ShantanuT01/DACTYL-Pretraining huggingface dataset:
We test the effects of reconstruction techniques on 2D data to determine the best approach. We obtained a time-series of spectropolarimetric data in the Fe I line at 630.25 nm with the Goettingen Fabry-Perot Interferometer (FPI) that are accompanied by imaging data at 431.3 nm and Ca II H. We apply both speckle and (MO)MFBD techniques. We compare the spatial resolution and investigate the impact of the reconstruction on spectral characteristics. The speckle reconstruction and MFBD perform similar for our imaging data with nearly identical intensity contrasts. MFBD provides a better and more homogeneous resolution at the shortest wavelength. The MOMFBD and speckle deconvolution of the intensity spectra lead to similar results, but our choice of settings for the MOMFBD yields an intensity contrast smaller by about 2% at a comparable spatial resolution. None of the reconstruction techniques introduces artifacts in the intensity spectra. The speckle deconvolution (MOMFBD) has a rms noise in V/I of 0.32% (0.20%). The deconvolved spectra thus require a high significance threshold of about 1.0%. A comparison to spectra with a significantly higher S/N ratio and to spectra from a MHD simulation reveals that the Goettingen FPI can only detect about 30% of the polarization signal in quiet Sun. The distribution of NCP values for the speckle-deconvolved data matches that of observations with higher S/N better than MOMFBD, but shows seemingly artificially sharp boundaries and unexpected changes of the sign. For the spectropolarimetric data, the higher intensity contrast of the speckle deconvolution is balanced by the smaller amplification of the noise level in the MOMFBD at a comparable spatial resolution. The noise level prevents the detection of weak and diffuse magnetic fields.
We investigate the total and baryonic mass distributions in deflector number 31 of the Cambridge And Sloan Survey Of Wide ARcs in the skY (CASSOWARY). We confirm spectroscopically a four-image lensing system at redshift 1.4870 with VLT/X-shooter observations. The lensed images are distributed around a bright early-type galaxy at redshift 0.683, surrounded by several smaller galaxies at similar photometric redshifts. We use available optical and X-ray data to constrain the deflector total, stellar, and hot gas mass through, respectively, strong lensing, stellar population analysis, and plasma modelling. We derive a total mass projected within the Einstein radius R_Ein = 70 kpc of (40 +/- 1) x 10^12 M_Sun, and a central logarithmic slope of -1.7 +/- 0.2 for the total mass density. Despite a very high stellar mass and velocity dispersion of the central galaxy of (3 +/- 1) x 10^12 M_Sun and (450 +/- 80) km/s, respectively, the cumulative stellar-to-total mass profile of the deflector implies a remarkably low stellar mass fraction of 20% (3%-6%) in projection within the central galaxy effective radius R_e = 25 kpc (R = 100 kpc). We also find that the CSWA 31 deflector has properties suggesting it to be among the most distant and massive fossil systems studied so far. The unusually strong central dark matter dominance and the possible fossil nature of this system renders it an interesting target for detailed tests of cosmological models and structure formation scenarios.
We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve defined over ${\mathbb Q}$. We produce the lift by showing that the coefficients of the initial, weak eigenform (almost all) occur as traces of Frobenii in the Galois representation on the 4-torsion of the elliptic curve. The example is remarkable as the initial form is known not to be liftable to any characteristic 0 eigenform of level 1. We use this example as illustrating certain questions that have arisen lately in the theory of modular forms modulo prime powers. We give a brief survey of those questions.
We address the task of aligning CAD models to a video sequence of a complex scene containing multiple objects. Our method can process arbitrary videos and fully automatically recover the 9 DoF pose for each object appearing in it, thus aligning them in a common 3D coordinate frame. The core idea of our method is to integrate neural network predictions from individual frames with a temporally global, multi-view constraint optimization formulation. This integration process resolves the scale and depth ambiguities in the per-frame predictions, and generally improves the estimate of all pose parameters. By leveraging multi-view constraints, our method also resolves occlusions and handles objects that are out of view in individual frames, thus reconstructing all objects into a single globally consistent CAD representation of the scene. In comparison to the state-of-the-art single-frame method Mask2CAD that we build on, we achieve substantial improvements on the Scan2CAD dataset (from 11.6% to 30.7% class average accuracy).
We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one logical qubit and additional auxiliary dimensions are used to create and purify entanglement between systems. Physical, possibly probabilistic two-system operations with error rates up to 2/3 are still tolerable to realize deterministic high quality two-qubit gates on the logical qubits. The achievable error rate is of the same order of magnitude as of the single-system operations. We investigate possible implementations of our scheme for several physical set-ups.
We consider multivalued maps between $\Omega \subset \mathbb{R}^N$ open ($N \ge 2$) and a smooth, compact Riemannian manifold $\mathcal{N}$ locally minimizing the Dirichlet energy. An interior partial H\"older regularity result in the spirit of R. Schoen and K. Uhlenbeck is presented. Consequently a minimizer is H\"older continuous outside a set of Hausdorff dimension at most $N-3$. F. Almgren's original theory includes a global interior H\"older continuity result if the minimizers are valued into some $\mathbb{R}^m$. It cannot hold in general if the target is changed into a Riemannian manifold, since it already fails for "classical" single valued harmonic maps.
In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W state or W - type state $|X>=\alpha|001>_{123}+\beta|010>_{123}+\gamma|100>_{123}, \alpha^{2} + \beta^{2} + \gamma^{2} = 1$ shared by three distant partners. Also we have considered the case $\beta=\gamma$, to obtain a range for $\alpha^2$, for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixed ness of inseparable states with their amount of inseparability, for that range of $\alpha^2$.
We study propagation of the Gabor wave front set for a Schr\"odinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with non-negative real part. We point out that the singular space associated to the quadratic form plays a crucial role for the understanding of this propagation. We show that the Gabor singularities of the solution to the equation for positive times are always contained in the singular space, and that they propagate in this set along the flow of the Hamilton vector field associated to the imaginary part of the quadratic form. As an application we obtain for the heat equation a sufficient condition on the Gabor wave front set of the initial datum tempered distribution that implies regularization to Schwartz regularity for positive times.
We examine the stability and observational consequences of mixing induced by 3He burning in the envelopes of first ascent red giants. We demonstrate that there are two unstable modes: a rapid, nearly adiabatic mode that we cannot identify with an underlying physical mechanism, and a slow, nearly radiative mode that can be identified with thermohaline convection. We present observational constraints that make the operation of the rapid mode unlikely to occur in real stars. Thermohaline convection turns out to be fast enough only if fluid elements have finger-like structures with a length to diameter ratio l/d > 10. We identify some potentially serious obstacles for thermohaline convection as the predominant mixing mechanism for giants. We show that rotation-induced horizontal turbulent diffusion may suppress the 3He-driven thermohaline convection. Another potentially serious problem for it is to explain observational evidence of enhanced extra mixing. The 3He exhaustion in stars approaching the red giant branch (RGB) tip should make the 3He mixing inefficient on the asymptotic giant branch (AGB). In spite of this, there are observational data indicating the presence of extra mixing in low-mass AGB stars similar to that operating on the RGB. Overmixing may also occur in carbon-enhanced metal-poor stars.
We use 21 Hubble parameter versus redshift data points, from Gazta\~{n}aga et al. (2009), Stern et al. (2010), and Moresco et al. (2012), to place constraints on model parameters of constant and time-evolving dark energy cosmologies. This is the largest set of H(z) data considered to date. The inclusion of the 8 new Moresco et al. (2012) measurements results in H(z) constraints more restrictive than those derived by Chen & Ratra (2011b). These constraints are now almost as restrictive as those that follow from current Type Ia supernova (SNIa) apparent magnitude versus redshift data (Suzuki et al. 2012), which now more carefully account for systematic uncertainties. This is a remarkable result. We emphasize however that SNIa data have been studied for a longer time than the H(z) data, possibly resulting in a better estimate of potential systematic errors in the SNIa case. A joint analysis of the H(z), baryon acoustic oscillation peak length scale, and SNIa data favors a spatially-flat cosmological model currently dominated by a time-independent cosmological constant but does not exclude slowly-evolving dark energy.
We consider the so-called $\natural$-model. It is an one-default model which gives the conditional law of a random time with respect to a reference filtration. This model has been studied in the case where the parameters are continuous. In this paper we will establish the $\natural$-model in the case of jump parameters. We then prove the corresponding enlargement of filtration formula and we compute the derivative of the conditional distribution functions of the random time.
We present the review of some new problems in cosmology and physics of stars in connection with future launching of WSO. We discuss three problems. UV observations of distant z > 6 quasars allow to obtain information on the soft < 1 KeV X-ray radiation of the accretion disk around a supermassive black hole because of its cosmological redshift. Really the region of X-ray radiation is insufficiently investigated because of high galactic absorption. In a result one will get important information on the reionization zone of the Universe. Astronomers from ESO revealed the effect of alignment of electric vectors of polarized QSOs. One of the probable mechanism of such alignment is the conversion of QSO radiation into low mass pseudoscalar particles (axions) in the extragalactic magnetic field. These boson like particles have been predicted by new SUSY particle physics theory. Since the probability of such conversion is increasing namely in UV spectral range one can expect the strong correlation between UV spectral energy distribution of QSO radiation and polarimetric data in the optical range. In the stellar physics one of the interesting problems is the origin of the X-ray sources with super Eddington luminosities. The results of UV observations of these X-ray sources will allow to find the origin of these sources as accreting intermediate mass black holes.
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen relatively little application in one area of interest, type II critical collapse, where the challenges for a numerical code are particularly severe. Using the critical collapse of a massless scalar field in spherical symmetry as a test case, we study a generalization of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation due to Brown that is suited for use with curvilinear coordinates. We adopt standard dynamical gauge choices, including 1+log slicing and a shift that is either zero or evolved by a Gamma-driver condition. With both choices of shift we are able to evolve sufficiently close to the black hole threshold to (1) unambiguously identify the discrete self-similarity of the critical solution (2) determine an echoing exponent consistent with previous calculations and (3) measure a mass scaling exponent, also in accord with prior computations. Our results can be viewed as an encouraging first step towards the use of hyperbolic formulations in more generic type II scenarios, including the as yet unresolved problem of critical collapse of axisymmetric gravitational waves.
The properties of dark matter halos, including mass growth, correlate with larger scale environment at fixed mass, an effect known as assembly bias. However, whether this environmental dependence manifests itself in galaxy properties remains unclear. We apply a group-finding algorithm to DR7 of the SDSS to estimate the halo mass of each galaxy and to decompose galaxies into those that exist at the centers of distinct halos and those that orbit as satellites within larger halos. Using the 4000-A break as a measure of star formation history, we examine the correlation between the quenched fraction of galaxies, f_q, and large-scale environment, rho. At all galaxy magnitudes, there is a positive, monotonic relationship between f_q and rho. We use the group catalog to decompose this correlation into the contribution from central and satellite galaxies as a function of halo mass. Because satellites are more likely to be quenched than central galaxies, the observed f_q-rho correlation is primarily due to variations of the halo mass function with environment, which causes a larger fraction of satellite galaxies at high rho. For low-mass central galaxies (Mgal <~ 10^10.0 Msol/h^2), there is no correlation between f_q and rho. These results are inconsistent with the strong assembly bias of dark matter halos seen in this mass regime if recent galaxy growth at all correlates with recent halo growth, as we demonstrate through a high resolution N-body simulation. We also find that the mean stellar age of quenched central galaxies is independent of rho at fixed Mgal, while the formation times of low mass halos vary significantly. We conclude that the processes that halt the star formation of low mass central galaxies are not correlated to the formation histories of their host halos, and old galaxies do not reside preferentially in old halos. (Abridged)
We show that well-posed, conformally-decomposed formulations of the 3+1 Einstein equations can be obtained by densitizing the lapse and by combining the constraints with the evolution equations. We compute the characteristics structure and verify the constraint propagation of these new well-posed formulations. In these formulations, the trace of the extrinsic curvature and the determinant of the 3-metric are singled out from the rest of the dynamical variables, but are evolved as part of the well-posed evolution system. The only free functions are the lapse density and the shift vector. We find that there is a 3-parameter freedom in formulating these equations in a well-posed manner, and that part of the parameter space found consists of formulations with causal characteristics, namely, characteristics that lie only within the lightcone. In particular there is a 1-parameter family of systems whose characteristics are either normal to the slicing or lie along the lightcone of the evolving metric.
We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic different from 2 remains non-hyperbolic over some splitting field of the algebra.
We present a high-resolution radio survey of the Sloan Digital Sky Survey (SDSS) Southern Equatorial Stripe, a.k.a. Stripe 82. This 1.4 GHz survey was conducted with the Very Large Array (VLA) primarily in the A-configuration, with supplemental B-configuration data to increase sensitivity to extended structure. The survey has an angular resolution of 1.8" and achieves a median rms noise of 52 microJy/bm over 92 deg^2. This is the deepest 1.4 GHz survey to achieve this large of an area, filling a gap in the phase space between small, deep and large, shallow surveys. It also serves as a pilot project for a larger high-resolution survey with the Expanded Very Large Array (EVLA). We discuss the technical design of the survey and details of the observations, and we outline our method for data reduction. We present a catalog of 17,969 isolated radio components, for an overall source density of ~195 sources/deg^2. The astrometric accuracy of the data is excellent, with an internal check utilizing multiply-observed sources yielding an rms scatter of 0.19" in both right ascension and declination. A comparison to the SDSS DR7 Quasar Catalog further confirms that the astrometry is well tied to the optical reference frame, with mean offsets of 0.02" +/- 0.01" in right ascension, and 0.01" +/- 0.02" in declination. A check of our photometry reveals a small, negative CLEAN-like bias on the level of 35 microJy. We report on the catalog completeness, finding that 97% of FIRST-detected quasars are recovered in the new Stripe 82 radio catalog, while faint, extended sources are more likely to be resolved out by the resolution bias. We conclude with a discussion of the optical counterparts to the catalog sources, including 76 newly-detected radio quasars. The full catalog as well as a search page and cutout server are available online at http://third.ucllnl.org/cgi-bin/stripe82cutout.
Recently cosmological dynamics of anisotropic Universe in $f(T)$ gravity became an area of intense investigations. Some earlier papers devoted to this issue contain contradictory claims about the nature and propertied of vacuum solutions in this theory. The goal of the present paper is to clarify this situation. We compare properties of $f(T)$ and $f(R)$ vacuum solutions and outline differences between them. The Kasner solution appears to be an exact solution for the $T=0$ branch, and an asymptotic solution for $T \ne 0$ branch. It is shown that Kasner solution is the past attractor if $T<0$, being past and future attractor for $T>0$ branch.
Based on the equations of state, one can infer the underlying interaction potentials among the black hole molecules in the case of Schwarzschild-AdS and charged AdS black holes. The microscopic molecules with the interaction potential arrange in a specific way to form the mesostructure, whose size is between the macro (black hole system) and the micro (black hole molecules). As a result, the mesostructure leads to the emergence of the macroscopic phase. However, the information about the mesostructure of the AdS black hole are still elusive. In this Letter, the radial distribution function is introduced to probe the mesostructure of the AdS black hole. We find that the mesostructure of the Schwarzschild-AdS black hole behaves as the ideal gas when the temperature is high. Furthermore, we find the mesostructure for the liquid-like (gas-like) phase of the small (large) charged AdS black hole. A sudden change of the mesostructure emerges from the liquid-like phase to the gas-like phase when the charged AdS black hole undergoes a phase transition from the small to large black hole, consistent with the viewpoint that the phase transition of the charged AdS black hole is reminiscent of that of the vdW fluid. This study provides a new angle towards understanding the black hole from its mesostructure.
We address the problem, previously considered by Ginocchio and Haxton (G-H), of the number of states for three identical particles in a single j-shell with angular momentum J=j. G-H solved this problem in the context of the quantum Hall effect. We address it in a more direct way. We also consider the case J=j+1 to show that our method is more general, and we show how to take care of added complications for a system of five identical particles.
One proves the uniqueness of distributional solutions to nonlinear Fokker--Planck equations with monotone diffusion term and derive as a consequence (restricted) uniqueness in law for the corresponding McKean--Vlasov stochastic differential equation (SDE).
The Casimir effect at finite temperature is investigated for a dilute dielectric ball; i.e., the relevant internal and free energies are calculated. The starting point in this study is a rigorous general expression for the internal energy of a system of noninteracting oscillators in terms of the sum over the Matsubara frequencies. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. For removing the divergences the renormalization procedure is applied that has been developed in the calculation of the corresponding Casimir energy at zero temperature. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated.
We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion.
In this paper we discuss existence, uniqueness and some properties of a class of solitons to the anisotropic mean curvature flow, i.e., graphical translators, either in the plane or under an assumption of cylindrical symmetry on the anisotropy and the mobility. In these cases, the equation becomes an ordinary differential equation, and this allows to find explicitly the translators and describe their main features.
We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime.
The fermion spin-flip conversion $f_L \to f_R + \gamma$ is considered, caused by the difference of the additional energies of the electroweak origin, acquired by left- and right-handed fermions (neutrino, electron) in medium. An accurate taking account of the fermion and photon dispersion in medium is shown to be important.