ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will also map our model to a diffusive system of particles on a ring and reinterpret our results in this new setting.
We develop a local probe to estimate the connectivity of complex quantum networks. Our results show how global properties of different classes of complex networks can be estimated - in quantitative manner with high accuracy - by coupling a probe to a single node of the network. Here, our interest is focused on probing the connectivity, i.e. the degree sequence, and the value of the coupling constant within the complex network. The scheme combines results on classical graph theory with the ability to develop quantum probes for networks of quantum harmonic oscillators. Whilst our results are proof-of-principle type, within the emerging field of quantum complex networks they may have potential applications for example to the efficient transfer of quantum information or energy or possibly to shed light on the connection between network structure and dynamics.
We present photometric and spectroscopic observations of the Type IIn supernova SN 2019zrk (also known as ZTF20aacbyec). The SN shows a $\gtrsim$ 100 day precursor, with a slow rise, followed by a rapid rise to M $\sim -19.2$ in the $r$ and $g$ bands. The post-peak light-curve decline is well fit with an exponential decay with a timescale of $\sim 39$ days, but it shows prominent undulations, with an amplitude of $\sim 1$ mag. Both the light curve and spectra are dominated by an interaction with a dense circumstellar medium (CSM), probably from previous mass ejections. The spectra evolve from a scattering-dominated Type IIn spectrum to a spectrum with strong P-Cygni absorptions. The expansion velocity is high, $\sim 16,000$ km s$^{-1}$, even in the last spectra. The last spectrum $\sim 110$ days after the main eruption reveals no evidence for advanced nucleosynthesis. From analysis of the spectra and light curves, we estimate the mass-loss rate to be $\sim 4 \times 10^{-2}$ M$_\odot$ yr$^{-1}$ for a CSM velocity of 100 km s$^{-1}$, and a CSM mass of $\gtrsim 1$ M$_\odot$. We find strong similarities for both the precursor, general light curve, and spectral evolution with SN 2009ip and similar SNe, although SN 2019zrk displays a brighter peak magnitude. Different scenarios for the nature of the 09ip-class of SNe, based on pulsational pair instability eruptions, wave heating, and mergers, are discussed. }
An important result of Koml\'os [Tiling Tur\'an theorems, Combinatorica, 2000] yields the asymptotically exact minimum degree threshold that ensures a graph $G$ contains an $H$-tiling covering an $x$th proportion of the vertices of $G$ (for any fixed $x \in (0,1)$ and graph $H$). We give a degree sequence strengthening of this result which allows for a large proportion of the vertices in the host graph $G$ to have degree substantially smaller than that required by Koml\'os' theorem. We also demonstrate that for certain graphs $H$, the degree sequence condition is essentially best possible in more than one sense.
We revisit here the problem of generalized cosmology using renormalization group approach. A complete analysis of these cosmologies, where specific models appear as asymptotic fixed-points, is given here along with their linearized stability analysis.
Aperture photometry from our own observations and the literature is presented for the 12\um\ Galaxies in the near infrared J, H and K bands and, in some cases, in the L band. These data are corrected to ``total'' near--infrared magnitudes, (with a typical uncertainty of 0.3 magnitudes) for a direct comparison with our IRAS fluxes which apply to the entire galaxy. The corrected data are used to derive integrated total NIR and FIR luminosities. We then combine these with blue photometry and an estimate of the flux contribution from cold dust at wavelengths longward of 100\um\ to derive the first {\it bolometric\/} luminosities for a large sample of galaxies. We use multiwavelength correlations to identify several combinations of infrared colors which discriminate between Seyfert~1 and~2 galaxies, LINERs, and ultraluminous starbursts. We find that bolometric luminosity is more closely proportional to 12-micron luminosity than to 60-micron, 25-micron or optical luminosity.
It is well-known that the coordinator polynomials of the classical root lattice of type $A_n$ and those of type $C_n$ are real-rooted. They can be obtained, either by the Aissen-Schoenberg-Whitney theorem, or from their recurrence relations. In this paper, we develop a trigonometric substitution approach which can be used to establish the real-rootedness of coordinator polynomials of type $D_n$. We also find the coordinator polynomials of type $B_n$ are not real-rooted in general. As a conclusion, we obtain that all coordinator polynomials of Weyl group lattices are log-concave.
In this paper, we consider a Class of Hessian quotient equations in Euclidean space. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the Hessian quotient equations.
We present a detailed study of a high-redshift iron low-ionization broad absorption line (FeLoBAL) quasar (SDSS1214 at $z = 1.046$), including new interferometric $^{12}$CO $J$=2-1 observations, optical through far-infrared photometry, and mid-infrared spectroscopy. The CO line is well-fit by a single Gaussian centered 40 kms$^{-1}$ away from the systemic velocity and implies a total molecular gas mass of $M_\textrm{gas} = 7.3 \times 10^{10} \textrm{M}_\odot$. The infrared SED requires three components: an active galactic nucleus (AGN) torus, an AGN polar dust component, and a starburst. The starburst dominates the infrared emission with a luminosity of log($L_\textrm{SB}[\textrm{L}_\odot]) = 12.91^{+0.02}_{-0.02}$, implying a star formation rate of about 2000 $\textrm{M}_{\odot}$yr$^{-1}$, the highest known among FeLoBAL quasars. The AGN torus and polar dust components are less luminous, at log($L_\textrm{AGN}[\textrm{L}_\odot]) = 12.36^{+0.14}_{-0.15}$ and log($L_\textrm{dust}[\textrm{L}_\odot]) = 11.75^{+0.26}_{-0.46}$, respectively. If all of the molecular gas is used to fuel the ongoing star formation, then the lower limit on the subsequent duration of the starburst is 40 Myr. We do not find conclusive evidence that the AGN is affecting the CO gas reservoir. The properties of SDSS1214 are consistent with it representing the endpoint of an obscured starburst transitioning through a LoBAL phase to that of a classical quasar.
The degree chromatic polynomial $Pm(G,k)$ of a graph $G$ counts the number of $k$-colorings in which no vertex has $m$ adjacent vertices of its same color. We prove Humpert and Martin's conjecture on the leading terms of the degree chromatic polynomial of a tree.
The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.
We discuss evidence that quasars, and more generally radio jets, may have played an active role in the formation stage of galaxies by inducing star formation, i.e. through positive feedback. This mechanism first proposed in the 70's has been considered as anecdotic until now, contrary to the opposite effect that is generally put forward, the quenching of star formation in massive galaxies to explain the galaxy bimodality, downsizing and the universal black hole mass over bulge stellar mass ratio. This suggestion is based on the recent discovery of an ultra-luminous infrared galaxies, i.e. an extreme starburst, which appears to be triggered by a radio jet from the QSO HE0450-2958 at z=0.2863, together with the finding in several systems of an offset between molecular gas and quasars, which may be explained by the positive feedback effect of radio jets on their local environment.
Following from our recent work, we present here a detailed structural analysis of a representative sample of nearby spiral and early-type galaxies taken from the KINGFISH/ SINGS survey. The photometric parameters of bulges are obtained from bulge-disc decompositions using GALFIT data analysis algorithm. The method and corrections for projection and dust effects previously obtained are used to derive intrinsic photometric and structural bulge parameters. We show the main bulge scaling relations and the black hole relations, both observed and intrinsic ones, in B band. We find dust and inclination effects to produce more important changes in the parameters of the Kormendy relation for spiral galaxies, with the respective bulges of late-type galaxies residing on a steeper slope relation that the early-type galaxies. We observe that the Kormendy relation in combination with a bulge S\'{e}rsic index ($n_{b}$) threshold, does not produce a conclusive morphological separation of bulges. The $n_{b}$- bulge-to-total flux ratio ($B/T$) and $B/T$-stellar mass could be used to discriminate between late-type and early-type galaxies, while a further use of these parameters to divide bulges with different morphologies is problematic due to overlaps in the two distributions or large spread in values. We confirm the existence of two distinct intrinsic relations between the bulge luminosity (or absolute magnitude) and S\'{e}rsic index for late- and early-type galaxies, while the relations between the black-hole mass ($M_{BH}$) and bulge luminosity are not found to be statistically different at p<0.05. Within errors, we find statistically similar intrinsic $M_{BH}-n_{b}$ relations for all bulges.
The propagation of dissipationless, hydromagnetic, non-WKB, purely toroidal Alfv\'en waves in a realistic background three-fluid solar wind with axial symmetry and differential proton-alpha flow is investigated. The wave equations are derived from standard multi-fluid 5-moment equations. The Alfv\'enic point, where the combined poloidal Alfv\'en Mach number $M_T=1$, is found to be a singular point for the wave equation, which is then numerically solved for three representative angular frequencies $\omega=10^{-3}$, $10^{-4}$ and $10^{-5}$ rad s$^{-1}$ with a fixed wave amplitude of 10 km s$^{-1}$ imposed at the coronal base (1 $R_\odot$). Between 1 $R_\odot$ and 1 AU, the numerical solutions show substantial deviation from the WKB expectations. Even for the relatively high frequency $\omega=10^{-3}$ rad s$^{-1}$, a WKB-like behavior can be seen only in regions $r\gtrsim 10$ $R_\odot$. In the low-frequency case $\omega=10^{-5}$ rad s$^{-1}$, the computed profiles of wave-related parameters show a spatial dependence distinct from the WKB one, the deviation being particularly pronounced in interplanetary space. In the inner corona $r\lesssim 4$ $R_\odot$, the computed ion velocity fluctuations are considerably smaller than the WKB expectations in all cases, as is the computed wave-induced acceleration exerted on protons or alpha particles. With the chosen base wave amplitude, the wave acceleration has negligible effect on the ion force balance in the corona. Hence processes other than the non-WKB wave acceleration are needed to accelerate the ions out of the gravitational potential well of the Sun. However, at large distances beyond the Alfv\'enic point, the low-frequency waves can play an important role in the ion dynamics, with the net effect being to equalize the speeds of the two ion species considered.
We apply the Tremaine-Weinberg method to 19 nearby galaxies using stellar mass surface densities and velocities derived from the PHANGS-MUSE survey, to calculate (primarily bar) pattern speeds ($\Omega_{\rm P}$). After quality checks, we find that around half (10) of these stellar mass-based measurements are reliable. For those galaxies, we find good agreement between our results and previously published pattern speeds, and use rotation curves to calculate major resonance locations (co-rotation radii and Lindblad resonances). We also compare these stellar-mass derived pattern speeds with H$\alpha$ (from MUSE) and CO($J=2{-}1$) emission from the PHANGS-ALMA survey. We find that in the case of these clumpy ISM tracers, this method erroneously gives a signal that is simply the angular frequency at a representative radius set by the distribution of these clumps ($\Omega_{\rm clump}$), and that this $\Omega_{\rm clump}$ is significantly different to $\Omega_{\rm P}$ ($\sim$20% in the case of H$\alpha$, and $\sim$50% in the case of CO). Thus, we conclude that it is inadvisable to use "pattern speeds" derived from ISM kinematics. Finally, we compare our derived pattern speeds and co-rotation radii, along with bar properties, to the global parameters of these galaxies. Consistent with previous studies, we find that galaxies with a later Hubble type have a larger ratio of co-rotation radius to bar length, more molecular-gas rich galaxies have higher $\Omega_{\rm P}$, and more bulge-dominated galaxies have lower $\Omega_{\rm P}$. Unlike earlier works, however, there are no clear trends between the bar strength and $\Omega_{\rm P}$, nor between the total stellar mass surface density and the pattern speed.
Human Body Dimensions Estimation (HBDE) is a task that an intelligent agent can perform to attempt to determine human body information from images (2D) or point clouds or meshes (3D). More specifically, if we define the HBDE problem as inferring human body measurements from images, then HBDE is a difficult, inverse, multi-task regression problem that can be tackled with machine learning techniques, particularly convolutional neural networks (CNN). Despite the community's tremendous effort to advance human shape analysis, there is a lack of systematic experiments to assess CNNs estimation of human body dimensions from images. Our contribution lies in assessing a CNN estimation performance in a series of controlled experiments. To that end, we augment our recently published neural anthropometer dataset by rendering images with different camera distance. We evaluate the network inference absolute and relative mean error between the estimated and actual HBDs. We train and evaluate the CNN in four scenarios: (1) training with subjects of a specific gender, (2) in a specific pose, (3) sparse camera distance and (4) dense camera distance. Not only our experiments demonstrate that the network can perform the task successfully, but also reveal a number of relevant facts that contribute to better understand the task of HBDE.
We propose a systematic expansion method which is applied to freely evolving granular fluids contained in sufficiently small systems. Restricting ourselves to small systems, we show that there exists a small parameter which characterizes a typical size of density and temperature inhomogeneities. A solution of the hydrodynamic equations for a fluid of inelastic hard spheres is expanded in the small parameter. It is shown that our method quantitatively describes the asymptotic state of the system, such as flow profiles, density and temperature inhomogeneities, and the decay law of the global temperature and the energy per particle.
The 1D Cauchy problem for the Dirac-Klein-Gordon system is shown to be locally well-posed for low regularity Dirac data in $\hat{H^{s,p}}$ and wave data in $\hat{H^{r,p}} \times \hat{H^{r-1,p}}$ for $1<p\le 2$ under certain assumptions on the parameters r and s, where $\|f\|_{\hat{H^{s,p}}} := \| < \xi >^s \hat{f}\|_{L^{p'}}$, generalizing the results for $p=2$ by Selberg and Tesfahun. Especially we are able to improve the results from the scaling point of view with respect to the Dirac part.
We discuss the effects of a gauge freedom in representing quantum information processing devices, and its implications for characterizing these devices. We demonstrate with experimentally relevant examples that there exists equally valid descriptions of the same experiment which distribute errors differently among objects in a gate-set, leading to different error rates. Consequently, it can be misleading to attach a concrete operational meaning to figures of merit for individual gate-set elements. We propose an alternative operational figure of merit for a gate-set, the mean variation error, and a protocol for measuring this figure.
A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition of $G$ into cliques, such that any vertex belongs to at most $k$ cliques and any two cliques have at most $m$ vertices in common. The {\it $m$-krausz} dimension $kdim_m(G)$ of the graph $G$ is the minimum number $k$ such that $G$ has a krausz $(k,m)$-partition. 1-krausz dimension is known and studied krausz dimension of graph $kdim(G)$.   In this paper we prove, that the problem $"kdim(G)\leq 3"$ is polynomially solvable for chordal graphs, thus partially solving the problem of P. Hlineny and J. Kratochvil. We show, that the problem of finding $m$-krausz dimension is NP-hard for every $m\geq 1$, even if restricted to (1,2)-colorable graphs, but the problem $"kdim_m(G)\leq k"$ is polynomially solvable for $(\infty,1)$-polar graphs for every fixed $k,m\geq 1$.
We study entry loci of varieties and their irreducibility from the perspective of $X$-ranks with respect to a projective variety $X$. These loci are the closures of the points that appear in an $X$-rank decomposition of a general point in the ambient space. We look at entry loci of low degree normal surfaces in $\mathbb P^4$ using Segre points of curves; the smooth case was classically studied by Franchetta. We introduce a class of varieties whose generic rank coincides with the one of its general entry locus, and show that any smooth and irreducible projective variety admits an embedding with this property.
We study the approximation of the nonlocal-interaction equation restricted to a compact manifold $\mathcal{M}$ embedded in $\mathbb{R}^d$, and more generally compact sets with positive reach (i.e. prox-regular sets). We show that the equation on $\mathcal{M}$ can be approximated by the classical nonlocal-interaction equation on $\mathbb{R}^d$ by adding an external potential which strongly attracts to $\mathcal{M}$. The proof relies on the Sandier--Serfaty approach to the $\Gamma$-convergence of gradient flows. As a by-product, we recover well-posedness for the nonlocal-interaction equation on $\mathcal{M}$. Uniqueness, on the other hand, is established using a stability argument. We also provide an another approximation to the interaction equation on $\mathcal{M}$, based on iterating approximately solving an interaction equation on $\mathbb{R}^d$ and projecting to $\mathcal{M}$. We show convergence of this scheme, together with an estimate on the rate of convergence. Finally, we conduct numerical experiments, for both the attractive-potential-based and the projection-based approaches, that highlight the effects of the geometry on the dynamics.
Let $E$ be an elliptic curve over $\Q$ without complex multiplication, and which is not isogenous to a curve with non-trivial rational torsion. For each prime $p$ of good reduction, let $|E(\F_p)|$ be the order of the group of points of the reduced curve over $\F_p$. We prove in this paper that, under the GRH, there are at least $2.778 C_E^{\rm twin} x / (\log{x})^2$ primes $p$ such that $|E(\F_p)|$ has at most 8 prime factors, counted with multiplicity. This improves previous results of Steuding & Weng and Murty & Miri. This is also the first result where the dependence on the conjectural constant $C_E^{\rm twin}$ appearing in the twin prime conjecture for elliptic curves (also known as Koblitz's conjecture) is made explicit. This is achieved by sieving a slightly different sequence than the one used by previous authors. By sieving the same sequence and using Selberg's linear sieve, we can also improve the constant appearing in the upper bound for the number of primes $p$ such that $|E(\F_p)|$ is prime. Finally, we remark that our results still hold under an hypothesis weaker than the GRH.
The quality assessment of edges in an image is an important topic as it helps to benchmark the performance of edge detectors, and edge-aware filters that are used in a wide range of image processing tasks. The most popular image quality metrics such as Mean squared error (MSE), Peak signal-to-noise ratio (PSNR) and Structural similarity (SSIM) metrics for assessing and justifying the quality of edges. However, they do not address the structural and functional accuracy of edges in images with a wide range of natural variabilities. In this review, we provide an overview of all the most relevant performance metrics that can be used to benchmark the quality performance of edges in images. We identify four major groups of metrics and also provide a critical insight into the evaluation protocol and governing equations.
A nontrivial conformally invariant model is obtained via generalization the method of obtaining conformally invariant models in $2D$ Euclidean space to the Euclidean space with dimension $D>2$. This method was previously developed by E.S. Fradkin and M.Ya. Palchik (see [7] and reference therein). The partial wave expansion of a four-point function $\langle j_{\mu}(x_{1})j_{\nu}(x_{2})\varphi(x_{3})\varphi(x_{4})\rangle$ containing two conserved vector fields $j_{\mu}$ and two scalars $\varphi$ of dimension $ d $ in a $D$ -dimensional Euclidean space is considered. The requirement of the absence the vector operator of the dimension $d + 1$ in this expansion allows us to find the relationship between all the coupling constants in such a model.
In this proceedings for the MG14 conference, we discuss the construction of a phenomenology of Planck-scale effects in curved spacetimes, underline a few open issues and describe some perspectives for the future of this research line.
Combined ISO SWS and LWS spectroscopy is presented of the late WC-type planetary nebula nucleus CPD-56 8032 and its carbon-rich nebula. The extremely broad coverage (2.4-197 microns) enables us to recognize the clear and simultaneous presence of emission features from both oxygen- and carbon- rich circumstellar materials. Removing a smooth continuum highlights bright emission bands characteristic of polycyclic aromatic hydrocarbons (hereafter PAHs) in the 3-14 micron region, bands from crystalline silicates longwards of 18 microns, and the 43- and 62-micron bands of crystalline water ice. We discuss the probable evolutionary state and history of this unusual object in terms of (a) a recent transition from an O-rich to a C-rich outflow following a helium shell flash; or (b) a carbon-rich nebular outflow encountering an O-rich comet cloud.
Quasielastic electron scattering $(e,e')$ from $^{56}$Fe is calculated at large electron energies (2-4 GeV) and large three momentum transfer (0.5-1.5 GeV/c). We use a relativistic mean-field single particle model for the bound and continuum nucleon wavefunctions based on the $\sigma-\omega$ model and we include the effects of electron Coulomb distortion in the calculation. The calculations are compared to high energy data from SLAC and more recent data from Jefferson Laboratory, particularly for kinematics where the energy transfer is less than 500 to 600 MeV and the quasielastic process is expected to dominate the cross section. The effects of the predicted weakening of the strong scalar and vector potentials of the $\sigma-\omega$ model at high energy are investigated. Possible evidence for `longitudinal suppression' or modifications of nucleon form factors in the medium is considered, but neither is necessary to explain the quasielastic data for four momentum transfers less than 1 (GeV/c)$^2$.