ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS_5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d N=2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Nunez. This suggests different completions of the long quiver describing the CFT dual to the non-Abelian T-dual background that match different observables.
The function $h^0$ for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. In this paper, we prove the conjecture of van der Geer and Schoof about the maximality of $h^0$ at the trivial Arakelov divisor for quadratic extensions of complex quadratic fields.
Let $\vfi$ be Euler's function, $\ga$ be Euler's constant and $N_k$ be the product of the first $k$ primes. In this article, we consider the function $c(n) =(n/\vfi(n)-e^\ga\log\log n)\sqrt{\log n}$. Under Riemann's hypothesis, it is proved that $c(N_k)$ is bounded and explicit bounds are given while, if Riemann's hypothesis fails, $c(N_k)$ is not bounded above or below.
In this paper, we provide formulas for partial sums of weighted averages over regular integers modulo $n$ of the $\gcd$-sum function with any arithmetic function. Many interesting applications of the results are also given.
A four-dimensional timelike brane is considered as the boundary of the $SAdS_{5}$ bulk background. Exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis, can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of $SAdS_{5}$ bulk black hole as the source for stiff matter. A very interesting feature of the solutions of FRW equation is that they all (for $k=0,\pm1$) have a non-vanishing minimum value for the scale factor.
Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract information than the previous layer. The simplicity and elegance of the convolutional filtering process makes them perfect for structured problems such as image, video, or voice, where vertices are homogeneous in the sense of number, location, and strength of neighbors. The vast majority of classification problems, for example in the pharmaceutical, homeland security, and financial domains are unstructured. As these problems are formulated into unstructured graphs, the heterogeneity of these problems, such as number of vertices, number of connections per vertex, and edge strength, cannot be tackled with standard convolutional techniques. We propose a novel neural learning framework that is capable of handling both homogeneous and heterogeneous data, while retaining the benefits of traditional CNN successes.   Recently, researchers have proposed variations of CNNs that can handle graph data. In an effort to create learnable filter banks of graphs, these methods either induce constraints on the data or require preprocessing. As opposed to spectral methods, our framework, which we term Graph-CNNs, defines filters as polynomials of functions of the graph adjacency matrix. Graph-CNNs can handle both heterogeneous and homogeneous graph data, including graphs having entirely different vertex or edge sets. We perform experiments to validate the applicability of Graph-CNNs to a variety of structured and unstructured classification problems and demonstrate state-of-the-art results on document and molecule classification problems.
We simulate a heavy-ion collision using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory (Cb-TDHFB) treating pairing correlation in the three-dimensional coordinate space. We apply the Cb-TDHFB to 22O+22O collision with a contact-type pairing energy functional, and compare results of Cb-TDHFB and TDHF to investigate the effects of pairing correlations in nuclear fusion. Our results seem to indicate that pairing effects do not increase the fusion cross section in this system.
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations decay algebraically with the diffusive rate t^{-n/2} in space dimension n. We also compute the leading order term in the asymptotic expansion of the solution, and show that it corresponds to a spatially localized modulation of the phase. Our approach is based on a normal form transformation in the kinetics ODE which partially decouples the phase equation, at the expense of making the whole system quasilinear. Stability is then obtained by a global fixed point argument in temporally weighted Sobolev spaces.
The Feshbach theory of the optical potential naturally leads to a microscopic description of scattering in terms of the many-body self-energy. We consider a recent calculation of this quantity for 16O and study the possibility of applying it at astrophysical energies. The results obtained for the phase shifts and the 16O(p,\gamma) capture suggest that such studies are feasible but the calculations require some improvement geared to this specific task.
Metallicity gradients in the Sagittarius dwarf Galaxy (Sgr) are investigated by using infrared photometric data from the 2MASS survey. To search for metallicity effects, the giant branch in a field situated near the Center of the Sgr is compared to the giant branch in a field situated near its southern edge. The contamination of Sgr giant branch by foreground Galactic stars is canceled by statistical subtraction of diagrams symmetrical in Galactic latitude. After subtraction it is possible to reconstruct the Sgr giant branch with excellent accuracy. The giant branch in the two fields have similar slopes but are shifted in color. Even after correction for the differential reddening between the fields, the shift in color between the branch remains, and is very significant. This variation in the color of the giant branch corresponds to a metallicity variation of about -0.25 Dex. The existence of a metallicity gradient in Sgr may indicate that there are two different stellar population in Sgr. One has low metallicity, and another one of higher metallicity has a smaller spatial extension.
The chiral effective meson-baryon Lagrangian for the description of interactions between the doubly charmed baryons and Goldstone bosons is constructed up to the order of $q^{4}$. The numbers of linearly independent invariant monomials of $\mathcal{O}(q^2)$, $\mathcal{O}(q^3)$ and $\mathcal{O}(q^4)$ are 8, 32 and 218, in order. The obtained Lagrangian can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at complete one-loop level in future. For completeness, the non-relativistic reduction of the Lagrangian is also discussed.
We provide a simple way of searching for formulas of the Bailey--Borwein--Plouffe type together with an algorithm and an implementation in \texttt{sage}. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for $\sqrt{3}\pi$. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases but with integer coefficients. As an example of this, searching in various Pisot bases, we have discovered a formula for $\pi$ in base $1 + \sqrt{3}$, along with additional formulas.
We study a torus-like compactification of type IIB maximally supersymmetric PP-wave background. As the most general case, we discuss a T^8 compactification of all the transverse directions. A nontrivial structure of the isometry group requires an additional light-like compactification. This additional S^1 fiber is twisted on the T^8. We determine the spectrum of closed strings in this twisted torus background and compute the thermal partition function.
Recently, a homogenization procedure has been proposed, based on the tight lower bounds of the Bergman-Milton formulation, and successfully applied to dilute ternary nanocomposites to predict optical data without using any fitting parameters [Garcia et al. Phys. Rev. B, 75, 045439 (2007)]. The procedure has been extended and applied to predict the absorption coefficient of a quaternary nanocomposite consisting of Cu, Ag, and Au nanospheres embedded in a SiO2 host matrix. Significant enhancement of the absorption coefficient is observed over the spectral range 350-800 nm. The magnitude of this enhancement can be controlled by varying the nanosphere diameter and the individual metal volume fraction with respect to the host matrix. We have determined the optimal composition resulting in enhanced broadband (350nm-800nm) absorption of the solar spectrum using a simulated annealing algorithm. Fabricating such composite materials with a desired optical absorption has potential applications in solar energy harvesting.
Pfaffians of matrices with entries z[i,j]/(x\_i+x\_j), or determinants of matrices with entries z[i,j]/(x\_i-x\_j), where the antisymmetrical indeterminates z[i,j] satisfy the Pl\"ucker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young's orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature.
We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.
Massive stars (M $\gsim 10$ \msun) form from collapse of parsec-scale molecular clumps. How molecular clumps fragment to give rise to massive stars in a cluster with a distribution of masses is unclear. We search for cold cores that may lead to future formation of massive stars in a massive ($> 10^3$ \msun), low luminosity ($4.6 \times 10^2$ \lsun) infrared dark cloud (IRDC) G030.88+00.13. The \nh3 data from VLA and GBT reveal that the extinction feature seen in the infrared consists of two distinctive clumps along the same line of sight: The C1 clump at 97 \kms-1 coincides with the extinction in the Spitzer 8 and 24 $\mu$m. Therefore, it is responsible for the majority of the IRDC. The C2 clump at 107 \kms-1 is more compact and has a peak temperature of 45 K. Compact dust cores and \h2O masers revealed in the SMA and VLA observations are mostly associated with C2, and none is within the IRDC in C1. The luminosity indicates that neither the C1 nor C2 clump has yet to form massive protostars. But C1 might be at a precluster forming stage. The simulated observations rule out 0.1pc cold cores with masses above 8 \msun\ within the IRDC. The core masses in C1 and C2, and those in high-mass protostellar objects suggest an evolutionary trend that the mass of cold cores increases over time. Based on our findings, we propose an empirical picture of massive star formation that protostellar cores and the embedded protostars undergo simultaneous mass growth during the protostellar evolution.
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their canonical bundles, and show that they are rarely tilting. We also give a moduli construction for these total spaces for weighted projective lines with three orbifold points.
An analysis of archival mid-infrared (mid-IR) spectra of Seyfert galaxies from the Spitzer Space Telescope observations is presented. We characterize the nature of the mid-IR active nuclear continuum by subtracting a template starburst spectrum from the Seyfert spectra. The long wavelength part of the spectrum contains a strong contribution from the starburst-heated cool dust; this is used to effectively separate starburst-dominated Seyferts from those dominated by the active nuclear continuum. Within the latter category, the strength of the active nuclear continuum drops rapidly beyond ~ 20 micron. On average, type 2 Seyferts have weaker short-wavelength active nuclear continua as compared to type 1 Seyferts. Type 2 Seyferts can be divided into two types, those with strong poly-cyclic aromatic hydrocarbon (PAH) bands and those without. The latter type show polarized broad emission lines in their optical spectra. The PAH-dominated type 2 Seyferts and Seyfert 1.8/1.9s show very similar mid-IR spectra. However, after the subtraction of the starburst component, there is a striking similarity in the active nuclear continuum of all Seyfert optical types. PAH-dominated Seyfert 2s and Seyfert 1.8/1.9s tend to show weak active nuclear continua in general. A few type 2 Seyferts with weak/absent PAH bands show a bump in the spectrum between 15 and 20 micron. We suggest that this bump is the peak of a warm (~200 K) blackbody dust emission, which becomes clearly visible when the short-wavelength continuum is weaker. This warm blackbody emission is also observed in other Seyfert optical subtypes, suggesting a common origin in these active galactic nuclei.
We present low-resolution phase-resolved spectra of the polar MT Dra during its high states in 2006 and 2009. Balmer series, He I and He II 4686 \AA\ emission lines have complex shapes and show similar profile variations over an orbital cycle. The radial velocities vary with orbital period and display motions of the gas falling close to the magnetic poles of the white dwarf.
The security of quantum key distribution (QKD) has been proven for different protocols, in particular for the BB84 protocol. It has been shown that this scheme is robust against eventual imperfections in the state preparation, and sending only three different states delivers the same secret key rate achievable with four states. In this work, we prove, in a finite-key scenario, that the security of this protocol can be maintained even with less measurement operators on the receiver. This allows us to implement a time-bin encoding scheme with a minimum amount of resources.
We study how optical galaxy morphology depends on mass and star formation rate (SFR) in the Illustris Simulation. To do so, we measure automated galaxy structures in 10808 simulated galaxies at z=0 with stellar masses 10^9.7 < M_*/M_sun < 10^12.3. We add observational realism to idealized synthetic images and measure non-parametric statistics in rest-frame optical and near-IR images from four directions. We find that Illustris creates a morphologically diverse galaxy population, occupying the observed bulge strength locus and reproducing median morphology trends versus stellar mass, SFR, and compactness. Morphology correlates realistically with rotation, following classification schemes put forth by kinematic surveys. Type fractions as a function of environment agree roughly with data. These results imply that connections among mass, star formation, and galaxy structure arise naturally from models matching global star formation and halo occupation functions when simulated with accurate methods. This raises a question of how to construct experiments on galaxy surveys to better distinguish between models. We predict that at fixed halo mass near 10^12 M_sun, disc-dominated galaxies have higher stellar mass than bulge-dominated ones, a possible consequence of the Illustris feedback model. While Illustris galaxies at M_* ~ 10^11 M_sun have a reasonable size distribution, those at M_* ~ 10^10 M_sun have half-light radii larger than observed by a factor of two. Furthermore, at M_* ~ 10^10.5-10^11 M_sun, a relevant fraction of Illustris galaxies have distinct "ring-like" features, such that the bright pixels have an unusually wide spatial extent.
Autoparallel curves along with geodesic curves can arise as trajectories of physical test bodies. We explicitly derive autoparallels as effective post-Riemannian geometric constructs, and at the same time we argue \emph{against} postulating autoparallels as fundamental equations of motion for test bodies in alternative gravity theories.
Phenomena originated from spin-orbit interaction, such as magnetic anisotropy (MA), Rashba-type interactions, or topological insulators, have drawn huge attention for its intriguing physics. In particular, the search for a novel antiferromagnetic material, with potentially large perpendicular MA (PMA), has been becoming very intensive for next-generation high density memory applications. Here, we propose that substitutions of transition metals Ru and Ir, neighboring and same group elements in the periodic table, for the Rh site in the vicinity of surface can induce a substantially large PMA, up to an order of magnitude of 20 erg/cm2, in FeRh films on MgO. The main driving mechanism for this huge PMA is the interplay between the dxy and dx2-y2 states of strong spin-orbit 4d and 5d orbitals. Further investigations demonstrate that magnetization direction of PMA undergoes a transition into an in-plane magnetization at the antiferromagnetic-to-ferromagnetic phase transition, which provides a viable route for achieving large and switchable PMA associated with the magnetic-phase transition in antiferromagnetic spintronics.
The affine and Euclidean normalizers of the subperiodic groups, the Frieze groups, the rod groups, and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane group Euclidean normalizers have been considered.
We distinguish between Local Group field galaxies which may have passed through the virial volume of the Milky Way, and those which have not, via a statistical compari- son against populations of dark matter haloes in the Via Lactea II (VLII) simulation with known orbital histories. Analysis of VLII provides expectations for this escaped population: they contribute 13 per cent of the galactic population between 300 and 1500 kpc from the Milky Way, and hence we anticipate that about 7 of the 54 known Local Group galaxies in that distance range are likely to be Milky Way escapees. These objects can be of any mass below that of the Milky Way, and they are expected to have positive radial velocities with respect to the Milky Way. Comparison of the radius-velocity distributions of VLII populations and measurements of Local Group galaxies presents a strong likelihood that Tucana, Cetus, NGC3109, SextansA, SextansB, Antlia, NGC6822, Phoenix, LeoT, and NGC185 have passed through the Milky Way. Most of these dwarfs have a lower HI mass fraction than the majority of dwarfs lying at similar distances to either the Milky Way or M31. Indeed, several of these galaxies - especially those with lower masses - contain signatures in their morphology, star formation history and/or gas content indicative of evolution seen in simulations of satellite/parent galactic interactions. Our results offer strong support for scenarios in which dwarfs of different types form a sequence in morphology and gas content, with evolution along the sequence being driven by interaction history.
We investigate the low-temperature properties of the Ising-like screw chain antiferromagnet SrCo$_2$V$_2$O$_8$ under a longitudinal magnetic field by susceptibility and $^{51}$V NMR measurements. The bulk susceptibility $\chi$ shows an onset of long-range Ising-antiferromagnetic (AFM) order and the suppression of the order by field with the N\'{e}el temperature dropped from 5.1~K to 2~K when field increases from 0.1~T to 4~T. The suppression of the AFM order by the field is also observed by the NMR spectra and the spin-lattice relaxation $1/T_1$. At fields above 4~T, $\chi$ shows a low-temperature upturn, which is consistent with the onset of a transverse antiferromagnetic order as supported by the quantum Monte Carlo simulations. A line splitting in the NMR spectra is also observed at high temperatures. We show that the line split characterizes the onset of a short-range transverse antiferromagnetic order with magnetic moments orientated along the crystalline [110]/[1$\bar1$0] directions. The $1/T_1$ data at higher temperature show a power-law behavior $1/T_1{\sim}T^{\alpha}$, which is consistent with the Tomonaga-Luttinger-liquid behavior. With increasing the field, the power-law exponent $\alpha$ changes from negative to positive, which clearly shows an inversion of the Luttinger exponent $\eta$, where the dominant low-energy spin fluctuations switch from the longitudinal type to the transverse type at a high field of 7~T.
The formaldehyde $\rm H_2CO(1_{10} - 1_{11})$ absorption line and H$110\alpha$ radio recombination line (RRL) have been observed toward the Aquila Molecular Cloud using the Nanshan 25 m telescope operated by the Xinjiang Astronomical Observatory CAS. These first observations of the $\rm H_2CO$ $(1_{10} - 1_{11})$ absorption line determine the extent of the molecular regions that are affected by the ongoing star formation in the Aquila molecular complex and show some of the dynamic properties. The distribution of the excitation temperature $T_{ex}$ for $\rm H_2CO$ identifies the two known star formation regions W40 and Serpens South as well as a smaller new region Serpens 3. The intensity and velocity distributions of $\rm H_2CO$ and $\rm ^{13}CO(1-0)$ do not agree well with each other, which confirms that the $\rm H_2CO$ absorption structure is mostly determined by the excitation of the molecules resulting from the star formation rather than by the availability of molecular material as represented by the distribution. Some velocity-coherent linear $\rm ^{13}CO(1-0)$ structures have been identified in velocity channel maps of $\rm H_2CO$ and it is found that the three star formation regions lie on the intersect points of filaments. The $\rm H110\alpha$ emission is found only at the location of the W40 H II region and spectral profile indicates a redshifted spherical outflow structure in the outskirts of the H II region. Sensitive mapping of $\rm H_2CO$ absorption of the Aquila Complex has correctly identified the locations of star-formation activity in complex molecular clouds and the spectral profiles reveal the dominant velocity components and may identify the presence of outflows.
We present a detailed investigation of the magnetic properties of the spin-$\frac{3}{2}$ system Li$_2$Co(WO$_4$)$_2$ by means of magnetic susceptibility and specific heat. Our experimental results show that in Li$_2$Co(WO$_4$)$_2$ a short-range antiferromagnetic (AFM) correlations appear near $\chi$$_{max}$ $\sim$ 11 K and two successive long-range AFM phase transitions are observed at T$_{N1}$$\sim$ 9 K and T$_{N2}$$\sim$ 7 K. The frustration factor, $\mid$$\Theta$$\mid$/T$_{N1}$$\sim$3, indicates that the system is moderately frustrated, which is identifiable by the broken triangular symmetry within both $ab$- and $bc$-planes for the triclinic crystal structure. The magnetic isotherm at temperatures below T$_{N2}$ shows a field-induced spin-flop transition, and a complete H-T phase diagram for the two-step AFM system is mapped. $Ab$~$initio$ band structure calculations suggest that the strongest exchange coupling does not correspond to the shortest Co-Co distance along the $a$-axis, but rather along the diagonal direction through a Co-O-W-O-Co super-superexchange path within the $bc$-plane