ShantanuT01/DACTYL-Pretraining huggingface dataset:
A maximal minor $M$ of the Laplacian of an $n$-vertex Eulerian digraph $\Gamma$ gives rise to a finite group $\mathbb{Z}^{n-1}/\mathbb{Z}^{n-1}M$ known as the sandpile (or critical) group $S(\Gamma)$ of $\Gamma$. We determine $S(\Gamma)$ of the generalized de Bruijn graphs $\Gamma=\mathrm{DB}(n,d)$ with vertices $0,\dots,n-1$ and arcs $(i,di+k)$ for $0\leq i\leq n-1$ and $0\leq k\leq d-1$, and closely related generalized Kautz graphs, extending and completing earlier results for the classical de Bruijn and Kautz graphs.   Moreover, for a prime $p$ and an $n$-cycle permutation matrix $X\in\mathrm{GL}_n(p)$ we show that $S(\mathrm{DB}(n,p))$ is isomorphic to the quotient by $\langle X\rangle$ of the centralizer of $X$ in $\mathrm{PGL}_n(p)$. This offers an explanation for the coincidence of numerical data in sequences A027362 and A003473 of the OEIS, and allows one to speculate upon a possibility to construct normal bases in the finite field $\mathbb{F}_{p^n}$ from spanning trees in $\mathrm{DB}(n,p)$.
New fibre spectroscopy and radial velocities from the WIYN telescope are used to measure photospheric lithium in 242 high-probability, zero-age-main-sequence (ZAMS) F- to K-type members of the rich cluster M35. Combining these with published rotation periods, the connection between lithium depletion and rotation is studied in unprecedented detail. At $T_{\rm eff}<5500$ K there is a strong relationship between faster rotation and less Li depletion, although with a dispersion larger than measurement uncertainties. Components of photometrically identified binary systems follow the same relationship. A correlation is also established between faster rotation rate (or smaller Rossby number), decreased Li depletion and larger stellar radius at a given $T_{\rm eff}$. These results support models where starspots and interior magnetic fields lead to inflated radii and reduced Li depletion during the pre main sequence (PMS) phase for the fastest rotators. However, the data are also consistent with the idea that all stars suffered lower levels of Li depletion than predicted by standard PMS models, perhaps because of deficiencies in those models or because saturated levels of magnetic activity suppress Li depletion equally in PMS stars of similar $T_{\rm eff}$ regardless of rotation rate, and that slower rotators subsequently experience more mixing and post-PMS Li depletion.
Combining Freiman's theorem with Balog-Szemeredi-Gowers theorem one can show that if an additive set has large additive energy, then a large piece of the set is contained in a generalized arithmetic progression of small rank and size. In this paper, we prove the above statement with the optimal bound for the rank of the progression. The proof strategy involves studying upper bounds for additive energy of subsets of R^d and Z^d.
K\"uhn, Osthus and Taraz showed that for each \gamma>0 there exists C such that any n-vertex graph with minimum degree \gamma n contains a planar subgraph with at least 2n-C edges. We find the optimum value of C for all \gamma<1/2 and sufficiently large n.
Evidence has recently emerged for a hidden symmetry of scattering amplitudes in N=4 super Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS_5. In this paper we study dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagrams through four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes representations, also finding explicit expressions for their infrared singularities.
Recent WMAP observations indicate that the primordial abundance of lithium should have been 2-4 times higher than the value measured in low-metallicity stars. We show that this discrepancy can be explained by the process of ambipolar diffusion in protostellar clouds, which leads to depletion of elements with low ionization potential, such as lithium and sodium. In high-metallicity stars, [Fe/H]>~-1, the depletion of lithium due to this process is found to be negligible, but for [Fe/H]<~-1.5 the lithium abundance falls by a factor of ~3, consistent with WMAP observations.
We use a combination of dynamical mean-field model calculations and LDA+U material specific calculations to investigate the low temperature phase transition in the compounds from the (Pr$_{1-y}$R$_y$)$_x$Ca$_{1-x}$CoO$_3$ (R=Nd, Sm, Eu, Gd, Tb, Y) family (PCCO). The transition, marked by a sharp peak in the specific heat, leads to an exponential increase of dc resistivity and a drop of the magnetic susceptibility, but no order parameter has been identified yet. We show that condensation of spin-triplet, atomic-size excitons provides a consistent explanation of the observed physics. In particular, it explains the exchange splitting on the Pr sites and the simultaneous Pr valence transition. The excitonic condensation in PCCO is an example of a general behavior expected in certain systems in the proximity of a spin-state transition.
It is shown that the hadronic dissociation of space-like $(Q^2>0)$ photons can be directly probed by performing measurements in the fragmentation region of transversely polarized and unpolarized proton beams at the electron-proton collider HERA. Measurements of momentum-distributions in the photon-fragmentation region in normal and in LRG (large rapidity gap) events are also suggested --- especially when the scattered proton or neutron in the proton-beam direction is tagged. It is pointed out that such distributions can yield useful information on the mechanisms of hadronic fragmentation in general, and answer the following questions in particular: Is the well-known hypothesis of limiting fragmentation (HFL) valid in color-exchange, in flavor-exchange, or only in vacuum-quantum-number-exchange processes ?
(Abridged) Following on from a recently completed radial-velocity survey of the old (7 Gyr) open cluster NGC 188 in which we study in detail the solar-type hard binaries and blue stragglers of the cluster, here we investigate the dynamical evolution of NGC 188 through a sophisticated N-body model. We employ the observed binary properties of the young (150 Myr) open cluster M35, where possible, to guide our choices for parameters of the initial binary population. At 7 Gyr the main-sequence solar-type hard-binary population in the model matches that of NGC 188 in both binary frequency and distributions of orbital parameters. This agreement between the model and observations is in a large part due to the similarities between the NGC 188 and M35 solar-type binaries. Indeed, among the 7 Gyr main-sequence binaries in the model, only those with P>1000 days show potentially observable evidence for modifications by dynamical encounters. This emphasizes the importance of defining accurate initial conditions for star cluster models, which we propose is best accomplished through comparisons with observations of young open clusters like M35. Furthermore, this suggests that observations of the present-day binaries in even old open clusters can provide valuable information on their primordial binary populations. However, despite the model's successes at matching the true cluster, the model underproduces blue stragglers and produces an overabundance of long-period circular main-sequence--white-dwarf binaries as compared to NGC 188. We conclude that improvements in the physics of mass transfer and common envelope may in fact solve both discrepancies with the observations. This project highlights the unique accessibility of open clusters to both comprehensive observational surveys and full-scale N-body simulations, and underscores the importance of open clusters to the study of star cluster dynamics.
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance of the same order of magnitude of the materials in consideration. The macroscopic governing equations and the effective conductivity of the homogenized model are obtained by means of the two scale convergence technique. We show that under some hypothesis the homogenized systems contain convective terms of order one.
We investigate nucleosynthesis and element formation in the early universe in the framework of higher dimensional cosmology. For this purpose we utilize a previous solution of the present author, which may be termed as the generalized Friedmann-Robertson-Walker model. We find that temperature decays less rapidly in higher dimensional cosmology, which we believe may have nontrivial consequences \emph{vis-a-vis} primordial physics.
Interstellar synchrotron emission depends on Galactic magnetic fields and on cosmic-ray leptons. Observations of radio emission are an important tool for studying cosmic-ray propagation models and interstellar electron spectrum and distribution in the Galaxy. We present the latest developments in our modeling of Galactic synchrotron emission with the GALPROP code, including polarization, absorption, and free-free emission. Using surveys over a wide range of radio frequencies and polarization measurements, we derive constraints on the low-energy interstellar cosmic-ray electron spectrum, magnetic fields and cosmic-ray propagation models. This work is of interest for studies of interstellar gamma-ray emission with Fermi-LAT, and synchrotron for the Planck mission.
In this paper, we consider the exterior Dirichlet problem for Hessian quotient equations with the right hand side $g$, where $g$ is a positive function and $g=1+O(|x|^{-\beta})$ near infinity, for some $\beta>2$. Under a prescribed generalized symmetric asymptotic behavior at infinity, we establish an existence and uniqueness theorem for viscosity solutions, by using comparison principles and Perron's method. This extends the previous results for Monge--Amp\`ere equations and Hessian equations.
Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source vs.~a time-dependent, nonequilibrium hadronization off a quark-gluon plasma droplet. Due to the time-dependent particle evaporation off the hadronic surface in the latter approach the hadron ratios change (by factors of $<\approx 5$) in time. Final particle yields reflect time averages over the actual thermodynamic properties of the system at a certain stage of the evolution. Calculated hadron, strangelet and (anti-)cluster yields as well as freeze-out times are presented for different systems. Due to strangeness distillation the system moves rapidly out of the T, $\mu_q$ plane into the $\mu_s$-sector. Strangeness to baryon ratios f_s=1-2 prevail during a considerable fraction (50%) of the time evolution (i.e. $\Lambda$-droplets or even $\Xi^-$-droplets form the system at the late stage: The possibility of observing this time evolution via HBT correlations is discussed). The observed hadron ratios require $T_c\approx 160 MeV$ and $B^{1/4}>\approx 200 MeV$. If the present model is fit to the extrapolated hadron yields, metastable hypermatter can only be produced with a probability $p< 10^{-8}$ for $A \ge 4$.
We study the electron momentum distribution function (EMDF) for the two-dimensional t-t'-J model doped with one hole on finite clusters by the method of twisted boundary conditions. The results quantitatively agree with our analytical results for a single hole in the antiferromagnetic background, based on the self-consistent Born approximation (SCBA). Moreover, within the SCBA an anomalous momentum dependence of EMDF is found, pointing to an emerging large Fermi surface. The analysis shows that the presence of next-nearest-neighbor (NNN) hopping terms changes EMDF only quantitatively.
We introduce and compute the class of a number of effective divisors on the moduli space of stable maps $\bar M_{0,0}(P^{r},d)$, which, for small d, provide a good understanding of the extremal rays and the stable base locus decomposition for the effective cone. We also discuss various birational models that arise in Mori's program, including the Hilbert scheme, the Chow variety, the space of $k$-stable maps, the space of branchcurves and the space of semi-stable sheaves.
We calculate simultaneously the radio and optical luminosity evolutions of quasars, and the distribution in radio loudness R defined as the ratio of radio and optical luminosities, using a flux limited data set containing 636 quasars with radio and optical fluxes from White et al. We first note that when dealing with multivariate data it is imperative to first determine the true correlations among the variables, not those introduced by the observational selection effects, before obtaining the individual distributions of the variables. We use the methods developed by Efron and Petrosian which are designed to obtain unbiased correlations, distributions, and evolution with redshift from a data set truncated due to observational biases. It is found that the population of quasars exhibits strong positive correlation between the radio and optical luminosities. With this correlation, whether intrinsic or observationally induced accounted for, we find that there is a strong luminosity evolution with redshift in both wavebands, with significantly higher radio than optical evolution. We also construct the local radio and optical luminosity functions and the density evolution. Finally, we consider the distribution of the radio loudness parameter R obtained from careful treatment of the selection effects and luminosity evolutions with that obtained from the raw data without such considerations. We find a significant difference between the two distributions and no clear sign of bi-modality in the true distribution for the range of R values considered. Our results indicate therefore, somewhat surprisingly, that there is no critical switch in the efficiency of the production of disk outflows/jets between very radio quiet and very radio loud quasars, but rather a smooth transition. Also, this efficiency seems higher for the high-redshift and more luminous sources in the considered sample.
We review and study a one-parameter family of functional transformations, denoted by $(S^{(\beta)})_{\beta\in \R}$, which, in the case $\beta<0$, provides a path realization of bridges associated to the family of diffusion processes enjoying the time inversion property. This family includes the Brownian motion, Bessel processes with a positive dimension and their conservative $h$-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary crossing times for these diffusions over a given function $f$ to those over the image of $f$ by the mapping $S^{(\beta)}$, for some fixed $\beta\in \mathbb{R}$. We give some new examples of boundary crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family.
We present the results of deep I-band imaging of two BL Lacerate objects, RGB 0136+391 and PKS 0735+178, during an epoch when the optical nucleus was in a faint state in both targets. In PKS 0735+178 we find a significant excess over a point source, which, if fitted by the de Vaucouleurs model, corresponds to a galaxy with I = 18.64 +- 0.11 and r_eff = 1.8 +- 0.4 arcsec. Interpreting this galaxy as the host galaxy of PKS 0735+178 we derive z = 0.45 +- 0.06 using the host galaxy as a "standard candle". We also discuss the immediate optical environment of PKS 0735+178 and the identity of the MgII absorber at z = 0.424. Despite of the optimally chosen epoch and deep imaging we find the surface brightness profile of RGB 0136+391 to be consistent with a point source. By determining a lower limit for the host galaxy brightness by simulations, we derive z > 0.40 for this target.
It has been revealed using microlensing that a considerable part, possibly more than half, of the dark matter in the halo of our Galaxy consists of objects with a mass spectrum ranging from 0.05 to 0.8 of the solar mass. What is the nature of these objects? There exist two hypotheses. According to one, these are Jupiter type planets or small stars (brown and white dwarfs) consisting of normal baryonic matter. According to the other, these are non-compact objects, i.e., small-scale formations in non-baryonic dark matter. Here, a theory is proposed describing the possibility of the existence of non-compact objects in the halo of our Galaxy, their structure and formation from non-baryonic matter. The theory of microlensing on compact and non-compact objects is considered in detail. The results of microlensing observations are described and compared with theory. Possible astrophysical manifestations of the presence of small-scale structure are pointed out. The field is being extensively studied and is of fundamental interest for cosmology and astrophysics.
Conditional Equi-concentration of Types on I-projections is presented. It provides an extension of Conditional Weak Law of Large Numbers to the case of several I-projections. Also a multiple I-projections extension of Gibbs Conditioning Principle is developed. mu-projection variants of the probabilistic laws are stated. Implications of the results for Relative Entropy Maximization, Maximum Probability, Maximum Entropy in the Mean and Maximum Renyi-Tsallis Entropy methods are discussed.
We review the main observational properties of neutron star low mass transients in quiescence. We first survey the discoveries of BeppoSAX. We then focus on recent discoveries by Chandra and XMM-Newton, with special emphsasis on the detection of the quiescent counterpart of SAX J1808.4-3658 and the study of variability in the quiescent state.
We investigate the effect of electron-electron interactions on the conductance of quasi one-dimensional systems without potential scattering. For a finite temperature or system length, the short-range interaction is not renormalized to 0, and it gives rise to a finite correction to the conductance if we calculate it using Kubo formula. We show that this correction can be absorbed into the renormalization of the chemical potential and that the properly defined conductance to be observed in the experiments is equal to that of non-interacting electrons.
Let $M$ be a complete Riemannian manifold possibly with a boundary $\partial M$. For any $C^1$-vector field $Z$, by using gradient/functional inequalities of the (reflecting) diffusion process generated by $L:=\Delta+Z$, pointwise characterizations are presented for the Bakry-Emery curvature of $L$ and the second fundamental form of $\partial M$ if exists. These extend and strengthen the recent results derived by A. Naber for the uniform norm $\|{\mathbf{Ric}}_Z\|_\infty$ on manifolds without boundary. A key point of the present study is to apply the asymptotic formulas for these two tensors found by the first named author, such that the proofs are significantly simplified.
The CP-violating phases associated with Majorana neutrinos can give rise to CP-violating effects even in processes that conserve total Lepton number, such as \mu -> eee+, \mu + e -> e + e and others. After explaining the reasons that make this happen, we consider the calculation of the rates for the process of the form \ell_a + \ell_b -> \ell_a + \ell_c, and its conjugate \bar\ell_a + \bar\ell_b -> \bar\ell_a + \bar\ell_c, where \ell_a, \ell_b and \ell_c denote charged leptons of different flavors. In the context of the Standard Model with Majorana neutrinos, we show that the difference in the rates depends on such phases. Our calculations illustrate in detail the mechanics that operate behind the scene, and set the stage for carrying out the analogous, more complicated (as we explain), calculations for other processes such as \mu -> eee+ and its conjugate.
A Freidlin-Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast component is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [3].
By lifting full Yang-Mills theory to $R_4 \times S_2$, Mason et al. obtained MHV vertices by gauge transformation. Their Lagrangian depended on long intricate twistor manipulations. Spinor $S_2$ harmonics give a one page proof, eliminating all the $CP_3$ apparatus.
We report the detection of super-hard (>10 keV) X-ray emission extending up to 70 keV from the classical nova V2491 Cygni using the Suzaku observatory. We conducted two ~20 ks target-of-opportunity observations 9 and 29 days after the outburst on 2008 April 11, yielding wide energy range spectra by combining the X-ray Imaging Spectrometer and the Hard X-ray Detector. On day 9, a spectrum was obtained at 1.0-70 keV with the Fe XXV K\alpha line feature and a very flat continuum, which is explained by thermal plasma with a 3 keV temperature and power-law emission with a photon index of 0.1 attenuated by a heavy extinction of 1.4x10^{23} cm^{-2}. The 15-70 keV luminosity at 10.5 kpc is 6x10^{35} ergs s^{-1}. The super-hard emission was not present on day 29. This is the highest energy at which X-rays have been detected from a classical nova. We argue a non-thermal origin for the emission, which suggests the presence of accelerated charged particles in the nova explosion.
Various modern nucleon-nucleon (NN) potentials yield a very accurate fit to the nucleon-nucleon scattering phase shifts. The differences between these interactions in describing properties of nuclear matter are investigated. Various contributions to the total energy are evaluated employing the Hellmann - Feynman theorem. Special attention is paid to the two-nucleon correlation functions derived from these interactions. Differences in the predictions of the various interactions can be traced back to the inclusion of non-local terms.
We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.
We study the integrable XXZ model with general non-diagonal boundary terms at both ends. The Hamiltonian is considered in terms of a two boundary extension of the Temperley-Lieb algebra.   We use a basis that diagonalizes a conserved charge in the one-boundary case. The action of the second boundary generator on this space is computed. For the L-site chain and generic values of the parameters we have an irreducible space of dimension 2^L. However at certain critical points there exists a smaller irreducible subspace that is invariant under the action of all the bulk and boundary generators. These are precisely the points at which Bethe Ansatz equations have been formulated. We compute the dimension of the invariant subspace at each critical point and show that it agrees with the splitting of eigenvalues, found numerically, between the two Bethe Ansatz equations.