ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the base phi representation any natural number is written uniquely as a sum of powers of the golden mean with coefficients 0 and 1, where it is required that the product of two consecutive digits is always 0. In this self-contained paper we give a new, and short proof of the recursive structure of the base phi representations of the natural numbers.
We report on an observation of the Galactic black hole candidate GRS 1739-278 during its 2014 outburst, obtained with NuSTAR. The source was captured at the peak of a rising "low/hard" state, at a flux of ~0.3 Crab. A broad, skewed iron line and disk reflection spectrum are revealed. Fits to the sensitive NuSTAR spectra with a number of relativistically blurred disk reflection models yield strong geometrical constraints on the disk and hard X-ray "corona". Two models that explicitly assume a "lamppost" corona find its base to have a vertical height above the black hole of h = 5 (+7, -2) GM/c^2 and h = 18 +/-4 GM/c^2 (90% confidence errors); models that do not assume a "lamppost" return emissivity profiles that are broadly consistent with coronae of this size. Given that X-ray microlensing studies of quasars and reverberation lags in Seyferts find similarly compact coronae, observations may now signal that compact coronae are fundamental across the black hole mass scale. All of the models fit to GRS 1739-278 find that the accretion disk extends very close to the black hole - the least stringent constraint is r = 5 (+3,-4) GM/c^2. Only two of the models deliver meaningful spin constraints, but a = 0.8 +/-0.2 is consistent with all of the fits. Overall, the data provide especially compelling evidence of an association between compact hard X-ray coronae and the base of relativistic radio jets in black holes.
We measure FIR emission from tails of stripped dust following the ionised and atomic gas components in galaxies undergoing ram pressure stripping. We study the dust-to-gas relative distribution and mass ratio in the stripped interstellar medium and relate them to those of the intra-cluster medium, thus linking the cluster-ICM-galaxy evolution at small-scales. The galaxy sample consists of three Scd Virgo galaxies with stellar masses in the range $10^9\lesssim \mathrm{M_{*}} \lesssim 10^{10}\, \mathrm{M_{\odot}}$, and within 1 Mpc from the cluster centre, namely NGC 4330, NGC 4522, and NGC 4654. Through the analysis of VESTIGE H$\alpha$, $Herschel$ SPIRE far-infrared, and VIVA HI data, we trace the spatial distribution of the tails and infer the dust and gas masses from the measured far-infrared 250 $\mu$m and HI flux densities. Dust-to-gas mass ratios (DGRs) in the tails are analysed as a function of the galaxy mass, metallicity, and dust temperature. Along the stripped component, the dust distribution closely follows the HI and H$\alpha$ emitting gas, all extending beyond the optical disc. In these regions, the DGRs are $2.0\pm0.6\times10^{-3}$, $0.7\pm0.1\times10^{-3}$, and $0.4\pm0.03\times10^{-3}$, for NGC 4330, NGC 4522, and NGC 4654, respectively, i.e. up to a factor of 15 less than the values measured in the main body of nearby galaxies. We also find a negative trend in the DGR as a function of the metallicity that can be explained in terms of a dust component more centrally concentrated in more metal-rich systems. Together with the finding that the stripped dust is cold, $T_{d} \lesssim 25\, K$, our results support an outside-in stripping scenario of the galaxy interstellar medium. This study shows that ram pressure stripping is a key mechanism in the building up of the Virgo intra-cluster component injecting dust grains into the ICM, thus contributing to its metal enrichment.
Characteristic dimensions of carbon nanoscrolls - "buckyrolls" - are calculated by analyzing the competition between elastic, van der Waals, and electrostatic energies for representative models of suspended and substrate-deposited graphene samples. The results are consistent with both atomistic simulations and experimental observations of scrolled graphene edges. Electrostatic control of the wrapping is shown to be practically feasible and its possible device applications are indicated.
We study the acceleration of CR protons and nuclei at GRB internal shocks. Physical quantities and their time evolution are estimated using the internal shock modeling implemented by Daigne & Mochkovitch 1998. We consider different hypotheses about the way the energy dissipated at internal shocks is shared between accelerated CR, e- and B field. We model CR acceleration at mildly relativistic shocks, including all the significant energy loss processes. We calculate CR and neutrino release from single GRBs, assuming that nuclei heavier than protons are present in the relativistic wind. Protons can only reach maximum energies of ~ 10^19.5 eV, while intermediate and heavy nuclei are able to reach values of ~ 10^20 eV and above. The spectra of nuclei escaping from the acceleration site are found to be very hard while the combined spectrum of protons and neutrons is much softer. We calculate the diffuse UHECR flux expected on Earth using the GRB luminosity function from Wanderman & Piran 2010. Only the models assuming that the prompt emission represent a very small fraction of the energy dissipated at internal shocks, and that most of this dissipated energy is communicated to accelerated CR, are able to reproduce the magnitude of the UHECR flux observed. For these models, the observed shape of the UHECR spectrum can be well reproduced and the evolution of the composition is compatible with the trend suggested by Auger. We discuss implications of the softer proton component for the GCR to EGCR transition in the light of the recent composition analyses (KASCADE-Grande experiment). The associated secondary particle diffuse fluxes do not upset any current observational limit. Diffuse neutrino flux from GRB sources should however be detected with the lifetime of neutrino observatories.
Due to the numerical complexities of studying evolution in an anisotropic quantum spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic models has remained largely unexplored. In particular, robustness of bounce and the validity of effective dynamics have so far not been established. Our analysis fills these gaps for the case of vacuum Bianchi-I spacetime. To efficiently solve the quantum Hamiltonian constraint we perform an implementation of the Cactus framework which is conventionally used for applications in numerical relativity. Using high performance computing, numerical simulations for a large number of initial states with a wide variety of fluctuations are performed. Big bang singularity is found to be replaced by anisotropic bounces for all the cases. We find that for initial states which are sharply peaked at the late times in the classical regime and bounce at a mean volume much greater than the Planck volume, effective dynamics is an excellent approximation to the underlying quantum dynamics. Departures of the effective dynamics from the quantum evolution appear for the states probing deep Planck volumes. A detailed analysis of the behavior of this departure reveals a non-monotonic and subtle dependence on fluctuations of the initial states. We find that effective dynamics in almost all of the cases underestimates the volume and hence overestimates the curvature at the bounce, a result in synergy with earlier findings in isotropic case. The expansion and shear scalars are found to be bounded throughout the evolution.
Infrared pumping and its effect on the excitation of HCN molecules can be important when using rotational lines of HCN to probe dense molecular gas in galaxy nuclei. We report the first extragalactic detection of (sub)millimeter rotational lines of vibrationally excited HCN, in the dust-enshrouded nucleus of the luminous infrared galaxy NGC 4418. We estimate the excitation temperature of T_vib ~ 230 K between the vibrational ground and excited (v_2=1) states. This excitation is most likely due to infrared radiation. At this high vibrational temperature the path through the v_2=1 state must have a strong impact on the rotational excitation in the vibrational ground level, although it may not be dominant for all rotational levels. Our observations also revealed nearly confusion limited lines of CO, HCN, HCO+, H13CN, HC15N, CS, N2H+, and HC3N at lambda ~ 1 mm. Their relative intensities may also be affected by the infrared pumping.
The electronic and optical properties of self-assembled InN/GaN quantum dots (QDs) are investigated by means of a tight-binding model combined with configuration interaction calculations. Tight-binding single particle wave functions are used as a basis for computing Coulomb and dipole matrix elements. Within this framework, we analyze multi-exciton emission spectra for two different sizes of a lens-shaped InN/GaN QD with wurtzite crystal structure. The impact of the symmetry of the involved electron and hole one-particle states on the optical spectra is discussed in detail. Furthermore we show how the characteristic features of the spectra can be interpreted using a simplified Hamiltonian which provides analytical results for the interacting multi-exciton complexes. We predict a vanishing exciton and biexciton ground state emission for small lens-shaped InN/GaN QDs. For larger systems we report a bright ground state emission but with drastically reduced oscillator strengths caused by the quantum confined Stark effect.
We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\Gamma$. Under favorable conditions, the cohomology is freely generated in a single degree over this graded Hecke algebra.   From this construction we extract an action of certain $p$-adic Galois cohomology groups on $H^*(\Gamma, \mathbb{Q}_p)$, and formulate the central conjecture: the motivic $\mathbb{Q}$-lattice inside these Galois cohomology groups preserves $H^*(\Gamma,\mathbb{Q})$.
The light-cone Fock-state representation of QCD encodes the properties of a hadrons in terms of frame-independent wavefunctions, providing a systematic framework for evaluating structure functions, exclusive hadronic matrix elements, including time-like heavy hadron decay amplitudes, form factors, and deeply virtual Compton scattering. A new type of jet production reaction, "self-resolving diffractive interactions" can provide direct information on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom. The relation of the intrinsic sea to the light-cone wavefunctions is discussed. The decomposition of light-cone spin is illustrated for the quantum fluctuations of an electron.
We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous variant, we prove that the process can reach infinity in finite time i.e., explode. In particular, we prove that explosions occur almost surely on regular trees as well as oriented and unoriented two-dimensional integer lattices with sufficiently many particles per site. The oriented case requires an additional hypothesis about the existence and value of a certain critical exponent. We further prove that the process with one particle per site expands at a superlinear rate on integer lattices of any dimension. Some arguments use connections to critical first passage percolation, including a new result about the existence of an infinite path with finite passage time on the oriented two-dimensional lattice.
A time-dependent determining wavenumber was introduced in [5] to estimate the number of determining modes for the surface quasi-geostrophic (SQG) equation. In this paper we continue this investigation focusing on the subcritical case and study trajectories inside an absorbing set bounded in $L^\infty$. Utilizing this bound we find a time-independent determining wavenumber that improves the estimate obtained in [5]. This classical approach is more direct, but it is contingent on the existence of the $L^\infty$ absorbing set.
The re-ranking approach leverages high-confidence retrieved samples to refine retrieval results, which have been widely adopted as a post-processing tool for image retrieval tasks. However, we notice one main flaw of re-ranking, i.e., high computational complexity, which leads to an unaffordable time cost for real-world applications. In this paper, we revisit re-ranking and demonstrate that re-ranking can be reformulated as a high-parallelism Graph Neural Network (GNN) function. In particular, we divide the conventional re-ranking process into two phases, i.e., retrieving high-quality gallery samples and updating features. We argue that the first phase equals building the k-nearest neighbor graph, while the second phase can be viewed as spreading the message within the graph. In practice, GNN only needs to concern vertices with the connected edges. Since the graph is sparse, we can efficiently update the vertex features. On the Market-1501 dataset, we accelerate the re-ranking processing from 89.2s to 9.4ms with one K40m GPU, facilitating the real-time post-processing. Similarly, we observe that our method achieves comparable or even better retrieval results on the other four image retrieval benchmarks, i.e., VeRi-776, Oxford-5k, Paris-6k and University-1652, with limited time cost. Our code is publicly available.
We report on a theoretical study of the influence of electron-electron interactions on ARPES spectra in graphene that is based on the random-phase-approximation and on graphene's massless Dirac equation continuum model. We find that level repulsion between quasiparticle and plasmaron resonances gives rise to a gap-like feature at small k. ARPES spectra are sensitive to the electron-electron interaction coupling strength $\alpha_{\rm gr}$ and might enable an experimental determination of this material parameter.
We have investigated the influence of shot noise on the IV-curves of a single mesoscopic Josephson junction. We observe a linear enhancement of zero-bias conductance of the Josephson junction with increasing shot noise power. Moreover, the IV-curves become increasingly asymmetric. Our analysis on the asymmetry shows that the Coulomb blockade of Cooper pairs is strongly influenced by the non-Gaussian character of the shot noise.
We report on the first measurements of the isotopic ratio 14N/15N in N2H+ toward a statistically significant sample of high-mass star forming cores. The sources belong to the three main evolutionary categories of the high-mass star formation process: high-mass starless cores, high-mass protostellar objects, and ultracompact HII regions. Simultaneous measurements of 14N/15N in CN have been made. The 14N/15N ratios derived from N2H+ show a large spread (from ~180 up to ~1300), while those derived from CN are in between the value measured in the terrestrial atmosphere (~270) and that of the proto-Solar nebula (~440) for the large majority of the sources within the errors. However, this different spread might be due to the fact that the sources detected in the N2H+ isotopologues are more than those detected in the CN ones. The 14N/15N ratio does not change significantly with the source evolutionary stage, which indicates that time seems to be irrelevant for the fractionation of nitrogen. We also find a possible anticorrelation between the 14N/15N (as derived from N2H+) and the H/D isotopic ratios. This suggests that 15N enrichment could not be linked to the parameters that cause D enrichment, in agreement with the prediction by recent chemical models. These models, however, are not able to reproduce the observed large spread in 14N/15N, pointing out that some important routes of nitrogen fractionation could be still missing in the models.
The basic distinction between already known algorithmic characterizations of matroids and antimatroids is in the fact that for antimatroids the ordering of elements is of great importance.   While antimatroids can also be characterized as set systems, the question whether there is an algorithmic description of antimatroids in terms of sets and set functions was open for some period of time.   This article provides a selective look at classical material on algorithmic characterization of antimatroids, i.e., the ordered version, and a new unordered version. Moreover we empathize formally the correspondence between these two versions.
We present a new model for the redshift-space power spectrum of galaxies and demonstrate its accuracy in modeling the monopole, quadrupole, and hexadecapole of the galaxy density field down to scales of $k = 0.4 \ h\mathrm{Mpc}^{-1}$. The model describes the clustering of galaxies in the context of a halo model and the clustering of the underlying halos in redshift space using a combination of Eulerian perturbation theory and $N$-body simulations. The modeling of redshift-space distortions is done using the so-called distribution function approach. The final model has 13 free parameters, and each parameter is physically motivated rather than a nuisance parameter, which allows the use of well-motivated priors. We account for the Finger-of-God effect from centrals and both isolated and non-isolated satellites rather than using a single velocity dispersion to describe the combined effect. We test and validate the accuracy of the model on several sets of high-fidelity $N$-body simulations, as well as realistic mock catalogs designed to simulate the BOSS DR12 CMASS data set. The suite of simulations covers a range of cosmologies and galaxy bias models, providing a rigorous test of the level of theoretical systematics present in the model. The level of bias in the recovered values of $f \sigma_8$ is found to be small. When including scales to $k = 0.4 \ h\mathrm{Mpc}^{-1}$, we find 15-30\% gains in the statistical precision of $f \sigma_8$ relative to $k = 0.2 \ h\mathrm{Mpc}^{-1}$ and a roughly 10-15\% improvement for the perpendicular Alcock-Paczynski parameter $\alpha_\perp$. Using the BOSS DR12 CMASS mocks as a benchmark for comparison, we estimate an uncertainty on $f \sigma_8$ that is $\sim$10-20\% larger than other similar Fourier-space RSD models in the literature that use $k \leq 0.2 \ h\mathrm{Mpc}^{-1}$, suggesting that these models likely have a too-limited parametrization.
Stable massive neutral particles emitted by astrophysical sources undergo deflection under the gravitational potential of our own galaxy. The deflection angle depends on the particle velocity and therefore non-relativistic particles will be deflected more than relativistic ones. If these particles can be detected through neutrino telescopes, cosmic ray detectors or directional dark matter detectors, their arrival directions would appear aligned on the sky along the source-lens direction. On top of this deflection, the arrival direction of non-relativistic particles is displaced with respect to the relativistic counterpart also due to the relative motion of the source with respect to the observer; this induces an alignment of detections along the sky projection of the source trajectory. The final alignment will be given by a combination of the directions induced by lensing and source proper motion. We derive the deflection-velocity relation for the Milky Way halo and suggest that searching for alignments on detection maps of particle telescopes could be a way to find new particles or new astrophysical phenomena.
We study subexponential tail asymptotics for the distribution of the maximum $M_t:=\sup_{u\in[0,t]}X_u$ of a process $X_t$ with negative drift for the entire range of $t>0$. We consider compound renewal processes with linear drift and L\'evy processes. For both we also formulate and prove the principle of a single big jump for their maxima. The class of compound renewal processes particularly includes Cram\'er-Lundberg risk process.
Let $\mathbb{Z}^{+}$ be the set of positive integers. Let $C_{k}$ denote all subsets of $\mathbb{Z}^{+}$ such that neither of them contains $k + 1$ pairwise coprime integers and $C_k(n)=C_k\cap \{1,2,\ldots,n\}$. Let $f(n, k) = \text{max}_{A \in C_{k}(n)}|A|$, where $|A|$ denotes the number of elements of the set $A$. Let $E_k(n)$ be the set of positive integers not exceeding $n$ which are divisible by at least one of the primes $p_{1}, \dots{}, p_{k}$, where $p_{i}$ denote the $i$th prime number. In 1962, Erd\H{o}s conjectured that $f(n, k) = |E(n,k)|$ for every $n \ge p_{k}$. Recently Chen and Zhou proved some results about this conjecture. In this paper we solve an open problem of Chen and Zhou and prove several related results about the conjecture.
The effect of currents of mass on bending of light rays is considered in the weak field regime. Following Fermat's principle and the standard theory of gravitational lensing, we derive the gravitomagnetic correction to time delay function and deflection angle caused by a geometrically-thin lens. The cases of both rotating and shifting deflectors are discussed.
In this article, we first briefly introduce the history of the Weil-\'etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the Weil-etale cohomology to $S$-integers and compute the cohomology for constant sheaves $\mathbb{Z}$ or $\mathbb{R}$. We also define a Weil-\'etale cohomology with compact support $H_c(Y_W, -)$ for $Y=Spec \mathcal{O}_{F,S}$ where $F$ is a number field, and computed them. We verify that these cohomology groups satisfy the axioms state by Lichtenbaum. As an application, we derive a canonical representation of Tate sequence from $RGamma_c(Y_W,\mathbb{Z})$. Motivated by this result, in the final part, we define an \'etale complex $RGm$, such that the complexes $\mathbb{Z}$-dual of the complex $\RG(U_{et},R\Gm),\,\mathbb{Z})[2]$ is canonically quasi-isomorphic to $\tau^{\leq 3}\RG_c(U_W,\mathbb{Z})$ for arbitrary \'etale $U$ over $Spec \mathcal{O}_{F}$. This quasi-isomorphism provides a possible approach to define the Weil-etale cohomology for higher dimensional arithmetic schemes, as the Weil groups are not involved in the definition of $R\Gm$.
Values of quaternionic modular forms are related to twisted central $L$-values via periods and a theorem of Waldspurger. In particular, certain twisted $L$-values must be non-vanishing for forms with no zeroes. Here we study, theoretically and computationally, zeroes of definite quaternionic modular forms of trivial weight. Local sign conditions force certain forms to have trivial zeroes, but we conjecture that almost all forms have no nontrivial zeroes. In particular, almost all forms with appropriate local signs should have no zeroes. We show these conjectures follow from a conjecture on the average number of Galois orbits, and give applications to (non)vanishing of $L$-values.
It is well known that the rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force.   We examine numerically such shock waves in 1D and 2D accretion flows, taking account of cooling and heating of the gas and radiation transport.   The numerical results show that the shock location shifts outward compared with that in the adiabatic solutions and that the more rarefied ambient density leads to the more outward shock location.   In the 2D-flow, we find an intermediate frequency QPO behavior of the shock location as is observed in the black hole candidate   GRS 1915+105.
Entropy production due to shear viscosity during the continuous freeze-out of a longitudinally expanding dissipative fluid is addressed. Assuming the validity of the fluid dynamical description during the continuous removal of interacting matter we estimated a small entropy production as function of the freeze-out duration and the ratio of dissipative to non-dissipative quantities in case of a relativistic massless pion fluid.