ShantanuT01/DACTYL-Pretraining huggingface dataset:
RV variable stars are important in astrophysics. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic survey has provided ~ 6.5 million stellar spectra in its Data Release 4 (DR4). During the survey, ~ 4.7 million unique sources were targeted and ~ 1 million stars observed repeatedly. The probabilities of stars being RV variables are estimated by comparing the observed radial velocity variations with the simulated ones. We build a catalog of 80,702 RV variable candidates with probability greater than 0.60 by analyzing the duplicate-observed multi-epoch sources covered by the LAMOST DR4. Simulations and cross-identifications show that the purity of the catalog is higher than 80%. The catalog consists of 77% binary systems and 7% pulsating stars as well as 16% pollution by single stars. 3,138 RV variables are classified through cross-identifications with published results in literatures. By using the 3,138 sources common to both LAMOST and a collection of published RV variable catalogs we are able to analyze LAMOST's RV variable detection rate. The efficiency of the method adopted in this work relies not only on the sampling frequency of observations but also periods and amplitudes of RV variables. With the progress of LAMOST, Gaia and other surveys, more and more RV variables would will be confirmed and classified. This catalog is valuable for other large-scale surveys, especially for RV variable searches. The catalog will be released according to the LAMOST Data Policy via http://dr4.lamost.org.
A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Neel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gapless phases with magnon excitations. Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful S = 0, or 1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors are even partially coherent, they present a major obstacle to achieving robust computation. Here, we propose a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged. We prove that this randomization tailors the noise into stochastic Pauli errors, leading to dramatic reductions in worst-case and cumulative error rates, while introducing little or no experimental overhead. Moreover we prove that our technique is robust to variation in the errors over the gate sets and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity are sufficient to achieve fault-tolerant quantum computation, and, importantly, the worst case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking experiments. Remarkably, our method enables the realization of fault-tolerant quantum computation under the error rates observed in recent experiments.
Fuzzy Dark Matter (FDM) represents an alternative and intriguing description of the standard Cold Dark Matter (CDM) fluid, able to explain the lack of direct detection of dark matter particles in the GeV sector and to alleviate small scales tensions in the cosmic large-scale structure formation. Cosmological simulations of FDM models in the literature were performed either with very expensive high-resolution grid-based simulations of individual haloes or through N-body simulations encompassing larger cosmic volumes but resorting on significant approximations in the FDM non-linear dynamics to reduce their computational cost. With the use of the new N-body cosmological hydrodynamical code AX-GADGET, we are now able not only to overcome such numerical problems, but also to combine a fully consistent treatment of FDM dynamics with the presence of gas particles and baryonic physical processes, in order to quantify the FDM impact on specific astrophysical observables. In particular, in this paper we perform and analyse several hydrodynamical simulations in order to constrain the FDM mass by quantifying the impact of FDM on Lyman-$\alpha$ forest observations, as obtained for the first time in the literature in a N-body setup without approximating the FDM dynamics. We also study the statistical properties of haloes, exploiting the large available sample, to extract information on how FDM affects the abundance, the shape, and density profiles of dark matter haloes.
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider $2+1$ gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known --for both the continuum and the lattice-- and can be compared.
We show that the minimal R-parity breaking model characterized by an effective bilinear violation of R-parity in the superpotential is consistent with minimal N=1 supergravity unification with radiative breaking of the electroweak symmetry and universal scalar and gaugino masses. This one-parameter extension of the MSSM-SUGRA model provides therefore the simplest reference model for the breaking of R-parity and constitutes a consistent truncation of the complete dynamical models with spontaneous R-parity breaking proposed previously. We comment on the lowest-lying CP-even Higgs boson mass and discuss its minimal N=1 supergravity limit, determine the ranges of $\tan\beta$ and bottom quark Yukawa couplings allowed in the model, as well as the relation between the tau neutrino mass and the bilinear R-parity violating parameter.
We compile published spectroscopic data and [O III] magnitudes of almost 500 extragalactic planetary nebulae (PNe) in 13 galaxies of various masses and morphological types. This is the first paper of a series that aims to analyze the PN populations and their progenitors in these galaxies. Although the samples are not complete or homogeneous we obtain some first findings through the comparison of a few intensity line ratios and nebular parameters. We find that the ionized masses and the luminosities in H$\beta$, L$_{H\beta}$, of around 30 objects previously identified as PNe indicate that they are most likely compact HII regions. We find an anticorrelation between the electron densities and the ionized masses in M31, M33, and NGC 300 which suggests that most of the PNe observed in these galaxies are probably ionization bounded. This trend is absent in LMC and SMC suggesting that many of their PNe are density bounded. The He II/H$\beta$ values found in many PNe in LMC and some in M33 and SMC are higher than in the other galaxies. Photoionization models predict that these high values can only be reached in density bounded PNe. We also find that the brightest PNe in the sample are not necessarily the youngest since there is no correlation between electron densities and the H$\beta$ luminosities. The strong correlation found between L$_{H\beta}$-L$_{[O III]}$ implies that the so far not understood cut off of the planetary luminosity function (PNLF) based on [O III] magnitudes can be investigated using L$_{H\beta}$, a parameter much easier to study.
It is proved that infinitesimal triangular arrays obtained from normalized partial sums of strongly mixing (but not necessarily stationary) random sequences, can produce as lilmits only selfdecomposable distributions.
This paper summarises an investigation of chaos in a toy potential which mimics much of the behaviour observed for the more realistic triaxial generalisations of the Dehnen potentials, which have been used to model cuspy triaxial galaxies both with and without a supermassive black hole. The potential is the sum of an anisotropic harmonic oscillator potential,   V_o=(1/2)*(a^{2}x^{2}+b^{2}y^{2}+c^{2}z^{2}), and a spherical Plummer potential,   V_o=-M_{BH}/(r^{2}+e^{2})^{1/2} with r^{2}=x^{2}+y^{2}+z^{2}. Attention focuses on three issues related to the properties of ensembles of chaotic orbits which impact on chaotic mixing and the possibility of constructing self-consistent equilibria: (1) What fraction of the orbits are chaotic? (2) How sensitive are the chaotic orbits, i.e., how large are their largest (short time) Lyapunov exponents? (3) To what extent is the motion of chaotic orbits impeded by Arnold webs, i.e.,, how `sticky' are the chaotic orbits? These questions are explored as functions of the axis ratio a:b:c, black hole mass M_BH, softening length e, and energy E with the aims of understanding how the manifestations of chaos depend on the shape of the system and why the black hole generates chaos. The simplicity of the model makes it amenable to a perturbative analysis. That it mimics the behaviour of more complicated potentials suggests that much of this behaviour should be generic.
A simple functional form has been found that gives a good representation of the total reaction cross sections for the scattering from ${}^{208}$Pb of protons with energies in the range 30 to 300 MeV.
We introduce and study a generalization of Schur's $P$-/$Q$-functions associated to a polynomial sequence, which can be viewed as ``Macdonald's ninth variation'' for $P$-/$Q$-functions. This variation includes as special cases Schur's $P$-/$Q$-functions, Ivanov's factorial $P$-/$Q$-functions and the $t=-1$ specialization of Hall--Littlewood functions associated to the classical root systems. We establish several identities and properties such as generalizations of Schur's original definition of Schur's $Q$-functions, Cauchy-type identity, J\'ozefiak--Pragacz--Nimmo formula for skew $Q$-functions, and Pieri-type rule for multiplication.
GRB200522A is a short duration gamma-ray burst (GRB) at redshift $z$=0.554 characterized by a bright infrared counterpart. A possible, although not unambiguous, interpretation of the observed emission is the onset of a luminous kilonova powered by a rapidly rotating and highly-magnetized neutron star, known as magnetar. A bright radio flare, arising from the interaction of the kilonova ejecta with the surrounding medium, is a prediction of this model. Whereas the available dataset remains open to multiple interpretations (e.g. afterglow, r-process kilonova, magnetar-powered kilonova), long-term radio monitoring of this burst may be key to discriminate between models. We present our late-time upper limit on the radio emission of GRB200522A, carried out with the Karl G. Jansky Very Large Array at 288 days after the burst. For kilonova ejecta with energy $E_{\rm ej} \approx 10^{53} \rm erg$, as expected for a long-lived magnetar remnant, we can already rule out ejecta masses $M_{\rm ej} \lesssim0.03 \mathrm{M}_\odot$ for the most likely range of circumburst densities $n\gtrsim 10^{-3}$ cm$^{-3}$. Observations on timescales of $\approx$3-10 yr after the merger will probe larger ejecta masses up to $M_{\rm ej} \sim 0.1 \mathrm{M}_\odot$, providing a robust test to the magnetar scenario.
We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.
With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. First, we show that the negative tangential pressure is independent of the four-velocity of a very thin hyper-surface. Second, we relate the 3-pressure of a surface layer to the normal curvature and the surface tension. Third, we relate the surface tension to the energy of the surface layer. Four, we show that the delta like energy flows across the hyper-surface will be zero for such a representation of intrinsic 3-pressure. Five, for the weak field approximation and for static spherically symmetric configuration, we deduce the classical Kelvin's relation. Six, we write a modified action for the boundary having contributions both from surface tension and normal curvature of the surface layer. Also we propose a method to find the physical action assuming a reference background, where the background is not flat.
We present a catalog of radio afterglow observations of gamma-ray bursts (GRBs) over a 14 year period from 1997 to 2011. Our sample of 304 afterglows consists of 2995 flux density measurements (including upper limits) at frequencies between 0.6 GHz and 660 GHz, with the majority of data taken at 8.5 GHz frequency band (1539 measurements). We use this dataset to carry out a statistical analysis of the radio-selected sample. The detection rate of radio afterglows has stayed unchanged almost at 31% before and after the launch of the {\em Swift} satellite. The canonical long-duration GRB radio light curve at 8.5 GHz peaks at 3-6 days in the source rest frame, with a median peak luminosity of $10^{31}$ erg s$^{-1}$ Hz$^{-1}$. The peak radio luminosities for short-hard bursts, X-ray flashes and the supernova-GRB classes are an order of magnitude or more fainter than this value. There are clear relationships between the detectability of a radio afterglow and the fluence or energy of a GRB, and the X-ray or optical brightness of the afterglow. However, we find few significant correlations between these same GRB and afterglow properties and the peak radio flux density. We also produce synthetic light curves at centimeter (cm) and millimeter (mm) bands using a range of blastwave and microphysics parameters derived from multiwavelength afterglow modeling, and we use them to compare to the radio sample. Finding agreement, we extrapolate this behavior to predict the cm and mm behavior of GRBs observed by the Expanded Very Large Array and the Atacama Large Millimeter Array.
We have observed 10 interacting galaxy pairs using the Fabry-Perot interferometer GH$\alpha$FaS (Galaxy H$\alpha$ Fabry-Perot system) on the $4.2\rm{m}$ William Herschel Telescope (WHT) at the Observatorio del Roque de los Muchachos, La Palma. We present here the H$\alpha$ surface brightness, velocity and velocity dispersion maps for the 10 systems we have not previously observed using this technique, as well as the physical properties (sizes, H$\alpha$ luminosities and velocity dispersion) of 1259 HII regions from the full sample. We also derive the physical properties of 1054 HII regions in a sample of 28 isolated galaxies observed with the same instrument in order to compare the two populations of HII regions. We find a population of the brightest HII regions for which the scaling relations, for example the relation between the H$\alpha$ luminosity and the radius, are clearly distinct from the relations for the regions of lower luminosity. The regions in this bright population are more frequent in the interacting galaxies. We find that the turbulence, and also the star formation rate, are enhanced in the HII regions in the interacting galaxies. We have also extracted the H$\alpha$ equivalent widths for the HII regions of both samples, and we have found that the distribution of HII region ages coincides for the two samples of galaxies. We suggest that the SFR enhancement is brought about by gas flows induced by the interactions, which give rise to gravitationally bound gas clouds which grow further by accretion from the flowing gas, producing conditions favourable to star formation.
In the monograph 'Association schemes', C. Godsil derived a necessary condition for equitable partitions of association schemes and noticed that it could be used to show that certain equitable partitions do not exist. In this short note, we show that, in fact, this condition is not stronger than the well-known Lloyd theorem.
We give a simple proof of Hardy's inequality, based on the logarithmic Caccioppoli estimate for p-superharmonic functions in several variables.
We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in $C^2 \otimes C^4$. Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in $C^2 \otimes C^4$. The results are generalized to $C^2 \otimes C^d$ $(d\geq 3)$ and a concrete example in $C^2 \otimes C^8$ is given.
We review recent work on wormhole geometries in the context of modified theories of gravity, in particular, in f(R) gravity and with a nonminimal curvature-matter coupling, and in the recently proposed hybrid metric-Palatini theory. In principle, the normal matter threading the throat can be shown to satisfy the energy conditions and it is the higher order curvatures terms that sustain these wormhole geometries. We also briefly review the conversion of wormholes into time-machines, explore several of the time travel paradoxes and possible remedies to these intriguing side-effects in wormhole physics.
We study the DC spin current induced into an unbiased quantum spin Hall system through a two-point contacts setup with time dependent electron tunneling amplitudes. By means of two external gates, it is possible to drive a current with spin-preserving and spin-flipping contributions showing peculiar oscillations as a function of pumping frequency, electron-electron interaction and temperature. From its interference patterns as a function of the Fabry-Perot and Aharonov-Bohm phases, it is possible to extract information about the helical nature of the edge states and the intensity of the electron-electron interaction.
Analysing human gait has found considerable interest in recent computer vision research. So far, however, contributions to this topic exclusively dealt with the tasks of person identification or activity recognition. In this paper, we consider a different application for gait analysis and examine its use as a means of deducing the physical well-being of people. The proposed method is based on transforming the joint motion trajectories using wavelets to extract spatio-temporal features which are then fed as input to a vector quantiser; a self-organising map for classification of walking patterns of individuals with and without pathology. We show that our proposed algorithm is successful in extracting features that successfully discriminate between individuals with and without locomotion impairment.
We introduce Seshadri constants for line bundles in a relative setting. They generalize the classical Seshadri constants of line bundles on projective varieties and their extension to vector bundles studied by Beltrametti-Schneider-Sommese and Hacon. There are similarities to the classical theory. In particular, we give a Seshadri-type ampleness criterion, and we relate Seshadri constants to jet separation and to asymptotic base loci.   We give three applications of our new version of Seshadri constants. First, a celebrated result of Mori can be restated as saying that any Fano manifold whose tangent bundle has positive Seshadri constant at a point is isomorphic to a projective space. We conjecture that the Fano condition can be removed. Among other results in this direction, we prove the conjecture for surfaces. Second, we restate a classical conjecture on the nef cone of self-products of curves in terms of semistability of higher conormal sheaves, which we use to identify new nef classes on self-products of curves. Third, we prove that our Seshadri constants can be used to control separation of jets for direct images of pluricanonical bundles, in the spirit of a relative Fujita-type conjecture of Popa and Schnell.
We study aspects of the enumeration of permutation classes, sets of permutations closed downwards under the subpermutation order.   First, we consider monotone grid classes of permutations. We present procedures for calculating the generating function of any class whose matrix has dimensions $m \times 1$ for some $m$, and of acyclic and unicyclic classes of gridded permutations. We show that almost all large permutations in a grid class have the same shape, and determine this limit shape.   We prove that the growth rate of a grid class is given by the square of the spectral radius of an associated graph and deduce some facts relating to the set of grid class growth rates. In the process, we establish a new result concerning tours on graphs. We also prove a similar result relating the growth rate of a geometric grid class to the matching polynomial of a graph, and determine the effect of edge subdivision on the matching polynomial. We characterise the growth rates of geometric grid classes in terms of the spectral radii of trees.   We then investigate the set of growth rates of permutation classes and establish a new upper bound on the value above which every real number is the growth rate of some permutation class. In the process, we prove new results concerning expansions of real numbers in non-integer bases in which the digits are drawn from sets of allowed values.   Finally, we introduce a new enumeration technique, based on associating a graph with each permutation, and determine the generating functions for some previously unenumerated classes. We conclude by using this approach to provide an improved lower bound on the growth rate of the class of permutations avoiding the pattern $1324$. In the process, we prove that, asymptotically, patterns in {\L}ukasiewicz paths exhibit a concentrated Gaussian distribution.