ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study general non-equatorial motion of photons in the Kerr-de Sitter black hole and naked singularity spacetimes. The motion is governed by the impact parameter $X$ related to axial symmetry of the spacetime, and impact parameter $q$ related to its hidden symmetry. Appropriate 'effective potentials' governing the latitudinal and radial motion are introduced and their behaviour is examined by 'Chinese boxes' technique giving regions allowed for the motion in terms of the impact parameters. Limits on the impact parameter $X$ and $q$ are established in dependence on the spacetime parameters $M, \Lambda, a$. The motion can be of orbital type (crossing the equatorial plane, $q>0$) and vortical type (tied above or bellow the equatorial plane, $q<0$). It is shown that for negative values of $q$ the reality conditions imposed on the latitudinal motion yield stronger constraints on the parameter $X$ than that following from the reality condition of motion in the radial direction, which, e. g., exclude possibility of existence of vortical motion of constant radius. Several other consequences are determined and a classification of Kerr-de Sitter spacetimes reflecting the behaviour of the effective potentials is given.
The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schr\"{o}dinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, $\theta\sim10^{-9}\lambda_e^2$.
M54 is the central cluster of the Sagittarius dwarf galaxy. This stellar system is now in process of being disrupted by the tidal interaction with the Milky Way and represents one of the building blocks of the Galactic Halo. Recent discoveries, based on the synergy of photometry and spectroscopy have revealed that the color-magnitude diagram of some massive, anomalous, Globular Clusters (GCs) host stellar populations with different content of heavy elements.In this paper, I use multi-wavelength Hubble Space Telescope photometry to detect and characterize multiple stellar populations in M54. I provide empirical evidence that this GC shares photometric and spectroscopic similarities with the class of anomalous GCs. These findings make it tempting to speculate that, similarly to Sagittarius nuclear cluster M54, other anomalous GCs were born in an extra-Galactic environment.
The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the other hand, the main core of the work is devoted to providing an alternative proof of the aforementioned result. The importance of this original contribution relies on the fact that, unlike the approach used in [4], the strategy adopted here is not sensitive of the two dimensional setting of the problem and therefore could be adapted to higher dimensional Zakharov-Kuznetsov equations for which, as far as we know, a proof of an analogous optimal unique continuation principle is still missing. For sake of clearness we focus here on the 2D case only, the higher dimensional analysis will be discussed somewhere else.
In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schr\"odinger operator in dimension $n\geq 3$. We assume that the inaccessible part of the boundary is part of a hyperplane. We improve the identifiability result obtained by Krupchyck, Lassas and Uhlmann [14] and also derive the corresponding stability estimates. We obtain $\log$-estimates for magnetic and electric potentials.
Accreting highly magnetized pulsars in binary systems are among the brightest X-ray emitters in our Galaxy. Although a number of high statistical quality broad-band (0.1-100 keV) X-ray observations are available, the spectral energy distribution of these sources is usually investigated by adopting pure phenomenological models, rather than models linked to the physics of accretion. In this paper, a detailed spectral study of the X-ray emission recorded from the high-mass X-ray binary pulsars Cen X-3, 4U 0115+63, and Her X-1 is carried out by using BeppoSAX and joined Suzaku+NuStar data, together with an advanced version of the compmag model. The latter provides a physical description of the high energy emission from accreting pulsars, including the thermal and bulk Comptonization of cyclotron and bremsstrahlung seed photons along the neutron star accretion column. The compmag model is based on an iterative method for solving second-order partial differential equations, whose convergence algorithm has been improved and consolidated during the preparation of this paper. Our analysis shows that the broad-band X-ray continuum of all considered sources can be self-consistently described by the compmag model. The cyclotron absorption features, not included in the model, can be accounted for by using Gaussian components. From the fits of the compmag model to the data we inferred the physical properties of the accretion columns in all sources, finding values reasonably close to those theoretically expected according to our current understanding of accretion in highly magnetized neutron stars. The updated version of the compmag model has been tailored to the physical processes that are known to occur in the columns of highly magnetized accreting neutron stars and it can thus provide a better understanding of the high energy radiation from these sources.
For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.
In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.
Localizing functional regions of objects or affordances is an important aspect of scene understanding. In this work, we cast the problem of affordance segmentation as that of semantic image segmentation. In order to explore various levels of supervision, we introduce a pixel-annotated affordance dataset of 3090 images containing 9916 object instances with rich contextual information in terms of human-object interactions. We use a deep convolutional neural network within an expectation maximization framework to take advantage of weakly labeled data like image level annotations or keypoint annotations. We show that a further reduction in supervision is possible with a minimal loss in performance when human pose is used as context.
The question whether ferroelectricity (FE) may coexist with a metallic or highly conducting state, or rather it must be suppressed by the screening from the free charges, is the focus of a rapidly increasing number of theoretical studies and is finally receiving positive experimental responses. The issue is closely related to the thermoelectric and multiferroic (also magnetic) applications of FE materials, where the electrical conductivity is required or spurious. In these circumstances, the traditional methods for probing ferroelectricity are hampered or made totally ineffective by the free charges, which screen the polar response to an external electric field. This fact may explain why more than 40 years passed between the first proposals of FE metals and the present experimental and theoretical activity. The measurement of the elastic moduli, Young's modulus in the present case, versus temperature is an effective method for studying the influence of doping on a FE transition because the elastic properties are unaffected by electrical conductivity. In this manner, it is shown that the FE transitions of BaTiO3-d are not suppressed by electron doping through O vacancies; only the onset temperatures are depressed, but the magnitudes of the softenings, and hence of the piezoelectric activity, are initially even increased.
Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, while ignoring the accretion disk leads to a further ~50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures for the black hole energy extraction process. Third, we compute the effective resistance of the load region and show that the load and the black hole achieve near perfect impedance matching. Taken together, these results increase our confidence in the BZ model as the correct description of jets observed from astrophysical black holes.
In R-parity violating supersymmetric models both leptogenesis and the correct neutrino masses are hard to achieve together. The presence of certain soft nonholomorphic R-parity violating terms helps to resolve this problem. We consider a scenario where the lightest and the second-lightest neutralino are nearly degenerate in mass and enough CP-asymmetry can be produced through resonant leptogenesis. In this model, the lighter chargino and the lightest neutralino are highly degenerate. We have relatively lighter gauginos which can be produced at the LHC leading to heavily ionizing charged tracks. At the same time this model can also generate the correct neutrino mass scale. Thus our scenario is phenomenologically rich and testable at colliders.
We introduce a notion of duality (due to Brylawski) that generalizes matroid duality to arbitrary rank functions. This generalized duality allows for generalized operations (deletion and contraction) and a generalized polynomial based on the matroid Tutte polynomial. This polynomial satisfies a deletion-contraction recursion. We explore this notion of duality for greedoids, antimatroids and demi-matroids, proving that matroids correspond precisely to objects that are simultaneously greedoids and "dual" greedoids.
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^2 related norms, with dispersive estimates, which give decay in L^\infty. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
We study the effects of hole doping on the two-dimensional Heisenberg-Kondo model around the quantum critical point, where the spin liquid phase (Kondo insulator) and the magnetically ordered phase are separated via a second-order phase transition. By means of the self-consistent Born approximation within the bond operator formalism as well as the standard spin wave theory, we discuss dynamical properties of a doped hole. It is clarified that a quasi-particle state stabilized in the spin liquid phase is gradually obscured as the system approaches the quantum critical point. This is also the case for the magnetically ordered phase. We argue the similarity and the difference between these two cases.
What range of momentum components in the deuteron wave function are available e d elastic scattering data sensitive to ? This question is addressed within the context of a model calculation of the deuteron form factors, based on realistic interactions and currents. It is shown that the data on the $A(q)$, $B(q)$, and $T_{20}(q)$ observables at $q \leq 6$ fm$^{-1}$ essentially probe momentum components up to $\simeq 4 m_\pi$.
We study hadronic models of broad-band emission of jets in radio-loud active galactic nuclei, and their implications for the accretion in those sources. We show that the models that account for broad-band spectra of blazars emitting in the GeV range in the sample of Boettcher et al. have highly super-Eddington jet powers. Furthermore, the ratio of the jet power to the radiative luminosity of the accretion disc is $\sim 3000$ on average and can be as high as $\sim 10^5$. We then show that the measurements of the radio core shift for the sample imply low magnetic fluxes threading the black hole, which rules out the Blandford-Znajek mechanism to produce powerful jets. These results require that the accretion rate necessary to power the modelled jets is extremely high, and the average radiative accretion efficiency is $\sim 4 \times 10^{-5}$. Thus, if the hadronic model is correct, the currently prevailing picture of accretion in AGNs needs to be significantly revised. Also, the obtained accretion mode cannot be dominant during the lifetimes of the sources, as the modelled very high accretion rates would result in too rapid growth of the central supermassive black holes. Finally, the extreme jet powers in the hadronic model are in conflict with the estimates of the jet power by other methods.
We consider the exchange Hamiltonian H_ST = -J Sum_{<rr'>} (2 S_r S_r' - 1/2) (2 T_r T_r' - 1/2) describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on equivalent bonds. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit. To investigate the ground state properties we use a Green's Function Monte Carlo, calculating energy gaps and correlation functions, the latter through the forward walking technique. In one dimension we find that the ground state is a ``crystal'' of valence bond dimers. In two dimensions, the spin gap appears to remain finite in the thermodynamic limit, and, consistently, the staggered magnetization -- signal of Neel long range order -- seems to vanish. From the analysis of dimer-dimer correlation functions, however, we find no sign of a valence bond crystal. A spin liquid appears as a plausible scenario compatible with our findings.
We construct the Liouville operator for the SU(2) classical colored Coulomb plasma (cQGP) for arbitrary values of the Coulomb coupling $\Gamma=V/K$, the ratio of the mean Coulomb to kinetic energy. We show that its resolvent in the classical colored phase space obeys a hierarchy of equations. We use a free streaming approximation to close the hierarchy and derive an integral equation for the time-dependent structure factor. Its reduction by projection yields hydrodynamical equations in the long-wavelength limit. We discuss the character of the hydrodynamical modes at strong coupling. The shear viscosity is shown to exhibit a minimum at $\Gamma\approx 8$ near the liquid point. This minimum follows from the cross-over between the single particle collisional regime which drops as $1/\Gamma^{5/2}$ and the hydrodynamical collisional regime which rises as $\Gamma^{1/2}$. The self-diffusion constant drops as $1/\Gamma^{3/2}$ irrespective of the regime. We compare our results to molecular dynamics simulations of the SU(2) colored Coulomb plasma. We also discuss the relevance of our results for the quantum and strongly coupled quark gluon plasma (sQGP)
We start by asking an interesting yet challenging question, "If an eyewitness can only recall the eye features of the suspect, such that the forensic artist can only produce a sketch of the eyes (e.g., the top-left sketch shown in Fig. 1), can advanced computer vision techniques help generate the whole face image?" A more generalized question is that if a large proportion (e.g., more than 50%) of the face/sketch is missing, can a realistic whole face sketch/image still be estimated. Existing face completion and generation methods either do not conduct domain transfer learning or can not handle large missing area. For example, the inpainting approach tends to blur the generated region when the missing area is large (i.e., more than 50%). In this paper, we exploit the potential of deep learning networks in filling large missing region (e.g., as high as 95% missing) and generating realistic faces with high-fidelity in cross domains. We propose the recursive generation by bidirectional transformation networks (r-BTN) that recursively generates a whole face/sketch from a small sketch/face patch. The large missing area and the cross domain challenge make it difficult to generate satisfactory results using a unidirectional cross-domain learning structure. On the other hand, a forward and backward bidirectional learning between the face and sketch domains would enable recursive estimation of the missing region in an incremental manner (Fig. 1) and yield appealing results. r-BTN also adopts an adversarial constraint to encourage the generation of realistic faces/sketches. Extensive experiments have been conducted to demonstrate the superior performance from r-BTN as compared to existing potential solutions.
In this article, models are constructed of the compact jet in GRS 1915+105 during an epoch of optimal data capture. On April 02, 2003, the object was observed in the hard X-ray/soft gamma ray band (INTEGRAL), hard X-ray band (RXTE), near IR (ESO/New Technology Telescope) and the VLBA (8.3 GHz and 15 GHz). The source was in a so-called "high plateau state." The large radio flux provides high signal to noise ratios in the radio images. Thus, one can image the jet out to large distances ($ > 10^{15}$ cm). This combined with the broadband coverage make this epoch the best suited for modeling the jet. The parametric method developed in the papers \cite{ghi85,ghi89,ghi96,sam97} that has been successfully utilized in the realm of extragalactic radio jets is implemented. The basic model is one where external inverse Compton (EIC) scattering of accretion disk photons by jet plasma provides the hard X-ray powerlaw. Unlike AGN jets, it is found that the radio jet must be highly stratified in the transverse direction in order to produce the observed surface brightness distribution in the radio images. Various jet models are considered. The jet power is $Q \approx 3-4 \times 10^{38}$ ergs/sec if the hard X-ray powerlaw luminosity is from EIC in the jet and $Q \approx 2 - 9 \times 10^{37}$ ergs/sec if the X-rays are emitted from the accretion disk corona. These estimates indicate that the jet power can be as high as 60% of the total X-ray luminosity.
Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization on the Euclidean space. In this paper, we propose several novel PLSR models on Riemannian manifolds and develop optimization algorithms based on Riemannian geometry of manifolds. This algorithm can calculate all the factors of PLSR globally to avoid suboptimal solutions. In a number of experiments, we have demonstrated the benefits of applying the proposed model and algorithm to a variety of learning tasks in pattern recognition and object classification.
The spatial distribution of 3.3 \mum PAH and associated emission in the 3.3" x 6.0" inner region of the Red Rectangle nebula has been determined using the UIST imager-spectrometer at the United Kingdom Infrared Telescope (UKIRT). Interpretation of the 3.3 \mum feature as comprising two spectroscopic components centred at 3.30 \mum and 3.28 \mum, as put forward by Song et al. (2003, 2007), is supported by these data which reveal that they have different spatial distributions. It is deduced that there are two classes of 3.3 \mum band carrier with a peak wavelength separation of ~0.02 \mum. From comparison of the 3.3 \mum observations with laboratory and theoretical spectra for a range of PAH molecules it is proposed that the 3.28 \mum and 3.30 \mum components arise from 'bay' and 'non-bay' hydrogen sites, respectively, on the periphery of small neutral PAHs. Observational data are also obtained for L-band continuum emission and for the Pfund \epsilon hydrogen recombination line.
Using Chandra imaging spectroscopy and VLA L-band maps, we have identified radio galaxies at P(1.4 GHz) >= 3x10^{23} W Hz^{-1} and X-ray point sources (XPSs) at L(0.3-8 keV) >= 10^{42} ergs s^{-1} in 11 moderate redshift (0.2<z<0.4) clusters of galaxies. Each cluster is uniquely chosen to have a total mass similar to predicted progenitors of the present-day Coma Cluster. Within a projected radius of 1 Mpc we detect 20 radio galaxies and 8 XPSs confirmed to be cluster members above these limits. 75% of these are detected within 500 kpc of the cluster center. This result is inconsistent with a random selection from bright, red sequence ellipticals at the > 99.999% level. All but one of the XPSs are hosted by luminous ellipticals which otherwise show no other evidence for AGN activity. These objects are unlikely to be highly obscured AGN since there is no evidence for large amounts of X-ray or optical absorption. The most viable model for these sources are low luminosity BL Lac Objects. The expected numbers of lower luminosity FR 1 radio galaxies and BL Lacs in our sample converge to suggest that very deep radio and X-ray images of rich clusters will detect AGN in a large fraction of bright elliptical galaxies in the inner 500 kpc. Because both the radio galaxies and the XPSs possess relativistic jets, they can inject heat into the ICM. Using the most recent scalings of P_jet ~ L_radio^{0.5} from Birzan et al. (2008), radio sources weaker than our luminosity limit probably contribute the majority of the heat to the ICM. If a majority of ICM heating is due to large numbers of low power radio sources, triggered into activity by the increasing ICM density as they move inward, this may be the feedback mechanism necessary to stabilize cooling in cluster cores.