ShantanuT01/DACTYL-Pretraining huggingface dataset:
A maximally reduced system of equations corresponding to the twisting type N Einstein metrics is given. When the cosmological constant $\lambda\to 0$ they reduce to the standard equations for the vacuum twisting type N's. All the metrics which are conformally equivalent to the twisting type N metrics and which admit 3-dimensional conformal group of symmetries are presented. In the Feferman class of metrics an example is given of a twisting type N metric which satisfies Bach's equations but is not Einstein.
We extend the action for evolution equations of KdV and MKdV type which was derived in [Capel/Nijhoff] to the case of not periodic, but only equivariant phase space variables, introduced in [Faddeev/Volkov]. The difference of these variables may be interpreted as reduced phase space variables via a Marsden-Weinstein reduction where the monodromies play the role of the momentum map. As an example we obtain the doubly discrete sine-Gordon equation and the Hirota equation and the corresponding symplectic structures.
NLO QCD corrections to charged and neutral current Drell-Yan processes and their implementation in the computer system SANC are considered. On the partonic level both quark-antiquark and quark-gluon scattering channels are taken into account. Subtractions of the collinear singularities in the massive case are compared with ones in the MS-bar scheme. Results of SANC on the hadronic level are presented. Comparison with results of the MCFM package is shown.
We detect the optical afterglow and host galaxy of GRB 070714B. Our observations of the afterglow show an initial plateau in the lightcurve for approximately the first 5 to 25 minutes, then steepening to a powerlaw decay with index alpha= 0.86 +/- 0.10 for the period between 1 to 24 hours post burst. This is consistent with the X-ray light-curve which shows an initial plateau followed by a similar subsequent decay. At late time, we detect a host galaxy at the location of the optical transient. Gemini Nod & Shuffle spectroscopic observations of the host show a single emission line at 7167 angstroms which, based on a grizJHK photometric redshift, we conclude is the 3727 angstrom [O II] line. We therefore find a redshift of z=0.923. This redshift, as well as a subsequent probable spectroscopic redshift determination of GRB 070429B at z=0.904 by two other groups, significantly exceeds the previous highest spectroscopically confirmed short burst redshift of z=0.546 for GRB 051221. This dramatically moves back the time at which we know short bursts were being formed, and suggests that the present evidence for an old progenitor population may be observationally biased.
Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to $1/\nu$, which is much faster than what would be produced by the static fluid if its viscosity is $0 < \nu \ll 1$. This phenomenon is analyzed rigorously using the linear PDE governing the evolution of the solute. It is shown that the solution can be split into two pieces, an approximate solution and a remainder term. The approximate solution is governed by an infinite-dimensional system of ODEs that possesses a finite-dimensional center manifold, on which the dynamics correspond to diffusion at a rate proportional to $1/\nu$. The remainder term is shown to decay at a rate that is much faster than the leading order behavior of the approximate solution. This is proven using a spectral decomposition in Fourier space and a hypocoercive estimate to control the intermediate Fourier modes.
We investigate the quantum metrological power of typical continuous-variable (CV) quantum networks. Particularly, we show that most CV quantum networks provide an entanglement to quantum states in distant nodes that enables one to achieve the Heisenberg scaling in the number of modes for distributed quantum displacement sensing, which cannot be attained using an unentangled probe state. Notably, our scheme only requires local operations and measurements after generating an entangled probe using the quantum network. In addition, we find a tolerable photon-loss rate that maintains the quantum enhancement. Finally, we numerically demonstrate that even when CV quantum networks are composed of local beam splitters, the quantum enhancement can be attained when the depth is sufficiently large.
The problems of attempting inflationary model-building in a theory containing a dilaton are explained. In particular, I study the shape of the dilaton potential today and during inflation, based on a weakly-coupled heterotic string model where corrections to the Kahler potential are assumed to be responsible for dilaton stabilization. Although no specific model-building is attempted, if the inflationary energy density is related to the scale of gaugino condensation, then the dilaton may be stabilized close enough to today's value that there is no significant change in the GUT scale coupling. This can occur in a very wide range of models, and helps to provide some justification for the standard predictions of the spectral index. I explain how this result can ultimately be traced to the supersymmetry structure of the theory.
Figueroa-Centeno et al. introduced the following product of digraphs: let $D$ be a digraph and let $\Gamma$ be a family of digraphs such that $V(F)=V$ for every $F\in \Gamma$. Consider any function $h:E(D)\longrightarrow\Gamma $. Then the product $D\otimes_{h} \Gamma$ is the digraph with vertex set $V(D)\times V$ and $((a,x),(b,y))\in E(D\otimes_h\Gamma)$ if and only if $(a,b)\in E(D)$ and $(x,y)\in E(h (a,b))$.   In this paper, we introduce the undirected version of the $\otimes_h$-product, which is a generalization of the classical direct product of graphs and, motivated by it, we also recover a generalization of the classical lexicographic product of graphs that was introduced by Sabidussi en 1961. We study connectivity properties and other invariants in terms of the factors. We also present a new intersection graph that emerges when we characterize the connectivity of $\otimes_h$-product of graphs.
We study a continuous set of spin 1 measurements and show that for a special family of measurements parametrized by a single variable $\theta$ the possibility of hidden-variable description is a discontinuous property.
We first discuss, on a no-QGP basis, the two prominent indications of (a) enhanced strangeness production and of (b) anomalous $J/\psi $-suppression: We elaborate in particular on a recent idea of antihyperon production solely by multi-mesonic reactions. As a possible source for an enhanced dissociation of $c \bar{c}$ pairs we summarize the findings within the 'early'-comover absorption scenario of prehadronic string excitations. As an exotic candidate we then finally adress the stochastic formation of so called disoriented chiral condensates: An experimentally feasible DCC, if it does exist, has to be a rare event following an unusual and nontrivial distribution on an event by event basis.
The outer halo regions of early-type galaxies carry key information about their past accretion history. However, spectroscopically probing the stellar component at such galactocentric radii is still challenging. Using Keck/DEIMOS, we have been able to measure the metallicities of the stellar and globular cluster components in 12 early-type galaxies out to more than $10~\rm{R_{e}}$. We find similar metallicity gradients for the metal-poor and metal-rich globular cluster subpopulations, suggesting a common formation process for the two subpopulations. This is in conflict with most current theoretical predictions, where the metal-poor globular clusters are thought to be purely accreted and metal-rich globular clusters mostly formed in-situ. Moreover, we find that the globular cluster metallicity gradients show a trend with galaxy mass, being steeper in lower-mass galaxies than in higher-mass galaxies. This is similar to what we find for the outermost galaxy stars and suggests a more active accretion history, with a larger role played by major mergers, in the most massive galaxies. This conclusion is qualitatively consistent with expectations from two-phase galaxy assembly models. Finally, we find that the small difference in metallicity between galaxy stars and metal-rich globular clusters at $1~\rm{R_{e}}$ may correlate with galaxy mass. The origin of this difference is not currently clear.
A Kubo formalism is used to calculate the electronic and optical conductivity of a graphene superlattice with Y-shaped kekul\'e bond texture, similar to that visualized in recent experiments. We show that new conduction channels between the valleys in graphene are opened by the kekul\'e distortion. This intervalley contribution to the electronic transport is not present in pristine graphene and here appears due to the folding of the Dirac cones $K$, $K'$ on top of each other. The contribution of intervalley transport to the conductivity of graphene, as well as the modification of the intravalley transport, are analyzed in detail for different frequency, temperature, chemical potential and scattering rate limits. We obtain analytical expressions for the conductivity that reproduce previous expressions used to fit experimental measurements in graphene and compare with direct numerical evaluations of the Kubo formula, finding great agreement. The optical absorption arising from intervalley transitions displays a maximum at a special frequency that can be tuned by doping. Our results show how the single parameter describing the valley coupling in this system could be obtained by measuring graphene's optical absorbance in the region where interband transitions are blocked by the impurities. Finally, we use Fermi's golden rule to independently verify some of the previous results.
We investigate the distribution of the zeros of partial sums of the Riemann zeta-function, sum_{n\leq X}n^{-s}, estimating the number of zeros up to height T, the number of zeros to the right of a given vertical line, and other aspects of their horizontal distribution.
NGC 4477 is a low-mass lenticular galaxy in the Virgo Cluster, residing at 100\,kpc to the north of M87. Using a total of 116\,ks {\sl Chandra} observations, we study the interplay between its hot ($\sim$0.3\,keV) gas halo and the central supermassive black hole. A possible cool core is indicated by the short cooling time of the gas at the galaxy centre. We identify a pair of symmetric cavities lying 1.1\,kpc southeast and 0.9\,kpc northwest of the galaxy centre with diameters of 1.3\,kpc and 0.9\,kpc, respectively. We estimate that these cavities are newly formed with an age of $\sim$4\,Myr. No radio emission is detected at the positions of the cavities with the existing VLA data. The total energy required to produce the two cavities is $\sim$$10^{54}$\,erg, at least two orders of magnitude smaller than that of typical X-ray cavities. NGC 4477 is arguably far the smallest system and the only lenticular galaxy in which AGN X-ray cavities have been found. It falls on the scaling relation between the cavity power and the AGN radio luminosity, calibrated for groups and clusters. Our findings suggest that AGN feedback is universal among all cool core systems. Finally, we note the presence of molecular gas in NGC~4477 in the shape of a regular disk with ordered rotation, which may not be related to the feedback loop.
We search for nonlinear effects in nuclear giant resonances (GRs), in particular the isovector dipole and the isoscalar quadrupole modes. To that end, we employ a spectral analysis of time-dependent Hartree-Fock (TDHF) dynamics using Skyrme forces. Based on TDHF calculations over a wide range of excitation amplitudes, we explore the collectivity and degree of harmonic motion in these modes. Both GR modes turn out to be highly harmonic in heavy nuclei from A=100 on. There is no trace of a transition to irregular motion and multiple resonances are predicted. Slight anharmonicities are seen for light nuclei, particularly for $^{16}$O. These are mainly caused by the spin-orbit splitting.
We conducted astrometric VLBI observations of water-vapor maser emission in the massive star forming region IRAS 21379+5106 to measure the annual parallax and proper motion, using VERA. The annual parallax was measured to be $0.262 \pm 0.031$ mas corresponding to a trigonometric distance of $3.82^{+0.51}_{-0.41}$ kpc. The proper motion was $(\mu_\alpha\cos{\delta}, \mu_\delta)=(-2.74 \pm 0.08, -2.87 \pm 0.18)$ mas yr$^{-1}$. Using this result, the Galactic rotational velocity was estimated to be $V_\theta=218\pm 19$ km s$^{-1}$ at the Galactocentric distance $R=9.22\pm0.43$ kpc, when we adopted the Galactic constants $R_0=8.05\pm 0.45$ kpc and $V_0=238\pm 14$ km s$^{-1}$. With newly determined distance, {the bolometric luminosity of the central young stellar object was re-evaluated to $(2.15\pm 0.54)\times 10^3 L_\odot$, which corresponds to spectral type of} B2--B3. Maser features were found to be distributed along a straight line from south-west to north-east. In addition, a vector map of the internal motions constructed from the residual proper motions implies that maser features trace a bipolar flow and that it cannot be explained by simple ballistic motion.
We analyze the evolution of colour gradients predicted by the hydrodynamical models of early type galaxies (ETGs) in Pipino et al. (2008), which reproduce fairly well the chemical abundance pattern and the metallicity gradients of local ETGs. We convert the star formation (SF) and metal content into colours by means of stellar population synthetic model and investigate the role of different physical ingredients, as the initial gas distribution and content, and eps_SF, i.e. the normalization of SF rate. From the comparison with high redshift data, a full agreement with optical rest-frame observations at z < 1 is found, for models with low eps_SF, whereas some discrepancies emerge at 1 < z < 2, despite our models reproduce quite well the data scatter at these redshifts. To reconcile the prediction of these high eps_SF systems with the shallower colour gradients observed at lower z we suggest intervention of 1-2 dry mergers. We suggest that future studies should explore the impact of wet galaxy mergings, interactions with environment, dust content and a variation of the Initial Mass Function from the galactic centers to the peripheries.
Gamma ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram to very high redshift. To this aim, the luminosity (or isotropic emitted energy) of a GRB at redshift z must be evaluated from a correlation with a distance independent quantity so that one can then solve for the luminosity distance D_L(z) and hence the distance modulus mu(z). Averaging over five different two parameters correlations and using a fiducial cosmological model to calibrate them, Schaefer (2007) has compiled a sample of 69 GRBs with measured mu(z) which has since then been widely used to constrain cosmological parameters. We update here that sample by many aspects. First, we add a recently found correlation for the X - ray afterglow and use a Bayesian inspired fitting method to calibrate the different GRBs correlations known insofar assuming a fiducial LCDM model in agreement with the recent WMAP5 data. Averaging over six correlations, we end with a new GRBs Hubble diagram comprising 83 objects. We also extensively explore the impact of varying the fiducial cosmological model considering how the estimated mu(z) change as a function of the $(\Omega_M, w_0, w_a)$ parameters of the Chevallier - Polarski - Linder phenomenological dark energy equation of state. In order to avoid the need of assuming an {\it a priori} cosmological model, we present a new calibration procedure based on a model independent local regression estimate of mu(z) using the Union SNeIa sample to calibrate the GRBs correlations. This finally gives us a GRBs Hubble diagram made out of 69 GRBs whose estimated distance modulus mu(z) is almost independent on the underlying cosmological model.
We formulate WZW models based on a centrally extended version of the Euclidean group in $d$-dimensions. We obtain string backgrounds corresponding to conformal $\s$-models in $D=d^2$ space-time dimensions with exact central charge $c=d^2$ and $d(d-1)/2$ null Killing vectors. By identifying the corresponding conformal field theory we show that the one loop results coincide with the exact ones up to a shifting of a parameter.
Luminous quasars powered by accreting supermassive black holes (SMBHs) have been found in the early Universe at $z \gtrsim 7.5$, which set a strong constraint on both the seed black hole mass and the rapid growth of the SMBHs. In this work, we explore how the SMBHs are grown through Eddington limited accretion driven predominantly by magnetic outflows. Most angular momentum and the released gravitational energy in the disk can be removed by magnetic outflows, and therefore the mass accretion rate of the black hole (BH) can be high even if the disk is radiating at sub-Eddington luminosity. It is found that the SMBH with several billion solar masses discovered at $z\gtrsim 7$ may probably be grown through chaotic accretion predominantly driven by magnetic outflows from a stellar mass BH, when the disks are radiating at moderate luminosity ($\sim 0.5$ Eddington luminosity) with mild outflows. We find that most SMBHs are spinning at moderate values of spin parameter $a_*$, which implies only a small fraction of quasars may have radio jets.
We study in detail a system of two interferometers aimed to the detection of extremely faint phase-fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, that are limited by the shot noise. If the two interferometers experience identical phase-fluctuations, like the ones introduced by the so called "holographic noise", this signal should emerge if their output signals are correlated, while the fluctuations due to shot noise and other independent contributions will vanish. We show how the injecting quantum light in the free ports of the interferometers can reduce the photon noise of the system beyond the shot-noise, enhancing the resolution in the phase-correlation estimation. We analyze both the use of two-mode squeezed vacuum or twin-beam state (TWB) and of two independent squeezing states. Our results basically confirms the benefit of using squeezed beams together with strong coherent beams in interferometry, even in this correlated case. However, mainly we concentrate on the possible use of TWB, discovering interesting and probably unexplored areas of application of bipartite entanglement and in particular the possibility of reaching in principle surprising uncertainty reduction.
We calculate exotic cooling rates of stars due to photo-production of light particles (mostly scalars and pseudoscalars) which originate from the hidden sector of no scale supergravity theories. Using this we can restrict the gravitino mass $m_{3/2}$. The range of eliminated values of $m_{3/2}$ stretches over six orders of magnitude and is given by $\displaystyle{2 \times 10^8 < {m_{\tilde g} \over m_{3/2}} < 6 \times 10^{13}}$, $m_{\tilde g}$ being the gluino mass. Combining our result with the earlier analysis from colliders ($\displaystyle{ {m_{\tilde g} \over m_{3/2}} < 2.7 \times 10^{14}}$) we conclude that $\displaystyle{{m_{\tilde g} \over m_{3/2}} < {\cal O}(10^8)}$ except for a narrow window around $10^{14}$. Together with the current experimental limit on $m_{\tilde{g}}$ and cosmological constraints on $m_{3/2}$, albeit model dependent, our analysis shows that a light gravitino is on the verge of being ruled out.
We present results of $^{23}$Na and $^{19}$F nuclear magnetic resonance (NMR) measurements on NaCaCo$_2$F$_7$, a frustrated pyrochlore magnet with a Curie-Weiss temperature, $T_{cw}$ ~-140 K, and intrinsic bond disorder. Below 3.6 K both the $^{23}$Na and $^{19}$F spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80 \%) of the NMR signal intensity: This proves a broad quasi-static field distribution. The $^{19}$F spin-lattice relaxation rate $^{19}(1/T_1$) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the spin freezing to the presence of bond disorder. This is corroborated by large-scale Monte-Carlo simulations of a classical bond-disordered XY model on the pyrochlore lattice. The low freezing temperature, together with the very short magnetic correlation length not captured by the simulations, suggesting that quantum effects play a decisive role in NaCaCo$_2$F$_7$.
The lonely runner conjecture of Wills and Cusick, in its most popular formulation, asserts that if $n$ runners with distinct constant speeds run around a unit circle ${\bf R}/{\bf Z}$ starting at a common time and place, then each runner will at some time be separated by a distance of at least $\frac{1}{n+1}$ from the others. In this paper we make some remarks on this conjecture. Firstly, we can improve the trivial lower bound of $\frac{1}{2n}$ slightly for large $n$, to $\frac{1}{2n} + \frac{c \log n}{n^2 (\log\log n)^2}$ for some absolute constant $c>0$; previous improvements were roughly of the form $\frac{1}{2n} + \frac{c}{n^2}$. Secondly, we show that to verify the conjecture, it suffices to do so under the assumption that the speeds are integers of size $n^{O(n^2)}$. We also obtain some results in the case when all the velocities are integers of size $O(n)$.
Let P be a set of n points in the plane, not all on a line. We show that if n is large then there are at least n/2 ordinary lines, that is to say lines passing through exactly two points of P. This confirms, for large n, a conjecture of Dirac and Motzkin. In fact we describe the exact extremisers for this problem, as well as all sets having fewer than n - C ordinary lines for some absolute constant C. We also solve, for large n, the "orchard-planting problem", which asks for the maximum number of lines through exactly 3 points of P. Underlying these results is a structure theorem which states that if P has at most Kn ordinary lines then all but O(K) points of P lie on a cubic curve, if n is sufficiently large depending on K.
This paper has been withdrawn by the authors to avoid redundancy with e-print hep-ph0507031.
We built a custom video-based eye-tracker that saves every video frame as a full resolution image (MJPEG). Images can be processed offline for the detection of ocular features, including the pupil and corneal reflection (First Purkinje Image, P1) position. A comparison of multiple algorithms for detection of pupil and corneal reflection can be performed. The system provides for highly flexible stimulus creation, with mixing of graphic, image, and video stimuli. We can change cameras and infrared illuminators depending on the image qualities and frame rate desired. Using this system, we have detected the position of the Fourth Purkinje image (P4) in the frames. We show that when we estimate gaze by calculating P1-P4, signal compares well with gaze estimated with a DPI eye-tracker, which natively detects and tracks the P1 and P4.