ShantanuT01/DACTYL-Pretraining huggingface dataset:
For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the `expected reversed proportional shortfall order', and a new characterization of random lifetimes involving the reversed hazard rate function.
Aims. We aim to provide observational constraints on diffusion models that predict peculiar chemical abundances in the atmospheres of Am stars. We also intend to check if chemical peculiarities and slow rotation can be explained by the presence of a weak magnetic field.   Methods. We have obtained high resolution, high signal-to-noise ratio spectra of eight previously-classified Am stars, two normal A-type stars and one Blue Straggler, considered to be members of the Praesepe cluster. For all of these stars we have determined fundamental parameters and photospheric abundances for a large number of chemical elements, with a higher precision than was ever obtained before for this cluster. For seven of these stars we also obtained spectra in circular polarization and applied the LSD technique to constrain the longitudinal magnetic field.   Results. No magnetic field was detected in any of the analysed stars. HD 73666, a Blue Straggler previously considered as an Ap (Si) star, turns out to have the abundances of a normal A-type star. Am classification is not confirmed for HD 72942. For HD 73709 we have also calculated synthetic Delta-a photometry that is in good agreement with the observations. There is a generally good agreement between abundance predictions of diffusion models and values that we have obtained for the remaining Am stars. However, the observed Na and S abundances deviate from the predictions by 0.6 dex and >0.25 dex respectively. Li appears to be overabundant in three stars of our sample.
We show the existence of several infinite monochromatic patterns in the integers obtained as values of suitable symmetric polynomials. The simplest example is the following. For every finite coloring of the natural numbers $\mathbb{N}=C_1\cup\ldots\cup C_r$, there exists an increasing sequence $a<b<c<\ldots$ such that all elements below are monochromatic, that is, they belong to the same $C_i$: $$a,b,c,\ldots, a+b+ab, a+c+ac, b+c+bc,\ldots,a+b+c+ab+ac+bc+abc,\ldots.$$ The proofs use algebra in the space of ultrafilters $\beta\mathbb{Z}$.
We examine the dynamical implications of an interaction between some of the fluid components of the universe. We consider the combination of three matter components, one of which is a perfect fluid and the other two are interacting. The interaction term generalizes the cases found in scalar field cosmologies with an exponential potential. We find that attracting scaling solutions are obtained in several regions of parameter space, that oscillating behaviour is possible, and that new curvature scaling solutions exist. We also discuss the inflationary behaviour of the solutions and present some of the constraints on the strength of the coupling, namely those arising from nucleosynthesis.
Spinorial formalism is used to map every electromagnetic wave into the gravitational wave (within the linearized gravity). In this way we can obtain the gravitational counterparts of Bessel, Laguerre-Gauss, and other light beams carrying orbital angular momentum.
ARGO-YBJ is a "full coverage" air shower detector under construction at the YangBaJing Laboratory (4300 m a.s.l., Tibet, P.R. of China). Its main goals are gamma-ray astronomy and cosmic ray studies. In this paper we present the capabilities of ARGO-YBJ in detecting the emission from Gamma Ray Bursts (GRBs) at energies E>10 GeV.
In this paper, the existence, uniqueness and regularity properties, Strichartz type estimates for solution of multipoint Cauchy problem for linear and nonlinear Schr\"odinger equations with general elliptic leading part is obtained.
Motivated by reported claims of the measurements of a variation of the fine structure constant $\alpha$ we consider a theory where the electric charge, and consequently $\alpha$, is not a constant but depends on the Ricci scalar $R$. %We then show how this can be considered a particular case of the Bekenstein theory in which there is no need to %introduce an additional kinetic term for the scalar field associated to the electric charge, since the Einstein's% %equations are sufficient to determine the geometry and, consequently the Ricci scalar. We then study the cosmological implications of this theory, considering in particular the effects of dark energy and of a cosmological constant on the evolution of $\alpha$. Some low-red shift expressions for the variation of $\alpha(z)$ are derived, showing the effects of the equation of state of dark energy on $\alpha$ and observing how future measurements of the variation of the fine structure constant could be used to determine indirectly the equation of state of dark energy and test this theory. In the case of a $\Lambda CDM$ Universe, according to the current estimations of the cosmological parameters, the present value of the Ricci scalar is $\approx 10%$ smaller than its future asymptotic value determined by the value of the cosmological constant, setting also a bound on the future asymptotic value of $\alpha$.
We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the Molecular Dynamics (MD) ensemble, and test them with a short-ranged potential MD simulation.
The spectrum of O and B Supergiants is known to be affected by an important extra line-broadening (usually called macroturbulence) that adds to stellar rotation. Recent analysis of high resolution spectra has shown that the interpretation of this line-broadening as a consequence of large-scale turbulent motions would imply highly super-sonic velocity fields, making this scenario quite improbable. Stellar oscillations have been proposed as a likely alternative explanation. We present first encouraging results of an observational project aimed at investigating the $macroturbulent$ broadening in O and B Supergiants, and its possible connection with spectroscopic variability phenomena and stellar oscillations: a) all the studied B Supergiants show line profile variations, quantified by means of the first (< v >) and third velocity (< v^3 >) moments of the lines, b) there is a strong correlation between the peak-to-peak amplitudes of the < v > and < v^3 > variability and the size of the extra-broadening.
(Abridged) Radio relics in galaxy clusters are believed to be associated with powerful shock fronts that originate during cluster mergers, and are a testbed for the acceleration of relativistic particles in the intracluster medium. Recently, radio relic observations have pushed into the cm-wavelength domain (1-30 GHz) where a break from the standard synchrotron power-law spectrum has been found, most noticeably in the famous 'Sausage' relic. In this paper, we point to an important effect that has been ignored or considered insignificant while interpreting these new high-frequency radio data, namely the contamination due to the Sunyaev-Zel'dovich (SZ) effect that changes the observed synchrotron flux. Even though the radio relics reside in the cluster outskirts, the shock-driven pressure boost increases the SZ signal locally by roughly an order of magnitude. The resulting flux contamination for some well-known relics are non-negligible already at 10 GHz, and at 30 GHz the observed synchrotron fluxes can be diminished by a factor of several from their true values. Interferometric observations are not immune to this contamination, since the change in the SZ signal occurs roughly at the same length scale as the synchrotron emission, although there the flux loss is less severe than single-dish observations. We present a simple analytical approximation for the synchrotron-to-SZ flux ratio, based on a theoretical radio relic model that connects the non-thermal emission to the thermal gas properties, and show that by measuring this ratio one can potentially estimate the relic magnetic fields or the particle acceleration efficiency.
Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this chapter we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2,..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely to 2-column polyominoes, is unlikely to be solvable. We therefore define a class of polyominoes which interpolates between column-convex polygons and 2-column polyominoes. We derive the area generating function of that class, using an extension of an existing algorithm. The growth constant of the new class is greater than the growth constant of column-convex polygons. A rather tight lower bound on the growth constant complements a compelling numerical analysis.
Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\left\|\boldsymbol{X}(t)\right\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution we are concerned with the exact tail asymptotics of $\left\|\boldsymbol{X}(t)\right\|^c_p,\ c>0, $ with trend $g(t)$ over $[0,T]$. Both scenarios that $\boldsymbol{X}(t)$ is locally stationary and non-stationary are considered. Important examples include $\sum_{i=1}^d \left|X_i(t)\right|+g(t)$ and chi-square processes with trend, i.e., $\sum_{i=1}^d X_i^2(t)+g(t)$. These results are of interest in applications in engineering, insurance and statistics, etc.
IGR~J18245--2452/PSR J1824--2452I is one of the rare transitional accreting millisecond X-ray pulsars, showing direct evidence of switches between states of rotation powered radio pulsations and accretion powered X-ray pulsations, dubbed transitional pulsars. IGR~J18245--2452 is the only transitional pulsar so far to have shown a full accretion episode, reaching an X-ray luminosity of $\sim10^{37}$~erg~s$^{-1}$ permitting its discovery with INTEGRAL in 2013. In this paper, we report on a detailed analysis of the data collected with the IBIS/ISGRI and the two JEM-X monitors on-board INTEGRAL at the time of the 2013 outburst. We make use of some complementary data obtained with the instruments on-board XMM-Newton and Swift in order to perform the averaged broad-band spectral analysis of the source in the energy range 0.4 -- 250~keV. We have found that this spectrum is the hardest among the accreting millisecond X-ray pulsars. We improved the ephemeris, now valid across its full outburst, and report the detection of pulsed emission up to $\sim60$ keV in both the ISGRI ($10.9 \sigma$) and Fermi/GBM ($5.9 \sigma$) bandpass. The alignment of the ISGRI and Fermi GBM 20 -- 60 keV pulse profiles are consistent at a $\sim25\ \mu$s level. We compared the pulse profiles obtained at soft X-rays with \xmm\ with the soft \gr-ray ones, and derived the pulsed fractions of the fundamental and first harmonic, as well as the time lag of the fundamental harmonic, up to $150\ \mu$s, as a function of energy. We report on a thermonuclear X-ray burst detected with \Integ, and using the properties of the previously type-I X-ray burst, we show that all these events are powered primarily by helium ignited at a depth of $y_{\rm ign} \approx 2.7\times10^8$ g cm${}^{-2}$. For such a helium burst the estimated recurrence time of $\Delta t_{\rm rec}\approx5.6$ d is in agreement with the observations.
For a fixed graph $F$ and an integer $t$, the \dfn{rainbow saturation number} of $F$, denoted by $sat_t(n,\mathfrak{R}(F))$, is defined as the minimum number of edges in a $t$-edge-colored graph on $n$ vertices which does not contain a \dfn{rainbow copy} of $F$, i.e., a copy of $F$ all of whose edges receive a different color, but the addition of any missing edge in any color from $[t]$ creates such a rainbow copy. Barrus, Ferrara, Vardenbussche and Wenger prove that $sat_t(n,\mathfrak{R}(P_\ell))\ge n-1$ for $\ell\ge 4$ and $sat_t(n,\mathfrak{R}(P_\ell))\le \lceil \frac{n}{\ell-1} \rceil \cdot \binom{\ell-1}{2}$ for $t\ge \binom{\ell-1}{2}$, where $P_\ell$ is a path with $\ell$ edges. In this short note, we improve the upper bounds and show that $sat_t(n,\mathfrak{R}(P_\ell))\le \lceil \frac{n}{\ell} \rceil \cdot \left({{\ell-2}\choose {2}}+4\right)$ for $\ell\ge 5$ and $t\ge 2\ell-5$.
N-body simulations of dark matter halos show that the density profiles of halos behave as $\rho(r)\propto r^{-\alpha(r)}$, where the density logarithmic slope $\alpha \simeq 1\sim1.5$ in the center and $\alpha \simeq 3\sim 4$ in the outer parts of halos. However, some observations are not in agreement with simulations in the very central region of halos. The simulations also show that velocity dispersion anisotropy parameter $\beta\approx 0$ in the inner part of the halo and the so called "pseudo phase-space density" $\rho/\sigma^3$ behaves as a power-law in radius $r$. With these results in mind, we study the distribution function and the pseudo phase-space density $\rho/\sigma^3$ of the center of dark matter halos and find that they are closely-related.
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers the corresponding weak formulation and aims at using the Theorem of Lax-Milgram to assert the existence of a solution. To this end we have to resort to weighted Sobolev spaces. Our analysis shows that solutions do not exist unconditionally. The weights need some regularity and fulfil certain growth conditions. The results from this work complement findings which were previously only available for a discrete setup.
The Large Magellanic Cloud (LMC) currently hosts around 23 high mass X-ray binaries (HMXBs) of which most are Be/X-ray binaries. The LMC XMM-Newton survey provided follow-up observations of previously known X-ray sources that were likely HMXBs, as well as identifying new HMXB candidates. In total 19 candidate HMXBs were selected based on their X-ray hardness ratios. In this paper we present red and blue optical spectroscopy, obtained with SALT and the SAAO 1.9-m telescope, plus a timing analysis of the long term optical light curves from OGLE to confirm the nature of these candidates. We find that 9 of the candidates are new Be/X-ray Binaries, substantially increasing the LMC Be/X-ray binary population. Furthermore, we present the optical properties of these new systems, both individually and as a group of all the BeXBs identified by the XMM-Newton survey of the LMC.
We study the nonequilibrium exciton-polariton condensation in 1D to 0D and 1D to 2D junctions by means of non-resonant spectroscopy. The shape of our potential landscape allows to probe the resonant transmission of a propagating condensate between a quasi-1D waveguide and cylindrically symmetric states. We observe a distinct mode selection by varying the position of the non-resonant pump laser. Moreover, we study the the case of propagation from a localized trapped condensate state into a waveguide channel. Here, the choice of the position of the injection laser allows us to tune the output in the waveguide. Our measurements are supported by an accurate Ginzburg-Landau modeling of the system shining light on the underlying mechanisms.
The ATLASGAL 870mum continuum survey conducted with the APEX telescope is the first survey covering the whole inner Galactic plane (60deg>l>-60deg & b<1.5deg) in submm continuum emission tracing the cold dust of dense and young star-forming regions. Here, we present the overall distribution of sources within our Galactic disk. The submm continuum emission is confined to a narrow range around the galactic plane, but shifted on average by ~0.07deg below the plane. Source number counts show strong enhancements toward the Galactic center, the spiral arms and toward prominent star-forming regions. Comparing the distribution of ATLASGAL dust continuum emission to that of young intermediate- to high-mass young stellar objects (YSOs) derived from Spitzer data, we find similarities as well as differences. In particular, the distribution of submm dust continuum emission is significantly more confined to the plane than the YSO distribution (FWHM of 0.7 and 1.1deg, corresponding to mean physical scale heights of approximately 46 and 80pc, respectively). While this difference may partly be caused by the large extinction from the dense submm cores, gradual dispersal of stellar distributions after their birth could also contribute to this effect. Compared to other tracers of Galactic structure, the ATLASGAL data are strongly confined to a narrow latitude strip around the Galactic plane.
Circumbinary disks have been hypothesized to exist around a number of binary post-AGB stars. Although most of the circumbinary disks have been inferred through the near IR excess, a few of them are strong emitters of molecular emission. Here we present high angular resolution observations of the emission of $^{12}$CO and its isotopomer $^{13}$CO J=2--1 line from the circumstellar envelope around the binary post-AGB star IRAS 08544$-$4431, which is one of the most prominent members of this class of objects. We find that the envelope is resolved in our observations and two separate components can be identified: (a) a central extended and strong component with very narrow linewidth between 2 - 6 \kms; (b) a weak bipolar outflow with expansion velocity up to 8 \kms. The central compact component possesses low and variable $^{12}$CO/$^{13}$CO J=2--1 line ratio, indicating optically thick emission of the main isotope. We estimate a molecular gas mass of 0.0047 M$_\odot$ for this component based on the optically thinner $^{13}$CO J=2--1 line. We discuss the relation of the molecular envelope and the circumbinary disk inferred from near IR excess and compare with other known cases where the distribution of molecular gas has been imaged at high angular resolution.
We draw some rigorous conclusions about the functional properties of the $\mu-\rho$ relation in the Hubbard model based on symmetry considerations and unitary transformations. It is shown that the charge susceptibility reaches its local extreme at half-filling. Exact expressions are obtained in two limiting cases.
The analysis of the BRITE oscillation spectrum of the main sequence early B-type star $\nu$ Eridani is presented. Only models with the modified mean opacity profile can account for the observed frequency ranges as well as for the values of some individual frequencies. The number of the $\kappa$ modified seismic models is constrained by the nonadiabatic parameter $f$, which is very sensitive to the opacity changes in the subphotospheric layers where the pulsations are driven. We present an example of the model that satisfies all the above conditions. It seems that the OPLIB opacities are preferred over those from the OPAL and OP projects. Moreover, we discuss additional consequences of the opacity modification, namely, an enhancement of the efficiency of convection in the Z-bump as well as an occurrence of close radial modes which is a kind of avoided-crossing phenomenon common for nonradial modes in standard main sequence models.
Stereo superpixel segmentation aims at grouping the discretizing pixels into perceptual regions through left and right views more collaboratively and efficiently. Existing superpixel segmentation algorithms mostly utilize color and spatial features as input, which may impose strong constraints on spatial information while utilizing the disparity information in terms of stereo image pairs. To alleviate this issue, we propose a stereo superpixel segmentation method with a decoupling mechanism of spatial information in this work. To decouple stereo disparity information and spatial information, the spatial information is temporarily removed before fusing the features of stereo image pairs, and a decoupled stereo fusion module (DSFM) is proposed to handle the stereo features alignment as well as occlusion problems. Moreover, since the spatial information is vital to superpixel segmentation, we further design a dynamic spatiality embedding module (DSEM) to re-add spatial information, and the weights of spatial information will be adaptively adjusted through the dynamic fusion (DF) mechanism in DSEM for achieving a finer segmentation. Comprehensive experimental results demonstrate that our method can achieve the state-of-the-art performance on the KITTI2015 and Cityscapes datasets, and also verify the efficiency when applied in salient object detection on NJU2K dataset. The source code will be available publicly after paper is accepted.
We design a Stern-Gerlach apparatus that separates quasispin components on the lattice, without the use of external fields. The effect is engineered using intrinsic parameters, such as hopping amplitudes and on-site potentials. A theoretical description of the apparatus relying on a generalized Foldy-Wouthuysen transformation beyond Dirac points is given. Our results are verified numerically by means of wavepacket evolution, including an analysis of Zitterbewegung on the lattice. The necessary tools for microwave realizations, such as complex hopping amplitudes and chiral effects, are simulated.
We investigate the possible modifications of the nucleons' electromagnetic form factors in the framework of a modified Skyrme model allowing for nucleon deformation and using realistic nuclear mass distributions. We show that such effects are small in light nuclei.
Feature extraction is one of the fundamental problems of character recognition. The performance of character recognition system is depends on proper feature extraction and correct classifier selection. In this article, a rapid feature extraction method is proposed and named as Celled Projection (CP) that compute the projection of each section formed through partitioning an image. The recognition performance of the proposed method is compared with other widely used feature extraction methods that are intensively studied for many different scripts in literature. The experiments have been conducted using Bangla handwritten numerals along with three different well known classifiers which demonstrate comparable results including 94.12% recognition accuracy using celled projection.
Generalizing the notion of composite fermions to the "pseudo-relativistic" Quantum Hall phenomena in graphene, we discuss a possible emergence of compressible states at the filling factors -3/2, -1/2, 1/2, 3/2. This analysis is further extended to the nearby incompressible states viewed as the Integer Quantum Hall Effect of the composite Dirac fermions, as well as those that might occur at the filling factors -1, 0, 1 as a result of the (pseudo)spin-singlet pairing between them.