ShantanuT01/DACTYL-Pretraining huggingface dataset:
I present a comparison between published dynamical (ATLAS3D) and spectroscopic (Conroy & van Dokkum) constraints on the stellar initial mass function (IMF) in early-type galaxies, using the 34 galaxies in common between the two works. Both studies infer an average IMF mass factor $\alpha$ (the stellar mass relative to a Kroupa-IMF population of similar age and metallicity) greater than unity, i.e. both methods favour an IMF which is heavier than that of the Milky Way, on average over the sample. However, on a galaxy-by-galaxy basis, there is no correlation between $\alpha$ inferred from the two approaches. I investigate how the two estimates of $\alpha$ are correlated systematically with the galaxy velocity dispersion, $\sigma$, and with the Mg/Fe abundance ratio. The spectroscopic method, based on the strengths of metal absorption lines, yields a correlation only with metal abundance ratios: at fixed Mg/Fe, there is no residual correlation with $\sigma$. The dynamical method, applied to exactly the same galaxy sample, yields the opposite result: the IMF variation correlates only with dynamics, with no residual correlation with Mg/Fe after controlling for $\sigma$. Hence although both methods indicate a heavy IMF on average in ellipticals, they lead to incompatible results for the systematic trends, when applied to the same set of galaxies. The sense of the disagreement could suggest that one (or both) of the methods has not accounted fully for the main confounding factors, i.e. element abundance ratios or dark matter contributions. Alternatively, the poor agreement might indicate additional variation in the detailed shape of the IMF, beyond what can currently be inferred from the spectroscopic features.
We present the very long baseline interferometry H2O maser monitoring observations of the red supergiant, PZ Cas, at 12 epochs from 2006 April to 2008 May. We fitted maser motions to a simple model composed of a common annual parallax and linear motions of the individual masers. The maser motions with the parallax subtracted were well modeled by a combination of a common stellar proper motion and a radial expansion motion of the circumstellar envelope. We obtained an annual parallax of 0.356+/-0.026 mas and a stellar proper motion of {\mu}*{\alpha}cos{\delta}=-3.7+/-0.2 and {\mu}*{\delta}=-2.0+/-0.3 mas/yr eastward and northward, respectively. The annual parallax corresponds to a trigonometric parallax of 2.81+0.22-0.19 kpc. By rescaling the luminosity of PZ Cas in any previous studies using our trigonometric parallax, we estimated the location of PZ Cas on a Hertzsprung-Russell diagram and found that it approaches a theoretically evolutionary track around an initial mass of ~25M(sun). The sky position and the distance to PZ Cas are consistent with the OB association, Cas OB5, which is located in a molecular gas super shell. The proper motion of PZ Cas is close to that of the OB stars and other red supergiants in Cas OB5 measured by the Hipparcos satellite. We derived the peculiar motion of PZ Cas of Us = 22.8+/-1.5, Vs = 7.1+/-4.4, and Ws = -5.7+/-4.4 km/s. This peculiar motion has rather a large Us component, unlike those of near high-mass star-forming regions with negatively large Vs motions. The uniform proper motions of the Cas OB5 member stars suggest random motions of giant molecular clouds moving into local potential minima in a time-dependent spiral arm, rather than a velocity field caused by the spiral arm density wave.
We describe and analyze how reinforced random walks can eventually localize, i.e. only visit finitely many sites. After introducing vertex and edge self-interacting walks on a discrete graph in a general setting, and stating the main results and conjectures so far on the topic, we present martingale techniques that provide an alternative proof of the a.s. localization of vertex-reinforced random walks (VRRWs) on the integers on finitely many sites and, with positive probability, on five consecutive sites, initially proved by Pemantle and Volkov (1999).   Next we introduce the continuous time-lines representation (sometimes called Rubin construction) and its martingale counterpart, and explain how it has been used to prove localization of some reinforced walks on one attracting edge. Then we show how a modified version of this construction enables one to propose a new short proof of the a.s. localization of VRRWs on five sites on Z.
We introduce two operators on stable configurations of the sandpile model that provide an algorithmic bijection between recurrent and parking configurations. This bijection preserves their equivalence classes with respect to the sandpile group. The study of these operators in the special case of the complete bipartite graph ${K}_{m,n}$ naturally leads to a generalization of the well known Cyclic Lemma of Dvoretsky and Motzkin, via pairs of periodic bi-infinite paths in the plane having slightly different slopes. We achieve our results by interpreting the action of these operators as an action on a point in the grid $\mathbb{Z}^2$ which is pointed to by one of these pairs of paths. Our Cyclic lemma allows us to enumerate several classes of polyominoes, and therefore builds on the work of Irving and Rattan (2009), Chapman et al. (2009), and Bonin et al. (2003).
We propose a method that allows for the efficient solution of the three-body Faddeev equations in the presence of infinitely rising confinement interactions. Such a method is useful in calculations of nonrelativistic and especially semirelativistic constituent quark models. The convergence of the partial wave series is accelerated and possible spurious contributions in the Faddeev components are avoided. We demonstrate how the method works with the example of the Goldstone-boson-exchange chiral quark model for baryons.
Several independent pieces of information have recently hinted at a prominent role of cosmic rays in controlling their own transport, within and around the sources as well as throughout their propagation on Galactic scales and even possibly during their escape from the Galaxy. I will discuss this topic with special attention to the theoretical implications and possible additional observational evidence that we may seek with upcoming experiments.
In a popular scenario for the coevolution of massive black holes and galaxies, major mergers of gas-rich galaxies fuel vigorous star formation and obscured (type 2) quasar activity until energy feedback from the active galactic nucleus clears away the gas and dust to reveal an unobscured (type 1) quasar. Under this scenario, the precursor type 2 quasars should be more gas-rich than their type 1 counterparts, and both types of quasars are expected to be gas-deficient relative to normal, star-forming galaxies of similar stellar mass. We test this evolutionary hypothesis by investigating the infrared (~ 1-500 micron) spectral energy distribution of 86 optically selected z < 0.5 type 2 quasars, matched in redshift and [O III] luminosity to a comparison sample of type 1 quasars. Contrary to expectations, the gas content of the host galaxies of type 2 quasars is nearly indistinguishable from that of type 1 quasar hosts, and neither type exhibits the predicted deficit in gas relative to normal galaxies. The gas mass fraction of quasar hosts appears unaffected by the bolometric luminosity of the active nucleus, although their interstellar radiation field is preferentially higher than that of normal galaxies, potentially implicating active galactic nucleus heating of the large-scale galactic dust.
We study the occupation measure of various sets for a symmetric transient random walk in $Z^d$ with finite variances. Let $\mu^X_n(A)$ denote the occupation time of the set $A$ up to time $n$. It is shown that $\sup_{x\in Z^d}\mu_n^X(x+A)/\log n$ tends to a finite limit as $n\to\infty$. The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green's function of $X$ restricted to the set $A$. Some examples are discussed and the connection to similar results for Brownian motion is given.
We use hyperentangled photons to experimentally implement an entanglement-assisted quantum process tomography technique known as Direct Characterization of Quantum Dynamics. Specifically, hyperentanglement-assisted Bell-state analysis enabled us to characterize a variety of single-qubit quantum processes using far fewer experimental configurations than are required by Standard Quantum Process Tomography (SQPT). Furthermore, we demonstrate how known errors in Bell-state measurement may be compensated for in the data analysis. Using these techniques, we have obtained single-qubit process fidelities as high as 98.2% but with one-third the number experimental configurations required for SQPT. Extensions of these techniques to multi-qubit quantum processes are discussed.
We report photometry and spectroscopy of the evolution of Nova Sagittarii 1994 #1 (V4332 Sagittarii) during outburst. We compare the photometric and spectral evolution of this outburst to known classes of outbursts -- including classical novae and outbursts occurring on symbiotic stars -- and find this object does NOT conform to any known class of outburst. The closest match to the behavior of this unusual object is M31 RV, an extremely luminous and red variable object discovered in the bulge of M31 in 1988. However, the temporal behavior and maximum luminosity of the two events differ by several orders of magnitude, requiring substantial intrinsic variation if these two events are members the same type of outburst.   Our model of the spectroscopic evolution of this outburst shows that the effective temperature cooled from 4400 K to 2300 K over the three month span of our observations. In combination with line diagnostics in our later spectra, including [OI] lambda 5577 and the dramatic increase in the Halpha to Hbeta ratio, we infer the existence of a cool, dense (N_e ~ 10^{8-9} cm^{-3}) envelope that is optically thick in the Hydrogen Balmer recombination lines (case C). We suggest that a nuclear event in a single star, in which a slow shock drove the photosphere outwards, can power the observed luminosity evolution and the emission spectrum.
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
We use zoom hydrodynamical simulations to investigate the properties of satellites within galaxy-sized dark-matter haloes with different assembly histories. We consider two classes of haloes at redshift $z=0$: `stalled' haloes that assembled at $z>1$ and `accreting' ones that are still forming nowadays. Previously, we showed that the stalled haloes are embedded within thick filaments of the cosmic web while the accreting ones lie where multiple thin filaments converge. We find that satellites in the two classes have both similar and different properties. Their mass spectra, radial count profiles, baryonic and stellar content, and the amount of material they shed are indistinguishable. However, the mass fraction locked in satellites is substantially larger for the accreting haloes as they experience more mergers at late times. The largest difference is found in the satellite kinematics. Substructures fall towards the accreting haloes along quasi-radial trajectories whereas an important tangential velocity component is developed, before accretion, while orbiting the filament that surrounds the stalled haloes. Thus, the velocity anisotropy parameter of the satellites ($\beta$) is positive for the accreting haloes and negative for the stalled ones. This signature enables us to tentatively categorize the Milky Way halo as stalled based on a recent measurement of $\beta$. Half of our haloes contain clusters of satellites with aligned orbital angular momenta corresponding to flattened structures in space. These features are not driven by baryonic physics and are only found in haloes hosting grand-design spiral galaxies, independently of their assembly history.
We calculate the scale dependence of nonsinglet nucleon structure functions. Due to anomalous axial symmetry breaking a large flavour asymmetry of the quark--antiquark sea is generated nonperturbatively. This produces a strong scale dependence of the nonsinglet structure function in an intermediate range of $Q^2$. Evolving nonperturbatively a pure valence distribution from an infrared scale we can thus compute $F_2^p-F_2^n$ as measured by the NMC, and give detailed predictions for its $Q^2$ dependence at fixed $x$. We also compare our results with Drell--Yan data.
Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main purpose is to show that several properties of the generating functions of snakes, such as differential equations or closed form as trigonometric functions, can be lifted at the level of noncommutative symmetric functions or free quasi-symmetric functions. The results take the form of algebraic identities for type B noncommutative symmetric functions, noncommutative supersymmetric functions and colored free quasi-symmetric functions.
Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements [10]. Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.
In this paper we prove two results which further classify smoothness properties of Hilbert schemes of points. This is done by counting classes of arrows on Young diagrams corresponding to monomial ideals, building on the approach taken by Jan Cheah to show smoothness in the 2 dimensional case. We prove sufficient conditions for points to be smooth on Hilbert schemes of points in 3 dimensions and on nested schemes in 2 dimensions in terms of the geometry of the Young diagram. In particular, we proved that when the region between the two diagrams at a point of the nested scheme is rectangular, the corresponding point is smooth. We also proved that if the three dimensional Young diagram at a point can be oriented such that its horizontal layers are rectangular, then the point is smooth.
The {\it{Polaron measure}} is defined as the transformed path measure   $$\widehat{\mathbb P}_{\epsilon,T}= Z_{\epsilon,T}^{-1}\,\, \exp\bigg\{\frac{1}{2}\int_{-T}^T\int_{-T}^T\frac{\epsilon\e^{-\epsilon|t-s|}}{|\omega(t)-\omega(s)|} \,\d s \,\d t\bigg\}\d\mathbb P$$ with respect to the law $\mathbb P$ of three dimensional Brownian increments on a finite interval $[-T,T]$, and $ Z_{\epsilon,T}$ is the partition function with $\epsilon>0$ being a constant. The logarithmic asymptotic behavior of the partition function $Z_{\epsilon,T}$ was analyzed in \cite{DV83} showing that $$ g_0=\lim_{\epsilon \to 0}\bigg[\lim_{T\to\infty}\frac{\log Z_{\eps,T}}{2T}\bigg]=\sup_{\heap{\psi\in H^1(\R^3)}{\|\psi\|_2=1}} \bigg\{\int_{\mathbb R^3}\int_{\mathbb R^3}\d x\d y\,\frac {\psi^2(x) \psi^2(y)}{|x-y|} -\frac 12\big\|\nabla \psi\big\|_2^2\bigg\}. $$ In \cite{MV18} we analyzed the actual path measures and showed that the limit ${\widehat {\mathbb P}}_{\eps}=\lim_{T\to\infty}\widehat{\mathbb P}_{\eps,T}$ exists and identified this limit explicitly, and as a corollary, we also deduced the central limit theorem for   $(2T)^{-1/2}(\omega(T)-\omega(-T))$ under $\widehat{\mathbb P}_{\eps,T}$ and obtained an expression for the limiting variance $\sigma^2(\eps)$.   In the present article, we investigate the {\it{strong coupling limit}} $\lim_{\eps\to 0} \lim_{T\to\infty} \widehat{\mathbb P}_{\eps,T}=\lim_{\eps\to 0} \widehat {\mathbb P}_\eps$ and show that this limit coincides with the increments of the stationary Pekar process with generator   $$   \frac 12 \Delta+ \bigg(\frac{\nabla\psi}\psi\bigg)\cdot \nabla   $$ for any maximizer $\psi$ of the free enrgy $g_0$. The Pekar process was also earlier identified in \cite{MV14}, \cite{KM15} and \cite{BKM15} as the limiting object of the {\it{mean-field Polaron}} measures.}
We study some counting questions concerning products of positive integers $u_1, \ldots, u_n$ which form a non-zero perfect square, or more generally, a perfect $k$-th power. We obtain an asymptotic formula for the number of such integers of bounded size and in particular improve and generalize a result of D. I. Tolev (2011). We also use similar ideas to count the discriminants of number fields which are multiquadratic extensions of $\mathbb{Q}$ and improve and generalize a result of N. Rome (2017).
Preconception-free analyses of the inclusive invariant transverse-momentum distribution data taken from the measurements of Au+Au collisions at $\sqrt{s_{NN}}=130$ GeV and $\sqrt{s_{NN}}=200$ GeV have been performed. It is observed that the distributions exhibit for $p_{T}\geq 2$ GeV/c remarkably good power-law behavior ($p_{T}$-scaling) with general regularities. This power-law behavior leads us in particular to recognize that the concept of centrality, albeit its simple appearance, is rather complex; its underlying geometrical structure has to be understood in terms of fractal dimensions. Experimental evidences and theoretical arguments are given which show that the observed striking features are mainly due to geometry and self-organized criticality. A simple model is proposed which approximately reproduces the above-mentioned data for the ``suppression'' without any adjustable parameter. Further heavy-ion collision experiments are suggested.
We present the first simultaneous infrared (IR) and visible spectro-polarimetric observations of a solar internetwork region. The Fe I lines at 6301.6 A, 6302.5 A, 15648 A, and 15652 A were observed, with a lag of only 1 min, using highly sensitive spectro-polarimeters operated in two different telescopes (VTT and THEMIS at the Observatorio del Teide). Some 30% of the observed region shows IR and visible Stokes V signals above noise. These polarization signals indicate the presence of kG magnetic field strengths (traced by the visible lines) co-existing with sub-kG fields (traced by the infrared lines). In addition, one quarter of the pixels with signal have visible and IR Stokes V profiles with opposite polarity. We estimate the probability density function of finding each longitudinal magnetic field strength in the region. It has a tail of kG field strengths that accounts for most of the (unsigned) magnetic flux of the region.
We axiomatize the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalized automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves of Jacobi forms and weakly holomorphic modular forms. Using this machinery we give a short and purely algebraic proof of the proportionality theorem of Hirzebruch and Mumford.
We provide the first black hole solutions with Lifshitz asymptotics found in string theory. These are expected to be dual to models enjoying anisotropic scale invariance with dynamical exponent z=2 at finite temperature. We employ a consistent truncation of type IIB supergravity to four dimensions with an arbitrary 5-dimensional Einstein manifold times a circle as internal geometry. New interesting features are found that significantly differ from previous results in phenomenological models. In particular, small black holes are shown to be thermodynamically unstable, analogously to the usual AdS-Schwarzschild black holes, and extremality is never reached. This signals a possible Hawking-Page like phase transition at low temperatures.
We study the magnetism in NdFe$_2$Ga$_8$ by the neutron-diffraction and temperature-modulated linear {Gr\"uneisen} parameter measurements. Previous thermodynamical measurements have demonstrated that there are two magnetic transitions at 10 and 14.5 K, respectively. Neutron-diffraction measurements confirm that the lower one is an antiferromagnetic (AFM) transition with a commensurate magnetic structure. Both the commensurate and the incommensurate (IC) magnetic peaks are found below the higher transition but their intensities only gradually increase with decreasing temperature. Below 10 K, the commensurate peak intensity increases quickly with decreasing temperature, signaling the AFM transition, while the IC peak intensity disappears below 5 K. The linear {Gr\"uneisen} parameter along the $c$ axis, $\Gamma_c$, shows a hysteresis behavior that is different from the hysteresis behavior for the magnetization $M$. We give a discussion of the origin of the magnetism in NdFe$_2$Ga$_8$.
We present transport measurements of silicon MOS split gate structures with and without Sb implants. We observe classical point contact (PC) behavior that is free of any pronounced unintentional resonances at liquid He temperatures. The implanted device has resonances superposed on the point contact transport indicative of transport through the Sb donors. We fit the differential conductance to a rectangular tunnel barrier model with a linear barrier height dependence on source-drain voltage and non-linear dependence on gate bias. Effects such as Fowler-Nordheim (FN) tunneling and image charge barrier lowering (ICBL) are considered. Barrier heights and widths are estimated for the entire range of relevant biases. The barrier heights at the locations of some of the resonances for the implanted tunnel barrier are between 15-20 meV, which are consistent with transport through shallow partially hybridized Sb donors. The dependence of width and barrier height on gate voltage is found to be linear over a wide range of gate bias in the split gate geometry but deviates considerably when the barrier becomes large and is not described completely by standard 1D models such as FN or ICBL effects.
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth order equation of gradient elasticity. Two alternative methodologies are developed and presented in the present work. The first approach is based on the framework of the pseudo-differential calculus and exploits the special characteristics of this approach to deal with the non local behavior of gradient elasticity. The second implementation is purely differential and is based on the augmentation of the independent variables of the problem. Under this concept, the constitutive equations of gradient elasticity become part of the differential system itself and the whole framework is reminiscent of the transformation of the wave equation to a first order differential system. Crucial issues like existence, uniqueness and stability of the corresponding initial boundary value problems are also encountered via the new concepts.