ShantanuT01/DACTYL-Pretraining huggingface dataset:
The $G$-graph $\Gamma(G,S)$ is a graph from the group $G$ generated by $S\subseteq G$, where the vertices are the right cosets of the cyclic subgroups $\langle s \rangle, s\in S$ with $k$-edges between two distinct cosets if there is an intersection of $k$ elements. In this thesis, after presenting some important properties of $G$-graphs, we show how the $G$-graph depends on the generating set of the group. We give the $G$-graphs of the symmetric group, alternating group and the semi-dihedral group with respect to various generating sets. We give a characterisation of finite $G$-graphs; in the general case and a bipartite case. Using these characterisations, we give several classes of graphs that are $G$-graphs. For instance, we consider the Tur\'{a}n graphs, the platonic graphs and biregular graphs such as the Levi graphs of geometric configurations. We emphasis the structural properties of $G$-graphs and their relations to the group $G$ and the generating set $S$.   As preliminary results for further studies, we give the adjacency matrix and spectrum of various finite $G$-graphs. As an application, we compute the energy of these graphs. We also present some preliminary results on infinite $G$-graphs where we consider the $G$-graphs of the infinite group $SL_2(\mathbb{Z})$ and an infinite non-Abelian matrix group.
The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi level) and it finds application, for example, in the numerical renormalization group (NRG) approach to quantum impurity problems (Kondo model), where the continuum of the conduction band states needs to be reduced to a finite number of levels with good sampling near the Fermi level. The discretization schemes under discussion are required to reproduce the original function after averaging over different interleaved discretization meshes, thus systematic deviations which appear in the conventional logarithmic discretization are eliminated. An improved scheme is proposed in which the discretization-mesh points themselves are determined in an adaptive way; they are denser in the regions where the function has higher values. Such schemes help in reducing the residual numeric artefacts in NRG calculations in situations where the density of states approaches zero over extended intervals. A reference implementation of the solver for the differential equations which determine the full set of discretization coefficients is also described.
We derive the dynamics of magnetohydrodynamic waves in two-fluid partially ionized plasmas and to compare the results with those obtained under single-fluid description. Two-fluid magnetohydrodynamic equations are used, where ion-electron plasma and neutral particles are considered as separate fluids. Dispersion relations of linear magnetohydrodynamic waves are derived for simplest case of homogeneous medium. Frequencies and damping rates of waves are obtained for different parameters of background plasma. We found that two- and single-fluid descriptions give similar results for low frequency waves. However, the dynamics of MHD waves in two-fluid approach is significantly changed when the wave frequency becomes comparable or higher than ion-neutral collision frequency. Alfven and fast magneto-acoustic waves attain their maximum damping rate at particular frequencies (for example, the peak frequency equals 2.5 ion-neutral collision frequency for 50 % of neutral Hydrogen) in wave spectrum. The damping rates are reduced for higher frequency waves. The new mode of slow magneto-acoustic wave appears for higher frequency branch, which is connected to neutral hydrogen fluid. The single-fluid approach perfectly deals with slow processes in partially ionized plasmas, but fails for time-scales smaller than ion-neutral collision time. Therefore, two-fluid approximation should be used for the description of relatively fast processes. Some results of single-fluid description, for example the damping of high-frequency Alfven waves in the solar chromosphere due to ion-neutral collisions, should be revised in future.
A stellar population synthesis model, suitable for comparison with Giant Extragalactic HII Regions (GEHRs), is constructed incorporating the recent developments in modelling stellar evolution by Maeder and co-workers and stellar atmospheres by Kurucz. A number of quantities suitable for comparison with broad band data of GEHRs in visible and near infrared parts of the spectrum are synthesized in addition to the hydrogen and helium ionizing photon production rates at solar metallicities, for three scenarios of star formation --- (i) Instantaneous burst (IB) (ii) Continuous star formation (CSF) and (iii) Two bursts of star formation, with the older burst rich in red supergiants. For IB case, evolution of colors shows three distinct phases --- an initial steady blue phase, followed by a red bump (5--15~Myr) and another steady phase with colors intermediate to the earlier two phases. CSF colors asymptotically reach peak values at $\sim 10$~Myr, never reaching the reddest IB colors. Ionizing photon production rate falls off by an order of magnitude in 6~Myr for IB, where as it almost remains constant for CSF model. Two-burst models with burst separations $\sim 10$~Myr have properties of both IB and CSF, simultaneously producing the red IB colors and high ionizing photon rate, making such regions easily distinguishable using optical observations. Flat IMFs result in bluest colors when the massive stars are on the main sequence and reddest colors during the red supergiant phase of the evolving massive stars. Errors on the computed quantities due to the statistical uncertainties inherent in the process of star formation become negligible for cluster masses in excess of $10^5$\,\msun.
We use an optical cavity in the regime of intermediate coupling between atom and cavity mode to detect single moving atoms. Degenerate polarization modes allow excitation of the atoms in one mode and collection of spontaneous emission in the other, while keeping separate the two sources of light; we obtain a higher confidence and efficiency of detection by adding cavity-enhanced Faraday rotation. Both methods greatly benefit from coincidence detection of photons, attaining fidelities in excess of 99% in less than 1 microsecond. Detailed studies of the second-order intensity autocorrelation function of light from the signal mode reveal evidence of antibunched photon emissions and the dynamics of single-atom transits.
Tamm polaritons (TPs) are formed at the interface between two semi-infinite periodic dielectric structures (Bragg mirrors) or other reflectors. Contrary to usual surface polaritons, TPs exist inside the "light cone", even though their amplitude also decreases exponentially with the distance from the interface as it is characteristic of evanescent waves. They couple to elementary excitations in the materials or structures that form the interface, such as metal plasmons or semiconductor excitons. Here we discuss the formation of TPs in the far-infrared (FIR) spectral range, in the optical-phonon reststrahlen band of a polar semiconductor such as GaAs, with a Bragg reflector (BR) as the second mirror. Their dispersion relation and the frequency window for the TP existence are discussed for a GaAs-BR interface. Structures containing a gap between the two reflectors are also considered. Further investigation is performed on a structure containing a layer of graphene between the two reflectors.
In gamma-ray-bursts (GRB), ultra-relativistic blast waves are ejected into the circumburst medium. We analyse in unprecedented detail the deceleration of a self-similar Blandford-McKee blast wave from a Lorentz factor 25 to the nonrelativistic Sedov phase. Our goal is to determine the stability properties of its frontal shock. We carried out a grid-adaptive relativistic 2D hydro-simulation at extreme resolving power, following the GRB jet during the entire afterglow phase. We investigate the effect of the finite initial jet opening angle on the deceleration of the blast wave, and identify the growth of various instabilities throughout the coasting shock front. We find that during the relativistic phase, the blast wave is subject to pressure-ram pressure instabilities that ripple and fragment the frontal shock. These instabilities manifest themselves in the ultra-relativistic phase alone, remain in full agreement with causality arguments, and decay slowly to finally disappear in the near-Newtonian phase as the shell Lorentz factor drops below 3. From then on, the compression rate decreases to levels predicted to be stable by a linear analysis of the Sedov phase. Our simulations confirm previous findings that the shell also spreads laterally because a rarefaction wave slowly propagates to the jet axis, inducing a clear shell deformation from its initial spherical shape. The blast front becomes meridionally stratified, with decreasing speed from axis to jet edge.
Magneto-optical transitions between Landau levels can provide precise spectroscopic information on the electronic structure and excitation spectra of graphene, enabling probes of substrate and many-body effects. We calculate the magneto-optical conductivity of large-size graphene flakes using a tight-binding approach. Our method allows us to directly compare the magneto-optical response of an isolated graphene flake with one aligned on hexagonal boron nitride giving rise to a periodic superlattice potential. The substrate interaction induces band gaps away from the Dirac point. In the presence of a perpendicular magnetic field Landau-level like structures emerge from these zero-field band gaps. The energy dependence of these satellite structures is, however, not easily accessible by conventional probes of the density of states by varying the back-gate voltage. Here we propose the magneto-optical probing of the superlattice perturbed spectrum. Our simulation includes magneto-excitonic effects in first-order perturbation theory. Our approach yields a quantitative explanation of recently observed Landau-level dependent renormalizations of the Fermi velocity.
The Hall constant R_H is considered for the stripe structures. In order to explain the vanishing of R_H in LNSCO at x = 1/8, we use the relation of R_H to the Drude weight D as well as direct numerical calculation, to obtain results within the t-J model, where the stripes are imposed via a charge potential and a staggered magnetic field. The origin of R_H ~ 0 is related to a maximum in D and the minimal kinetic energy in stripes with a hole filling ~ 1/2. The same argument indicates on a possibility of R_H ~ 0 in the whole range of static stripes for x < 1/8.
We present the two first terms in the threshold expansion of Higgs production partonic cross-sections at hadron colliders for processes with three partons in the final state. These are contributions to the inclusive Higgs cross-section in gluon fusion at N3LO. We have developed a new technique for the expansion of the squared matrix-elements around the soft limit and for the reduction of the required phase-space integrals to only ten single-scale master integrals. We compute the master integrals building upon modern techniques for the integration of multidimensional integrals in dimensional regularization. Our results constitute an important step towards a systematic computation of the Higgs boson cross-section as an expansion around the threshold limit.
The aim of this paper is to construct certain closed embeddings of Grassmannian varieties, using tensor operations on vector bundles. These embeddings generalize Segre and Pl\"ucker morphisms.
We announce the discovery of SST-Lup3-1, a very low mass star close to the brown dwarf boundary in Lupus III with a circum(sub)stellar disk, discovered by the `Cores to Disks' Spitzer Legacy Program from mid-, near-infrared and optical data, with very conspicuous crystalline silicate features in its spectrum. It is the first of such objects with a full 5 to 35 micron spectrum taken with the IRS and it shows strong 10 and 20 micron silicate features with high feature to continuum ratios and clear crystalline features out to 33 micron. The dust in the disk upper layer has a crystalline silicate grain fraction between 15% and 33%, depending on the assumed dust continuum. The availability of the full Spitzer infrared spectrum allows an analysis of the dust composition as a function of temperature and position in the disk. The hot (~ 300 K) dust responsible for the 10 micron feature consists of a roughly equal mix of small (~ 0.1 micron) and large (~ 1.5 micron) grains, whereas the cold (~ 70 K) dust responsible for the longer wavelength silicate features contains primarily large grains (> 1 micron). Since the cold dust emission arises from deeper layers in the inner (< 3 AU) disk as well as from the surface layers of the outer (3-5 AU) disk, this provides direct evidence for combined grain growth and settling in the disk. The inferred crystalline mass fractions in the two components are comparable. Since only the inner 0.02 AU of the disk is warm enough to anneal the amorphous silicate grains, even the lowest fraction of 15% of crystalline material requires either very efficient mixing or other formation mechanisms.
In this paper we study the Chaplygin gas model as a candidate for inflation in the framework of the Randall Sundrum type-II braneworld model. We consider the original and generalized Chaplygin gas model in the presence of monomial potential. The inflationary spectrum perturbation parameters are reformulated and evaluated in the high-energy limit and we found that they depend on several parameters. We also showed that these perturbation parameters are widely compatible with the recent Planck data for a particular choice of the parameters space of the model. A suitable observational central value of $n_{s}\simeq $ $0.965$ is also obtained in the case of original and generalized Chaplygin gas.
The doping induced insulator-metal transition in $La_{1-x}Sr_{x}TiO_{3}$ is studied using the ab-initio LDA+DMFT method. Combining the LDA bandstructure for the actual, distorted structure found recently with multi-orbital DMFT to treat electronic correlations, we find: $(i)$ ferro-orbital order in the Mott insulating state without orbital degeneracy, $(ii)$ a continuous filling induced transition to the paramagnetic metal (PM) with $x$, and $(iii)$ excellent quantitative agreement with published photoemission data for the case of 6% doping. Our results imply that this system can be described as a Mott-Hubbard system without orbital (liquid) degeneracy.
Any exchangeable Markov processes on $[k]^{\mathbb{N}}$ with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded variation. Furthermore, any such process has a de Finetti-type description as a mixture of i.i.d. copies of time-inhomogeneous Markov processes on $[k]$. In the Feller case, these time-inhomogeneous Markov processes have a relatively simple structure; however, in the non-Feller case a greater variety of behaviors is possible since the transition law of the underlying Markov process on $[k]^{\zz{N}}$ can depend in a non-trivial way on the exchangeable $\sigma$-algebra of the process.
Transport properties of irradiated graphene (electrical conductivity and mobility) are numerically investigated using the real-space Kubo formalism. A micrometer-sized system consisting of millions of atoms with nanopores of various sizes and concentrations is described. Electrical conductivity and mobility as a function of carrier (hole) density are calculated to provide possible comparisons with experiments.
A procedure to define the BRST charge from the Noether one in extended phase space is given. It is outlined how this prescription can be applied to a Friedmann-Robertson-Walker space-time with a differential gauge condition and it allows us to reproduce the results of [19]. Then we discuss the cohomological classes associated with functions in extended phase space having ghost number one and we recover the frozen formalism for classical observables. Finally, we consider the quantization of BRST-closed states and we define a scalar product which implements the superHamiltonian constraint.
We study $p$-harmonic maps, $p$-harmonic morphisms, biharmonic maps, and quasiregular mappings into submanifolds of warped product Riemannian manifolds ${I}\times_f S^{m-1}(k)\, $ of an open interval and a complete simply-connecteded $(m-1)$-dimensional Riemannian manifold of constant sectional curvature $k$. We establish an existence theorem for $p$-harmonic maps and give a classification of complete stable minimal surfaces in certain three dimensional warped product Riemannian manifolds ${\bf R}\times_f S^{2}(k)\, ,$ building on our previous work. When $f \equiv\, $ Const. and $k=0$, we recapture a generalized Bernstein Theorem and hence the Classical Bernstein Theorem in $R^3$. We then extend the classification to parabolic stable minimal hypersurfaces in higher dimensions.
Underwater object detection technique is of great significance for various applications in underwater the scenes. However, class imbalance issue is still an unsolved bottleneck for current underwater object detection algorithms. It leads to large precision discrepancies among different classes that the dominant classes with more training data achieve higher detection precisions while the minority classes with fewer training data achieves much lower detection precisions. In this paper, we propose a novel class-wise style augmentation (CWSA) algorithm to generate a class-balanced underwater dataset Balance18 from the public contest underwater dataset URPC2018. CWSA is a new kind of data augmentation technique which augments the training data for the minority classes by generating various colors, textures and contrasts for the minority classes. Compare with previous data augmentation algorithms such flipping, cropping and rotations, CWSA is able to generate a class balanced underwater dataset with diverse color distortions and haze-effects.
SN 1961V, one of Zwicky's defining Type V supernovae (SN), was a peculiar transient in NGC 1058 that has variously been categorized as either a true core collapse SN leaving a black hole (BH) or neutron star (NS) remnant, or an eruption of a luminous blue variable (LBV) star. The former case is suggested by its association with a decaying non-thermal radio source, while the latter is suggested by its peculiar transient light curve and its low initial expansion velocities. The crucial difference is that the star survives a transient eruption but not an SN. All stars identified as possible survivors are significantly fainter, L_opt ~ 10^5 Lsun, than the L_opt ~ 3 10^6 Lsun progenitor star at optical wavelengths. While this can be explained by dust absorption in a shell of material ejected during the transient, the survivor must then be present as a L_IR ~ 3 10^6 Lsun mid-infrared source. Using archival Spitzer observations of the region, we show that such a luminous mid-IR source is not present. The brightest source of dust emission is only L_IR ~ 10^5 Lsun and does not correspond to the previously identified candidates for the surviving star. The dust cannot be made sufficiently distant and cold to avoid detection unless the ejection energy, mass and velocity scales are those of a SN or greater. We conclude that SN 1961V was a peculiar, but real, supernova. Its peculiarities are probably due to enhanced mass loss just prior to the SN, followed by the interactions of the SN blast wave with this ejecta. This adds to the evidence that there is a population of SN progenitors that have major mass loss episodes shortly before core collapse. The progenitor is a low metallicity, ~1/3 solar, high mass, M_ZAMS > 80 Msun, star, which means either that BH formation can be accompanied by an SN or that surprisingly high mass stars can form a NS.
We consider the signature rank of the units in real multiquadratic fields. When the three quadratic subfields of a real biquadratic field $K$ either (a) all have signature rank 2 (that is, fundamental units of norm $-1$), or (b) all have signature rank 1 (that is, have totally positive fundamental units), we provide explicit examples to show there exist infinitely many $K$ having each of the possible unit signature ranks (namely signature rank 3 or 4 in case (a) and signature rank 1,2, or 3 in case (b)). We make some additional remarks for higher rank real multiquadratic fields, in particular proving the rank of the totally positive units modulo squares in such extensions (hence also in the totally real subfield of cyclotomic fields) can be arbitrarily large.
Soit $E/\BmQ$ une courbe elliptique. Soit $D<0$ un discriminant fondamental suffisamment grand. Si $E(\bar{\BmQ})$ contient des points de Heegner de discriminant $D$, ces points engendrent un sous-groupe dont le rang est sup\'erieur \`a $\pabs{D}^{0.0009}$. Ce r\'esultat est en accord avec la conjecture de Birch et Swinnerton-Dyer.   ---   Let $E/\BmQ$ be an elliptic curve. Let $D<0$ be a sufficiently large fundamental discriminant. If $E(\bar{\BmQ})$ contains Heegner points of discriminant $D$, these points generate a subgroup of rank greater than $\pabs{D}^{0.0009}$. This result is in agreement with the conjecture of Birch and Swinnerton-Dyer.
If the Standard Model is embedded in a left-right symmetric gauge theory at the TeV scale, the pair production of light W-bosons in e^+e^- collisions, e^+e^- -> W^+W^-, will be affected by mixings in the gauge and neutrino sectors, and by the t-channel exchange of a heavy right-handed neutrino. The modification of the cross section by these new effects is studied for high--energy e^+e^- colliders.
Nuclear spirals are ubiquitous in galaxy centers. They exist not only in strong barred galaxies but also in galaxies without noticeable bars. We use high-resolution hydrodynamic simulations to study the properties of nuclear gas spirals driven by weak bar-like and oval potentials. The amplitude of the spirals increases toward the center by a geometric effect, readily developing into shocks at small radii even for very weak potentials. The shape of the spirals and shocks depends rather sensitively on the background shear. When shear is low, the nuclear spirals are loosely wound and the shocks are almost straight, resulting in large mass inflows toward the center. When shear is high, on the other hand, the spirals are tightly wound and the shocks are oblique, forming a circumnuclear disk through which gas flows inward at a relatively lower rate. The induced mass inflow rates are enough to power black hole accretion in various types of Seyfert galaxies as well as to drive supersonic turbulence at small radii.
We prove the non-uniqueness of weak solutions to 3D magnetohydrodynamic (MHD for short) equations. The constructed weak solutions do not conserve the magnetic helicity and can be close to any given smooth, divergence-free and mean-free velocity and magnetic fields. Furthermore, we prove that the weak solutions constructed by Beekie-Buckmaster-Vicol [2] for the ideal MHD can be obtained as a strong vanishing viscosity and resistivity limit of a sequence of weak solutions to MHD equations. This shows that, in contrast to the weak ideal limits, Taylor's conjecture does not hold along the vanishing viscosity and resistivity limits. Unlike in the context of the NSE [13] and the ideal MHD [2], new types of velocity and magnetic flows, featuring both the refined spatial and temporal intermittency, are constructed to respect the geometry of MHD and to control the strong viscosity and resistivity. Compatible algebraic structure is derived in the convex integration scheme. More interestingly, the new intermittent flows indeed enable us to prove the aforementioned results for the hyper-viscous and hyper-resistive MHD equations up to the sharp exponent $5/4$, which coincides exactly with the Lions exponent for 3D hyper-viscous NSE.