ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating matchings of planar graphs, up to matrix operations on their rows and columns. If such a matrix is defined over a principal ideal domain, this is equivalent to considering its Smith normal form or its cokernel. Many variations of the enumeration methods result in equivalent matrices. In particular, Gessel-Viennot matrices are equivalent to Kasteleyn-Percus matrices.   We apply these ideas to plane partitions and related planar of tilings. We list a number of conjectures, supported by experiments in Maple, about the forms of matrices associated to enumerations of plane partitions and other lozenge tilings of planar regions and their symmetry classes. We focus on the case where the enumerations are round or $q$-round, and we conjecture that cokernels remain round or $q$-round for related ``impossible enumerations'' in which there are no tilings. Our conjectures provide a new view of the topic of enumerating symmetry classes of plane partitions and their generalizations. In particular we conjecture that a $q$-specialization of a Jacobi-Trudi matrix has a Smith normal form. If so it could be an interesting structure associated to the corresponding irreducible representation of $\SL(n,\C)$. Finally we find, with proof, the normal form of the matrix that appears in the enumeration of domino tilings of an Aztec diamond.
Cosmicflows-2 is a compilation of distances and peculiar velocities for over 8000 galaxies. Numerically the largest contributions come from the luminosity-linewidth correlation for spirals, the TFR, and the related Fundamental Plane relation for E/S0 systems, but over 1000 distances are contributed by methods that provide more accurate individual distances: Cepheid, Tip of the Red Giant Branch, Surface Brightness Fluctuation, SNIa, and several miscellaneous but accurate procedures. Our collaboration is making important contributions to two of these inputs: Tip of the Red Giant Branch and TFR. A large body of new distance material is presented. In addition, an effort is made to assure that all the contributions, our own and those from the literature, are on the same scale. Overall, the distances are found to be compatible with a Hubble Constant H_0 = 74.4 +-3.0 km/s/Mpc. The great interest going forward with this data set will be with velocity field studies. Cosmicflows-2 is characterized by a great density and high accuracy of distance measures locally, falling to sparse and coarse sampling extending to z=0.1.
Electron flow through a quantum point contact in presence of spin-orbit coupling is investigated theoretically in the context of the scanning gate microscopy (SGM) conductance mapping. Although in the absence of the floating gate the spin-orbit coupling does not significantly alter the conductance, we find that the angular dependence of the SGM images of the electron flow at the conductance plateaux is substantially altered as the spin-orbit interaction mixes the orbital modes that enter the quantum point contact. The radial interference fringes that are obtained in the SGM maps at conductance steps are essentially preserved by the spin-orbit interaction as backscattering by the tip preserves the electron spin although the effects of the mode mixing are visible.
Face recognition remains a challenging task in unconstrained scenarios, especially when faces are partially occluded. To improve the robustness against occlusion, augmenting the training images with artificial occlusions has been proved as a useful approach. However, these artificial occlusions are commonly generated by adding a black rectangle or several object templates including sunglasses, scarfs and phones, which cannot well simulate the realistic occlusions. In this paper, based on the argument that the occlusion essentially damages a group of neurons, we propose a novel and elegant occlusion-simulation method via dropping the activations of a group of neurons in some elaborately selected channel. Specifically, we first employ a spatial regularization to encourage each feature channel to respond to local and different face regions. In this way, the activations affected by an occlusion in a local region are more likely to be located in a single feature channel. Then, the locality-aware channel-wise dropout (LCD) is designed to simulate the occlusion by dropping out the entire feature channel. Furthermore, by randomly dropping out several feature channels, our method can well simulate the occlusion of larger area. The proposed LCD can encourage its succeeding layers to minimize the intra-class feature variance caused by occlusions, thus leading to improved robustness against occlusion. In addition, we design an auxiliary spatial attention module by learning a channel-wise attention vector to reweight the feature channels, which improves the contributions of non-occluded regions. Extensive experiments on various benchmarks show that the proposed method outperforms state-of-the-art methods with a remarkable improvement.
We present Chandra High Resolution Camera observations of CID-42, a candidate recoiling supermassive black hole (SMBH) at z=0.359 in the COSMOS survey. CID-42 shows two optical compact sources resolved in the HST/ACS image embedded in the same galaxy structure and a velocity offset of ~1300 km/s between the H\beta\ broad and narrow emission line, as presented by Civano et al. (2010). Two scenarios have been proposed to explain the properties of CID-42: a GW recoiling SMBH and a double Type 1/ Type 2 AGN system, where one of the two is recoiling because of slingshot effect. In both scenario, one of the optical nuclei hosts an unobscured AGN, while the other one, either an obscured AGN or a star forming compact region. The X-ray Chandra data allow to unambiguously resolve the X-ray emission, and unveil the nature, of the two optical sources in CID-42. We find that only one of the optical nuclei is responsible for the whole X-ray unobscured emission observed and a 3sigma upper limit on the flux of the second optical nucleus is measured. The upper limit on the X-ray luminosity plus the analysis of the multiwavelength spectral energy distribution indicate the presence of a starforming region in the second source rather than an obscured SMBH, thus favoring the GW recoil scenario. However the presence of a very obscured SMBH cannot be fully ruled-out. A new X-ray feature, in a SW direction with respect to the main source, is discovered and discussed.
We present the EpIC Monte Carlo event generator for exclusive processes sensitive to generalised parton distributions. EpIC utilises the PARTONS framework, which provides a flexible software architecture and a variety of modelling options for the partonic description of the nucleon. The generator offers a comprehensive set of features, including multi-channel capabilities and radiative corrections. It may be used both in analyses of experimental data, as well as in impact studies, especially for future electron-ion colliders.
The reprocessed X-ray emission from Active Galactic Nuclei (AGN) is an important diagnostic tool to study the dynamics and geometry of the matter surrounding the supermassive black holes (SMBHs). We present a broadband (optical-UV to hard X-ray) spectral study of the bare Seyfert 1 galaxy, ESO~511--G030, using multi-epoch Suzaku and XMM-Newton data from 2012 and 2007 respectively. The broadband spectra of ESO~511--G030 exhibit a UV bump, a prominent soft-excess below 2 keV, a relatively broad ($\sigma=0.08 - 0.14$ keV) Fe emission line at 6.4 keV and a weak Compton hump at E > 10 keV. The soft X-ray excess in ESO~511--G030 can be described either as the thermal Comptonization of disk seed photons by a warm ($0.40^{+0.02}_{-0.02}$ keV), optically thick ($\tau = 12.7^{+0.5}_{-0.4}$) and compact ($< 15 \rm r_{g}$) corona or as the blurred reflection from an untruncated and moderate to highly ionized accretion disk. However, for the blurred reflection, the model requires some extreme configuration of the disk and corona. Both these models prefer a rapidly spinning black hole ($a>0.78$) and a compact corona, indicating a relativistic origin of the broad Fe emission line. We found an inner disk temperature of $\sim 2-3$ eV that characterises the UV bump and the SMBH accretes at a sub-Eddington rate ($\lambda_{Edd} = 0.004-0.008$).
Let $\lambda>0$ and $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator on $\mathbb R_+:=(0,\infty)$. We show that the oscillation operator ${\mathcal O(P^{[\lambda]}_\ast)}$ and variation operator ${\mathcal V}_\rho(P^{[\lambda]}_\ast)$ of the Poisson semigroup $\{P^{[\lambda]}_t\}_{t>0}$ associated with $\Delta_\lambda$ are both bounded on $L^p(\mathbb R_+, dm_\lambda)$ for $p\in(1, \infty)$, $BMO({{\mathbb R}_+},dm_\lambda)$, from $L^1({{\mathbb R}_+},dm_\lambda)$ to $L^{1,\,\infty}({{\mathbb R}_+},dm_\lambda)$, and from $H^1({{\mathbb R}_+},dm_\lambda)$ to $L^1({{\mathbb R}_+},dm_\lambda)$, where $\rho\in(2, \infty)$ and $dm_\lambda(x):=x^{2\lambda}\,dx$. As an application, an equivalent characterization of $H^1({{\mathbb R}_+},dm_\lambda)$ in terms of ${\mathcal V}_\rho(P^{[\lambda]}_\ast)$ is also established. All these results hold if $\{P^{[\lambda]}_t\}_{t>0}$ is replaced by the heat semigroup $\{W^{[\lambda]}_t\}_{t>0}$. }
Majority bootstrap percolation on a graph $G$ is an epidemic process defined in the following manner. Firstly, an initially infected set of vertices is selected. Then step by step the vertices that have more infected than non-infected neighbours are infected. We say that percolation occurs if eventually all vertices in $G$ become infected.   In this paper we study majority bootstrap percolation on the Erd\H{o}s-R\'enyi random graph $G(n,p)$ above the connectivity threshold. Perhaps surprisingly, the results obtained for small $p$ are comparable to the results for the hypercube obtained by Balogh, Bollob\'as and Morris (2009).
Cold neutral gas is a key ingredient for growing the stellar and central black hole mass in galaxies throughout cosmic history. We have used the Atacama Large Millimetre Array (ALMA) to detect a rare example of redshifted $^{12}$CO(2-1) absorption in PKS B1740-517, a young ($t \sim 1.6 \times 10^{3}$ yr) and luminous ($L_{\rm 5 GHz} \sim 6.6 \times 10^{43}$ erg s$^{-1}$ ) radio galaxy at $z = 0.44$ that is undergoing a tidal interaction with at least one lower-mass companion. The coincident HI 21-cm and molecular absorption have very similar line profiles and reveal a reservoir of cold gas ($M_{\rm gas} \sim 10^{7} - 10^{8}$ M$_{\odot}$), likely distributed in a disc or ring within a few kiloparsecs of the nucleus. A separate HI component is kinematically distinct and has a very narrow line width ($\Delta{v}_{\rm FWHM} \lesssim 5$ km s$^{-1}$), consistent with a single diffuse cloud of cold ($T_{\rm k} \sim 100$ K) atomic gas. The $^{12}$CO(2-1) absorption is not associated with this component, which suggests that the cloud is either much smaller than 100 pc along our sight-line and/or located in low-metallicity gas that was possibly tidally stripped from the companion. We argue that the gas reservoir in PKS B1740-517 may have accreted onto the host galaxy $\sim$50 Myr before the young radio AGN was triggered, but has only recently reached the nucleus. This is consistent with the paradigm that powerful luminous radio galaxies are triggered by minor mergers and interactions with low-mass satellites and represent a brief, possibly recurrent, active phase in the life cycle of massive early type galaxies.
In this paper, we essentially compute the set of $x,y>0$ such that the mapping $z \longmapsto \Big{(}1-r+r e^z\Big{)}^x \Big{(}\dis\frac{\lambda}{\lambda-z}\Big{)}^{y}$ is a Laplace transform. If $X$ and $Y$ are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by $\mu$ the distribution of $X+Y.$ The above problem is equivalent to finding the set of $x>0$ such that $\mu^{{\ast}x}$ exists.
VLBI at millimeter wavelengths (mm-VLBI) allows the detailed imaging of compact galactic and extragalactic radio sources with micro-arcsecond scale resolution, unaccessible by other observing techniques. Here we discuss the scientific potential of mm-VLBI for present and future research on `Active Galactic Nuclei' (AGN) and their powerful relativistic jets. With the new generation of large radio telescopes and interferometer arrays operating in the millimeter radio bands (e.g. ALMA), the ultimate vicinity of super massive Black Holes, and eventually even their event horizon, could be imaged. With its large collecting area, and in combination with these future telescopes, the Sardinia Radio Telescope could form the World's `sharpest' astronomical imaging machine.
The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression of the degenerate hyperharmonic numbers in terms of the degenerate harmonic numbers. This is a degenerate version of the corresponding identity representing the hyperharmonic numbers in terms of harmonic numbers due to Conway and Guy.
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general circuits. Here, we analyze the probability of staying in such symmetry-preserved subspaces under noise, providing an exact formula for local depolarizing noise. We apply our findings to benchmark, under depolarizing noise, the symmetry robustness of XY-QAOA, which has local particle number conserving symmetries, and is a special case of the Quantum Alternating Operator Ansatz. We also analyze the influence of the choice of encoding the problem on the symmetry robustness of the algorithm and discuss a simple adaption of the bit flip code to correct for symmetry-breaking errors with reduced resources.
This White Paper explores advances in the study of Active Galaxies which will be enabled by new observing capabilities at MeV energies (hard X-rays to gamma-rays; 0.1-1000 MeV), with a focus on multi-wavelength synergies. This spectral window, covering four decades in energy, is one of the last frontiers for which we lack sensitive observations. Only the COMPTEL mission, which flew in the 1990s, has significantly probed this energy range, detecting a handful of AGN. In comparison, the currently active Fermi Gamma-ray Space Telescope, observing at the adjacent range of 0.1-100 GeV, is 100-1000 times more sensitive. This White Paper describes advances to be made in the study of sources as diverse as tidal disruption events, jetted AGN of all classes (blazars, compact steep-spectrum sources, radio galaxies and relics) as well as radio-quiet AGN, most of which would be detected for the first time in this energy regime. New and existing technologies will enable MeV observations at least 50-100 times more sensitive than COMPTEL, revealing new source populations and addressing several open questions, including the nature of the corona emission in non-jetted AGN, the precise level of the optical extragalactic background light, the accretion mode in low-luminosity AGN, and the structure and particle content of extragalactic jets.
Cultural heritage is the asset of all the peoples of the world. The preservation and inheritance of cultural heritage is conducive to the progress of human civilization. In northwestern China, there is a world heritage site -- Mogao Grottoes -- that has a plenty of mural paintings showing the historical cultures of ancient China. To study these historical cultures, one critical procedure is to date the mural paintings, i.e., determining the era when they were created. Until now, most mural paintings at Mogao Grottoes have been dated by directly referring to the mural texts or historical documents. However, some are still left with creation-era undetermined due to the lack of reference materials. Considering that the drawing style of mural paintings was changing along the history and the drawing style can be learned and quantified through painting data, we formulate the problem of mural-painting dating into a problem of drawing-style classification. In fact, drawing styles can be expressed not only in color or curvature, but also in some unknown forms -- the forms that have not been observed. To this end, besides sophisticated color and shape descriptors, a deep convolution neural network is designed to encode the implicit drawing styles. 3860 mural paintings collected from 194 different grottoes with determined creation-era labels are used to train the classification model and build the dating method. In experiments, the proposed dating method is applied to seven mural paintings which were previously dated with controversies, and the exciting new dating results are approved by the Dunhuang expert.
We aim to shed light on the physical properties and kinematics of the molecular material in the nucleus of one of the closest type 2 active galaxies.   To this end, we obtained high angular resolution ALMA observations of the nucleus of the Circinus galaxy. The observations map the emission at 350GHz and 690GHz with spatial resolutions of ~3.8pc and ~2.2pc, respectively.   The continuum emission traces cold ($T\lesssim100$K) dust in a circumnuclear disk with spiral arms on scales of 25pc, plus a marginally resolved nuclear emission peak. The latter is not extended in polar direction as claimed based on earlier ALMA observations. A significant amount (of the order of 40%) of the 350GHz emission is not related to dust, but most likely free-free emission instead. We detect CO(3-2) and CO(6-5) as well as HCO$^+$(4-3), HCN(4-3), and CS(4-3). The CO emission is extended, showing a spiral pattern, similar to the extended dust emission. Towards the nucleus, CO is excited to higher transitions and its emission is self-absorbed, leading to an apparent hole in the CO(3-2) but not the CO(6-5) emission. On the other hand, the high gas density tracers HCO$^+$, HCN, and CS show a strong, yet unresolved (($\lesssim4$pc) concentration of the emission at the nucleus, pointing at a very small 'torus'. The kinematics are dominated by rotation and point at a geometrically thin disk down to the resolution limit of our observations. In contrast to several other AGNs, no HCN enhancement is found towards the nucleus.   The Circinus nucleus is therefore composed of at least two distinct components: (1) an optically thin, warm outflow of ionised gas containing clouds of dust; and (2) a cold molecular and dusty disk. These findings support the most recent radiative transfer calculations of the obscuring structures in AGNs, which find a similar two-component structure. (Abridged)
Lines of diatomic molecules are more temperature and pressure sensitive than atomic lines, which makes them ideal tools for studying cool stellar atmospheres an internal structure of sunspots and starspots. The FeH F^4 Delta-X^4 Delta system represents such an example that exhibits in addition a large magnetic field sensitivity. The current theoretical descriptions of these transitions including the molecular constants involved are only based on intensity measurements because polarimetric observations have not been available so far, which limits their diagnostic value. We present for the first time spectropolarimetric observations of the FeH F^4 Delta-X^4 Delta system measured in sunspots to investigate their diagnostic capabilities for probing solar and stellar magnetic fields. We investigate whether the current theoretical model of FeH can reproduce the observed Stokes profiles including their magnetic properties. The polarimetric observations are compared with synthetic Stokes profiles modeled with radiative transfer calculations. This allows us to infer the temperature and the magnetic field strength of the observed sunspots. We find that the current theory successfully reproduces the magnetic properties of a large number of lines in the FeH F^4 Delta-X^4 Delta system. In a few cases the observations indicate a larger Zeeman splitting than predicted by the theory. There, our observations have provided additional constraints, which allowed us to determine empirical molecular constants. The FeH F^4 Delta-X^4 Delta system is found to be a very sensitive magnetic diagnostic tool. Polarimetric data of these lines provide us with more direct information to study the coolest parts of astrophysical objects.
We present a new model to compute the luminosity of emission lines in star forming galaxies and apply this in the semi-analytical galaxy formation code GALFORM. The model combines a pre-computed grid of HII region models with an empirical determination of how the properties of HII regions depend on the macroscopic properties of galaxies based on observations of local galaxies. The new model gives a very good reproduction of the locus of star-forming galaxies on standard line ratio diagnostic diagrams. The new model shows evolution in the locus of star forming galaxies with redshift on this line ratio diagram, with a good match to the observed line ratios at $z=1.6$. The model galaxies at high redshift have gas densities and ionisation parameters that are predicted to be $\approx 2-3$ times higher than in local star forming galaxies, which is partly driven by the changing selection with redshift to mimic the observational selection. Our results suggest that the observed evolution in emission line ratios requires other HII region properties to evolve with redshift, such as the gas density, and cannot be reproduced by HII model grids that only allow the gas metallicity and ionisation parameter to vary.
While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to non-uniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.