ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\text{X}$ denote a projective variety over an algebraically closed field on which a linear algebraic group acts with finitely many orbits. Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands' philosophy, postulates that the equivariant derived category of bounded complexes with constructible equivariant cohomology sheaves on $\text{X}$ is equivalent to a full subcategory of the derived category of modules over a graded ring defined as a suitable graded $Ext$. Only special cases of this conjecture have been proven so far. {\it The purpose of this paper is to provide a proof of this conjecture for all projective toroidal imbeddings of complex reductive groups.} In fact, we show that the methods used by Lunts for a proof in the case of toric varieties can be extended with suitable modifications to handle the toroidal imbedding case. {\it Since every equivariant imbedding of a complex reductive group is dominated by a toroidal imbedding, the class of varieties for which our proof applies is quite large.}   We also show that, in general, there exist a countable number of obstructions for this conjecture to be true and that half of these vanish when the odd dimensional equivariant intersection cohomology sheaves on the orbit closures vanish. This last vanishing condition had been proven to be true in many cases of spherical varieties by Michel Brion and the author in prior work.
Machine learning is transforming the video editing industry. Recent advances in computer vision have leveled-up video editing tasks such as intelligent reframing, rotoscoping, color grading, or applying digital makeups. However, most of the solutions have focused on video manipulation and VFX. This work introduces the Anatomy of Video Editing, a dataset, and benchmark, to foster research in AI-assisted video editing. Our benchmark suite focuses on video editing tasks, beyond visual effects, such as automatic footage organization and assisted video assembling. To enable research on these fronts, we annotate more than 1.5M tags, with relevant concepts to cinematography, from 196176 shots sampled from movie scenes. We establish competitive baseline methods and detailed analyses for each of the tasks. We hope our work sparks innovative research towards underexplored areas of AI-assisted video editing.
For a pair $(E,P)$ of an elliptic curve $E/\mathbb{Q}$ and a nontorsion point $P\in E(\mathbb{Q})$, the sequence of \emph{elliptic Fermat numbers} is defined by taking quotients of terms in the corresponding elliptic divisibility sequence $(D_{n})_{n\in\mathbb{N}}$ with index powers of two, i.e. $D_{1}$, $D_{2}/D_{1}$, $D_{4}/D_{2}$, etc. Elliptic Fermat numbers share many properties with the classical Fermat numbers, $F_{k}=2^{2^k}+1$. In the present paper, we show that for magnified elliptic Fermat sequences, only finitely many terms are prime. We also define \emph{generalized elliptic Fermat numbers} by taking quotients of terms in elliptic divisibility sequences that correspond to powers of any integer $m$, and show that many of the classical Fermat properties, including coprimality, order universality and compositeness, still hold.
The volume function defined by a domain in Euclidean space $\mathbb{R}^n$ is the function on the space of affine hyperplanes equal to volumes cut by these hyperplanes from the domain. The study of these functions originates from the works of Archimedes and Newton and is closely related to the theory of lacunas of hyperbolic partial differential equations.The volume functions are regular at the hyperplanes of general position with respect to the boundary of the cut domain. We study their behavior at the non-regular hyperplanes, which are either tangent to the boundary of the domain at its finite points or have asymptotic direction. In both cases the local regularity of the restriction of the volume function to a local connected component of the set of regular planes depends on the triviality of a certain relative homology class, the (generalized) even Petrovsky class. In the first case (of finite tangencies) the study of these classes and enumeration of components of regularity (so called local lacunas) at simple singularities of wave fronts was essentially done by V. A. Vassiliev; it is formulated in terms of deformations of simple real function singularities. We show that the analogous study for asymptotic hyperplanes is related in the same way with the study of boundary function singularities. We define and calculate local Petrovsky classes for this case and find lacunas, i.e. the local components of the complement of corresponding discriminant in which all local Petrovsky classes are trivial. If component is not lacuna we prove that the corresponding volume function cannot be algebraic. Also we calculate the local monodromy groups, describing the ramification of volume functions.
Superconductivity in heavy-fermion materials can sometimes appear in the incoherent regime and in proximity to an antiferromagnetic quantum critical point. Here we study these phenomena using large scale determinant quantum Monte Carlo simulations and the dynamical cluster approximation with various impurity solvers for the periodic Anderson model with frustrated hybridization. We obtain solid evidence for a $d_{x^2-y^2}$ superconducting phase arising from an incoherent normal state in the vicinity of an antiferromagnetic quantum critical point. There is a coexistence region and the width of the superconducting dome increases with frustration. Through a study of the pairing dynamics we find that the retarded spin-fluctuations give the main contribution to the pairing glue. These results are relevant for unconventional superconductivity in the Ce-$115$ family of heavy-fermions.
By collecting both quantum and gravitational principles, a space-time uncertainty relation $(\delta t)(\delta r)^{3}\geqslant\pi r^{2}l_{p}^{2}$ is derived. It can be used to facilitate the discussion of several profound questions, such as computational capacity and thermodynamic properties of the universe and the origin of holographic dark energy. The universality and validity of the proposed relation are illustrated via these examples.
The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of $K_{2n+1}$ into edge-disjoint copies of a given $2$-factor. We show that this can be achieved for all large $n$. We actually prove a significantly more general result, which allows for decompositions into more general types of factors. In particular, this also resolves the Hamilton-Waterloo problem for large $n$.
We propose six new benchmark scenarios for Higgs boson searches in the Minimal Supersymmetric Standard Model. Our calculations follow the recommendations of the LHC Higgs Cross Section Working Group, and benefit from recent developments in the predictions for the Higgs-boson masses and mixing. All of the proposed scenarios are compatible with the most recent results from Run 2 of the LHC. In particular, they feature a scalar with mass and couplings compatible with those of the observed Higgs boson, and a significant portion of their parameter space is allowed by the limits from the searches for SUSY particles and additional Higgs bosons. We define a scenario where all SUSY particles are relatively heavy, and two scenarios with light colorless SUSY particles (charginos, neutralinos and, in one case, staus). In addition, we present two scenarios featuring alignment without decoupling, realized with either the lighter or the heavier scalar being SM-like, and a scenario with CP violation.
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimization of the scalar complexity, according to parameterizable criteria. As an example, we apply this analysis to the construction of type elliptic Chudnovsky$^2$ multiplication algorithms for small extensions. As a case study, we significantly improve the Baum-Shokrollahi construction for multiplication in $\mathbb F_{256}/\mathbb F_4$.
We present two-dimensional gaseous kinematics of the inner 1.1 x 1.6kpc^2 of the Seyfert 2 galaxy NGC2110, from optical spectra obtained with the GMOS integral field spectrograph on the Gemini South telescope at a spatial resolution of 100pc. Gas emission is observed over the whole field-of-view, with complex - and frequently double - emission-line profiles. We have identified four components in the emitting gas, according to their velocity dispersion (sigma), which we refer to as: (1) warm gas disk (sigma = 100-220km/s); (2) cold gas disk (sigma = 60-90km/s); (3) nuclear component (sigma = 220-600km/s); and (4) northern cloud (sigma = 60-80km/s). Both the cold and warm disk components are dominated by rotation and have similar gas densities, but the cold gas disk has lower velocity dispersions and reaches higher rotation velocities. We attribute the warm gas disk to a thick gas layer which encompasses the cold disk as observed in some edge-on spiral galaxies. After subtraction of a rotation model from the cold disk velocity field, we observe excess blueshifts of 50km/s in the far side of the galaxy as well as similar excess redshifts in the near side. These residuals can be interpreted as due to nuclear inflow in the cold gas, with an estimated ionized gas mass inflow rate of 2.2 x 10^(-2)Msun/yr. We have also subtracted a rotating model from the warm disk velocity field and found excess blueshifts of 100km/s to the SW of the nucleus and excess redshifts of 40km/s to the NE, which we attribute to gas disturbed by an interaction with a nuclear spherical outflow. This nuclear outflow is the origin of the nuclear component observed within the inner 300pc and it has a mass outflow rate of 0.9Msun/yr. In a region between 1" and 4" north of the nucleus we find a new low sigma component of ionized gas which we attribute to a high latitude cloud photoionized by the nuclear source.
The Kepler mission has provided exquisite data to perform an ensemble asteroseismic analysis on evolved stars. In this work we systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data. We produced a homogeneous catalog of the frequency of maximum power (typical uncertainty $\sigma_{\nu_{\rm max}}$=1.6\%), the mean large frequency separation ($\sigma_{\Delta\nu}$=0.6\%), oscillation amplitude ($\sigma_{\rm A}$=4.7\%), granulation power ($\sigma_{\rm gran}$=8.6\%), power excess width ($\sigma_{\rm width}$=8.8\%), seismically-derived stellar mass ($\sigma_{\rm M}$=7.8\%), radius ($\sigma_{\rm R}$=2.9\%), and thus surface gravity ($\sigma_{\log g}$=0.01 dex). Thanks to the large red giant sample, we confirm that red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ in the distribution of oscillation amplitude, granulation power, and width of power excess, which is mainly due to the mass difference. The distribution of oscillation amplitudes shows an extremely sharp upper edge at fixed $\nu_{\rm max}$, which might hold clues to understand the excitation and damping mechanisms of the oscillation modes. We find both oscillation amplitude and granulation power depend on metallicity, causing a spread of 15\% in oscillation amplitudes and a spread of 25\% in granulation power from [Fe/H]=-0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as reliable distance indicators and age proxies for mapping and dating galactic stellar populations observed by Kepler. They will also provide an excellent opportunity to test asteroseismology using Gaia parallaxes, and lift degeneracies in deriving atmospheric parameters in large spectroscopic surveys such as APOGEE and LAMOST.
We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight qubits. Our simulations show that simple quantum circuits can solve the standard quantum mechanical problems.
Millimeter and sub-millimeter observations have made fundamental contributions to our current understanding of the transition from AGB stars to white dwarfs. The approaching era of ALMA brings significantly enhanced observing capabilities at these wavelengths and promises to push back the frontiers in a number of ways. We examine the scientific prospects of this new era for PNe, with an emphasis on how developments may contribute to the goals of the asymmetric PNe community.
We study the obscuring structure of circumnuclear disks (CNDs) by considering supernova (SN) feedbacks from nuclear starburst and the effect of anisotropic radiative pressure from AGNs. We suppose that the mass accretion onto a central supermassive black hole (SMBH) is triggered by SN-driven turbulence within CNDs, and we explore how the structures of CNDs depend on the BH mass ($M_{\rm BH}$) and AGN luminosity ($L_{\rm AGN}$). We find that the obscuring fraction ($f_{\rm obs}$) peaks at $\sim10\%$ of the Eddington luminosity ($L_{\rm Edd}$), and its maximal value is $f_\mathrm{obs} \sim 0.6$ for less massive SMBHs (e.g., $M_{\rm BH} < 10^{8}M_{\odot}$). This is because the scale height of CNDs is determined by the SN-driven accretion for a smaller $L_{\rm AGN}$, while the dusty molecular gas in CNDs is blown away by the radiation pressure from AGNs beyond the critical luminosity. On the other hand, for massive SMBHs (e.g., $M_{\rm BH} > 10^{8}M_{\odot}$), $f_{\rm obs}$ is always smaller than $0.2$, and it is almost independent of $L_{\rm AGN}$ because the scale height of CNDs is mainly controlled by the maximal star-formation efficiency ($C_{\rm *, max}$) in CNDs. By comparison with the obscuring fractions suggested from the mid-infrared observations of nearby AGNs, the SN plus radiative feedback model with $C_{\rm *, max} = 10^{-7}\, {\rm yr}^{-1}$ well reproduces the observations for $M_\mathrm{BH} = 10^8 M_\odot$. We also find that the intense starburst or the existence of dust-free absorbers inside CNDs are necessary, to explain X-ray observations.
Quantum entanglement can manifest itself in the narrowing of wavepackets. We define the phenomenon of phase entanglement and describe its effect on the interpretation of spatial localization experiments.
We consider the localization game played on graphs in which a cop tries to determine the exact location of an invisible robber by exploiting distance probes. The corresponding graph parameter $\zeta(G)$ for a given graph $G$ is called the localization number. In this paper, we improve the bounds for dense random graphs determining an asymptotic behaviour of $\zeta(G)$. Moreover, we extend the argument to sparse graphs.
In this work, we consider the rational points on elliptic curves over finite fields F_{p}. We give results concerning the number of points on the elliptic curve y^2{\equiv}x^3+a^3(mod p)where p is a prime congruent to 1 modulo 6. Also some results are given on the sum of abscissae of these points. We give the number of solutions to y^2{\equiv}x^3+a^3(modp), also given in ([1], p.174), this time by means of the quadratic residue character, in a different way, by using the cubic residue character. Using the Weil conjecture, one can generalize the results concerning the number of points in F_{p} to F_{p^{r}}.
Superluminal electromagnetic fields of dyons are described in T^{4}- space and Quaternion formulation of various quantum equations is derived. It is shown that on passing from subluminal to superluminal realm via quaternion the theory of dyons becomes the Tachyonic dyons. Corresponding field Equations of Tachyonic dyons are derived in consistent, compact and simpler form.   Abstract Key words- Monopoles, Dyons, Tachyons, Quaternions, Superluminal and Electromagnetic fields.   Abstract PACS Nos- 03.50 De, 14.80 Hv.
For an arbitrary smooth hypersurface X in a projective space, we construct its LG moduli of quasimaps with P fields. Apply Kiem-Li's cosection localization we obtain a virtual fundamental class. We show the class coincides, up to sign, with that of moduli of quasimaps to X. This generalizes Chang-Li's numerical identity to the cycle level, and from Gromov Witten invariants to quasimap invariants.
In this talk, I review recent progress made in two areas of thermal field theory. In particular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate.
In this paper, we describe an entry to the third Emotion Recognition in the Wild Challenge, EmotiW2015. We detail the associated experiments and show that, through more accurately locating the facial landmarks, and considering only the distances between them, we can achieve a surprising level of performance. The resulting system is not only more accurate than the challenge baseline, but also much simpler.
In the general framework of $d\times d$ mixed states, we derive an explicit bound for bipartite NPT entanglement based on the mixedness characterization of the physical system. The result derived is very general, being based only on the assumption of finite dimensionality. In addition it turns out to be of experimental interest since some purity measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.
The transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated. Upon including spin-orbit coupling and curvature effects, two main phenomena are analyzed which crucially depend on the tube's chirality: i) Finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states. This phenomenon occurs due to the magnetic-field dependent open boundary conditions obeyed by the carbon nanotube's wave functions. The transport is fully suppressed above threshold values of the magnetic field which depend on the nanotube chirality, length and on the spin-orbit coupling. ii) Reversible spin polarized currents can be obtained upon tuning the magnetic field, exploiting the curvature-induced spin-orbit splitting.
We propose a method for observation of the quasi-stationary states of neutrons, localized near the curved mirror surface. The bounding effective well is formed by the centrifugal potential and the mirror Fermi-potential. This phenomenon is an example of an exactly solvable "quantum bouncer" problem that could be studied experimentally. It could provide a promising tool for studying fundamental neutron-matter interactions, as well as quantum neutron optics and surface physics effects. We develop formalism, which describes quantitatively the neutron motion near the mirror surface. The effects of mirror roughness are taken into account.
We report the discovery and constrain the physical conditions of the interstellar medium of the highest-redshift millimeter-selected dusty star-forming galaxy (DSFG) to date, SPT-S J031132-5823.4 (hereafter SPT0311-58), at $z=6.900 +/- 0.002$. SPT0311-58 was discovered via its 1.4mm thermal dust continuum emission in the South Pole Telescope (SPT)-SZ survey. The spectroscopic redshift was determined through an ALMA 3mm frequency scan that detected CO(6-5), CO(7-6) and [CI](2-1), and subsequently confirmed by detections of CO(3-2) with ATCA and [CII] with APEX. We constrain the properties of the ISM in SPT0311-58 with a radiative transfer analysis of the dust continuum photometry and the CO and [CI] line emission. This allows us to determine the gas content without ad hoc assumptions about gas mass scaling factors. SPT0311-58 is extremely massive, with an intrinsic gas mass of $M_{\rm gas} = 3.3 \pm 1.9 \times10^{11}\,M_{\odot}$. Its large mass and intense star formation is very rare for a source well into the Epoch of Reionization.
The supermassive black hole in the center of our Galaxy, Sgr A*, is unique because the angular size of the black hole is the largest in the sky thus providing detailed boundary conditions on, and much less freedom for, accretion flow models. In this paper I review advection-dominated accretion flow (ADAF; another name is radiatively inefficient accretion flow) models for Sgr A*. This includes the developments and dynamics of ADAFs, and how to explain observational results including the multi-waveband spectrum, radio polarization, IR and X-ray flares, and the size measurements at radio wavebands.
We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in our previous papers and can be regarded as a random joint of two independent Poisson processes.
In non-equilibrium steady states (NESS) far from equilibrium, it is known that the Einstein relation is violated. Then, the ratio of the diffusion coefficient to the mobility is called an effective temperature, and the physical relevance of this effective temperature has been studied in several works. Although the physical relevance is not yet completely clear, it has been found that the role of an effective temperature in NESS is indeed analogous to that of the temperature in equilibrium systems in a number of respects. In this paper, we find further evidence establishing this analogy. We employ a non-equilibrium Langevin system as a thermostat for a Hamiltonian system and find that the kinetic temperature of this Hamiltonian system is equal to the effective temperature of the thermostat.
Spherically symmetric, static model of the cosmological voids is constructed in the framework of the Tolman-Oppenheimer-Volkov equation with the cosmological constant. Extension of the Tooper result (dimensionless form of the TOV equation) is provided for non-zero $\Lambda$. Then, the equation is simplified in $\alpha \to 0$, $\lambda \to 0$, $\lambda/\alpha = const$ regime, suitable for largest structures in $\Lambda$-dominated universe. Voids are treated as an underdensity regions in the static Einstein universe. Both overdensity and underdensity (relative to static universe) solutions exist. They are identified with standard astrophysical spherical objects and voids, respectively. Model is tested against observed properties (the radius - the central density relation) and density profiles of voids. Analytical formulae for radial density contrast profile and radii of the voids are derived. Some consequences for cosmological n-body simulations are suggested. Hints on the dark matter/dark energy EOS filling the voids are provided.
The non-centrosymmetric semiconductors BiTeX (X = Cl, Br, I) show large Rashba-type spin-orbit splittings in their electronic structure making them candidate materials for spin-based electronics. However, BiTeI(0001) single crystal surfaces usually consist of stacking-fault-induced domains of Te and I terminations implying a spatially inhomogeneous electronic structure. Here we combine scanning tunneling microscopy (STM), photoelectron spectroscopy (ARPES, XPS) and density functional theory (DFT) calculations to systematically investigate the structural and electronic properties of BiTeX(0001) surfaces. For X = Cl, Br we observe macroscopic single-terminated surfaces. We discuss chemical characteristics among the three materials in terms of bonding character, surface electronic structure, and surface morphology.