ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use surveys covering the redshift range $0.05 < z < 3.8$ to explore quiescent galaxy scaling relations and the redshift evolution of the velocity dispersion, size, and dynamical mass at fixed stellar mass. For redshift $z < 0.6$ we derive mass limited samples and demonstrate that these large samples enhance constraints on the evolution of the quiescent population. The constraints include 2985 new velocity dispersions from the SHELS F2 survey (Geller et al. 2014). In contrast with the known substantial evolution of size with redshift, evolution in the velocity dispersion is negligible. The dynamical-to-stellar mass ratio increases significantly as the universe ages, in agreement with recent results that combine high redshift data with the SDSS. Like other investigators, we interpret this result as an indication that the dark matter fraction within the effective radius increases as a result of the impact of the minor mergers that are responsible for size growth. We emphasize that dense redshift surveys covering the range $0.07 < z < 1$ along with strong and weak lensing measurements could remove many ambiguities in evolutionary studies of the quiescent population.
The {\em Liouville function} is defined by $\gl(n):=(-1)^{\Omega(n)}$ where $\Omega(n)$ is the number of prime divisors of $n$ counting multiplicity. Let $\z_m:=e^{2\pi i/m}$ be a primitive $m$--th root of unity. As a generalization of Liouville's function, we study the functions $\gl_{m,k}(n):=\z_m^{k\Omega(n)}$. Using properties of these functions, we give a weak equidistribution result for $\Omega(n)$ among residue classes. More formally, we show that for any positive integer $m$, there exists an $A>0$ such that for all $j=0,1,...,m-1,$ we have $$#\{n\leq x:\Omega(n)\equiv j (\bmod m)\}=\frac{x}{m}+O(\frac{x}{\log^A x}).$$ Best possible error terms are also discussed. In particular, we show that for $m>2$ the error term is not $o(x^\ga)$ for any $\ga<1$.
We present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions. We derive a necessary and sufficient condition for the spin correlators to exhibit a long ranged power-law behavior in the presence of such perturbations. We substantiate our result by a study of the phase diagram of the Kitaev model augmented by a loop term and perturbed by an Ising term, within a RVB mean-field theory. We estimate the stability of the spin-liquid phase against such perturbations and show that this model exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases as well as topological quantum phase transitions between gapped and gapless spin liquid phases.
We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragm\'{e}n--Lindel\"{o}f-type theorem for analytic functions on ${\mathbb{C}}_+^n$.
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes based upon these algorithms are shown to satisfy tests of robust stability for random constraint violating initial data and random boundary data; and shown to give excellent performance for the evolution of typical physical data. The results are obtained for plane boundaries as well as piecewise cubic spherical boundaries cut out of a Cartesian grid.
In this work, we establish a new method to find critical points of differentiable functionals defined in Banach spaces which belong to a suitable class ($\mathcal{J}$) of functionals. Once given a functional $J$ in the class ($\mathcal{J}$), the central idea of the referred method consists in defining a real function $\zeta$ of a real variable, called {\it energy function}, which is naturally associated to $J$ in the sense that the existence of real critical points for $\zeta$ guarantees the existence of critical points for the functional $J$. As a consequence, we are able to solve some variational elliptic problems, whose associated energy functional belongs to ($\mathcal{J}$) and provide a version of the mountain pass theorem for functionals in the class ($\mathcal{J}$) that allows us to obtain mountain pass solutions without the so-called Ambrosetti-Rabinowitz condition.
I have combined the Emsellem et al. ATLAS3D rotation measures of a large sample of early-type galaxies with HST-based classifications of their central structure to characterize the rotation velocities of galaxies with cores. "Core galaxies" rotate slowly, while "power-law galaxies" (galaxies that lack cores) rotate rapidly, confirming the analysis of Faber et al. Significantly, the amplitude of rotation sharply discriminates between the two types in the -19 > Mv > -22 domain over which the two types coexist. The slow rotation in the small set of core galaxies with Mv > -20, in particular, brings them into concordance with the more massive core galaxies. The ATLAS3D "fast-rotating" and "slow-rotating" early-type galaxies are essentially the same as power-law and core galaxies, respectively, or the Kormendy & Bender two families of elliptical galaxies based on rotation, isophote shape, and central structure. The ATLAS3D fast rotators do include roughly half of the core galaxies, but their rotation-amplitudes are always at the lower boundary of that subset. Essentially all core galaxies have ATLAS3D rotation-amplitudes lambda_(R_e/2) <= 0.25, while all galaxies with lambda_(R_e/2) > 0.25 and figure eccentricity > 0.2 lack cores. Both figure rotation and the central structure of early-type galaxies should be used together to separate systems that appear to have formed from "wet" versus "dry" mergers.
For a finite undirected graph $G = (V,E)$, let $p_{u,v}(t)$ denote the probability that a continuous-time random walk starting at vertex $u$ is in $v$ at time $t$. In this note we give an example of a Cayley graph $G$ and two vertices $u,v \in G$ for which the function \[ r_{u,v}(t) = \frac{p_{u,v}(t)}{p_{u,u}(t)} \qquad t \geq 0 \] is not monotonically non-decreasing. This answers a question asked by Peres in 2013.
We review recent work on resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We derive a general expression for the current flowing in the structure and discuss the linear and non-linear transport in the nonperturbative regime. New effects associated to the Kondo resonance combined with the two-particle tunneling arise. The Kondo anomaly in the $I-V$ characteristics depends on the relative size of the gap energy and the Kondo temperature.
Let $a(r,n)$ be $r$th coefficient of $n$th cyclotomic polynomial. Suzuki proved that $\{a(r,n)|r\geq 1,n\geq 1\}=\mathbb{Z}$. If $m$ and $n$ are two natural numbers we prove an analogue of Suzuki's theorem for divisors of $x^n-1$ with exactly $m$ irreducible factors. We prove that for every finite sequence of integers $n_1,\ldots,n_r$ there exists a divisor $f(x)=\sum_{i=0}^{deg(f)}c_ix^i$ of $x^n-1$ for some $n\in \mathbb{N}$ such that $c_i=n_i$ for $1\leq i \leq r$. Let $H(r,n)$ denote the maximum absolute value of $r$th coefficient of divisors of $x^n-1$. In the last section of the paper we give tight bounds for $H(r,n)$.
Absorption lines in the spectra of distant quasars whose sightlines pass through foreground galaxies provide a valuable tool to probe the dust and gas compositions of the interstellar medium (ISM) in galaxies. The first evidence of silicate dust in a quasar absorption system (QAS) was provided through our detection of the 10 micron silicate feature in the z=0.52 absorber toward the quasar AO 0235+164. We present results from 2 follow-up programs using archival Spitzer Space Telescope infrared spectra to study the interstellar silicate dust grain properties in a total of 13 QASs at 0.1<z<1.4. We find clear detections of the 10 micron silicate feature in the QASs studied. We also detect the 18 micron silicate feature in the sources with adequate spectral coverage. We find variations in the breadth, peak wavelength, and substructure of the 10 micron interstellar silicate absorption features among the absorbers. This suggests that the silicate dust grain properties in these distant galaxies may differ relative to one another, and relative to those in the Milky Way. We also find suggestions in several sources, based on comparisons with laboratory-derived profiles from the literature, that the silicate dust grains may be significantly more crystalline than those in the amorphous Milky Way ISM. This is particularly evident in the z=0.89 absorber toward the quasar PKS 1830-211, where substructure near 10 micron is consistent with a crystalline olivine composition. If confirmed, these grain property variations may have implications for both dust and galaxy evolution over the past 9 Gyrs, and for the commonly-made assumption that high-redshift dust is similar to local dust. We also discuss indications of trends between silicate dust absorption strength and both carbonaceous dust properties and gas-phase metal properties, such as the gas velocity spread, determined from UV/optical spectra.
We present the discovery of the X-ray and optical afterglows of the short-duration GRB 150101B, pinpointing the event to an early-type host galaxy at z=0.1343 +/- 0.0030. This makes GRB 150101B the most nearby short GRB with an early-type host galaxy discovered to date. Fitting the spectral energy distribution of the host galaxy results in an inferred stellar mass of ~7x10^10 M_sol, stellar population age of ~2-2.5 Gyr, and star formation rate of <0.4 M_sol yr^-1. The host of GRB 150101B is one of the largest and most luminous short GRB host galaxies, with a B-band luminosity of ~4.3L* and half-light radius of ~8 kpc. GRB 150101B is located at a projected distance of 7.35 +/- 0.07 kpc from its host center, and lies on a faint region of its host rest-frame optical light. Its location, combined with the lack of associated supernova, is consistent with a NS-NS/NS-BH merger progenitor. From modeling the evolution of the broad-band afterglow, we calculate isotropic-equivalent gamma-ray and kinetic energies of ~1.3x10^49 erg and ~(6-14)x10^51 erg, respectively, a circumburst density of ~(0.8-4)x10^-5 cm^-3, and a jet opening angle of >9 deg. Using observations extending to ~30 days, we place upper limits of <(2-4)x10^41 erg s^-1 on associated kilonova emission. We compare searches following previous short GRBs to existing kilonova models, and demonstrate the difficulty of performing effective kilonova searches from cosmological short GRBs using current ground-based facilities. We show that at the Advanced LIGO/VIRGO horizon distance of 200 Mpc, searches reaching depths of ~23-24 AB mag are necessary to probe a meaningful range of kilonova models.
We extend the weak-strong uniqueness principle to general models of compressible viscous fluids near/on the vacuum. In particular, the physically relevant case of positive density with polynomial decay at infinity is considered.
In this paper, we propose a coupled spatial-temporal attention (CSTA) model for skeleton-based action recognition, which aims to figure out the most discriminative joints and frames in spatial and temporal domains simultaneously. Conventional approaches usually consider all the joints or frames in a skeletal sequence equally important, which are unrobust to ambiguous and redundant information. To address this, we first learn two sets of weights for different joints and frames through two subnetworks respectively, which enable the model to have the ability of "paying attention to" the relatively informative section. Then, we calculate the cross product based on the weights of joints and frames for the coupled spatial-temporal attention. Moreover, our CSTA mechanisms can be easily plugged into existing hierarchical CNN models (CSTA-CNN) to realize their function. Extensive experimental results on the recently collected UESTC dataset and the currently largest NTU dataset have shown the effectiveness of our proposed method for skeleton-based action recognition.
The $T \overline{T}$ operator provides a universal irrelevant deformation of two-dimensional quantum field theories with remarkable properties, including connections to both string theory and holography beyond $\mathrm{AdS}$ spacetimes. In particular, it appears that a $T \overline{T}$-deformed theory is a kind of new structure, which is neither a local quantum field theory nor a full-fledged string theory, but which is nonetheless under some analytic control. On the other hand, supersymmetry is a beautiful extension of Poincar\'e symmetry which relates bosonic and fermionic degrees of freedom. It is natural to ask what one can learn about irrelevant deformations in supersymmetric quantum field theories.   In this thesis, we describe a presentation of the $T \overline{T}$ deformation in manifestly supersymmetric settings. We define a "supercurrent-squared" operator, which is closely related to $T \overline{T}$, in any two-dimensional theory with $(0, 1)$, $(1, 1)$, or $(2, 2)$ supersymmetry. This deformation generates a flow equation for the superspace Lagrangian of the theory, which therefore makes the supersymmetry manifest. In certain examples, the deformed theories produced by supercurrent-squared are related to superstring and brane actions, and some of these theories possess extra non-linearly realized supersymmetries. We then show that $T \overline{T}$ defines a new theory of both abelian and non-abelian gauge fields coupled to charged matter, which includes models compatible with maximal supersymmetry.   Most of this thesis is adapted from previous publications. However, the final chapter presents new results on $T \overline{T}$-like deformations of general gauge theories in an arbitrary number of spacetime dimensions; this analysis has not appeared in past work.
Tuza's Conjecture states that if a graph $G$ does not contain more than $k$ edge-disjoint triangles, then some set of at most $2k$ edges meets all triangles of $G$. We prove Tuza's Conjecture for all graphs $G$ having no subgraph with average degree at least $7$. As a key tool in the proof, we introduce a notion of reducible sets for Tuza's Conjecture; these are substructures which cannot occur in a minimal counterexample to Tuza's Conjecture. We also introduce weak K\"onig--Egerv\'ary graphs, a generalization of the well-studied K\"onig--Egerv\'ary graphs.
Interacting binaries consist of a secondary star which fills or is very close to filling its Roche lobe, resulting in accretion onto the primary star, which is often, but not always, a compact object. In many cases, the primary star, secondary star, and the accretion disk can all be significant sources of luminosity. SIM Lite will only measure the photocenter of an astrometric target, and thus determining the true astrometric orbits of such systems will be difficult. We have modified the Eclipsing Light Curve code (Orosz & Hauschildt 2000) to allow us to model the flux-weighted reflex motions of interacting binaries, in a code we call REFLUX. This code gives us sufficient flexibility to investigate nearly every configuration of interacting binary. We find that SIM Lite will be able to determine astrometric orbits for all sufficiently bright interacting binaries where the primary or secondary star dominates the luminosity. For systems where there are multiple components that comprise the spectrum in the optical bandpass accessible to SIM Lite, we find it is possible to obtain absolute masses for both components, although multi-wavelength photometry will be required to disentangle the multiple components. In all cases, SIM Lite will at least yield accurate inclinations, and provide valuable information that will allow us to begin to understand the complex evolution of mass-transferring binaries. It is critical that SIM Lite maintains a multi-wavelength capability to allow for the proper deconvolution of the astrometric orbits in multi-component systems.
One-stage detector basically formulates object detection as dense classification and localization. The classification is usually optimized by Focal Loss and the box location is commonly learned under Dirac delta distribution. A recent trend for one-stage detectors is to introduce an individual prediction branch to estimate the quality of localization, where the predicted quality facilitates the classification to improve detection performance. This paper delves into the representations of the above three fundamental elements: quality estimation, classification and localization. Two problems are discovered in existing practices, including (1) the inconsistent usage of the quality estimation and classification between training and inference and (2) the inflexible Dirac delta distribution for localization when there is ambiguity and uncertainty in complex scenes. To address the problems, we design new representations for these elements. Specifically, we merge the quality estimation into the class prediction vector to form a joint representation of localization quality and classification, and use a vector to represent arbitrary distribution of box locations. The improved representations eliminate the inconsistency risk and accurately depict the flexible distribution in real data, but contain continuous labels, which is beyond the scope of Focal Loss. We then propose Generalized Focal Loss (GFL) that generalizes Focal Loss from its discrete form to the continuous version for successful optimization. On COCO test-dev, GFL achieves 45.0\% AP using ResNet-101 backbone, surpassing state-of-the-art SAPD (43.5\%) and ATSS (43.6\%) with higher or comparable inference speed, under the same backbone and training settings. Notably, our best model can achieve a single-model single-scale AP of 48.2\%, at 10 FPS on a single 2080Ti GPU. Code and models are available at https://github.com/implus/GFocal.
We study the broad band (3-100 keV) spectrum of Cygnus X-2 with INTEGRAL. We find that the spectrum is well fitted by a Comptonized component with a seed-photons temperature of ~1 keV, an electron temperature of ~3 keV and an optical depth tau ~ 8. Assuming spherical geometry, the radius of the seed-photons emitting region is ~17 km. The source shows no hard X-ray emission; it was detected only at a 3 sigma level above 40 keV. We also analyzed public ISGRI data of Cyg X--2 to investigate the presence of a hard X-ray component. We report the possible presence of hard X-ray emission in one data set.
We study the energy dependence of the cross sections for nucleon removal of 8B projectiles. It is shown that the Glauber model calculations with nucleon-nucleon t-matrix reproduce well the energy dependence of the breakup cross sections of 8B. A DWBA model for the breakup cross section is also proposed and results are compared with those of the Glauber model. We show that to obtain an agreement between the DWBA calculations, the Glauber formalism, and the experimental data, it is necessary to modify the energy behavior of the effective interaction. In particular, the breakup potential has a quite different energy dependence than the strong absorption potential.
We present a method to measure the growth of structure and the background geometry of the Universe -- with no a priori assumption about the underlying cosmological model. Using Canada-France-Hawaii Lensing Survey (CFHTLenS) shear data we simultaneously reconstruct the lensing amplitude, the linear intrinsic alignment amplitude, the redshift evolving matter power spectrum, P(k,z), and the co-moving distance, r(z). We find that lensing predominately constrains a single global power spectrum amplitude and several co-moving distance bins. Our approach can localise precise scales and redshifts where Lambda-Cold Dark Matter (LCDM) fails -- if any. We find that below z = 0.4, the measured co-moving distance r (z) is higher than that expected from the Planck LCDM cosmology by ~1.5 sigma, while at higher redshifts, our reconstruction is fully consistent. To validate our reconstruction, we compare LCDM parameter constraints from the standard cosmic shear likelihood analysis to those found by fitting to the non-parametric information and we find good agreement.
An important and usual problem is to search all states we want from a database with a large number of states. In such, recall is vital. Grover's original quantum search algorithm has been generalized to the case of multiple solutions, but no one has calculated the query complexity in this case. We will use a generalized algorithm with higher precision to solve such a search problem that we should find all marked states and show that the practical query complexity increases with the number of marked states. In the end we will introduce an algorithm for the problem on a ``duality computer'' and show its advantage over other algorithms.
Image compositing is a key step in film making and image editing that aims to segment a foreground object and combine it with a new background. Automatic image compositing can be done easily in a studio using chroma-keying when the background is pure blue or green. However, image compositing in natural scenes with complex backgrounds remains a tedious task, requiring experienced artists to hand-segment. In order to achieve automatic compositing in natural scenes, we propose a fully automated method that integrates instance segmentation and image matting processes to generate high-quality semantic mattes that can be used for image editing task. Our approach can be seen both as a refinement of existing instance segmentation algorithms and as a fully automated semantic image matting method. It extends automatic image compositing techniques such as chroma-keying to scenes with complex natural backgrounds without the need for any kind of user interaction. The output of our approach can be considered as both refined instance segmentations and alpha mattes with semantic meanings. We provide experimental results which show improved performance results as compared to existing approaches.
We discuss orbifold version of the Schur index defined as the supersymmetric partition function in S^3/Z_n x S^1. We first give a general formula for Lagrangian theories obtained by localization technique, and then suggest a generalization of the Cordova and Shao's IR formula. We confirm the generalized IR formula gives the correct answer for systems with free hypermultiplets if we tune the background fields so that they are invariant under the orbifold action. Unfortunately, we find disagreement for theories with dynamical vector multiplets.
We considered the structure of steady-state radiative shock waves propagating in the partially ionized hydrogen gas with density rho1 = 1e-10 gm/cm^3 and temperature 3000K <= T1 <= 8000K. The radiative shock wave models with electron thermal conduction in the vicinity of the viscous jump are compared with pure radiative models. The threshold shock wave velocity above of which effects of electron thermal conduction become perceptible is of U1=70 km/s and corresponds to the upstream Mach numbers from M1= 6 at T1=8000K to M1=11 at T1=3000K. In shocks with efficient electron heat conduction more than a half of hydrogen atoms are ionized in the radiative precursor, whereas behind the viscous jump the hydrogen gas undergoes the full ionization. The existence of the electron conductive precursor leads to the enhancement of the Lyman continuum flux trapped in the surroundings of the discontinuous jump. For upstream velocities ranged within 70 km/s <= U1 <= 85 km/s the partially ionized hydrogen gas of the radiative precursor undergoes the additional ionization (<= 5%), whereas the total radiave flux emerging from the shock wave increases by 10% <= delta(FRad) <= 25% .