ShantanuT01/DACTYL-Pretraining huggingface dataset:
A strongly polynomial sequence of graphs $(G_n)$ is a sequence $(G_n)_{n\in\mathbb{N}}$ of finite graphs such that, for every graph $F$, the number of homomorphisms from $F$ to $G_n$ is a fixed polynomial function of $n$ (depending on $F$). For example, $(K_n)$ is strongly polynomial since the number of homomorphisms from $F$ to $K_n$ is the chromatic polynomial of $F$ evaluated at $n$. In earlier work of de la Harpe and Jaeger, and more recently of Averbouch, Garijo, Godlin, Goodall, Makowsky, Ne\v{s}et\v{r}il, Tittmann, Zilber and others, various examples of strongly polynomial sequences and constructions for families of such sequences have been found.   We give a new model-theoretic method of constructing strongly polynomial sequences of graphs that uses interpretation schemes of graphs in more general relational structures. This surprisingly easy yet general method encompasses all previous constructions and produces many more. We conjecture that, under mild assumptions, all strongly polynomial sequences of graphs can be produced by the general method of quantifier-free interpretation of graphs in certain basic relational structures (essentially disjoint unions of transitive tournaments with added unary relations). We verify this conjecture for strongly polynomial sequences of graphs with uniformly bounded degree.
Raman measurements are performed on defect-free wurzite GaP nanowires. Resonance Raman measurements are carried out over the excitation energy range between 2.19 and 2.71 eV. Resonances at 2.38 eV and 2.67 eV of the E1(LO) mode and at 2.67 eV of the A1(LO) are observed. The presence of these intensity resonances clearly demonstrates the existence of energy states with Gamma_9hh and Gamma_7V (Gamma_7C) symmetries of the valence (conduction) band and allows to measure WZ phase GaP band energies at the Gamma point. In addition, we have investigated temperature dependent resonant Raman measurements, which allowed us to extrapolate the zero temperature values of Gamma point energies, along with the crystal field and spin-orbit splitting energies. Above results provide a feedback for refining available theoretical calculations to derive the correct wurtzite III-V semiconductor band structure.
The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactons. We propose a new method to obtain the degeneracy of the edge states from the perspective of entanglement entropy, which is very useful to identify interacting topological states. Employing the determinant quantum Monte Carlo technique, we investigate the interaction effect on two representative models of fermionic topological insulators in one and two dimensions, respectively. In the two topologically nontrivial phases, the edge degeneracies are reduced by interactions but remain to be nontrivial.
We present an analysis of star-formation and nuclear activity in galaxies as a function of both luminosity and environment in the SDSS DR4 dataset. Using a sample of 27753 galaxies at 0.005<z<0.037 that is >90% complete to Mr=-18.0 we find that the EW(Ha) distribution is strongly bimodal, allowing galaxies to be robustly separated into passive and star-forming populations about a value EW(Ha)=2A. In high-density regions ~70% of galaxies are passive independent of luminosity. In the rarefied field however, the fraction of passively-evolving galaxies is a strong function of luminosity, dropping from ~50% for Mr<-21 to zero by Mr~-18. Indeed for the lowest luminosity range covered (-18<Mr<-16) none of the ~600 galaxies in the lowest density quartile are passive. The few passively-evolving dwarf galaxies in field regions appear as satellites to bright (~L*) galaxies. The fraction of galaxies with optical AGN signatures decreases steadily from ~50% at Mr~-21 to ~0% by Mr~-18 closely mirroring the luminosity-dependence of the passive galaxy fraction in low-density environments. This result reflects the increasing importance of AGN feedback with galaxy mass for their evolution, such that the star-formation histories of massive galaxies are primarily determined by their past merger history. In contrast, the complete absence of passively-evolving dwarf galaxies more than ~2 virial radii from the nearest massive halo (i.e. cluster, group or massive galaxy) indicates that internal processes, such as merging, AGN feedback or gas consumption through star-formation, are not responsible for terminating star-formation in dwarf galaxies. Instead the evolution of dwarf galaxies is primarily driven by the mass of their host halo, probably through the combined effects of tidal forces and ram-pressure stripping.
G292.0+1.8 is the Cas A-like supernova remnant containing the young pulsar PSR J1124-5916, which powers a compact torus-like pulsar wind nebula with a jet visible in X-rays. We have performed deep optical observations of the pulsar field to detect the optical counterpart of the pulsar and its nebula. The observations were carried out using the direct imaging mode of FORS2 at the ESO VLT/UT1 telescope in the V, R, and I bands. We also analyzed archival images obtained with the Chandra/ACIS-I, ACIS-S, and HRC-S in X-rays. In all three optical bands we detect a faint elliptical nebulosity, whose brightness peak and center position are consistent at a sub-arcsecond level with the X-ray position of the pulsar. The field is densely packed with background stars, but after subtraction of these stars the morphology of the object and the orientation of its major axis appear to be in a good agreement with the brightest inner part of the pulsar nebula torus region seen almost edge on in X-rays. Within the nebulosity we do not resolve any point-like optical object that could be identified with the pulsar and estimate its contribution to the observed nebulosity flux as <~20%. Extracting the X-ray spectrum from the physical region equivalent to the optical source position and extent and combining that with the measured optical fluxes, we compile a tentative multi-wavelength spectrum of the inner part of the nebula. Within uncertainties of the interstellar extinction towards G292.0+1.8 it is reminiscent of either the Crab or PSR B540-69 and J0205+6449 pulsar wind nebula spectra. The position, morphology, and spectral properties of the detected nebulosity suggest that it is the likely optical counterpart of the pulsar plus its wind nebula system in G292.0+1.8.
The recent detection of pulsations from the ultra luminous X-ray source (ULX) NuSTAR J095551+6940.8 in M82 by Bachetti et al. indicates that the object is an accreting neutron star in a high mass X-ray binary (HMXB) system. The super-Eddington luminosity of the object implies that the magnetic field is sufficiently strong to suppress the scattering cross-section unless its beam is viewed at a favourable angle. We show that the torque equilibrium condition for the pulsar indicates the dipole magnetic field of the neutron star is $6.7 \times 10^{13}$ G, two orders of magnitude higher than that estimated by Bachetti et al., and further point to the possibility that even stronger magnetic fields could well be in the higher multipoles. This supports the recent view that magnetars descent from HMXBs if the magnetic field decays an order of magnitude during the process of transition.
We study the effect of magnetic fields up to 15 T on the heavy fermion state of YbRh$_2$Si$_2$ via Hall effect and magnetoresistance measurements down to 50 mK. Our data show anomalies at three different characteristic fields. We compare our data to renormalized band structure calculations through which we identify Lifshitz transitions associated with the heavy fermion bands. The Hall measurements indicate that the de-renormalization of the quasiparticles, {\it i.e} the destruction of the local Kondo singlets, occurs smoothly while the Lifshitz transitions occur within rather confined regions of the magnetic field.
In this paper we study the clockwise simply connected rotating patches for Euler equations. By using the moving plane method we prove that Rankine vortices are the only solutions to this problem in the class of {\it slightly} convex domains. We discuss in the second part of the paper the case where the angular velocity $\Omega=\frac12$ and we show without any geometric condition that the set of the V-states is trivial and reduced to the Rankine vortices.
A double-rephasing photon-echo (DRPE) scheme inherently satisfies no-population inversion condition for quantum memory applications, while the resultant absorptive coherence prohibits echo radiation out of the medium. To solve the absorptive echo problem in the DRPE scheme, a controlled double-rephasing echo protocol has been presented and discussed for the collective atom phase control. In the DRPE scheme, however, a typical Gaussian light can cause imperfect rephasing processes resulting in a partial emission of photon echoes. Here, the rephasing process of individual ensemble atoms is thoroughly investigated to discuss the unpermitted echo observations in the DRPE scheme, where its maximum efficiency is as high as 26% in amplitude.
We present deep Giant Metrewave Radio Telescope (GMRT) radio observations at 240, 330 and 610 MHz of the complex radio source at the center of the NGC1407 galaxy group. Previous GMRT observations at 240 MHz revealed faint, diffuse emission enclosing the central twin-jet radio galaxy. This has been interpreted as an indication of two possible radio outbursts occurring at different times. Both the inner double and diffuse component are detected in the new GMRT images at high levels of significance. Combining the GMRT observations with archival Very Large Array data at 1.4 and 4.9 GHz, we derive the total spectrum of both components. The inner double has a spectral index \alpha=0.7, typical for active, extended radio galaxies, whereas the spectrum of the large-scale emission is very steep, with \alpha=1.8 between 240 MHz and 1.4 GHz. The radiative age of the large-scale component is very long, ~300 Myr, compared to ~30 Myr estimated for the central double, confirming that the diffuse component was generated during a former cycle of activity of the central galaxy. The current activity have so far released an energy which is nearly one order of magnitude lower than that associated with the former outburst. The group X-ray emission in the Chandra and XMM-Newton images and extended radio emission show a similar swept-back morphology. We speculate that the two structures are both affected by the motion of the group core, perhaps due to the core sloshing in response to a recent encounter with the nearby elliptical galaxy NGC1400.
This paper is concerned with the uniqueness of solutions to the following nonlocal semi-linear elliptic equation \begin{equation}\label{ellip}\tag{$\ast$} \Delta u-\beta u+\lambda\frac{e^u}{\int_{\Omega}e^u}=0~\mathrm{in}~\Omega, \end{equation} where $\Omega$ is a bounded domain in $\mathbb{R}^2$ and $\beta, \lambda$ are positive parameters. The above equation arises as the stationary problem of the well-known classical Keller-Segel model describing chemotaxis. For equation \eqref{ellip} with Neumann boundary condition, we establish an integral inequality and prove that the solution of (\ref{ellip}) is unique if $0<\lambda \leq 8\pi$ and $u$ satisfies some symmetric properties. While for \eqref{ellip} with Dirichlet boundary condition, the same uniqueness result is obtained without symmetric condition by a different approach inspired by some recent works [19,21]. As an application of the uniqueness results, we prove that the radially symmetric solution of the classical Keller-Segel system with subcritical mass subject to Neumann boundary conditions will converge to the unique constant equilibrium as time tends to infinity if $\Omega$ is a disc in two dimensions. As far as we know, this is the first result that asserts the exact asymptotic behavior of solutions to the classical Keller-Segel system with subcritical mass in two dimensions.
An essential aspect of cosmic voids is that these underdense regions provide complementary information about the properties of our Universe. Unlike dense regions, voids are avoided by matter and are less contaminated by baryonic processes. The first step to understanding the properties of cosmic voids is to correctly infer their mass profiles. In the literature, various techniques have been implemented. In this paper, we review them and implement a new technique that is based on Doppler lensing. We use a relativistic $N$-body code, \textsc{Gevolution}, to generate cosmological mass perturbations and implement a three-dimensional ray-tracing technique, which follows the evolution of a ray-bundles. We focus on the various properties of cosmic voids (e.g. void size function, 2-point correlation function, and the density profile of voids), and compare the results with their universal trends. We show that when weak-lensing is combined with the Doppler lensing we obtain even tighter constraints than weak-lensing alone. We also obtain better agreement between density profiles within central parts of voids inferred from lensing and density profiles inferred from halo tracers. The implication of the result relevant to the ongoing and prospective low-redshift spectroscopic surveys is briefly discussed.
The IceCube Neutrino Observatory at the South Pole detects Cherenkov light emitted by charged secondary particles created by primary neutrino interactions. Double pulse waveforms can arise from charged current interactions of astrophysical tau neutrinos with nucleons in the ice and the subsequent decay of tau leptons. The previous 8-year tau double pulse analysis found three tau neutrino candidate events. Among them, the most promising one observed in 2014 is located very near the dust layer in the middle of the detector. A posterior analysis on this event will be presented in this paper, using a new ice model treatment with continuously varying nuisance parameters to do the targeted Monte Carlo re-simulation for tau and other background neutrino ensembles. The impact of different ice models on the expected signal and background statistics will also be discussed.
We assume that the nuclear potential for distances larger than 2.5 fm is given just by the exchanges of one and two pions and, for the latter, we adopt a model based on chiral symmetry and subthreshold pion-nucleon amplitudes, which contains no free parameters. The predictions produced by this model for nucleon-nucleon observables are calculated and shown to agree well with both experiment and those due to phenomenological potentials.
We have calculated the $W$-loop contribution to the amplitude of the decay $H \to Z \gamma$ in the unitary gauge through the dispersion method and in the $R_\xi$ gauge using dimensional regularization (DimReg). We show that the results of the calculations with DimReg and the dispersion method, adopting the boundary condition at the limit $M_W \to 0$ defined by the Goldstone boson equivalence theorem (GBET), completely coincide. This implies that the dispersion method obeying the GBET is compatible with DimReg. The advantage of the applied dispersion method is that we work with finite quantities and no regularization is required.
We present an HI 21cm absorption study of a sample of 26 radio-loud active galactic nuclei (AGN) at $0.25 < z < 0.4$ carried out with the Karl G. Jansky Very Large Array. Our aim was to study the rate of incidence of HI in various classes of radio AGN, the morphology and kinematics of the HI, and the nature of the interaction between the HI and the radio source. Our sample consists of 14 extended sources and 12 compact sources in the radio-power range 10$^{25.7}$W/Hz$~-~10^{26.5}$W/Hz. We detect HI in 5 sources with a detection rate of $\sim$19%, similar to the detection rate at lower redshifts. The rest-frame UV luminosities of most of the sources in the sample, including all the detections, are below the proposed threshold above which the HI is supposed to have been ionised. The optical emission-line spectra show that despite their high radio powers, one-third of the sample, including two detections, are low-ionisation sources. The radio continuum emission from the HI detections is unresolved at kpc scales, but is extended on parsec scales. The detections have complex HI 21cm absorption profiles with FWZI ranging from 60 km/s to 700 km/s and exhibit remarkably high HI column densities in the range 10$^{21}$ cm$^{-2}$ to 10$^{22}$ cm$^{-2}$ for T$_{\rm spin}=$100 K and unit covering factor. A modelling of the HI 21cm absorption profiles suggests that in 2 sources the gas is disturbed, and in 3 cases, including the one with disturbed HI, the majority of the absorption is consistent with arising from an HI disc. Though we detect no fast HI outflows, the optical emission lines in the HI detections show the presence of highly disturbed gas in the nuclear region. Since some of our detections are low-ionisation AGN, this disturbance may be caused by the radio jets. Overall, our findings point towards a continuation of the low-$z$ trends in the incidence of HI in radio AGN up to $z \sim 0.4$.
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model is obtained as a local limit of the proposed theory.
We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate different families of power series which involve odd harmonic numbers and central binomial coefficients. Furthermore it is shown that based on these series a new type of nonlinear Euler sums that involve odd harmonic numbers can be calculated in terms of zeta functions.
Despite the rapidly growing number of stellar-mass binary black hole mergers discovered through gravitational waves, the origin of these binaries is still not known. In galactic centers, black holes can be brought to each others' proximity by dynamical processes, resulting in mergers. It is also possible that black holes formed in previous mergers encounter new black holes, resulting in so-called hierarchical mergers. Hierarchical events carry signatures such as higher-than usual black hole mass and spin. Here we show that the recently reported gravitational-wave candidate, GW170817A, could be the result of such a hierarchical merger. In particular, its chirp mass $\sim40$ M$_\odot$ and effective spin of $\chi_{\rm eff}\sim0.5$ are the typically expected values from hierarchical mergers within the disks of active galactic nuclei. We find that the reconstructed parameters of GW170817A strongly favor a hierarchical merger origin over having been produced by an isolated binary origin (with an Odds ratio of $>10^3$, after accounting for differences between the expected rates of hierarchical versus isolated mergers)
We study the properties of the light pseudoscalar mesons in a three flavor chiral quark model with nonlocal separable interactions. We concentrate on the evaluation of meson masses and decay constants, considering both the cases of Gaussian and Lorentzian nonlocal regulators. The results are found to be in quite good agreement with the empirical values, in particular in the case of the ratio f_K/f_pi and the anomalous decay pi^0 --> gamma gamma. In addition, the model leads to a reasonable description of the observed phenomenology in the eta-eta' sector, even though it implies the existence of two significantly different state mixing angles.
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a practical setting is that for any distribution with stability index not equal to 1 and with a polynomial spectral spherical density, the series representation converges absolutely with all terms being calculable in closed form. Asymptotic expansions consisting of spherical harmonics are also considered for probability density functions.
We prove necessary and sufficient criteria of invertibility for planar harmonic mappings which generalize a classical result of H. Kneser, also known as the Rad\'{o}-Kneser-Choquet theorem.
Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients lambda_n, indexed by the integers. We define similar coefficients attached to principal automorphic L-functions over GL(N). We relate these coefficients to values of Weil's quadratic functional for the associated automorphic representation, and deduce a Riemann hypothesis criterion in terms of positivity of the real parts of these coefficients. We determine asymptotics of the coefficients, both unconditionally and on the Riemann hypothesis, as n increases. We show the existence of an entire function of exponential type that interpolates the generalized Li coefficients at integer values.
We present a study of outflow, infall, and rotation in a ~10^5 Lsun (solar luminosity) star-forming region, IRAS 18360-0537, with Submillimeter Array (SMA) and IRAM 30m observations. The 1.3 mm continuum map shows a 0.5 pc dust ridge, of which the central compact part has a mass of ~80 Msun (solar mass) and harbors two condensations, MM1 and MM2. The CO (2--1) and SiO (5--4) maps reveal a biconical outflow centered at MM1, which is a hot molecular core (HMC) with a gas temperature of 320+/-50 K and a mass of ~13 Msun. The outflow has a gas mass of 54 Msun and a dynamical timescale of 8,000 yr. The kinematics of the HMC is probed by high-excitation CH3OH and CH3CN lines, which are detected at sub-arcsecond resolution and unveil a velocity gradient perpendicular to the outflow axis, suggesting a disk-like rotation of the HMC. An infalling envelope around the HMC is evidenced by CN lines exhibiting a profound inverse P-Cygni profile, and the estimated mass infall rate, 1.5x10^{-3} Msun/yr, is well comparable to that inferred from the mass outflow rate. A more detailed investigation of the kinematics of the dense gas around the HMC is obtained from the 13CO and C18O (2--1) lines; the position-velocity diagrams of the two lines are consistent with the model of a free-falling and Keplerian-like rotating envelope. The observations suggest that the protostar of a current mass ~10 Msun embedded within MM1 will develop into an O star via disk accretion and envelope infall.
We investigate a random matrix model [Phys. Rev. C {\bf 65} 024302 (2002] for the decay-out of a superdeformed band as a function of the parameters: $\Gamma^\downarrow/\Gamma_S$, $\Gamma_N/D$, $\Gamma_S/D$ and $\Delta/D$. Here $\Gamma^\downarrow$ is the spreading width for the mixing of an SD state $|0>$ with a normally deformed (ND) doorway state $|d>$, $\Gamma_S$ and $\Gamma_N$ are the electromagnetic widths of the the SD and ND states respectively, $D$ is the mean level spacing of the compound ND states and $\Delta$ is the energy difference between $|0>$ and $|d>$. The maximum possible effect of an order-chaos transition is inferred from analytical and numerical calculations of the decay intensity in the limiting cases for which the ND states obey Poisson and GOE statistics. Our results show that the sharp attenuation of the decay intensity cannot be explained solely by an order-chaos transition.
The effect of electron correlation on the photocurrent of self-assembled InAs/InGaAs quantum dot infrared photo-detector (QDIPs) is studied. It is found that Coulomb interaction and level mixing in the many-body open system lead to double peaks associated with the intra-band transitions involving two lowest levels of the quantum dot. Furthermore, the photocurrent is a nonlinear function of the steady-state carrier density and it displays a plateau due to Coulomb blockade.