ShantanuT01/DACTYL-Pretraining huggingface dataset:
A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the edges of $G$ by nonnegative integers such that for each vertex $v\in V$, the sum of labels of all edges incident to $v$ is equal to the same number $s$. Stanley gave remarkable results on magic labellings, but the distinct labelling case is much more complicated. We consider the complete construction of all magic labellings of a given graph $G$. The idea is illustrated in detail by dealing with three regular graphs. We give combinatorial proofs. The structure result was used to enumerate the corresponding magic distinct labellings.
I describe an algebro-geometric theory of skeleta, which provides a unified setting for the study of tropical varieties, skeleta of non-Archimedean analytic spaces, and affine manifolds with singularities. Skeleta are spaces equipped with a structure sheaf of topological semirings, and are locally modelled on the spectra of the same. The primary result of this paper is that the topological space underlying a non-Archimedean analytic space may locally be recovered from the sheaf of `pointwise valuations' of its analytic functions.
We present deep Hubble Space Telescope imaging of five faint dwarf galaxies associated with the nearby spiral NGC 253 (D$\approx$3.5 Mpc). Three of these are newly discovered ultra-faint dwarf galaxies, while all five were found in the Panoramic Imaging Survey of Centaurus and Sculptor (PISCeS), a Magellan$+$Megacam survey to identify faint dwarfs and other substructures in resolved stellar light around massive galaxies outside of the Local Group. Our HST data reach $\gtrsim$3 magnitudes below the tip of the red giant branch for each dwarf, allowing us to derive their distances, structural parameters, and luminosities. All five systems contain predominantly old, metal-poor stellar populations (age$\sim$12 Gyr, [M/H]$\lesssim$$-$1.5) and have sizes ($r_{h}$$\sim$110-3000 pc) and luminosities ($M_V$$\sim$$-7$ to $-12$ mag) largely consistent with Local Group dwarfs. The three new NGC 253 satellites are among the faintest systems discovered beyond the Local Group. We also use archival HI data to place limits on the gas content of our discoveries. Deep imaging surveys such as our program around NGC 253 promise to elucidate the faint end of the satellite luminosity function and its scatter across a range of galaxy masses, morphologies, and environments in the decade to come.
In this talk we analyse the claim that supersymmetry (SUSY) naturally accounts for the observed dark matter density. In many cases, it is necessary to tune the parameters of a SUSY model to fit the WMAP data. We provide a quantitative analysis of the degree of tuning required for different annihilation channels. Some regions are natural, requiring no tuning at all, whereas others require tuning at the 0.1% level.
The model of magnetic braking of solar rotation considered by Charbonneau & MacGregor (1993) has been modified so that it is able to reproduce for the first time the rotational evolution of both the fastest and slowest rotators among solar-type stars in open clusters of different ages, without coming into conflict with other observational constraints, such as the time evolution of the atmospheric Li abundance in solar twins and the thinness of the solar tachocline. This new model assumes that rotation-driven turbulent diffusion, which is thought to amplify the viscosity and magnetic diffusivity in stellar radiative zones, is strongly anisotropic with the horizontal components of the transport coefficients strongly dominating over those in the vertical direction. Also taken into account is the poloidal field decay that helps to confine the width of the tachocline at the solar age. The model's properties are investigated by numerically solving the azimuthal components of the coupled momentum and magnetic induction equations in two dimensions using a finite element method
The element specificity of soft X-ray spectroscopy makes it an ideal tool for analyzing the microscopic origin of ultrafast dynamics induced by localized optical excitation in metal-insulator heterostructures. Using [Fe/MgO]$_n$ as a model system, we perform ultraviolet pump/soft X-ray probe experiments, which are sensitive to all constituents of these heterostructures, to probe both electronic and lattice excitations. Complementary ultrafast electron diffraction experiments independently analyze the lattice dynamics of the Fe constituent, and together with ab initio calculations yield comprehensive insight into the microscopic processes leading to local relaxation within a single constituent or non-local relaxation between two constituents. Besides electronic excitations in Fe, which are monitored at the Fe L$_3$ absorption edge and relax within 1 ps by electron-phonon coupling, soft X-ray analysis identifies a change at the oxygen K absorption edge of the MgO layers which occurs within 0.5 ps. This ultrafast energy transfer across the Fe-MgO interface is mediated by high-frequency, interface vibrational modes, which are excited by hot electrons in Fe and couple to vibrations in MgO in a mode-selective, non-thermal manner. A second, slower timescale is identified at the oxygen K pre-edge and the Fe L$_3$ edge. The slower process represents energy transfer by acoustic phonons and contributes to thermalization of the entire heterostructure. We thus find that the interfacial energy transfer is associated with non-equilibrium behavior in the phonon system. Because our experiments lack signatures of charge transfer across the interface, we conclude that phonon-mediated processes dominate the competition of electronic and lattice excitations in these non-local, non-equilibrium dynamics.
We discuss selection rules and intensities of photocurrent of a two-dimensional electron gas in a strong magnetic field via absorptions of orbital angular momentum carried by obliquely irradiated optical vortex beams. By angular deflection, optical vortex beams on the two-dimensional electron gas interface can be seen as a superposition of the various orbital angular momentum states. As a result, it is demonstrated that it is yielded that the angular momentum selection rules and induced currents are modified from the case of vertical incidence.
An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index $n$, on the leading order gravitational waveforms is studied.
We consider the following nonlinear Choquard equation with Dirichlet boundary condition $$-\Delta u =\left(\int_{\Omega}\frac{|u|^{2_{\mu}^{\ast}}}{|x-y|^{\mu}}dy\right)|u|^{2_{\mu}^{\ast}-2}u+\lambda f(u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \Omega, $$ where $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$, $\lambda>0$, $N\geq3$, $0<\mu<N$ and $2_{\mu}^{\ast}$ is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on different types of nonlinearities $f(u)$, we are able to prove some existence and multiplicity results for the equation by variational methods.
We give a formula for the Chern character on the DG-category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\mathcal{O}_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern character coincides with the classical one for perfect complexes.
The rotation periods of the magnetic Ap stars span five to six orders of magnitude. Period differentiation must have taken place at the pre-main sequence stage, but the physical processes that lead to it remain elusive. The study of Ap stars that have rotation periods of tens to hundreds of years represents a promising avenue to gain additional insight into the origin and evolution of rotation in Ap stars.   Historically, almost all the longest period Ap stars known have been found to be strongly magnetic; very few weakly magnetic Ap stars with very long periods have been identified and studied. We performed a systematic search based on TESS data to identify super-slowly rotating Ap (ssrAp) stars independently of the strengths of their magnetic fields, with the intention to characterise the distribution of the longest Ap star rotation periods in an unbiased manner. We find 67 Ap stars with no rotational variability in the northern ecliptic hemisphere TESS data. Among them, 46 are newly identified ssrAp star candidates, which is double the number previously found in the southern ecliptic hemisphere.   We confirm that super-slow rotation tends to occur less frequently in weakly magnetic Ap stars than in strongly magnetic stars. We present new evidence of the existence of a gap between ~2 kG and ~3 kG in the distribution of the magnetic field strengths of long period Ap stars. We also confirm that the incidence of roAp stars is higher than average in slowly rotating Ap stars. We report the unexpected discovery of nine definite and five candidate {\delta} Sct stars, and of two eclipsing binaries. This work paves the way for a systematic, unbiased study of the longest period Ap stars, with a view to characterise the correlations between their rotational, magnetic, and pulsational properties.
We present a measurement of the expansion and brightening of G1.9+0.3, the youngest Galactic supernova remnant, comparing Chandra X-ray images obtained in 2007 and 2009. A simple uniform expansion model describes the data well, giving an expansion rate of 0.642 +/- 0.049 % yr^-1, and a flux increase of 1.7 +/- 1.0 % yr^-1. Without deceleration, the remnant age would then be 156 +/- 11 yr, consistent with earlier results. Since deceleration must have occurred, this age is an upper limit; we estimate an age of about 110 yr, or an explosion date of about 1900. The flux increase is comparable to reported increases at radio wavelengths. G1.9+0.3 is the only Galactic supernova remnant increasing in flux, with implications for the physics of electron acceleration in shock waves
Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this note, we exhibit explicit examples contradicting the full conjecture as it currently stands.
In this paper, we study split graphs and related classes of graphs from the perspective of their sequence of vertex degrees and an associated lattice under majorization. Following the work of Merris in 2003, we define blocks $[\alpha(\pi)|\beta(\pi)]$, where $\pi$ is the degree sequence of a graph, and $\alpha(\pi)$ and $\beta(\pi)$ are sequences arising from $\pi$. We use the block representation $[\alpha(\pi)|\beta(\pi)]$ to characterize membership in each of the following classes: unbalanced split graphs, balanced split graphs, pseudo-split graphs, and three kinds of Nordhaus-Gaddum graphs (defined by Collins and Trenk in 2013). As in Merris' work, we form a poset under the relation majorization in which the elements are the blocks $[\alpha(\pi)|\beta(\pi)]$ representing split graphs with a fixed number of edges. We partition this poset in several interesting ways using what we call amphoras, and prove upward and downward closure results for blocks arising from different families of graphs. Finally, we show that the poset becomes a lattice when a maximum and minimum element are added, and we prove properties of the meet and join of two blocks.
Based on the generalized non-Markovian equations obtained earlier for a nonequilibrium one-particle distribution function and potential part of the averaged enthalpy density [Markiv B.B., Omelyan I.P, Tokarchuk M.V., Condens. Matter Phys., 2010, 13, 23005] a spectrum of collective excitations is investigated, where the potential of interaction between particles is presented as a sum of the potential of hard spheres and a certain long-range potential.
We present high-precision photometric light curves of five O-type stars observed with the refurbished {\it Kepler\/} satellite during its Campaign 0. For one of the stars, we also assembled high-resolution ground-based spectroscopy with the {\sc hermes} spectrograph attached to the 1.2-m Mercator telescope. The stars EPIC202060097 (O9.5V) and EPIC202060098 (O7V) exhibit monoperiodic variability due to rotational modulation with an amplitude of 5.6 mmag and 9.3 mmag and a rotation period of 2.63 d and 5.03 d, respectively. EPIC202060091 (O9V) and EPIC202060093 (O9V:pe) reveal variability at low frequency but the cause is unclear. EPIC202060092 (O9V:p) is discovered to be a spectroscopic binary with at least one multiperiodic $\beta\,$Cep-type pulsator whose detected mode frequencies occur in the range $[0.11,6.99]$ d$^{-1}$ and have amplitudes between 0.8 and 2.0 mmag. Its pulsation spectrum is shown to be fully compatible with the ones predicted by core-hydrogen burning O-star models. Despite the short duration of some 33\,d and the limited data quality with a precision near 100 $\mu$mag of these first K2 data, the diversity of possible causes for O-star variability already revealed from campaigns of similar duration by the MOST and CoRoT satellites is confirmed with {\it Kepler}. We provide an overview of O-star space photometry and give arguments why future K2 monitoring during Campaigns 11 and 13 at short cadence, accompanied by time-resolved high-precision high-resolution spectroscopy opens up the possibility of in-depth O-star seismology.
Using ideal relativistic hydrodynamics in 2+1 dimensions, we study the collision energy dependence of radial and elliptic flow, of the emitted hadron spectra, and of the transverse momentum dependence of several hadronic particle ratios, covering the range from Alternating Gradient Synchrotron (AGS) to Large Hadron Collider (LHC) energies. These calculations establish an ideal fluid dynamic baseline that can be used to assess non-equilibrium features manifest in future LHC heavy-ion experiments. Contrary to earlier suggestions we find that a saturation and even decrease of the differential elliptic flow v_2(p_T) with increasing collision energy cannot be unambiguously associated with the QCD phase transition.
A Euclidean distance matrix $D(\alpha)$ is defined by $D_{ij}=(\alpha_i-\alpha_j)^2$, where $\alpha=(\alpha_1,\ldots,\alpha_n)$ is a real vector. We prove that $D(\alpha)$ cannot be written as a sum of $\left[2\sqrt{n}-2\right]$ nonnegative rank-one matrices, provided that the coordinates of $\alpha$ are algebraically independent. This result allows one to solve several open problems in computation theory. In particular, we provide an asymptotically optimal separation between the complexities of quantum and classical communication protocols computing a matrix in expectation.
We derive analytic formula for electric and magnetic fields produced by a moving charged particle in a conducting medium with the electric conductivity $\sigma$ and the chiral magnetic conductivity $\sigma_{\chi}$. We use the Green function method and assume that $\sigma_{\chi}$ is much smaller than $\sigma$. The compact algebraic expressions for electric and magnetic fields without any integrals are obtained. They recover the Lienard-Wiechert formula at vanishing conductivities. Exact numerical solutions are also found for any values of $\sigma$ and $\sigma_{\chi}$ and are compared to analytic results. Both numerical and analytic results agree very well for the scale of high energy heavy ion collisions. The space-time profiles of electromagnetic fields in non-central Au+Au collisions have been calculated based on these analytic formula as well as exact numerical solutions.
We characterized CO2 adsorption and diffusion on the missing row reconstructed Cu(100)-O surface using a combination of scanning tunneling microscopy (STM) and density functional theory (DFT) calculations with dispersion. We deposited CO2 molecules in situ at 5K, which allowed us to unambiguously identify individual CO2 molecules and their adsorption sites. Based on a comparison of experimental and DFT-generated STM images, we find that the CO2 molecules sit in between the O atoms in the missing row reconstructed Cu(100)-O surface. The CO2 molecules are easily perturbed by the STM tip under typical imaging conditions, suggesting that the molecules are weakly bound to the surface. The calculated adsorption energy, vibrational modes, and diffusion barriers of the CO2 molecules also indicate weak adsorption, in qualitative agreement with the experiments. A comparison of tunneling spectroscopy and DFT-calculated density of states shows that the primary change near the Fermi level is associated with changes to the surface states with negligible contribution from the CO2 molecular states.
We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.
We constructed a comprehensive model atom for C\ione\ -- C\ii\ using the most up-to-date atomic data available and evaluated the non-local thermodynamic equilibrium (NLTE) line formation for C\ione\ and C\ii\ in classical 1D models representing the atmospheres of A and late B-type stars. Our NLTE calculations predict the emission that appears at effective temperature of 9250 to 10\,500~K depending on log~$g$ in the C\ione\ 8335, 9405\,\AA\ singlet lines and at \Teff~$>$~15\,000~K (log~$g$ = 4) in the C\ione\ 9061 -- 9111\,\AA\,, 9603 -- 9658\,\AA\, triplet lines. A prerequisite of the emission phenomenon is the overionization-recombination mechanism resulting in a depopulation of the lower levels of C\ione\ to a greater extent than the upper levels. Extra depopulation of the lower levels of the transitions corresponding to the near-infrared lines, is caused by photon loss in the UV lines C\ione\ 2479, 1930, and 1657\,\AA. We analysed the lines of C\ione\ and C\ii\ in Vega, HD~73666, Sirius, 21~Peg, $\pi$~Cet, HD~22136, and $\iota$ Her taking advantage of their observed high-resolution spectra. The C\ione\ emission lines were detected in the four hottest stars, and they were well reproduced in our NLTE calculations. For each star, the mean NLTE abundances from lines of the two ionization stages, C\ione\ and C\ii, including the C\ione\ emission lines, were found to be consistent. We show that the predicted C\ione\ emission phenomenon depends strongly on whether accurate or approximate electron-impact excitation rates are applied.
This work is devoted to prove the existence of global strong solution in dimension $N\geq 2$ for a isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see \cite{fDS}), which can be used as a phase transition model. We will restrict us to the case of the so called compressible Navier-Stokes system with quantum pressure which corresponds to consider the capillary coefficient $\kappa(\rho)=\frac{\kappa_1}{\rho}$ with $\kappa_1>0$. In a first part we prove the existence of strong solution in finite time for large initial data with a precise bound by below on the life span $T^*$. This one depends on the norm of the initial data $(\rho_0,v_0)$. The second part consists in proving the existence of global strong solution with particular choice on the capillary coefficient ( where $\kappa_1=\mu^2$) and on the viscosity tensor which corresponds to the viscous shallow water case $-2\mu{\rm div}(\rho Du)$. To do this we derivate different energy estimate on the density and the effective velocity $v$ which ensures that the strong solution can be extended beyond $T^*$. The main difficulty consists in controlling the vacuum or in other words to estimate the $L^\infty$ norm of $\frac{1}{\rho}$. The proof relies mostly on a method introduced by De Giorgi \cite{DG} (see also Ladyzhenskaya et al in \cite{La} for the parabolic case) to obtain regularity results for elliptic equations with discontinuous diffusion coefficients and a suitable bootstrap argument.
An overview of neutrino electromagnetic properties, which open a door to the new physics beyond the Standard Model, is given. The effects of neutrino electromagnetic interactions both in terrestrial experiments and in astrophysical environments are discussed. The experimental bounds on neutrino electromagnetic characteristics are summarized. Future astrophysical probes of electromagnetic neutrinos are outlined.
In the framework of the Magnetism in Massive Stars (MiMeS) project, a HARPSpol Large Program at the 3.6m-ESO telescope has recently started to collect high-resolution spectropolarimetric data of a large number of Southern massive OB stars in the field of the Galaxy and in many young clusters and associations. In this Letter, we report on the first discoveries of magnetic fields in two massive stars with HARPSpol - HD 130807 and HD 122451, and confirm the presence of a magnetic field at the surface of HD 105382 that was previously observed with a low spectral resolution device. The longitudinal magnetic field measurements are strongly varying for HD 130807 from $\sim$-100 G to $\sim$700 G. Those of HD 122451 and HD 105382 are less variable with values ranging from $\sim$-40 to -80 G, and from $\sim$-300 to -600 G, respectively. The discovery and confirmation of three new magnetic massive stars, including at least two He-weak stars, is an important contribution to one of the MiMeS objectives: the understanding of origin of magnetic fields in massive stars and their impacts on stellar structure and evolution.