ShantanuT01/DACTYL-Pretraining huggingface dataset:
A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing. The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a good drawing of $G$ in the plane. The {\it $n$-dimensional augmented cube} $AQ_n$, proposed by S.A. Choudum and V. Sunitha, is an important interconnection network with good topological properties and applications. In this paper, we obtain an upper bound on the crossing number of $AQ_n$ less than $26/324^{n}-(2n^2+7/2n-6)2^{n-2}$.
Temperley's bijection relates the toroidal dimer model to cycle rooted spanning forests ($CRSF$) on the torus. The height function of the dimer model and the homology class of $CRSF$ are naturally related. When the size of the torus tends to infinity, we show that the measure on $CRSF$ arising from the dimer model converges to a measure on (disconnected) spanning forests or spanning trees. There is a phase transition, which is determined by the average height change.
Three Algol-type binary systems (IO Cep, IM Cep and TX Ari) showing cyclic orbital period changes are studied. The combination of time of minimum data from the ground-based observations together with high precision photometric data from the TESS satellite enabled us to estimate the basic light curve elements of binary systems and mass functions for distant components around the systems. The relation of mass ratio to the system geometry in semi-detached binary stars allowed us to determine the mass ratio of the binary components without using spectra. By using the color and distance information from the GAIA EDR3 and light contributions of the components from the light curve analysis, the astrophysical parameters of the binary components as well as the minimum masses of the distant components are obtained with an uncertainty of ~10-20 per cent indicating that the method can be a good guide for those studying with faint systems where spectra with sufficient resolution and S/N ratio are difficult to acquire.
We consider diploid bi-parental analogues of Cannings models: in a population of fixed size $N$ the next generation is composed of $V_{i,j}$ offspring from parents $i$ and $j$, where $V=(V_{i,j})_{1\le i\neq j \le N}$ is a (jointly) exchangeable (symmetric) array. Every individual carries two chromosome copies, each of which is inherited from one of its parents. We obtain general conditions, formulated in terms of the vector of the total number of offspring to each individual, for the convergence of the properly scaled ancestral process for an $n$-sample of genes towards a ($\Xi$-)coalescent. This complements M\"ohle and Sagitov's (2001) result for the haploid case and sharpens the profile of M\"ohle and Sagitov's (2003) study of the diploid case, which focused on fixed couples, where each row of $V$ has at most one non-zero entry.   We apply the convergence result to several examples, in particular to two diploid variations of Schweinsberg's (2003) model, leading to Beta-coalescents with two-fold and with four-fold mergers, respectively.
An effective time--dependent cosmological constant can be recovered for higher--order theories of gravity by extending to these ones the no--hair conjecture. The results are applied to some specific cosmological models.
Eighty years ago Eyring proposed that the shear viscosity of a liquid, $\eta$, has a quantum limit $\eta \gtrsim n\hbar$ where $n$ is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound $\frac{\eta}{s}\geq \frac{\hbar}{4\pi k_{B}}$ for the ratio between the shear viscosity and the entropy density, $s$. Using Dynamical Mean-Field Theory (DMFT) we calculate the shear viscosity and entropy density for a fermionic fluid described by a single band Hubbard model at half filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid $^{3}$He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid $1/T^{2}$ dependence, where $T$ is the temperature. With increasing temperature and interaction strength $U$ there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasi-particle based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid $^{3}$He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge transfer salts.
We use the theta lift to study the multiplicity with which certain automorphic representations of cohomological type occur in a family of congruence covers of an arithmetic manifold. When the family of covers is a so-called `p-adic congruence tower' we obtain sharp asymptotics for the number of representations which occur as lifts. When combined with theorems on the surjectivity of the theta lift due to Howe and Li, and Bergeron, Millson and Moeglin, this allows us to verify certain cases of a conjecture of Sarnak and Xue.
We apply the diabatic framework, a QCD-based formalism for the unified study of quarkoniumlike systems in terms of heavy quark-antiquark and open-flavor meson-meson components, to the description of coupled-channel meson-meson scattering. For this purpose, we first introduce a numerical scheme to find the solutions of the diabatic Schr\"odinger equation for energies in the continuum, then we derive a general formula for calculating the meson-meson scattering amplitudes from these solutions. We thus obtain a completely nonperturbative procedure for the calculation of open-flavor meson-meson scattering cross sections from the diabatic potential, which is directly connected to lattice QCD calculations. A comprehensive analysis of various elastic cross sections for open-charm and open-bottom meson-meson pairs is performed in a wide range of the center-of-mass energies. The relevant structures are identified, showing a spectrum of quasi-conventional and unconventional quarkoniumlike states. In addition to the customary Breit-Wigner peaks we obtain nontrivial structures such as threshold cusps and minimums. Finally, our results are compared with existing data and with results from our previous bound-state--based analysis, finding full compatibility with both.
This paper is devoted to compute the energy-momentum densities for two exact solutions of the Einstein field equations by using the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and M\"{o}ller. The spacetimes under consideration are the Weyl-Lewis-Papapetrou and the Levi-Civita metrics. The Weyl metric becomes the special case of the Weyl-Lewis-Papapetrou solution. The Levi-Civita metric provides constant momentum in each prescription with different energy density. The Weyl-Lewis-Papapetrou metric yields all the quantities different in each prescription. These differences support the well-defined proposal developed by Cooperstock and from the energy-momentum tensor itself.
The theoretical predictions in the MSSM for Higgs-boson production at a future e^+e^- Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider.
Sch\"utzenberger's jeu de taquin is an algorithm on the structure of tableaux, which transforms a skew tableau into a Young one by local transformation rules on the columns of the tableaux. This algorithm defines an equivalence relation on tableaux compatible with the plactic congruence, and gives a proof of the Littlewood-Richardson rule on Schur polynomials. In this article, we introduce the notion of string of columns rewriting system as mechanism of transformations of glued sequences of columns. We describe the execution of the jeu de taquin algorithm as rewriting paths of a string of columns rewriting. We deduce algebraic properties on the plastic congruence and we relate the jeu de taquin to insertion algorithms on tableaux.
We prove an analogue of Kac's Theorem, describing the dimension vectors of indecomposable coherent sheaves, or parabolic bundles, over weighted projective lines. We use a theorem of Peng and Xiao to associate a Lie algebra to the category of coherent sheaves for a weighted projective line over a finite field, and find elements of this Lie algebra which satisfy the relations defining the loop algebra of a Kac-Moody Lie algebra.
Slow nucleons emitted during a hadron-nucleus interaction can give information on the centrality, impact parameter of the collision. The aim of this note is to provide the reader with the important characteristics of the slow nucleons, focusing on their spectra, correlations. This study tries to build on evidences, hence more weight is put on experimental results than on models.
Dwarf galaxies found in isolation in the Local Group (LG) are unlikely to have interacted with the large LG spirals, and therefore environmental effects should not be the main drivers of their evolution. We aim to provide insight into the internal mechanisms shaping LG dwarf galaxies by increasing our knowledge of the internal properties of isolated systems. We focus on the evolved stellar component of the Aquarius dwarf, whose kinematic and metallicity properties have only recently started to be explored. We have obtained spectroscopic data in the the near-infrared CaII triplet lines region with FORS2 at the Very Large Telescope for 53 red giant branch (RGB) stars, to derive line-of-sight velocities and [Fe/H] of the individual RGB stars. We have derived a systemic velocity of $-142.2^{+1.8}_{-1.8}$ km s$^{-1}$, in agreement with previous measurements from both the HI gas and stars. The internal kinematics of Aquarius appears to be best modelled by a combination of random motions (l.o.s. velocity dispersion of $10.3^{+1.6}_{-1.3}$ km s$^{-1}$) and linear rotation (with a gradient $-5.0^{+1.6}_{-1.9}$ km s$^{-1}$ arcmin$^{-1}$) along a P.A.=$139_{-27}^{+17}$ deg, consistent with the optical projected major axis. This rotation signal is significantly misaligned or even counter-rotating to that derived from the HI gas. We also find the tentative presence of a mild negative metallicity gradient and indications that the metal-rich stars have a colder velocity dispersion than the metal-poor ones. This work represents a significant improvement with respect to previous measurements of the RGB stars of Aquarius, as it doubles the number of member stars studied in the literature. We speculate that the misaligned rotation between the HI gas and evolved stellar component might have been the result of recent accretion of HI gas or re-accretion after gas-loss due to internal stellar feedback.
A simple phenomenological model, based on the \'Swi{\c a}tecki idea for evaluation of the spontaneous fission half-lives is proposed. The model contains only one adjustable parameter fixed to the data for even-even nuclei and two additional hindrance factors to the life-times, which give the effect of odd particles. A good agreement with the experimental data for all fissioning nuclei is achieved.
We describe descent on families of torsors of a constant torus. A recent result of Browning and Matthiesen then implies that the Brauer--Manin obstruction controls the Hasse principle and weak approximation when the ground field is the field of rational numbers and the singular fibres are all defined over this field.
We present the calculation of Next-to-Leading-Order Quantum Chromo Dynamics corrections for the production of a W or Z weak boson associated with a bottom anti-bottom quark pair at hadron colliders (p anti-p, pp to W/Z b anti-b), including the effects of a non-zero bottom-quark mass. We find a considerable reduction of the renormalization and factorization scale dependence of our results with respect to Leading-Order calculations. In particular, we study the impact of the corrections on the total cross section and invariant mass distributions of the bottom anti-bottom quark pair at the Fermilab Tevatron collider. We perform a detailed comparison with a calculation that considers massless bottom quarks and find significant deviations in regions of phase space with small invariant mass of the bottom anti-bottom quark pair. Our results will be relevant to ongoing and future searches at hadron colliders, as the W/Z b anti-b production mode is the main background to important signals, such as light Standard Model Higgs boson production or single top-quark production.
The pioneering computer simulations of the energy relaxation mechanisms performed by Fermi, Pasta and Ulam can be considered as the first attempt of understanding energy relaxation and thus heat conduction in lattices of nonlinear oscillators. In this paper we describe the most recent achievements about the divergence of heat conductivity with the system size in 1d and 2d FPU-like lattices. The anomalous behavior is particularly evident at low energies, where it is enhanced by the quasi-harmonic character of the lattice dynamics. Remakably, anomalies persist also in the strongly chaotic region where long--time tails develop in the current autocorrelation function. A modal analysis of the 1d case is also presented in order to gain further insight about the role played by boundary conditions.
We give upper bounds for triples of subsets of a finite group such that the triples of elements that multiply to 1 form a perfect matching. Our bounds are the first to give exponential savings in powers of an arbitrary finite group. Previously, Blasiak-Church-Cohn-Grochow-Naslund-Sawin-Umans gave similar bounds in abelian groups of bounded exponent, and Petrov gave exponential bounds in certain p-groups.
In $L_2({\mathbb R}^d;{\mathbb C}^n)$, we study a selfadjoint strongly elliptic operator $A_\varepsilon$ of order $2p$ given by the expression $b({\mathbf D})^* g({\mathbf x}/\varepsilon) b({\mathbf D})$, $\varepsilon >0$. Here $g({\mathbf x})$ is a bounded and positive definite $(m\times m)$-matrix-valued function in ${\mathbb R}^d$; it is assumed that $g({\mathbf x})$ is periodic with respect to some lattice. Next, $b({\mathbf D})=\sum_{|\alpha|=p}^d b_\alpha {\mathbf D}^\alpha$ is a differential operator of order $p$ with constant coefficients; $b_\alpha$ are constant $(m\times n)$-matrices. It is assumed that $m\ge n$ and that the symbol $b({\boldsymbol \xi})$ has maximal rank. For the resolvent $(A_\varepsilon - \zeta I)^{-1}$ with $\zeta \in {\mathbb C} \setminus [0,\infty)$, we obtain approximations in the norm of operators in $L_2({\mathbb R}^d;{\mathbb C}^n)$ and in the norm of operators acting from $L_2({\mathbb R}^d;{\mathbb C}^n)$ to the Sobolev space $H^p({\mathbb R}^d;{\mathbb C}^n)$, with error estimates depending on $\varepsilon$ and $\zeta$.
The light curve of V921 Her in ultraviolet band observed by the Lunar-based Ultraviolet Telescope (LUT) is analyzed by the Wilson-Devinney code. Our solutions conclude that V921 Her is an early type marginal contact binary system with an additional close-in component. The binary system is under poor thermal contact with a temperature difference of nearly $700K$ between the two components. The close-in component contributes about $19\,\%$ of the total luminosity in the triple system. Combining the radial velocity study together with our photometric solutions, the mass of the primary star and secondary one are calculated to be $M_1 = 1.784(\pm0.055)M_\odot$, $M_2 = 0.403(\pm0.012)M_\odot$. The evolutionary scenario of V921 Her is discussed. All times of light minimum of V921 Her available in the bibliography are taken into account and the $O - C$ curve is analyzed for the first time. The most probable fitting results are discussed in the paper, which also confirm the existence of a third component ($P_3=10.2$ year) around the binary system. The period of V921 Her is also undergoing a continuously rapid increase at a rate of $dP/dt=+2.79\times{10^{-7}}day\cdot year^{-1}$, which may due to mass transfer from the less massive component to the more massive one.
We present the analysis of two Suzaku observations of GX 301-2 at two orbital phases after the periastron passage. Variations in the column density of the line-of-sight absorber are observed, consistent with accretion from a clumpy wind. In addition to a CRSF, multiple fluorescence emission lines were detected in both observations. The variations in the pulse profiles and the CRSF throughout the pulse phase have a signature of a magnetic dipole field. Using a simple dipole model we calculated the expected magnetic field values for different pulse phases and were able to extract a set of geometrical angles, loosely constraining the dipole geometry in the neutron star. From the variation of the CRSF width and energy, we found a geometrical solution for the dipole, making the inclination consistent with previously published values.
We consider the residual B-model variation of Hodge structure of Iritani defined by a family of toric Calabi--Yau hypersurfaces over a punctured disk $D \setminus \{ 0\}$. It is naturally extended to a logarithmic variation of polarized Hodge structure of Kato--Usui on the whole disk $D$. By restricting it to the origin, we obtain a polarized logarithmic Hodge structure (PLH) on the standard log point. In this paper, we describe the PLH in terms of the integral affine structure of the dual intersection complex of the toric degeneration in the Gross--Siebert program.
We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the path till the time it reaches a distant site. In that purpose, we adapt the method developed in the ballistic case by Comets et al (2014) and Falconnet, Loukianova and Matias (2014). Using a supplementary assumption due to the specificity of the sub-ballistic regime, we prove consistency and asymptotic normality as the distant site tends to infinity. To emphazis the role of the additional assumption, we investigate the Temkin model with unknown support, and it turns out that the MLE is consistent but, unlike in the ballistic regime, the Fisher information is infinite. We also explore the numerical performance of our estimation procedure.
At the turn of the decade we arguably move from the era of precision cosmology to the era of galaxy formation. One approach to this problem will be via the construction of comprehensive galaxy samples. In this review I take the opportunity to highlight a number of challenges which must be overcome before we can use such data to construct a robust empirical blueprint of galaxy evolution. The issues briefly highlighted here are: the Hubble tuning fork versus galaxy components, the hierarchy of structure, the accuracy of structural decompositions, galaxy photometry, incompleteness, cosmic variance, photometric versus spectroscopic redshifts, wavelength bias, dust attenuation, and the disconnect with theory. These concerns essentially form one of the key motivations of the GAMA survey which, as one of its goals, will establish a complete comprehensive kpc-resolution 3D multi-wavelength (UV-Opt-IR-Radio) database of 250k galaxy systems to z <0.5.
An extension of the previously proposed Variable Moment of Inertia with Softness model VMIS has been applied to describe successfully the effect of backbending in some deformed e-e nuclei. The model shows good results in the rare earth and actinide regions.
In this work, we report on the emergence of a photonic Hall effect (PHE) system within a narrow filtered background of a one-dimensional defective optical dielectric structure with graphene under the static QHE regime. It is observed that at low temperature and relatively strong applied magnetic fields, electromagnetic defective transmission spectra corresponding to the two decoupled right- and left-handed polarized modes possess a step-like transmission feature which are referred to as "quantum Hall defect modes" (QHD modes or QHDs) in this paper. Tunable growing transitional transmission steps for QHDs with increasing the magnetic field intensity was shown to be possible. Observation of sensitive magneto-transmission oscillations to the thermal excitations in the last plateaus with slow ascending toward unity is another special feature noted in this work. The results of this study which is carried out based on a rapid standard calculations for transfer matrix approach is supplied with commercial simulations marking the first PHE system promise an proper candidate for new photonic applications, especially new tunable magneto-based lenses and photonic magneto-thermal sensors.
Using molecular-dynamics simulation and finite-element modelling, we simulate nanoindentation into the three principal surfaces -- the (100), (110) and (111) surface -- of Cu and Al. In the elastic regime, the simulation data agree fairly well with the linear elastic theory of indentation into an elastically anisotropic substrate. With increasing indentation, the effect of pressure hardening becomes visible. When the critical stress for dislocation nucleation is reached, even the elastically isotropic Al shows a strong dependence of the surface orientation on the force-displacement curves. After the load drop, when plasticity ahs set in, the influence of the surface orientation is lost, and the contact pressure (hardness) becomes independent of the surface orientation.
We present the results of 3 GHz radio continuum observations of the 8 host galaxies of super-luminous supernovae (SLSNe) at $0.1 < z < 0.3$ by using the Karl G. Jansky Very Large Array. Four host galaxies are detected significantly, and two of them are found to have high star-formation rates (SFRs $>$ 20 $M_{\odot}$ yr$^{-1}$) derived from radio emission, making them the most intensely star-forming host galaxies among SLSN host galaxies. We compare radio SFRs and optical SFRs, and find that three host galaxies have an excess in radio SFRs by a factor of $>$2, suggesting the existence of dust-obscured star formation, which cannot be traced by optical studies. Two of the three host galaxies, which are located in the galaxy main sequence based on optical SFRs, are found to be above the main sequence based on their radio SFRs. This suggests a higher fraction of starburst galaxies in SLSN hosts than estimated in previous studies. We calculate extinction from the ratio between radio SFRs and dust-uncorrected optical SFRs and find that the hosts are on the trend of increasing extinction with metallicity, which is consistent with the relation in local star-forming galaxies. We also place a constraint on a pulsar-driven SN model, which predicts quasi-steady synchrotron radio emission.
We give an example of a BH(5; 5) matrix M satisfying that the eigenvalues of the unitary matrix $\frac{1}{\sqrt5}M$ are all primitive 10-th roots of unity and such that $\frac{1}{5}M^3$ is not a BH(5; 5) matrix. This example gives a negative answer to a conjecture proposed by R. Egan and P. O. Cathain.