ShantanuT01/DACTYL-Pretraining huggingface dataset:
For any scheme $M$ with a perfect obstruction theory, Jiang and Thomas associate a scheme $N$ with symmetric perfect obstruction theory. The scheme $N$ is a cone over $M$ given by the dual of the obstruction sheaf of $M$, and contains $M$ as its zero section. Locally $N$ is the critical locus of a regular function.   In this note we prove that $N$ is a $d$-critical scheme in the sense of Joyce. By assuming an orientation on $N$ there exists a global motive for $N$ locally given by the motive of vanishing cycles of the local regular function. We prove a motivic localization formula under the good and circle compact $\C^*$-action for $N$. When taking Euler characteristic the weighted Euler characteristic of $N$ weighted by the Behrend function is the signed Euler characteristic of $M$ by motivic method.   As applications we calculate the motivic generating series of the motivic Vafa-Witten invariants for K3 surfaces. This motivic series gives the result of the $\chi_y$-genus for Vafa-Witten invariants of K3 surfaces, which is the same (at instanton branch) as the K-theoretical Vafa-Witten invariants of Thomas.
The Chandra Carina Complex contains 200 known O- and B type stars. The Chandra survey detected 68 of the 70 O stars and 61 of 127 known B0-B3 stars. We have assembled a publicly available optical/X-ray database to identify OB stars that depart from the canonical Lx/Lbol relation, or whose average X-ray temperatures exceed 1 keV. Among the single O stars with high kT we identify two candidate magnetically confined wind shock sources: Tr16-22, O8.5 V, and LS 1865, O8.5 V((f)). The O4 III(fc) star HD 93250 exhibits strong, hard, variable X-rays, suggesting it may be a massive binary with a period of >30 days. The visual O2 If* binary HD 93129A shows soft 0.6 keV and hard 1.9 keV emission components, suggesting embedded wind shocks close to the O2 If* Aa primary, and colliding wind shocks between Aa and Ab. Of the 11 known O-type spectroscopic binaries, the long orbital-period systems HD 93343, HD 93403 and QZ Car have higher shock temperatures than short-period systems such as HD 93205 and FO 15. Although the X-rays from most B stars may be produced in the coronae of unseen, low-mass pre-main-sequence companions, a dozen B stars with high Lx cannot be explained by a distribution of unseen companions. One of these, SS73 24 in the Treasure Chest cluster, is a new candidate Herbig Be star.
We consider the effect of exotic S=+1 resonances Theta+ and Theta++ on K+p elastic scattering data (total cross section) and the process K0_Lp-->K0_Sp. Data near the observed Theta+(1540) are examined for evidence of additional states. The width limit for a Theta++ state is reconsidered and shown to be much less than 1 MeV.
Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Heegner points of discriminant $d <0$ on $X(D,1)$ as $d \to -\infty$. We prove that if $|d|$ is sufficiently large compared to the radius $r \approx \log X$ of the circle, we can improve on the classical $O(X^{2/3})$-bound of Selberg. Our result extends the result of Petridis and Risager for the modular surface to arithmetic compact Riemann surfaces.
This paper provides a technical description of the SuperNova Early Warning System (SNEWS), an international network of experiments with the goal of providing an early warning of a galactic supernova.
Burst-only sources are X-ray sources showing up only during short bursts but with no persistent emission (at least with the monitoring instrument which led to their discovery). These bursts have spectral characteristics consistent with thermonuclear (type I) burst from the neutron star surface, linking burst-only sources to neutron star X-ray binary transients. We have carried out a series of snapshot observations of the entire sample of burst-only sources with the Swift satellite. We found a few sources in outburst and detect faint candidates likely representing their quiescent counterparts. In addition, we observed three quasi-persistent faint X-ray binary transients. Finally we discuss burst-only sources and quasi-persistent sources in the framework of neutron star transients.
We prove that each bounded polytope can be represented as a polynomial zonotope, which we refer to as the Z-representation of polytopes. Previous representations are the vertex representation (V-representation) and the halfspace representation (H-representation). Depending on the polytope, the Z-representation can be more compact than the V-representation and the H-representation. In addition, the Z-representation enables the computation of linear maps, Minkowski addition, and convex hull with a computational complexity that is polynomial in the representation size. The usefulness of the new representation is demonstrated by range bounding within polytopes.
Metal-to-insulator transitions (MITs) are a dramatic manifestation of strong electron correlations in solids1. The insulating phase can often be suppressed by quantum tuning, i.e. varying a nonthermal parameter such as chemical composi- tion or pressure, resulting in a zero-temperature quantum phase transition (QPT) to a metallic state driven by quantum fluctuations, in contrast to conventional phase transitions driven by thermal fluctuations. Theories of exotic phenomena known to occur near the Mott QPT such as quantum criticality and high-temperature superconductivity often assume a second-order QPT, but direct experimental evidence for either first- or second-order behavior at the magnetic QPT associated with the Mott transition has been scarce and further masked by the superconducting phase in unconventional superconductors. Most measurements of QPTs have been performed by volume-integrated probes, such as neutron scattering, magnetization, and transport, in which discontinuous behavior, phase separation, and spatially inhomogeneous responses are averaged and smeared out, leading at times to misidentification as continuous second-order transitions. Here, we demonstrate through muon spin relaxation/rotation (MuSR) experiments on two archetypal Mott insulating systems, composition-tuned RENiO3 (RE=rare earth element) and pressured-tuned V2O3, that the QPT from antiferromagnetic insulator to paramagnetic metal is first-order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value across the phase diagram until it is suddenly destroyed at the QPT. These findings call for further investigation into the role of inelastic soft modes and the nature of dynamic spin and charge fluctuations underlying the transition.
We study the stability of vortex-lines in trapped dilute gases subject to rotation. We solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a 3d condensate in spherically and cilyndrically symmetric stationary traps, from small to very large nonlinearities. In the stationary case it is found that the vortex states with unit and $m=2$ charge are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the $m=1$ vortex-line, and that the multicharged vortices are never a local minimum of the energy functional, which implies that the absolute minimum of the energy is not an eigenstate of the $L_z$ operator, when the angular speed is above a certain value, $\Omega > \Omega_2$.
Taub numbers are studied on asymptotically flat backgrounds with Killing symmetries. When the field equations are solved for a background spacetime and higher order functional derivatives (higher order variational derivatives of the Hilbert Lagrangean) are solved for perturbations from the background, such perturbed space-times admit zeroth, first, and second order Taub numbers. Zeroth order Taub numbers are Komar constants (upto numerical factors) or Penrose-Goldberg constants of the background. For a Killing symmetry of the background, first order Taub numbers give the contribution of the linearized perturbation to the associated backgound quantity, such as the perturbing mass. Second order Taub numbers give the contribution of second order perturbations to the background quantity. The Bondi mass is a sum of first and second order Taubs numbers on a Minkowski background.
Stanley defined the chromatic symmetric function of a graph, and Shareshian and Wachs introduced a refinement, namely the chromatic quasisymmetric function of a labeled graph. In this paper, we define the chromatic quasisymmetric function of a directed graph, which agrees with the Shareshian-Wachs definition in the acyclic case. We give an F-basis expansion for all digraphs in terms of a permutation statistic, which we call G-descents. We use this expansion to derive a p-positivity formula for all digraphs with symmetric chromatic quasisymmetric functions. We show that the chromatic quasisymmetric functions of a certain class of digraphs, called circular indifference digraphs, have symmetric coefficients. We present an e-positivity formula for the chromatic quasisymmetric function of the directed cycle, which is a t-analog of a result of Stanley. Lastly, we give a generalization of the Shareshian-Wachs e-positivity conjecture to a larger class of digraphs.
We quantize the space of 2-charge fuzzballs in IIB supergravity on $K3$. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of $K3$ fuzzballs, filling a small gap in the literature.
We describe a model of dark matter halo abundances and clustering which combines the two most widely used approaches to this problem: that based on peaks and the other based on excursion sets. Our approach can be thought of as addressing the cloud-in-cloud problem for peaks and/or modifying the excursion set approach so that it averages over a special subset, rather than all possible walks. In this respect, it seeks to account for correlations between steps in the walk as well as correlations between walks. We first show how the excursion set and peaks models can be written in the same formalism, and then use this correspondence to write our combined excursion set peaks model. We then give simple expressions for the mass function and bias, showing that even the linear halo bias factor is predicted to be k-dependent as a consequence of the nonlocality associated with the peak constraint. At large masses, our model has little or no need to rescale the variable delta_c from the value associated with spherical collapse, and suggests a simple explanation for why the linear halo bias factor appears to lie above that based on the peak-background split at high masses when such a rescaling is assumed. Although we have concentrated on peaks, our analysis is more generally applicable to other traditionally single-scale analyses of large-scale structure.
We analyze the statistical properties of the turbulent velocity field in the deflagration model for Type Ia supernovae. In particular, we consider the question of whether turbulence is isotropic and consistent with the Kolmogorov theory at small length scales. Using numerical data from a high-resolution simulation of a thermonuclear supernova explosion, spectra of the turbulence energy and velocity structure functions are computed. We show that the turbulent velocity field is isotropic at small length scales and follows a scaling law that is consistent with the Kolmogorov theory until most of the nuclear fuel is burned. At length scales greater than a certain characteristic scale, turbulence becomes anisotropic. Here, the radial velocity fluctuations follow the scaling law of the Rayleigh-Taylor instability, whereas the angular component still obeys Kolmogorov scaling. In the late phase of the explosion, this characteristic scale drops below the numerical resolution of the simulation. The analysis confirms that a subgrid-scale model for the unresolved turbulence energy is required for the consistent calculation of the flame speed in deflagration models of Type Ia supernovae, and that the assumption of isotropy on these scales is appropriate.
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite counterparts in connection with symmetric polynomials and some arithmetic quantities called powerful numbers.
The microquasar GX 339-4 was observed by Suzaku five times, spaced by a few days, during its transition back to the hard state at the end of its 2010-2011 outburst. The 2-10 keV source flux decreases by a factor ~10 between the beginning and the end of the monitoring. Simultaneous radio and OIR observations highlighted the re-ignition of the radio emission just before the beginning of the campaign, the maximum radio emission being reached between the two first Suzaku pointings, while the IR peaked a few weeks latter. A fluorescent iron line is always significantly detected. Fits with a gaussian or Laor profiles give statistically equivalent results. In the case of a Laor profile, fits of the five data sets simultaneously agree with a disk inclination angle of ~20 degrees. The disk inner radius is <10-30 R_g in the first two observations but almost unconstrained in the last three. A soft X-ray excess is also present in these two first observations. Fits with a multicolor disk component give disk inner radii in agreement with those obtained with the iron line fits. The use of a physically more realistic model, including a blurred reflection component and a comptonization continuum, give some hints of the increase of the disk inner radius but the significances are always weak. Interestingly, the addition of warm absorption significantly improves the fit of OBS1 while it is not needed in the other observations. The radio-jet re-ignition occurring between OBS1 and OBS2, these absorption features may indicate the natural evolution from a disk wind and a jet. The comparison with a long 2008 Suzaku observation of GX 339-4 in a persistent faint hard state where a narrow iron line clearly indicates a disk recession, is discussed.
Cardiac segmentation is an essential step for the diagnosis of cardiovascular diseases. However, pixel-wise dense labeling is both costly and time-consuming. Scribble, as a form of sparse annotation, is more accessible than full annotations. However, it's particularly challenging to train a segmentation network with weak supervision from scribbles. To tackle this problem, we propose a new scribble-guided method for cardiac segmentation, based on the Positive-Unlabeled (PU) learning framework and global consistency regularization, and termed as ShapePU. To leverage unlabeled pixels via PU learning, we first present an Expectation-Maximization (EM) algorithm to estimate the proportion of each class in the unlabeled pixels. Given the estimated ratios, we then introduce the marginal probability maximization to identify the classes of unlabeled pixels. To exploit shape knowledge, we apply cutout operations to training images, and penalize the inconsistent segmentation results. Evaluated on two open datasets, i.e, ACDC and MSCMRseg, our scribble-supervised ShapePU surpassed the fully supervised approach respectively by 1.4% and 9.8% in average Dice, and outperformed the state-of-the-art weakly supervised and PU learning methods by large margins. Our code is available at https://github.com/BWGZK/ShapePU.
We present the MOdel for the Rise of GAlaxies aNd Active nuclei (MORGANA). Starting from the merger trees of dark matter halos and a model for the evolution of substructure within the halos, the complex physics of baryons is modeled with a set of state-of-the-art models that describe the mass, metal and energy flows between the various components and phases of a galaxy. The processes of shock-heating and cooling, star formation, feedback, galactic winds and super-winds, accretion onto BHs and AGN feedback are described by new models. In particular, the evolution of the halo gas explicitly follows the thermal and kinetic energies of the hot and cold phases, while star formation and feedback follow the results of the multi-phase model by Monaco (2004a). The increased level of sophistication allows to move from a phenomenological description of gas physics, based on simple scalings with the depth of the DM halo potential, toward a fully physically motivated one. The comparison of the predictions of MORGANA with a basic set of galactic data reveals from the one hand an overall rough agreement, and from the other hand highlights a number of well- or less-known problems: (i) producing the cutoff of the luminosity function requires to force the quenching of the late cooling flows by AGN feedback, (ii) the normalization of the Tully-Fisher relation of local spirals cannot be recovered unless the dark matter halos are assumed to have a very low concentration, (iii) the mass function of HI gas is not easily fitted at small masses, unless a similarly low concentration is assumed, (iv) there is an excess of small elliptical galaxies at z=0. These discrepancies, more than the points of agreement with data, give important clues on the missing ingredients of galaxy formation. (ABRIDGED)
We present results of spectrometric studies based on the observations of very strong 3C 279 flares in high and very-high-energy bands and discuss their implications regarding the origin of radiation mechanisms. The FSRQ 3C 279 (z=0.536) is one of the most luminous gamma-ray emitting AGN. It shows variability on time scales down to minutes during strong flares detected by the Fermi-LAT. We have analyzed LAT and Swift-XRT data for the flaring periods in June 2015 and January 2018, when the flux above 100 MeV during hourly time intervals could exceed $3 \times 10^{-5}$ ph cm$^{-2}$ s$^{-1}$. The X-ray flux derived from Swift X-ray observations described by a very hard spectrum with photon index ~1.5 is typically explained by Inverse Compton scattering of low energy electrons and protons. Here we consider an alternative interpretation which describes the entire band from X-ray to very high energy as a results of synchrotron emission by ultra relativistic electrons or protons.
Can a classical system command a general adversarial quantum system to realize arbitrary quantum dynamics? If so, then we could realize the dream of device-independent quantum cryptography: using untrusted quantum devices to establish a shared random key, with security based on the correctness of quantum mechanics. It would also allow for testing whether a claimed quantum computer is truly quantum. Here we report a technique by which a classical system can certify the joint, entangled state of a bipartite quantum system, as well as command the application of specific operators on each subsystem. This is accomplished by showing a strong converse to Tsirelson's optimality result for the Clauser-Horne-Shimony-Holt (CHSH) game: the only way to win many games is if the bipartite state is close to the tensor product of EPR states, and the measurements are the optimal CHSH measurements on successive qubits. This leads directly to a scheme for device-independent quantum key distribution. Control over the state and operators can also be leveraged to create more elaborate protocols for realizing general quantum circuits, and to establish that QMIP = MIP*.
We report the spectroscopic confirmation of a sub-mm galaxy (SMG) at z=4.547 with an estimated L_IR=0.5-2.0x10^13 L_sun. The spectra, mid-IR, and X-ray properties indicate the bolometric luminosity is dominated by star formation at a rate of >1000M_sun per yr. Multiple, spatially separated components are visible in the Ly-Alpha line with an observed velocity difference of up to 380 km/sec and the object morphology indicates a merger. The best fit spectral energy distribution and spectral line indicators suggest the object is 2-8 Myr old and contains >10^10 M_sun of stellar mass. This object is a likely progenitor for the massive early type systems seen at z~2.
We consider the transverse structure and stability properties of relativistic jets formed in the course of the collapse of a massive progenitor. Our numerical simulations show the presence of a strong shear in the bulk velocity of such jets. This shear can be responsible for a very rapid shear--driven instability that arises for any velocity profile. This conclusion has been confirmed both by numerical simulations and theoretical analysis. The instability leads to rapid fluctuations of the main hydrodynamical parameters (density, pressure, Lorentz factor, etc.). However, the perturbations of the density are effectively decoupled from those of the pressure because the beam of the jet is radiation--dominated. The characteristic growth time of instability is much shorter than the life time of the jet and, therefore, may lead to a complete turbulent beam. In the course of the non-linear evolution, these fluctuations may yield to internal shocks which can be randomly distributed in the jet. In the case that internal shocks in a ultrarelativistic outflow are responsible for the observed phenomenology of gamma-ray bursts, the proposed instability can well account for the short-term variability of gamma-ray light curves down to milliseconds.
The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.
We study the effects on the Higgs boson mass from LEP precision data of the new physics explaining $R_b$-$R_c$ crisis. We implement a fit to LEP observables with the new physics. We obtain $M_H^{\rm New Physics} = 85 ^{+ 467}_{-56} ~~{\rm GeV}$. Comparing with the value of the SM fit, $M_H^{\rm SM} = 38^{+ 96}_{-21} ~~{\rm GeV}$, the errors are larger and the central value is higher. The new physics may allow $M_H$ to have a value out of the range of ${\cal O}(M_Z)$.
The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.
We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background there are many string field theories corresponding to different decomposition of moduli space of Riemann surfaces. It is shown that any classical open string field theories on a fixed conformal background are $A_\infty$-quasi-isomorphic to each other. This indicates that they have isomorphic moduli space of classical solutions. The minimal model theorem in $A_\infty$-algebras plays a key role in these results. Its natural and geometric realization on formal supermanifolds is also given. The same results hold for classical closed string field theories, whose algebraic structure is governed by $L_\infty$-algebras.