ShantanuT01/DACTYL-Pretraining huggingface dataset:
The purpose of this study is to carry out a thorough investigation of the changes in morphology of the red giant branch (RGB) of Galactic globular clusters (GGC) as a function of metallicity, in the V,I bands. To this aim, two key points are developed in the course of the analysis.   (a) Using our photometric V,I database for Galactic globular clusters (the largest homogeneous data sample to date; Rosenberg et al. 1999) we measure a complete set of metallicity indices, based on the morphology and position of the red-giant branch. In particular, we provide here the first calibration of the S, DV_(1.1) and DV_(1.4) indices in the (V-I,V) plane. We show that our indices are internally consistent, and we calibrate each index in terms of metallicity, both on the Zinn & West (1984) and the Carretta & Gratton (1997) scales. Our new calibrations of the (V-I)o,g, DV_(1.2), (V-I)_(-3.0) and (V-I)_(-3.5) indices are consistent with existing relations.   (b) Using a grid of selected RGB fiducial points, we define a function in the {(V-I)o,Mi,[Fe/H]} space which is able to reproduce the whole set of GGC giant branches in terms of a single parameter (the metallicity). As a first test, we show that the function is able to predict the correct trend of our observed indices with metallicity.   The usage of this function will improve the current determinations of metallicity and distances within the Local Group, since it allows to easily map [(V-I)o,Mi] coordinates into {[Fe/H],Mi} ones. To this aim the ``synthetic'' RGB distribution is generated both for the currently used Lee et al. (1990) distance scale, and for the most recent results on the RR Lyr distance scale.
Superpotentials (antisymmetric tensor densities) in Einstein-Gauss-Bonnet (EGB) gravity for arbitrary types of perturbations on arbitrary curved backgrounds are constructed. As a basis, the generalized conservation laws in the framework of an arbitrary D-dimensional metric theory, where conserved currents are expressed through divergences of superpotentials, are used. Such a derivation is exact (perturbations are not infinitesimal) and is approached, when a one solution (dynamical) is considered as a perturbed system with respect to another solution (background). Three known prescriptions are elaborated: these are the canonical N{\oe}ther theorem, the Belinfante symmetrization rule and the field-theoretical derivation. All the three approaches are presented in an unique way convenient for comparisons and a development. Exact expressions for the 01-component of the three types of the superpotentials are derived in the case, when an arbitrary static Schwarzschild-like solution in the EGB gravity is considered as a perturbed system with respect to a background of the same type. These formulae are used for calculating the mass of the Schwarzschild-anti-de Sitter black hole in the EGB gravity. As a background both the anti-de Sitter spacetime in arbitrary dimensions and a not maximally symmetric "mass gap" vacuum in 5 dimensions are considered. Problems and perspectives for a future development, including the Lovelock gravity, are discussed.
This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the origin. The already existent machinery of Wasserstein gradient flow is well posed for lambda-convex potential. In this case this property is lost, but it is proven that in the one dimensional case existence and uniqueness of the solution is still achieved.
We verify the Morrison--Kawamata conjecture for a certain class of rational threefolds, namely blowups of P^3 in the base locus of a net of quadrics with no reducible members. This seems to be the first verified case of the conjecture for klt Calabi--Yau pairs in dimension 3 with non-zero boundary divisor.
Using the topological flux insertion procedure, the ground-state degeneracy of an insulator on a periodic lattice with filling factor $\nu=p/q$ was found to be at least $q$-fold. Applying the same argument in a lattice with edges, we show that the degeneracy is modified by the additional edge density $\nu_{\mysw{E}}$ associated with the open boundaries. In particular, we demonstrate that these edge corrections may even make an insulator with integer bulk filling degenerate.
We study the diameter of the graph $G(w)$ of reduced words of an element $w$ in a Coxeter group $W$ whose edges correspond to applications of the Coxeter relations. We resolve conjectures of Reiner--Roichman and Dahlberg--Kim by proving a tight lower bound on this diameter when $W=S_n$ is the symmetric group and by characterizing the equality cases. We also give partial results in other classical types which illustrate the limits of current techniques.
Autograd-based software packages have recently renewed interest in image registration using homography and other geometric models by gradient descent and optimization, e.g., AirLab and DRMIME. In this work, we emphasize on using complex matrix exponential (CME) over real matrix exponential to compute transformation matrices. CME is theoretically more suitable and practically provides faster convergence as our experiments show. Further, we demonstrate that the use of an ordinary differential equation (ODE) as an optimizable dynamical system can adapt the transformation matrix more accurately to the multi-resolution Gaussian pyramid for image registration. Our experiments include four publicly available benchmark datasets, two of them 2D and the other two being 3D. Experiments demonstrate that our proposed method yields significantly better registration compared to a number of off-the-shelf, popular, state-of-the-art image registration toolboxes.
The microquasar GRS 1915+105 is known to exhibit a very variable X-ray emission on different time scales and patterns. We propose a system of two ordinary differential equations, adapted from the Hindmarsh-Rose model, with two dynamical variables x(t), y(t) and an input constant parameter J_0, to which we added a random white noise, whose solutions for the x(t) variable reproduce consistently the X-ray light curves of several variability classes as well as the development of low frequency Quasi-Periodic Oscillations (QPO). We show that changing only the value of J_0 the system moves from stable to unstable solutions and the resulting light curves reproduce those of the quiescent classes like phi and chi, the delta class and the spiking rho class. Moreover, we found that increasing the values of J_0 the system induces high frequency oscillations that evolve to QPO when it moves into another stable region. This system of differential equations gives then a unified view of the variability of GRS 1915+105 in term of transitions between stable and unstable states driven by a single input function J_0. We also present the results of a stability analysis of the equilibrium points and some considerations on the existence of periodic solutions.
In this article we compute the $q$th power values of the quadratic polynomials $f$ with negative squarefree discriminant such that $q$ is coprime to the class number of the splitting field of $f$ over $\mathbb{Q}$. The theory of unique factorisation and that of primitive divisors of integer sequences is used to deduce a bound on the values of $q$ which is small enough to allow the remaining cases to be easily checked. The results are used to determine all perfect power terms of certain polynomially generated integer sequences, including the Sylvester sequence.
Multiwavelength (MWL) observations of the blazar PKS 2155-304 during two weeks in July and August 2006, the period when two exceptional flares at very high energies (VHE, E>= 100 GeV) occurred, provide a detailed picture of the evolution of its emission. The complete data set from this campaign is presented, including observations in VHE gamma-rays (H.E.S.S.), X-rays (RXTE, CHANDRA, SWIFT XRT), optical (SWIFT UVOT, Bronberg, Watcher, ROTSE), and in the radio band (NRT, HartRAO, ATCA). Optical and radio light curves from 2004 to 2008 are compared to the available VHE data from this period, to put the 2006 campaign into the context of the long-term evolution of the source. The X-ray and VHE gamma-ray emission are correlated during the observed high state of the source, but show no direct connection with longer wavelengths. The long-term flux evolution in the optical and radio bands is found to be correlated and shows that the source reaches a high state at long wavelengths after the occurrence of the VHE flares. Spectral hardening is seen in the SWIFT XRT data. The nightly averaged high-energy spectra of the non-flaring nights can be reproduced by a stationary one-zone SSC model, with only small variations in the parameters. The spectral and flux evolution in the high-energy band during the night of the second VHE flare is modelled with multi-zone SSC models, which can provide relatively simple interpretations for the hour time-scale evolution of the high-energy emission, even for such a complex data set. For the first time in this type of source, a clear indication is found for a relation between high activity at high energies and a long-term increase in the low frequency fluxes.
Plasma with a temperature close to the chromospheric one is ejected in solar eruptions. Such plasma can occult some part of emission of compact sources in active regions as well as quiet solar areas. Absorption phenomena can be observed in the microwave range as the so-called 'negative bursts' and also in the He II 304 A line. The paper considers three eruptive events associated with rather powerful flares. Parameters of absorbing material of an eruption are estimated from multi-frequency records of a 'negative burst' in one event. 'Destruction' of an eruptive filament and its dispersion like a cloud over a huge area observed as a giant depression of the 304 A line emission has been revealed in a few events. One such event out of three ones known to us is considered in this paper. Another event is a possibility.
Using log convergent topoi, %In the derived category of filtered complexes of %sheaves of modules over %an isostructure we define two fundamental filtered complexes $(E_{conv},P)$ and $(C_{conv},P)$ for the log scheme obtained by a smooth scheme with a relative simple normal crossing divisor over a scheme of characteristic $p>0$. Using $(C_{conv},P)$, we prove the $p$-adic purity. As a corollary of it, we prove that $(E_{conv},P)$ and $(C_{conv},P)$ are canonically isomorphic. These filtered complexes produce the weight spectral sequence of the log convergent cohomology sheaf of the log scheme. We also give the comparison theorem between the projections of $(E_{conv},P)$ and $(C_{conv},P)$ to the derived category of bounded below filtered complexes of sheaves of modules in the Zariski topos of the log scheme and the weight-filtered isozariskian filtered complex $(E_{zar},P)_{Q}$ of the log scheme defined in our previous book.
The phenomenon of vacuum decay, i.e. electron-positron pair production due to the instability of the quantum electrodynamics vacuum in an external field, is a remarkable prediction of Dirac theory whose experimental observation is still lacking. Here a classic wave optics analogue of vacuum decay, based on light propagation in curved waveguide superlattices, is proposed. Our photonic analogue enables a simple and experimentally-accessible visualization in space of the process of pair production as break up of an initially negative-energy Gaussian wave packet, representing an electron in the Dirac sea, under the influence of an oscillating electric field.
The actual value of the oxygen abundance of the metal-poor planetary nebula PN G135.9+55.9 has frequently been debated in the literature. We wanted to clarify the situation by making an improved abundance determination based on a study that includes both new accurate observations and new models. We made observations using the method of integral field spectroscopy with the PMAS instrument, and also used ultraviolet observations that were measured with HST-STIS. In our interpretation of the reduced and calibrated spectrum we used for the first time, recent radiation hydrodynamic models, which were calculated with several setups of scaled values of mean Galactic disk planetary nebula metallicities. For evolved planetary nebulae, such as PN G135.9+55.9, it turns out that departures from thermal equilibrium can be significant, leading to much lower electron temperatures, hence weaker emission in collisionally excited lines. Based on our time-dependent hydrodynamic models and the observed emission line [OIII]5007, we found a very low oxygen content of about 1/80 of the mean Galactic disk value. This result is consistent with emission line measurements in the ultraviolet wavelength range. The C/O and Ne/O ratios are unusually high and similar to those of another halo object, BoBn-1.
A construction described by the current author (2017) uses two linear prototypes to build a compound graph with Ramsey properties inherited from the prototype graphs. The resulting graph is linear; and cyclic if both prototypes are cyclic. However, it will not generate a cyclic graph from a general linear prototype. Building on the properties of that construction, this paper proves that a general linear prototype graph of order m can be extended using a single new colour to produce a new cyclic graph of order $3m - 1$ which is triangle-free in the new colour, and has the same clique-number as the prototype in every other colour. The paper then describes a cyclic Ramsey $(3;3;4;4; 173)$-graph derived by constrained tree search, thus proving that $R(3;3;4;4) \ge 174$. Using a quadrupling construction to produce a further cyclic graph, it is shown that $R(3;4;5;5) \ge 693$. A compound cyclic Ramsey $(3;7;7; 622)$-graph derived by a limited manual search is then described. Further construction steps produce a $(8;8;8; 6131)$-graph, showing that $R_3(8) \ge 6132$. The paper concludes by showing that $R_4(7) \ge 81206$ and $R_4(9) \ge 630566$, implying corresponding improvements in the lower bounds for $R_5(7)$ and $R_5(9)$ and beyond. These results follow from the existence of cyclic prototype graphs derived by Mathon-Shearer 'doubling'.
We investigate the emission properties that a large-scale helical magnetic field imprints on AGN jet synchrotron radiation. A cylindrically symmetric relativistic jet and large-scale helical magnetic field produce significant asymmetrical features in transverse profiles of fractional linear polarization, intensity, Faraday rotation, and spectral index. The asymmetrical features of these transverse profiles correlate with one another in ways specified by the handedness of the helical field, the jet viewing angle (theta_ob), and the bulk Lorentz factor of the flow (Gamma). Thus, these correlations may be used to determine the structure of the magnetic field in the jet. In the case of radio galaxies (theta_ob~1 radian) and a subclass of blazars with particularly small viewing angles (theta_ob << 1/Gamma), we find an edge-brightened intensity profile that is similar to that observed in the radio galaxy M87. We present observations of the AGNs 3C 78 and NRAO 140 that display the type of transverse asymmetries that may be produced by large-scale helical magnetic fields.
We present a mean-field theoretical study on the effect of a single non-magnetic impurity in quasi-one dimensional unconventional density wave. The local scattering potential is treated within the self-consistent $T$-matrix approximation. The local density of states around the impurity shows the presence of resonant states in the vicinity of the Fermi level, much the same way as in $d$-density waves or unconventional superconductors. The assumption for different forward and backscattering, characteristic to quasi-one dimensional systems in general, leads to a resonance state that is double peaked in the pseudogap. The Friedel oscillations around the impurity are also explored in great detail, both within and beyond the density wave coherence length $\xi_0$. Beyond $\xi_0$ we find power law behavior as opposed to the exponential decay of conventional density wave. The entropy and specific heat contribution of the impurity are also calculated for arbitrary scattering strengths.
Previously we calculated the binding energies of the triton and hypertriton, using an SU_6 quark-model interaction derived from a resonating-group method of two baryon clusters. In contrast to the previous calculations employing the energy-dependent interaction kernel, we present new results using a renormalized interaction, which is now energy independent and reserves all the two-baryon data. The new binding energies are slightly smaller than the previous values. In particular the triton binding energy turns out to be 8.14 MeV with a charge-dependence correction of the two-nucleon force, 190 keV, being included. This indicates that about 350 keV is left for the energy which is to be accounted for by three-body forces.
The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections {\delta}c for the 0+\to0+ superallowed Fermi transitions. With these {\delta}c values, together with the available experimental ft values and the improved radiative corrections, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined. Even with the consideration of uncertainty, the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% for all the employed relativistic energy functionals.
Deep learning-based Multiple Object Tracking (MOT) currently relies on off-the-shelf detectors for tracking-by-detection.This results in deep models that are detector biased and evaluations that are detector influenced. To resolve this issue, we introduce Deep Motion Modeling Network (DMM-Net) that can estimate multiple objects' motion parameters to perform joint detection and association in an end-to-end manner. DMM-Net models object features over multiple frames and simultaneously infers object classes, visibility, and their motion parameters. These outputs are readily used to update the tracklets for efficient MOT. DMM-Net achieves PR-MOTA score of 12.80 @ 120+ fps for the popular UA-DETRAC challenge, which is better performance and orders of magnitude faster. We also contribute a synthetic large-scale public dataset Omni-MOT for vehicle tracking that provides precise ground-truth annotations to eliminate the detector influence in MOT evaluation. This 14M+ frames dataset is extendable with our public script (Code at Dataset <https://github.com/shijieS/OmniMOTDataset>, Dataset Recorder <https://github.com/shijieS/OMOTDRecorder>, Omni-MOT Source <https://github.com/shijieS/DMMN>). We demonstrate the suitability of Omni-MOT for deep learning with DMMNet and also make the source code of our network public.
We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in several models in applications, in particular in Mathematical Biology. We point out the role both of the nonlinearity and of geometric objects such as the Ricci curvature of the manifold, the second fundamental form of the boundary of the domain and its mean curvature. Special attention is devoted to surfaces of revolution and to spherically symmetric manifolds, where we prove refined results.
We present a theory describing the mechanism for the two-dimensional (2D) metal-insulator transition (MIT) in absence of disorder. A two-band Hubbard model is introduced, describing vacancy-interstitial pair excitations within the Wigner crystal. Kinetic energy gained by delocalizing such excitations is found to lead to an instability of the insulator to self-doping above a critical carrier concentration $n=n_c$, mapping the problem to a density-driven Mott MIT. This mechanism provides a natural microscopic picture of several puzzling experimental features, including the large effective mass enhancement, the large resistivity drop, and the large positive magneto-resistance on the metallic side of the transition. We also present a global phase diagram for the clean 2D electron gas as a function of $n$ and parallel magnetic field $B_{\shortparallel}$, which agrees well with experimental findings in ultra clean samples.
Various quantities of an attractively interacting fermion system at the unitary limit are determined by extrapolating Monte Carlo results of low-density neutron matter. Smooth extrapolation in terms of $1/(k_F a_0)$ ($k_F$ is the Fermi momentum, and $a_0$ is the ${}^1S_0$ scattering length) is found with the quantities examined: the ground-state energy, the pairing gap at $T \approx 0$, and the critical temperature of the normal-to-superfluid phase transition. We emphasize proximity of the physics of low-density neutron matter to that at the unitary limit. The extrapolated quantities are in a reasonable agreement with those in the literature.
We first construct generalized Riemann-normal coordinates by using autoparallels, instead of geodesics, in an arbitrary Riemann-Cartan spacetime. With the aid of generalized Riemann-normal coordinates and their associated orthonormal frames, we obtain a momentum-space representation of the Feynman propagator for scalar fields, which is a direct generalization of Bunch and Parker's works to curved spacetime with torsion. We further derive the proper-time representation in $n$ dimensional Riemann-Cartan spacetime from the momentum-space representation. It leads us to obtain the renormalization of one-loop effective Lagrangians of free scalar fields by using dimensional regularization. When torsion tensor vanishes, our resulting momentum-space representation returns to the standard Riemannian results.
Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no chance devices. Also the games have the finite descent property (every game terminates in a finite number of moves). The two players are usually called Left and Right. The games often break up into components and the players must choose one of the components in which to play. One main aim of CGT is to analyze the components individually (rather than analyzing the sum as a whole) then use this information to analyze the sum.   In this paper, the players move simultaneously in a combinatorial game. Three sums are considered which are defined by the termination rules: (i) one component does not have a simultaneous move; (ii) no component has a simultaneous move; (iii) one player has no move in any component. These are combined with a winning convention which is either: (i) based on which player has moves remaining; or (ii) the greatest score. In each combination, we show that equality of games induces an equivalence relation and the equivalence classes are partially ordered. Also, where possible, given games $A$ and $B$, we give checks to determine if Left prefers to replace $A$ by $B$ in a sum.
We address the problem of Dirac fermions graphene quantum well and we focus on the low energy approximation for the Hamiltonian of the system where the former can be described by a Dirac-like Hamiltonian. Interesting relations are obtained and used to discuss the influence of the spin-orbit coupling, which induces an effective mass-like term, on the transport properties of Single-layer graphene quantum well. It's found that the reflection probability of incident electrons is sensitive to the effective mass-like term. This can be explained by the dependence of R on the incident electrons direction and their energies. Notably, we found that the reflection probability for massive fermions with a very small angle, i.e. the wave-vector along the transport direction is zero in the GQW, can be greatly suppressed.