ShantanuT01/DACTYL-Pretraining huggingface dataset:
Spectroscopy with HST/STIS Echelle and VLT/UVES of the bright QSO HE 0515-4414 (z_em =1.73, B = 15.0) offers for the first time the opportunity to study the Lyman alpha forest in the redshift range 0.9 < z < 1.7 at a resolution ~ 10 km/s. The number density evolution of the Lyman alpha lines is well described by the power law approach dn/dz = (dn/dz)_0 (1+z)^gamma. We derive gamma = 2.23 +/- 1.21 for the strong lines (13.64 < log N_HI < 16.00), in agreement with the Lyman alpha forest evolution for z > 1.7. The expected slow-down in their evolution does not appear earlier than z ~ 1. For the weak lines (13.10 < log N_HI < 14.00) we find that the HE 0515-4414 data for z > 1 follow the trend with gamma = 1.40 known from z > 1.7 observations, i.e. we confirm the difference in evolution between weak and strong lines. We use the two-point velocity correlation function (TPCF) to search for clustering of the Lyman alpha lines, yet we detect no excess in the TPCF on scales up to 10,000 km/s.
Chiral molecules may exist in superpositions of left- and right-handed states. We show how the amplitudes of such superpositions may be teleported to the polarization degrees of freedom of a photon and thus measured. Two experimental schemes are proposed, one leading to perfect, the other to state-dependent teleportation. Both methods yield complete information about the amplitudes.
We prove a number of unconditional statistical results of the Hecke coefficients for unitary cuspidal representations of $\operatorname{GL}(2)$ over number fields. Using partial bounds on the size of the Hecke coefficients, instances of Langlands functoriality, and properties of Rankin-Selberg $L$-functions, we obtain bounds on the set of places where linear combinations of Hecke coefficients are negative. Under a mild functoriality assumption we extend these methods to $\operatorname{GL}(n)$. As an application, we obtain a result related to a question of Serre about the occurrence of large Hecke eigenvalues of Maass forms. Furthermore, in the cases where the Ramanujan conjecture is satisfied, we obtain distributional results of the Hecke coefficients at places varying in certain congruence or Galois classes.
Black hole quasinormal frequencies are complex numbers that encode information on how a black hole relaxes after it has been perturbed and depend on the features of the geometry and on the type of perturbations. On the one hand, the examples studied so far in the literature focused on the case of black hole geometries with singularities in their interior. On the other hand, it is expected that quantum or classical modifications of general relativity may correct the pathological singular behavior of classical black hole solutions. Despite the fact that we do not have at hand a complete theory of quantum gravity, regular black hole solutions can be constructed by coupling gravity to an external form of matter, sometimes modeled by one form or another of nonlinear electrodynamics. It is therefore relevant to compute quasinormal frequencies for these regular solutions and see how differently, from the ordinary ones, regular black holes ring. In this paper, we take a step in this direction and, by computing the quasinormal frequencies, study the quasinormal modes of neutral and charged scalar field perturbations on regular black hole backgrounds in a variety of models.
The purpose of this short note is to study dominant rational maps from punctual Hilbert schemes of length $k>1$ of projective K3 surfaces $S$ containing infinitely many rational curves. Precisely, we prove that their image is necessarily rationally connected if this rational map is not generically finite. As an application, we simplify the proof of C. Voisin's of the fact that symplectic involutions of any projective K3 surface $S$ act trivially on $\mathrm{CH}_0(S)$.
(Abriged) Blue compact galaxies (BCGs) are low-luminosity, metal-poor, gas-rich objects that form stars at high rates, excellent analogs to the high-redshift star-forming galaxy population. Being low-mass starbursts, they also constitute ideal laboratories for investigating star formation and massive stellar feedback. This work presents results from integral field spectroscopic observations of the BCG Haro 14 taken with the Multi Unit Spectroscopic Explorer (MUSE). The large MUSE field of view enables simultaneous observations of the starburst and the host galaxy. We built galaxy maps in continuum and in emission lines and generated synthetic VRI images, from which we produced color index maps and surface brightness profiles. We detected numerous clumps spread throughout the galaxy, both in continuum and in emission lines, and produced a catalog with their position, size, and photometry. This analysis allowed us to study the morphology and stellar populations of Haro 14 in detail. The stellar distribution shows a pronounced asymmetry; the intensity peak in continuum is not centered with respect to the stellar host but is displaced by about 500 pc southwest. At the position of the continuum peak we find a bright stellar cluster that with M$_{V}=-12.18$ appears as a strong super stellar cluster candidate. We also find a highly asymmetric, blue, but nonionizing stellar component that occupies almost the whole eastern part of the galaxy. We conclude that there are at least three different stellar populations in Haro 14: the current starburst of about 6 Myr; an intermediate-age component of between ten and several hundred million years; and a red and regular host of several gigayears. The pronounced lopsidedness in the continuum and also in the color maps, and the presence of numerous stellar clusters, are consistent with a scenario of mergers or interactions acting in Haro 14.
We prove Artin's axioms satisfy a compatibility for composition of 1-morphisms of stacks in groupoids. Consequently, some natural stacks in groupoids are algebraic, including a common generalization of Vistoli's Hilbert stack and the stack of branchvarieties of Alexeev and Knutson.
We previously derived a theorem about the {\em coherent} quasielastic neutron-scattering signal from a $d$-dimensional lattice of $N$ molecules that are undergoing rotational jump diffusion (around an $n$-fold axis), assuming that there are no correlations between the molecules. In the present paper molecular correlations are treated, but only in the sense that several molecules could reorient simultaneously as in a cog-wheel mechanism. Moreover, we do not examine the possibility that the relaxation times of these combined reorientations could depend on details of the local environment created by the neighbouring molecules. Finally also an ergodicity condition has to be fulfilled. Admitting for all these assumptions we can show that the correlations do not affect the coherent quasielastic scattering pattern in the following sense: The functions of $Q$ that intervene in the description of the intensities remain unaltered, while the functions of $\omega$ can undergo a renormalization of the time scales. The latter changes cannot be detected as the time scales that would occur if the dynamics were independent are not available for comparison. In other words: Coherent quasielastic neutron scattering is not able to betray the existence of correlations of the restricted type that occur in our model.
In this paper, we give p-adic q-integral representation for the Kim's q-Bernstein polynomials and we give some interesting formulae realted to Carlitz's q-Bernoulli numbers.
We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\mathcal{N}=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$, $SO(2N+1)$, $USp(2N)$. These integrated correlators are expressed as two-dimensional lattice sums by considering derivatives of the localised partition functions, generalising the expression obtained for $SU(N)$ in our previous works. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality. The integrated correlators can also be formally written as infinite sums of non-holomorphic Eisenstein series with integer indices and rational coefficients. Furthermore, the action of the hyperbolic Laplace operator with respect to the complex coupling $\tau=\theta/(2\pi) + 4\pi i /g^2_{_{YM}}$ on any integrated correlator for gauge group $G_N$ relates it to a linear combination of correlators with gauge groups $G_{N+1}$, $G_N$ and $G_{N-1}$. These "Laplace-difference equation" determine the expressions of integrated correlators for all classical gauge groups for any value of $N$ in terms of the correlator for the gauge group $SU(2)$. The perturbation expansions of these integrated correlators for any finite value of $N$ agree with properties obtained from perturbative Yang--Mills quantum field theory, together with various multi-instanton calculations which are also shown to agree with those determined by supersymmetric localisation. The coefficients of terms in the large-$N$ expansion are sums of non-holomorphic Eisenstein series with half-integer indices, which extend recent results and make contact with low order terms in the low energy expansion of type IIB superstring theory in an $AdS_5\times S^5/\mathbb{Z}_2$ background.
The longitudinal and Hall resistances have recently been measured for quantum Hall bilayers at total filling $\nu=1$ in the superfluid state with interlayer pairing, both for currents flowing parallel to one another and for "counterflowing" currents in the two layers. Here I examine the contribution to these resistances from the motion of unpaired vortices in these systems, developing some possible explanations of various qualitative features of these data.
We describe a technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain 4th-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a 4th-order correlator of physical interest, the tension-force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized-emission observations in the Faraday-rotation-free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic-electron distribution that has a power-law energy spectrum with a spectral index p=3, and assumes statistical isotropy of the turbulent field. We carry out tests of our method using synthetic data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index, and that the observed tension-force spectrum allows one to distinguish between, e.g., a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.
This paper introduces single-image geometric and appearance reconstruction from water reflection photography, i.e., images capturing direct and water-reflected real-world scenes. Water reflection offers an additional viewpoint to the direct sight, collectively forming a stereo pair. The water-reflected scene, however, includes internally scattered and reflected environmental illumination in addition to the scene radiance, which precludes direct stereo matching. We derive a principled iterative method that disentangles this scene radiometry and geometry for reconstructing 3D scene structure as well as its high-dynamic range appearance. In the presence of waves, we simultaneously recover the wave geometry as surface normal perturbations of the water surface. Most important, we show that the water reflection enables calibration of the camera. In other words, for the first time, we show that capturing a direct and water-reflected scene in a single exposure forms a self-calibrating HDR catadioptric stereo camera. We demonstrate our method on a number of images taken in the wild. The results demonstrate a new means for leveraging this accidental catadioptric camera.
We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\mathbf{Q}$-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.
It is well known that in dimension one the set of Dirichlet improvable real numbers consists precisely of badly approximable and singular numbers. We show that in higher dimensions this is not the case by proving that there exist continuum many Dirichlet improvable vectors that are neither badly approximable nor singular. This is a consequence of a stronger statement that involves very well approximable points. In the last section we formulate the notion of intermediate Dirichlet improvable sets concerning approximations by rational planes of every intermediate dimension and show that they coincide. This naturally extends a classical theorem of Davenport and Schmidt (1969) which states that the simultaneous form of Dirichlet's theorem is improvable if and only if the dual form is improvable. Consequently, our main "continuum" result is equally valid for the corresponding intermediate Diophantine sets of badly approximable, singular and Dircihlet improvable points.
We assess the ability to image the photosphere of red supergiants and, in particular Betelgeuse, through the modelling of the observed linear polarization in atomic spectral lines. We also aim to analyse the resulting images over time, to measure the size and dynamics of the convective structures in these stars. Rayleigh scattering polarizes the continuum and spectral lines depolarize it.This depolarization is seen as a linear polarization signal parallel to the radial direction on the stellar disk. Integrated over the disk, it would result in a null signal, except if brightness asymmetries/inhomogeneities are present. This is the basic concept behind our imaging technique. The several tests and comparisons performed prove that our technique reliably retrieves the salient brightness structures in the photosphere of Betelgeuse, and should be relevant to other red supergiants. We demonstrate that these structures are convective cells, with a characteristic size of more than 60% of the stellar radius. We also derive the characteristic upflow and downflow speeds, 22 and 10 km/s respectively. We find weak magnetic fields concentrated in the downflow lanes in between granules. We follow those convective structures in time. Changes happen on timescales of one week, but individual structures can be tracked over four years of observations.
We will review our recent analysis of the magnetic properties of the O9IV star HD 57682, using spectropolarimetric observations obtained with ESPaDOnS at the Canada-France-Hawaii telescope within the context of the Magnetism in Massive Stars (MiMeS) Large Program. We discuss our most recent determination of the rotational period from longitudinal magnetic field measurements and H_alpha variability - the latter obtained from over a decade's worth of professional and amateur spectroscopic observations. Lastly, we report on our investigation of the magnetic field geometry and the effects of the field on the circumstellar environment.
We consider strips of Ising spins at criticality. For strips of width $N$ sites, subdominant (additive) finite-size corrections to scaling are assumed to be of the form $a_k/N^k$ for the free energy, and $b_k/N^k$ for inverse correlation length, with integer values of $k$. We investigate the set $\{a_k,b_k\}$ ($k \geq 2$) by exact evaluation and numerical transfer-matrix diagonalization techniques, and their changes upon varying anisotropy of couplings, spin quantum number $S$, and (finite) interaction range, in all cases for both periodic (PBC) and free (FBC) boundary conditions across the strip. We find that the coefficient ratios $b_k/a_k$ remain constant upon varying coupling anisotropy for $S=1/2$ and first-neighbor couplings, for both PBC and FBC (albeit at distinct values in either case). Such universal behavior is not maintained upon changes in $S$ or interaction range.
We provide a test for numerical simulations, for several two dimensional incompressible flows, that appear to develop sharp fronts. We show that in order to have a front the velocity has to have uncontrolled velocity growth.
Inner bars are frequent structures in the local Universe and thought to substantially influence the nuclear regions of disc galaxies. In this study we explore the structure and dynamics of inner bars by deriving maps and radial profiles of their mean stellar population content and comparing them to previous findings in the context of main bars. To this end, we exploit observations obtained with the integral-field spectrograph MUSE of three double-barred galaxies in the TIMER sample. The results indicate that inner bars can be distinguished based on their stellar population properties alone. More precisely, inner bars show elevated metallicities and depleted [$\alpha$/Fe] abundances. Although they exhibit slightly younger stellar ages compared to the nuclear disc, the typical age differences are small, except at their outer ends. These ends of the inner bars are clearly younger compared to their inner parts, an effect known from main bars as orbital age separation. In particular, the youngest stars (i.e. those with the lowest radial velocity dispersion) seem to occupy the most elongated orbits along the (inner) bar major axis. We speculate that these distinct ends of bars could be connected to the morphological feature of ansae. Radial profiles of metallicity and [$\alpha$/Fe] enhancements are flat along the inner bar major axis, but show significantly steeper slopes along the minor axis. This radial mixing in the inner bar is also known from main bars and indicates that inner bars significantly affect the radial distribution of stars. In summary, based on maps and radial profiles of the mean stellar population content and in line with previous TIMER results, inner bars appear to be scaled down versions of the main bars seen in galaxies. This suggests the picture of a "galaxy within a galaxy", with inner bars in nuclear discs being dynamically equivalent to main bars in main galaxy discs.
We present a spectral analysis of three simultaneous NuSTAR and Swift/XRT observations of the transient Be-neutron star binary KS 1947+300 taken during its outburst in 2013/2014. These broad-band observations were supported by Swift/XRT monitoring snap-shots every 3 days, which we use to study the evolution of the spectrum over the outburst. We find strong changes of the power-law photon index, which shows a weak trend of softening with increasing X-ray flux. The neutron star shows very strong pulsations with a period of P ~ 18.8 s. The 0.8-79 keV broad-band spectrum can be described by a power-law with an exponential cutoff and a black-body component at low energies. During the second observation we detect a cyclotron resonant scattering feature at 12.5 keV, which is absent in the phase-averaged spectra of observations 1 and 3. Pulse phase-resolved spectroscopy reveals that the strength of the feature changes strongly with pulse phase and is most prominent during the broad minimum of the pulse profile. At the same phases the line also becomes visible in the first and third observation at the same energy. This discovery implies that KS 1947+300 has a magnetic field strength of B ~ 1.1e12 (1+z)G, which is at the lower end of known cyclotron line sources.
We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops which can exchange length between each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip-links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.
Facial expressions have essential cues to infer the humans state of mind, that conveys adequate information to understand individuals actual feelings. Thus, automatic facial expression recognition is an interesting and crucial task to interpret the humans cognitive state through the machine. In this paper, we proposed an Exigent Features Preservative Network (EXPERTNet), to describe the features of the facial expressions. The EXPERTNet extracts only pertinent features and neglect others by using exigent feature (ExFeat) block, mainly comprises of elective layer. Specifically, elective layer selects the desired edge variation features from the previous layer outcomes, which are generated by applying different sized filters as 1 x 1, 3 x 3, 5 x 5 and 7 x 7. Different sized filters aid to elicits both micro and high-level features that enhance the learnability of neurons. ExFeat block preserves the spatial structural information of the facial expression, which allows to discriminate between different classes of facial expressions. Visual representation of the proposed method over different facial expressions shows the learning capability of the neurons of different layers. Experimental and comparative analysis results over four comprehensive datasets CK+, MMI DISFA and GEMEP-FERA, ensures the better performance of the proposed network as compared to existing networks.
Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then apply our result to the case when S consists of sqares. In this case we obtain an estimate which improves a recent result by L. Zhao.