ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report on the recently proposed joint resolution of two long-standing puzzles in weak radiative (WR) and nonleptonic (NL) hyperon decays (HD). First, a good VMD-based description of WRHD is presented. In particular, the large negative asymmetry observed in the \Sigma^+ \to p \gamma decay is explained through a calculably large SU(3)-breaking effect in the relevant parity-violating amplitude. Second, the achieved description of the parity-violating WRHD amplitudes permits the extraction, via the SU(2)_W + VMD route, of the non-soft-pion correction term in the parity-violating NLHD amplitudes. The latter subtracts a substantial amount from the current-algebra commutator term, thus leading to the resolution of the old S:P discrepancy in NLHD.
The nuclear deformation and neutron-transfer process have been identified as playing a major role in the magnitude of the sub-barrier fusion (capture) cross sections. There are a several experimental evidences which confirm the importance of nuclear deformation on the fusion. The influence of nuclear deformation is straightforward. If the target nucleus is prolate in the ground state, the Coulomb field on its tips is lower than on its sides, that then increases the capture or fusion probability at energies below the barrier corresponding to the spherical nuclei. The role of neutron transfer reactions is less clear. The importance of neutron transfer with positive Q-values on nuclear fusion (capture) originates from the fact that neutrons are insensitive to the Coulomb barrier and therefore they can start being transferred at larger separations before the projectile is captured by target-nucleus. Therefore, it is generally thought that the sub-barrier fusion cross section will increase because of the neutron transfer. The fusion (capture) dynamics induced by loosely bound radioactive ion beams is currently being extensively studied. However, the long-standing question whether fusion (capture) is enhanced or suppressed with these beams has not yet been answered unambiguously. The study of the fusion reactions involving nuclei at the drip-lines has led to contradictory results.
Binary stars provide a valuable test of stellar structure and evolution, because the masses of the individual stellar components can be derived with high accuracy and in a model-independent way. In this work, we study Spica, an eccentric double-lined spectroscopic binary system with a beta Cep type variable primary component. We use state-of-the-art modelling tools to determine accurate orbital elements of the binary system and atmospheric parameters of both stellar components. We interpret the short-period variability intrinsic to the primary component, detected on top of the orbital motion both in the photometric and spectroscopic data. The non-LTE based spectrum analysis reveals two stars of similar atmospheric chemical composition consistent with the present day cosmic abundance standard defined by Nieva&Przybilla (2012). The masses and radii of the stars are found to be 11.43+/-1.15 M_sun and 7.21+/-0.75 M_sun, and 7.47+/-0.54 R_sun and 3.74+/-0.53 R_sun for the primary and secondary, respectively. We find the primary component to pulsate in three independent modes, of which one is identified as a radial mode, while the two others are found to be non-radial, low degree l modes. The frequency of one of these modes is an exact multiple of the orbital frequency, and the l=m=2 mode identification suggests a tidal nature for this particular mode. We find a very good agreement between the derived dynamical and evolutionary masses for the Spica system to within the observational errors of the measured masses. The age of the system is estimated to be 12.5+/-1 Myr.
We study the Dirichlet problem for subelliptic partial differential equations of Monge-Ampere type involving the derivates with respect to a family X of vector fields of Carnot type. The main result is a comparison principle among viscosity subsolutions, convex with respect to X, and viscosity supersolutions (in a weaker sense than usual), which implies the uniqueness of solution to the Dirichlet problem. Its assumptions include the equation of prescribed horizontal Gauss curvature in Carnot groups. By Perron method we also prove the existence of a solution either under a growth condition of the nonlinearity with respect to the gradient of the solution, or assuming the existence of a subsolution attaining continuously the boundary data, therefore generalizing some classical result for Euclidean Monge-Ampere equations.
The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We find that in general HF+RPA gives a very good approximation to the ``exact'' ground state energy. In those cases where RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wavefunction.
The edge domination number $\gamma_e(G)$ of a graph $G$ is the minimum size of a maximal matching in $G$. It is well known that this parameter is computationally very hard, and several approximation algorithms and heuristics have been studied. In the present paper, we provide best possible upper bounds on $\gamma_e(G)$ for regular and non-regular graphs $G$ in terms of their order and maximum degree. Furthermore, we discuss algorithmic consequences of our results and their constructive proofs.
Popular Hough Transform-based object detection approaches usually construct an appearance codebook by clustering local image features. However, how to choose appropriate values for the parameters used in the clustering step remains an open problem. Moreover, some popular histogram features extracted from overlapping image blocks may cause a high degree of redundancy and multicollinearity. In this paper, we propose a novel Hough Transform-based object detection approach. First, to address the above issues, we exploit a Bridge Partial Least Squares (BPLS) technique to establish context-encoded Hough Regression Models (HRMs), which are linear regression models that cast probabilistic Hough votes to predict object locations. BPLS is an efficient variant of Partial Least Squares (PLS). PLS-based regression techniques (including BPLS) can reduce the redundancy and eliminate the multicollinearity of a feature set. And the appropriate value of the only parameter used in PLS (i.e., the number of latent components) can be determined by using a cross-validation procedure. Second, to efficiently handle object scale changes, we propose a novel multi-scale voting scheme. In this scheme, multiple Hough images corresponding to multiple object scales can be obtained simultaneously. Third, an object in a test image may correspond to multiple true and false positive hypotheses at different scales. Based on the proposed multi-scale voting scheme, a principled strategy is proposed to fuse hypotheses to reduce false positives by evaluating normalized pointwise mutual information between hypotheses. In the experiments, we also compare the proposed HRM approach with its several variants to evaluate the influences of its components on its performance. Experimental results show that the proposed HRM approach has achieved desirable performances on popular benchmark datasets.
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of polynomial sequences developed by J. L. Gross, T. Mansour, T. W. Tucker, and D. G. L. Wang, we show that the roots of these `sign-alternating Gibonacci polynomials' are real and distinct, and we obtain explicit bounds on these roots. We also derive Binet-type closed expressions for the polynomials. Some of these results are applied to resolve finiteness questions pertaining to a one-player combinatorial game (or puzzle) modelled after a well-known puzzle we call the `Networked-numbers Game.' Elsewhere, the first- and second-named authors, in collaboration with A. Nance, have found rank symmetric `diamond-colored' distributive lattices naturally related to certain representations of the special linear Lie algebras. Those lattice cardinalities can be computed using sign-alternating Fibonacci polynomials, and the lattice rank generating functions correspond to the rows of some new and easily defined triangular integer arrays. Here, we present Gibonaccian, and in particular Lucasian, versions of those symmetric Fibonaccian lattices/results, but without the algebraic context of the latter.
For a sequence of independent events $E_n$ the sum of the associated zero-one random variables $1_{E_n}$ is almost surely finite or almost surely infinite according as the sum of the probabilities converges or diverges. In this paper the events $E_n$ are contaminated. What can one say about $\sum1_{D_n}$ when $D_n=E_n\setminus A_n$ for a sequence of events $A_n$ with vanishing probability? The behaviour depends on the relation between the events $E_n$ and $A_n$ and on the size of the events. We prove a Borel-Cantelli lemma for the contaminated variables and give an application in extreme value theory.
The Neutron-star Interior Composition Explorer (NICER) is an X-ray astrophysics payload that will be placed on the International Space Station. Its primary science goal is to measure with high accuracy the pulse profiles that arise from the non-uniform thermal surface emission of rotation-powered pulsars. Modeling general relativistic effects on the profiles will lead to measuring the radii of these neutron stars and to constraining their equation of state. Achieving this goal will depend, among other things, on accurate knowledge of the source, sky, and instrument backgrounds. We use here simple analytic estimates to quantify the level at which these backgrounds need to be known in order for the upcoming measurements to provide significant constraints on the properties of neutron stars. We show that, even in the minimal-information scenario, knowledge of the background at a few percent level for a background-to-source countrate ratio of 0.2 allows for a measurement of the neutron star compactness to better than 10% uncertainty for most of the parameter space. These constraints improve further when more realistic assumptions are made about the neutron star emission and spin, and when additional information about the source itself, such as its mass or distance, are incorporated.
We report the effect of epitaxial strain on the magnitude and retention of the ferroelectric field effect in high quality PbZr$_{0.3}$Ti$_{0.7}$O$_3$ (PZT)/3.8-4.3 nm Sm$_{0.5}$Nd$_{0.5}$NiO$_3$ (SNNO) heterostructures grown on (001) LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) substrates. For SNNO on LAO, which exhibits a first-order metal-insulator transition (MIT), switching the polarization of PZT induces a 10 K shift in the transition temperature $T_{MI}$, with a maximum resistance change between the on and off states of $\Delta$$R$/$R_{on}$ ~75%. In sharp contrast, only up to 5% resistance change has been induced in SNNO on STO, where the MIT is second-order, with the modulation of $T_{MI}$ negligibly small. We also observe thermally activated retention of the off state resistance $R_{off}$ in both systems, with the activation energy of 22 meV (28 meV) for devices on LAO (STO). The time dynamics and thermal response of the field effect instability points to phonon-assisted interfacical trapping of charged mobile defects, which are attributed to strain induced oxygen vacancies. At room temperature, $R_{off}$ stabilizes at ~55% and ~19% of the initial switching levels for SNNO on LAO and STO, respectively, reflecting the significantly different oxygen vacancy densities in these two systems. Our results reveal the critical role of strain in engineering and modeling the complex oxide composite structures for nanoelectronic and spintronic applications.
We study the covering radii of $2$-transitive permutation groups of Lie rank one, giving bounds and links to finite geometry.
We construct three new families of fibrations $\pi : S \to B$ where $S$ is an algebraic complex surface and $B$ a curve that violate Xiao's conjecture relating the relative irregularity and the genus of the general fiber. The fibers of $\pi$ are certain \'etale cyclic covers of hyperelliptic curves that give coverings of $P^1$ with dihedral monodromy.   As an application, we also show the existence of big and nef effective divisors in the Brill-Noether range.
The Optical-to-Near-infrared variability time delay have already been reported for a small number (about 7) of AGNs and has been firmly established only for 5 of them. The time delay is probably increasing with the IR wavelengths. The most naturally this time delay can be interpreted by the model where IR emission is attributed to circumnuclear dust heated by the nuclear radiation. In given model a suggestion on narrowness of the near-infrared (NIR) emission region is quite natural, as far as the dust can be not saved on distances from the nucleus closer then some critical value, on which it is reached the sublimation temperature for graphite particles (Barvainis, 1987). For NGC 4151 case it has been shown that the NIR region has a form of thin ring or torus. The radius of this ring correlates with level of the nucleus activity (Oknyanskij et al. 1999). This dependency of radius of the NIR emission region from luminosity reveals itself as under object variability (as in the case of NGC4151), and also when objects with high and low luminosity are considered. We assume that the observed time delays allow us to derive a redshift independent luminosity distances to AGNs and estimate a Hubble constant.   Some problems of using this strategy for the Hubble constant determination are discussed.
In these notes, we explain residue formulae for volumes of convex polytopes, and for Ehrahrt polynomials based on the notion of total residue. We apply this method to the computation of the volume of the Chan-Robbins polytope. The final computation is based on a total residue formula for the system $A_n$, similar to Morris identity. For flow polytopes, a formula of change of variables in total residues leads to a "nice formula" for Ehrhart polynomials in function of mixed volumes. We apply it to Pitman-Stanley polytope.
Pure gravity in (2+1)-dimensions with negative cosmological constant is classically equivalent Chern-Simons gauge theory with gauge group SO(2; 2), which may be realized on chiral and antichiral gauge connections. This paper looks at half-AdS geometries i.e. those with a trivial rightmoving gauge connection while the left-moving connection is a standard (Banados-Teitelboim- Zanelli) BTZ connection. These are shown to be related by diffeomorphism to a BTZ geometry with different mass and angular momentum. Generically this is over-spinning, leading to a naked closed timelike curves. Other closely related solutions are also studied. These results suggest that the measure of the Chern-Simons path integral cannot factorize in a chiral way, if it is to represent a sum over physically sensible states.
A mixed graph is cospectral to its converse, with respect to the usual adjacency matrices. Hence, it is easy to see that a mixed graph whose eigenvalues occur uniquely, up to isomorphism, must be isomorphic to its converse. It is therefore natural to ask whether or not this is a common phenomenon. This note contains the theoretical evidence to confirm that the fraction of self-converse mixed graphs tends to zero.
The Extragalactic Background Light (EBL) can be probed via the absorption imprint it leaves in the spectra of gamma-ray sources ($\gamma\gamma \rightarrow e^-e^+$). We recently developed a dedicated technique to reconstruct the EBL, and its evolution with redshift, from $\gamma$ ray optical depth data using a large sample of blazars detected by the $Fermi$ Large Area Telescope. Here, we extend this dataset to the TeV regime using ground-based Cherenkov observations of 38 blazars and report the first homogeneous measurement of the EBL spectral intensity covering the ultraviolet to infrared wavelengths ($\sim$0.1-100$\mathrm{\mu m}$). A minimal EBL throughout the wavelength range with respect to integrated galaxy light is found, allowing little additional unresolved emission from faint or truly diffuse populations setting an upper limit of $\lesssim 4~{\rm nW\cdot m^{-2}sr^{-1}}$ at 1.4 ${\rm \mu m}$. In particular, the cosmic optical background (COB) at $z=0$ is found to be $27.8_{-2.0}^{+2.1}~{\rm nW\cdot m^{-2}sr^{-1}}$. This work lays the foundation for accurate gamma-ray measurements of the EBL across its whole spectral range using a combination of GeV and TeV data.
The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied by a random fitness. We concentrate on the typical behaviour of the graph by calculating the fitness distribution of a vertex chosen proportional to its degree. For a particular variant of the model, this analysis was first carried out by Borgs, Chayes, Daskalakis and Roch. However, we present a new method, which is robust in the sense that it does not depend on the exact specification of the attachment law. In particular, we show that a peculiar phenomenon, referred to as Bose-Einstein condensation, can be observed in a wide variety of models. Finally, we also compute the joint degree and fitness distribution of a uniformly chosen vertex.
Optically-detected magnetic resonance (ODMR) and positron annihilation spectroscopy (PAS) experiments have been employed to study magnesium-doped GaN layers grown by metal-organic vapor phase epitaxy. As the Mg doping level is changed, the combined experiments reveal a strong correlation between the vacancy concentrations and the intensity of the red photoluminescence band at 1.8 eV. The analysis provides strong evidence that the emission is due to recombination in which electrons both from effective mass donors and from deeper donors recombine with deep centers, the deep centers being vacancy-related defects.
Magnetars are slowly-rotating neutron stars with extremely strong magnetic fields ($10^{13-15}$ G), episodically emitting $\sim100$ ms long X-ray bursts with energies of $\sim10^{40-41}$ erg. Rarely, they produce extremely bright, energetic giant flares that begin with a short ($\sim0.2$ s), intense flash, followed by fainter, longer lasting emission modulated by the magnetar spin period (typically 2-12 s), thus confirming their origin. Over the last 40 years, only three such flares have been observed in our local group; they all suffered from instrumental saturation due to their extreme intensity. It has been proposed that extra-galactic giant flares likely constitute a subset of short gamma-ray bursts, noting that the sensitivity of current instrumentation prevents us from detecting the pulsating tail, while the initial bright flash is readily observable out to distances $\sim 10-20$ Mpc. Here, we report X- and gamma-ray observations of GRB 200415A, which exhibits a rapid onset, very fast time variability, flat spectra and significant sub-millisecond spectral evolution. These attributes match well with those expected for a giant flare from an extra-galactic magnetar, noting that GRB 200415A is directionally associated with the galaxy NGC 253 ($\sim$3.5 Mpc away). The detection of $\sim3$ MeV photons provides definitive evidence for relativistic motion of the emitting plasma. The observed rapid spectral evolution can naturally be generated by radiation emanating from such rapidly-moving gas in a rotating magnetar.
A generalized stepping stone model with $\Xi$-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman's coalescent is replaced by $\Xi$-coalescent. We prove the existence of such a process by specifying its moments using the dual function-valued $\Xi$-coalescent process with geographical labels and migration, and then verifying a multidimensional Hausdorff moment problem. We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.
The large-scale structure in the Universe is believed to arise out of small random density perturbations generated in the very early Universe, that are amplified by gravity. Large and usually intricate N-body simulations are typically employed to model the complex nonlinear dynamics in a self gravitating medium. We suggest a very simple model which predicts, on large scales, the correct density and velocity distributions. The model does not involve an explicit computation of the gravitational force. It is based on a simple transformation of the variables and local conservation laws of mass and {\it generalized} linear momentum. The model demonstrates that the overall appearance of large-scale structure in the Universe is explicitly determined by the initial velocity field and it reveals the most significant large-scale effects of gravity on the formation of structure.
A disturbing aspect of Hawking's derivation of black hole radiance is the need to invoke extreme conditions for the quantum field that originates the emitted quanta. It is widely argued that the derivation requires the validity of the conventional relativistic field theory to arbitrarily high, trans-Planckian scales. We stress in this note that this is not necessarily the case if the question is presented in a covariant way. We point out that Hawking radiation is immediately robust against an invariant Planck-scale cutoff. This important feature of Hawking radiation is relevant for a quantum gravity theory that preserves, in some way, the Lorentz symmetry.
The volume fluctuations in the steady state reached by a vibrated granular gas of hard particles confined by a movable piston on the top are investigated by means of event driven simulations. Also, a compressibility factor, measuring the response in volume of the system to a change in the mass of the piston, is introduced and measured. From the second moment of the volume fluctuations and the compressibility factor, an effective temperature is defined, by using the same relation as obeyed by equilibrium molecular systems. The interpretation of this effective temperature and its relationship with the granular temperature of the gas, and also with the velocity fluctuations of the movable piston, is discussed. It is found that the ratio of the temperature based on the volume fluctuations to the temperature based on the piston kinetic energy, obeys simple dependencies on the inelasticity and on the piston-particle mass ratio.
We study the circumstellar evolution of the binary HD101584, consisting of a post-AGB star and a low-mass companion, which is most likely a post-common-envelope-evolution system. We used ALMA observations of the 12CO, 13CO, and C18O J=2-1 lines and the 1.3mm continuum to determine the morphology, kinematics, masses, and energetics of the circumstellar environment. The circumstellar medium has a bipolar hour-glass structure, seen almost pole-on, formed by an energetic jet, about 150 km/s. We conjecture that the circumstellar morphology is related to an event that took place about 500 year ago, possibly a capture event where the companion spiraled in towards the AGB star. However, the kinetic energy of the accelerated gas exceeds the released orbital energy, and, taking into account the expected energy transfer efficiency of the process, the observed phenomenon does not match current common-envelope scenarios. This suggests that another process must augment, or even dominate, the ejection process. A significant amount of material resides in an unresolved region, presumably in the equatorial plane of the binary system.