ShantanuT01/DACTYL-Pretraining huggingface dataset:
A number of recent works in E-print arXiv have addressed the foundation of gauge gravitation theory again. As is well known, differential geometry of fibre bundles provides the adequate mathematical formulation of classical field theory, including gauge theory on principal bundles. Gauge gravitation theory is formulated on the natural bundles over a world manifold whose structure group is reducible to the Lorentz group. It is the metric-affine gravitation theory where a metric (tetrad) gravitational field is a Higgs field.
SECCO is a survey devoted to the search for stellar counterparts within Ultra Compact High Velocity Clouds. In this contribution we present the results of a set of simulations aimed at the quantitative estimate of the sensitivity of the survey as a function of the total luminosity, size and distance of the stellar systems we are looking for. For all our synthetic galaxies we assumed an exponential surface brightness profile and an old and metal-poor population. The synthetic galaxies are simulated both on the images and on the photometric catalogs, taking into account all the observational effects. In the fields where the available observational material is of the top quality we detect synthetic galaxies as >=5 sigma over-densities of resolved stars down to muV,h=30.0 mag/arcsec2, for D<=1.5 Mpc, and down to muV,h~29.5 mag/arcsec2, for D<=2.5 Mpc. In the field with the worst observational material of the whole survey we detect synthetic galaxies with muV,h<=28.8 mag/arcsec2 out to D<=1.0 Mpc, and those with muV,h<=27.5 mag/arcsec2 out to D<=2.5 Mpc. Dwarf galaxies with MV=-10, with sizes in the range spanned by known dwarfs, are detected by visual inspection of the images up to D=5 Mpc independently of the image quality. In the best quality images dwarfs are partially resolved into stars up to D=3.0 Mpc, and completely unresolved at D=5 Mpc. As an independent test of the sensitivity of our images to low surface brightness galaxies we report on the detection of several dwarf spheroidal galaxies probably located in the Virgo cluster with MV<=-8.0 and muV,h<=26.8 mag/arcsec2. The nature of the previously discovered SECCO 1 stellar system, also likely located in the Virgo cluster, is re-discussed in comparison with these dwarfs. While specific for the SECCO survey, our study may also provide general guidelines for detection of faint stellar systems with 8m class telescopes.
This paper is concerned with highway traffic estimation using traffic sensing data, in a Lagrangian-based modeling framework. We consider the Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956) in Lagrangian-coordinates, and provide rigorous mathematical results regarding the equivalence of viscosity solutions to the Hamilton-Jacobi equations in Eulerian and Lagrangian coordinates. We derive closed-form solutions to the Lagrangian-based Hamilton-Jacobi equation using the Lax-Hopf formula (Daganzo, 2005; Aubin et al., 2008), and discuss issues of fusing traffic data of various types into the Lagrangian-based H-J equation. A numerical study of the Mobile Century field experiment (Herrera et al., 2009) demonstrates the unique modeling features and insights provided by the Lagrangian-based approach.
We present the analysis of 11 nights of V and I time-series observations of the globular cluster NGC 1904 (M 79). Using this we searched for variable stars in this cluster and attempted to refine the periods of known variables, making use of a time baseline spanning almost 8 years. We use our data to derive the metallicity and distance of NGC 1904. We used difference imaging to reduce our data to obtain high-precision light curves of variable stars. We then estimated the cluster parameters by performing a Fourier decomposition of the light curves of RR Lyrae stars for which a good period estimate was possible. We also derive an estimate for the age of the cluster by fitting theoretical isochrones to our colour-magnitude diagram (CMD). Out of 13 stars previously classified as variables, we confirm that 10 are bona fide variables. We cannot detect variability in one other within the precision of our data, while there are two which are saturated in our data frames, but we do not find sufficient evidence in the literature to confirm their variability. We also detect a new RR Lyrae variable, giving a total number of confirmed variable stars in NGC 1904 of 11. Using the Fourier parameters, we find a cluster metallicity [Fe/H]_ZW=-1.63 +- 0.14, or [Fe/H]_UVES=-1.57 \pm 0.18, and a distance of 13.3 +- 0.4 kpc (using RR0 variables) or 12.9 kpc (using the one RR1 variable in our sample for which Fourier decomposition was possible).
Freestanding graphene membranes were successfully functionalized with platinum nanoparticles (Pt NPs). High-resolution transmission electron microscopy revealed a homogeneous distribution of single-crystal Pt NPs that tend to exhibit a preferred orientation. Unexpectedly, the NPs were also found to be partially exposed to the vacuum with the top Pt surface raised above the graphene substrate, as deduced from atomic-scale scanning tunneling microscopy images and detailed molecular dynamics simulations. Local strain accumulation during the growth process is thought to be the origin of the NP self-organization. These findings are expected to shape future approaches in developing Pt NP catalysts for fuel cells as well as NP-functionalized graphene based high-performance electronics.
We report here the structure and dielectric studies on a new lead free (1-x)BaTiO3-xBi(Mg1/2Zr1/2)O3 solid solution to explore the morphotropic phase boundary. The powder x-ray diffraction studies on (1-x)BaTiO3-xBi(Mg1/2Zr1/2)O3 solid solution suggests that structure is tetragonal (P4mm) for the composition with x=0.05 and cubic for the composition with x=0.30 and 0.40. Morphotropic phase boundary is observed in the composition range 0.10<x<0.30, where phase coexistence is observed and composition dependence of room temperature permittivity shows a peak. High temperature dielectric measurement for the composition with x=0.20 exhibits diffuse phase transition having peak temperature around ~ 396 K at 10 kHz. The diffuseness parameter ({\gamma}) was obtained to be 1.68 for composition with x=0.20.
The High Altitude Water Cherenkov (HAWC) observatory is an array of large water Cherenkov detectors sensitive to gamma rays and hadronic cosmic rays in the energy band between 100 GeV and 100 TeV. The observatory will be used to measure high-energy protons and cosmic rays via detection of the energetic secondary particles reaching the ground when one of these particles interacts in the atmosphere above the detector. HAWC is under construction at a site 4100 meters above sea level on the northern slope of the volcano Sierra Negra, which is located in central Mexico at 19 degrees N latitude. It is scheduled for completion in 2014. In this paper we estimate the sensitivity of the HAWC instrument to point-like and extended sources of gamma rays. The source fluxes are modeled using both unbroken power laws and power laws with exponential cutoffs. HAWC, in one year, is sensitive to point sources with integral power-law spectra as low as 5x10^-13 cm^-2 sec^-1 above 2 TeV (approximately 50 mCrab) over 5 sr of the sky. This is a conservative estimate based on simple event parameters and is expected to improve as the data analysis techniques are refined. We discuss known TeV sources and the scientific contributions that HAWC can make to our understanding of particle acceleration in these sources.
Deuterium is the best indicator of the baryon density; however, only its present abundance is known (and only locally) and its chemical evolution is intertwined with that of $^3$He. Because galactic abundances are spatially heterogeneous, mean chemical-evolution models are not well suited for extrapolating the pre-solar D and $^3$He abundances to their primeval values. We introduce a new approach which explicitly addresses heterogeneity, and show that the decade-old big-bang nucleosynthesis concordance interval $\eta \approx (2 -8)\times 10^{-10}$ based on D and $^3$He is robust.
The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.
We extend the known classification of threefolds of general type that are complete intersections to various classes of non-complete intersections, and find other classes of polarised varieties, including Calabi-Yau threefolds with canonical singularities, that are not complete intersections. Our methods apply more generally to construct orbifolds described by equations in given Gorenstein formats.
In non-central heavy ion collisions, identical two particle Hanbury-Brown/Twiss (HBT) correlations C(K,q) depend on the azimuthal direction of the pair momentum K. We investigate the consequences for a harmonic analysis of the corresponding HBT radius parameters. Our discussion includes both, a model- independent analysis of these parameters in the Gaussian approximation, and the study of a class of hydrodynamical models which mimic essential geometrical and dynamical properties of peripheral heavy ion collisions. Also, we discuss the additional geometrical and dynamical information contained in the harmonic coefficients of these HBT radius parameters. The leading contribution of their first and second harmonics are found to satisfy simple constraints. This allows for a minimal, azimuthally sensitive parametrization of all first and second harmonic coefficients in terms of only two additional fit parameters. We determine to what extent these parameters can be extracted from experimental data despite finite multiplicity fluctuations and the resulting uncertainty in the reconstruction of the reaction plane.
We study the lamppost model, in which the X-ray source in accreting black-hole systems is located on the rotation axis close to the horizon. We point out a number of inconsistencies in the widely used lamppost model relxilllp, e.g., the neglect of the redshift of the photons emitted by the lamppost and directly observed. They appear to invalidate those model fitting results for which the source distances from the horizon are within several gravitational radii. Furthermore, if those results were correct, most of the photons produced in the lamppost would be trapped by the black hole, and the luminosity generated in the source as measured at infinity would be much larger than that observed. This appears to be in conflict with the observed smooth state transitions between the hard and soft states of X-ray binaries. The required increase of the accretion rate and the associated efficiency reduction present also a problem for AGNs. Then, those models imply the luminosity measured in the local frame to be much higher than that produced in the source and measured at infinity, due to the additional effects of time dilation and redshift, and the electron temperature to be higher significantly than that observed. We show that these conditions imply that the fitted sources would be out of the pair equilibrium. On the other hand, the above issues pose relatively minor problems for sources at large distances from the black hole, where relxilllp can still be used.
We investigate how each aspect of a multi-channel stellar feedback model drives the chemodynamical evolution of a low-mass, isolated dwarf galaxy using a suite of high-resolution simulations. Our model follows individual star particles sampled randomly from an adopted initial mass function, considering independently feedback from: supernovae; stellar radiation causing photoelectric heating of dust grains, ionization and associated heating, Lyman-Werner (LW) dissociation of H$_2$, and radiation pressure; and winds from massive main sequence (neglecting their energy input) and asymptotic giant branch (AGB) stars. Radiative transfer is done by ray tracing. We consider the effects each of these processes have on regulating the star formation rate, global properties, multi-phase interstellar medium (ISM), and driving of galactic winds. We follow individual metal species from distinct nucleosynthetic enrichment channels (AGB winds, massive star stellar winds, core collapse and Type Ia supernovae) and pay particular attention to how these feedback processes regulate metal mixing in the ISM, the metal content of outflows, and the stellar abundance patterns in our galaxy. We find that---for a low-metallicity, low-mass dwarf galaxy ---stellar radiation, particularly ionizing radiation and LW radiation, are important sources of stellar feedback whose effects dominate over photoelectric heating and HI radiation pressure. However, feedback is coupled non-linearly, and the inclusion or exclusion of each process produces non-negligible effects. We find strong variations with: the star formation history; the ejection fractions of metals, mass, and energy; and the distribution of elements from different nucleosynthetic sources in both the gas and stars.
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum memory loads, to encode the function values. Instead, we use a template quantum eigenvalue transformation circuit to convert a low cost block encoding of the sine function into the desired function. Our method uses only 4 ancilla qubits (3 if the approximating polynomial has definite parity), providing order-of-magnitude qubit count reductions compared to state-of-the-art approaches, while using a similar number of Toffoli gates if the function can be well represented by a polynomial or Fourier approximation. Like black-box methods, the complexity of our approach depends on the 'L2-norm filling-fraction' of the function. We demonstrate the efficiency of our method for preparing states commonly used in quantum algorithms, such as Gaussian and Kaiser window states.
The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles and random characteristic polynomials evaluated at 1 for matrices in the Circular and Circular Jacobi beta ensembles. We use the framework of mod-Gaussian convergence to provide quantitative estimates of their logarithmic behavior, as the size of the ensemble grows to infinity. We establish central limit theorems, Berry-Esseen bounds, moderate deviations and local limit theorems. Furthermore, we identify the scale at which the validity of the Gaussian approximation for the tails breaks. With the exception of the Gaussian ensemble, all the results are obtained for a continuous choice of the Dyson parameter, that is for general $\beta>0$. The proofs rely on explicit computations which are possible thanks to closed product formulas of the Laplace transforms.
A vertical resonant tunneling diode (RTD) based on the paramagnetic Zn1-x-yMnyCdxSe system has been fabricated with a pillar diameter down to ~ 6 micron. The diode exhibits high quality resonant tunneling characteristics through the electron sub-band of the quantum well at a temperature of 4.2K, where a clear phonon replica was observable in addition to the primary peak. Both peaks show a giant Zeeman splitting in an applied magnetic field. Employing a self-consistent real-time Green's function method, the current-voltage characteristic was simulated, showing good agreement with the measured result.
Determining the maximum number of edges under degree and matching number constraints have been solved for general graphs by Chv\'{a}tal and Hanson (1976), and by Balachandran and Khare (2009). It follows from the structure of those extremal graphs that deciding whether this maximum number decreases or not when restricted to claw-free graphs, to $C_4$-free graphs or to triangle-free graphs are separately interesting research questions. The first two cases being already settled, respectively by Dibek, Ekim and Heggernes (2017), and by Blair, Heggernes, Lima and D.Lokshtanov (2020). In this paper we focus on triangle-free graphs. We show that unlike most cases for claw-free graphs and $C_4$-free graphs, forbidding triangles from extremal graphs causes a strict decrease in the number of edges and adds to the hardness of the problem. We provide a formula giving the maximum number of edges in a triangle-free graph with degree at most $d$ and matching number at most $m$ for all cases where $d\geq m$, and for the cases where $d<m$ with either $d\leq 6$ or $Z(d)\leq m < 2d$ where $Z(d)$ is a function of $d$ which is roughly $5d/4$. We also provide an integer programming formulation for the remaining cases and as a result of further discussion on this formulation, we conjecture that our formula giving the size of triangle-free extremal graphs is also valid for these open cases.
Asteroseismology can provide joint constraints on masses and radii of individual stars. While this approach has been extensively tested for red giant branch (RGB) stars, it has been more difficult to test for helium core-burning red-clump (RC) giants because of the lack of fundamental calibrators. To provide independent mass estimates, we utilize a number of widely used horizontal-branch (HB) models in the literature, and derive photometric masses from a comparison with $griBVI_CJHK_s$ photometry. Our selected models disagree with each other on the predicted mass-luminosity-temperature relation. We adopt first-order corrections on colors and magnitudes to minimize the dispersion between different models by forcing models to match the observed location in the solar-metallicity cluster M67. Even for these calibrated models, however, the internal consistency between models deteriorates at higher metallicities, and photometric masses become smaller than asteroseismic masses, as seen from metal-rich field RC stars with Gaia parallaxes. Similarly, the average photometric mass for metal-rich NGC 6791 stars ranges from $0.7\ M_\odot$ to $1.1\ M_\odot$, depending on the specific set of models employed. An ensemble average of the photometric masses ($0.88\pm0.16\ M_\odot$) in NGC 6791 is marginally consistent with the asteroseismic mass ($1.16\pm0.04\ M_\odot$). There is a clear tension between the masses that one would predict from photometry for metal-rich field RC stars, asteroseismic masses, and those that would be expected from the ages of stars in the Galactic disk populations and canonical RGB mass loss. We conclude that standard RC models need to be re-examined in light of these powerful new data sets.
Rapid and low power computation of optical flow (OF) is potentially useful in robotics. The dynamic vision sensor (DVS) event camera produces quick and sparse output, and has high dynamic range, but conventional OF algorithms are frame-based and cannot be directly used with event-based cameras. Previous DVS OF methods do not work well with dense textured input and are designed for implementation in logic circuits. This paper proposes a new block-matching based DVS OF algorithm which is inspired by motion estimation methods used for MPEG video compression. The algorithm was implemented both in software and on FPGA. For each event, it computes the motion direction as one of 9 directions. The speed of the motion is set by the sample interval. Results show that the Average Angular Error can be improved by 30\% compared with previous methods. The OF can be calculated on FPGA with 50\,MHz clock in 0.2\,us per event (11 clock cycles), 20 times faster than a Java software implementation running on a desktop PC. Sample data is shown that the method works on scenes dominated by edges, sparse features, and dense texture.
We present the first 3D simulation of the last minutes of oxygen shell burning in an 18 solar mass supernova progenitor up to the onset of core collapse. A moving inner boundary is used to accurately model the contraction of the silicon and iron core according to a 1D stellar evolution model with a self-consistent treatment of core deleptonization and nuclear quasi-equilibrium. The simulation covers the full solid angle to allow the emergence of large-scale convective modes. Due to core contraction and the concomitant acceleration of nuclear burning, the convective Mach number increases to ~0.1 at collapse, and an l=2 mode emerges shortly before the end of the simulation. Aside from a growth of the oxygen shell from 0.51 to 0.56 solar masses due to entrainment from the carbon shell, the convective flow is reasonably well described by mixing length theory, and the dominant scales are compatible with estimates from linear stability analysis. We deduce that artificial changes in the physics, such as accelerated core contraction, can have precarious consequences for the state of convection at collapse. We argue that scaling laws for the convective velocities and eddy sizes furnish good estimates for the state of shell convection at collapse and develop a simple analytic theory for the impact of convective seed perturbations on shock revival in the ensuing supernova. We predict a reduction of the critical luminosity for explosion by 12--24% due to seed asphericities for our 3D progenitor model relative to the case without large seed perturbations.
Fix an integral Soddy sphere packing P. Let K be the set of all curvatures in P. A number n is called represented if n is in K, that is, if there is a sphere in P with curvature equal to n. A number n is called admissible if it is everywhere locally represented, meaning that n is in K(mod q) for all q. It is shown that every sufficiently large admissible number is represented.
The Higgs spectrum of the minimal composite Higgs model, based on the SO(5)/SO(4) coset, consists of a unique Higgs doublet whose phenomenology does not differ greatly from the Standard Model (SM). Nevertheless, extensions beyond this minimal coset structure exhibit a richer Higgs spectrum and therefore very different Higgs physics. We explore one of these extensions, the SO(6)/SO(5) model, whose Higgs spectrum contains a CP-odd singlet scalar, eta, in addition to the Higgs doublet. Due to the pseudo-Nambu-Goldstone nature of these Higgs bosons, their physical properties can be derived from symmetry considerations alone. We find that the mass of eta can be naturally light, opening up the possibility that the SM Higgs decays predominantly to the singlet, and therefore lowering the LEP bound on its mass to 86 GeV. We also show that eta can have interesting consequences in flavour-violating processes, as well as induce spontaneous CP-violation in the Higgs sector. The model can also have anomalies, giving rise to interactions between the SM gauge bosons and eta which, if measured at the LHC, would give quantitative information about the structure of the high energy theory.
We classify all quadratic homogeneous polynomial maps $H$ and Keller maps of the form $x + H$, for which $rk J H = 3$, over a field $K$ of arbitrary characteristic. In particular, we show that such a Keller map (up to a square part if $char K=2$) is a tame automorphism.