ShantanuT01/DACTYL-Pretraining huggingface dataset:
Any second order homogeneous linear ordinary differential equation can be transformed into a first order non-linear Riccati equation. We argue that the Riccati form of the linearized fluctuation equations that determine the holographic 2-point functions simplifies considerably the numerical computation of such 2-point functions and of the corresponding transport coefficients by computing directly the response functions, eliminating the arbitrary source from the start. Moreover, it provides a neat criterion for the infrared regularity of the fluctuations. In particular, it is shown that the infrared regularity conditions for scalar and tensor fluctuations coincide, and hence they are either both regular or both singular. We demonstrate our numerical recipe based on the Riccati equations by computing the holographic 2-point functions for the stress tensor and a scalar operator in a number of asymptotically anti de Sitter backgrounds of bottom up scalar-gravity models. Analytical results are obtained for the 2-point function of the transverse traceless part of the stress tensor in two confining geometries, including a geometry that belongs to the class of IHQCD. We find that in this background the spin-2 spectrum is linear and, as expected, the position space 2-point function decays exponentially at large distances at a rate proportional to the confinement scale.
We performed a detailed analysis of the use of [C/N] measured in red giant branch stars between the completion of the first dredge up and the red giant branch bump ([C/N]_{FDU}) as age indicator. [C/N]_{FDU} cannot give accurate ages for individual stars, but may provide a general chronology for the formation of composite populations and add constraints to analyses of red giants from surface gravity-effective temperature diagrams. We provide a theoretical calibration of [C/N]_{FDU} in terms of total metallicity [M/H] and age, for ages greater than 1 Gyr, which we tested against variations in the initial heavy element distribution (scaled-solar vs alpha-enhanced), efficiency of overshooting from MS convective cores and from the convective envelopes, variations in the initial He abundance and in the mixing length parameter. Our calibration is compared with a small sample of available measurements of [C/N]_{FDU} in star clusters and halo field stars, which at least qualitatively confirm the overall trend of the predicted [C/N]_{FDU} with age and [M/H]. The use of [C/N]_{FDU}-[M/H]-age relations obtained from independent sets of stellar evolution calculations cause age differences (for a given [C/N]_{FDU} and [M/H] pair) up to about 2~Gyr. More accurate spectroscopic measurements of [C/N]_{FDU} in star clusters with well-established ages and metallicities are required to better test theoretical calibrations of this age indicator.
A giant asymmetry in the magnetoresistance was revealed in high-mobility, two-dimensional electron gas on a cylindrical surface. The longitudinal resistance along the magnetic-field gradient impressed by the surface curvature was found to vanish if measured along one of the edges of the curved Hall bar. If the external magnetic field is reversed, then the longitudinal resistance vanishes at the opposite edge of the Hall bar. This asymmetry is analyzed quantitatively in terms of the Landauer-Buettiker formalism.
A Mathematica implementation of the program LERG-I is presented that performs the reduction of tensor integrals, encountered in one-loop Feynman diagram calculations, to scalar integrals. The program was originally coded in REDUCE and in that incarnation was applied to a number of problems of physical interest.
Six degrees-of-freedom (6-DoF) video provides telepresence by enabling users to move around in the captured scene with a wide field of regard. Compared to methods requiring sophisticated camera setups, the image-based rendering method based on photogrammetry can work with images captured with any poses, which is more suitable for casual users. However, existing image-based rendering methods are based on perspective images. When used to reconstruct 6-DoF views, it often requires capturing hundreds of images, making data capture a tedious and time-consuming process. In contrast to traditional perspective images, 360{\deg} images capture the entire surrounding view in a single shot, thus, providing a faster capturing process for 6-DoF view reconstruction. This paper presents a novel method to provide 6-DoF experiences over a wide area using an unstructured collection of 360{\deg} panoramas captured by a conventional 360{\deg} camera. Our method consists of 360{\deg} data capturing, novel depth estimation to produce a high-quality spherical depth panorama, and high-fidelity free-viewpoint generation. We compared our method against state-of-the-art methods, using data captured in various environments. Our method shows better visual quality and robustness in the tested scenes.
We analyze ~600 ks data from the X-ray observatory Rossi X-ray Timing Explorer of the neutron star low mass X-ray binary and atoll source 4U 1636-53. These observations span almost three years, from April 1996 to February 1999. The color-color and hardness-intensity diagrams show significant secular shifts of the atoll track, similar to what is observed for some Z sources. These are most evident in the hardness-intensity diagram, where shifts in intensity up to 20% are observed. We find that the intensity shifts in the hardness-intensity diagram are responsible for the parallel tracks observed in the kilohertz quasi periodic oscillations frequency vs. intensity diagram. While the parallel tracks in the frequency vs. color plane partially overlap, systematic long term shifts are still evident. We also study the broad band power spectra of 4U 1636-53 as a function of the source position Sa along the track in the color-color diagram. These power spectra are all characteristic of the lower and upper banana state in atoll sources, showing very low frequency noise, band limited noise, and sometimes one or two kHz QPOs. We find that the very low frequency noise in some intervals is not well described by a power law because of an excess of power between 20 and 30 mHz, which can be fitted by a Lorentzian. Also, the characteristic frequency of the band limited noise shows a trend to decrease with increasing Sa at high Sa values.
The chromatic number of the plane is the chromatic number of the uncountably infinite graph that has as its vertices the points of the plane and has an edge between two points if their distance is 1. This chromatic number is denoted $\chi(\mathcal{R}^2)$. The problem was introduced in 1950, and shortly thereafter it was proved that $4\le \chi(\mathcal{R}^2)\le 7$. These bounds are both easy to prove, but after more than 60 years they are still the best known. In this paper, we investigate $\chi_f(\mathcal{R}^2)$, the fractional chromatic number of the plane. The previous best bounds (rounded to five decimal places) were $3.5556 \le \chi_f(\mathcal{R}^2)\le 4.3599$. Here we improve the lower bound to $76/21\approx3.6190$.
The Finslerian post-Lorentzian kinematic transformations can explicitly be obtained under uni-directional breakdown of spatial isotropy, provided that the requirement that the relativistic unit hypersurface (indicatrix or mass shell) be a space of constant negative curvature is still fulfilled. The method consists in evaluating respective Finslerian tetrads and then treating them as the bases of inertial reference frames. The Transport Synchronization has rigorously been proven, which opens up the ways proper to favour the concept of one-way light velocity. Transition to the Hamiltonian treatment is straightforward, so that the Finslerian transformation laws for momenta and frequences, as well as due Finslerian corrections to Doppler effect, become clear. An important common feature of the ordinary pseudo-Euclidean theory of special relativity and of the Finslerian relativistic approach under study is that they both endeavour to establish a universal prescription for applying the theory to systems in differing states of motion.
We investigate certain families of meromorphic Siegel modular functions on which Galois groups act in a natural way. By using Shimura's reciprocity law we construct some algebraic numbers in the ray class fields of CM-fields in terms of special values of functions in these Siegel families.
We determine the Galois representations inside the $l$-adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to arbitrary levels at $p$, and confirm the expected description of the cohomology due to Langlands and Kottwitz.
Using the MegaCam imager on the Canada-France-Hawaii Telescope, we have resolved individual stars in the outskirts of the nearby large spiral galaxy M81 (NGC 3031) well below the tip of the red giant branch of metal-poor stellar populations over 60 kpc * 58 kpc. In this paper, we report the discovery of new young stellar systems in the outskirts of M81. The most prominent feature is a chain of clumps of young stars distributed along the extended southern HI tidal arm connecting M 81 and NGC 3077. The colour-magnitude diagrams of these stellar systems show plumes of bright main sequence stars and red supergiant stars, indicating extended events of star formation. The main sequence turn-offs of the youngest stars in the systems are consistent with ages of ~40 Myr. The newly reported stellar systems show strong similarities with other known young stellar systems in the debris field around M81, with their properties best explained by these systems being of tidal origin.
Ebeling and Ploog \cite{EbelingPloog} studied a duality of bimodular singularities which is part of the Berglund--H$\ddot{\textnormal{u}}$bsch mirror symmetry. Mase and Ueda \cite{MU} showed that this duality leads to a polytope mirror symmetry of families of $K3$ surfaces. We discuss in this article how this symmetry extends to a symmetry between lattices.
Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter" spaces is treated in an elementary way, using visualizable models. Among the objects discussed are black holes, spaces with multiple black holes, their horizon structure, closed universes, and the topologies that are possible.
We present the Fundamental Plane (FP) in the z = 0.28 cluster of galaxies RX J0142.0+2131. There is no evidence for a difference in the slope of the FP when compared with the Coma cluster, although the internal scatter is larger. On average, stellar populations in RX J0142.0+2131 have rest-frame V-band mass-to-light ratios (M/L_V) 0.29+-0.03 dex lower than in Coma. This is significantly lower than expected for a passively-evolving cluster formed at z_f=2. Lenticular galaxies have lower average M/L_V and a distribution of M/L_V with larger scatter than ellipticals. Lower mass-to-light ratios are not due to recent star formation: our previous spectroscopic observations of RX J0142.0+2131 E/S0 galaxies showed no evidence for significant star-formation within the past ~4 Gyr. However, cluster members have enhanced alpha-element abundance ratios, which may act to decrease M/L_V. The increased scatter in the RX J0142.0+2131 FP reflects a large scatter in M/L_V implying that galaxies have undergone bursts of star formation over a range of epochs. The seven easternmost cluster galaxies, including the second brightest member, have M/L_V consistent with passive evolution and z_f = 2. We speculate that RX J0142.0+2131 is a cluster-cluster merger where the galaxies to the east are yet to fall into the main cluster body or have not experienced star formation as a result of the merger.
In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently" asymmetric initial condition where the number of possible choices for each individual is S=2 and $\Gamma<+\infty$. An upper bound for the asymptotic behavior, as the number of agents grows to infinity, of the waiting time for reaching the stationary state is then obtained.
A persistent kink in the pressure dependence of the \hidden order" (HO) transition temperature of URu2-xRexSi2 is observed at a critical pressure Pc=15 kbar for 0 < x < 0.08. In URu2Si2, the kink at Pc is accompanied by the destruction of superconductivity; a change in the magnitude of a spin excitation gap, determined from electrical resistivity measurements; and a complete gapping of a portion of the Fermi surface (FS), inferred from a change in scattering and the competition between the HO state and superconductivity for FS fraction.
We use new HST images of nine Green Pea Galaxies (GPGs) to study their resolved structure and color. The choice of filters, F555W and F850LP, together with the redshift of the galaxies ($z\sim 0.25$), minimizes the contribution of the nebular [O\thinspace{\sc iii}] and H$\alpha$ emission lines to the broad-band images. While these galaxies are typically very blue in color, our analysis reveals that it is only the dominant stellar clusters that are blue. Each GPG does clearly show the presence of at least one bright and compact star-forming region, but these are invariably superimposed on a more extended and lower surface brightness emission. Moreover, the colors of the star forming regions are on average bluer than those of the diffuse emission, reaching up to 0.6 magnitudes bluer. Assuming that the diffuse and compact components have constant and single burst Star Formation Histories, respectively, the observed colors imply that the diffuse components (possibly the host galaxy of the star-formation episode) have, on average, old stellar ages ($>1$Gyr), while the star-clusters are younger than 500Myrs. We also discuss the possibility that the diffuse red emission is due to a varying relative contribution of nebular continuum, rather than a different stellar population. With the available data, however, it is not possible to distinguish between these two interpretations. A substantial presence of old stars would indicate that the mechanisms that allow large escape fractions in these local galaxies may be different from those at play during the reionization epoch.
We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its \'etale and local parts. Pierre Deligne pointed out an error in the first version of this article. We profoundly thank him, in particular for sending us his enlightning example reproduced in Remark 2.4 2).
We demonstrate, for the first time, successful S-matrix to potential inversion for spin one projectiles with non-diagonal $S^j_{ll'}$ yielding a $T_{\rm R}$ interaction. The method is a generalization of the iterative-perturbative, IP, method. We present a test case indicating the degree of uniqueness of the potential. The method is adapted, using established procedures, into direct observable to potential inversion, fitting $\sigma$, ${\rm i}T_{11}$, $T_{20}$, $T_{21}$ and $T_{22}$ for d + alpha scattering over a range of energies near 10 MeV. The $T_{\rm R}$ interaction which we find is very different from that proposed elsewhere, both real and imaginary parts being very different for odd and even parity channels.
We investigate up to the fourth order normalized factorial moments of free-propagating and pulsed single photons displaced in phase space in a phase-averaged manner. Due to their loss independence, these moments offer expedient methods for quantum optical state characterization. We examine quantum features of the prepared displaced states, retrieve information on their photon-number content and study the reliability of the state reconstruction method used.
We develop a framework to apply tropical and nonarchimedean analytic techniques to multiplication maps on linear series and study degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a tropical criterion for a curve over a valued field to be Gieseker-Petri general.
Very massive stars are thought to be formed in the early Universe because of a lack of cooling process by heavy elements, and might have been responsible for the later evolution of the Universe. We had an interest in vibrational stability of their evolution and carried out the linear nonadiabatic analysis of radial and nonradial oscillations for population III very massive main-sequence stars with $500-3000M_{\sun}$. We found that only the radial fundamental mode becomes unstable due to the $\varepsilon$-mechanism for these stars. The instability appears just after the CNO cycle is activated and the nuclear energy generation rate becomes large enough to stop the pre--main-sequence contraction, and continues during the early stage of the core hydrogen burning. Besides, we roughly estimated amount of mass loss due to the instability to know its significance.
We show that the recently discovered binary 2M05215658+4359220 (2M0521), comprised of a giant star (GS) orbiting a suspected black hole (BH) in a ~80 day orbit, may be instrumental in shedding light on uncertain BH-formation physics and can be a test case for studying wind accretion models. Using binary population synthesis with a realistic prescription for the star formation history and metallicity evolution of the Milky Way, we analyze the evolution of binaries containing compact objects (COs) in orbit around GSs with properties similar to 2M0521. We find ~100-1000 CO-GS binaries in the Milky Way observable by Gaia, and 0-12 BH-GS and 0-1 neutron star-GS binaries in the Milky Way with properties similar to 2M0521. We find that all CO-GSs with Porb<5 yr, including 2M0521, go through a common envelope (CE) and hence form a class of higher mass analogs to white dwarf post-CE binaries. We further show how the component masses of 2M0521-like binaries depend strongly on the supernova-engine model we adopt. Thus, an improved measurement of the orbit of 2M0521, imminent with Gaia's third data release, will strongly constrain its component masses and as a result inform supernova-engine models widely used in binary population synthesis studies. These results have widespread implications for the origins and properties of CO binaries, especially those detectable by LIGO and LISA. Finally, we show that the reported X-ray non-detection of 2M0521 is a challenge for wind accretion theory, making 2M0521-like CO-GS binaries a prime target for further study with accretion models.
We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra to that of the all-ones hypermatrix. Several of the ingredients along a possible path to this conjecture are established, and may be of independent interest in spectral hypergraph/hypermatrix theory. In particular, we provide a bound on the spectral radius of the symmetric Bernoulli hyperensemble, and show that the spectrum of the complete \(k\)-uniform hypergraph for \(k=2,3\) is close to that of an appropriately scaled all-ones hypermatrix.
We investigate the energy spectrum of single layer black phosphorene nanoribbons (BPN) by means of a low-energy expansion of a recently proposed tight-binding model that describes electron and hole bands close to the Fermi energy level. Using the continuum approach, we propose boundary conditions based on sublattice symmetries for BPN with zigzag and armchair edges and show that our results for the energy spectra exhibit good agreement with those obtained by using the five-parameter tight-binding model. We also explore the behaviour of the energy gap versus the nanoribbon width $W$. Our findings demonstrate that band gap of armchair BPNs scale as $1/W^2$, while zigzag BPNs exhibit a $1/W$ tendency. We analyse the different possible combinations of the zigzag edges that result two-fold degenerate and non-degenerate edge states. Furthermore, we obtain expressions for the wave functions and discuss the limit of validity of such analytical model.
Consider a set of continuous maps from the interval $[0,1]$ to a domain in ${\mathbb R}^d$. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV functions) on the Wiener space and the theory of Dirichlet forms, we can discuss the existence of the surface measure and the Skorokhod representation of the reflecting Ornstein-Uhlenbeck process associated with the canonical Dirichlet form on this set.
Context: Mass loss from red giants in old globular clusters affects the horizontal branch (HB) morphology and post-HB stellar evolution including the production of ultraviolet-bright stars, dredge up of nucleosynthesis products and replenishment of the intra-cluster medium. Studies of mass loss in globular clusters also allows one to investigate the metallicity dependence of the mass loss from cool, low-mass stars down to very low metallicities.   Aims: We present an analysis of new VLT/UVES spectra of 47 red giants in the Galactic globular clusters 47 Tuc (NGC 104), NGC 362, omega Cen (NGC 5139), NGC 6388, M54 (NGC 6715) and M15 (NGC 7078). The spectra cover the wavelength region 6100-9900A at a resolving power of R = 110,000. Some of these stars are known to exhibit mid-infrared excess emission indicative of circumstellar dust. Our aim is to detect signatures of mass loss, identify the mechanism(s) responsible for such outflows, and measure the mass-loss rates.   Methods: We determine for each star its effective temperature, luminosity, radius and escape velocity. We analyse the H-alpha and near-infrared calcium triplet lines for evidence of outflows, pulsation and chromospheric activity, and present a simple model for estimating mass-loss rates from the H-alpha line profile. We compare our results with a variety of other, independent methods.   Results: We argue that a chromosphere persists in Galactic globular cluster giants and controls the mass-loss rate to late-K/early-M spectral types, where pulsation becomes strong enough to drive shock waves at luminosities above the RGB tip. This transition may be metallicity-dependent. We find mass-loss rates of ~10^-7 to 10^-5 solar masses per year, largely independent of metallicity.
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.
We study the value of unique games as a graph-theoretic parameter. This is obtained by labeling edges with permutations. We describe the classical value of a game as well as give a necessary and sufficient condition for the existence of an optimal assignment based on a generalisation of permutation graphs and graph bundles. In considering some special cases, we relate XOR games to EDGE BIPARTIZATION, and define an edge-labeling with permutations from Latin squares.