ShantanuT01/DACTYL-Pretraining huggingface dataset:
We select a sample of 70378 E/S0 (early-type) galaxies at 0<z<0.36 from the Sloan Digital Sky Survey, excluding disk and star-forming galaxies. We estimate g and r magnitudes in the observer- and rest-frames directly from the SDSS DR6 spectra; this provides an object-by-object estimate of the k-correction. We use the k-corrections from the spectra to study the evolution of the rest-frame colour-magnitude relation (CMR) and colour-sigma (velocity dispersion) relation (CsigmaR). The evolution is very sensitive to the k-correction. Both the CMR and CsigmaR evolve blueward with increasing redshift, approximately in agreement with passive evolution models with age approx. 12 Gyr. The slope and zero-point of the CMR depend on whether colours were defined in fixed physical or angular apertures, a consequence of the fact that the centers of these objects tend to be redder: the relation is steeper for fixed angular apertures. One the other hand, the CsigmaR slope does not show this dependence on the aperture in which the colour was defined, suggesting that colour gradients are correlated with residuals from the sigma-M_r relation. As these residuals are age indicators, our findings suggest that colour gradients correlate with the age of the stellar population.
We consider systems of interacting Generalized Friedman's Urns (GFUs) having irreducible mean replacement matrices. The interaction is modeled through the probability to sample the colors from each urn, that is defined as convex combination of the urn proportions in the system. From the weights of these combinations we individuate subsystems of urns evolving with different behaviors. We provide a complete description of the asymptotic properties of urn proportions in each subsystem by establishing limiting proportions, convergence rates and Central Limit Theorems. The main proofs are based on a detailed eigenanalysis and stochastic approximation techniques.
X-ray resonant magnetic reflectivity (XRMR) is a powerful method to determine the optical, structural and magnetic depth profiles of a variety of thin films. Here, we investigate samples of different complexity all measured at the Pt L$_3$ absorption edge to determine the optimal procedure for the analysis of the experimental XRMR curves, especially for nontrivial bi- and multilayer samples that include differently bonded Pt from layer to layer. The software tool ReMagX is used to fit these data and model the magnetooptic depth profiles based on a highly adaptable layer stack which is modified to be a more precise and physically consistent representation of the real multilayer system. Various fitting algorithms, iterative optimization approaches and a detailed analysis of the asymmetry ratio features as well as $\chi^2$ (goodness of fit) landscapes are utilized to improve the agreement between measurements and simulations. We present a step-by-step analysis procedure tailored to the Pt thin film systems to take advantage of the excellent magnetic sensitivity and depth resolution of XRMR.
For the description of the Universe expansion, compatible with observational data, a model of modified gravity - Lovelock gravity with dilaton - is investigated. D-dimensional space with 3- and (D-4)-dimensional maximally symmetric subspaces is considered. Space without matter and space with perfect fluid are under test. In various forms of the theory under way (third order without dilaton and second order - Einstein-Gauss-Bonnet gravity - with dilaton and without it) stationary, power-law, exponential and exponent-of-exponent form cosmological solutions are obtained. Last two forms include solutions which are clear to describe accelerating expansion of 3-dimensional subspace. Also there is a set of solutions describing cosmological expansion which does not tend to isotropization in the presence of matter.
An outline of recent work on complex networks is given from the point of view of a physicist. Motivation, achievements and goals are discussed with some of the typical applications from a wide range of academic fields. An introduction to the relevant literature and useful resources is also given.
The Fundamental Morphism Theorem is a categorical version of the First Noether Isomorphism Theorem for categories that do not have kernels or cokernels. We consider two categories of graphs. Both categories will admit graphs with multiple edges and loops, and are distinguished by allowing two different types of homomorphisms, standard graph homomorphisms and more general graph homomorphisms where the contraction of an edge is allowed. We establish the Fundamental Morphism Theorem in these two categories of graphs. We then use the result to provide an equivalent reformulation of the vertex and edge reconstruction conjectures. This reformulation shows that reconstructability is equivalent to the existence of a graph homomorphism satisfying an equation.
In this paper, we first find the distribution of nth power residues modulo a prime $p$ by analyzing sums involving Dirichlet characters. We then extend this method to characterize the distribution of powers in arbitrary finite fields.
A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter \zeta, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (\zeta = 1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance to include the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size and initial redshift). We find that, the nonlinear power spectra can differ by ~30% for 10% deviation from GR (|\zeta-1| = 0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.
We classify all the surfaces of general type whose canonical map is composed with a pencil if they are the quotient of the diagonal action by an Abelian group acting over the product of two curves. As far as we know all the previous examples with isotrivial canonical map are very particular cases of our construction; moreover we find an unexpected action by a group of order 16. This construction can be easily generalizable to all dimensions.
Computational simulations of turbulent flows indicate that the regions of low dissipation/enstrophy production feature high degree of local alignment between the velocity and the vorticty, i.e., the flow is locally near-Beltrami. Hence one could envision a geometric scenario in which the persistence of the local near-Beltramy property might be consistent with a (possible) finite-time singularity formation. The goal of this note is to show that this scenario is in fact prohibited if the sine of the angle between the velocity and the vorticty is small enough with respect to the local enstrophy.
We theoretically investigate a tight binding model of fermions hopping on the square-octagon lattice which consists of a square lattice with plaquette corners themselves decorated by squares. Upon the inclusion of second neighbor spin-orbit coupling or non-Abelian gauge fields, time-reversal symmetric topological Z_2 band insulators are realized. Additional insulating and gapless phases are also realized via the non-Abelian gauge fields. Some of the phase transitions involve topological changes to the Fermi surface. The stability of the topological phases to various symmetry breaking terms is investigated via the entanglement spectrum. Our results enlarge the number of known exactly solvable models of Z_2 band insulators, and are potentially relevant to the realization and identification of topological phases in both the solid state and cold atomic gases.
Electronic and transport properties of a short Ni nanowire suspended between two semi-infinite ferromagnetic Ni leads are explored in the framework of density-functional theory. The spin-dependent ballistic conductance of the nanowire is calculated using a scattering-based approach and the Landauer-Buttiker formula. The total calculated conductance in units of $G_0 = 2e^2/h$ is around 1.6, in fairly good agreement with the broad peak observed around 1.5 for the last conductance step in break junctions. Separating contributions from different spins, we find nearly 0.5 $G_0$ from the majority spin $s$-like channel, whereas the remaining minority spin conductance of 1.1 $G_0$ contains significant contributions from several $d$ states, but much less than 0.5 $G_0$ from $s$ states. The influence of the structural relaxation on the magnetic properties and the ballistic conductance of the nanowire is also studied.
The morphological development of step edge patterns in the presence of meandering instability during step flow growth is studied by simulations and numerical integration of a continuum model. It is demonstrated that the kink Ehrlich-Schwoebel barrier responsible for the instability leads to an invariant shape of the step profiles. The step morphologies change with increasing coverage from a somewhat triangular shape to a more flat, invariant steady state form. The average pattern shape extracted from the simulations is shown to be in good agreement with that obtained from numerical integration of the continuum theory.
We investigate the potential sources of theoretical systematics in the anisotropic Baryon Acoustic Oscillation (BAO) distance scale measurements from the clustering of galaxies in configuration space using the final Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS). We perform a detailed study of the impact on BAO measurements from choices in the methodology such as fiducial cosmology, clustering estimators, random catalogues, fitting templates, and covariance matrices.   The theoretical systematic uncertainties in BAO parameters are found to be 0.002 in the isotropic dilation $\alpha$ and 0.003 in the quadrupolar dilation $\epsilon$. The leading source of systematic uncertainty is related to the reconstruction techniques. Theoretical uncertainties are sub-dominant compared with the statistical uncertainties for BOSS survey, accounting $0.2\sigma_{stat}$ for $\alpha$ and $0.25\sigma_{stat}$ for $\epsilon$   ($\sigma_{\alpha,stat} \sim$0.010 and $\sigma_{\epsilon,stat}\sim$ 0.012 respectively). We also present BAO-only distance scale constraints from the anisotropic analysis of the correlation function. Our constraints on the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$, including both statistical and theoretical systematic uncertainties, are 1.5\% and 2.8\% at $z_{\rm eff}=0.38$, 1.4\% and 2.4\% at $z_{\rm eff}=0.51$, and 1.7\% and 2.6\% at $z_{\rm eff}=0.61$. This paper is part of a set that analyzes the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are cross-checked with other BAO analysis in \citet{Acacia16}. The systematic error budget concerning the methodology on post-reconstruction BAO analysis presented here is used in \citet{Acacia16} to produce the final cosmological constraints from BOSS.
In this work we derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways, it is applicable both in the adiabatic and in the non-adiabatic regimes and it takes into account also the effect of an external environment. More specifically, by applying Floquet theory to Cooper pair pumping, we show that under a cyclic evolution the total charge transferred through the circuit is proportional to the derivative of the associated Floquet quasi-energy with respect to the superconducting phase difference. In the presence of an external environment the expression for the transferred charge acquires a transparent form in the Floquet representation. It is given by the weighted sum of the charge transferred in each Floquet state, the weights being the diagonal components of the stationary density matrix of the system expressed in the Floquet basis. In order to test the power of this formulation we apply it to the study of pumping in a Cooper pair sluice. We reproduce the known results in the adiabatic regime and we show new data in the non-adiabatic case.
We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P , its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. At the blob size P/a^2 , where a is the size of a monomer, the statistics becomes that of an ideal chain. As the blob size further decreases to below the persistence length P, the statistics is that of a rigid rod. We argue that semi-flexible polymer in translocation should include the three regions: a self-avoiding region, an ideal chain region and a rigid rod region, under uneven tension propagation, instead of a uniform scaling picture as in the case of a completely flexible polymer. In various regimes under the effect of weak, intermediate and strong driving forces we derive equations from which we can calculate the translocation time of the polymer. The translocation exponent is given by \alpha=1+\mu, where \mu is an effective exponent for the end-to-end distance of the semi-flexible polymer, having a value between 1/2 and 3/5, depending on the total contour length of the polymer. Our results are of relevance for forced translocation of biological polymers such as DNA through a nanopore.
We report on Chandra, RXTE, Swift/BAT and MAXI observations of a ~1 day X-ray flare and subsequent outburst of a transient X-ray source observed in October-November 2011 in the globular cluster Terzan 5. We show that the source is the same as the transient that was active in 2000, i.e., the neutron star low-mass X-ray binary EXO 1745-248. For the X-ray flare we estimate a 6-11 hr exponential decay time and a radiated energy of 2-9 x 10^42 erg. These properties, together with strong evidence of decreasing blackbody temperature during the flare decay, are fully consistent with what is expected for a thermonuclear superburst. We use the most recent superburst models and estimate an ignition column depth of ~10^12 g cm^-2 and an energy release between 0.1-2 x 10^18 erg g^-1, also consistent with expected superburst values. We conclude therefore that the flare was most probably a superburst. We discuss our results in the context of theoretical models and find that even when assuming a few days of low level accretion before the superburst onset (which is more than what is suggested by the data), the observations of this superburst are very challenging for current superburst ignition models.
We prove that the peakons are asymptotically H 1-stable, under the flow of the Degasperis-Procesi equation, in the class of functions with a momentum density that belongs to M + (R). The key argument is a rigidity result for uniformly in time exponentially decaying global solutions that is shared by the Holm-Staley b-family of equations for b $\ge$ 1. This extends previous results obtained for the Camassa-Holm equation (b = 2).
Let $W\subset \mathbb {P}^n$, $n\ge 3$, be a degree $k$ hypersurface. Consider a "general" reducible, but connected, curve $Y\subset \mathbb {P}^n$, for instance a sufficiently general connected and nodal union of lines with $p_a(Y)=0$, i.e. a tree of lines. We study the Hilbert function of the set $Y\cap W$ with cardinality $k\deg (Y)$ and prove when it is the expected one. We give complete classification of the exceptions for $k=2$ and for $n=k=3$. We apply these results and tools to the case in which $Y$ is a smooth curve with $\mathcal {O}_Y(1)$ non-special.
A chain poset, by definition, consists of chains of ordered elements in a poset. We study the chain posets associated to two posets: the Boolean algebra and the poset of isotropic flags. We prove that, in both cases, the chain posets satisfy the strong Sperner property and are rank-log concave.
Using a set of compilations of measurements for extragalactic radio sources we construct all-sky maps of the Faraday Rotation produced by the Galactic magnetic field. In order to generate the maps we treat the radio source positions as a kind of "mask" and construct combinations of spherical harmonic modes that are orthogonal on the masked sky. As long as relatively small multipoles are used the resulting maps are quite stable to changes in selection criteria for the sources, and show clearly the structure of the local Galactic magnetic field. We also suggest the use of these maps as templates for CMB foreground analysis, illustrating the idea with a cross-correlation analysis between the Wilkinson Microwave Anisotropy Probe (WMAP) data and our maps. We find a significant cross-correlation, indicating the presence of significant residual contamination.
We show that there exist arbitrarily large sets $S$ of $s$ prime numbers such that the equation $a+b=c$ has more than $\exp(s^{2-\sqrt{2}-\epsilon})$ solutions in coprime integers $a$, $b$, $c$ all of whose prime factors lie in the set $S$. We also show that there exist sets $S$ for which the equation $a+1=c$ has more than $\exp(s^{\frac 1{16}})$ solutions with all prime factors of $a$ and $c$ lying in $S$.
We provide characterizations for boundedness of multilinear Fourier operators on Hardy-Lebesgue spaces with symbols locally in Sobolev spaces. Let $H^q(\mathbb R^n)$ denote the Hardy space when $0<q\le 1$ and the Lebesgue space $L^q(\mathbb R^n)$ when $1<q\le \infty$. We find optimal conditions on $m$-linear Fourier multiplier operators to be bounded from $H^{p_1}\times \cdots \times H^{p_m}$ to $L^p$ when $1/p=1/p_1+\cdots +1/p_m$ in terms of local $L^2$-Sobolev space estimates for the symbol of the operator. Our conditions provide multilinear analogues of the linear results of Calder\'on and Torchinsky [http://www.sciencedirect.com/science/article/pii/S0001870877800169] and of the bilinear results of Miyachi and Tomita [http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=29&iss=2&rank=4]. The extension to general $m$ is significantly more complicated both technically and combinatorially, the optimal Sobolev space smoothness required of the symbol depends on the Hardy-Lebesgue exponents and is constant on various convex simplices formed by configurations of $m2^{m-1} +1$ points in $[0,\infty)^m$.
We shall review conformal gravity as a gauge natural theory and discuss the consequences of Weyl covariance on the definition of physical states.
In this article, we have found a series solution of 3D Einstein equations describing a wormhole for an inhomogeneous distribution of phantom energy. Here, we assume equation of state is linear but highly anistropic.
We study some reparametrization invariant theories in context of the BRST-co-BRST quantization method. The method imposes restrictions on the possible gauge fixing conditions and leads to well defined inner product states through a gauge regularisation procedure. Two explicit examples are also treated in detail.
We present the first grid of mean three-dimensional (3D) spectra for pure-hydrogen (DA) white dwarfs based on 3D model atmospheres. We use CO5BOLD radiation-hydrodynamics 3D simulations instead of the mixing-length theory for the treatment of convection. The simulations cover the effective temperature range of 6000 < Teff (K) < 15,000 and the surface gravity range of 7 < log g < 9 where the large majority of DAs with a convective atmosphere are located. We rely on horizontally averaged 3D structures (over constant Rosseland optical depth) to compute <3D> spectra. It is demonstrated that our <3D> spectra can be smoothly connected to their 1D counterparts at higher and lower Teff where the 3D effects are small. Analytical functions are provided in order to convert spectroscopically determined 1D effective temperatures and surface gravities to 3D atmospheric parameters. We apply our improved models to well studied spectroscopic data sets from the Sloan Digital Sky Survey and the White Dwarf Catalog. We confirm that the so-called high-log g problem is not present when employing <3D> spectra and that the issue was caused by inaccuracies in the 1D mixing-length approach. The white dwarfs with a radiative and a convective atmosphere have derived mean masses that are the same within ~0.01 Msun, in much better agreement with our understanding of stellar evolution. Furthermore, the 3D atmospheric parameters are in better agreement with independent Teff and log g values from photometric and parallax measurements.
We study general properties of the mapping between 5$d$ and 4$d$ superconformal field theories (SCFTs) under both twisted circle compactification and tuning of local relevant deformation and CB moduli. After elucidating in generality when a 5$d$ SCFT reduces to a 4$d$ one, we identify nearly all $\mathcal{N}=1$ 5$d$ SCFT parents of rank-2 4$d$ $\mathcal{N}=2$ SCFTs. We then use this result to map out the mass deformation trajectories among the rank-2 theories in 4$d$. This can be done by first understanding the mass deformations of the 5$d$ $\mathcal{N}=1$ SCFTs and then map them to 4$d$. The former task can be easily achieved by exploiting the fact that the 5$d$ parent theories can be obtained as the strong coupling limit of Lagrangian theories, and the latter by understanding the behavior under compactification. Finally we identify a set of general criteria that 4$d$ moduli spaces of vacua have to satisfy when the corresponding SCFTs are related by mass deformations and check that all our RG-flows satisfy them. Many of the mass deformations we find are not visible from the corresponding complex integrable systems.