ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present the analysis of the broadened, flourescent iron Kalpha line in simultaneous XMM-Newton and RXTE data from the black hole Cygnus X-1. The XMM-Newton data were taken in a modified version of the timing mode of the EPIC-pn camera. In this mode the lower energy threshold of the instrument is increased to 2.8 keV to avoid telemetry drop outs due to the brightness of the source, while at the same time preserving the signal-to-noise ratio in the Fe Kalpha band. We find that the best-fit spectrum consists of the sum of an exponentially cut off power-law and relativistically smeared, ionized reflection. The shape of the broadened Fe Kalpha feature is due to strong Compton broadening combined with relativistic broadening. Assuming a standard, thin accretion disk, the black hole is close to rotating maximally.
Quantum computation places very stringent demands on gate fidelities, and experimental implementations require both the controls and the resultant dynamics to conform to hardware-specific constraints. Superconducting qubits present the additional requirement that pulses must have simple parameterizations, so they can be further calibrated in the experiment, to compensate for uncertainties in system parameters. Other quantum technologies, such as sensing, require extremely high fidelities. We present a novel, conceptually simple and easy-to-implement gradient-based optimal control technique named Gradient Optimization of Analytic conTrols (GOAT), which satisfies all the above requirements, unlike previous approaches. To demonstrate GOAT's capabilities, with emphasis on flexibility and ease of subsequent calibration, we optimize fast coherence-limited pulses for two leading superconducting qubits architectures - flux-tunable transmons and fixed-frequency transmons with tunable couplers.
In this paper, we use the method of Thue and Siegel, based on explicit Pade approximations to algebraic functions, to completely solve a family of quartic Thue equations. From this result, we can also solve the diophantine equation in the title. We prove that this equation has at most one solution in positive integers when $d \geq 3$. Moreover, when such a solution exists, it is of the form $(u,\sqrt{v})$ where $(u,v)$ is the fundamental solution of $X^{2}+1=dY^{2}$.
The nuclear norm minimization (NNM) is commonly used to approximate the matrix rank by shrinking all singular values equally. However, the singular values have clear physical meanings in many practical problems, and NNM may not be able to faithfully approximate the matrix rank. To alleviate the above-mentioned limitation of NNM, recent studies have suggested that the weighted nuclear norm minimization (WNNM) can achieve a better rank estimation than NNM, which heuristically set the weight being inverse to the singular values. However, it still lacks a rigorous explanation why WNNM is more effective than NMM in various applications. In this paper, we analyze NNM and WNNM from the perspective of group sparse representation (GSR). Concretely, an adaptive dictionary learning method is devised to connect the rank minimization and GSR models. Based on the proposed dictionary, we prove that NNM and WNNM are equivalent to L1-norm minimization and the weighted L1-norm minimization in GSR, respectively. Inspired by enhancing sparsity of the weighted L1-norm minimization in comparison with L1-norm minimization in sparse representation, we thus explain that WNNM is more effective than NMM. By integrating the image nonlocal self-similarity (NSS) prior with the WNNM model, we then apply it to solve the image denoising problem. Experimental results demonstrate that WNNM is more effective than NNM and outperforms several state-of-the-art methods in both objective and perceptual quality.
That $\mu \to e, \gamma$ and $\tau \to \mu,\gamma$ are sensitive probes of SUSY models with a see-saw mechanism is a well accepted fact. Here we propose a `top-down' approach in a general SUSY SO(10) scheme. In this framework, we show that at least one of the neutrino Yukawa couplings is as large as the top Yukawa coupling. This leads to a strong enhancement of these leptonic flavour changing decay rates. We examine two `extreme' cases, where the lepton mixing angles in the neutrino Yukawa couplings are either small (CKM-like) or large (PMNS-like). In these two cases, we quantify the sensitivity of leptonic radiative decays to the SUSY mass spectrum. In the PMNS case, we find that the ongoing experiments at the B-factories can completely probe the spectrum up to gaugino masses of 500 GeV (any tan $\beta$). Even in the case of CKM-like mixings, large regions of the parameter space will be probed in the near future, making these two processes leading candidates for indirect SUSY searches.
For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular configuration $\Delta$ thus provides a geometric representation of $C$ which carries its weight enumerator. This is the initial step in the suggestion by M. Loebl, to extend the theory of Pfaffian orientations from graphs to general linear binary codes. Then we carry out also the second step by constructing, for every triangular configuration $\Delta$, a triangular configuration $\Delta'$ and a bijection between the cycle space of $\Delta$ and the set of the perfect matchings of $\Delta'$.
The centrality dependence of thermal parameters describing hadron multiplicities and intermediate-mass dilepton spectra in heavy-ion collisions at SPS and RHIC is analyzed. From experimental hadron multiplicities we deduce evidence for strangeness saturation at high energy and maximum centrality. The observed dilepton spectra can be parameterized by a centrality independent temperature.
Let (X,H) be a polarized, smooth, complex projective surface, and let v be a Chern character on X with positive rank and sufficiently large discriminant. In this paper, we compute the Gieseker wall for v in a slice of the stability manifold of X. We construct explicit curves parameterizing non-isomorphic Gieseker stable sheaves that become S-equivalent along the wall. As a corollary, we conclude that if there are no strictly semistable sheaves of character v, the Bayer-Macri divisor associated to the wall is a boundary nef divisor on the moduli space of sheaves M_H(v). We recover previous results for the projective plane and K3 surfaces, and illustrate applications to higher Picard rank surfaces with an example on a quadric surface.
In the current era of Gaia and large, high signal to noise stellar spectroscopic surveys, there is an unmet need for a reliable library of fundamentally calibrated stellar effective temperatures based on accurate stellar diameters. Here we present a set of precision diameters and temperatures for a sample of 6 dwarf, 5 sub-giant, and 5 giant stars observed with the PIONIER beam combiner at the VLTI. Science targets were observed in at least two sequences with five unique calibration stars each for accurate visibility calibration and to reduce the impact of bad calibrators. We use the standard PIONIER data reduction pipeline, but bootstrap over interferograms, in addition to employing a Monte-Carlo approach to account for correlated errors by sampling stellar parameters, limb darkening coefficients, and fluxes, as well as predicted calibrator angular diameters. The resulting diameters were then combined with bolometric fluxes derived from broadband Hipparcos-Tycho photometry and MARCS model bolometric corrections, plus parallaxes from Gaia to produce effective temperatures, physical radii, and luminosities for each star observed. Our stars have mean angular diameter and temperatures uncertainties of 0.8% and 0.9% respectively, with our sample including diameters for 10 stars with no pre-existing interferometric measurements. The remaining stars are consistent with previous measurements, with the exception of a single star which we observe here with PIONIER at both higher resolution and greater sensitivity than was achieved in earlier work.
The present NLL prediction for the decay rate of the rare inclusive process $\bar B \to X_s \gamma$ has a large uncertainty due to the charm mass renormalization scheme ambiguity. We estimate that this uncertainty will be reduced by a factor of 2 at the NNLL level. This is a strong motivation for the on-going NNLL calculation, which will thus significantly increase the sensitivity of the observable $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM. We also give a brief status report of the NNLL calculation.
A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.
We consider N=2 supersymmetric Yang-Mills theories in four dimensions with gauge group SU(N) for N larger than two. Using the cubic curve for a matter hypermultiplet transforming in the symmetric representation, obtained from M-theory by Landsteiner and Lopez, we calculate the prepotential up to the one instanton correction. We treat the curve to be approximately hyperelliptic and perform a perturbation expansion for the Seiberg-Witten differential to get the one instanton contribution. We find that it reproduces the correct result for one-loop, and we obtain the prediction for that curve for the one instanton correction term.
During July 2009 we observed the first confirmed superoutburst of the eclipsing dwarf nova SDSS J150240.98+333423.9 using CCD photometry. The outburst amplitude was at least 3.9 magnitudes and it lasted at least 16 days. Superhumps having up to 0.35 peak-to-peak amplitude were present during the outburst, thereby establishing it to be a member of the SU UMa family. The mean superhump period during the first 4 days of the outburst was Psh = 0.06028(19) d, although it increased during the outburst with dPsh/dt = + 2.8(1.0) x 10-4. The orbital period was measured as Porb = 0.05890946(5) d from times of eclipses measured during outburst and quiescence. Based on the mean superhump period, the superhump period excess was 0.023(3). The FWHM eclipse duration declined from a maximum of 10.5 min at the peak of the outburst to 3.5 min later in the outburst. The eclipse depth increased from ~0.9 mag to 2.1 mag over the same period. Eclipses in quiescence were 2.7 min in duration and 2.8 mag deep.
In this paper, based on an ideal of Tian, we establish a new sufficient condition for a positive integer to be a congruent number in terms of Legendre symbols of prime factors of the positive integer. Our criterion generalizes previous criterions of Heegner, and Birch--Stephens, Monsky, and Tian, and conjecturally provides a list of positive density of congruent numbers. Our method of proving our criterion is to give formulae for the analytic Tate--Shafarevich number in terms of the so-called genus periods and genus points. These formulae are derived from the Waldspurger formula and the generalized Gross--Zagier formula of Yuan-Zhang-Zhang.
We detail a technique for estimating the UV extinction and luminosity of UV selected galaxies using UV quantities alone. The technique is based on a tight correlation between the ratios of far infrared (FIR) to UV flux ratios and UV color for a sample of local starbursts. A simple empirical fit to this correlation can be used to estimate UV extinction as a function of color. This method is applied to a sample of Lyman-break systems selected from the HDF and having $z \approx 3$. The resultant UV emissivity is at least nine times higher than the original Madau et al. (1996) estimate. This technique can be readily applied to other rest-frame UV surveys.
Tunneling between two-dimensional electron layers with mutually correlated disorder potentials is studied theoretically. Due to this correlation, the diffusive eigenstates in different layers are almost orthogonal to each other. As a result, a peak in the tunnel I-V characteristics shifts towards small bias, V. This "protects" the peak against the interaction-induced smearing, since the relaxation rate near the Fermi level is low. If the correlation in disorder potentials is complete, the peak position and width are governed by the spin-orbit coupling in the layers; this coupling lifts the orthogonality of the eigenstates. Possibility to use inter-layer tunneling for experimental determination of weak intrinsic spin-orbit splitting of the Fermi surface is discussed.
A popular model for the circumstellar disks of Be stars is that of a geometrically thin disk with a density in the equatorial plane that drops as a power law of distance from the star. It is usually assumed that the vertical structure of such a disk (in the direction parallel to the stellar rotation axis) is governed by the hydrostatic equilibrium set by the vertical component of the star's gravitational acceleration. Previous radiative equilibrium models for such disks have usually been computed assuming a fixed density structure. This introduces an inconsistency as the gas density is not allowed to respond to temperature changes and the resultant disk model is not in vertical, hydrostatic equilibrium. In this work, we modify the {\sc bedisk} code of \citet{sig07} so that it enforces a hydrostatic equilibrium consistent with the temperature solution. We compare the disk densities, temperatures, H$\alpha$ line profiles, and near-IR excesses predicted by such models with those computed from models with a fixed density structure. We find that the fixed models can differ substantially from the consistent hydrostatic models when the disk density is high enough that the circumstellar disk develops a cool ($T\lesssim10,000 $K) equatorial region close to the parent star. Based on these new hydrostatic disks, we also predict an approximate relation between the (global) density-averaged disk temperature and the $T_{\rm eff}$ of the central star, covering the full range of central Be star spectral types.
Finsler geometry has been recently re-discovered as an interesting possibility to describe spacetime geometry beyond Riemannian geometry. The most evident effect of this class of models is the prediction of modified dispersion relations for particles moving in such backgrounds. In this paper, we are going to consider the effects of modified dispersion relations on a gauge field theory with spontaneous symmetry breaking (SSB) associated to a Higgs field. The percolation of higher dimensional, Lorentz violating operators to lower dimensional ones is discussed. We also discuss the issue of SSB in a mono-metric Finsler scenario like the one associated to the so-called very special relativity.
A recent publication by Clark et.al (2019, CX19) uses both GALFA-HI observational data and numerical simulations to address the nature of intensity fluctuations in Position-Position-Velocity (PPV) space. The study questions the validity and applicability of the statistical theory of PPV space fluctuations formulated in Lazarian & Pogosyan (2000, LP00) to HI gas and concludes that $"${\it a significant reassessment of many observational and theoretical studies of turbulence in HI}$"$. This implies that dozens of papers that used LP00 theory to explore interstellar turbulence as well as the ongoing research based on LP00 theory are in error. This situation motivates the urgency of our public response. In our Comment we explain why we believe the criticism in CX19 is based on the incorrect understanding of the LP00 theory. In particular, we illustrate that the correlation between PPV slices and dust emissions in CX19 does not properly reveal the relative importance of velocity and density fluctuations in velocity channel maps. While CX19 provides an explanation of the change of the spectral index with respect to the thickness of PPV slice based on the two-phase nature of H1 gas, we failed to see any observational support for this idea. On the contrary, we show that the observations both in two-phase HI and one phase CO show similar results. Moreover, the observed change is in good agreement with LP00 predictions and spectral indexes of velocity and density spectra that are obtained following LP00 procedures are in good agreement with the numerically confirmed expectations of compressible MHD turbulence theory. In short, we could not find any justification of the criticism of LP00 theory that is provided in CX19. On the contrary, our analysis testifies that both available observational and numerical data agree well with the predictions of LP00 theory.
Recent Hubble Space Telescope observations have unveiled the white dwarf cooling sequence of the Galactic bulge. Although the degenerate sequence can be well fitted employing the most up-to-date theoretical cooling sequences, observations show a systematic excess of red objects that cannot be explained by the theoretical models of single carbon-oxygen white dwarfs of the appropriate masses. Here we present a population synthesis study of the white dwarf cooling sequence of the Galactic bulge that takes into account the populations of both single white dwarfs and binary systems containing at least one white dwarf. These calculations incorporate state-of-the-art cooling sequences for white dwarfs with hydrogen-rich and hydrogen-deficient atmospheres, for both white dwarfs with carbon-oxygen and helium cores, and also take into account detailed prescriptions of the evolutionary history of binary systems. Our Monte Carlo simulator also incorporates all the known observational biases. This allows us to model with a high degree of realism the white dwarf population of the Galactic bulge. We find that the observed excess of red stars can be partially attributed to white dwarf plus main sequence binaries, and to cataclysmic variables or dwarf novae. Our best fit is obtained with a higher binary fraction and an initial mass function slope steeper than standard values, as well as with the inclusion of differential reddening and blending. Our results also show that the possible contribution of double degenerate systems or young and thick-disk bulge stars is negligible.
In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This framework can be used to represent e.g. a lumped mass fixed to a beam or a system with delay. This work generalizes the sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a recently developed concept of fundamental state and the associated boundary-condition-free representation. The conditions of the generalized KYP are tested using the PQRS positive matrix parameterization of operators resulting in a finite-dimensional LMI, feasibility of which implies prima facie provable passivity or L2-gain of the system. No discretization or approximation is involved at any step and we use numerical examples to demonstrate that the bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs.
We report the first direct spectroscopic measurement of the velocity dispersion function (VDF) for the high-mass red sequence (RS) galaxy population at redshift $z\sim0.55$. We achieve high precision by using a sample of 600,000 massive galaxies with spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third Sloan Digital Sky Survey (SDSS-III), covering stellar masses $M_*\gtrsim10^{11}~M_{\odot}$. We determine the VDF by projecting the joint probability-density function (PDF) of luminosity $L$ and velocity dispersion $\sigma$, i.e. $p(L,\sigma)$, defined by our previous measurements of the RS luminosity function and $L-\sigma$ relation for this sample. These measurements were corrected from red--blue galaxy population confusion, photometric blurring, incompleteness and selection effects within a forward-modeling framework that furthermore correctly accommodates the low spectroscopic signal-to-noise ratio of individual BOSS spectra. Our $z\sim0.55$ RS VDF is in overall agreement with the $z\sim0$ early-type galaxy (ETG) VDF at $\log_{10}\sigma\gtrsim2.47$, however the number density of $z=0.55$ RS galaxies that we report is larger than that of $z=0$ ETG galaxies at $2.35\gtrsim\log_{10}\sigma\gtrsim 2.47$. The extrapolation of an intermediate-mass L-$\sigma$ relation towards the high-mass end in previous low-z works may be responsible for this disagreement. Evolutionary interpretation of this comparison is also subject to differences in the way the respective samples are selected; these differences can be mitigated in future work by analyzing $z=0$ SDSS data using the same framework presented in this paper. We also provide the sample PDF for the RS population (i.e. uncorrected for incompleteness), which is a key ingredient for gravitational lensing analyses using BOSS.
Analytic properties of hard exclusive processes described by Generalized Parton Distributions (GPD's) are considered. The analytic continuation of GPD is provided by Generalized Distribution Amplitudes (GDA). The GDA's for the production of two $\rho-$mesons may give an access to four-quark exotic states. The crucial role in the proof of analyticity is played by the Cavalieri conditions (polynomiality), resulting in the "holographic" property of GPD, when the full information about various hard processes is contained in the one dimensional sections ($x=\pm \xi$)of GPD. The applicability of analyticity for description of the double diffractive production of dileptons and Higgs bosons is discussed.
Deep convolutional neural network (DCNN) has achieved remarkable performance on object detection and speech recognition in recent years. However, the excellent performance of a DCNN incurs high computational complexity and large memory requirement. In this paper, an equal distance nonuniform quantization (ENQ) scheme and a K-means clustering nonuniform quantization (KNQ) scheme are proposed to reduce the required memory storage when low complexity hardware or software implementations are considered. For the VGG-16 and the AlexNet, the proposed nonuniform quantization schemes reduce the number of required memory storage by approximately 50\% while achieving almost the same or even better classification accuracy compared to the state-of-the-art quantization method. Compared to the ENQ scheme, the proposed KNQ scheme provides a better tradeoff when higher accuracy is required.
We propose a precise and efficient normal estimation method that can deal with noise and nonuniform density for unstructured 3D point clouds. Unlike existing approaches that directly take patches and ignore the local neighborhood relationships, which make them susceptible to challenging regions such as sharp edges, we propose to learn graph convolutional feature representation for normal estimation, which emphasizes more local neighborhood geometry and effectively encodes intrinsic relationships. Additionally, we design a novel adaptive module based on the attention mechanism to integrate point features with their neighboring features, hence further enhancing the robustness of the proposed normal estimator against point density variations. To make it more distinguishable, we introduce a multi-scale architecture in the graph block to learn richer geometric features. Our method outperforms competitors with the state-of-the-art accuracy on various benchmark datasets, and is quite robust against noise, outliers, as well as the density variations.