ShantanuT01/DACTYL-Pretraining huggingface dataset:
We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type of interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.
We study in detail the dynamics and stability of marginally trapped surfaces during a binary black hole merger. This is the second in a two-part study. The first part studied the basic geometric aspects of the world tubes traced out by the marginal surfaces and the status of the area increase law. Here we continue and study the dynamics of the horizons during the merger, again for the head-on collision of two non-spinning black holes. In particular we follow the spectrum of the stability operator during the course of the merger for all the horizons present in the problem and implement systematic spectrum statistics for its analysis. We also study more physical aspects of the merger, namely the fluxes of energy which cross the horizon and cause the area to change. We construct a natural coordinate system on the horizon and decompose the various fields appearing in the flux, primarily the shear of the outgoing null normal, in spin weighted spherical harmonics. For each of the modes we extract the decay rates as the final black hole approaches equilibrium. The late part of the decay is consistent with the expected quasi-normal mode frequencies, while the early part displays a much steeper fall-off. Similarly, we calculate the decay of the horizon multipole moments, again finding two different regimes. Finally, seeking an explanation for this behavior, motivated by the membrane paradigm interpretation, we attempt to identify the different dynamical timescales of the area increase. This leads to the definition of a ``slowness parameter'' for predicting the onset of transition from a faster to a slower decay.
Given a finite simple graph $G$, an odd cover of $G$ is a collection of complete bipartite graphs, or bicliques, in which each edge of $G$ appears in an odd number of bicliques and each non-edge of $G$ appears in an even number of bicliques. We denote the minimum cardinality of an odd cover of $G$ by $b_2(G)$ and prove that $b_2(G)$ is bounded below by half of the rank over $\mathbb{F}_2$ of the adjacency matrix of $G$. We show that this lower bound is tight in the case when $G$ is a bipartite graph and almost tight when $G$ is an odd cycle. However, we also present an infinite family of graphs which shows that this lower bound can be arbitrarily far away from $b_2(G)$.   Babai and Frankl (1992) proposed the "odd cover problem," which in our language is equivalent to determining $b_2(K_n)$. Radhakrishnan, Sen, and Vishwanathan (2000) determined $b_2(K_n)$ for an infinite but density zero subset of positive integers $n$. In this paper, we determine $b_2(K_n)$ for a density $3/8$ subset of the positive integers.
Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not been found in photonic systems yet. In this article, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically non-trivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily-fabricated structure of the photonic crystals, we can realize different topological phases with unique topological boundary states straightforwardly. Our result can be generalized to higher dimensions and provides unprecedented venues for higher-order photonic topological insulators and semimetals.
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a nice ``trick'' which allows to avoid the Dirac algebra constraints in formulating our relativistic equation. A brief comparison with other quaternionic formulations is also presented.
In X-ray spectra of several active galactic nuclei and Galactic black hole binaries a broad relativistically smeared iron line is observed. This feature arises by fluorescence when the accretion disc is illuminated by hot corona above it. Due to central location of the corona the illumination and thus also the line emission decrease with radius. It was reported in the literature that this decrease is very steep in some of the sources, suggesting a highly compact corona.   We revisit the lamp-post setup in which the corona is positioned on the axis above the rotating black hole and investigate to what extent the steep emissivity can be explained by this scenario. We show the contributions of the relativistic effects to the disc illumination by the primary source - energy shift, light bending and aberration. The lamp-post radial illumination pattern is compared to the widely used radial broken power-law emissivity profile. We find that very steep emissivities require the primary illuminating source to be positioned very near the black hole horizon and/or the spectral power-law index of the primary emission to be very high. The broken power-law approximation of the illumination can be safely used when the primary source is located at larger heights. However, for low heights the lamp-post illumination considerably differs from this approximation.   We also show the variations of the iron line local flux over the disc due to the flux dependence on incident and emission angles. The former depends mainly on the height of the primary source while the latter depends on the inclination angle of the observer. Thus the strength of the line varies substantially across the disc. This effect may contribute to the observed steeper emissivity.
The universal link between the processes of accretion and ejection leads to the formation of jets and outflows around accreting compact objects. Incoherent synchrotron emission from these outflows can be observed from a wide range of accreting binaries, including black holes, neutron stars, and white dwarfs. Monitoring the evolution of the radio emission during their sporadic outbursts provides important insights into the launching of jets, and, when coupled with the behaviour of the source at shorter wavelengths, probes the underlying connection with the accretion process. Radio observations can also probe the impact of jets/outflows (including other explosive events such as magnetar giant flares) on the ambient medium, quantifying their kinetic feedback.   The high sensitivity of the SKA will open up new parameter space, enabling the monitoring of accreting stellar-mass compact objects from their bright, Eddington-limited outburst states down to the lowest-luminosity quiescent levels, whose intrinsic faintness has to date precluded detailed studies. A census of quiescently accreting black holes will also constrain binary evolution processes. By enabling us to extend our existing investigations of black hole jets to the fainter jets from neutron star and white dwarf systems, the SKA will permit comparative studies to determine the role of the compact object in jet formation. The high sensitivity, wide field of view and multi-beaming capability of the SKA will enable the detection and monitoring of all bright flaring transients in the observable local Universe, including the ULXs, ...   [Abridged]   This chapter reviews the science goals outlined above, demonstrating the progress that will be made by the SKA. We also discuss the potential of the astrometric and imaging observations that would be possible should a significant VLBI component be included in the SKA.
We present the first analysis of the stellar content of the structures and substructures identified in the peculiar star-forming galaxy NGC5474, based on Hubble Space Telescope resolved photometry from the LEGUS survey. NGC5474 is a satellite of the giant spiral M101, and is known to have a prominent bulge that is significantly off-set from the kinematic center of the underlying HI and stellar disc. The youngest stars (age~ 100 Myr) trace a flocculent spiral pattern extending out to ~8 kpc from the center of the galaxy. On the other hand intermediate-age (age > 500 Myr) and old (age > 2 Gyr) stars dominate the off-centred bulge and a large substructure residing in the South Western part of the disc and not correlated with the spiral arms (SW over-density). The old age of the stars in the SW over-density suggests that this may be another signature of the dynamical interaction/s that have shaped this anomalous galaxy. We suggest that a fly by with M101, generally invoked as the origin of the anomalies, may not be sufficient to explain all the observations. A more local and more recent interaction may help to put all the pieces of this galactic puzzle together.
Asteroseismology provides global stellar parameters such as masses, radii or surface gravities using the mean global seismic parameters as well as the effective temperature for thousands of low-mass stars $(0.8 M_\odot <M<3 M_\odot)$. This methodology has been successfully applied to stars in which acoustic modes excited by turbulent convection are measured. Other techniques such as the Flicker can also be used to determine stellar surface gravities, but only works for $\log{g}$ above $2.5$ dex. In this work, we present a new metric called FliPer (the acronym stands for Flicker in spectral power density, in opposition to the standard Flicker measurement which is computed in the time domain that is able to extend the range for which reliable surface gravities can be obtained ($0.1<\log{g}<4.6$ dex) without performing any seismic analysis for stars brighter than $\textit{Kp}$ $<$ 14. FliPer takes into account the average variability of a star measured in the power density spectrum in a given range of frequencies. However, FliPer values calculated on several ranges of frequency are required to better characterize a star. Using a large set of asteroseismic targets it is possible to calibrate the behavior of surface gravity with FliPer through machine learning. This calibration made with a random forest regressor covers a wide range of surface gravities from main-sequence stars to subgiants and red giants, with very small uncertainties from $0.04$ to $0.1$ dex. FliPer values can be inserted in automatic global seismic pipelines to either give an estimation of the stellar surface gravity or to assess the quality of the seismic results by detecting any outliers in the obtained $\nu_{max}$ values. FliPer also constrain the surface gravities of main-sequence dwarfs using only long cadence data for which the Nyquist frequency is too low to measure the acoustic-mode properties.
We derive the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon W state, by accessing only one photon of the initial W state and adding n photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n-1 polarization-independent beamsplitters.
Monocular depth estimation is a fundamental task in computer vision and has drawn increasing attention. Recently, some methods reformulate it as a classification-regression task to boost the model performance, where continuous depth is estimated via a linear combination of predicted probability distributions and discrete bins. In this paper, we present a novel framework called BinsFormer, tailored for the classification-regression-based depth estimation. It mainly focuses on two crucial components in the specific task: 1) proper generation of adaptive bins and 2) sufficient interaction between probability distribution and bins predictions. To specify, we employ the Transformer decoder to generate bins, novelly viewing it as a direct set-to-set prediction problem. We further integrate a multi-scale decoder structure to achieve a comprehensive understanding of spatial geometry information and estimate depth maps in a coarse-to-fine manner. Moreover, an extra scene understanding query is proposed to improve the estimation accuracy, which turns out that models can implicitly learn useful information from an auxiliary environment classification task. Extensive experiments on the KITTI, NYU, and SUN RGB-D datasets demonstrate that BinsFormer surpasses state-of-the-art monocular depth estimation methods with prominent margins. Code and pretrained models will be made publicly available at \url{https://github.com/zhyever/Monocular-Depth-Estimation-Toolbox}.
We study the effects of frame-dragging on the structure of force-free magnetospheres around rotating black holes. For slowly rotating black holes, analytic explorations often focus on transforming an exact force-free solution applicable to a static black hole into a solution approximately applicable to a slowly-rotating black hole via perturbations in black hole spin. We show that the single perturbed monopolar solution most commonly arrived at using such techniques is in fact a separatrix between two broad classes of solutions: those with poloidal magnetic fields that bend upwards towards the azimuthal axis and those that bend downwards towards the equatorial plane. This is because frame-dragging affects the toroidal magnetic field distributions, changing the force balance between poloidal magnetic field lines.
The Hilbert scheme of $n$ points in the affine plane contains the open subscheme parametrizing $n$ distinct points in the affine plane, and the closed subscheme parametrizing ideals of codimension $n$ supported at the origin of the affine plane. Both schemes admit Bia{\l}ynicki-Birula decompositions into moduli spaces of ideals with prescribed lexicographic Gr\"obner deformations. We show that both decompositions are stratifications in the sense that the closure of each stratum is a union of certain other strata. We show that the corresponding two partial orderings on the set of of monomial ideals are dual to each other.
Let $\mathcal{V}$ be an integral normal complex projective variety of dimension $n\geq 3$ and denote by $\mathcal{L}$ an ample line bundle on $\mathcal{V}$. By imposing that the linear system $|\mathcal{L}|$ contains an element $A=A_{1}+...+A_{r}, r\geq 1$, where all the $A_{i}$'s are distinct effective Cartier divisors with Pic$(A_i)=\mathbb{Z}$, we show that such a $\mathcal{V}$ is as special as the components $A_i$ of $A\in |\mathcal{L}|$. After making a list of some consequences about the positivity of the components $A_i$, we characterize pairs $(\mathcal{V}, \mathcal{L})$ as above when either $A_1\cong\mathbb{P}^{n-1}$ and Pic$(A_j)=\mathbb{Z}$ for $j=2,...,r,$ or $\mathcal{V}$ is smooth and each $A_i$ is a variety of small degree with respect to $[H_i]_{A_i}$, where $[H_i]_{A_i}$ is the restriction to $A_i$ of a suitable line bundle $H_i$ on $\mathcal{V}$.
It is shown that the massless $j=1$ Weinberg-Tucker-Hammer equations reduce to the Maxwell's equations for electromagnetic field under the definite choice of field functions and initial and boundary conditions. Thus, the former appear to be of use in a description of some physical processes for which that could be necessitated or be convenient. The possible consequences are discussed.
With the advent of new wide-field, high-cadence optical transient surveys, our understanding of the diversity of core-collapse supernovae has grown tremendously in the last decade. However, the pre-supernova evolution of massive stars, that sets the physical backdrop to these violent events, is theoretically not well understood and difficult to probe observationally. Here we report the discovery of the supernova iPTF13dqy = SN 2013fs, a mere ~3 hr after explosion. Our rapid follow-up observations, which include multiwavelength photometry and extremely early (beginning at ~6 hr post-explosion) spectra, map the distribution of material in the immediate environment (<~ 10^15 cm) of the exploding star and establish that it was surrounded by circumstellar material (CSM) that was ejected during the final ~1 yr prior to explosion at a high rate, around 10^-3 solar masses per year. The complete disappearance of flash-ionised emission lines within the first several days requires that the dense CSM be confined to within <~ 10^15 cm, consistent with radio non-detections at 70--100 days. The observations indicate that iPTF13dqy was a regular Type II SN; thus, the finding that the probable red supergiant (RSG) progenitor of this common explosion ejected material at a highly elevated rate just prior to its demise suggests that pre-supernova instabilities may be common among exploding massive stars.
Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of the stability of rare-earth magnetic atoms exposed to crystal or ligand fields of various symmetry and to exchange scattering with an electron bath. By analyzing the properties of the atomic wavefunction, we show that certain combinations of symmetry and total angular momentum are inherently stable against first or even higher order interactions with electrons. Further, we investigate the effect of an external magnetic field on the magnetic stability.
The physical origin of the backbendings in the equations of state of finite but not necessarily small systems is studied in the Ising model with fixed magnetization (IMFM) by means of the topological properties of the observable distributions and the analysis of the largest cluster with increasing lattice size. Looking at the convexity anomalies of the IMFM thermodynamic potential, it is shown that the order of the transition at the thermodynamic limit can be recognized in finite systems independently of the lattice size. General statistical mechanics arguments and analytical calculations suggest that the backbending in the caloric curve is a transient behaviour which should not converge to a plateau in the thermodynamic limit, while the first order transition is signalled by a discontinuity in other observables.
The methods of panoramic (3D) spectroscopy are used in a detailed study of galaxies with ongoing star formation chosen from among objects in seven selected fields of the Second Byurakan Survey (SBS). This article deals with the irregular galaxy SBS 1202+583, which our classification scheme identifies as being in a continuous phase of starformation. Observations were made with the panoramic spectrographs MPFS at the 6-m telescope of the Special Astrophysical Observatory (SAO) of the Russian Academy of Sciences and VAGR at the 2.6-m telescope of the Byurakan Astrophysical Observatory (BAO) in Armenia. The data are used to construct charts of the radiative fluxes in the continuum and various emission lines. Special attention is devoted to analyzing the emission in the H{\alpha} hydrogen recombination line and in the forbidden low-ionization doublets of nitrogen [NII]{\lambda}{\lambda}6548, 6583 and sulfur [SII]{\lambda}{\lambda} 6716,6731, and the ratios of the intensities of the forbidden lines to H{\alpha}. The observable characteristics (sizes, H{\alpha} fluxes, etc.) of nine HII regions are studied. The estimated current rates of starformation in the individual HII regions based on the H{\alpha} fluxes lie within the range of 0.3-1.2 Msun/year. The dependence of the ratio of the intensities of the emission in these two forbidden doublets on the rate of star formation in the HII regions is found.
We examine the structure of the underlying event in neutral Higgs production at the Superconducting-Supercollider (SSC). Gaps, regions of rapidity containing no soft particle production, can provide a clean signature for $W$ boson fusion to the heavy Higgs. We first examine the physical basis of gap production and estimate the survival probability of gaps in the minijet model. Then, using PYTHIA, and HERWIG we compare gap events to $W$ pair production from top decay and $q\bar{q}$ fusion. We find that, if experimental problems can be overcome, gaps should provide a small, but clean, signal for heavy Higgs production at the SSC.
Employing the $\mathbf{k}\cdot\mathbf{p}$ expansion for a family of tight-binding models for SmB$_6$, we analytically compute topological surface states on a generic $(lmn)$ surface. We show how the Dirac-cone spin structure depends on model ingredients and on the angle $\theta$ between the surface normal and the main crystal axes. We apply the general theory to $(001)$, $(110)$, $(111)$, and $(210)$ surfaces, for which we provide concrete predictions for the spin pattern of surface states which we also compare with tight-binding results. As shown in previous work, the spin pattern on a $(001)$ surface can be related to the value of mirror Chern numbers, and we explore the possibility of topological phase transitions between states with different mirror Chern numbers and the associated change of the spin structure of surface states. Such transitions may be accessed by varying either the hybridization term in the Hamiltonian or the crystal-field splitting of the low-energy $f$ multiplets, and we compute corresponding phase diagrams.
Autonomous driving is becoming a future practical lifestyle greatly driven by deep learning. Specifically, an effective traffic sign detection by deep learning plays a critical role for it. However, different countries have different sets of traffic signs, making localized traffic sign recognition model training a tedious and daunting task. To address the issues of taking amount of time to compute complicate algorithm and low ratio of detecting blurred and sub-pixel images of localized traffic signs, we propose Multi-Scale Deconvolution Networks (MDN), which flexibly combines multi-scale convolutional neural network with deconvolution sub-network, leading to efficient and reliable localized traffic sign recognition model training. It is demonstrated that the proposed MDN is effective compared with classical algorithms on the benchmarks of the localized traffic sign, such as Chinese Traffic Sign Dataset (CTSD), and the German Traffic Sign Benchmarks (GTSRB).
We consider the phase transition in the dual Yang-Mills theory at finite temperature $T$. The phase transition is associated with a change (breaking) of symmetry. The effective mass of the dual gauge field is derived as a function of $T$-dependent gauge coupling constant. We investigate the analytical criterion constraining the existence of a quark-antiquark bound state at temperatures higher than the temperature of deconfinement.
Colmez conjectured a product formula for periods of abelian varieties over number fields with complex multiplication and proved it in some cases. His conjecture is equivalent to a formula for the Faltings height of CM abelian varieties in terms of the logarithmic derivatives at $s=0$ of certain Artin $L$-functions.   In a series of articles we investigate the analog of Colmez's theory in the arithmetic of function fields. There abelian varieties are replaced by Drinfeld modules and their higher dimensional generalizations, so-called $A$-motives. In the present article we prove the product formula for the Carlitz module and we compute the valuations of the periods of a CM $A$-motive at all finite places in terms of Artin $L$-series. The latter is achieved by investigating the local shtukas associated with the $A$-motive.