ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by $40\%$ with respect to previous work, with $4.5\%$ fractional difference for eccentricity $e=0.9$ and black hole dimensionless spin $-0.9\leq \hat{a}\leq +0.9$. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.
We obtain the quite exact exponential bounds for tails of distributions of sums of Banach space valued random variables uniformly over the number of summands under natural for the Law of Iterated Logarithm (LIL) norming.   We study especially the case of the so-called mixed (anisotropic) Lebesgue-Riesz spaces, on the other words, Bochner's spaces, for instance, continuous-Lebesgue spaces, which appear for example in the investigation of non-linear Partial Differential Equations of evolutionary type.   We give also some examples in order to show the exactness of our estimates.
We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).
A key capability of an intelligent system is deciding when events from past experience must be remembered and when they can be forgotten. Towards this goal, we develop a predictive model of human visual event memory and how those memories decay over time. We introduce Memento10k, a new, dynamic video memorability dataset containing human annotations at different viewing delays. Based on our findings we propose a new mathematical formulation of memorability decay, resulting in a model that is able to produce the first quantitative estimation of how a video decays in memory over time. In contrast with previous work, our model can predict the probability that a video will be remembered at an arbitrary delay. Importantly, our approach combines visual and semantic information (in the form of textual captions) to fully represent the meaning of events. Our experiments on two video memorability benchmarks, including Memento10k, show that our model significantly improves upon the best prior approach (by 12% on average).
It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the free field Dirac in $AdS_{d+1}$ backgrounds is analytically solved obtaining the formula of the energy levels and the corresponding normalized eigenspinors.
In this paper, we address unsupervised pose-guided person image generation, which is known challenging due to non-rigid deformation. Unlike previous methods learning a rock-hard direct mapping between human bodies, we propose a new pathway to decompose the hard mapping into two more accessible subtasks, namely, semantic parsing transformation and appearance generation. Firstly, a semantic generative network is proposed to transform between semantic parsing maps, in order to simplify the non-rigid deformation learning. Secondly, an appearance generative network learns to synthesize semantic-aware textures. Thirdly, we demonstrate that training our framework in an end-to-end manner further refines the semantic maps and final results accordingly. Our method is generalizable to other semantic-aware person image generation tasks, eg, clothing texture transfer and controlled image manipulation. Experimental results demonstrate the superiority of our method on DeepFashion and Market-1501 datasets, especially in keeping the clothing attributes and better body shapes.
The total entropy production and its three constituent components are described both as fluctuating trajectory-dependent quantities and as averaged contributions in the context of the continuous Markovian dynamics, described by stochastic differential equations with multiplicative noise, of systems with both odd and even coordinates with respect to time reversal, such as dynamics in full phase space. Two of these constituent quantities obey integral fluctuation theorems and are thus rigorously positive in the mean by Jensen's inequality. The third, however, is not and furthermore cannot be uniquely associated with irreversibility arising from relaxation, nor with the breakage of detailed balance brought about by non-equilibrium constraints. The properties of the various contributions to total entropy production are explored through the consideration of two examples: steady state heat conduction due to a temperature gradient, and transitions between stationary states of drift-diffusion on a ring, both in the context of the full phase space dynamics of a single Brownian particle.
We prove that the appropriately normalized maximum of the Gaussian $1/f^{\alpha}$-noise with $\alpha<1$ converges in distribution to the Gumbel double-exponential law.
We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. In examples the appropriate screening radii are given. We also numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for a screened Coulomb potential alone in the limit of large screening radii and confirm analytically predicted properties for off-shell, half-shell and on-shell Coulomb t-matrices. These 3-dimensional solutions will form a basis for a novel approach to include the pp Coulomb interaction into the 3N Faddeev framework.
Galaxy spectral energy distributions (SEDs) remain among the most challenging yet informative quantities to reproduce in simulations due to the large and complex mixture of physical processes that shape the radiation output of a galaxy. With the increasing number of surveys utilising broadband colours as part of their target selection criteria, the production of realistic SEDs in simulations is necessary for assisting in survey design and interpretation of observations. The recent success in reproducing the observed luminosity functions (LF) from far-UV to far-IR, using the state-of-the-art semi-analytic model \shark\ and the SED generator \prospect, represents a critical step towards better galaxy colour predictions. We show that with \shark\ and \prospect\ we can closely reproduce the optical colour distributions observed in the panchromatic GAMA survey. The treatment of feedback, star formation, central-satellite interactions and radiation re-processing by dust are critical for this achievement. The first three processes create a bimodal distribution, while dust attenuation defines the location and shape of the blue and red populations. While a naive comparison between observation and simulations displays the known issue of over-quenching of satellite galaxies, the introduction of empirically-motivated observational errors and classification from the same group finder used in GAMA greatly reduces this tension. The introduction of random re-assignment of $\sim 15\%$ of centrals/satellites as satellites/centrals on the simulation classification closely resembles the outcome of the group finder, providing a computationally less intensive method to compare simulations with observations.
We introduce a new approach of computing the automorphism group and the field of moduli of points $\p=[C]$ in the moduli space of hyperelliptic curves $\H_g$. Further, we show that for every moduli point $\p \in \H_g(L)$ such that the reduced automorphism group of $\p$ has at least two involutions, there exists a representative $C$ of the isomorphism class $\p$ which is defined over $L$.
We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.
We give an algebraic identity for cubic polynomials which generalizes Brahmagupta's identity and facilitates arithmetic in cubic fields. We also pose a question about a relationship between the elements of a cubic field of fixed trace and fixed norm and rational points of an elliptic curve.
Consider a family of random walks $S_n^{(a)}=X_1^{(a)}+\cdots+X_n^{(a)}$ with negative drift $\mathbf E X_1^{(a)}=-a<0$ and finite variance $\mbox{var}(X_1^{(a)})=\sigma^2<\infty$.Let $M^{(a)}=\max_{n\ge 0} S_n^{(a)}$ be the maximums of the random walks. The exponential asymptotics $\mathbf P(aM^{(a)}>x)\sim e^{-2x/\sigma^2}$, as $a\to 0$, were found by Kingman and are known as heavy traffic approximation in the queueing theory. For subexponential random variables the large deviation asymptotics for $\mathbf P(M^{(a)}>x)\sim \frac{1}{a}\overline F^I(x)$ hold for fixed $a$ as $x\to\infty$. In this paper we present asymptotics for $\mathbf P(M^{(a)}>x)$, which hold uniformly on the whole positive axis, as $a\to 0$. Thus, these uniform asymptotics include both the regime of normal and large deviations. We identify the regions where exponential or subexponential asymptotics hold. Our approach is based on construction of corresponding super/sub - martingales to obtain sharp upper and lower bounds.
Given sufficiently deep optical spectroscopy, the age estimation of high-redshif t ($z > 1$) galaxies has been claimed to be a relatively robust process (e.g. Dunlop et al. 1996) due to the fact that, for ages $< 5$Gyr, the near-ultraviolet light of a stellar population is expected to be dominated by `well-understood' main-sequence (MS) stars. Recently, however, the reliability of this process has been called into question by Yi et al (2000), who claim to have developed models in which the spectrum produced by the main sequence reddens much more rapidly than in the models of Jimenez et al (2000a), leading to much younger age estimates for the reddest known high-redshift ellipticals. In support of their revised age estimates, Yi et al cite the fact that their models can reproduce the spectrum of the Sun at an age of 5 Gyr, whereas the solar spectrum is not reproduced by the Jimenez et al models until $\simeq 10$ Gyr. Here we confirm this discrepancy, but point out that this is in fact a {\it strength} of the Jimenez et al models and indicative of some flaw in the models of Yi et al (which, in effect, imply that the Sun will turn into a red giant any minute now). We have also explored the models of Worthey (1994) (which are known to differ greatly from those of Jimenez et al in the treatment of post-MS evolution) and find that the main-sequence component of Worthey's models also cannot reproduce the solar spectrum until an age of 9-10 Gyr. We conclude that either the models of Yi et al are not as main-sequence dominated at 4-5 Gyr as claimed, or that the stellar evolutionary timescale in these models is in error by a factor possibly as high as two. (abridged)
We present solutions to the classical Liouville equation for ergodic and completely integrable systems - systems that are known to attain equilibrium. Ergodic systems are known to thermal equilibrate with a Maxwell-Boltzmann distribution and we show a simple derivation of this distribution that also leads to a derivation of the distribution at any time t. For illustrative purposes, we apply the method to the problem of a one-dimensional gravitational gas even though its ergodicity is debatable. For completely integrable systems, the Liouville equation in the original phase space is rather involved because of the group structure of the integral invariants, which hints of a gauge symmetry. We use Dirac's constrained formalism to show the change in the Liouville equation, which necessitates the introduction of gauge-fixing conditions. We then show that the solution of the Liouville equation is independent of the choice of gauge, which it must be because physical quantities are derived from the distribution. Instead, we derive the solution to the classical Liouville equation in the phase space where the dynamics involve ignorable coordinates, a technique that is akin to the use of the unitarity gauge in spontaneously broken gauge theories to expose the physical degrees of freedom. It turns out the distribution is time-independent and precisely given by the generalized Gibbs ensemble (GGE), which was solved by Jaynes using the method of constrained optimization. As an example, we apply the method to the problem of two particles in 3D interacting via a central potential.
We present polarization maps of G30.79 FIR 10 (in W43) from thermal dust emission at 1.3 mm and from CO J=$2 \to 1$ line emission. The observations were obtained using the Berkeley-Illinois-Maryland Association array in the period 2002-2004. The G30.79 FIR 10 region shows an ordered polarization pattern in dust emission, which suggests an hourglass shape for the magnetic field. Only marginal detections for line polarization were made from this region. Application of the Chandrashkar-Fermi method yielded $B_{pos} \approx 1.7$ mG and a statistically corrected mass to magnetic flux ratio $\lambda_{C} \approx 0.9$, or essentially critical.
This is a translation of a final paper. It contains proofs of some well-known Positivstellens\"atze. The approach in this paper differs in two respects from presentations in literature. We use the Stone-Weierstrass Theorem directly to prove an inductive property, which makes the Kadison-Dubois Theorem superfluous in our paper, and we also consider homogeneous and projective Positivstellens\"atze. This leads us to a homogeneous version of Schm\"udgen's theorem and a projective version of Putinar's theorem.
3D hand-mesh reconstruction from RGB images facilitates many applications, including augmented reality (AR). However, this requires not only real-time speed and accurate hand pose and shape but also plausible mesh-image alignment. While existing works already achieve promising results, meeting all three requirements is very challenging. This paper presents a novel pipeline by decoupling the hand-mesh reconstruction task into three stages: a joint stage to predict hand joints and segmentation; a mesh stage to predict a rough hand mesh; and a refine stage to fine-tune it with an offset mesh for mesh-image alignment. With careful design in the network structure and in the loss functions, we can promote high-quality finger-level mesh-image alignment and drive the models together to deliver real-time predictions. Extensive quantitative and qualitative results on benchmark datasets demonstrate that the quality of our results outperforms the state-of-the-art methods on hand-mesh/pose precision and hand-image alignment. In the end, we also showcase several real-time AR scenarios.
Any subset Q' of the domain Q of a learning space defines a projection of that learning space on Q' which is itself a learning space consistent with the original one. Moreover, such a construction defines a partition of Q having each of its classes defining a learning space also consistent with the original learning space. We give a direct proof of these facts which are instrumental in parsing large learning spaces.
We investigate the clustering properties of radio sources in the Alternative Data Release 1 of the TIFR GMRT Sky Survey (TGSS), focusing on large angular scales, where previous analyses have detected a large clustering signal. After appropriate data selection, the TGSS sample we use contains ~110,000 sources selected at 150 MHz over ~70% of the sky. The survey footprint is largely superimposed on that of the NRAO VLA Sky Survey (NVSS) with the majority of TGSS sources having a counterpart in the NVSS sample. These characteristics make TGSS suitable for large-scale clustering analyses and facilitate the comparison with the results of previous studies. In this analysis we focus on the angular power spectrum, although the angular correlation function is also computed to quantify the contribution of multiple-component radio sources. We find that on large angular scales, corresponding to multipoles $2 \leq \ell \leq 30$, the amplitude of the TGSS angular power spectrum is significantly larger than that of the NVSS. We do not identify any observational systematic effects that may explain this mismatch. We have produced a number of physically motivated models for the TGSS angular power spectrum and found that all of them fail to match observations, even when taking into account observational and theoretical uncertainties. The same models provide a good fit to the angular spectrum of the NVSS sources. These results confirm the anomalous nature of the TGSS large-scale power, which has no obvious physical origin and seems to indicate that unknown systematic errors are present in the TGSS dataset.
We argue that a relatively simple model containing only SU(2)-invariant chiral three-spin interactions on a Kagome lattice of S=1/2 spins can give rise to both a gapped and a gapless quantum spin liquid. Our arguments are rooted in a formulation in terms of network models of edge states and are backed up by a careful numerical analysis. For a uniform choice of chirality on the lattice, we realize the Kalmeyer-Laughlin state, i.e. a gapped spin liquid which is identified as the nu=1/2 bosonic Laughlin state. For staggered chiralities, a gapless spin liquid emerges which exhibits gapless spin excitations along lines in momentum space, a feature that we probe by studying quasi-two-dimensional systems of finite width. We thus provide a single, appealingly simple spin model (i) for what is probably the simplest realization of the Kalmeyer-Laughlin state to date, as well as (ii) for a non-Fermi liquid state with lines of gapless SU(2) spin excitations.
PKS 0558-504 is a highly variable, X-ray bright, radio-loud, Narrow-Line Seyfert 1 galaxy with super-Eddington accretion rate and extended jets that do not dominate the emission beyond the radio band. Therefore, this source represents an ideal laboratory to shed some light on the central engine in highly accreting systems and specifically on the link between accretion disc and corona. Here we present the results from a 1.5 year monitoring with Swift XRT and UVOT. The simultaneous coverage at several wavelengths confirms that PKS 0558-504 is highly variable in any band from optical, to UV and X-rays, with the latter showing the largest amplitude changes but with the UV emission dominating the radiative output. A cross-correlation analysis reveals a tight link between the emission in the optical and UV bands and provides suggestive evidence in favor of a scenario where the variability originates in the outer part of the accretion flow and propagates inwards before triggering the activity of the X-ray emitting corona. Finally, a positive correlation between the soft X-ray flux and the hard photon index suggests that in PKS 0558-504 the seed photons are provided to the corona by the soft excess component.
We present a catalogue of 3405 X-ray sources from the ROSAT All Sky Survey (RASS) Bright Source Catalogue which fall within the area covered by the 6dF Galaxy Survey (6dFGS). The catalogue is count-rate limited at 0.05 cts\s in the X-ray and covers the area of sky with delta < 0 deg and |b|>10 deg. The RASS--6dFGS sample was one of the additional target catalogues of the 6dFGS and as a result we obtained optical spectra for 2224 (65%) RASS sources. Of these, 1715 (77%) have reliable redshifts with a median redshift of z=0.16 (excluding the Galactic sources). For the optically bright sources (b_J < 17.5) in the observed sample, over 90% have reliable redshifts. The catalogue mainly comprises QSOs and active galaxies but also includes 238 Galactic sources. Of the sources with reliable redshifts the majority are Type 1 AGN (69%), while 12% are Type 2 AGN, 6% absorption-line galaxies and 13% are stars. We also identify a small number of optically-faint, very low redshift, compact objects which fall outside the general trend in the b_J-z plane.   We detect 918 sources (27%) of the RASS--6dFGS sample in the radio using either the 1.4 GHz NRAO VLA Sky Survey (NVSS) or the 843 MHz Sydney University Molonglo Sky Survey (SUMSS) catalogues and find that the detection rate changes with redshift. At redshifts larger than 1 virtually all of these sources have radio counterparts and with a median flux density of 1.15 Jy, they are much stronger than the median flux density of 28.6 mJy for the full sample. We attribute this to the fact that the X-ray flux of these objects is being boosted by a jet component, possibly Doppler boosted, that is only present in radio-loud AGN. (abridged version)
Thermal conduction between a cool accretion disk and a hot inner corona can result in either evaporation of the disk or condensation of the hot corona. At low mass accretion rates, evaporation dominates and can completely remove the inner disk. At higher mass accretion rates, condensation becomes more efficient in the very inner regions, so that part of the mass accretes via a weak (initially formed) inner disk which is separated from the outer disk by a fully evaporated region at mid radii. At still higher mass accretion rates, condensation dominates everywhere, so there is a continuous cool disk extending to the innermost stable circular orbit. We extend these calculations by including the effect of irradiation by the hot corona on the disk structure. The flux which is not reflected is reprocessed in the disk, adding to the intrinsic thermal emission from gravitational energy release. This increases the seed photons for Compton cooling of the hot corona, enhancing condensation of the hot flow and re-inforcing the residual inner disk rather than evaporating it. Our calculations confirm that a residual inner disk can co-exist with a hard, coronally dominated, spectrum over a range of $0.006<\dot m<0.016$ (for $\alpha=0.2$). This provides an explanation for the weak thermal component seen recently in the low/hard state of black hole X-ray binary systems.