ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present new dynamical models of the merger remnant NGC 7252 which include star formation simulated according to various phenomenological rules. By using interactive software to match our model with the observed morphology and gas velocity field, we obtain a consistent dynamical model for NGC 7252. In our models, this proto-elliptical galaxy formed by the merger of two similar gas-rich disk galaxies which fell together with an initial pericentric separation of ~2 disk scale lengths approximately 620 Myr ago. Results from two different star formation rules--- density-dependent and shock-induced--- show significant differences in star formation during and after the first passage. Shock-induced star formation yields a prompt and wide-spread starburst at the time of first passage, while density-dependent star formation predicts a more slowly rising and centrally concentrated starburst. A comparison of the distributions and ages of observed clusters with results of our simulations favors shock-induced mechanism of star formation in NGC 7252. We also present simulated color images of our model of NGC 7252, constructed by incorporating population synthesis with radiative transfer and dust attenuation. Overall the predicted magnitudes and colors of the models are consistent with observations, although the simulated tails are fainter and redder than observed. We suggest that a lack of star formation in the tails, reflected by the redder colors, is due to an incomplete description of star formation in our models rather than insufficient gas in the tails.
Based on a realistic spin Hamiltonian for a frustrated quasi-two dimensional spin-1/2 antiferromagnet Cs$_{2}$CuCl$_{4}$, a three-dimensional spin ordering in the applied magnetic field $B$ near the saturation value $B_{c}$ is studied within the magnon Bose-Einstein condensation (BEC) scenario. With the use of a hard-core boson formulation of the spin model, a strongly anysotropic magnon dispersion in Cs$_{2}$CuCl$_{4}$ is calculated. In the dilute magnon limit near $B_{c}$, the hard-core boson constraint is resulted in an effective magnon interaction which is treated in the Hartree-Fock approximation. The critical temperature $T_{c}$ is calculated as a function of a magnetic field $B$ and compared with the phase boundary $T_{c}(B) $ experimentally determined in Cs$_{2}$CuCl$_{4}$ [Phys. Rev. Lett. \textbf{95}, 127202 (2005)].
We introduce the notion of alternate product of Frobenius manifolds and we give, after [math.AG/0610265], an interpretation of the Frobenius manifold structure canonically attached to the quantum cohomology of G(r,n+1) in terms of alternate products. We also investigate the relationship with the alternate Thom-Sebastiani product of Laurent polynomials.
The existence of gauge pathologies associated with the Bona-Masso family of generalized harmonic slicing conditions is proven for the case of simple 1+1 relativity. It is shown that these gauge pathologies are true shocks in the sense that the characteristic lines associated with the propagation of the gauge cross, which implies that the name ``gauge shock'' usually given to such pathologies is indeed correct. These gauge shocks are associated with places where the spatial hypersurfaces that determine the foliation of spacetime become non-smooth.
The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman and Machedon, and of Sogge for the variable coefficient boundaryless case. The estimates are used to prove a local existence theorem for semilinear wave equations satisfying the null condition.
We present an abstract model of quantum computation, the "Pauli Fusion" model, whose primitive operations correspond closely to generators of the ZX calculus (a formal graphical language for quantum computing). The fundamental operations of Pauli Fusion are also straightforward abstractions of basic processes in some leading proposed quantum technologies. These operations have non-deterministic heralded effects, similarly to measurement-based quantum computation. We describe sufficient conditions for Pauli Fusion procedures to be deterministically realisable, so that it performs a given transformation independently of its non-deterministic outcomes. This provides an operational model to realise ZX terms beyond the circuit model.
We develop a local positivity theory for movable curves on projective varieties similar to the classical Seshadri constants of nef divisors. We give analogues of the Seshadri ampleness criterion, of a characterization of the augmented base locus of a big and nef divisor, and of the interpretation of Seshadri constants as an asymptotic measure of jet separation. We also study the case of arbitrary codimension.
According to the decomposition and relative hard Lefschetz theorems, given a projective map of complex quasi projective algebraic varieties and a relatively ample line bundle, the rational intersection cohomology groups of the domain of the map split into various direct summands. While the summands are canonical, the splitting is certainly not, as the choice of the line bundle yields at least three different splittings by means of three mechanisms in a triangulated category introduced by Deligne. It is known that these three choices yield splittings of mixed Hodge structures. In this paper, we use the relative hard Lefschetz theorem and elementary linear algebra to construct five distinct splittings, two of which seem to be new, and to prove that they are splittings of mixed Hodge structures.
The velocity distribution in a homogeneously cooling granular gas has been studied in the viscoelastic regime when the restitution coefficient of colliding particles depends on the impact velocity. We show that for viscoelastic particles the simple scaling hypothesis is violated, i.e., that the time dependence of the velocity distribution does not scale with the mean square velocity as in the case of particles interacting via a constant restitution coefficient. The deviation from the Maxwellian distribution does not depend on time monotonously. For the case of small dissipation we detected two regimes of evolution of the velocity distribution function: Starting from the initial Maxwellian distribution, the deviation first increases with time on a collision time-scale saturating at some maximal value; then it decays to zero on much larger time-scale which corresponds to the temperature relaxation. For larger values of the dissipation parameter there appears an additional intermediate relaxation regime. Analytical calculations for small dissipation agrees well with the results of a numerical analysis.
We report our new observations of redshifted carbon monoxide emission from six z~6 quasars, using the PdBI. CO (6-5) or (5-4) line emission was detected in all six sources. Together with two other previous CO detections, these observations provide unique constraints on the molecular gas emission properties in these quasar systems close to the end of the cosmic reionization. Complementary results are also presented for low-J CO lines observed at the GBT and the VLA, and dust continuum from five of these sources with the SHARC-II bolometer camera at the CSO. We then present a study of the molecular gas properties in our combined sample of eight CO-detected quasars at z~6. The detections of high-order CO line emission in these objects indicates the presence of highly excited molecular gas, with estimated masses on the order of 10^10 M_sun within the quasar host galaxies. No significant difference is found in the gas mass and CO line width distributions between our z~6 quasars and samples of CO-detected $1.4\leq z\leq5$ quasars and submillimeter galaxies. Most of the CO-detected quasars at z~6 follow the far infrared-CO luminosity relationship defined by actively star-forming galaxies at low and high redshifts. This suggests that ongoing star formation in their hosts contributes significantly to the dust heating at FIR wavelengths. The result is consistent with the picture of galaxy formation co-eval with supermassive black hole (SMBH) accretion in the earliest quasar-host systems. We investigate the black hole--bulge relationships of our quasar sample, using the CO dynamics as a tracer for the dynamical mass of the quasar host. The results place important constraints on the formation and evolution of the most massive SMBH-spheroidal host systems at the highest redshift.
Deep Neural Networks trained in a fully supervised fashion are the dominant technology in perception-based autonomous driving systems. While collecting large amounts of unlabeled data is already a major undertaking, only a subset of it can be labeled by humans due to the effort needed for high-quality annotation. Therefore, finding the right data to label has become a key challenge. Active learning is a powerful technique to improve data efficiency for supervised learning methods, as it aims at selecting the smallest possible training set to reach a required performance. We have built a scalable production system for active learning in the domain of autonomous driving. In this paper, we describe the resulting high-level design, sketch some of the challenges and their solutions, present our current results at scale, and briefly describe the open problems and future directions.
We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove the global-in-time existence of the regular solutions of the models as well as their temporal decays in two and three dimensions. We also show that the total masses of egg and sperm density have positive lower bounds as time tends to infinity in three dimensions.
In this article, we present an alternate proof of a vanishing result of \'etale cohomology on perfectoid rings due to \v{C}esnavi\v{c}ius and more recently proved by a different approach by Bhatt and Scholze. To establish that, we prove a tilting equivalence of \'etale cohomology of perfectoid rings taking values in commutative, finite \'etale group schemes. On the way, we algebraically establish an analogue of the tilting correspondences of Scholze, between the category of finite \'etale schemes over a perfectoid ring and that over its tilt, without using tools from almost ring theory or adic spaces.
We look at colourings of $r$-uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the partition of $r$ induced by the colour classes of the vertices in $E$. Let $Q$ be a set of partitions of $r$. A $Q$-colouring of $H$ is a colouring of its vertices such that only patterns appearing in $Q$ are allowed. We first show that many known hypergraph colouring problems, including Ramsey theory, can be stated in the language of $Q$-colourings. Then, using as our main tools the notions of $Q$-colourings and $\Sigma$-hypergraphs, we define and prove a result on tight colourings, which is a strengthening of the notion of unique colourability. $\Sigma$-hypergraphs are a natural generalisation of $\sigma$-hypergraphs introduced by the first two authors in an earlier paper. We also show that there exist $\Sigma$-hypergraphs with arbitrarily large $Q$-chromatic number and chromatic number but with bounded clique number. Dvorak et al. have characterised those $Q$ which can lead to a hypergraph with a gap in its $Q$-spectrum. We give a short direct proof of the necessity of their condition on $Q$. We also prove a partial converse for the special case of $\Sigma$-hypergraphs. Finally, we show that, for at least one family $Q$ which is known to yield hypergraphs with gaps, there exist no $\Sigma$-hypergraphs with gaps in their $Q$-spectrum.
We demonstrate a sub-shot-noise-limit discrimination of on-off keyed coherent signals by an optimal displacement quantum receiver in which a superconducting transition edge sensor is installed. Use of a transition edge sensor and a fiber beam splitter realizes high total detection efficiency and high interference visibility of the receiver and the observed average error surpasses the shot-noise-limit in a wider range of the signal power. Our technique opens up a new technology for the sub-shot-noise-limit detection of coherent signals in optical communication channels.
We present a many-body approach to the electronic and magnetic properties of the (multiband) Kondo-lattice model with ferromagnetic interband exchange. The coupling between itinerant conduction electrons and localized magnetic moments leads, on the one hand, to a distinct temperature-dependence of the electronic quasiparticle spectrum and, on the other hand, to magnetic properties, as e.~g.the Curie temperature T_C or the magnon dispersion, which are strongly influenced by the band electron selfenergy and therewith in particular by the carrier density. We present results for the single-band Kondo-lattice model in terms of quasiparticle densities of states and quasiparticle band structures and demonstrate the density-dependence of the self-consistently derived Curie temperature. The transition from weak-coupling (RKKY) to strong-coupling (double exchange) behaviour is worked out.   The multiband model is combined with a tight-binding-LMTO bandstructure calculation to describe real magnetic materials. As an example we present results for the archetypal ferromagnetic local-moment systems EuO and EuS. The proposed method avoids the double counting of relevant interactions and takes into account the correct symmetry of atomic orbitals.
Let $f$ and $g$ be holomorphic cusp forms for the modular group $SL_2(\mathbb Z)$ of weight $k_1$ and $k_2$ with Fourier coefficients $\lambda_f(n)$ and $\lambda_g(n)$, respectively. For real $\alpha\neq0$ and $0<\beta\leq1$, consider a smooth resonance sum $S_X(f,g;\alpha,\beta)$ of $\lambda_f(n)\lambda_g(n)$ against $e(\alpha n^\beta)$ over $X\leq n\leq2X$. Double square moments of $S_X(f,g;\alpha,\beta)$ over both $f$ and $g$ are nontrivially bounded when their weights $k_1$ and $k_2$ tend to infinity together. By allowing both $f$ and $g$ to move, these double moments are indeed square moments associated with automorphic forms for $GL(4)$. By taking out a small exceptional set of $f$ and $g$, bounds for individual $S_X(f,g;\alpha,\beta)$ will then be proved. These individual bounds break the resonance barrier of $X^\frac58$ for $\frac16<\beta<1$ and achieve a square-root cancellation for $\frac13<\beta<1$ for almost all $f$ and $g$ as an evidence for Hypothesis S for cusp forms over integers. The methods used in this study include Petersson's formula, Poisson's summation formula, and stationary phase integrals.
The inverse Galois problem is concerned with finding a Galois extension of a field $K$ with given Galois group. In this paper we consider the particular case where the base field is $K=\F_p(t)$. We give a conjectural formula for the minimal number of primes, both finite and infinite, ramified in $G$-extensions of $K$, and give theoretical and computational proofs for many cases of this conjecture.
We consider stochastic differential equations dY=V(Y)dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Y(t) admits a density for t in (0,T] provided (i) the vector fields V=(V_1,...,V_d) satisfy Hoermander's condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fractional Brownian motion with Hurst parameter H>1/4, the Brownian Bridge returning to zero after time T and the Ornstein-Uhlenbeck process.
We present the detection of an unresolved radio source coincident with the position of the Type I superluminous supernova (SLSN) PTF10hgi ($z=0.098$) about 7.5 years post-explosion, with a flux density of $F_\nu(6\,\,{\rm GHz)}\approx 47.3\ \mu Jy$ and a luminosity of $L_\nu(6\,\,{\rm GHz})\approx 1.1\times 10^{28}$ erg s$^{-1}$ Hz$^{-1}$. This represents the first detection of radio emission coincident with a SLSN on any timescale. We investigate various scenarios for the origin of the radio emission: star formation activity, an active galactic nucleus, and a non-relativistic supernova blastwave. While any of these would be quite novel if confirmed, none appear likely when taken in context of the other properties of the host galaxy, previous radio observations of SLSNe, and the general population of hydrogen-poor SNe. Instead, the radio emission is reminiscent of the quiescent radio source associated with the repeating FRB 121102, which has been argued to be powered by a magnetar born in a SLSN or LGRB explosion several decades ago. We show that the properties of the radio source are consistent with a magnetar wind nebula or an off-axis jet, indicating the presence of a central engine. Our directed search for FRBs from the location of PTF10hgi using 40 min of VLA phased-array data reveals no detections to a limit of $22$ mJy ($10\sigma$; 10 ms duration). We outline several follow-up observations that can conclusively establish the origin of the radio emission.
By means of self-consistent 3D MHD numerical simulations, we analyze magnetized solar-like stellar winds and their dependence on the plasma-beta parameter. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from 1 to 20G. We show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. The increase of the field intensity generates a larger dead zone in the wind, i. e., the closed loops that inhibit matter to escape from latitudes lower than ~45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B0=20G, the system recover back to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite of its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We analyze the influence of gamma in our results and we show that it is also important in determining the wind structure. (Abridged)
This set of lectures provides an overview of the basic theory and phenomenology of the cosmic microwave background. Topics include a brief historical review; the physics of temperature and polarization fluctuations; acoustic oscillations of the primordial plasma; the space of inflationary cosmological models; current and potential constraints on these models from the microwave background; and constraints on inflation.
Wide field BVI photometry and $^{12}$CO(1$\to$0) observations are presen ted in the region of the open cluster NGC 6520 and the dark molecular cloud Barnard~86. From the analysis of the optical data we find that the cluster is rather compact, with a radius of 1.0$\pm$0.5 arcmin, smaller than previous estimates. The cluster age is 150$\pm$50 Myr and the reddening E$_{B-V}$=0.42$\pm$0.10. The distance from the Sun is estimated to be 1900$\pm$100 pc, and it is larger than previous estimates. We finally derive basic properties of the dark nebula Barnard 86 on the assumption that it lies at the same distance of the cluster.
In this work we consider constructions of genus three curves $X$ such that $\mathrm{End}(\mathrm{Jac}(X)) \otimes Q$ contains the totally real cubic number field $Q(\zeta _ 7 + \overline{\zeta}_7)$. We construct explicit two-dimensional families defined over $Q(s; t)$ whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when X is hyperelliptic was studied by the authors Hoffman and Wang in a previous work. We calculate the zeta function of one of these curves. Conjecturally this zeta function is described by a modular form.
The role of relativistic corrections associated with lower Dirac components of the deuteron wavefunction, is examined for parity-violating (PV) electron scattering. The relation between these corrections and negative energy components of the struck nucleon in relativistic PWIA is elucidated. The model dependence induced by describing such effects, using different deuteron vertex functions and prescriptions for the half-off-shell nucleon vertices, is compared against the precision required for studies of nucleon strangeness in quasielastic PV $e-d$ scattering.
Coalescence of intermediate-mass black holes (IMBHs) as a result of the migration toward galactic centers via dynamical friction may contribute to the formation of supermassive BHs. Here we reinvestigate the gaseous dynamical friction, which was claimed to be inefficient with radiative feedback from BHs in literature, by performing 3D radiation-hydrodynamics simulations that solve the flow structure in the vicinity of BHs. We consider a $10^4~M_\odot$ BH moving at the velocity $V_{\rm flow}$ through the homogeneous medium with metallicity $Z$ in the range of $0-0.1~Z_\odot$ and density $n_{\infty}$. We show that, if $n_{\infty} \lesssim 10^{6}~{\rm cm^{-3}}$ and $V_{\rm flow} \lesssim 60~{\rm km~s^{-1}}$, the BH is accelerated forward because of the gravitational pull from a dense shell ahead of an ionized bubble around the BH, regardless of the value of $Z$. If $n_{\infty} \gtrsim 10^{6}~{\rm cm^{-3}}$, however, our simulation shows the opposite result. The ionized bubble and associating shell temporarily appear, but immediately go downstream with significant ram pressure of the flow. They eventually converge into a massive downstream wake, which gravitationally drags the BH backward. The BH decelerates over the timescale of $\sim 0.01$~Myr, much shorter than the dynamical timescale in galactic disks. Our results suggest that IMBHs that encounter the dense clouds rapidly migrate toward galactic centers, where they possibly coalescence with others.
We report on a new all-sky search for periodic gravitational waves in the frequency band 475-2000 Hz and with a frequency time derivative in the range of [-1.0e-8, +1e-9] Hz/s. Potential signals could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy.   This search uses the data from Advanced LIGO's first observational run O1. No gravitational wave signals were observed, and upper limits were placed on their strengths. For completeness, results from the separately published low frequency search 20-475 Hz are included as well.   Our lowest upper limit on worst-case (linearly polarized) strain amplitude h_0 is 4e-25 near 170 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of 1.3e-24. For a circularly polarized source (most favorable orientation), the smallest upper limit obtained is ~1.5e-25.
We present an estimation of the strong coupling constant alphas(MZ) using, for the first time, the production of prompt photon process in proton-proton collisions at the LHC. ATLAS measurements of the inclusive isolated prompt photon cross section at 7 TeV are exploited. Both theoretical and experimental uncertainties are estimated and the strong coupling constant has been determined to be alphas(MZ)= 0.1183 +- 0.0038, to NLO accuracy.