-hot IGM with a spectral model on the best candidates of our sample, obtaining an average IGM density of $n_0=1.01^{+0.53}_{-0.72}\times10^{-7}$ cm$^{-3}$ and temperature of $\log(T/\text{K})=6.45^{+0.51}_{-2.12}$. A more dedicated study is currently beyond reach, but our results can be used as a stepping stone for future more accurate analysis, involving Athena.
We consider neutralino production and decay e^+e^ --> chi^0_i chi^0_j, chi^0_j --> chi^0_1 f \bar{f} at a linear collider with transverse e^+ and e^- beam polarization. We propose CP asymmetries by means of the azimuthal distribution of the produced neutralinos and of that of the final leptons, while taking also into account the subsequent decays of the neutralinos. We include the complete spin correlations between production and decay. Our framework is the Minimal Supersymmetric Standard Model with complex parameters. In a numerical study we show that there are good prospects to observe these CP asymmetries at the International Linear Collider and estimate the accuracy expected for the determination of the phases in the neutralino sector.
In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.