ShantanuT01/DACTYL-Pretraining huggingface dataset:
Given a finite word $w$ over a finite alphabet $V$, consider the graph with vertex set $V$ and with an edge between two elements of $V$ if and only if the two elements alternate in the word $w$. Such a graph is said to be word-representable or 11-representable by the word $w$; this latter terminology arises from the phenomenon that the condition of two elements $x$ and $y$ alternating in a word $w$ is the same as the condition of the subword of $w$ induced by $x$ and $y$ avoiding the pattern 11. In this paper, we first study minimal length words which word-represent graphs, giving an explicit formula for both the length and the number of such words in the case of trees and cycles. We then extend the notion of word-representability (or 11-representability) of graphs to $t$-representability of graphs, for any pattern $t$ on two letters. We prove that every graph is $t$-representable for any pattern $t$ on two letters (except for possibly one class of $t$). Finally, we pose a few open problems for future consideration.
The radial thermal expansion {\alpha}r of bundles of single-walled carbon nanotubes saturated with 3He up to the molar concentration 9.4% has been investigated in the temperature interval 2.1-9.5 K by high-sensitivity capacitance dilatometry. In the interval 2.1-7 K a negative {\alpha}r was observed, with a magnitude which exceeded the largest negative {\alpha}r values of pure and 4He-saturated nanotubes by three and two orders of magnitude, respectively. The contributions of the two He isotope impurities to the negative thermal expansion of the nanotube bundles are most likely connected with the spatial redistribution of 4He and 3He atoms by tunneling at the surface and inside nanotube bundles. The isotope effect turned out to be huge, probably owing to the higher tunneling probability of 3He atoms.
We present results on resistivity ($\rho$), magnetization ($M$), thermal conductivity ($\kappa$), magnetostriction ($\frac{\Delta L}{L(0)}$) and specific heat ($C_{p}$) of charge-orbital ordered antiferromagnetic Nd$_{0.8}$Na$_{0.2}$MnO$_{3}$ compound. Magnetic field-induced antiferromagnetic/charge-orbital ordered insulating to ferromagnetic metallic transition leads to giant magnetothermal conductivity and magnetostriction effect. The low-temperature irreversibility behavior in $\rho$, $M$, $\kappa$ and $\frac{\Delta L}{L(0)}$ due to field cycling together with striking similarity among the field and temperature dependence of these parameters manifest the presence of strong and complex spin-charge-lattice coupling in this compound. The giant magnetothermal conductivity is attributed mainly to the suppression of phonon scattering due to the destabilization of spin fluctuations and static/dynamic Jahn-Teller distortion by the application of magnetic field.
The Bayesian isochrone fitting using the Markov chain Monte Carlo algorithm is applied, to derive the probability distribution of the parameters age, metallicity, reddening, and absolute distance modulus. We introduce the \texttt{SIRIUS} code by means of simulated color-magnitude diagrams, including the analysis of multiple stellar populations. The population tagging is applied from the red giant branch to the bottom of the main sequence. Through sanity checks using synthetic {\it HST} color-magnitude diagrams of globular clusters we verify the code reliability in the context of simple and multiple stellar populations. In such tests, the formal uncertainties in age or age difference, metallicity, reddening, and absolute distance modulus can reach $400$ Myr, $0.03$ dex, $0.01$ mag, and $0.03$ mag, respectively. We apply the method to analyse NGC 6752, using Dartmouth stellar evolutionary models. Assuming a single stellar population, we derive an age of $13.7\pm0.5$ Gyr and a distance of $d_{\odot}=4.11\pm 0.08$ kpc, with the latter in agreement within $~3\sigma$ with the inverse Gaia parallax. In the analysis of the multiple stellar populations, three {populations} are clearly identified. From the Chromosome Map and UV/Optical two-color diagrams inspection, we found a fraction of stars of $25\pm5$, $46\pm7$, and $29\pm5$ per cent, for the first, second, and third generations, respectively. These fractions are in good agreement with the literature. An age difference of $500\pm410$ Myr between the first and the third generation is found, with the uncertainty decreasing to $400$ Myr when the helium enhancement is taken into account.
This paper describes a new feature set for use in the recognition of on-line handwritten Devanagari script based on Fuzzy Directional Features. Experiments are conducted for the automatic recognition of isolated handwritten character primitives (sub-character units). Initially we describe the proposed feature set, called the Fuzzy Directional Features (FDF) and then show how these features can be effectively utilized for writer independent character recognition. Experimental results show that FDF set perform well for writer independent data set at stroke level recognition. The main contribution of this paper is the introduction of a novel feature set and establish experimentally its ability in recognition of handwritten Devanagari script.
We have obtained deep near-infrared $J$- (1.25 $\mu$m), $H$- (1.65$ \mu$m) and $K_s$-band (2.15 $\mu$m) imaging for a sample of six dwarf galaxies ($M_B\ga-17$ mag) in the Local Volume (LV, $D\la10$ Mpc). The sample consists mainly of early-type dwarf galaxies found in various environments in the LV. Two galaxies (LEDA 166099 and UGCA 200) in the sample are detected in the near-infrared for the first time. The deep near-infrared images allow for a detailed study of the photometric and structural properties of each galaxy. The surface brightness profiles of the galaxies are detected down to the ~$24 mag arcsec^{-2}$ isophote in the $J$- and $H$-bands, and $23 mag arcsec^{-2}$ in the $K_s$-band. The total magnitudes of the galaxies are derived in the three wavelength bands. For the brightest galaxies ($M_B\la-15.5$ mag) in the sample, we find that the Two Micron All Sky Survey (2MASS) underestimates the total magnitudes of these systems by up to $\la0.5$ mag. The radial surface brightness profiles of the galaxies are fitted with an exponential (for those galaxies having a stellar disk) or S\'ersic law to derive the structure of the underlying stellar component. In particular, the effective surface brightness ($\mu_e$) and effective radius ($r_e$) are determined from the analytic fits to the surface brightness profile. The $J$-$K_s$ colours for the galaxies have been measured to explore the luminosity-metallicity relation for early-type dwarfs. In addition, the $B$-$K_s$ colours of the galaxies are used to assess their evolutionary state relative to other galaxy morphologies. The total stellar masses of the dwarf galaxies are derived from the $H$-band photometric measurements. These will later be compared to the dynamical mass estimates for the galaxies to determine their dark matter content.
Systematic calculations of fission barriers allowing for triaxial deformation are performed for even-even superheavy nuclei with charge number $Z=112-120$ using three classes of covariant density functional models. The softness of nuclei in the triaxial plane leads to an emergence of several competing fission pathes in the region of the inner fission barrier in some of these nuclei. The outer fission barriers are considerably affected by triaxiality and octupole deformation. General trends of the evolution of the inner and the outer fission barrier heights are discussed as a function of the particle numbers.
We present a search for HI in the circumgalactic medium (CGM) of 21 massive ($\langle \log M_\star \rangle \sim 11.4$), luminous red galaxies (LRGs) at $z\sim0.5$. Using UV spectroscopy of QSO sightlines projected within 500 kpc ($\sim R_{vir}$) of these galaxies, we detect HI absorption in 11/21 sightlines, including two partial Lyman limit systems and two Lyman limit systems. The covering factor of $\log N(HI) \ge 16.0$ gas within the virial radius of these LRGs is $f_c(\rho \le R_{vir}) = 0.27^{+0.11}_{-0.10}$, while for optically-thick gas ($\log N(HI) \ge 17.2$) it is $f_c(\rho \le R_{vir}) = 0.15^{+0.10}_{-0.07}$. Combining this sample of massive galaxies with previous galaxy-selected CGM studies, we find no strong dependence of the HI covering factor on galaxy mass, although star-forming galaxies show marginally higher covering factors. There is no evidence for a critical mass above which dense, cold ($T \sim 10^4$ K) gas is suppressed in the CGM of galaxies (spanning stellar masses $9.5 \lesssim \log M_\star \lesssim 11.8$). The metallicity distribution in LRGs is indistinguishable from those found about lower-mass star-forming galaxies, and we find low-metallicity gas with $[{\rm X/H}] \approx -1.8$ (1.5% solar) and below about massive galaxies. About half the cases show super-solar [FeII/MgII] abundances as seen previously in cool gas near massive galaxies. While the high-metallicity cold gas seen in LRGs could plausibly result from condensation from a corona, the low-metallicity gas is inconsistent with this interpretation.
In this paper, we will study the Lie algebra of the prounipotent radical of the relative completion of the mapping class group of genus two. In particular, we will partially determine a minimal presentation of the Lie algebra by determining the generators and bounding the degree of the relations.
Peculiarities of transport properties of three- and two-dimensional half-metallic ferromagnets are investigated, which are connected with the absence of spin-flip scattering processes. The temperature and magnetic field dependences of resistivity in various regimes are calculated. The resistivity is proportional to T^{9/2} for T<T* and to T^{7/2} for T>T*, T* being the crossover temperature for longitudinal scattering processes. The latter scale plays also an important role in magnetoresistance. The contribution of non-quasiparticle (incoherent) states to the transport properties is discussed. It is shown that they can dominate in the temperature dependence of the impurity-induced resistivity and in the tunnel junction conductivity.
A system of fermions with a short-range interaction proportional to the scattering length $a$ is studied at finite density. At any order $a^n$, we evaluate the complete contributions to the energy per particle $\bar E(k_f)$ arising from combined (multiple) particle-particle and hole-hole rescatterings in the medium. This novel result is achieved by simply decomposing the particle-hole propagator into the vacuum propagator plus a medium-insertion and correcting for certain symmetry factors in the $(n-1)$-th power of the in-medium loop. Known results for the low-density expansion up to and including order $a^4$ are accurately reproduced. The emerging series in $a k_f$ can be summed to all orders in the form of a double-integral over an arctangent function. In that representation the unitary limit $a\to \infty$ can be taken and one obtains the value $\xi= 0.5067$ for the universal Bertsch parameter. We discuss also applications to the equation of state of neutron matter at low densities and mention further extensions of the resummation method.
Opacity calculations are basic ingredients of stellar modelling. They play a crucial role in the interpretation of acoustic modes detected by SoHO, COROT and KEPLER. In this review we present our activities on both theoretical and experimental sides. We show new calculations of opacity spectra and comparisons between eight groups who produce opacity spectra calculations in the domain where experiments are scheduled. Real differences are noticed with real astrophysical consequences when one extends helioseismology to cluster studies of different compositions. Two cases are considered presently: (1) the solar radiative zone and (2) the beta Cephei envelops. We describe how our experiments are performed and new preliminary results on nickel obtained in the campaign 2010 at LULI 2000 at Polytechnique.
Context: Because it is viewed simply edge-on, the HH212 protostellar system is an ideal laboratory for studying the interplay of infall, outflow, and rotation in the earliest stages of low-mass star formation. Aims: We wish to exploit the unmatched combination of high angular resolution, high sensitivity, high-imaging fidelity, and spectral coverage provided by ALMA to shed light on the complex kinematics of the innermost central regions of HH212. Methods: We mapped the inner 10" (4500 AU) of the HH212 system at about 0.5 arcsec resolution in several molecular tracers and in the 850 $\mu$m dust continuum using the ALMA interferometer in band 7 in the extended configuration of the Early Science Cycle 0 operations. Results: Within a single ALMA spectral set-up, we simultaneously identify all the crucial ingredients known to be involved in the star formation recipe namely: (i) the fast, collimated bipolar SiO jet driven by the protostar, (ii) the large-scale swept-up CO outflow, (iii) the flattened rotating and infalling envelope, with bipolar cavities carved by the outflow (in C$^{17}$O(3--2)), and (iv) a rotating wide-angle flow that fills the cavities and surrounding the axial jet (in C$^{34}$S(7--6)). In addition, the compact high-velocity C$^{17}$O emission ($\pm$ 1.9--3.5 km s$^{-1}$ from systemic) shows a velocity gradient along the equatorial plane consistent with a rotating disk of about 0.2 arcsec = 90 AU around a $\simeq 0.3 \pm 0.1 M_{\rm \odot}$ source. The rotating disk is possibly Keplerian. Conclusions: HH212 is the third Class 0 protostar with possible signatures of a Keplerian disk of radius $\geq 30 AU$. The warped geometry in our CS data suggests that this large keplerian disk might result from misaligned magnetic and rotation axes during the collapse phase. The wide-angle CS flow suggests that disk winds may be present in this source.
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta function. The results originate from attempts to extend the zeta function by classical means on the complex plane. This is particularly of interest for representations which converge rapidly in a given area of the complex plane, or for the purpose to make error bounds available.
A systematic and detailed investigation of the finite-temperature behavior of small sodium clusters, Na_n, in the size range of n= 8 to 50 are carried out. The simulations are performed using density-functional molecular-dynamics with ultrasoft pseudopotentials. A number of thermodynamic indicators such as specific heat, caloric curve, root-mean-square bond length fluctuation, deviation energy, etc. are calculated for each of the clusters. Size dependence of these indicators reveals several interesting features. The smallest clusters with n= 8 and 10, do not show any signature of melting transition. With the increase in size, broad peak in the specific heat is developed, which alternately for larger clusters evolves into a sharper one, indicating a solidlike to liquidlike transition. The melting temperatures show irregular pattern similar to experimentally observed one for larger clusters [ M. Schmidt et al., Nature (London) 393, 238 (1998) ]. The present calculations also reveal a remarkable size-sensitive effect in the size range of n= 40 to 55. While Na_40 and Na_55 show well developed peaks in the specific heat curve, Na_50 cluster exhibits a rather broad peak, indicating a poorly-defined melting transition. Such a feature has been experimentally observed for gallium and aluminum clusters [ G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); G. A.Breaux et al., Phys. Rev. Lett. 94, 173401 (2005) ].
Extensions of the Shastry-Sutherland model are possible in various ways. In particular, it is possible to construct a natural model in three dimensions which has the exact dimer ground state. Recently found spin gap system SrCu_2(BO_3)_2 has this structure. The exchange constants between the layers is expected to be smaller than the intra-layer couplings. However, the exactness of the dimer state for the three dimensional structure is important to understand why magnetic properties of SrCu_2(BO_3)_2 are described well by the two dimensional model.
Probabilistic image registration methods estimate the posterior distribution of transformation. The conventional way of interpreting the transformation posterior is to use the mode as the most likely transformation and assign its corresponding intensity to the registered voxel. Meanwhile, summary statistics of the posterior are employed to evaluate the registration uncertainty, that is the trustworthiness of the registered image. Despite the wide acceptance, this convention has never been justified. In this paper, based on illustrative examples, we question the correctness and usefulness of conventional methods. In order to faithfully translate the transformation posterior, we propose to encode the variability of values into a novel data type called ensemble fields. Ensemble fields can serve as a complement to the registered image and a foundation for developing advanced methods to characterize the uncertainty in registration-based tasks. We demonstrate the potential of ensemble fields by pilot examples
In this article we study the problem of recovering the initial data of the two-dimensional wave equation from Neumann measurements on a convex domain with smooth boundary in the plane. We derive an explicit inversion formula of a so-called back-projection type and deduce exact inversion formulas for circular and elliptical domains. In addition, for circular domains, we show that the initial data can also be recovered from any linear combination of its solution and its normal derivative on the boundary. Numerical results of our implementation of the derived inversion formulas are presented demonstrating their accuracy and stability.
While metastability enhanced water-oxidation activity was experimentally reported, the reason behind this effect is still unclear. We determine here, using density functional theory calculations, oxygen evolution reaction overpotentials for a variety of defective (001) surfaces of three different perovskite materials. For all three, we find a large range of overpotentials for different reaction sites including also overpotentials at the top of the activity volcano. Assuming that these sites dominate the apparent catalytic activity, this implies that a large number of geometrically different reaction sites, as they occur when a catalyst is operated at the border of its stability conditions, can lead to a strong enhancement of the apparent activity. This also implies that a pre-treatment of the catalyst creating a variety of different reactive sites could lead to superior catalytic activities for thermodynamically stable materials.
Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The paper exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the Geodesic Postulate, we find all the equations that are experimentally (by the 3 classical tests) indistinguishable from Einstein field equations. This family includes, of course, also Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the paper is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations.
We present the results of a Monte-Carlo study of the sensitivity of the planned IceCube detector to predicted fluxes of muon neutrinos at TeV to PeV energies. A complete simulation of the detector and data analysis is used to study the detector's capability to search for muon neutrinos from sources such as active galaxies and gamma-ray bursts. We study the effective area and the angular resolution of the detector as a function of muon energy and angle of incidence. We present detailed calculations of the sensitivity of the detector to both diffuse and pointlike neutrino emissions, including an assessment of the sensitivity to neutrinos detected in coincidence with gamma-ray burst observations. After three years of datataking, IceCube will have been able to detect a point source flux of E^2*dN/dE = 7*10^-9 cm^-2s^-1GeV at a 5-sigma significance, or, in the absence of a signal, place a 90% c.l. limit at a level E^2*dN/dE = 2*10^-9 cm^-2s^-1GeV. A diffuse E-2 flux would be detectable at a minimum strength of E^2*dN/dE = 1*10^-8 cm^-2s^-1sr^-1GeV. A gamma-ray burst model following the formulation of Waxman and Bahcall would result in a 5-sigma effect after the observation of 200 bursts in coincidence with satellite observations of the gamma-rays.
The Ehrhart polynomial $L_P$ of an integral polytope $P$ counts the number of integer points in integral dilates of $P$. Ehrhart polynomials of polytopes are often described in terms of their Ehrhart $h^*$-vector (aka Ehrhart $\delta$-vector), which is the vector of coefficients of $L_P$ with respect to a certain binomial basis and which coincides with the $h$-vector of a regular unimodular triangulation of $P$ (if one exists). One important result by Stanley about $h^*$-vectors of polytopes is that their entries are always non-negative. However, recent combinatorial applications of Ehrhart theory give rise to polytopal complexes with $h^*$-vectors that have negative entries.   In this article we introduce the Ehrhart $f^*$-vector of polytopes or, more generally, of polytopal complexes $K$. These are again coefficient vectors of $L_K$ with respect to a certain binomial basis of the space of polynomials and they have the property that the $f^*$-vector of a unimodular simplicial complex coincides with its $f$-vector. The main result of this article is a counting interpretation for the $f^*$-coefficients which implies that $f^*$-coefficients of integral polytopal complexes are always non-negative integers. This holds even if the polytopal complex does not have a unimodular triangulation and if its $h^*$-vector does have negative entries. Our main technical tool is a new partition of the set of lattice points in a simplicial cone into discrete cones. Further results include a complete characterization of Ehrhart polynomials of integral partial polytopal complexes and a non-negativity theorem for the $f^*$-vectors of rational polytopal complexes.
We examine the early angular momentum history of stars in young clusters via 197 photometric periods in fields flanking the Orion Nebula Cluster (ONC), 81 photometric periods in NGC 2264, and 202 measurements of v sin i in the ONC itself. We show that PMS stars spanning an age range from 0.1 to 3 Myr do not appear to conserve stellar angular momentum as they evolve down their convective tracks, but instead preserve the same range of periods even though they have contracted by about a factor of three. This result seems to require a mechanism that regulates the angular velocities of young stars. We discuss several candidate mechanisms. The most plausible appears to be disk-locking, though most of our stars do not have (I-K) excesses suggestive of disks. However, a decisive test of this hypothesis requires a more sensitive diagnostic than the (I-K) excesses used here.