ShantanuT01/DACTYL-Pretraining huggingface dataset:
We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on $\mathbb{Z}^d$, in dimension $d\ge 5$, both in the upward and downward directions. The results are analogous to those we obtained for the volume of the range in two companion papers [AS17, AS19]. Interestingly, the main steps of the strategy we developed for the latter apply in this seemingly different setting, yet the details of the analysis are different
The Degasperis-Procesi equation is the integrable Camassa-Holm-type model which is an asymptotic approximation for the unidirectional propagation of shallow water waves. This work establishes the orbital stability of localized smooth solitary waves to the Desgasperis-Procesi (DP) equation on the real line. %extending our previous work on their spectral stability \cite{LLW}. The main difficulty stems from the fact that the translation symmetry for the DP equation gives rise to a conserved quantity equivalent to the $L^2$-norm, which by itself can not bound the higher-order nonlinear terms in the Lagrangian. The remedy is to observe that, given a sufficiently smooth initial condition satisfying a measurable constraint, the $L^\infty$ orbital norm of the perturbation is bounded above by a function of its $L^2$ orbital norm, yielding the orbital stability in the $L^2\cap L^\infty$ space.
Gravitational domain wall solutions in gauged supergravity are often constructed within truncations that do not include vectors. As a consequence the gauge group is only a global symmetry of this truncation. The consistency of the truncation requires the restriction to solutions with vanishing Noether charge under this global symmetry, since otherwise vector fields are sourced. We show that this has interesting consequences for the orbit structure of the solutions under the global symmetries. We investigate this for $\text{CSO}(p,q,r)$-gaugings in various dimensions with scalar fields truncated to the $\text{SL}(n,\mathbb{R})/\text{SO}(n)$ subcoset. We prove that the seed solution $-$ which generates all other solutions using only global transformations $-$ has a diagonal coset matrix. This means that there exists a transformation at the boundary of the geometry that diagonalises the coset matrix and that this same transformation also diagonalises the whole flow as a consequence of the vanishing charge.
Let $H$ be a connected semisimple linear algebraic group defined over $\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial stable principal $H$-bundles over $X$ whose automorphism group coincides with the centre of $H$. It is a Zariski open dense subset of the moduli space of stable principal $H$-bundles. We prove that there is a universal principal $H$-bundle over $X\times {\mathcal M}'_X(H)$ if and only if $H$ is an adjoint group (that is, the centre of $H$ is trivial).
The upper bound and the lower bound of average numbers of divisors of Euler Phi function and Carmichael Lambda function are obtained by Luca and Pomerance (see \cite{LP}). We improve the lower bound and provide a heuristic argument which suggests that the upper bound given by \cite{LP} is indeed close to the truth.
We present an alternative method for calculating amplitudes for correlated pi pi exchange in the ``sigma'' and rho channel in piN scattering. Starting from a fixed mass meson exchange potential, we introduce the width of the exchanged particles by integrating over a mass spectral function. The spectral functions are constructed from the pseudoempirical N\bar{N} -> pi pi data. Using this approach we develop a prescription for resolving ambiguities of the correlated pi pi exchange in the rho channel that occur when different dispersion theoretical formulations of rho exchange are used to construct piN potentials.
Recent analyses have shown that close encounters between stars and stellar black holes occur frequently in dense star clusters. Depending upon the distance at closest approach, these interactions can lead to dissipating encounters such as tidal captures and disruptions, or direct physical collisions, all of which may be accompanied by bright electromagnetic transients. In this study, we perform a wide range of hydrodynamic simulations of close encounters between black holes and main-sequence stars that collectively cover the parameter space of interest, and we identify and classify the various possible outcomes. In the case of nearly head-on collisions, the star is completely disrupted with roughly half of the stellar material becoming bound to the black hole. For more distant encounters near the classical tidal-disruption radius, the star is only partially disrupted on the first pericenter passage. Depending upon the interaction details, the partially disrupted stellar remnant may be tidally captured by the black hole or become unbound (in some cases, receiving a sufficiently large impulsive kick from asymmetric mass loss to be ejected from its host cluster). In the former case, the star will undergo additional pericenter passages before ultimately being disrupted fully. Based on the properties of the material bound to the black hole at the end of our simulations (in particular, the total bound mass and angular momentum), we comment upon the expected accretion process and associated electromagnetic signatures that are likely to result.
We present new Jansky Very Large Array observations of five pre-Swift gamma-ray bursts for which an ultraluminous (SFR > 100 M_sun/yr) dusty host galaxy had previously been inferred from radio or submillimetre observations taken within a few years after the burst. In four of the five cases we no longer detect any source at the host location to limits much fainter than the original observations, ruling out the existence of an ultraluminous galaxy hosting any of these GRBs. We continue to detect a source at the position of GRB 980703, but it is much fainter than it was a decade ago and the inferred radio star-formation rate (~80 M_sun) is relatively modest. The radio flattening at 200-1000 days observed in the light curve of this GRB may have been caused by a decelerating counterjet oriented 180 degrees away from the viewer, although an unjetted wind model can also explain the data. Our results eliminate all well-established pre-Swift ULIRG hosts, and all cases for which an unobscured GRB was found in a galaxy dominated by heavily-obscured star-formation. When GRBs do occur in ULIRGs the afterglow is almost always observed to be heavily obscured, consistent with the large dust opacities and high dust covering fractions characteristic of these systems.
We study how diffuse interstellar bands (DIBs) measured toward distance-distributed target stars can be used to locate dense interstellar (IS) clouds in the Galaxy and probe a line-of-sight (LOS) kinematical structure, a potential useful tool when gaseous absorption lines are saturated or not available in the spectral range. Cool target stars are numerous enough for this purpose. We have devised automated DIB fitting methods appropriate to cool star spectra and multiple IS components. The data is fitted with a combination of a synthetic stellar spectrum, a synthetic telluric transmission, and empirical DIB profiles. In parallel, stellar distances and extinctions are estimated self-consistently by means of a 2D Bayesian method, from spectroscopically-derived stellar parameters and photometric data. We have analyzed Gaia-ESO Survey (GES) and previously recorded spectra that probe between $\sim$ 2 and 10 kpc long LOS in five different regions of the Milky Way. Depending on the observed spectral intervals, we extracted one or more of the following DIBs: $\lambda\lambda$ 6283.8, 6613.6 and 8620.4. For each field, we compared the DIB strengths with the Bayesian distances and extinctions, and the DIB Doppler velocities with the HI emission spectra. For all fields, the DIB strength and the target extinction are well correlated. In case of targets widely distributed in distance, marked steps in DIBs and extinction radial distance profiles match with each other and broadly correspond to the expected locations of spiral arms. For all fields, the DIB velocity structure agrees with HI emission spectra and all detected DIBs correspond to strong NaI lines. This illustrates how DIBs can be used to locate the Galactic interstellar gas and to study its kinematics at the kpc scale.
We prove that the solution of the Kac analogue of Boltzmann's equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few classical statements pertaining to the central limit theorem. In particular, a new proof of the convergence to the Maxwellian distribution is provided, with a rate information both under the sole hypothesis that the initial energy is finite and under the additional condition that the initial distribution has finite moment of order $2+\delta$ for some $\delta$ in $(0,1]$. Moreover, it is proved that finiteness of initial energy is necessary in order that the solution of Kac's equation can converge weakly. While this statement may seem to be intuitively clear, to our knowledge there is no proof of it as yet.
In this paper, we discuss and calculate the electroweak parameters $R_l$, $A_l$, and $N_{\nu}^l$ in a model that combine inverse seesaw with the scotogenic model. Dark matter relic density is also considered. Due to the stringent constraint from the ATLAS experimental data, it is difficult to detect the loop effect on $R_l$, $A_l$ in this model considering both the theoretical and future experimental uncertainties. However, $N_{\nu}^l$ can sometimes become large enough for the future experiments to verify.
A detailed study of the low-temperature physics of an interacting double quantum dot system in a T-shape configuration is presented. Each quantum dot is modeled by a single Anderson impurity and we include an inter-dot electron-electron interaction to account for capacitive coupling that may arise due to the proximity of the quantum dots. By employing a numerical renormalization group approach to a multi-impurity Anderson model, we study the thermodynamical and transport properties of the system in and out of the Kondo regime. We find that the two-stage-Kondo effect reported in previous works is drastically affected by the inter-dot Coulomb repulsion. In particular, we find that the Kondo temperature for the second stage of the two-stage-Kondo effect increases exponentially with the inter-dot Coulomb repulsion, providing a possible path for its experimental observation.
We propose a procedure to determine the effective nuclear shell-model Hamiltonian in a truncated space from a self-consistent mean-field model, e.g., the Skyrme model. The parameters of pairing plus quadrupole-quadrupole interaction with monopole force are obtained so that the potential energy surface of the Skyrme Hartree-Fock + BCS calculation is reproduced. We test our method for $N=Z$ nuclei in the $fpg$- and $sd$-shell regions. It is shown that the calculated energy spectra with these parameters are in a good agreement with experimental data, in which the importance of the monopole interaction is discussed. This method may represent a practical way of defining the Hamiltonian for general shell-model calculations.
We study the lifetimes of TeV-scale heavy neutral leptons (Majorana neutrinos) that appear in a model suggested by Okamura et al. [2]. We develop a convenient way to parametrize the neutrino mass texture of the model, and illustrate our method by calculating the mass spectrum, decay widths, and lifetimes of the heavy particles over the entire parameter space. From the mass spectrum, we find that for most of the parameter space, only two-body decays are relevant in the calculation of the lifetime, with typical values falling in the range of 10^(-26) to 10^(-24) seconds. If the particles discussed here are created at colliders, their lifetimes are short enough for them to decay inside the detector, while long enough to lead to a narrow peak in the invariant mass spectrum of the decay products. However, an analysis by Dicus, Karatas, and Roy [16] suggests that they may be difficult to observe at the LHC.
CP-violation in the loop-mediated photon-photon interactions would modify the birefringence of the quantum vacuum. We discuss the implications of this effect on the PVLAS-Phase II experiment, in which a time-dependent magnetic field is modulated. We show that the violation of CP would imply the existence of characteristic Fourier components, in the intensity spectrum of the outgoing wave. In order to estimate the magnitude of this effect within the Standard Model, we use chiral perturbation theory to compute the theta-term contribution to the coefficient of the leading CP-odd vertex, in the low-energy effective field theory for photon dynamics.
We present the third installment of HI sources extracted from the Arecibo Legacy Fast ALFA extragalactic survey. This dataset continues the work of the Virgo ALFALFA catalog. The catalogs and spectra published here consist of data obtained during the 2005 and 2006 observing sessions of the survey. The catalog consists of 578 HI detections within the range 11h 36m < R.A.(J2000) < 13h 52m and +08 deg < Dec.(J2000) < +12 deg, and cz_sun < 18000 km/s. The catalog entries are identified with optical counterparts where possible through the examination of digitized optical images. The catalog detections can be classified into three categories: (a) detections of high reliability with S/N > 6.5; (b) high velocity clouds in the Milky Way or its periphery; and (c) signals of lower S/N which coincide spatially with an optical object and known redshift. 75% of the sources are newly published HI detections. Of particular note is a complex of HI clouds projected between M87 and M49 that do not coincide with any optical counterparts. Candidate objects without optical counterparts are few. The median redshift for this sample is 6500 km/s and the cz distribution exhibits the local large scale structure consisting of Virgo and the background void and the A1367-Coma supercluster regime at cz_sun ~7000 km/s. Position corrections for telescope pointing errors are applied to the dataset by comparing ALFALFA continuum centroid with those cataloged in the NRAO VLA Sky Survey. The uncorrected positional accuracy averages   27 arcsec ~(21 arcsec ~median) for all sources with S/N > 6.5 and is of order ~21 arcsec ~(16 arcsec ~median) for signals with S/N > 12. Uncertainties in distances toward the Virgo cluster can affect the calculated HI mass distribution.
We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and sufficient conditions for the existence of equivalences between the twisted derived categories of two Kummer surfaces in terms of Hodge isometries between the generalized transcendental lattices of the corresponding abelian surfaces.
This paper studies the components of the moduli space of rank 1, torsion-free sheaves, or compactified Jacobian, of a non-Gorenstein curve. We exhibit a generically reduced component of dimension equal to the arithmetic genus and prove that this is the only non-smoothable component when the curve has a unique singularity that is of finite representation type. Analogous results are proven for the Hilbert scheme of points and the Quot scheme parameterizing quotients of the dualizing sheaf.
Each of several possible definitions of local injectivity for a homomorphism of an oriented graph $G$ to an oriented graph $H$ leads to an injective oriented colouring problem. For each case in which such a problem is solvable in polynomial time, we identify a set $\mathcal{F}$ of oriented graphs such that an oriented graph $G$ has an injective oriented colouring with the given number of colours if and only if there is no $F \in \mathcal{F}$ for which there is a locally-injective homomorphism of $F$ to $G$.
For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1] used the totally asymmetric simple exclusion process (TASEP) to study the height fluctuations in systems of the KPZ universality class for Brownian interfaces with arbitrary diffusion constant. They showed that there is a one-parameter family of long-time distributions, parametrized by the diffusion constant of the initial random height profile. They also computed these distributions numerically by using Monte Carlo (MC) simulations. Here we address this problem analytically and focus on the distribution tails at short times. We determine the (stretched exponential) tails of the height distribution by applying the Optimal Fluctuation Method (OFM) to the KPZ equation. We argue that, by analogy with other initial conditions, the "slow" tail holds at arbitrary times and therefore provides a proper asymptotic to the family of long-time distributions studied in Ref. [1]. We verify this hypothesis by performing large-scale MC simulations of a TASEP with a parallel-update rule. The "fast" tail, predicted by the OFM, is also expected to hold at arbitrary times, at sufficiently large heights.
Lattice path matroids and bicircular matroids are two well-known classes of transversal matroids. In the seminal work of Bonin and de Mier about structural properties of lattice path matroids, the authors claimed that lattice path matroids significantly differ from bicircular matroids. Recently, it was proved that all cosimple lattice path matroids have positive double circuits, while it was shown that there is a large class of cosimple bicircular matroids with no positive double circuits. These observations support Bonin and de Miers' claim. Finally, Sivaraman and Slilaty suggested studying the intersection of lattice path matroids and bicircular matroids as a possibly interesting research topic. In this work, we exhibit the excluded bicircular matroids for the class of lattice path matroids, and we propose a characterization of the graph family whose bicircular matroids are lattice path matroids. As an application of this characterization, we propose a geometric description of $2$-connected lattice path bicircular matroids.
This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we show that Aut(X) is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.
Quantization of the free and interacting Rarita-Schwinger field is considered using the Hamiltonian path-integral formulation. The particular interaction we study in detail is the $\pi N \De$ coupling used in the phenomenology of the pion-nucleon and nucleon-nucleon systems. Within the Dirac constraint analysis, we show that there is an excess of degrees of freedom in the model, as well as the inconsistency related to the Johnson-Sudarshan-Velo-Zwanzinger problem. It is further suggested that couplings invariant under the gauge transformation of the Rarita-Schwinger field are generally free from these inconsistencies. We then construct and briefly analyse some lowest in derivatives gauge-invariant $\pi N \De$ couplings.
Results are presented from NIR spectroscopy of a sample of BzK-selected, massive star-forming galaxies (sBzKs) at 1.5<z<2.3 that were obtained with OHS/CISCO at Subaru and with SINFONI at VLT. Among the 28 sBzKs observed, Ha emission was detected in 14 objects, and for 11 of them the [NII]6583 was also measured. Multiwavelength photometry was also used to derive stellar masses and extinction parameters, whereas Ha and [NII] have allowed us to estimate SFR, metallicities, ionization mechanisms, and dynamical masses. In order to enforce agreement between SFRs from Ha with those derived from rest-frame UV and MIR, additional obscuration for the emission lines (that originate in HII regions) was required compared to the extinction derived from the slope of the UV continuum. We have also derived the stellar mass-metallicity relation, as well as the relation between stellar mass and specific SFR, and compared them to the results in other studies. At a given stellar mass, the sBzKs appear to have been already enriched to metallicities close to those of local star-forming galaxies of similar mass. The sBzKs presented here tend to have higher metallicities compared to those of UV-selected galaxies, indicating that NIR selected galaxies tend to be a chemically more evolved population. The sBzKs show specific SFRs that are systematically higher, by up to ~2 orders of magnitude, compared to those of local galaxies of the same mass. The empirical correlations between stellar mass and metallicity, and stellar mass and specific SFR are then compared with those of population synthesis models constructed either with the simple closed-box assumption, or within an infall scenario. Within the assumptions that are built-in such models, it appears that a short timescale for the star-formation (~100 Myr) and large initial gas mass appear to be required if one wants to reproduce both relations simultaneously.
In this paper, we address the shape-from-shading problem by training deep networks with synthetic images. Unlike conventional approaches that combine deep learning and synthetic imagery, we propose an approach that does not need any external shape dataset to render synthetic images. Our approach consists of two synergistic processes: the evolution of complex shapes from simple primitives, and the training of a deep network for shape-from-shading. The evolution generates better shapes guided by the network training, while the training improves by using the evolved shapes. We show that our approach achieves state-of-the-art performance on a shape-from-shading benchmark.
Low temperatures are necessary for the observation of strongly correlated quantum phases of fermionic atoms in optical lattices. We analyze how the temperature of a Fermi gas is altered when the fermions are loaded into an optical lattice with an underlying harmonic confining potential and show how the temperature can be measured. The temperature of the atoms in the optical lattice determines the fraction of doubly occupied lattice sites of a two-component Fermi gas. We analytically calculate this quantity and find a strong temperature dependence. This fraction can be measured by studying the production of molecules in the lattice using a Feshbach resonance which allows for precise thermometry of atoms in an optical lattice.
A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions with respect to the outermost characteristic and initial data is imposed on the expanded grid boundary. We discuss a related method that removes the need for imposing boundary conditions: the computational domain is excised along a direction spacelike with respect to the innermost going characteristic. We compare the two methods, and provide example evolutions from a code that implements the excision method: evolution of a massless self-gravitating scalar field in spherical symmetry.
Based on the recent finding that the difference in proper time of two clocks in prograde and retrograde equatorial orbits about the Earth is of the order 10^{-7}s per revolution, the possibility of detecting the terrestrial gravitomagnetic field by means of clocks carried by satellites is discussed. A mission taking advantage of this influence of the rotating Earth on the proper time is outlined and the conceptual difficulties are briefly examined.