ShantanuT01/DACTYL-Pretraining huggingface dataset:
Approximate solutions representing the gravitational-electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the present time, the only known exact solutions which can be interpreted as the non-linear superposition of two spherically symmetric (Reissner-Nordstrom) bodies without an intervening strut has been for critically charged masses, $M^2_i = Q^2_i$. In the present paper, an exact electrostatic solution of the Einstein-Maxwell equations representing the exterior field of two arbitrary charged Reissner-Nordstrom bodies in equilibrium is studied. The invariant physical charge for each source is found by direct integration of Maxwell's equations. The physical mass for each source is invariantly defined in a manner similar to which the charge was found. It is shown through numerical methods that balance without tension or strut can occur for non-critically charged bodies. It is demonstrated that other authors have not identified the correct physical parameters for the mass and charge of the sources. Further properties of the solution, including the multipole structure and comparison with other parameterizations, are examined.
We report observations of 15 high redshift (z = 1-5) galaxies at 350 microns using the Caltech Submillimeter Observatory and SHARC-II array detector. Emission was detected from eight galaxies, for which far-infrared luminosities, star formation rates, total dust masses, and minimum source size estimates are derived. These galaxies have star formation rates and star formation efficiencies comparable to other high redshift molecular emission line galaxies. The results are used to test the idea that star formation in these galaxies occurs in a large number of basic units, the units being similar to star-forming clumps in the Milky Way. The luminosity of these extreme galaxies can be reproduced in a simple model with (0.9-30) *10^6 dense clumps, each with a luminosity of 5 *10^5 Lsun, the mean value for such clumps in the Milky Way. Radiative transfer models of such clumps can provide reasonable matches to the overall SEDs of the galaxies. They indicate that the individual clumps are quite opaque in the far-infrared. Luminosity to mass ratios vary over two orders of magnitude, correlating strongly with the dust temperature derived from simple fits to the SED. The gas masses derived from the dust modeling are in remarkable agreement with those from CO luminosities, suggesting that the assumptions going into both calculations are reasonable.
We introduce a novel CNN-based feature point detector - GLAMpoints - learned in a semi-supervised manner. Our detector extracts repeatable, stable interest points with a dense coverage, specifically designed to maximize the correct matching in a specific domain, which is in contrast to conventional techniques that optimize indirect metrics. In this paper, we apply our method on challenging retinal slitlamp images, for which classical detectors yield unsatisfactory results due to low image quality and insufficient amount of low-level features. We show that GLAMpoints significantly outperforms classical detectors as well as state-of-the-art CNN-based methods in matching and registration quality for retinal images. Our method can also be extended to other domains, such as natural images. Training code and model weights are available at https://github.com/PruneTruong/GLAMpoints_pytorch.
A vertex triple $(u,v,w)$ of a graph is called a $2$-geodesic if $v$ is adjacent to both $u$ and $w$ and $u$ is not adjacent to $w$. A graph is said to be $2$-geodesic transitive if its automorphism group is transitive on the set of $2$-geodesics. In this paper, a complete classification of $2$-geodesic transitive graphs of order $p^n$ is given for each prime $p$ and $n\leq 3$. It turns out that all such graphs consist of three small graphs: the complete bipartite graph $K_{4,4}$ of order $8$, the Schl\"{a}fli graph of order $27$ and its complement, and fourteen infinite families: the cycles $C_p, C_{p^2}$ and $C_{p^3}$, the complete graphs $K_p, K_{p^2}$ and $K_{p^3}$, the complete multipartite graphs $K_{p[p]}$, $K_{p[p^2]}$ and $K_{p^2[p]}$, the Hamming graph $H(2,p)$ and its complement, the Hamming graph $H(3,p)$, and two infinite families of normal Cayley graphs on extraspecial group of order $p^3$ and exponent $p$.
We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but faster than the surface area. By targeting a specified form of the structure factor at small wavenumbers using collective density variables, we are able to tailor the form of asymptotic local density fluctuations while simultaneously measuring the effect of imposing weak and strong constraints on the available degrees of freedom within the system. Even in one dimension, the long-range effective interactions induce clustering and nontrivial phase transitions in the resulting ground-state configurations. We provide an analytical connection between the fraction of contrained degrees of freedom within the system and the disorder-order phase transition for a class of target structure factors by examining the realizability of the constrained contribution to the pair correlation function. Our results explicitly demonstrate that disordered hyperuniform many-particle ground states, and therefore also point distributions, with substantial clustering can be constructed. We directly relate the local coordination structure of our point patterns to the distribution of the void space external to the particles, and we provide a scaling argument for the configurational entropy of the systems when only a small fraction of the degrees of freedom are constrained. By emphasizing the intimate connection between geometrical constraints on the particle distribution and structural regularity, our work has direct implications for higher-dimensional systems, including an understanding of the appearance of hyperuniformity and quasi-long-range pair correlations in maximally random strictly jammed packings of hard spheres.
The spectrum of excited baryons in the $N$ = 2 band is reanalys9 pagesed in the $1/N_c$ expansion method, with emphasis on hyperons. Predictions are made for the classification of these excited baryons into SU(3) singlets, octets and decuplets.
We use simple analytical models of the build up of the dust component and compare these with radial dust distributions derived from observations of SINGS galaxies. The observations show that dust gradients are indeed typically steeper than the corresponding metallicity gradients and our models indicate very little dust destruction, but significant dust growth in the ISM for most of these galaxies. Hence, we conclude that there is evidence for significant non-stellar dust production, and little evidence for dust destruction due to SNe shock waves. We find that dust is reprocessed rather than destroyed by shocks from SNe. Finally, we argue that dust abundances derived using standard methods may be overestimated, since even very 'generous' estimates of the metallicity results in dust-to-metals ratios above unity in several cases, if the dust abundances given in the literature are taken at face value.
Let $W$ be a subset of the set of real points of a real algebraic variety $X$. We investigate which functions $f: W \to \mathbb R$ are the restrictions of rational functions on $X$. We introduce two new notions: ${\it curve-rational \, functions}$ (i.e., continuous rational on algebraic curves) and ${\it arc-rational\, functions}$ (i.e., continuous rational on arcs of algebraic curves). We prove that under mild assumptions the following classes of functions coincide: continuous hereditarily rational (introduced recently by the first named author), curve-rational and arc-rational. In particular, if $W$ is semialgebraic and $f$ is arc-rational, then $f$ is continuous and semialgebraic. We also show that an arc-rational function defined on an open set is arc-analytic (i.e., analytic on analytic arcs). Furthermore, we study rational functions on products of varieties. As an application we obtain a characterization of regular functions. Finally, we get analogous results in the framework of complex algebraic varieties.
We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results.
In this paper, we revisit the lattice vibration of one-dimensional monatomic linear chain under open and periodic boundary conditions, and give the exact conditions for the emergence of the local vibration mode when one of the atoms is replaced by an impurity. Our motivation is twofold. Firstly, in deriving the dispersion relation of the atoms, periodic boundary condition is overwhelmingly utilized while open boundary condition is seldomly referred. Therefore we manage to obtain the dispersion relation under both boundary conditions simultaneously by Molinari formula. Secondly, in the presence of impurity, local vibration mode can emerge as long as the mass of the impurity $m'$ is smaller than the mass of the perfect atom $m$ to certain degree, which can be measured by the mass ratio $\delta=\frac{m-m'}{m}$. At periodic boundary condition, the critical mass ratio is $0$ or $\frac{1}{N}$, depending on whether the length $N$ of the chain is even or odd. At open boundary condition, the critical mass ratio is $\frac{N}{2N-1}$ if the impurity locates at the end of the chain, while it is $\frac{N}{(2N_l+1)(2N_r+1)}$ with $N_l$ and $N_r$ be the number of atoms at the left and right hand sides of the impurity if the impurity locates at the middle.
We present a systematic study on the exciton relaxation in high purity AlGaAs epilayers. The time for the excitonic photoluminescence to reach its maximum intensity (t_max) shows a non-monotonic dependence on excitation density which is attributed to a competition between exciton localization and carrier-carrier scattering. A phenomenological four level model fully describes the influence of exciton localization on t_max. This localization effect is enhanced by the increase of the Al content in the alloy and disappears when localization is hindered by rising the lattice temperature above the exciton trapping energy.
Unpolarized 1.047 GeV proton inelastic scatterings from Ni isotopes, $^{62}$Ni and $^{64}$Ni are analyzed phenomenologically employing an optical potential model and the first order collective model in the relativistic Dirac coupled channel formalism. The Dirac equations are reduced to the Schr\"{o}dinger-like second-order differential equations and the effective central and spin-orbit optical potentials are analyzed by considering mass number dependence. The multistep excitation via $2^+$ state is found to be important for the $4^+$ state excitation in the ground state rotational band at the proton inelastic scatterings from the Ni isotopes. The calculated deformation parameters for the 2$^+$, the 4$^+$ states of the ground state rotational band and the first 3$^-$ state are found to agree pretty well with those obtained in the nonrelativistic calculations.
A systematic study of low energy nuclear structure at normal deformation is carried out using the Hartree-Fock-Bogoliubov theory extended by the Generator Coordinate Method and mapped onto a 5-dimensional collective quadrupole Hamiltonian. Results obtained with the Gogny D1S interaction are presented from dripline to dripline for even-even nuclei with proton numbers Z=10 to Z=110 and neutron numbers N less than 200. The properties calculated for the ground states are their charge radii, 2-particle separation energies, correlation energies, and the intrinsic quadrupole shape parameters. For the excited spectroscopy, the observables calculated are the excitation energies and quadrupole as well as monopole transition matrix elements. We examine in this work the yrast levels up to J=6, the lowest excited 0^+ states, and the two next yrare 2^+ states. The theory is applicable to more than 90% of the nuclei which have tabulated measurements. The data set of the calculated properties of 1712 even-even nuclei, including spectroscopic properties for 1693 of them, are provided in CEA website and EPAPS repository with this article \cite{epaps}.
The extreme space weather conditions resulting from high energetic events likes solar flares and Coronal Mass Ejections (CMEs) demand for reliable space weather forecasting. The magnetic flux tubes while rising through the convection zone gets twisted by the turbulent plasma flows, energizing the system and resulting in flares. We investigate the relationship between the subsurface plasma flows associated with flaring active regions and their surface magnetic flux and current helicity. The near-surface horizontal velocities derived from the ring-diagram analysis of active region patches using Global Oscillation Network Group (GONG) Doppler velocity measurements are used to compute the fluid dynamics descriptors like vertical divergence, vorticity and kinetic helicity used in this work. The flaring active regions are observed to have large value of vertical vorticity and kinetic helicity. Also, the horizontal flow divergence, vorticity, flux, kinetic and current helicities are observed to be significantly correlated and evolve in phase with each other. We observe that the integrated values of the above flow and magnetic parameters observed one day prior to the flare are significantly correlated with the integrated flare intensity of the active region. Hence, we show that strong vorticity/kinetic helicities lead to larger active region twisting, presumably generating high-intensity flares.
Out of several dozen z > 7 candidate galaxies observed spectroscopically, only five have been confirmed via Lyman-alpha emission, at z=7.008, 7.045, 7.109, 7.213 and 7.215. The small fraction of confirmed galaxies may indicate that the neutral fraction in the intergalactic medium (IGM) rises quickly at z > 6.5, as Lyman-alpha is resonantly scattered by neutral gas. However, the small samples and limited depth of previous observations makes these conclusions tentative. Here we report the results of a deep near-infrared spectroscopic survey of 43 z > 6.5 galaxies. We detect only a single galaxy, confirming that some process is making Lyman-alpha difficult to detect. The detected emission line at 1.0343 um is likely to be Lyman-alpha emission, placing this galaxy at a redshift z = 7.51, an epoch 700 million years after the Big Bang. This galaxy's colors are consistent with significant metal content, implying that galaxies become enriched rapidly. We measure a surprisingly high star formation rate of 330 Msol/yr, more than a factor of 100 greater than seen in the Milky Way. Such a galaxy is unexpected in a survey of our size, suggesting that the early universe may harbor more intense sites of star-formation than expected.
We present the solution of the time development of an unstable initial density perturbation in the linearized Vlasov equation, completing the previous analysis in the literature. The additional contributions found are usually damped and can be neglected at large times in the unstable region. The work clarifies also the problem of the normalization of the solution with respect to the initial perturbation of the density.
Given a finite simplicial complex $X$ and a connected graph $T$ of diameter $1$, in \cite{anton} Dochtermann had conjectured that $\text{Hom}(T,G_{1,X})$ is homotopy equivalent to $X$. Here, $G_{1, X}$ is the reflexive graph obtained by taking the $1$-skeleton of the first barycentric subdivision of $X$ and adding a loop at each vertex. This was proved by Dochtermann and Schultz in \cite{ds12}.   In this article, we give an alternate proof of this result by understanding the structure of the cells of Hom$(K_n,G_{1,X})$, where $K_n$ is the complete graph on $n$ vertices. We prove that the neighborhood complex of $G_{1,X}$ is homotopy equivalent to $X$ and Hom$(K_n,G_{1,X})\simeq $ Hom$(K_{n-1},G_{1,X})$, for each $n\geq 3$.
Due to the difficulties of obtaining multimodal paired images in clinical practice, recent studies propose to train brain tumor segmentation models with unpaired images and capture complementary information through modality translation. However, these models cannot fully exploit the complementary information from different modalities. In this work, we thus present a novel two-step (intra-modality and inter-modality) curriculum disentanglement learning framework to effectively utilize privileged semi-paired images, i.e. limited paired images that are only available in training, for brain tumor segmentation. Specifically, in the first step, we propose to conduct reconstruction and segmentation with augmented intra-modality style-consistent images. In the second step, the model jointly performs reconstruction, unsupervised/supervised translation, and segmentation for both unpaired and paired inter-modality images. A content consistency loss and a supervised translation loss are proposed to leverage complementary information from different modalities in this step. Through these two steps, our method effectively extracts modality-specific style codes describing the attenuation of tissue features and image contrast, and modality-invariant content codes containing anatomical and functional information from the input images. Experiments on three brain tumor segmentation tasks show that our model outperforms competing segmentation models based on unpaired images.
We determine the conditions under which singular values of multiple $\eta$-quotients of square-free level, not necessarily prime to~6, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index $2^{k' - 1}$ when $k' \geq 2$ primes dividing the level are ramified in the imaginary-quadratic field, which leads to faster computations of elliptic curves with prescribed complex multiplication. The result is generalised to singular values of modular functions on $X_0^+ (p)$ for $p$ prime and ramified.
We have obtained high-spatial resolution ultraviolet and optical STIS spectroscopy and imaging of the metal-rich nuclear starburst in NGC3049. The stellar continuum and the absorption line spectrum in the ultraviolet are used to constrain the massive stellar population. The strong, blueshifted stellar lines of CIV and SiIV detected in the UV spectra indicate a metal-rich, compact, massive (1E6 Msol) cluster of age 3--4 Myr emitting the UV-optical continuum. We find strong evidence against a depletion of massive stars in this metal-rich cluster. The derived age and the upper mass-limit cut-off of the initial mass function are also consistent with the detection of Wolf-Rayet (WR) features at optical wavelengths. As a second independentconstraint on the massive stellar content, the nebular emission-line spectrum is modeled with photoionization codes using stellar spectra from evolutionary synthesis models. However, the nebular lines are badly reproduced by 3--4 Myr instantaneous bursts, as required by the UV line spectrum, when unblanketed WR and/or Kurucz stellar atmospheres are used. The corresponding number of photons above 24 and 54 eV in the synthetic models is too high in comparison with values suggested by the observed line ratios. Since the ionizing spectrum in this regime is dominated by emission from WR stars, this discrepancy between observations and models is most likely the result of incorrect assumptions about the WR stars. Thus we conclude that the nebular spectrum of high-metallicity starbursts is poorly reproduced by models for WR dominated populations. However, the new model set of Smith et al. (2002) with blanketed WR and O atmospheres and adjusted WR temperatures predicts a softer far-UV radiation field, providing a better match to the data.
In this article, we consider the problem of periodic homogenization of a Feller process generated by a pseudo-differential operator, the so-called L\'evy-type process. Under the assumptions that the generator has rapidly periodically oscillating coefficients, and that it admits "small jumps" only (that is, the jump kernel has finite second moment), we prove that the appropriately centered and scaled process converges weakly to a Brownian motion with covariance matrix given in terms of the coefficients of the generator. The presented results generalize the classical and well-known results related to periodic homogenization of a diffusion process.
We demonstrate that under the "symmetric zero texture" with minimal Majorana mass matrix, neutrino masses and mixing angles are expressed in terms of up-quark masses, $m_t,m_c,m_u$. This provides interesting relations among neutrino mixing angles and up-type quark masses. Especially we predict $|U_{e3}| \leq 0.11$ even if we include the small mixing effects coming from charged lepton side. Also absolute masses of three neutrinos are predicted almost uniquely. This is quite in contrast to the case where bi-large mixings come from the charged lepton sector with non-symmetric charged lepton mass matrix.
In this paper, we study the effects of Generalized Uncertainty Principle(GUP) and Modified Dispersion Relations(MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.
We explore the theory of connected Gromov-Witten invariants of the symmetric product stack [Sym^n(A_r)]. We derive closed-form expressions for all equivariant invariants with two insertions and reveal a natural correspondence between the theory and the relative Gromov-Witten theory of the threefold A_r x P^1. When n is less than or equal to 3, we determine 3-point (usual) Gromov-Witten invariants of [Sym^n(A_1)].
We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behaviour. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a non-universal behaviour depending on the ratio of noise strength to the magnitude of the spatial coupling.
If the dark sector of the Universe consists of ultra-light scalars, their coupling to photon via a Chern-Simons term would induce a rotation of the polarization plane of the cosmic microwave background (CMB). This rotation would convert E -mode polarization into B -mode polarization, resulting in new CMB BB correlation and parity-violating TB and EB cross correlations. We review the subject giving details about the derivation of the rotational effects and summarizing the possible signals in current and future CMB B-mode experiments.