ShantanuT01/DACTYL-Pretraining huggingface dataset:
One way to study certain classes of polynomials is by considering examples that are attached to combinatorial objects. Any graph $G$ has an associated reciprocal polynomial $R_G$, and with two particular classes of reciprocal polynomials in mind one can ask the questions: (a) when is $R_G$ a product of cyclotomic polynomials (giving the cyclotomic graphs)? (b) when does $R_G$ have the minimal polynomial of a Salem number as its only non-cyclotomic factor (the non-trival Salem graphs)? Cyclotomic graphs were classified by Smith in 1970. Salem graphs are `spectrally close' to being cyclotomic, in that nearly all their eigenvalues are in the critical interval [-2,2]. On the other hand Salem graphs do not need to be `combinatorially close' to being cyclotomic: the largest cyclotomic induced subgraph might be comparatively tiny.   We define an $m$-Salem graph to be a connected Salem graph $G$ for which $m$ is minimal such that there exists an induced cyclotomic subgraph of $G$ that has $m$ fewer vertices than $G$. The 1-Salem subgraphs are both spectrally close and combinatorially close to being cyclotomic. Moreover, every Salem graph contains a 1-Salem graph as an induced subgraph, so these 1-Salem graphs provide some necessary substructure of all Salem graphs. The main result of this paper is a complete combinatorial description of all 1-Salem graphs: there are 26 infinite families and 383 sporadic examples.
The black hole candidate MAXI J1836-194 was discovered in 2011 when it went into an outburst, and was the subject of numerous, quasi-simultaneous, multi-wavelength observations in the radio, infrared, optical and X-rays. In this paper, we model its multi-wavelength radio to optical spectral energy distributions (SEDs) with an internal shock jet model. The jet emission is modelled on five dates of the outburst, during which the source is in the hard and hard intermediate X-ray spectral states. The model assumes that fluctuations of the jet velocity are driven by the variability in the accretion flow which is traced by the observed X-ray timing properties of the source. While the global shape of the SED is well reproduced by this model for all the studied observations, the variations in bolometric flux and typical energies require at least two parameters to evolve during the outburst. Here we investigate variations of the jet power and mean Lorentz factor, which are both found to increase with the source luminosity. Our results are compatible with the evolution of the jet Lorentz factor reported in earlier studies of this source. However, due to the large degeneracy of the parameters of the ishem model, our proposed scenario is not unique.
The oscillations of a slowly rotating star have long been classified into spheroidal and toroidal modes. The spheroidal modes include the well-known 5-min acoustic modes used in helioseismology. Here we report observations of the Sun's toroidal modes, for which the restoring force is the Coriolis force and whose periods are on the order of the solar rotation period. By comparing the observations with the normal modes of a differentially rotating spherical shell, we are able to identify many of the observed modes. These are the high-latitude inertial modes, the critical-latitude inertial modes, and the equatorial Rossby modes. In the model, the high-latitude and critical-latitude modes have maximum kinetic energy density at the base of the convection zone, and the high-latitude modes are baroclinically unstable due to the latitudinal entropy gradient. As a first application of inertial-mode helioseismology, we constrain the superadiabaticity and the turbulent viscosity in the deep convection zone.
The decay of top-quark to light quarks and Higgs boson is an extremely rare process in the Standard Model (SM) framework. Any measurable signal for this process at the LHC is a smoking gun for new physics. In the framework of Minimal Supersymmetric Standard Model (MSSM) there is a possibility that the branching ratio for this process to reach values several orders of magnitude larger than the corresponding of SM. Having as a primary goal the search of Flavour Changing Neutral Currents (FCNC) processes that could be measurable at current or future LHC runing, we present a calculation in the framework of R-parity conserving MSSM for the decay of top quark to light quarks and the Higgs boson. Considering different constraints, and carefully looking at the cancellations that occur between different contributions, we deduce that there are two possible enhanced scenarios for this process: the first arises from the holomorphic SUSY breaking terms containing right handed up squark mass insertions and the second comes from the dominance of non-holomorphic SUSY breaking terms in combination with a light Higgs boson sector.
We propose an extension of the GC3 streamer finding method of Johnston et al. 1996 that can be applied to the future Gaia database. The original method looks for streamers along great circles in the sky, our extension adds the kinematical restriction that velocity vectors should also be constrained to lie along these great circles, as seen by a Galactocentric observer. We show how to use these combined criteria starting from heliocentric observables. We test it by using the mock Gaia catalogue of Brown et al. 2005, which includes a realistic Galactic background and observational errors, but with the addition of detailed star formation histories for the simulated satellites. We investigate its success rate as a function of initial satellite luminosity, star formation history and orbit. We find that the inclusion of the kinematical restriction vastly enhances the contrast between a streamer and the background, even in the presence of observational errors, provided we use only data with good astrometric quality (fractional errors of 30 per cent or better). The global nature of the method diminishes the erasing effect of phase mixing and permits the recovery of merger events of reasonable dynamical age. Satellites with a star formation history different to that of the Galactic background are also better isolated. We find that satellites in the range of 10^8-10^9 Lsun can be recovered even for events as old as ~10 Gyr. Even satellites with 4-5x10^7 Lsun can be recovered for certain combinations of dynamical ages and orbits.
The possibility that ultra-diffuse galaxies lacking dark matter has recently stimulated interest to check the validity of Modified Newton Dynamics (MOND) predictions on the scale of such galaxies. It has been shown that the External Field Effect (EFE) induced by the close-by galaxy can suppress the velocity dispersion of these systems, so that they appear almost dark matter free in the Newtonian context. Here, following up on this, we are making a priori predictions for the velocity dispersion of 22 ultra-diffuse galaxies in the nearby Universe. This sample can be used to test MOND and the EFE with future follow-up measurements. We construct a catalog of nearby ultra-diffuse galaxies in galaxy group environments, and set upper and lower limits for the possible velocity dispersion allowed in MOND, taking into account possible variations in the mass-to-light ratio of the dwarf and in the distance to the galaxy group. The prediction for the velocity dispersion is made as a function of the three dimensional separation of the dwarf to its host. In 17 out of 22 cases, the EFE plays a crucial role in the prediction.
This paper develops a damage model for unfilled cross-linked rubbers based on the concept of scission of polymer chains. The model is built up on the well-known Gent elastic potential complemented by a kinetic equation describing effects of polymer chain scission. The macroscopic parameters in the damage model are evaluated through the parameters for undamaged elastomer. Qualitative analysis of changing molecular parameters of rubbers under scission of polymer chains resulted in easy scaling modeling the dependences of these parameters on the damage factor. It makes possible to predict the rubber failure in molecular terms as mechanical de-vulcanization. The model was tested in tensile quasi-static experiments with both the monotonous loading and repeated loading-unloading.
The origin of the 0.7-conductance anomaly in quantum point contacts (QPCs) has been a subject of lively discussions since its discovery more than 10 years ago. In a recent letter, based on spin density functional theory (DFT), Rejec and Meir explained the origin of the 0.7-anomaly as being due to the formation of a magnetic impurity in the QPCs [T. Rejec and Y. Meir, Nature 442, 900 (2006)]. They did not, however, perform transport conductance calculations so the central question whether the 0.7-anomaly is indeed related to the formation of a magnetic impurity has remained unanswered. In this communication, we perform spin DFT transport calculations for the structures considered by Rejec and Meir. While we recover the findings reported by Rejec and Meir concerning the formation of localized spin-degenerate quasi-bound states, our transport calculations do not contain the 0.7 anomaly in the conductance. We suggest that the inability of the DFT to reproduce quantitatively the 0.7 anomaly may be due to the uncorrected self-interaction errors in the DFT calculation of electronic transport for the case when localization of charge is expected to occur, so that the magnetic impurity formation may be an artefact of DFT due to the spurious self-interaction.
While 3D-3D registration is traditionally tacked by optimization-based methods, recent work has shown that learning-based techniques could achieve faster and more robust results. In this context, however, only PRNet can handle the partial-to-partial registration scenario. Unfortunately, this is achieved at the cost of relying on an iterative procedure, with a complex network architecture. Here, we show that learning-based partial-to-partial registration can be achieved in a one-shot manner, jointly reducing network complexity and increasing registration accuracy. To this end, we propose an Optimal Transport layer able to account for occluded points thanks to the use of outlier bins. The resulting OPRNet framework outperforms the state of the art on standard benchmarks, demonstrating better robustness and generalization ability than existing techniques.
A simple method for calculating the asymptotic $D$ state observables for light nuclei is suggested. The method exploits the dominant clusters of the light nuclei. The method is applied to calculate the $^4He$ asymptotic $D$ to $S$ normalization ratio $\rho^\alpha$ and the closely related $D$ state parameter $D_2^\alpha$. The study predicts a correlation between $D_2^\alpha$ and $B_\alpha$, and between $\rho^\alpha$ and $B_\alpha$, where $B_\alpha$ is the binding energy of $^4He$. The present study yields $\rho^\alpha \simeq -0.14$ and $D_2^\alpha \simeq -0.12$ fm$^2$ consistent with the correct experimental $\eta^D$ and the binding energies of the deuteron, triton, and the $\alpha$ particle, where $\eta^d$ is the deuteron $D$ state to $S$ state normalization ratio.
We show that recent observations of the compact binary, AM CVn type system, ES Ceti are fully consistent with theoretical predictions of stable mass transfer moderated by angular momentum loss due to gravitational-wave radiation. One of the main predictions of this model (for degenerate donors) is a widening of the binary. The mass transfer rate inferred from the observed rate of change in the orbital frequency is consistent with that inferred from the observed flux using the recent Gaia DR2 parallax
We present a light curve analysis and radial velocity study of KOI-74, an eclipsing A star + white dwarf binary with a 5.2 day orbit. Aside from new spectroscopy covering the orbit of the system, we used 212 days of publicly available Kepler observations and present the first complete light curve fitting to these data, modelling the eclipses and transits, ellipsoidal modulation, reflection, and Doppler beaming. Markov Chain Monte Carlo simulations are used to determine the system parameters and uncertainty estimates. Our results are in agreement with earlier studies, except that we find an inclination of 87.0 \pm 0.4\degree, which is significantly lower than the previously published value. We find that the mass ratio derived from the radial velocity amplitude (q=0.104 \pm 0.004) disagrees with that derived from the ellipsoidal modulation (q=0.052 \pm 0.004} assuming corotation). This was found before, but with our smaller inclination, the discrepancy is even larger than previously reported. Accounting for the rapid rotation of the A-star is found to increase the discrepancy even further by lowering the mass ratio to q=0.047 \pm 0.004. These results indicate that one has to be extremely careful in using the amplitude of an ellipsoidal modulation signal in a close binary to determine the mass ratio, when a proof of corotation is not firmly established. The radial velocities that can be inferred from the detected Doppler beaming in the light curve are found to be in agreement with our spectroscopic radial velocity determination. We also report the first measurement of R{\o}mer delay in a light curve of a compact binary. This delay amounts to -56 \pm 17 s and is consistent with the mass ratio derived from the radial velocity amplitude. The firm establishment of this mass ratio at q=0.104 \pm 0.004 leaves little doubt that the companion of KOI-74 is a low mass white dwarf.
Learning deep neural network (DNN) classifier with noisy labels is a challenging task because the DNN can easily over-fit on these noisy labels due to its high capability. In this paper, we present a very simple but effective training paradigm called P-DIFF, which can train DNN classifiers but obviously alleviate the adverse impact of noisy labels. Our proposed probability difference distribution implicitly reflects the probability of a training sample to be clean, then this probability is employed to re-weight the corresponding sample during the training process. P-DIFF can also achieve good performance even without prior knowledge on the noise rate of training samples. Experiments on benchmark datasets also demonstrate that P-DIFF is superior to the state-of-the-art sample selection methods.
We present solutions of the coupled, non-relativistic $^3S_1$-$^3D_1$ gap equations for neutron-proton pairing in symmetric nuclear matter, and estimate relativistic effects by solving the same gap equations modified according to minimal relativity and using single-particle energies from a Dirac-Brueckner-Hartree-Fock calculation. As a main result we find that relativistic effects decrease the value of the gap at the saturation density $k_F=1.36 fm^{-1}$ considerably, in conformity with the lack of evidence for strong neutron-proton pairing in finite nuclei.
Using a newly-developed modeling technique, we present orbit-based dynamical models of the Carina, Draco, Fornax, Sculptor, and Sextans dwarf spheroidal (dSph) galaxies. These models calculate the dark matter profiles non-parametrically without requiring any assumptions to be made about their profile shapes. By lifting this restriction we discover a host of dark matter profiles in the dSphs that are different from the typical profiles suggested by both theorists and observers. However, when we scale these profiles appropriately and plot them on a common axis they appear to follow an approximate r^-1 power law with considerable scatter.
We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof of the Fibonacci dichotomy: the number of permutations of length n in a permutation class is either at least as large as the nth Fibonacci number or is eventually polynomial.
The use of the equations of motion and meson field redefinitions allows the development of a simplified resonance chiral theory lagrangian: terms including resonance fields and a large number of derivatives can be reduced into corresponding O(p2) resonance operators, containing the lowest possible number of derivatives. This is shown by means of the explicit computation of the pion vector form-factor up to next-to-leading order in 1/Nc. The study of the renormalization group equations for the corresponding couplings demonstrates the existence of an infrared fixed point in the resonance theory. The possibility of developing a perturbative 1/Nc expansion in the slow running region around the fixed point is shown here.
We compare local Fermi gas and shell model in muon capture in nuclei in order to estimate the effect of finite nuclear size in low energy weak reactions.
We present a detailed comparison of the Milky Way (MW) globular cluster (GC) kinematics with the 25 Milky Way-mass cosmological simulations from the E-MOSAICS project. While the MW falls within the kinematic distribution of GCs spanned by the simulations, the relative kinematics of its metal-rich ($[\rm{Fe/H}]>-1.2$) versus metal-poor ($[\rm{Fe/H}]<-1.2$), and inner ($r<8\rm{kpc}$) versus outer ($r>8\rm{kpc}$) populations are atypical for its mass. To understand the origins of these features, we perform a comprehensive statistical analysis of the simulations, and find 18 correlations describing the assembly of $L^*$ galaxies and their dark matter haloes based on their GC population kinematics. The correlations arise because the orbital distributions of accreted and in-situ GCs depend on the masses and accretion redshifts of accreted satellites, driven by the combined effects of dynamical fraction, tidal stripping, and dynamical heating. Because the kinematics of in-situ/accreted GCs are broadly traced by the metal-rich/metal-poor and inner/outer populations, the observed GC kinematics are a sensitive probe of galaxy assembly. We predict that relative to the population of $L^*$ galaxies, the MW assembled its dark matter and stellar mass rapidly through a combination of in-situ star formation, more than a dozen low-mass mergers, and $1.4\pm1.2$ early ($z=3.1\pm1.3$) major merger. The rapid assembly period ended early, limiting the fraction of accreted stars. We conclude by providing detailed quantitative predictions for the assembly history of the MW.
We present numerical simulations of the axisymmetric accretion of a massive magnetized plasma torus on a rotating black hole. We use a realistic equation of state, which takes into account neutrino cooling and energy loss due to nucleus dissociations. We simulated various magnetic field configurations and torus models, both optically thick and thin for neutrinos. It is shown that the neutrino cooling does not significantly change either the structure of the accretion flow or the total energy release of the system. The calculations evidence heating of the wind surrounding the collapsar by the shock waves generated at the jet-wind border. This mechanism can give rise to a hot corona around the binary system like SS433.   Angular momentum of the accreting matter defines the time scale of the accretion. Due to the absence of the magnetic dynamo in our calculations, the initial strength and topology of the magnetic field determines magnetization of the black hole, jet formation properties and the total energy yield. We estimated the total energy transformed to jets as $1.3\times 10^{52}$ {ergs} which was sufficient to explain hypernova explosions like GRB 980425 or GRB 030329.
We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are $N^2$ different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by $\sqrt{N}$ is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.
We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest second occurrence time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of this function. Then, we establish a new result on repetitions in Sturmian words and show that it is best possible. Let $b \ge 2$ be an integer. We deduce a lower bound for the irrationality exponent of real numbers whose sequence of $b$-ary digits is a Sturmian sequence over $\{0,1,\ldots, b-1\}$ and we prove that this lower bound is best possible. As an application, we derive some information on the $b$-ary expansion of $\log(1+\frac{1}{a})$,for any integer $a \ge 34$.
We investigate the accretion induced spin up of the black hole via numerical simulations. Our method is based on general-relativistic magneto-hydrodynamics of the slowly-rotating flows in the Kerr metric, where possibly transonic shock fronts may form. We account for the changing black hole mass and spin during accretion which enforces dynamical evolution of the space-time metric. We first study non-magnetized flows with shocks, and we also include magnetic field endowed in the gas. The aim of this study is to verify whether the high mass black holes may be produced with large spins, even though at birth the collapsars might have contained slowly, or moderately spinning cores. In this way, we put constraints on the content of angular momentum in the collapsing massive stars. Our studies are also showing that shock fronts and magnetic fields may halt accretion and limit the black hole spin-up in the exploding supernovae.
Extending work of E, Khanin, Mazel and Sinai (1997 PRL 78:1904-1907) on the one-dimensional Burgers equation, we show that density pdf's have universal power-law tails with exponent -7/2. This behavior stems from singularities, other than shocks, whose nature is quite different in one and several dimensions. We briefly discuss the possibility of detecting singularities of Navier-Stokes turbulence using pdf tails.
A surface-based diffeomorphic algorithm to generate 3D coordinate grids in the cortical ribbon is described. In the grid, normal coordinate lines are generated by the diffeomorphic evolution from the grey/white (inner) surface to the grey/csf (outer) surface. Specifically, the cortical ribbon is described by two triangulated surfaces with open boundaries. Conceptually, the inner surface sits on top of the white matter structure and the outer on top of the gray matter. It is assumed that the cortical ribbon consists of cortical columns which are orthogonal to the white matter surface. This might be viewed as a consequence of the development of the columns in the embryo. It is also assumed that the columns are orthogonal to the outer surface so that the resultant vector field is orthogonal to the evolving surface. Then the distance of the normal lines from the vector field such that the inner surface evolves diffeomorphically towards the outer one can be construed as a measure of thickness. Applications are described for the auditory cortices in human adults and cats with normal hearing or hearing loss. The approach offers great potential for cortical morphometry.