ShantanuT01/DACTYL-Pretraining huggingface dataset:
To approximate the trajectories of a stochastic process by the solution of some differential equation is widely used in the fields of probability, computer science and combinatorics. In this paper, the convergence of coupon collecting processes is studied via the differential equation techniques originally proposed in Wormald(1995) and modified in Warnke(2019). In other words, we give a novel approach to analysis the classical coupon collector's problem and keep track of all coupons in the process of collecting.
The strong lensing modelling of gravitational ``rings'' formed around massive galaxies is sensitive to the amplitude of the external shear and convergence produced by nearby mass condensations. In current wide field surveys, it is now possible to find out a large number of rings, typically 10 gravitational rings per square degree. We propose here, to systematically study gravitational rings around galaxy clusters to probe the cluster mass profile beyond the cluster strong lensing regions. For cluster of galaxies with multiple arc systems, we show that rings found at various distances from the cluster centre can improve the modelling by constraining the slope of the cluster mass profile. We outline the principle of the method with simple numerical simulations and we apply it to 3 rings discovered recently in Abell~1689. In particular, the lens modelling of the 3 rings confirms that the cluster is bimodal, and favours a slope of the mass profile steeper than isothermal at a cluster radius $\sim 300 \kpc$. These results are compared with previous lens modelling of Abell~1689 including weak lensing analysis. Because of the difficulty arising from the complex mass distribution in Abell~1689, we argue that the ring method will be better implemented on simpler and relaxed clusters.
We suggest an approach for characterizing the zero-field spin splitting of high mobility two-dimensional electron systems, when beats are not readily observable in the Shubnikov-de Haas effect. The zero-field spin splitting and the effective magnetic field seen in the reference frame of the electron is evaluated from a quantitative study of beats observed in radiation-induced magnetoresistance oscillations.
We review several aspects of clusters of galaxies and their application to cosmology. We present first results of numerical simulations of the dynamics of the intra-cluster gas and of different interaction processes between cluster galaxies and the intra-cluster gas. In particular metallicity maps are very useful to determine the importance of the different interaction processes. Also mass determination methods and possible sources for uncertainties in the measurements are shown.
The Yale/SMARTS optical-near-IR monitoring program has followed the variations in emission of the Fermi-LAT monitored blazars in the southern sky with closely spaced observations since 2008. We report the discovery of an optical-near-IR (OIR) outburst with no accompanying gamma-rays in the blazar PKS 0208-512, one of the targets of this program. While the source undergoes three outbursts of 1 mag or more at OIR wavelengths lasting for longer than 3 months during 2008-2011, only interval 1 and 3 have corresponding bright phases in GeV energies lasting longer than 1 month. The OIR outburst during interval 2 is comparable in brightness and temporal extent to the OIR flares during intervals 1 and 3 which do have gamma-ray counterparts. Gamma-ray and OIR variability are very well-correlated in most cases in the Fermi blazars and the lack of correlation in this case is anomalous. By analyzing the gamma-ray, OIR, and supporting multi-wavelength variability data in details, we speculate that the location of the outburst in the jet during interval 2 was closer to the black hole where the jet is more compact and the magnetic field strength is higher, and the bulk Lorentz factor of the material in the jet is smaller. These result in a much lower Compton dominance and no observable gamma-ray outburst during interval 2.
Research into developing dual modality probes enabled for magnetic resonance imaging (MRI) and positron emission tomography (PET) has been on the rise recently due to the potential to combine the high resolution of MRI and the high sensitivity of PET. Current synthesis techniques for developing multimodal probes is largely hindered in part by prolonged reaction times during radioisotope incorporation - leading to a weakening of the radioactivity. Along with a time-efficient synthesis, the resulting products must fit within a critical size range (between 20-100nm) to increase blood retention time. In this work, we describe a novel, rapid, microwave-based synthesis technique to grow dextran-coated iron oxide nanoparticles doped with copper (DIO/Cu). Traditional methods for coprecipitation of dextran-coated iron oxide nanoparticles require refluxing for 2 hours and result in approximately 50 nm diameter particles. We demonstrate that microwave synthesis can produce 50 nm nanoparticles with 5 minutes of heating. We discuss the various parameters used in the microwave synthesis protocol to vary the size distribution of DIO/Cu, and demonstrate the successful incorporation of 64Cu into these particles with the aim of future use for dual-mode MR/PET imaging.
We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and non-generic singularities that break asymptotic silence. The emphasis in this paper is on the latter class which have not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.
An explicit hybrid estimate for $L(1/2+it,\chi)$ is derived, where $\chi$ is a Dirichlet character modulo $q$. The estimate applies when $t$ is bounded away from zero, and is most effective when $q$ is powerfull, yielding an explicit Weyl bound in this case. The estimate takes a particularly simple form if $q$ is a sixth power. Several hybrid lemmas of van der Corput--Weyl type are presented.
To date, most of the luminous quasars known at $z\sim6$ have been found to be in maximal accretion with the Eddington ratios, $\lambda_{\rm{Edd}}\sim1$, suggesting enhanced nuclear activities in the early universe. However, this may not be the whole picture of supermassive black hole (SMBH) growth since previous studies have not reached on faint quasars that are more likely to harbor SMBHs with low $\lambda_{\rm{Edd}}$. To gain a better understanding on the accretion activities in quasars in the early universe, we obtained a deep near-infrared (NIR) spectrum of a quasar, IMS J220417.92+011144.8 (hereafter IMS J2204+0112), one of the faintest quasars that have been identified at $z\sim6$. From the redshifted C IV $\lambda 1549$ emission line in the NIR spectrum, we find that IMS J2204+0112 harbors a SMBH with about a billion solar mass and $\lambda_{\rm{Edd}} \sim 0.1$, but with a large uncertainty in both quantities (0.41 dex). IMS J2204+0112 has one of the lowest Eddington ratios among quasars at $z\sim6$, but a common value among quasars at $z\sim2$. Its low $\lambda_{\rm{Edd}}$ can be explained with two scenarios; the SMBH growth from a stellar mass black hole through short-duration super-Eddington accretion events or from a massive black hole seed ($\sim10^{5}\,M_{\odot}$) with Eddington-limited accretion. NIR spectra of more faint quasars are needed to better understand the accretion activities of SMBHs at $z \sim 6$.
The discovery of GW170817 with gravitational waves (GWs) and electromagnetic (EM) radiation is prompting new questions in strong-gravity astrophysics. Importantly, it remains unknown whether the progenitor of the merger comprised two neutron stars (NSs), or a NS and a black hole (BH). Using new numerical-relativity simulations and incorporating modeling uncertainties we produce novel GW and EM observables for NS-BH mergers with similar masses. A joint analysis of GW and EM measurements reveals that if GW170817 is a NS-BH merger, <40% of the binary parameters consistent with the GW data are compatible with EM observations.
In this paper we show how using complex valued edge weights in a graph can completely suppress the flow of probability amplitude in a continuous time quantum walk to specific vertices of the graph when the edge weights, graph topology and initial state of the quantum walk satisfy certain conditions. The conditions presented in this paper are derived from the so-called chiral quantum walk, a variant of the continuous time quantum walk which incorporates directional bias with respect to site transfer probabilities between vertices of a graph by using complex edge weights. We examine the necessity to break the time reversal symmetry in order to achieve zero transfer in continuous time quantum walks. We also consider the effect of decoherence on zero transfer and suggest that this phenomena may be used to detect decoherence in the system.
A future measurement of cosmic microwave \mu-distortions by an experiment with the specifications of PIXIE will provide an equivalent 3-sigma detection of the running of running of the spectral index of scalar perturbations, \beta = d\alpha/dln(k), if \mu > 7.75 E-8, covering much of the PIXIE sensitivity range. This corresponds to a resolution limit of \beta > 0.015 which is relatively large given any presumption of slow roll, a result of the current tight constraints on \alpha < 0 on CMB scales. We show that a detection of \beta at this level is in conflict with slow roll conditions if the primordial signal can be distinguished from any post-inflationary contamination.
The Fermi Large Area Telescope (Fermi-LAT) Collaboration reported the Second Gamma-ray Burst Catalog (2FLGC), which comprises a subset of 29 bursts with photon energies above 10 GeV. Although the standard synchrotron forward-shock model has successfully explained the Gamma-ray burst (GRB) afterglow observations, energetic photons higher than 10 GeV from these transient events can hardly be described in this scenario. We present the closure relations (CRs) of synchrotron self-Compton (SSC) afterglow model in the adiabatic and radiative scenario and when the central engine injects continuous energy into the blastwave to study the evolution of the spectral and temporal indexes of those bursts reported in 2FLGC. We consider the SSC afterglow model evolving in stellar-wind and interstellar medium, and the CRs as a function of the radiative parameter, the energy injection index, and the electron spectral index for $1<p<2$ and $ 2\leq p$. We select all GRBs that have been modeled with both a simple or a broken power law in the 2FLGC. We found that the CRs of the SSC model can satisfy a significant fraction of burst that cannot be interpreted in the synchrotron scenario, even though those that require an intermediate density profile (e.g., GRB 130427A) or an atypical fraction of total energy given to amplify the magnetic field ($\varepsilon_B$). The value of this parameter in the SSC model ranges ($\varepsilon_B\approx 10^{-5} - 10^{-4}$) when the cooling spectral break corresponds to the Fermi-LAT band for typical values of GRB afterglow. The analysis shows that ISM is preferred for the scenario without energy injection and the stellar wind medium for an energy injection scenario.
We discuss form factors and coupling constants for the $\gamma^* \pi^0 \gamma$, $\rho\pi\pi$ and $\gamma \pi \rho$ interactions generated by a model field theory that produces finite size $\bar{q}q$ meson modes. The approach implements dressing of the vertices and propagators consistent with dynamical chiral symmetry breaking, gauge invariance, quark confinement and perturbative QCD.
We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound. As an application we show that the Coleman-Oort conjecture holds for Shimura curves associated to partial corestriction upon a suitable choice of parameters, which generalizes a construction due to Mumford.
The class of generalized Petersen graphs was introduced by Coxeter in the 1950s. Frucht, Graver and Watkins determined the automorphism groups of generalized Petersen graphs in 1971, and much later, Nedela and \v{S}koviera and (independently) Lovre\v{c}i\v{c}-Sara\v{z}in characterised those which are Cayley graphs. In this paper we extend the class of generalized Petersen graphs to a class of GI-graphs.   For any positive integer n and any sequence j_0,j_1,....,j_{t-1} of integers mod n, the GI-graph GI(n;j_0,j_1,....,j_{t-1}) is a (t+1)-valent graph on the vertex set Z_t x Z_n, with edges of two kinds:   - an edge from (s,v) to (s',v), for all distinct s,s' in Z_t and all v in Z_n,   - edges from (s,v) to (s,v+j_s) and (s,v-j_s), for all s in Z_t and v in Z_n.   By classifying different kinds of automorphisms, we describe the automorphism group of each GI-graph, and determine which GI-graphs are vertex-transitive and which are Cayley graphs. A GI-graph can be edge-transitive only when t < 4 or equivalently, for valence at most 4. We present a unit-distance drawing of a remarkable GI(7;1,2,3).
An accurate and consistent theory of phonons in metals requires that all long-range Coulomb interactions between charged particles (electrons and ions) be treated on equal footing. So far, all attempts to deal with this non-perturbative system were relying on uncontrolled approximations in the absence of small parameters. In this work, we develop the Diagrammatic Monte Carlo approach for a two-component Coulomb system that obtains the solution to this fundamental problem in an approximation free way by computing vertex corrections from higher-order skeleton graphs. The feasibility of the method is demonstrated by calculating the spectrum of longitudinal acoustic phonons in a simple cubic lattice, determining their sound velocity, and obtaining the phonon spectral densities by analytic continuation of the Matsubara Green's functions. Final results are checked against the lowest-order fully self-consistent GW-approximation in both adiabatic and non-adiabatic regimes.
We argue that measurements of identified-particle elliptic flow in a wide energy range could shed light on the possible phase change in high-energy heavy ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC). When the hadronization process is dominated by quark coalescence, the number-of-constituent-quark (NCQ) scaling for the identified-particle elliptic flow can serve as a probe for studying the strong interacting partonic matter. In the upcoming RHIC low-energy runs, the NCQ scaling behavior may be broken because of the change of the effective degrees of freedom of the hot dense matter, which corresponds to the transition from the dominant partonic phase to the dominant hadronic phase. A multiphase transport model is used to present the dependence of NCQ scaling behavior on the different hadronization mechanisms.
The XMM-RM project was designed to provide X-ray coverage of the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) field. 41 XMM-Newton exposures, placed surrounding the Chandra AEGIS field, were taken, covering an area of 6.13 deg^2 and reaching a nominal exposure depth of ~15 ks. We present an X-ray catalog of 3553 sources detected in these data, using a PSF-fitting algorithm and a sample selection threshold that produces a ~5% fraction of spurious sources. In addition to the PSF-fitting likelihood, we calculate a second source reliability measure based on Poisson theory using source and background counts within an aperture. Using the Poissonian likelihood, we select a sub-sample with a high purity and find that it has similar number count profiles to previous X-ray surveys. The Bayesian method "NWAY" was employed to identify counterparts of the X-ray sources from the optical Legacy and the IR unWISE catalogs, using a 2-dimensional unWISE magnitude-color prior created from optical/IR counterparts of Chandra X-ray sources. A significant number of the optical/IR counterparts correspond to sources with low detection likelihoods, proving the value of retaining the low-likelihood detections in the catalog. 932 of the XMM-RM sources are covered by SDSS spectroscopic observations. 89% of them are classified as AGN, and 71% of these AGN are in the SDSS-RM quasar catalog. Among the SDSS-RM quasars, 80% are detectable at the depth of the XMM observations.
In the framework of BCS model, we have applied the isothermal probability distribution to take into account the statistical fluctuations in calculation of thermodynamical properties of nuclei. The energy and the heat capacity are calculated in $^{94}Mo$ nucleus using the mean gap parameter. The results are compared with the values obtained based on the most probable values, experimental data as well as some other theoretical models. We have shown that heat capacity versus temperature behaves smoothly instead of singular behaviour predicted by the standard BCS model. Also a smooth peak in heat capacity is observed which is a signature of transition from normal to super fluid phase.
We investigate the problem of whether one can anticipate any features of the graviton without a detailed knowledge of a full quantum gravity. Assuming that in linearized gravity the graviton is in a sense similar to the photon, we derive a curious large number coincidence between the number of gravitons emitted by a solar planet during its orbital period and the number of its nucleons. In Einstein's GR the analogy between the graviton and the photon is ill founded. A generic relationship between quanta of a quantum field and plane waves of the corresponding classical field is broken in the case of GR. The graviton cannot be classically approximated by a generic pp wave nor by the exact plane wave. Most important, the ADM energy is a zero frequency characteristic of any asymptotically flat spacetime and this means that any general relationship between energy and frequency is a priori impossible. In particular the formula $E=\hbar \omega$ does not hold. The graviton must have features different from those of the photon and these cannot be predicted from classical general relativity.
We call the scheme parameterizing homogeneous ideals with fixed initial ideal the Gr\"obner scheme. We introduce a Bia{\l}ynicki-Birula decomposition of the Hilbert scheme $\mathrm{Hilb}^{P}_n$ for any Hilbert polynomial $P$ such that the cells are the Gr\"obner schemes in set-theoretically. Then we obtain a computable homology formula for smooth Hilbert schemes. As a corollary of our argument, we show that the Gr\"obner scheme for a monomial ideal defining a smooth point in the Hilbert scheme is smooth.
The optimisation of two-dimensional (2D) lattice ion trap geometries for trapped ion quantum simulation is investigated. The geometry is optimised for the highest ratio of ion-ion interaction rate to decoherence rate. To calculate the electric field of such array geometries a numerical simulation based on a "Biot-Savart like law" method is used. In this article we will focus on square, hexagonal and centre rectangular lattices for optimisation. A method for maximising the homogeneity of trapping site properties over an array is presented for arrays of a range of sizes. We show how both the polygon radii and separations scale to optimise the ratio between the interaction and decoherence rate. The optimal polygon radius and separation for a 2D lattice is found to be a function of the ratio between rf voltage and drive frequency applied to the array. We then provide a case study for 171Yb+ ions to show how a two-dimensional quantum simulator array could be designed.
The International Gamma-Ray Astrophysics Laboratory, i.e. the INTEGRAL satellite of ESA, in orbit since about 3 years, performs gamma-ray observations of the sky in the 15 keV to 8 MeV energy range. Thanks to its imager IBIS, and in particular the ISGRI detection plane based on 16384 CdTe pixels, it achieves an excellent angular resolution (12 arcmin) for point source studies with good continuum spectrum sensitivity. Thanks to its spectrometer SPI, based on 19 germanium detectors maintained at 85 K by a cryogenic system, located inside an active BGO veto shield, it achieves excellent spectral resolution of about 2 keV for 1 MeV photons, which permits astrophysical gamma-ray line studies with good narrow-line sensitivity. In this paper we review some goals of gamma-ray astronomy from space and present the INTEGRAL satellite, in particular its instruments ISGRI and SPI. Ground and in-flight calibration results from SPI are presented, before presenting some selected astrophysical results from INTEGRAL. In particular results on point source searches are presented, followed by results on nuclear astrophysics, exemplified by the study of the 1809 keV gamma-ray line from radioactive 26Al nuclei produced by the ongoing stellar nucleosynthesis in the Galaxy. Finally a review on the study of the positron-electron annihilation in the Galactic center region, producing 511 keV gamma-rays, is presented.
We compute the inertia group of the compositum of wildly ramified Galois covers. It is used to show that even the $p$-part of the inertia group of a Galois cover of $\PP^1$ branched only at infinity can be reduced if there is a jump in the ramification filtration at two (in the lower numbering) and certain linear disjointness statement holds.
Two-dimensional (2D) layered lead iodide (PbI2) is an important precursor and common residual species during the synthesis of lead-halide perovskites. There currently exist some debates and uncertainties about the effect of excess PbI2 on the efficiency and stability of the solar cell with respect to its energy alignment and energetics of defects. Herein, by applying the first-principles calculations, we investigate the energetics, changes of work function and the defective levels associated with the iodine vacancy (VI) and interstitial iodine (II) defects of monolayer PbI2 (ML-PbI2). We find that the PbI2 has a very low formation energy of VI of 0.77 and 0.19 eV for dilute and high concentration, respectively, reflecting coalescence tendency of isolated VI, much lower than that of vacancies in other 2D materials like phosphorene. Similar to VI, a low formation energy of II of 0.65 eV is found, implying a high population of such defects. Both defects generate in-gap defective levels which are mainly due to the unsaturated chemical bonds of p-orbitals of exposed Pb or inserted I. Such rich defective levels allow the VI and II as the reservoir or sinks of electron/hole carriers in PbI2. Our results suggest that the remnant PbI2 in perovskite MAPbI3 (or FAPbI3) would play dual opposite roles in affecting the efficiency of the perovskite: (1) Forming Schottky-type interface with MAPbI3 (or FAPbI3) in which the built-in potential would facilitate the electron-hole separation and prolong the carrier lifetime; (2) Acting as the recombination centers due to the deep defective levels. To promote the efficiency by the Schottky effect, our work reveals that the II defect is favored, and to reduce the recombination centers the VI defect should be suppressed. Our results shall be beneficial in improving strategies for the related optoelectronics applications.