ShantanuT01/DACTYL-Pretraining huggingface dataset:
One of the cornerstones of general relativity is the equivalence principle. However, the validity of the equivalence principle has only been established on solar system scales for standard matter fields; this result cannot be assumed to hold for the non-standard matter fields that dominate the gravitational dynamics on cosmological scales. Here we show how the equivalence principle may be tested on cosmological scales for non-standard matter fields using the odd multipoles of the galaxy cross-power spectrum and bispectrum. This test makes use of the imprint on the galaxy cross-power spectrum and bispectrum by the parity-violating general relativistic deformations of the past-light cone, and assumes that galaxies can be treated as test particles that are made of baryons and cold dark matter. This assumption leads to a non-zero galaxy-baryon relative velocity if the equivalence principle does not hold between baryons and dark matter. We show that the relative velocity can be constrained to be less than 28% of the galaxy velocity using the cross-power spectrum of the HI intensity mapping/H$\alpha$ galaxy survey and the bispectrum of the H$\alpha$ galaxy survey.
We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass $$-\Delta u = f(u), \qquad u\in D_0^{1,2}(\Omega_R),$$ where $\Omega_R:=\{x \in \mathbb{R}^N:|u|>R\}$ with $R>0$, $N\geq4$, and the nonlinearity $f$ is subcritical at infinity and supercritical near the origin. We show that the number of positive multipeak solutions becomes arbitrarily large as $R \to \infty$.
Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums $\sum_{k=1}^{n}X_ka_k $ with respect to the arithmetic structure of coefficients $a_k$ in the context of the Littlewood--Offord problem. In recent papers of Eliseeva, G\"otze and Zaitsev, we discussed the relations between the inverse principles stated by Nguyen, Tao and Vu and similar principles formulated by Arak in his papers from the 1980's. In this paper, we will derive some more general and more precise consequences of Arak's inequalities providing new results in the context of the Littlewood-Offord problem.
Using echelle spectroscopy, obtained at Las Campanas Observatory, we present a detailed study of the internal kinematics of the nebular material in multiple knots of the blue compact dwarf galaxy Haro 15. A detailed analysis of the complex emission line profiles show the presence of an underlying broad component in almost all knots, and the brightest star-forming region shows unmistakable signs for the presence of two distinct narrow kinematical components. We also study the information that our analysis provides regarding the motion of the individual knots in the Haro 15 galaxy potential, confirming that they follow galactic rotation. Finally, we examine the relation between their velocity dispersion and luminosity, finding that almost all knots follow the relation for virialised systems. This holds for the strong narrow components identified in complex fits and for single profile fits, although the latter show a flatter slope. In agreement with previous findings, in this paper we show that the existence of multiple kinematical components among massive starbursts cannot be overlooked, as it has a noticeable effect on any subsequent analysis that relies on basic parameters.
This paper is a step in our program for proving the Piece-Birkhoff Conjecture for regular rings of any dimension (this would contain, in particular, the classical Pierce-Birkhoff conjecture which deals with polynomial rings over a real closed field). We first recall the Connectedness and the Definable Connectedness conjectures, both of which imply the Pierce - Birkhoff conjecture. Then we introduce the notion of a system of approximate roots of a valuation v on a ring A (that is, a collection Q of elements of A such that every v-ideal is generated by products of elements of Q). We use approximate roots to give explicit formulae for sets in the real spectrum of A which we strongly believe to satisfy the conclusion of the Definable Connectedness conjecture. We prove this claim in the special case of dimension 2. This proves the Pierce-Birkhoff conjecture for arbitrary regular 2-dimensional rings.
This article discuss the problem of color image content comparison. Particularly, methods of image content comparison are analyzed, restrictions of color histogram are described and a modified method of images content comparison is proposed. This method uses the color histograms and considers color locations. Testing and analyzing of based and modified algorithms are performed. The modified method shows 97% average precision for a collection containing about 700 images without loss of the advantages of based method, i.e. scale and rotation invariant.
Dirac's theory of constrained Hamiltonian systems is applied to the minimal conformally invariant SU(5) grand-unified model studied at 1-loop level in a de Sitter universe. For this model, which represents a simple and interesting example of GUT theory and at the same time is a step towards theories with larger gauge group like SO(10), second-class constraints in the Euclidean-time regime exist. In particular, they enable one to prove that, to be consistent with the experimentally established electroweak standard model and with inflationary cosmology, the residual gauge-symmetry group of the early universe, during the whole de Sitter era, is bound to be SU(3) x SU(2) x U(1). Moreover, the numerical solution of the field equations subject to second-class constraints is obtained. This confirms the existence of a sufficiently long de Sitter phase of the early universe, in agreement with the initial assumptions.
Representing the spatial properties of facial attributes is a vital challenge for facial attribute recognition (FAR). Recent advances have achieved the reliable performances for FAR, benefiting from the description of spatial properties via extra prior information. However, the extra prior information might not be always available, resulting in the restricted application scenario of the prior-based methods. Meanwhile, the spatial ambiguity of facial attributes caused by inherent spatial diversities of facial parts is ignored. To address these issues, we propose a prior-free method for attribute spatial decomposition (ASD), mitigating the spatial ambiguity of facial attributes without any extra prior information. Specifically, assignment-embedding module (AEM) is proposed to enable the procedure of ASD, which consists of two operations: attribute-to-location assignment and location-to-attribute embedding. The attribute-to-location assignment first decomposes the feature map based on latent factors, assigning the magnitude of attribute components on each spatial location. Then, the assigned attribute components from all locations to represent the global-level attribute embeddings. Furthermore, correlation matrix minimization (CMM) is introduced to enlarge the discriminability of attribute embeddings. Experimental results demonstrate the superiority of ASD compared with state-of-the-art prior-based methods, while the reliable performance of ASD for the case of limited training data is further validated.
We formulate the conditions for the generalized fields in the space with additional commuting Weyl spinor coordinates which define the infinite half-integer spin representation of the four-dimensional Poincar\'e group. Using this formulation we develop the BRST approach and derive the Lagrangian for the half-integer infinite spin fields.
In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences. We present a general framework yielding higher Sobolev regularity for Dirichlet problems with affine data in $\text{int}(K^{lc})$. This allows us to simultaneously deal with linear and nonlinear differential inclusion problems. We show that the derived higher integrability and differentiability exponent has a lower bound, which is independent of the position of the Dirichlet boundary data in $\text{int}(K^{lc})$. As applications we discuss the regularity of weak isometric immersions in two and three dimensions as well as the differential inclusion problem for the geometrically linear hexagonal-to-rhombic and the cubic-to-orthorhombic phase transformations occurring in shape memory alloys.
We use SDSS-DR14 to construct a sample of galaxy systems consisting of a central object and two satellites. We adopt projected distance and radial velocity difference criteria and impose an isolation criterion to avoid membership in larger structures. We also classify the interaction between the members of each system through a visual inspection of galaxy images, finding $\sim80\%$ of the systems lack evidence of interactions whilst the remaining $\sim20\%$ involve some kind of interaction, as inferred from their observed distorted morphology. We have considered separately, samples of satellites and central galaxies, and each of these samples were tested against suitable control sets to analyse the results. We find that central galaxies showing signs of interactions present evidence of enhanced star formation activity and younger stellar populations. As a counterpart, satellite samples show these galaxies presenting older stellar populations with a lower star formation rate than the control sample. The observed trends correlate with the stellar mass content of the galaxies and with the projected distance between the members involved in the interaction. The most massive systems are less affected since they show no star formation excess, possibly due to their more evolved stage and less gas available to form new stars. Our results suggest that it is arguable a transfer of material during interactions, with satellites acting as donors to the central galaxy. As a consequence of the interactions, satellite stellar population ages rapidly and new bursts of star formation may frequently occur in the central galaxy.
We have observed the SiO J=5--4 line towards a sample of 25 low-luminosity (L* < 10^3 Lsun) protostellar outflow systems. The line was detected towards 7 of the 25 sources, a detection rate of 28 per cent. The majority (5 out of 7) of sources detected were of class 0 status. We detected a higher fraction of class 0 sources compared with the class I and II sources, although given the small numbers involved the significance of this result should be regarded as tentative. Most of the detected sources showed emission either at or close to the central position, coincident with the protostar. In four cases (HH211, HH25MMS, V-380 OriNE and HH212) emission was also detected at positions away from the center, and was stronger than that observed at the centre position.   SiO abundances of 10^(-8) to 8x10^(-7) are derived from LTE analysis. For 2 sources we have additional transitions which we use to conduct statistical equilibrium modeling to estimate the gas density in the SiO-emitting regions. For HH25MMS these results suggest that the SiO emission arises in a higher-density region than the methanol previously observed. We find that the most likely explanation for the preferential detection of SiO emission towards class 0 sources is the greater density of those environments, reinforced by higher shock velocities. We conclude that while not all class 0 sources exhibit SiO emission, SiO emission is a good signpost for the presence of class 0 sources.
We present an analysis of all available time-resolved photometry from the literature and new light curves obtained in 2013-2014 for the old nova RR Pictoris. The well-known hump light curve phased with the orbital period reveals significant variations over the last 42 years in shape, amplitude and other details which apparently are caused by long-term variations in the disc structure. In addition we found evidence for the presence of superhumps in 2007, with the same period (~9% longer than the orbital period), as reported earlier by other authors from observations in 2005. Possibly, superhumps arise quickly in RR Pic, but are sporadic events, because in all the other observing runs analysed no significant superhump signal was detected. We also determined an actual version of the Stolz--Schoembs relation between superhump period and orbital period, analysing separately dwarf novae, classical novae and nova-like stars, and conclude that this relation is of general validity for all superhumpers among the cataclysmic variables (CVs), in spite of small but significant differences among the sub-types mentioned above. We emphasize the importance of such a study in context with the still open question of the interrelation between the different sub-classes of CVs, crucial for our understanding of the long-term CV evolution.
An expression for rotational velocity of a test particle around the central mass in the invariant plane is derived. For this, a line element of Schwarzschild de-Sitter space-time is used to study the effect of cosmological constant ($\Lambda$) on the motion of both massive and massless particles. Using rotation curve data of 15 nearby spiral and barred spiral galaxies, we estimated the mass and $\Lambda$ of the galaxy. The mass of the galaxies are found to lie in the range 0.13-7.60 $\times$ 10$^{40}$ kg. The cosmological constant ($\Lambda$) is found to be negative ($-$0.03 to $-$0.10 $\times$ 10$^{-40}$ km$^{-2}$), suggesting the importance of anti-de Sitter space in the local bubble. Possible explanation of the results will be discussed.
Graphene, a single infinite, planar, sheet of graphite, has the same dielectric resonances as bulk graphite, but solid state theory indicates that its features are about half as wide. Based on this theory, the dielectric functions of mono- and multi-layer graphenes are deduced and compared with those of terrestrial graphite. The resonance width of an ordered stack of graphenes is found to increase with the number of layers while the central frequency stays constant. This is the basis of the polycrystalline model of the carrier of the 2175 Angstrom interstellar extinction band. In this model, the carrier dust grains derive from parent hydrocarbon grains. As a grain ages in the IS medium, the light atoms are expelled, hexagonal carbon rings lump together into compact planar clusters, which then assemble into stacks of parallel, equidistant, graphene-like layers. This so-called graphitization is well known to occur in the earth or under strong heating. As the number of layers in each stack increases and their relative orientational order improves, the pi resonance width increases asymptotically towards that of terrestrial graphite. Because of the initial random structure of the parent grains, many randomly oriented stacks may coexist in the same grain. Calculations of the dielectric response of this composite medium show that, for such a grain, the width of the extinction efficiency peak follows the same trend as the pi resonance of the average stack, and thus covers the observed range of IS feature widths, at very nearly constant peak frequency.
We present a new on-the-fly (OTF) mapping of CO(J=3-2) line emission with the Atacama Submillimeter Telescope Experiment (ASTE) toward the 8' x 8' (or 10.5 x 10.5 kpc at the distance of 4.5 Mpc) region of the nearby barred spiral galaxy M 83 at an effective resolution of 25''. Due to its very high sensitivity, our CO(J=3-2) map can depict not only spiral arm structures but also spur-like substructures extended in inter-arm regions. This spur-like substructures in CO(J=3-2) emission are well coincident with the distribution of massive star forming regions traced by Halpha luminosity and Spitzer/IRAC 8 um emission. We have identified 54 CO(J=3-2) clumps as Giant Molecular-cloud Associations (GMAs) employing the CLUMPFIND algorithm, and have obtained their sizes, velocity dispersions, virial masses, and CO luminosity masses. We found that the virial parameter alpha, which is defined as the ratio of the virial mass to the CO luminosity mass, is almost unity for GMAs in spiral arms, whereas there exist some GMAs whose alpha are 3 -- 10 in the inter-arm region. We found that GMAs with higher $\alpha$ tend not to be associated with massive star forming regions, while other virialized GMAs are. Since alpha mainly depends on velocity dispersion of the GMA, we suppose the onset of star formation in these unvirialized GMAs with higher alpha are suppressed by an increase in internal velocity dispersions of Giant Molecular Clouds within these GMAs due to shear motion.
This paper is devoted to investigate the exact solutions of Bianchi types I and V spacetimes in the context of f(R, T) gravity [1]. For this purpose, we found two exact solutions in each case by using assumption of constant deceleration parameter and the variation law of Hubble parameter. The obtained solutions correspond to two different models of this universe. The physical behavior of these models is also discussed.
For any positive integers $a$ and $b$, we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to $b$ modulo $a$. For the number of such partitions made by a fixed number of diagonals, we give both a recurrence relation and an explicit representation in terms of partial Bell polynomials. We use basic properties of these polynomials to efficiently incorporate restrictions on the type of polygons allowed in the partitions.
The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases to introduce an ad hoc parameter that reduces the size of the Coriolis interaction coupling the collective and single-particle motions. Of the numerous suggestions put forward for the origin of this supplementary interaction, none of those actually tested by calculations has been accepted as the solution of the problem. In this paper we seek a solution of the difficulty within the framework of a general formalism that starts from the spherical shell model and is capable of treating an arbitrary linear combination of multipole and pairing forces. With the restriction of the interaction to the familiar sum of a quadrupole multipole force and a monopole pairing force, we have previously studied a semi-microscopic version of the formalism whose framework is nevertheless more comprehensive than any previously applied to the problem. We obtained solutions for low-lying bands of several strongly deformed odd rare earth nuclei and found good agreement with experiment, except for an exaggerated staggering of levels for K=1/2 bands, which can be understood as a manifestation of the Coriolis attenuation problem. We argue that within the formalism utilized, the only way to improve the physics is to add interactions to the model Hamiltonian. We verify that by adding a magnetic dipole interaction of essentially fixed strength, we can fit the K=1/2 bands without destroying the agreement with other bands. In addition we show that our solution also fits 163Er, a classic test case of Coriolis attenuation that we had not previously studied.
A new procedure of the linear position measurement which allows to obtain sensitivity better than the Standard Quantum Limit and close to the Energetic Quantum Limit is proposed and analyzed in details. Proposed method is based on the principles of stroboscopic quantum measurement and variation quantum measurement and allows to avoid main disadvantages of both these procedures. This method can be considered as a good candidate for use as a local position meter in the ``intracavity'' topologies of the laser gravitational-wave antennae.
We have evaluated the centrifugal force acting on a fluid element and the ellipticity of the fluid configuration, which is slowly rotating, using the Hartle-Thorne solution for different equations of state. The centrifugal force shows a maximum in every case, whereas the reversal in sign could be seen in only one case, and the system becomes unstable in other cases. The ellipticity as calculated from the usual definition shows maxima, whereas the definition obtained from the equilibration of the inertial forces, shows a negative behaviour, indicating that the system is prolate and not oblate. This prolate shape of the configuration is similar to the one earlier found by Pfister and Braun for a rotating shell of matter, using the correct centrifugal force expression for the interior. The location of the centrifugal maxima gets farther away from the Schwarzschild radius as the equation of state gets softer.
That most deep learning models are purely data driven is both a strength and a weakness. Given sufficient training data, the optimal model for a particular problem can be learned. However, this is usually not the case and so instead the model is either learned from scratch from a limited amount of training data or pre-trained on a different problem and then fine-tuned. Both of these situations are potentially suboptimal and limit the generalizability of the model. Inspired by this, we investigate methods to inform or guide deep learning models for geospatial image analysis to increase their performance when a limited amount of training data is available or when they are applied to scenarios other than which they were trained on. In particular, we exploit the fact that there are certain fundamental rules as to how things are distributed on the surface of the Earth and these rules do not vary substantially between locations. Based on this, we develop a novel feature pooling method for convolutional neural networks using Getis-Ord Gi* analysis from geostatistics. Experimental results show our proposed pooling function has significantly better generalization performance compared to a standard data-driven approach when applied to overhead image segmentation.
Semilinear stochastic evolution equations with L\'evy noise and monotone nonlinear drift are considered. The existence and uniqueness of the mild solutions in $L^p$ for these equations is proved and a sufficient condition for exponential asymptotic stability of the solutions is derived. The main tool in our study is an It\^o type inequality for the $p$th power of stochastic convolution integrals in Hilbert spaces.
We present an analysis of an occulting galaxy pair, serendipitously discovered in ACS Nearby Galaxy Survey Treasury (ANGST) observations of NGC 253 taken with Hubble Space Telescope's Advanced Camera for Survey in F475W, F606W$ and F814W (SDSS-g, broad V and I). The foreground disk system (at z < 0.06) shows a dusty disk much more extended than the starlight, with spiral lanes seen in extinction out to 1.5 R\_25, approximately six half-light radii. This pair is the first where extinction can be mapped reliably out to this distance from the center. The spiral arms of the extended dust disk show typical extinction values of A\_F475W ~ 0.25, A\_F606W ~ 0.25, and A\_F814W ~ 0.15. The extinction law inferred from these measures is similar to the local Milky Way one, and we show that the smoothing effects of sampling at limited spatial resolution (<57 pc, in these data) flattens the observed function through mixing of regions with different extinction. This galaxy illustrates the diversity of dust distributions in spirals, and the limitations of adopting a single dust model for optically similar galaxies. The ideal geometry of this pair of overlapping galaxies and the high sampling of HST data make this dataset ideal to analyze this pair with three separate approaches to overlapping galaxies: (A) a combined fit, rotating copies of both galaxies, (B) a simple flip of the background image and (C) an estimate of the original fluxes for the individual galaxies based on reconstructions of their proper isophotes. We conclude that in the case of high quality data such as these, isophotal models are to be preferred.