ShantanuT01/DACTYL-Pretraining huggingface dataset:
Starting from an interaction Lagrangian formed out of local fields, an interacting four-momentum operator is constructed by integrating the interaction Lagrangian over the forward hyperboloid. Such a four-momentum operator has the property that the components commute among themselves; however, when the Fock space on which the four-momentum operator acts is truncated, the components no longer commute among themselves. By modifying matrix elements of the four-momentum operator on the truncated space, Bakamjian-Thomas mass operatorsare constructed which restore the Poincare relations. Examples for a simple Lagrangian are given.
Low energy theorems have been derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading nontrivial order in an expansion based $Q$ counting, a scheme in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Previous tests of these theorems based on coefficients extracted from scattering data indicate a pattern of gross violations which suggested serious problems for the perturbative treatment of pions implicit in $Q$ counting. We discuss the possibility that uncertainties associated with extracting the coefficients from the scattering data make such tests invalid. Here we show that errors in the s-wave phase shift extractions are sufficiently small to test direct test predictions from $Q$ counting at next to leading order. In particular we show that there exist low energy theorems for the sum of all terms in the effective range expansion beyond the first two which allow for precise tests. These low energy theorems fail badly which suggests that pionic aspects of $Q$ counting are not under control.
Inclusive cross-sections for gluon production in collision of two mucleons with two nucleons are studied in the BFKL approach. Various contributions include emission from the pomerons attached to the participants, from the BFKL interactions in between these pomerons and from the intermediate BKP state. The last contribution may be observable provided the growth with energy of the pomeron contribution is tamed in accordance with unitarity.
We present first-principles total-energy calculations of (001) surfaces of SrTiO3. Both SrO-terminated and TiO2-terminated surfaces are considered, and the results are compared with previous calculations for BaTiO3 surfaces. The major differences are in the details of the relaxed surface structures. Our calculations argue against the existence of a large ferroelectric relaxation in the surface layer, as had been previously proposed. We do find some indications of a weak surface ferroelectric instability, but so weak as to be easily destroyed by thermal fluctuations except perhaps at quite low temperatures. We also compute surface relaxation energies and surface electronic band structures, obtaining results that are generally similar to those for BaTiO3.
In order to study the circumnuclear star-forming activity along the Hubble sequence, we cross-correlate the Sloan Digital Sky Survey Data Release 2 (SDSS DR2) with the Third Reference Catalog of Bright Galaxies (RC3) to derive a large sample of 1015 galaxies with both morphological and spectral information. Among these, 385 sources are classified as star-forming galaxies and the SDSS fibre covered the circumnuclear regions (0.2 $-$ 2.0 kpc). By using the spectral synthesis method to remove the contribution from the underlying old stellar population, we measure the emission lines fluxes accurately which are then used to estimate the star formation rates(SFRs). Our main findings are that: (1) Early-type spirals show much larger H$\alpha$ luminosities and hence higher SFRs, they also suffer more extinctions than late-type ones. The equivalent widths (EWs) of H$\alpha$ emission lines show the similar trend, however, the very late types (Sdm $\sim$ Irr) do have large fractions of high EWs. (2) We confirm that D$_n(4000)$ has strong correlation with the strengthes of metallic absorption lines (such as CN band, G band and Mg Ib). Both these lines and the Balmer absorption lines show interesting variations between Sbc to Sd type galaxies. (3) The bar structure tightly relates with the enhanced star forming activity, this effect is even more significant in the early-type spirals. But we should note that the bar structure is not a necessary or sufficient condition for galaxies to harbor circumnuclear star formations.
We discuss toroidal compactifications of maximal supergravity coupled to an extended configuration of BPS states which transform consistently under the U-duality group. Under certain conditions this leads to theories that live in more than eleven spacetime dimensions, with maximal supersymmetry but only partial Lorentz invariance. We demonstrate certain features of this construction for the case of nine-dimensional N=2 supergravity.
Antiferromagnets (AFMs) exhibit intrinsic magnetization when the order parameter spatially varies. This intrinsic spin is present even at equilibrium and can be interpreted as a twisting of the homogeneous AFM into a state with a finite spin. Because magnetic moments couple directly to external magnetic fields, the intrinsic magnetization can alter the dynamics of antiferromagnetic textures under such influence. Starting from the discrete Heisenberg model, we derive the continuum limit of the free energy of AFMs in the exchange approximation and explicitly rederive that the spatial variation of the antiferromagnetic order parameter is associated with an intrinsic magnetization density. We calculate the magnetization profile of a domain wall and discuss how the intrinsic magnetization reacts to external forces. We show conclusively, both analytically and numerically, that a spatially inhomogeneous magnetic field can move and control the position of domain walls in AFMs. By comparing our model to a commonly used alternative parametrization procedure for the continuum fields, we show that the physical interpretations of these fields depend critically on the choice of parametrization procedure for the discrete-to-continuous transition. This can explain why a significant amount of recent studies of the dynamics of AFMs, including effective models that describe the motion of antiferromagnetic domain walls, have neglected the intrinsic spin of the textured order parameter.
A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projection of the desired one onto the set of admissible velocities. Instead of looking at a microscopic setting (where individuals are represented by rigid discs), here the macroscopic approach is investigated, where the unknwon is the evolution of the density . If a gradient structure is given, say U is the opposite of the gradient of D where D is, for instance, the distance to the exit door, the problem is presented as a Gradient Flow in the Wasserstein space of probability measures. The functional which gives the Gradient Flow is neither finitely valued (since it takes into account the constraints on the density), nor geodesically convex, which requires for an ad-hoc study of the convergence of a discrete scheme.
We show an explicit relation between an RG flow of a two-dimensional gravity and an on-shell tachyon condensation in the corresponding string theory, in the case when the string theory is supercritical. The shape of the tachyon potential in this case can, in principle, be obtained by examining various RG flows. We also argue that the shape of tachyon potential for a (sub)critical string can be obtained by analyzing a supercritical string which is obtained from the (sub)critical string.
The integrals defining the two-loop beta-function for the general renormalizable N=1 supersymmetric Yang--Mills theory, regularized by higher covariant derivatives, are investigated. It is shown that they are given by integrals of double total derivatives. These integrals are not equal to zero due to appearing of delta-functions. These delta-functions allow to reduce the two-loop integrals to one-loop integrals, which can be easily calculated. The result agrees with the exact NSVZ beta-function and calculations made by different methods.
We present measurements of electrical resistivity, thermal conductivity and thermopower of polycrystalline Sr-doped LaCoO3 with composition La0.95Sr0.05CoO3. Our data show that the investigated compound exhibits a very respectable room temperature thermoelectric figure of merit value of 0.18. Our results not only show that oxides are promising candidates for thermoelectric cooling applications, but also point towards the need for careful theoretical calculations that will serve as a guide in producing the next generation of thermoelectric materials.
We discuss production of heavy partciles during reheating. We find that the very energetic inflaton decay products can contribute to the production of massive stable particles, either through collisions with the thermal plasma, or through collisions with each other. If such reactions exist, the same massive particles can also be produced directly in inflaton decay, once higher--order processes are included. We show that these new, non--thermal production mechanisms often significantly strengthen constraints on the parameters of models containing massive stable particles.
We study the question of whether the topological quotient of a real linear representation of a simple three-dimensional compact Lie group is a manifold. We obtain an upper bound for the dimension of a representation whose quotient is a manifold, and examine most of the remaining cases.
Using the Dyson equation of motion for both the diagonal one-particle Green function, $G(\vec{k},\omega)$ and off--diagonal Green function, $F(\vec{k},\omega)$, at the level of the Hubbard--I decoupling scheme, we have found that they have four poles symmetric in pairs, justifying a more elaborated calculation done by the Z\"urich group by means of the $T$-Matrix approach (Pedersen et al, Z. Physik B {\bf 103}, 21 (1997)) and the moment approach of Nolting (Z. Physik {\bf 255}, 25 (1972)). We find that the energy spectra and the weights of $G(\vec{k},\omega)$ and $F(\vec{k},\omega)$ have to be calculated self-consistently. $G(\vec{k},\omega)$ satisfies the first two moments while $F(\vec{k},\omega)$ the first sum rule. Our {\it order parameter} $\alpha(T)$ is given by $1/N_s \sum_{{\vec{k}}} \epsilon({\vec{k}})\Delta({\vec{k}})$. Due to the fact that we have a purely local attractive interaction $\Delta(\vec{k})$ can be of {\it any} s--type wave. However, for a {\it pure s--wave}, for which $\alpha(T) = 0$, we go back to the mean--field $BCS$ results, with a renormalized chemical potential. In this case, the off--diagonal Green function, $F(\vec{k},\omega)$, satisfies the first two off--diagonal sum rules. We explicitly state the range of validity of our approximation.
A new candidate source of gravitational radiation is described: the nearly-perfect harmonic series from individual loops of cosmic string. It is argued that theories with light cosmic strings give rise to a population of numerous long-lived stable loops, many of which cluster gravitationally in galaxy halos along with the dark matter. Each cosmic string loop produces a spectrum of discrete frequencies in a nearly perfect harmonic series, a fundamental mode and its integer multiples. The gravitational wave signal from cosmic string loops in our Galactic halo is analyzed numerically and it is found that the for light strings, the nearest loops typically produce strong signals which stand out above the confusion noise from Galactic binaries. The total population of cosmic string loops in the Milky Way also produces a broad signal that acts as a confusion noise. Both signals are enhanced by the clustering of loops gravitationally bound to the Galaxy, which significantly decreases the average distance from the solar system to the nearest loop. Numerical estimates indicate that for dimensionless string tension G\mu< 10^{-11}, many loops are likely to be found in the Galactic halo. Lighter strings, down to G\mu=10^{-19}, are detectable by the Laser Interferometer Space Antenna (LISA). For these light strings, the fundamental and low-order harmonics of typical loops often lie in the band where LISA is sensitive, 0.1 to 100 mHz. The harmonic nature of the cosmic string loop modes leaves a distinct spectral signature different from any other known source of gravitational waves.
We present high-dispersion spectroscopic data of the compact planetary nebula Vy 1-2, where high expansion velocities up to 100 km/s are found in the Ha, [N II] and [O III] emission lines. HST images reveal a bipolar structure. Vy 1-2 displays a bright ring-like structure with a size of 2.4"x3.2" and two faint bipolar lobes in the west-east direction. A faint pair of knots is also found, located almost symmetrically on opposite sides of the nebula at PA=305 degrees. Furthermore, deep low-dispersion spectra are also presented and several emission lines are detected for the first time in this nebula, such as the doublet [Cl III] 5517, 5537 A, [K IV] 6101 A, C II 6461 A, the doublet C IV 5801, 5812 A. By comparison with the solar abundances, we find enhanced N, depleted C and solar O. The central star must have experienced the hot bottom burning (CN-cycle) during the 2nd dredge-up phase, implying a progenitor star of higher than 3 solar masses. The very low C/O and N/O abundance ratios suggest a likely post-common envelope close binary system.   A simple spherically symmetric geometry with either a blackbody or a H-deficient stellar atmosphere model is not able to reproduce the ionisation structure of Vy 1-2. The effective temperature and luminosity of its central star indicate a young nebula located at a distance of ~9.7 kpc with an age of ~3500 years. The detection of stellar emission lines, C II 6461 A, the doublet C IV {\lambda}{\lambda} 5801, 5812 A and O III 5592 A, emitted from a H-deficient star, indicates the presence of a late-type Wolf-Rayet or a WEL type central star.
Recent works on crowd counting mainly leverage CNNs to count by regressing density maps, and have achieved great progress. In the density map, each person is represented by a Gaussian blob, and the final count is obtained from the integration of the whole map. However, it is difficult to accurately predict the density map on dense regions. A major issue is that the density map on dense regions usually accumulates density values from a number of nearby Gaussian blobs, yielding different large density values on a small set of pixels. This makes the density map present variant patterns with significant pattern shifts and brings a long-tailed distribution of pixel-wise density values. We propose a simple and effective Learning to Scale (L2S) module, which automatically scales dense regions into reasonable closeness levels (reflecting image-plane distance between neighboring people). L2S directly normalizes the closeness in different patches such that it dynamically separates the overlapped blobs, decomposes the accumulated values in the ground-truth density map, and thus alleviates the pattern shifts and long-tailed distribution of density values. This helps the model to better learn the density map. We also explore the effectiveness of L2S in localizing people by finding the local minima of the quantized distance (w.r.t. person location map). To the best of our knowledge, such a localization method is also novel in localization-based crowd counting. We further introduce a customized dynamic cross-entropy loss, significantly improving the localization-based model optimization. Extensive experiments demonstrate that the proposed framework termed AutoScale improves upon some state-of-the-art methods in both regression and localization benchmarks on three crowded datasets and achieves very competitive performance on two sparse datasets.
We have investigated the nature of the antiferromagnetic (AF) phase induced by uniaxial stress sigma in URu2Si2, by performing elastic neutron scattering measurements up to 0.4 GPa. We have found that the AF Bragg-peak intensity shows a clear hysteresis loop with sigma under the zero-stress cooling condition. The result strongly suggests that the sigma-induced AF phase is metastable and separated from the coexisting "hidden ordered" phase by a first-order phase transition. We also present the analyses of the crystalline strain effects, and suggest that the c/a ratio plays an important role in the competition between these two phases.
Recognizing actions from still images is popularly studied recently. In this paper, we model an action class as a flexible number of spatial configurations of body parts by proposing a new spatial SPN (Sum-Product Networks). First, we discover a set of parts in image collections via unsupervised learning. Then, our new spatial SPN is applied to model the spatial relationship and also the high-order correlations of parts. To learn robust networks, we further develop a hierarchical spatial SPN method, which models pairwise spatial relationship between parts inside sub-images and models the correlation of sub-images via extra layers of SPN. Our method is shown to be effective on two benchmark datasets.
We study the imaging of a penetrable scatterer, aka target, in a waveguide with randomly perturbed boundary. The target is located between a partially coherent source which transmits the wave, and a detector which measures the spatially integrated energy flux of the wave. The imaging is impeded by random boundary scattering effects that accumulate as the wave propagates. We consider a very large distance (range) between the target and the detector, where that cumulative scattering is so strong that it distributes the energy evenly among the components (modes) of the wave. Conventional imaging is impossible in this equipartition regime. Nevertheless, we show that the target can be located with a ghost imaging modality. This forms an image using the cross-correlation of the measured energy flux, integrated over the aperture of the detector, with the time and space resolved energy flux in a reference waveguide, at the search range. We consider two reference waveguides: The waveguide with unperturbed boundary, in which we can calculate the energy flux, and the actual random waveguide, before the presence of the target, in which the energy flux should be measured. We analyze the ghost imaging modality from first principles and show that it can be efficient in a random waveguide geometry in which there is both strong modal dispersion and mode coupling induced by scattering, provided that the standard ghost imaging function is modified and integrated over a suitable time offset window in order to compensate for dispersion and diffusion. The analysis quantifies the resolution of the image in terms of the source and detector aperture, the range offset between the source and the target, and the duration of the measurements.
The merging of supermassive black holes (SMBHs) is a direct consequence of our hierarchical picture of galaxy evolution. It is difficult to track the merging process of SMBHs during mergers of galaxies as SMBHs are naturally difficult to observe. We want to characterise and confirm the presence of two independent active galactic nuclei (AGN) separated by a few kiloparsec in seven strongly interacting galaxies previously selected from the Sloan Digital Sky Survey (SDSS) as Seyfert-Seyfert pairs based on emission-line ratio diagnostics. Optical slit spectra taken with MODS at the Large Binocular Telescope (LBT) are presented to infer the detailed spatial distribution of optical emission lines, and their line ratios and AGN signatures with respect to the host galaxies, thereby quantifying the impact of beam smearing and large fibre apertures on the spectra captured by the SDSS. We find that at most two of the seven targets actually retain a Seyfert-Seyfert dual AGN, whereas the others may be more likely powered by post-AGB stars in retired galaxies or through shocks in the ISM based on spatially resolved optical line diagnostics. The major cause of this discrepancy is a bias caused by the spillover of flux from the primary source in the secondary SDSS fibre which can be more than an order of magnitude at <3" separations. Previously reported extremely low X-ray-to-[\ion{O}{iii}] luminosity ratios may be explained by this misclassification, as can heavily obscured AGN for the primaries. We also find that the nuclei with younger stellar ages host the primary AGN. Studies of close dual AGN selected solely from fibre-based spectroscopy can create severe biases in the sample selection and interpretation of the results. Spatially resolved spectroscopy should ideally be used in the future to characterise such compact systems together with multi-wavelength follow-up observations.
Recognition of floor plans has been a challenging and popular task. Despite that many recent approaches have been proposed for this task, they typically fail to make the room-level unified prediction. Specifically, multiple semantic categories can be assigned in a single room, which seriously limits their visual quality and applicability. In this paper, we propose a novel approach to recognize the floor plan layouts with a newly proposed Offset-Guided Attention mechanism to improve the semantic consistency within a room. In addition, we present a Feature Fusion Attention module that leverages the channel-wise attention to encourage the consistency of the room, wall, and door predictions, further enhancing the room-level semantic consistency. Experimental results manifest our approach is able to improve the room-level semantic consistency and outperforms the existing works both qualitatively and quantitatively.
A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.
In this paper we consider the natural random walk on a planar graph and scale it by a small positive number $\delta$. Given a simply connected domain $D$ and its two boundary points $a$ and $b$, we start the scaled walk at a vertex of the graph nearby $a$ and condition it on its exiting $D$ through a vertex nearby $b$, and prove that the loop erasure of the conditioned walk converges, as $\delta \downarrow 0$, to the chordal SLE$_{2}$ that connects $a$ and $b$ in $D$, provided that an invariance principle is valid for both the random walk and the dual walk of it.