ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop the BRST approach to Lagrangian formulation for massive bosonic and massless fermionic higher spin fields on a flat space-time of arbitrary dimension. General procedure of gauge invariant Lagrangian construction describing the dynamics of the fields with any spin is given. No off-shell constraints on the fields (like tracelessness) and the gauge parameters are imposed. The procedure is based on construction of new representations for the closed algebras generated by the constraints defining irreducible representations of the Poincare group. We also construct Lagrangians describing propagation of all massive bosonic fields and massless fermionic fields simultaneously.
We extend our earlier shear-transformation-zone (STZ) theory of amorphous plasticity to include the effects of thermally assisted molecular rearrangements. This version of our theory is a substantial revision and generalization of conventional theories of flow in noncrystalline solids. As in our earlier work, it predicts a dynamic transition between jammed and flowing states at a yield stress. Below that yield stress, it now describes thermally assisted creep. We show that this theory accounts for the experimentally observed strain-rate dependence of the viscosity of metallic glasses, and that it also captures many of the details of the transient stress-strain behavior of those materials during loading. In particular, it explains the apparent onset of superplasticity at sufficiently high stress as a transition between creep at low stresses and plastic flow near the yield stress. We also argue that there are internal inconsistencies in the conventional theories of these deformation processes, and suggest ways in which further experimentation as well as theoretical analysis may lead to better understanding of a broad range of nonequilibrium phenomena.
We study the Torelli locus T_g in the moduli space A_g of abelian varieties. We consider special subvarieties (Shimura subvarieties) contained in the Torelli locus. We review the construction of some non-trivial examples, and we discuss some conjectures, techniques and recent progress.
Schinzel's Hypothesis H is a general conjecture in number theory on prime values of polynomials that generalizes, e.g., the twin prime conjecture and Dirichlet's theorem on primes in arithmetic progression. We prove an arithmetic analog of this conjecture for polynomial rings over pseudo algebraically closed fields. This implies results over large finite fields. A main tool in the proof is an irreducibility theorems \`a la Hilbert.
We examine the properties of a previously discovered population of globular clusters in the heart of the rich galaxy cluster Abell 1185 that might be intergalactic in nature. Deep images obtained with the Advanced Camera for Surveys (ACS) aboard Hubble Space Telescope (HST) confirm the presence of ~ 1300 globular clusters brighter than I_{F814W} = 27.3 mag in a field devoid of any large galaxies. The luminosities and colors of these objects are found to be similar to those of metal-poor globular clusters observed in many galaxies to date. Although a significant fraction of the detected globular clusters undoubtedly reside in the outer halos of galaxies adjacent to this field, detailed modeling of their distribution suggests that the majority of these objects are likely to be intergalactic, in the sense that they are not gravitationally bound to any individual galaxy. We conclude that the true nature and origin of the globular cluster population in the core of A1185 -- galactic residents or intergalactic wanderers -- remains uncertain, and suggest how future observation could resolve this ambiguity.
We present high-resolution spectral line and continuum VLBI and VLA observations of the nuclear region of NGC 253 at 22 GHz. While the water vapor masers in this region were detected on arcsecond and milliarcsecond scales, we could not detect any compact continuum emission with a 5 sigma upper limit of ~ 1 mJy. The observations reveal that the water maser emission is not related to a possible low-luminosity active galactic nucleus but is almost certainly associated with star-formation activity. Not detecting any compact continuum source on milliarcsecond scales also questions the presence of a - previously assumed - active nucleus in NGC 253.
The Bianchi I metric describes a homogeneous, but anisotropic universe and is commonly used to fit cosmological data. A fit to the angular distribution of 740 supernovae of type Ia with measured redshift and apparent luminosity is presented. It contains an intriguing, yet non-significant signal of a preferred direction in the sky. The Large Synoptic Survey Telescope being built in Chile should measure some 500 000 supernovae within the next 20 years and verify or falsify this signal.
We analyze two approaches to elimination of a fast variable (velocity) in stochastic systems: moment and cumulant formalisms. With these approaches, we obtain the corresponding Smoluchovski-type equations, which contain only the coordinate/phase variable. The adiabatic elimination of velocity in terms of cumulants and moments requires the first three elements. However, for the case of small inertia, the corrected Smoluchowski equation in terms of moments requires five elements, while in terms of cumulants the same first three elements are sufficient. Compared to the method based on the expansion of the velocity distribution in Hermite functions, the considered approaches have comparable efficiency, but do not require individual mathematical preparation for the case of active Brownian particles, where one has to construct a new basis of eigenfunctions instead of the Hermite ones.
Consider the number of permutations in the symmetric group on n letters that contain c copies of a given pattern. As c varies (with n held fixed) these numbers form a sequence whose properties we study for the monotone patterns and the patterns 1, l, l-1, ..., 2. We show that, except for the patterns 1, 2 and 2, 1 where the sequence is well-known to be log concave, there are infinitely many n where the sequence has internal zeros.
Solar observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA) facilitate studying the atmosphere of the Sun at chromospheric heights at high spatial and temporal resolution at millimeter wavelengths. ALMA intensity data at mm-wavelengths are used for a first detailed systematic assessment of the occurrence and properties of small-scale dynamical features in the quiet Sun. ALMA Band 3 data (~ $3$ mm / $100$ GHz) with spatial resolution ~ $1.4$ - $2.1$ arcsec and a duration of ~ $40$ min are analysed together with SDO/HMI magnetograms. The temporal evolution of the mm-maps is studied to detect pronounced dynamical features which are connected to dynamical events via a k-means clustering algorithm. The physical properties of the resulting events are studied and it is explored if they show properties consistent with propagating shock waves. For this purpose, observable shock wave signatures at mm wavelengths are calculated from one- and three-dimensional model atmospheres. There are 552 dynamical events detected with an excess in brightness temperature ($\Delta T_\text{b}$) of at least $\geq 400$ K. The events show a large variety in size up to ~ $9$ arcsec, amplitude $\Delta T_\text{b}$ up to ~ $1200$ K with typical values between ~ $450$ - $750$ K and lifetime at FWHM of $\Delta T_\text{b}$ between ~ $43$ - $360$ s, with typical values between ~ $55$ - $125$ s. Furthermore, many of the events show signature properties that suggest that they are likely produced by propagating shock waves. There are a lot of small-scale dynamic structures detected in the Band 3 data, even though the spatial resolution sets limitations of the size of events that can be detected. The amount of dynamic signatures in the ALMA mm data is very low in areas with photospheric footpoints with stronger magnetic fields, which is consistent with the expectation for propagating shock waves.
Let $E_0,\ldots,E_n$ be a partition of the set of prime numbers, and define $E_j(x) := \sum_{p \in E_j \atop p \leq x} \frac{1}{p}$. Define $\pi(x;\mathbf{E},\mathbf{k})$ to be the number of integers $n \leq x$ with $k_j$ prime factors in $E_j$ for each $j$. Basic probabilistic heuristics suggest that $x^{-1}\pi(x;\mathbf{E},\mathbf{k})$, modelled as the distribution function of a random variable, should satisfy a joint Poisson law with parameter vector $(E_0(x),\ldots,E_n(x))$, as $x \rightarrow \infty$. We prove an asymptotic formula for $\pi(x;\mathbf{E},\mathbf{k})$ which contradicts these heuristics in the case that for each $j$, $E_j(x)^2 \leq k_j \leq \log^{\frac{2}{3}-\epsilon} x$ for each $j$ under mild hypotheses. As a particular application, we prove an asymptotic formula regarding integers with prime factors from specific arithmetic progressions, which generalizes a result due to Delange.
In the framework of chiral quark model, the mass spectrum of $\eta_c(ns) (n=1,...,6)$ is studied with Gaussian expansion method. With the wave functions obtained in the study of mass spectrum, the open flavor two-body strong decay widths are calculated by using $^3P_0$ model. The results show that the masses of $\eta_c(1S)$ and $\eta_c(2S)$ are consistent with the experimental data. The explanation of X(3940) as $\eta_c(3S)$ is disfavored for X(3940) is a narrow state, $\Gamma=37^{+26}_{-15} \pm 8 $ MeV, while the open flavor two-body strong decay width of $\eta_c(3S)$ is about 200 MeV in our calculation. Although the mass of X(4160) is about 100 MeV less than that of $\eta_c(4S)$, the assignment of X(4160) as $\eta_c(4S)$ can not be excluded because the open flavor two-body strong decay width of $\eta_c(4S)$ is consistent with the experimental value of X(4160) and the branching ratios of $\eta_c(4S)$ are compatible with that of X(4160), and the mass of $\eta_c(4S)$ can be shifted downwards by taking into account the coupling effect of the open charm channels. There are still no good candidates to $\eta_c(5S)$ and $\eta_c(6S)$.
Blazar OJ287 exhibits large thermal flares at least twice every 12 years. The times of these flares have been predicted successfully using the model of a quasi-Keplerian eccentric black hole binary where the secondary impacts the accretion disk of the primary, creating the thermal flares. New measurements of the historical light curve have been combined with the observations of the 2015 November/December flare to identify the impact record since year 1886, and to constrain the orbit of the binary. The orbit solution shows that the binary period, now 12.062 year, is decreasing at the rate of 36 days per century. This corresponds to an energy loss to gravitational waves that is 6.5 +- 4 % less than the rate predicted by the standard quadrupolar gravitational wave (GW) emission. We show that the difference is due to higher order gravitational radiation reaction terms that include the dominant order tail contributions.
The chiral and pion superfluidity phase transitions are studied within NJL model. The model parameters are fitted by pion mass and decay constant together with recent isospin density from lattice QCD. The dense and cold QCD matter suffered the first order chiral phase transition during the quark chemical potential increase. Based on the studies of phase structures, the equation of states~(EoS) of dense QCD matter are calculated with the conditions of $\beta$ equilibrium and electric charge neutrality. Take the EoS as input, the mass-radius relation of neutron stars are predicted, which is consistent with recent observations of heaviest mass and radius of $1.4M_\odot$.
The Ophiuchus stream is a short arc-like stellar feature of uncertain origin located $\sim 5$ kpc North of the Galactic centre. New proper motions from the second $Gaia$ data release reconcile the direction of motion of stream members with the stream arc, resolving a puzzling mismatch reported in earlier work. We use N-body simulations to show that the stream is likely only on its second pericentric passage, and thus was formed recently. The simulations suggest that the entire disrupted progenitor is visible in the observed stream today, and that little further tidal debris lies beyond the ends of the stream. The luminosity, length, width, and velocity dispersion of the stream suggest a globular cluster (GC) progenitor substantially fainter and of lower surface brightness than estimated in previous work, and unlike any other known globulars in the Galaxy. This result suggests the existence of clusters that would extend the known GC population to fainter and more weakly bound systems than hitherto known. How such a weakly-bound cluster of old stars survived until it was disrupted so recently, however, remains a mystery. Integrating backwards in time, we find that the orbits of Sagittarius and Ophiuchus passed within $\sim 5$ kpc of each other about $\sim 100$ Myrs ago, an interaction that might help resolve this puzzle.
Critical obstacles in training classifiers to detect facial actions are the limited sizes of annotated video databases and the relatively low frequencies of occurrence of many actions. To address these problems, we propose an approach that makes use of facial expression generation. Our approach reconstructs the 3D shape of the face from each video frame, aligns the 3D mesh to a canonical view, and then trains a GAN-based network to synthesize novel images with facial action units of interest. To evaluate this approach, a deep neural network was trained on two separate datasets: One network was trained on video of synthesized facial expressions generated from FERA17; the other network was trained on unaltered video from the same database. Both networks used the same train and validation partitions and were tested on the test partition of actual video from FERA17. The network trained on synthesized facial expressions outperformed the one trained on actual facial expressions and surpassed current state-of-the-art approaches.
We prove a kind of reflection principle for certain non-archimedean $L$-series in positive characteristic. We also prove the pseudo-cyclicity and pseudo-nullity of certain several variable generalizations of the class modules introduced by L. Taelman in 2010.
We study the effect of large-scale magnetic fields on the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the innermost regions of accretion discs around black holes (BHs). These global modes could provide an explanation for the high-frequency quasi-periodic oscillations (HFQPOs) observed in BH X-ray binaries. There may be observational evidence for the presence of such large-scale magnetic fields in the disks since episodic jets are observed in the same spectral state when HFQPOs are detected. We find that a large-scale poloidal magnetic field can enhance the corotational instability and increase the growth rate of the purely hydrodynamic overstable p-modes. In addition, we show that the frequencies of these overstable p-modes could be further reduced by such magnetic fields, making them agree better with observations.
An important family of stochastic processes arising in many areas of applied probability is the class of L\'evy processes. Generally, such processes are not simulatable especially for those with infinite activity. In practice, it is common to approximate them by truncating the jumps at some cut-off size $\varepsilon$ ($\varepsilon\searrow 0$). This procedure leads us to consider a simulatable compound Poisson process. This paper first introduces, for this setting, the statistical Romberg method to improve the complexity of the classical Monte Carlo one. Roughly speaking, we use many sample paths with a coarse cut-off $\varepsilon^{\beta},$ $\beta\in(0,1)$, and few additional sample paths with a fine cut-off $\varepsilon$. Central limit theorems of Lindeberg-Feller type for both Monte Carlo and statistical Romberg method for the inferred errors depending on the parameter $\varepsilon$ are proved. This leads to an accurate description of the optimal choice of parameters with explicit limit variances. Afterwards, the authors propose a stochastic approximation method of finding the optimal measure change by Esscher transform for L\'evy processes with Monte Carlo and statistical Romberg importance sampling variance reduction. Furthermore, we develop new adaptive Monte Carlo and statistical Romberg algorithms and prove the associated central limit theorems. Finally, numerical simulations are processed to illustrate the efficiency of the adaptive statistical Romberg method that reduces at the same time the variance and the computational effort associated to the effective computation of option prices when the underlying asset process follows an exponential pure jump CGMY model.
We present a simple protocol to purify a coherent-state superposition that has undergone a linear lossy channel. The scheme constitutes only a single beam splitter and a homodyne detector, and thus is experimentally feasible. In practice, a superposition of coherent states is transformed into a classical mixture of coherent states by linear loss, which is usually the dominant decoherence mechanism in optical systems. We also address the possibility of producing a larger amplitude superposition state from decohered states, and show that in most cases the decoherence of the states are amplified along with the amplitude.
The detection and recognition of unconstrained text is an open problem in research. Text in comic books has unusual styles that raise many challenges for text detection. This work aims to binarize text in a comic genre with highly sophisticated text styles: Japanese manga. To overcome the lack of a manga dataset with text annotations at a pixel level, we create our own. To improve the evaluation and search of an optimal model, in addition to standard metrics in binarization, we implement other special metrics. Using these resources, we designed and evaluated a deep network model, outperforming current methods for text binarization in manga in most metrics.
In this work, thick branes in Rastall gravity are investigated. Three types of maximally symmetric thick brane models are constructed and the linear tensor perturbation is analyzed. In the flat brane model, the tensor modes of the perturbation are either unstable or nonlocalizable for a nonvanishing Rastall parameter. In the de Sitter brane model, only the ground state of the tensor mode is localized. In the anti-de Sitter brane model, the number of the bound tensor states is infinity. For both the de Sitter and anti-de Sitter brane models, the condition of stability for the Rastall parameter is obtained.
It is shown that the derivation of the Hawking radiation from a rotating black hole on the basis of the tunneling mechanism is greatly simplified by using the technique of the dimensional reduction near the horizon. This technique is illustrated for the original derivation by Parikh and Wilczek, but it is readily applied to a variant of the method such as suggested by Banerjee and Majhi.
The effects of growth rate (G_r), deposition temperature (T_d), film thickness (t_F), and substrate induced strain (epsilon) on morphological, crystallographic and magnetic characteristics of equiatomic CoPt epitaxial films synthesized with PLD are investigated. The (001) substrates of MgO, STO and LAO provide different degree of epitaxial strain for growth of the disordered face centered cubic (fcc) and ordered face centered tetragonal (L1_0) phases of CoPt. The films deposited at T_d~600 ^0C on all three substrates are fcc with in-plane magnetization and a narrow hysteresis loop of width~200 Oe. The L1_0 phase, stabilized only at T_d~700 ^0C becomes predominantly c-axis oriented as T_d is increased to 800 ^0C. While the crystallographic structure of the films depends solely on the T_d, their microstructure and magnetization characteristics are decided by the growth rate. At the higher G_r (~1A/sec) the L1_0 films have a maze-like structure which converts to a continuous film as the t_F is increased from 20 to 50 nm. The H_c of these films increases as the L1_0 phase fraction grows with T_d and its orientation becomes out of the film plane. The evolution of microstructure with T_d is remarkably different at lower growth rate (~0.4A /sec). Here the structure changes from a self-similar fractal pattern to an assembly of nano-dots as the T_d is raised from 700 to 800 ^0C, and is understood in terms of the imbalance between strain and interfacial energies. MFM of such films reveals no distinct domain walls within the nano-islands while a clear contrast is seen between the islands of reversed magnetization. The simple picture of coherent rotation of moment appears incompatible with the time dependence of the remanent magnetization in these films.
We present a complete survey of CO 1->0 emission in the Local Group dwarf irregular IC 10. The survey, conducted with the BIMA interferometer, covers the stellar disk and a large fraction of the extended HI envelope with the sensitivity and resolution necessary to detect individual giant molecular clouds (GMCs) at the distance of IC 10 (950 kpc). We find 16 clouds with a total CO luminosity of 1 x 10^6 K km s^-1 pc^2, equivalent to 4 x 10^6 Msun of molecular gas using the Galactic CO-to-H2 conversion factor. Observations with the ARO 12m find that BIMA may resolve out as much as 50% of the CO emission, and we estimate the total CO luminosity as 2.2 x 10^6 K km s^-1 pc^2. We measure the properties of 14 GMCs from high resolution OVRO data. These clouds are very similar to Galactic GMCs in their sizes, line widths, luminosities, and CO-to-H2 conversion factors despite the low metallicity of IC 10 (Z ~ 1/5 Zsun). Comparing the BIMA survey to the atomic gas and stellar content of IC 10 we find that most of the CO emission is coincident with high surface density HI. IC 10 displays a much higher star formation rate per unit molecular (H2) or total (HI+H2) gas than most galaxies. This could be a real difference or may be an evolutionary effect - the star formation rate may have been higher in the recent past.
Using data from the Green Bank Telescope, we analyze the radio continuum (free-free) and radio recombination line (RRL) emission of the compact HII region NGC 7538 (Sharpless 158). We detect extended radio continuum and hydrogen RRL emission beyond the photodissociation region (PDR) toward the north and east, but a sharp decrease in emission toward the south and west. This indicates that a non-uniform PDR morphology is affecting the amount of radiation "leaking" through the PDR. The strongest carbon RRL emission is found in the western PDR that appears to be dense. We compute a leaking fraction $f_R = 15 \pm 5$ % of the radio continuum emission measured in the plane of the sky which represents a lower limit when accounting for the three-dimensional geometry of the region. We detect an average $^4\textrm{He}^+/\textrm{H}^+$ abundance ratio by number of $0.088 \pm 0.003$ inside the HII region and a decrease in this ratio with increasing distance from the region beyond the PDR. Using Herschel Space Observatory data, we show that small dust temperature enhancements to the north and east of NGC 7538 coincide with extended radio emission, but that the dust temperature enhancements are mostly contained within a second PDR to the east. Unlike the giant HII region W43, the radiation leaking from NGC 7538 seems to only affect the local ambient medium. This suggests that giant HII regions may have a large effect in maintaining the ionization of the interstellar medium.
The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Amp\`ere type known as generated Jacobian equations. These equations, whose general existence theory has been recently developed by Trudinger go beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under a condition analogous to the A3w condition of Ma, Trudinger and Wang. Estimates of this type have played an important role in the regularity theory for optimal transport maps and were previously unknown in this context, including the important case of the near field reflector problem.