ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider "Containment": a variation of the graph pursuit game of Cops and Robber in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop), and the cops win by "containing" the robber---that is, by occupying all $\deg(v)$ of the edges incident with a vertex $v$ while the robber is at $v$. We develop bounds that relate the minimal number of cops, $\xi(G)$, required to contain a robber to the well-known "cop-number" $c(G)$ in the original game: in particular, $c(G) {\le} \xi(G) {\le} \gamma(G) \Delta(G)$. We note that $\xi(G) {\geq} \delta(G)$ for all graphs $G$, and analyze several families of graphs in which equality holds, as well as several in which the inequality is strict. We also give examples of graphs which require an unbounded number of cops in order to contain a robber, and note that there exist cubic graphs with $\xi(G) \geq \Omega(n^{1/6})$.
We prove several necessary and sufficient conditions for the existence of (smooth) transition probability densities for L\'evy processes and isotropic L\'evy processes. Under some mild conditions on the characteristic exponent we calculate the asymptotic behaviour of the transition density as $t\to 0$ and $t\to\infty$ and show a ratio-limit theorem.
We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have non-trivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated Doubling Theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that on the 4D boundary of the 5D Weyl semimetal, there are 3D chiral Fermi hypersurfaces protected by bulk Weyl surfaces. On top of that, for bulk Weyl surfaces that are linked and carry nonzero second Chern numbers, the associated boundary 3D Fermi hypersurfaces will shrink to singularities at certain energies, which trace out a protected 1D Weyl nodal arc, in analogy to the Fermi arc on the 3D Weyl semimetal surface.
We propose a non-universal $U(1)_{X}$ extension to the Standard Model with three families and an additional global anomala Peccei-Quinn (PQ) symmetry. The breaking of the former allows us to give masses to the exotic fermionic sector and the later generates the necessary zeros in the mass matrices to explain the fermionic mass hierarchy. In addition, the large energy scale associated with the spontaneously breaking (SSB) of the PQ symmetry provides a solution to the strong CP-problem and an axion that could be a possible dark matter candidate. Also, the SSB allows to generate right-handed neutrino masses, so the active neutrinos acquire $eV$-mass values due to the see-saw mechanism implementation.
After a short summary of the predictions of the Parton Quenching Model (PQM) for the nuclear modification factor and its centrality dependence in Au-Au collisions at RHIC, we concentrate on back-to-back jet-like correlations at high transverse momentum. We illustrate how this probe is biased by the surface effect.
Ta films with tetragonal crystalline structure (beta-phase), deposited by magnetron sputtering on different substrates (steel, silicon and silicon dioxide), have been studied. In all cases, very highly preferred (001) orientation was observed in x-ray diffraction (XRD) measurements. All diffraction data revealed two weak reflections corresponding to d-spacing of 0.5272 and 0.1777 nm. The presence of the two peaks, attributed to (001) and (003) reflections, indicates that beta-Ta films exhibit a high preference for the space group of P-421m over P42/mnm, previously proposed for beta-Ta. Differences in relative intensities of (00l) reflections, calculated for single crystal beta-Ta sigma-type Frank-Kasper structure and those measured in the films, are attributed to defects in the films. Molecular dynamics simulations performed on tantalum clusters with six different initial configurations using the embedded-atom-method (EAM) potential revealed the stability of beta-Ta, which might explain its growth on many substrates under various deposition conditions.
We derive the best characterization to date of the properties of radio quiescent massive galaxy clusters through a statistical analysis of their average synchrotron emissivity. We stacked 105 radio images of clusters from the 843 MHz SUMSS survey, all with X-ray luminosities greater than 1.0E+44 erg/s and redshifts z < 0.2, after removing point-source contamination and rescaling to a common physical size. Each stacked cluster individually shows no significant large-scale diffuse radio emission at current sensitivity levels. Stacking of sub-samples leads to the following results: (i) clusters with L_{X} > 3.0E+44 erg/s show a 6-sigma detection of Mpc-scale diffuse emission with a 1.4 GHz luminosity of 2.4\pm0.4 x 1.0E+23 W/Hz. This is 1.5-2 times lower than the upper limits for radio quiescent clusters from the GMRT Radio Halo Survey (Venturi et al. 2008), and is the first independent confirmation of radio halo bi-modality; (ii) clusters with low X-ray concentrations have a mean radio luminosity (2.6\pm0.6 x 1.0E+23 W/Hz) that is at least twice that of high X-ray concentration clusters, and (iii) both of these detections are likely close to the low-level "off-state" of GRHs in most or all luminous X-ray clusters, and not due to contributions from a much smaller subset of "on-state" GRHs following the radio/X-ray luminosity correlation. Upcoming deep radio surveys will conclusively distinguish between these two options. We briefly discuss possible origins for the "off-state" emission and its implications for magnetic fields in most or all luminous X-ray clusters.
We investigate different scenarios for the origin of the extragalactic radio background. The surface brightness of the background, as reported by the ARCADE 2 collaboration, is several times higher than that which would result from currently observed radio sources. We consider contributions to the background from diffuse synchrotron emission from clusters and the intergalactic medium, previously unrecognized flux from low surface brightness regions of radio sources, and faint point sources below the flux limit of existing surveys. By examining radio source counts available in the literature, we conclude that most of the radio background is produced by radio point sources that dominate at sub microJy fluxes. We show that a truly diffuse background produced by electrons far from galaxes is ruled out because such energetic electrons would overproduce the obserevd X-ray/gamma-ray background through inverse Compton scattering of the other photon fields. Unrecognized flux from low surface brightness regions of extended radio sources, or moderate flux sources missed entirely by radio source count surveys, cannot explain the bulk of the observed background, but may contribute as much as 10 per cent. We consider both radio supernovae and radio quiet quasars as candidate sources for the background, and show that both fail to produce it at the observed level because of insufficient number of objects and total flux, although radio quiet quasars contribute at the level of at least a few percent. We conclude that if the radio background is at the level reported, a majority of the total surface brightness would have to be produced by ordinary starforming galaxies above redshift 1 characterized by an evolving radio far-infrared correlation, which changes toward the radio loud with redshift.
Polarized rational surfaces $(X, \mathcal L)$ of sectional genus two ruled in conics are studied. When they are not minimal, they are described as the blow-up of $\mathbb F_1$ at some points lying on distinct fibers. Ampleness and very ampleness of $\mathcal L$ are studied in terms of their location. When $\mathcal L$ is very ample and there is a line contained in $X$ and transverse to the fibers, the conic fibrations $(X, \mathcal L)$ are classified and a related property concerned with the inflectional locus is discussed.
I use spin as a guide through the labyrinth of possibilities and ideas that go beyond the established understanding of the fundamental interactions.
According to our modal-Hamiltonian interpretation (MHI) of quantum mechanics, the Hamiltonian of the closed system defines the set of its definite-valued observables. This definition seems to be incompatible with the pointer basis selected by the environment-induced decoherence (EID) of the open system. In this paper we argue that decoherence can be understood from a closed system perspective which (i) shows that the incompatibility between MHI and EID is only apparent, and (ii) solves certain conceptual challenges that the EID program still has to face.
Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail, Mikosch et al. (Ann Appl Probab, 12:23-68, 2002) and Kaj and Taqqu (Progress Probab, 60:383-427, 2008) have shown that traffic at large time scales can be approximated by either fractional Brownian motion (fBm) or stable Levy motion. We study distributional properties of cumulative traffic that consists of a finite number of independent streams and give an explanation of why Gaussian examples abound in practice but not stable Levy motion. We offer an explanation of how much vertical aggregation is needed for the Gaussian approximation to hold. Our results are expressed as limit theorems for a sequence of cumulative traffic processes whose session initiation intensities satisfy growth rates similar to those used in Mikosch et al. (Ann Appl Probab, 12:23-68, 2002).
We investigate the width of the Ginzburg critical region and experimental signatures of critical behavior in strongly interacting trapped Fermi gases close to unitarity, where the s-wave scattering length diverges. Despite the fact that the width of the critical region is of the order unity, evidence of critical behavior in the bulk thermodynamics of trapped gases is strongly suppressed by their inhomogeneity. The specific heat of a harmonically confined gas, for instance, is \textit{linear} in the reduced temperature $t = (T-T_{\mathrm{c}})/T_{\mathrm{c}}$ above $T_{\mathrm{c}}$. We also discuss the prospects of observing critical behavior in the local compressibility from measurements of the density profile.
The UVJ color-color diagram is a popular and efficient method to distinguish between quiescent and star-forming galaxies through their rest-frame $U-V$ vs. $V-J$ colors. Here we explore the information content of this color-color space using the Bayesian inference machine Prospector. We fit the same physical model to two datasets: (i) UVJ fluxes alone, and (ii) full UV-mid IR (MIR) broadband SEDs from the 3D-HST survey. Notably this model uses both nonparametric SFHs and a flexible dust attenuation curve, both of which have the potential to `break' the typical correlations observed in UVJ color-color space. Instead, these fits confirm observed trends between UVJ colors and observed galaxy properties, including specific star formation rate (sSFR), dust attenuation, stellar age, and stellar metallicity. They also demonstrate that UVJ colors do not, on their own, constrain stellar age or metallicity; the observed trends in the UVJ diagram are instead driven by galaxy scaling relationships and thus will evolve with cosmological time. We also show that UVJ colors 'saturate' below $\log(\mathrm{sSFR/yr}^{-1})\lesssim -10.5$, i.e. changing sSFR no longer produces substantial changes in UVJ colors. We show that far-UV and/or MIR fluxes continue to correlate with sSFR down to low sSFRs and can be used in color-color diagrams to efficiently target galaxies with much lower levels of ongoing star formation. We provide selection criteria in these new color-color spaces as a function of desired sample sSFR.
The high luminosity displayed by an active galactic nucleus (AGN) requires that gas be transported to the centre of the galaxy by some mechanism. Bar-driven processes are often pointed out in this context and a number of studies have addressed the bar-AGN connection, but with conflicting results. Some of the inconsistencies can be explained by the different spatial- and timescales involved in bar-driven gas inflows, accretion by the central black hole, and AGN emission. However, the discrepant results could also be due to sample biases, because both the AGN activity determination and the bar detection are influenced by the method employed. We revisit the bar-AGN connection in a sample of galaxies from SDSS, looking for evidence of the influence of bars on AGN activity. We determine AGN activity by emission line diagnostics and the properties of the bar were previously estimated with \texttt{BUDDA}, which performs 2D bulge-bar-disk decomposition. Before comparing active and inactive galaxies, we made a careful selection of the sample to minimise selection biases. We created control samples by matching them with the AGN sample using propensity score matching. This technique offers an analytical approach for creating control samples given some object parameters. We find that AGN are preferentially found in barred galaxies and that the accretion rate is higher in barred galaxies, but only when different M-$\sigma$ relations are used to estimate the black hole mass M$_\bullet$ in barred and unbarred galaxies (from the central velocity dispersion $\sigma$). On the other hand, we find no correlation between activity level and bar strength. Altogether, our results strengthen theoretical predictions that the bar is an important mechanism in disc galaxies, creating a gas reservoir to feed AGN, but they also indicate that other mechanisms can play a major role, particularly at scales <~100 pc.
We report the results of spectroscopic mapping observations carried out toward small (1 x 1 arcmin) regions within the supernova remnants W44, W28, IC443, and 3C391 using the Infrared Spectrograph of the Spitzer Space Telescope. These observations, covering the 5.2 - 37 micron spectral region, have led to the detection of a total of 15 fine structure transitions of Ne+, Ne++, Si+, P+, S, S++, Cl+, Fe+, and Fe++; the S(0) - S(7) pure rotational lines of molecular hydrogen; and the R(3) and R(4) transitions of hydrogen deuteride. In addition to these 25 spectral lines, the 6.2, 7.7, 8.6, 11.3 and 12.6 micron PAH emission bands were also observed. Most of the detected line transitions have proven strong enough to map in several sources, providing a comprehensive picture of the relative distribution of the various line emissions observable in the Spitzer/IRS bandpass. A principal component analysis of the spectral line maps reveals that the observed emission lines fall into five distinct groups, each of which may exhibit a distinct spatial distribution: (1) lines of S and H2 (J > 2); (2) the H2 S(0) line; (3) lines of ions with appearance potentials less than 13.6 eV; (4) lines of ions with appearance potentials greater than 13.6 eV, not including S++; (5) lines of S++. Lines of group (1) likely originate in molecular material subject to a slow, nondissociative shock that is driven by the overpressure within the supernova remnant, and lines in groups (3) - (5) are associated primarily with dissociative shock fronts with a range of (larger) shock velocities. The H2 S(0) line shows a low-density diffuse emission component, and - in some sources - a shock-excited component.
New images from the Hubble Space Telescope of the FRII radio galaxy Pictor A reveal a previously undiscovered tidal tail, as well as a number of jet knots coinciding with a known X-ray and radio jet. The tidal tail is approximately 5" wide (3 kpc projected), starting 18" (12 kpc) from the center of Pictor A, and extends more than 90" (60 kpc). The knots are part of a jet observed to be about 4' (160 kpc) long, extending to a bright hotspot. These images are the first optical detections of this jet, and by extracting knot flux densities through three filters we set constraints on emission models. While the radio and optical flux densities are usually explained by synchrotron emission, there are several emission mechanisms which might be used to explain the X-ray flux densities. Our data rule out Doppler boosted inverse Compton scattering as a source of the high energy emission. Instead, we find that the observed emission can be well described by synchrotron emission from electrons with a low energy index ($p\sim2$) that dominates the radio band, while a high energy index ($p\sim3$) is needed for the X-ray band and the transition occurs in the optical/infrared band. This model is consistent with a continuous electron injection scenario.
With the inclusion of arbitrary long-range hopping and (pseudo)spin-orbit coupling amplitudes, we formulate a generic model that can describe any two-dimensional two-band bulk insulators, thus providing a simple framework to investigate arbitrary adiabatic deformations upon the systems of any arbitrary Chern numbers. Without appealing to advanced techniques beyond the standard methods of solving linear difference equations and applying Cauchy's integral formula, we obtain a mathematically elementary yet rigorous proof of the bulk-boundary correspondence on a strip, which is robust against any adiabatic deformations upon the bulk Hamiltonian and any uniform edge perturbation along the edges. The elementary approach not only is more transparent about the underlying physics but also reveals various intriguing nontopological features of Chern insulators that have remained unnoticed or unclear so far. Particularly, if a certain condition is satisfied (as in most renowned models), the loci of edge bands in the energy spectrum and their (pseudo)spin polarizations can be largely inferred from the bulk Hamiltonian alone without invoking any numerical computation for the energy spectrum of a strip.
Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility to use relativistic systems for simulating rotating black hole solutions and possibly get an acoustic analogue of a Kerr black hole. In doing so we demonstrate a precise relation between non-relativistic and relativistic solutions and provide a new class of vortex solutions for relativistic systems. Such solutions might be used in the future as a test bed in numerical simulations as well as concrete experiments.
The holographic dual of a gravitational theory around the de Sitter background is argued to be a Euclidean conformal gravity theory in one fewer dimensions. The measure for the holographic theory naturally includes a sum over topologies as well as conformal structures.
We study orbital modulation of X-rays from Cyg X-3, using data from Swift, INTEGRAL and RXTE. Using the wealth of the presently available data and an improved averaging method, we obtain energy-dependent folded and averaged light curves with unprecedented accuracy. We find that above ~5 keV, the modulation depth decreases with the increasing energy, which is consistent with the modulation being caused by both bound-free absorption and Compton scattering in the stellar wind of the donor, with minima corresponding to the highest optical depth, which occurs around the superior conjunction. We find a decrease of the depth below ~3 keV, which appears to be due to re-emission of the absorbed continuum by the wind in soft X-ray lines. Based on the shape of the folded light curves, any X-ray contribution from the jet in Cyg X-3, which emits gamma-rays detected at energies >0.1 GeV in soft spectral states, is found to be minor up to ~100 keV. This implies the presence of a rather sharp low-energy break in the jet MeV-range spectrum. We also calculate phase-resolved RXTE X-ray spectra, and show the difference between the spectra corresponding to phases around the superior and inferior conjunctions can indeed be accounted for by a combined effect of bound-free absorption in an ionized medium and Compton scattering.
Most deterministic schemes for controlling temperature by kinetic variables (NH thermsotat), configurational variables (BT thermostat) and all phase space variables (PB thermostat) are non-ergodic for systems with a few degrees of freedom. While for the NH thermostat ergodicity has been achieved by controlling the higher order moments of kinetic energy, the issues of nonergodicity of BT and PB thermostats still persist. In this paper, we propose a family of modifications for improving their ergodic characteristics. To do so, we introduce two new measures of configurational temperature (second and third order) based on the generalized temperature - curvature relationship. The equations of motion for the existing thermostats are modified by controlling the relevant higher order temperature variables. The ergodic characteristics of the proposed modifications are tested using a single harmonic oscillator. For the PB thermostat, the fastest route to ergodicity is by controlling the usual configurational and kinetic temperatures along with the $2^{\text{nd}}$ order configurational temperature. For the BT thermostat, controlling the usual configurational temperature along with the $2^{\text{nd}}$ order configurational temperature is sufficient to make it ergodic. Our method also provides a new ergodic generalization of NH thermostat that reduces to kinetic moments method for a single harmonic oscillator.
We compute the electronic component of the thermal conductivity (TC) and the thermoelectric power (TEP) of monolayer graphene, within the hydrodynamic regime, taking into account the slow rate of carrier population imbalance relaxation. Interband electron-hole generation and recombination processes are inefficient due to the non-decaying nature of the relativistic energy spectrum. As a result, a population imbalance of the conduction and valence bands is generically induced upon the application of a thermal gradient. We show that the thermoelectric response of a graphene monolayer depends upon the ratio of the sample length to an intrinsic length scale l_Q, set by the imbalance relaxation rate. At the same time, we incorporate the crucial influence of the metallic contacts required for the thermopower measurement (under open circuit boundary conditions), since carrier exchange with the contacts also relaxes the imbalance. These effects are especially pronounced for clean graphene, where the thermoelectric transport is limited exclusively by intercarrier collisions. For specimens shorter than l_Q, the population imbalance extends throughout the sample; the TC and TEP asymptote toward their zero imbalance relaxation limits. In the opposite limit of a graphene slab longer than l_Q, at non-zero doping the TC and TEP approach intrinsic values characteristic of the infinite imbalance relaxation limit. Samples of intermediate (long) length in the doped (undoped) case are predicted to exhibit an inhomogeneous temperature profile, whilst the TC and TEP grow linearly with the system size. In all cases except for the shortest devices, we develop a picture of bulk electron and hole number currents that flow between thermally conductive leads, where steady-state recombination and generation processes relax the accumulating imbalance.
In this paper we study the evolution of density perturbations in the framework of Phase Coupling Gravity theory at the very early universe. We show that these perturbation display an exponential-like behaviour.