ShantanuT01/DACTYL-Pretraining huggingface dataset:
The purpose of this paper is to discuss the various types of physical universe which could exist according to modern mathematical physics. The paper begins with an introduction that approaches the question from the viewpoint of ontic structural realism. Section 2 takes the case of the 'multiverse' of spatially homogeneous universes, and analyses the famous Collins-Hawking argument, which purports to show that our own universe is a very special member of this collection. Section 3 considers the multiverse of all solutions to the Einstein field equations, and continues the discussion of whether the notions of special and typical can be defined within such a collection.
Undoped diamond, a remarkable bulk electrical insulator, exhibits a high surface conductivity in air when the surface is hydrogen-terminated. Although theoretical models have claimed that a two-dimensional hole gas is established as a result of surface energy band bending, no definitive experimental demonstration has been reported so far. Here, we prove the two-dimensional character of the surface conductivity by low temperature characterization of diamond in-plane gated field-effect transistors that enable the lateral confinement of the transistor's drain-source channel to nanometer dimensions. In these devices, we observe Coulomb blockade effects of multiple quantum islands varying in size with the gate voltage. The charging energy and thus the size of these zero-dimensional islands exhibits a gate voltage dependence which is the direct result of the two-dimensional character of the conductive channel formed at hydrogen-terminated diamond surfaces.
We present a new, publicly available, set of Los Alamos OPLIB opacity tables for the elements hydrogen through zinc. Our tables are computed using the Los Alamos ATOMIC opacity and plasma modeling code, and make use of atomic structure calculations that use fine-structure detail for all the elements considered. Our equation-of-state (EOS) model, known as ChemEOS, is based on the minimization of free energy in a chemical picture and appears to be a reasonable and robust approach to determining atomic state populations over a wide range of temperatures and densities. In this paper we discuss in detail the calculations that we have performed for the 30 elements considered, and present some comparisons of our monochromatic opacities with measurements and other opacity codes. We also use our new opacity tables in solar modeling calculations and compare and contrast such modeling with previous work.
It is generally acknowledged that the mass loss of Asymptotic Giant Branch (AGB) stars undergoes variations on different time scales. We constructed models for the dust envelopes for a sample of AGB stars to assess whether mass-loss variations influence the spectral energy distribution (SED). To constrain the variability, extra observations at millimetre wavelengths (1.2 mm) were acquired. From the analysis of the dust models, two indications for the presence of mass-loss variations can be found, being (1) a dust temperature at the inner boundary of the dust envelope that is far below the dust condensation temperature and (2) an altered density distribution with respect to rho(r) \propto r^{-2} resulting from a constant mass-loss rate. For 5 out of the 18 studied sources a two-component model of the envelope is required, consisting of an inner region with a constant mass-loss rate and an outer region with a less steep density distribution. For one source an outer region with a steeper density distribution was found. Moreover, in a search for time variability in our data set at 1.2 mm, we found that WX Psc shows a large relative time variation of 34% which might partially be caused by variable molecular line emission.
At present, there are theoretical models of radio pulsar evolution which predict both the alignment, i.e., evolution of inclination angle $\chi$ between magnetic and rotational axes to $0^{\circ}$, and its counter-alignment, i.e., evolution to $90^{\circ}$. At the same time, both models well describe the pulsar distribution on $P$-$\dot P$ diagram. For this reason, up to now it was impossible to determine the braking mechanisms since it was rather difficult to estimate inclination angle evolution on the basis of observation. In this paper we demonstrate that statistics of interpulse pulsars can give us the key to solve alignment/counter-alignment problem as the number of interpulse pulsars (both, having $\chi \sim 0^{\circ}$ and $\chi \sim 90^{\circ}$) drastically depends on evolution of inclination angle.
We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we deduce the uniqueness of the ergodic functions.
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
{We combine the results of our earlier study of the UV characteristics of 18 classical novae (CNe) with data from the literature and with the recent precise distance determinations from the Gaia satellite to investigate the statistical properties of old novae. All final parameters for the sample include a detailed treatment of the errors and their propagation. The physical properties reported here include the absolute magnitudes at maximum and minimum, a new maximum magnitude versus rate of decline (MMRD) relation, and the inclination-corrected 1100--6000-\AA\ accretion disk luminosity. Most importantly, these data have allowed us to derive a homogenous set of accretion rates in quiescence for the 18 novae.   All novae in the sample were super-Eddington during outburst, with an average absolute magnitude at maximum of $-7.5\pm1.0$. The average absolute magnitude at minimum corrected for inclination is $3.9\pm1.0$. The median mass accretion rate is $\log\dot{M}_{1M\odot}=-8.52$ (using $1M\odot$ as WD mass for all novae) or $\log\dot{M}_{M_{WD}}=-8.48$ (using the individual WD masses). These values are lower than those assumed in studies of CNe evolution and appear to attenuate the need for a hibernation hypothesis to interpret the nova phenomenon.   We identified a number of correlations among the physical parameters of the quiescent and eruptive phases, some already known but others new and even surprising. Several quantities correlate with the speed class $t_3$ including, unexpectedly, the mass accretion rate ($\dot{M)}$. This rate correlates also with the absolute magnitude at minimum corrected for inclination, and with the outburst amplitude, providing new and simple ways to estimate $\dot{M}$ through its functional dependence on (more) easily observed quantities. There is no correlation between $\dot{M}$ and the orbital period.}
We study long-distance effects in rare exclusive semileptonic decays B -> (K, K*) (l+ l-, nu bar{nu}) and analyze dilepton spectra and asymmetries within the framework of the Standard Model. The form factors, describing the meson transition amplitudes of the effective Hamiltonian are calculated within the lattice-constrained dispersion quark model: the form factors are given by dispersion representations through the wave functions of the initial and final mesons, and these wave functions are chosen such that the B -> K* transition form factors agree with the lattice results at large q**2. We calculate branching ratios of semileptonic B -> K, K* transition modes and study the sensitivity of observables to the long-distance contributions. The shape of the forward-backward asymmetry and the longitudinal lepton polarization asymmetry are found to be independent of the long-distance effects and mainly determined by the values of the Wilson coefficients in the Standard Model.
We propose a new Group Feature Selection method for Discriminative Correlation Filters (GFS-DCF) based visual object tracking. The key innovation of the proposed method is to perform group feature selection across both channel and spatial dimensions, thus to pinpoint the structural relevance of multi-channel features to the filtering system. In contrast to the widely used spatial regularisation or feature selection methods, to the best of our knowledge, this is the first time that channel selection has been advocated for DCF-based tracking. We demonstrate that our GFS-DCF method is able to significantly improve the performance of a DCF tracker equipped with deep neural network features. In addition, our GFS-DCF enables joint feature selection and filter learning, achieving enhanced discrimination and interpretability of the learned filters.   To further improve the performance, we adaptively integrate historical information by constraining filters to be smooth across temporal frames, using an efficient low-rank approximation. By design, specific temporal-spatial-channel configurations are dynamically learned in the tracking process, highlighting the relevant features, and alleviating the performance degrading impact of less discriminative representations and reducing information redundancy. The experimental results obtained on OTB2013, OTB2015, VOT2017, VOT2018 and TrackingNet demonstrate the merits of our GFS-DCF and its superiority over the state-of-the-art trackers. The code is publicly available at https://github.com/XU-TIANYANG/GFS-DCF.
Let $\Omega\subset \R^n$ be a bounded convex domain and $\phi\in C(\bar\Omega)$ be a convex function such that $\phi$ is sufficiently smooth on $\partial\Omega$ and the Monge--Amp\`ere measure $\det D^2\phi$ is bounded away from zero and infinity in $\Omega$. The corresponding linearized Monge--Amp\`ere equation is \[ \trace(\Phi D^2 u) =f, \] where $\Phi := \det D^2 \phi ~ (D^2\phi)^{-1}$ is the matrix of cofactors of $D^2\phi$. We prove a conjecture in \cite{GT} about the relationship between $L^p$ estimates for $D^2 u$ and the closeness between $\det D^2\phi$ and one. As a consequence, we obtain interior $W^{2,p}$ estimates for solutions to such equation whenever the measure $\det D^2\phi$ is given by a continuous density and the function $f$ belongs to $L^q(\Omega)$ for some $q> \max{\{p,n\}}$.
We investigate the effect of vibrational degrees of freedom on the linear thermoelectric transport through a single-level quantum dot described by the spinless Anderson-Holstein impurity model. To study the effects of strong electron-phonon coupling, we use the nonperturbative numerical renormalization group approach. We also compare our results, at weak to intermediate coupling, with those obtained by employing the functional renormalization group method, finding good agreement in this parameter regime. When applying a gate voltage at finite temperatures, the inelastic scattering processes, induced by phonon-assisted tunneling, result in an interesting interplay between electrical and thermal transport. We explore different parameter regimes and identify situations for which the thermoelectric power as well as the dimensionless figure of merit are significantly enhanced via a Mahan-Sofo type of mechanism. We show, in particular, that this occurs at strong electron-phonon coupling and in the antiadiabatic regime.
We uncover an interesting phenomenon that neutrino flavor transformation in slowly varying matter density imitates almost exactly that of vacuum neutrino oscillation under suitably chosen experimental parameters. It allows us to have relatively large CP violating measure \Delta P \equiv P(\nu_{\mu} \to \nu_e) - P(\bar{\nu}_{\mu} \to \bar{\nu}_e) which is essentially free from matter effect contamination. We utilize this phenomenon to design a low-energy long-baseline neutrino oscillation experiment to measure the leptonic CP violating phase.
Black phosphorous (BP) is is recently unveiled as a promising two-dimensional direct bandgap semiconducting material. Here, we report the ambipolar field effect transistor behavior of multilayers of BP with ferromagnetic tunnel contacts. We observe a reduced of Schottky barrier < 50 meV by using TiO${_2}$/Co contacts, which could be further tuned by gate voltages. Eminently a good transistor performance is achieved in BP devices, with drain current modulation on the order of four to six orders of magnitude. The charge carrier mobility is found to be $\sim$ 155 and 0.18 cm${^2}$ V${^{-1}}$ s${^{-1}}$ for holes and electrons respectively at room temperature. Furthermore, magnetoresistance calculations reveal that the resistances of the BP device with applied gate voltages are in the appropriate range for injection and detection of spin polarized holes. Our results demonstrate the prospect of engineering BP nanolayered devices for efficient nanoelectronic and spintronic applications.
The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.
The numbers of $\mathbb{F}_q$-points of nonsingular hypersurfaces of a fixed degree in an odd-dimensional projective space are investigated, and an upper bound for them is given. Also we give the complete list of nonsingular hypersurfaces each of which realizes the upper bound. This is a natural generalization of our previous study of surfaces in projective $3$-space.
We used the Nobeyama 45-m telescope to conduct a spectral line survey in the 3-mm band (85.1-98.4 GHz) toward one of the nearest galaxies with active galactic nucleus NGC 1068 and the prototypical starburst galaxy NGC 253. The beam size of this telescope is ~18", which was sufficient to spatially separate the nuclear molecular emission from the emission of the circumnuclear starburst region in NGC 1068. We detected rotational transitions of C2H, cyclic-C3H2, and H13CN in NGC 1068. These are detections of carbon-chain and carbon-ring molecules in NGC 1068. In addition, the C2H N = 1-0 lines were detected in NGC 253. The column densities of C2H were determined to be 3.4 x 10^15 cm^-2 in NGC 1068 and 1.8 x 10^15 cm^-2 in NGC 253. The column densities of cyclic-C3H2 were determined to be 1.7 x 10^13 cm^-2 in NGC 1068 and 4.4 x 10^13 cm^-2 in NGC 253. We calculated the abundances of these molecules relative to CS for both NGC 1068 and NGC 253, and found that there were no significant differences in the abundances between the two galaxies. This result suggests that the basic carbon-containing molecules are either insusceptible to AGN, or are tracing cold (T_rot ~10 K) molecular gas rather than X-ray irradiated hot gas.
We prove many new cases of the Inverse Galois Problem for those simple groups arising from orthogonal groups over finite fields. For example, we show that the finite simple groups Omega_{2n+1}(p) and POmega_{4n}^+(p) both occur as the Galois group of a Galois extension of the rationals for all integers n>1 and all primes p>3. We obtain our representations by studying families of twists of elliptic curves and using some known cases of the Birch and Swinnerton-Dyer conjecture along with a big monodromy result of Hall.
The galactic Cepheid S Muscae has recently been added to the important list of Cepheids linked to open clusters, in this case the sparse young cluster ASCC 69. Low-mass members of a young cluster are expected to have rapid rotation and X-ray activity, making X-ray emission an excellent way to discriminate them from old field stars. We have made an XMM-Newton observation centered on S Mus and identified (Table 1) a population of X-ray sources whose near-IR 2MASS counterparts lie at locations in the J, (J-K) color-magnitude diagram consistent with cluster membership at the distance of S Mus. Their median energy and X-ray luminosity are consistent with young cluster members as distinct from field stars. These strengthen the association of S Mus with the young cluster, making it a potential Leavitt Law (Period-Luminosity relation) calibrator.
Let S(g,N,p) be the Siegel modular variety of principally polarized abelian varieties of dimension g with a \Gamma_0(p)-level structure and a full N-level structure (where p is a prime not dividing N \geq 3 and \Gamma_0(p) is the inverse image of a Borel subgroup of Sp(2g,F_p) in Sp(2g,Z)). This variety has a natural integral model over Z[1/N] which is not semi-stable over the prime p if g>1.   Using the theory of local models of Rapoport-Zink, we construct a semi-stable model of S(g,N,p) over Z[1/N] for g=2 and g=3.   For g=2, our construction differs from de Jong's one though the resulting model is the same.
This work presents a novel method to estimate the effective opening angle of CBe star disks from projected axis ratio measurements, obtained by interferometry using Bayesian statistics. A Monte Carlo scheme was used to generate a large set of theoretical axis ratios from disk models using different distributions of disk densities and opening angles. These theoretical samples were then compared to observational samples, using a two-sample Kolmogorov-Smirnov test, to determine which theoretical distribution best reproduces the observations. The results suggest that the observed ratio distributions in the K-, H-, and N-band can best be explained by the presence of thin disks, with opening half-angles of the order of 0.15$^{\circ}$ to 4.0$^{\circ}$. Results for measurements over the H$\alpha$ line point toward slightly thicker disks, 3.7$^{\circ}$ to 14$^{\circ}$, which is consistent with a flaring disk predicted by the viscous disk model.
I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.
The $k$-dominating graph $D_k(G)$ of a graph $G$ is defined on the vertex set consisting of dominating sets of $G$ with cardinality at most $k$, two such sets being adjacent if they differ by either adding or deleting a single vertex. A graph is a dominating graph if it is isomorphic to $D_k(G)$ for some graph $G$ and some positive integer $k$. Answering a question of Haas and Seyffarth for graphs without isolates, it is proved that if $G$ is such a graph of order $n\ge 2$ and with $G\cong D_k(G)$, then $k=2$ and $G=K_{1,n-1}$ for some $n\ge 4$. It is also proved that for a given $r$ there exist only a finite number of $r$-regular, connected dominating graphs of connected graphs. In particular, $C_6$ and $C_8$ are the only dominating graphs in the class of cycles. Some results on the order of dominating graphs are also obtained.
The cross sections of solar coronal loops are suggested to be rarely circular. We examine linear kink oscillations in straight, density-enhanced, magnetic cylinders with elliptical cross-sections by solving the three-dimensional magnetohydrodynamic equations from an initial-value-problem perspective. Motivated by relevant eigen-mode analyses, we distinguish between two independent polarizations, one along the major axis (the M-modes) and the other along the minor one (the m-modes). We find that, as happens for coronal loops with circular cross-sections, the apparent damping of the transverse displacement of the loop axis is accompanied by the accumulation of transverse Alfv\'enic motions and the consequent development of small-scales therein, suggesting the robustness of the concepts of resonant absorption and phase-mixing. In addition, two stages can in general be told apart in the temporal evolution of the loop displacement; a Gaussian time dependence precedes an exponential one. For the two examined density ratios between loops and their surroundings, the periods of the M-modes (m-modes) tend to increase (decrease) with the major-to-minor-half-axis ratio, and the damping times in the exponential stage for the M-modes tend to exceed their m-mode counterparts. This is true for the two transverse profiles we examine. However, the relative magnitudes of the damping times in the exponential stage for different polarizations depend on the specification of the transverse profile and/or the density contrast. The applications of our numerical findings are discussed in the context of coronal seismology.
We review harmonic superspaces of the D=3, N=3 and 4 supersymmetries and gauge models in these superspaces. Superspaces of the D=3, N=5 supersymmetry use harmonic coordinates of the SO(5) group. The superfield N=5 actions describe the off-shell infinite-dimensional Chern-Simons supermultiplet.
In this paper, we examine the existence of traversable wormhole solutions within the Chern-Simons modified gravity. We find a non-trivial solution in the theory with dynamical Chern-Simons coefficient in the absence of matter sources. This result displays a situation opposite to GR where the matter sources violating the energy conditions are required.
The Cosmic Microwave Background (CMB) anisotropies measurements can provide many clues about the Universe. Although the common belief is that they will allow a very precise measurement of the cosmological parameters (that is, the current state of the Universe), they will alternatively give interesting informations about the state of the initial perturbations (that is, the state of the Universe at the end of inflation). In this paper, we study the observational consequences on the CMB anisotropies of some wide set of inital conditions, with a correlated mixture of adiabatic and isocurvature perturbations.
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio $p_1/p_2$ as well as the Stein kernel $\tau_1$ of $p_1$. The method of proof relies on a new variant of Stein's method which manipulates Stein operators.   We give several applications of these bounds. Our main application is in Bayesian statistics : we derive explicit data-driven bounds on the Wasserstein distance between the posterior distribution based on a given prior and the no-prior posterior based uniquely on the sampling distribution. This is the first finite sample result confirming the well-known fact that with well-identified parameters and large sample sizes, reasonable choices of prior distributions will have only minor effects on posterior inferences if the data are benign.