ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop an approximate analytical solution for the transfer of line-averaged radiation in the hydrogen recombination lines for the ionized cavity and molecular shell of a spherically symmetric planetary nebula. The scattering problem is treated as a perturbation, using a mean intensity derived from a scattering-free solution. The analytical function was fitted to Halpha and Hbeta data from the planetary nebula NGC6537. The position of the maximum in the intensity profile produced consistent values for the radius of the cavity as a fraction of the radius of the dusty nebula: 0.21 for Halpha and 0.20 for Hbeta. Recovered optical depths were broadly consistent with observed optical extinction in the nebula, but the range of fit parameters in this case is evidence for a clumpy distribution of dust.
A ground state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order $n a^3$ in the particle depletion and ground state energy density of a dilute Bose gas system, which corresponds to the density fluctuation contribution from the excited states. The coefficient of $n a^3$ term is shown to be $2(\pi - 8/3)$ for the particle depletion, and $16(\pi - 8/3)$ for the ground state energy density.
Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable L\'{e}vy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit L\'{e}vy tails. For the analytically known L\'{e}vy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the L\'{e}vy tail-distributions are characterized by a novel form of microscopic universality.
Recent results comparing interacting galaxies to the mass-metallicity relation show that their nuclear oxygen abundances are unexpectedly low. We present analysis of N-body/SPH numerical simulations of equal-mass mergers that confirm the hypothesis that these underabundances are accounted for by radial inflow of low-metallicity gas from the outskirts of the two merging galaxies. The underabundances arise between first and second pericenter, and the simulated abundance dilution is in good agreement with observations. The simulations further predict that the radial metallicity gradients of the disk galaxies flatten shortly after first passage, due to radial mixing of gas. These predictions will be tested by future observations of the radial metallicity distributions in interacting galaxies.
Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer and results by D. Roy, we establish that the spectrum of the $2n$ exponents of Diophantine approximation in dimension $n\geq3$ is a subset of $\mathbb{R}^{2n}$ with non empty interior.
Observed rotation curves in star-forming galaxies indicate a puzzling dearth of dark matter in extended flat cores within haloes of mass $\geq\! 10^{12}M_\odot$ at $z\!\sim\! 2$. This is not reproduced by current cosmological simulations, and supernova-driven outflows are not effective in such massive haloes. We address a hybrid scenario where post-compaction merging satellites heat up the dark-matter cusps by dynamical friction, allowing AGN-driven outflows to generate cores. Using analytic and semi-analytic models (SatGen), we estimate the dynamical-friction heating as a function of satellite compactness for a cosmological sequence of mergers. Cosmological simulations (VELA) demonstrate that satellites of initial virial masses $>\!10^{11.3}M_\odot$, that undergo wet compactions, become sufficiently compact for significant heating. Constituting a major fraction of the accretion onto haloes $\geq\!10^{12}M_\odot$, these satellites heat-up the cusps in half a virial time at $z\!\sim\! 2$. Using a model for outflow-driven core formation (CuspCore), we demonstrate that the heated dark-matter cusps develop extended cores in response to removal of half the gas mass, while the more compact stellar systems remain intact. The mergers keep the dark matter hot, while the gas supply, fresh and recycled, is sufficient for the AGN outflows. AGN indeed become effective in haloes $\geq\!10^{12}M_\odot$, where the black-hole growth is no longer suppressed by supernovae and its compaction-driven rapid growth is maintained by a hot CGM. For simulations to reproduce the dynamical-friction effects, they should resolve the compaction of the massive satellites and avoid artificial tidal disruption. AGN feedback could be boosted by clumpy black-hole accretion and clumpy response to AGN.
The phase diagram of the multivalent manganites $\rm La_{1-x}Ca_xMnO_3$, in space of temperature and doping $x$, is a challenge for the theoretical physics. It is an important test for the model used to study these compounds and the method of calculation. To obtain theoretically this diagram for $x<0.5$, we consider the two-band Double Exchange Model for manganites with added Jahn-Teller coupling and antiferromagnetic Heisenberg term. In order to calculate Curie and N\'{e}el temperatures we derive an effective Heisenberg model for a vector which describes the local orientation of the total magnetization of the system. The exchange constants of this model are different for different space directions and depend on the density of $e_g$ electrons, antiferromagnetic constants and the Jahn-Teller energy. To reproduce the well known phase transitions from A-type antiferromagnetism to ferromagnetism at low $x$ and C-type antiferromagnetism to G-type antiferromagnetism at large $x$, we argue that the antiferromagnetic exchange constants should depend on the lattice direction. We show that ferromagnetic to A-type antiferromagnetic transition results from the Jahn-Teller distortion. Accounting adequately for the magnon-magnon interaction, Curie and N\'{e}el temperatures are calculated. The results are in very good agreement with the experiment and provide values for the model parameters, which best describe the behavior of the critical temperature for $x<0.5$.
Visualizing the features captured by Convolutional Neural Networks (CNNs) is one of the conventional approaches to interpret the predictions made by these models in numerous image recognition applications. Grad-CAM is a popular solution that provides such a visualization by combining the activation maps obtained from the model. However, the average gradient-based terms deployed in this method underestimates the contribution of the representations discovered by the model to its predictions. Addressing this problem, we introduce a solution to tackle this issue by computing the path integral of the gradient-based terms in Grad-CAM. We conduct a thorough analysis to demonstrate the improvement achieved by our method in measuring the importance of the extracted representations for the CNN's predictions, which yields to our method's administration in object localization and model interpretation.
We present estimates of the nonlinear bias of cosmological halo formation, spanning a wide range in the halo mass from $\sim 10^{5} M_\odot$ to $\sim 10^{12} M_\odot$, based upon both a suite of high-resolution cosmological N-body simulations and theoretical predictions. The halo bias is expressed in terms of the mean bias and stochasticity as a function of local overdensity ($\delta$), under different filtering scales, which is realized as the density of individual cells in uniform grids. The sampled overdensities span a range wide enough to provide the fully nonlinear bias effect on the formation of haloes. A strong correlation between $\delta$ and halo population overdensity $\delta_h$ is found, along with sizable stochasticity. We find that the empirical mean halo bias matches, with good accuracy, the prediction by the peak-background split method based on the excursion set formalism, as long as the empirical, globally-averaged halo mass function is used. Consequently, this bias formalism is insensitive to uncertainties caused by varying halo identification schemes, and can be applied generically. We also find that the probability distribution function of biased halo numbers has wider distribution than the pure Poisson shot noise, which is attributed to the sub-cell scale halo correlation. We explicitly calculate this correlation function and show that both overdense and underdense regions have positive correlation, leading to stochasticity larger than the Poisson shot noise in the range of haloes and halo-collapse epochs we study.
A relation among the effective nucleon mass $M^*$, the incompressibility $K$ and the effective $\sigma$-meson mass $m_{\rm s}^*$ in nuclear matter is studied by using the relativistic nuclear model. We found that there is a strong correlation between $M^*$ and $m_{\rm s}^*$, while there is only a weak correlation between $K$ and $m_{\rm s}^*$. At the normal density, $m_{\rm s}^*$ is smaller than the one at zero density, if $M^*$ is smaller than 0.8 times of the nucleon mass at zero density. It is also found that the off-shell effective mass $\mu_{\rm s}^*$ is related directly to $K$ and $M^*$ at the normal density.
Given a coloration of the vertices of a triangulation of a manifold, we give homological conditions on the chromatic complexes under which it is possible to obtain a rainbow simplex
When $k$ and $s$ are natural numbers and $\mathbf h\in \mathbb Z^k$, denote by $J_{s,k}(X;\mathbf h)$ the number of integral solutions of the system \[ \sum_{i=1}^s(x_i^j-y_i^j)=h_j\quad (1\le j\le k), \] with $1\le x_i,y_i\le X$. When $s<k(k+1)/2$ and $(h_1,\ldots ,h_{k-1})\ne {\mathbf 0}$, Brandes and Hughes have shown that $J_{s,k}(X;\mathbf h)=o(X^s)$. In this paper we improve on quantitative aspects of this result, and, subject to an extension of the main conjecture in Vinogradov's mean value theorem, we obtain an asymptotic formula for $J_{s,k}(X;\mathbf h)$ in the critical case $s=k(k+1)/2$. The latter requires minor arc estimates going beyond square-root cancellation.
We report the discovery of a Jupiter-size planet transiting a relatively bright (V = 11.56) and metal-rich early K dwarf star with a period of about 2.9 days. On the basis of follow-up photometry and spectroscopy we determine the mass and radius of the planet, HAT-P-3b, to be M_p = 0.599 +/- 0.026 M_Jup and R_p = 0.890 +/- 0.046 R_Jup. The relatively small size of the object for its mass implies the presence of about 75 Earth masses worth of heavy elements (1/3 of the total mass) based on current theories of irradiated extrasolar giant planets, similar to the mass of the core inferred for the transiting planet HD 149026b. The bulk density of HAT-P-3b is found to be rho_p = 1.06 +/- 0.17 g/cm^3, and the planet orbits the star at a distance of 0.03894 AU. Ephemerides for the transit centers are T_c = 2,454,218.7594 +/- 0.0029 + N (2.899703 +/- 0.000054) (HJD).
In this notes we classify toric Fano 4-folds having positive second Chern Character.
We give generalizations and simple proofs of some $q$-identities of Dilcher, Fu and Lascoux related to divisor functions.
We study numerically large-scale magnetic field evolution and its enhancement in gaseous disks of spiral galaxies. We consider a set of models with the various spiral pattern parameters and the initial magnetic field strength with taking into account gas self-gravity and cooling/heating. In agreement with previous studies, we find out that galactic magnetic field is mostly aligned with gaseous structures, however small-scale gaseous structures (spurs and clumps) are more chaotic than the magnetic field structure. In spiral arms magnetic field strongly coexists with the gas distribution, in the inter-arm region we see filamentary magnetic field structure. Simulations reveal the presence of the small-scale irregularities of the magnetic field as well as the reversal of magnetic field at the outer edge of the large-scale spurs. We provide evidences that the magnetic field in the spiral arms has a stronger mean-field component, and there is a clear inverse correlation between gas density and plasma-beta parameter, compared to the rest of the disk with a more turbulent component of the field and an absence of correlation between gas density and plasma-beta. We show the mean field growth up to 3-10$\mu G$ in the cold gas during several rotation periods (500-800 Myr), whereas ratio between azimuthal and radial field is equal to 4/1. Mean field strength increases by a factor of 1.5-2.5 for models with various spiral pattern parameters. Random magnetic field component can reach up to 25 % from the total strength. By making an analysis of the time-depended evolution of radial Poynting flux we point out that the magnetic field strength is enhanced stronger at the galactic outskirts which is due to the radial transfer of magnetic energy by the spiral arms pushing the magnetic field outward. Our results also support the presence of sufficient conditions for development of MRI at distances >11 kpc.
In this semi-expository article we solve the diophantine equation $m^5+(4 \cdot 5^4 b^4)mn^4 - n^5=1$ for all integers $b \neq 0$. This gives an example of a family of quintic Thue equations that can be solved completely by using nothing more than Skolem's $p$-adic method. We also give a general introduction to Skolem's method from a modern perspective.
We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For beta < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarity drops from near 1 to near 0 in a window of order n centered at [2(1-beta)]^{-1} n log n. For beta = 1, we prove that the mixing time is of order n^{3/2}. For beta > 1, we study metastability. In particular, we show that the Glauber dynamics restricted to states of non-negative magnetization has mixing time O(n log n).
By resorting to sequential constructions of exchangeable random partitions (Pitman, 2006), and exploiting some known facts about generalized Stirling numbers, we derive a generalized Chinese restaurant process construction of exchangeable Gibbs partitions of type $\alpha$ (Gnedin and Pitman, 2006). Our construction represents the natural theoretical probabilistic framework in which to embed some recent results about a Bayesian nonparametric treatment of estimation problems arising in genetic experiment under Gibbs, species sampling, models priors.
Invariance under non-linear ${\sf {\hat W}}_{\infty}$ algebra is shown for the two-boson Liouville type of model and its algebraic generalizations, the extended conformal Toda models. The realization of the corresponding generators in terms of two boson currents within KP hierarchy is presented.
We study the effects of local inhomogeneities, i.e., slow sites of hopping rate $q<1$, in a totally asymmetric simple exclusion process (TASEP) for particles of size $\ell \geq 1$ (in units of the lattice spacing). We compare the simulation results of $\ell =1$ and $\ell >1$ and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the \emph{location} of the slow site for both $\ell =1$ and $\ell >1$ cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close together. In addition, we study the asymptotic behavior when   $q\to 0$. We also explore the associated density profiles and compare our findings to an earlier study using a simple mean-field theory. We then outline the biological significance of these effects.
In this paper we present a dense ground truth dataset of nonrigidly deforming real-world scenes. Our dataset contains both long and short video sequences, and enables the quantitatively evaluation for RGB based tracking and registration methods. To construct ground truth for the RGB sequences, we simultaneously capture Near-Infrared (NIR) image sequences where dense markers - visible only in NIR - represent ground truth positions. This allows for comparison with automatically tracked RGB positions and the formation of error metrics. Most previous datasets containing nonrigidly deforming sequences are based on synthetic data. Our capture protocol enables us to acquire real-world deforming objects with realistic photometric effects - such as blur and illumination change - as well as occlusion and complex deformations. A public evaluation website is constructed to allow for ranking of RGB image based optical flow and other dense tracking algorithms, with various statistical measures. Furthermore, we present an RGB-NIR multispectral optical flow model allowing for energy optimization by adoptively combining featured information from both the RGB and the complementary NIR channels. In our experiments we evaluate eight existing RGB based optical flow methods on our new dataset. We also evaluate our hybrid optical flow algorithm by comparing to two existing multispectral approaches, as well as varying our input channels across RGB, NIR and RGB-NIR.
We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The branching law is in the domain of attraction of a (1+$\beta$)-stable law and the initial condition is an equilibrium random measure for the system (defined below). In the paper we treat separately the cases of intermediate $\alpha/\beta<d<(1+\beta)\alpha/\beta$, critical $d=(1+\beta)\alpha/\beta$ and large $d>(1+\beta)\alpha/\beta $ dimensions. In the most interesting case of intermediate dimensions we obtain a version of a fractional stable motion. The long-range dependence structure of this process is also studied. Contrary to this case, limit processes in critical and large dimensions have independent increments.
Star-forming regions have been proposed as potential Galactic cosmic-ray accelerators for decades. Cosmic ray acceleration can be probed through observations of gamma-rays produced in inelastic proton-proton collisions, at GeV and TeV energies. We analyze more than 11 years of Fermi-LAT data from the direction of Westerlund 2, one of the most massive and best-studied star-forming regions in our Galaxy. The spectral and morphological characteristics of the LAT source agree with the ones in the TeV regime (HESS J1023-575), allowing the description of the gamma-ray source from a few hundreds of MeV to a few tens of TeVs. We will present the results and discuss the implications of the identification with the stellar cluster and the radiation mechanism involved.
A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight k-1, its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge substructure in the cohomology. We determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces. We use our results to prove the existence of a Kuga-Satake correspondance for certain cubic 4-folds.
In this paper we obtain a 2+2 double null Hamiltonian description of General Relativity using only the (complex) SO(3) connection and the components of the complex densitised self-dual bivectors. We carry out the general canonical analysis of this system and obtain the first class constraint algebra entirely in terms of the self-dual variables. The first class algebra forms a Lie algebra and all the first class constraints have a simple geometrical interpretation.
Description of superradiance of few quantum emitters with non-radiative decay in terms of quantum states is presented. Quantum efficiencies (QE) of SR of two and three emitters are calculated and compared with the case of two and three independent emitters. Maximum increase in QE is 8% for two emitters and 16% for three emitters, it is reached at certain ratios between non-radiative and radiative rates. Approach can be generalized with inclusion of the incoherent pump, dephasing and delay in emitter-emitter interaction.
We examined the complete short cadence sample of Kepler RR Lyrae stars to further investigate the recently discovered dynamical effects such as period doubling and additional modes. Here we present the findings on four stars. V450 Lyr may be a non-classical double-mode RR Lyrae star pulsating in the fundamental mode and the second overtone. In three cases we observe the interaction of three different modes. Since the period ratios are close to resonant values, we observe quasi-repetiting patterns in the pulsation cycles in the stars. These findings support the mode-resonance explanations of the Blazhko effect.
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. The weak-strong uniqueness principle holds for dissipative renormalised solutions, which in addition to the renormalised formulation obey suitable dissipation inequalities consistent with previous existence results. We treat general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems.
We present a detailed analysis of a large spectroscopic and photometric sample of DZ white dwarfs based on our latest model atmosphere calculations. We revise the atmospheric parameters of the trigonometric parallax sample of Bergeron, Leggett, & Ruiz (12 stars) and analyze 147 new DZ white dwarfs discovered in the Sloan Digital Sky Survey. The inclusion of metals and hydrogen in our model atmosphere calculations leads to different atmospheric parameters than those derived from pure helium models. Calcium abundances are found in the range from log (Ca/He) = -12 to -8. We also find that fits of the coolest objects show peculiarities, suggesting that our physical models may not correctly describe the conditions of high atmospheric pressure encountered in the coolest DZ stars. We find that the mean mass of the 11 DZ stars with trigonometric parallaxes, <M> = 0.63 Mo, is significantly lower than that obtained from pure helium models, <M> = 0.78 Mo, and in much better agreement with the mean mass of other types of white dwarfs. We determine hydrogen abundances for 27% of the DZ stars in our sample, while only upper limits are obtained for objects with low signal-to-noise ratio spectroscopic data. We confirm with a high level of confidence that the accretion rate of hydrogen is at least two orders of magnitude smaller than that of metals (and up to five in some cases) to be compatible with the observations. We find a correlation between the hydrogen abundance and the effective temperature, suggesting for the first time empirical evidence of a lower temperature boundary for the hydrogen screening mechanism. Finally, we speculate on the possibility that the DZA white dwarfs could be the result of the convective mixing of thin hydrogen-rich atmospheres with the underlying helium convection zone.