ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove the polynomiality of the bigraded ring $J_{*,*}^{w, W}(F_4)$ of weak Jacobi forms for the root system $F_4$ which are invariant with respect to the corresponding Weyl group. This work is a continuation of the joint article with V.A. Gritsenko, where the structure of algebras of the weak Jacobi forms related to the root systems of $D_n$ type for $2\leqslant n \leqslant 8$ was studied.
The Receiver Lab Telescope (RLT) is a ground-based terahertz telescope; it is currently the only instrument producing astronomical data between 1 and 2 THz. The capabilities of the RLT have been expanding since observations began in late 2002. Initial observations were limited to the 850 GHz and 1.03 THz windows due to the availability of solid state local oscillators. In the last year we have begun observations with new local oscillators for the 1.3 and 1.5 THz atmospheric windows. These oscillators provide access to the 11-10 and 13-12 lines of CO at 1.267 and 1.497 THz, as well as the [N II] line at 1.461 THz. We report on our first measurements of these high CO transitions, which represent the highest-frequency detections ever made from the ground. We also present initial observations of [N II] and discuss the implications of this non-detection for the standard estimates of the strength of this line.
In this paper, we study the asymptotic behaviour of one-dimensional integrated Ornstein-Uhlenbeck processes driven by $\alpha$-stable L\'{e}vy processes of small amplitude. We prove that the integrated Ornstein-Uhlenbeck process converges weakly to the underlying $\alpha$-stable L\'{e}vy process in the Skorokhod $M_1$-topology which secures the weak convergence of first passage times. This result follows from a more general result about approximations of an arbitrary L\'{e}vy process by continuous integrated Ornstein-Uhlenbeck processes in the $M_1$-topology.
We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,\beta)$ to the locus where $\theta$ degenerates; it then enables us to define the localized GW-invariant, an algebro-geometric analogue of the local invariant of Lee and Parker in symplectic geometry, which coincides with the ordinary GW-invariant when X is proper. It is deformation invariant. Using this, we prove formulas for low degree GW-invariants of minimal general type surfaces with p_g>0 conjectured by Maulik and Pandharipande.
In this paper we analyze a semilinear abstract damped wave-type equation with time delay. We assume that the delay feedback coefficient is variable in time and belonging to $L^1_{loc}([0, +\infty)).$ Under suitable assumptions, we show well-posedness and exponential stability for small initial data. Our strategy combines careful energy estimates and continuity arguments. Some examples illustrate the abstract results.
We have studied the spin dynamics in Pr$_{0.63}$Sr$_{0.37}$MnO$_3$ above and below the Curie temperature $T_C=301$ K. Three distinct new features have been observed: a softening of the magnon dispersion at the zone boundary for $T<T_C$, significant broadening of the zone boundary magnons as $T\to T_C$, and no evidence for residual spin-wave like excitations just above $T_C$. The results are inconsistent with double exchange models that have been successfully applied to higher $T_C$ samples, indicating an evolution of the spin system with decreasing $T_C$.
Rectifier neuron units (ReLUs) have been widely used in deep convolutional networks. An ReLU converts negative values to zeros, and does not change positive values, which leads to a high sparsity of neurons. In this work, we first examine the sparsity of the outputs of ReLUs in some popular deep convolutional architectures. And then we use the sparsity property of ReLUs to accelerate the calculation of convolution by skipping calculations of zero-valued neurons. The proposed sparse convolution algorithm achieves some speedup improvements on CPUs compared to the traditional matrix-matrix multiplication algorithm for convolution when the sparsity is not less than 0.9.
We theoretically investigate spin current and magnetic response induced by the twisting phonon mode in carbon nanotubes via the spin-rotation coupling. An effective magnetic field due to the twisting mode induces both spin and orbital magnetizations. The induced spin and orbital magnetizations have both radial and axial components. We show that ac pure spin current is generated by the twisting phonon mode. The magnitude of the spin current and orbital magnetization for a (10,10) armchair nanotube is estimated as an example. We find that the ac pure spin current is detectable in magnitude when the frequency of the twisting mode is of the order of GHz, and that the orbital magnetization is found to be larger than the spin magnetization.
We analyse observational signatures of magnetic fields for simulations of a Milky-Way like disc with supernova-driven interstellar turbulence and self-consistent chemical processes. In particular, we post-process two simulations data sets of the SILCC Project for two initial amplitudes of the magnetic field, $B_0 = $ 3 and 6 $\mu$G, to study the evolution of Faraday rotation measures (RM) and synchrotron luminosity. For calculating the RM, three different models of the electron density $n_e$ are considered. A constant electron density, and two estimations based on the density of ionized species and the fraction of the total gas, respectively. Our results show that the RM profiles are extremely sensitive to the $n_e$ models, which assesses the importance of accurate electron distribution observations/estimations for the magnetic fields to be probed using Faraday RMs. As a second observable of the magnetic field, we estimate the synchrotron luminosity in the simulations using a semi-analytical cosmic ray model. We find that the synchrotron luminosity decreases over time, which is connected to the decay of magnetic energy in the simulations. The ratios between the magnetic, the cosmic ray, and the thermal energy density indicate that the assumption of equipartition does not hold for most regions of the ISM. In particular, for the ratio of the cosmic ray to the magnetic energy the assumption of equipatition could lead to a wrong interpretation of the observed synchrotron emission.
We present the refinement of the crystal structure of charge-ordered LuFe2O4, based on single-crystal x-ray diffraction data. The arrangement of the different Fe-valence states, determined with bond-valence-sum analysis, corresponds to a stacking of charged Fe bilayers, in contrast to the polar bilayers previously suggested. This arrangement is supported by an analysis of x-ray magnetic circular dichroism spectra, which also evidences a strong charge-spin coupling. The non-polar bilayers are inconsistent with charge order based ferroelectricity.
We present a statistical comparison of three different estimates of cluster mass, namely, the dynamical masses obtained from the velocity dispersion of optical galaxies, the X-ray masses measured from the temperature of X-ray emitting gas under the assumption of isothermal hydrostatic equilibrium, and the gravitational lensing masses derived from the strong/weak distortions of background galaxy images. Using a sample of 29 lensing clusters available in literature, we have shown that the dynamical masses are in agreement with the gravitational lensing masses, while the X-ray method has systematically underestimated cluster masses by a factor 2-3 as compared with the others. These results imply that galaxies indeed trace the gravitational potential of their clusters, and there is no bias between the velocities of the dark matter particles and the galaxies in clusters. The X-ray cluster mass discrepancy is probably from the simplification in the models for the X-ray gas distribution and dynamical evolution.
The electronic structure of double perovskite Pr2MnNiO6 is studied using core x-ray photoelectron spectroscopy and x-ray absorption spectroscopy. The 2p x-ray absorption spectra show that Mn and Ni are in 2+ and 4+ states respectively. Using charge transfer multiplet analysis of Ni and Mn 2p XPS spectra, we find charge transfer energies {\Delta} of 3.5 and 2.5 eV for Ni and Mn respectively. The ground state of Ni2+ and Mn4+ reveal a higher d electron count of 8.21 and 3.38 respectively as compared to the atomic values of 8.00 and 3.00 respectively thereby indicating the covalent nature of the system. The O 1s edge absorption spectra reveal a band gap of 0.9 eV which is comparable to the value obtained from first principle calculations for U-J >= 2 eV. The density of states clearly reveal a strong p-d type charge transfer character of the system, with band gap proportional to average charge transfer energy of Ni2+ and Mn4+ ions.
Advances in our numerical and theoretical understanding of gamma-ray burst afterglow processes allow us to construct models capable of dealing with complex relativistic jet dynamics and non-thermal emission, that can be compared directly to data from instruments such as Swift. Because afterglow blast waves and power law spectra are intrinsically scale-invariant under changes of explosion energy and medium density, templates can be generated from large-scale hydrodynamics simulations. This allows for iterative template-based model fitting using the physical model parameters (quantifying the properties of the burster, emission and observer) directly as fit variables. Here I review how such an approach to afterglow analysis works in practice, paying special attention to the underlying model assumptions, possibilities, caveats and limitations of this type of analysis. Because some model parameters can be degenerate in certain regions of parameter space, or unconstrained if data in a limited number of a bands is available, a Bayesian approach is a natural fit. The main features of the standard afterglow model are reviewed in detail.
We investigate the electronic structure of SrMnO$_3$ with Density Functional Theory (DFT) plus Dynamical Mean-Field Theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal field splitting of the Mn-$3d$ orbitals and their separation from the O-2$p$ bands, SrMnO$_3$ is a material where on first sight a 3-band $d$-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a $d$-$dp$ model we observe a splitting of the \tg lower Hubbard band into a more complex spectral structure, not observable in $d$-only models. To illustrate these high-frequency differences we employ the recently developed Fork Tensor Product State (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-frequency axis. We find that the spectral structure of a 5-band $d$-$dp$ model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full 5-band DMFT calculations directly on the real-frequency axis.
We compute gauge theories of the Lorentz group. We discuss non-interacting, and interacting fermionic systems. The interacting system combines a local with a global Lorentz group, i.e, discusses a $SO(3,1)_{l}\times SO(3,1)_{g}$-theory. We compute the equations of motion and conservation laws for the fermionic matter current. The core of our work is the prediction of some new form of monopoles we call 'Dirac-Clifford-'t Hooft-Polyakov'-monopole. It resides in a state similar to color-flavor locking. Dirac-Clifford-'t Hooft-Polyakov-monopoles are invariant under global Lorentz transformations and are predicted to form vortices. The theory is renormalizable, since all Goldstone-Nambu modes are converted into massive vector gauge fields.
Of the almost 40 star forming galaxies at z>~5 (not counting QSOs) observed in [CII] to date, nearly half are either very faint in [CII], or not detected at all, and fall well below expectations based on locally derived relations between star formation rate (SFR) and [CII] luminosity. Combining cosmological zoom simulations of galaxies with SIGAME (SImulator of GAlaxy Millimeter/submillimeter Emission) we have modeled the multi-phased interstellar medium (ISM) and its emission in [CII], [OI] and [OIII], from 30 main sequence galaxies at z~6 with star formation rates ~3-23Msun/yr, stellar masses ~(0.7-8)x10^9Msun, and metallicities ~(0.1-0.4)xZsun. The simulations are able to reproduce the aforementioned [CII]-faintness at z>5, match two of the three existing z>~5 detections of [OIII], and are furthermore roughly consistent with the [OI] and [OIII] luminosity relations with SFR observed for local starburst galaxies. We find that the [CII] emission is dominated by the diffuse ionized gas phase and molecular clouds, which on average contribute ~66% and ~27%, respectively. The molecular gas, which constitutes only ~10% of the total gas mass is thus a more efficient emitter of [CII] than the ionized gas making up ~85% of the total gas mass. A principal component analysis shows that the [CII] luminosity correlates with the star formation activity as well as average metallicity. The low metallicities of our simulations together with their low molecular gas mass fractions can account for their [CII]-faintness, and we suggest these factors may also be responsible for the [CII]-faint normal galaxies observed at these early epochs.
We extend to arbitrary characteristic some known results about automorphisms of complex Enriques surfaces that act trivially on the cohomology or the cohomology modulo torsion.
At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example nearest-neighbour interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second--rank) order, in addition to the primary first-rank one; on the other hand, in the Literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with Finite-Size Scaling analysis have been used for characterizing its critical behaviour; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder.
Decayless kink oscillations of solar coronal loops (or decayless oscillations for short) have attracted great attention since their discovery. Coronal bright points (CBPs) are mini-active regions and consist of loops with a small size. However, decayless oscillations in CBPs have not been widely reported. In this study, we identified this kind of oscillations in some CBPs using 171 \AA\, images taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). After using the motion magnification algorithm to increase oscillation amplitudes, we made time-distance maps to identify the oscillatory signals. We also estimated the loop lengths and velocity amplitudes. We analysed 23 CBPs, and found 31 oscillation events in 16 of them. The oscillation periods range from 1 to 8 minutes (on average about 5 minutes), and the displacement amplitudes have an average value of 0.07 Mm. The average loop length and velocity amplitude are 23 Mm and 1.57 \kms, respectively. Relationships between different oscillation paraments are also examined. Additionally, we performed a simple forward model to illustrate how these sub-pixel oscillation amplitudes (less than 0.4 Mm) could be detected. Results of the model confirm the reliability of our data processing methods. Our study shows for the first time that decayless oscillations are common in small-scale loops of CBPs. These oscillations allow for seismological diagnostics of the Alfv\'{e}n speed and magnetic field strength in the corona.
Cosmological models have granted dwarf galaxies a key role: their properties constrain the distribution of dark matter and the physical evolution of their hosts. There is increasing evidence that objects with masses of dwarf galaxies form in the tidal tails of colliding galaxies and speculations that they could become satellite-like galaxies around their progenitors and thus be cosmologically important. Yet, whether these "Tidal Dwarf Galaxies" (TDGs) candidates are really long-lived and not only present in young interacting systems is still an open question to which numerical simulations may give answers. We present a set of 96 simulations of colliding galaxies with various mass ratios and encounter geometries, and statistically study the evolution of their TDG candidates. Among the 593 substructures initially identified in tidal tails, about 75% fall back onto their progenitor or are disrupted in a few 10^8 years. The remaining 25% become long-lived bound objects that typically survive more than 2Gyr with masses above 10^8 M_sun. These long-lived, satellite-like objects, are found to form in the outer most regions of the tidal tails. We infer several basic properties that dwarf galaxies should meet to have a tidal origin and apply these criteria to the Local Group dwarfs. We also find that the presence of TDGs would foster the anisotropy observed in the distribution of satellite galaxies around their host. Identifying the conditions required for interacting systems to form long-lived tidal dwarfs, we roughly estimate their contribution to the overall population of dwarfs. We conclude that a small but significant fraction of them - typically a few percent, and possibly more in dense environments or around early-type galaxies - could be of tidal origin.
Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "$ \phi $-$ \eta $-$ \theta $ model" proposed by Kobayashi [RIMS Kokyuroku, 1210 (2001), 68-77] as a phase-field model of planar grain boundary motion under isothermal solidification. Although each of the systems has specific characteristics and mathematical difficulties, the proofs of the main theorems are based on the time discretization method by means of a common approximating problem. As a consequence, we provide a uniform solution method for a wide scope of parabolic systems associated with the $ \phi $-$ \eta $-$ \theta $ model.
As adaptive optics technology continues to improve, the stellar coronagraph will play an ever increasing role in ground-based high-contrast imaging observations. Though several different image masks exist for the most common type of coronagraph, the Lyot coronagraph, it is not yet clear what level of wavefront correction must be reached in order to gain, either in starlight suppression or observing efficiency, by implementing a more sophisticated design. In this paper, we model image plane Lyot-style coronagraphs and test their response to a range of wavefront correction levels, in order to identify regimes of atmospheric compensation where the use of hard-edge, Gaussian, and band-limited image masks becomes observationally advantageous. To delineate performances, we calculate the speckle noise floor mean intensity. We find that apodized masks provide little improvement over hard-edge masks until on-sky Strehl ratios exceed $\sim0.88 \: S_{qs}$, where $S_{qs}$ is the intrinsic Strehl ratio provided by the optical system. Above this value, 4th-order band-limited masks out-perform Gaussian masks by generating comparable contrast with higher Lyot stop throughput. Below this level of correction, hard-edge masks may be preferentially chosen, since they are less susceptible to low-order aberration content. The use of higher-order band-limited masks is relegated to situations where quasi-static residual starlight cannot be sufficiently removed from the search area with speckle-nulling hardware.
Here, we numerically simulate probabilistic elementary entangling operations between rail-encoded photons for the purpose of scalable universal quantum computation or communication. We propose grouping logical qubits into single-photon blocks wherein single-qubit rotations and the CNOT gate are fully deterministic and simple to implement. Inter-block communication is then allowed through said probabilistic entangling operations. We find a promising trend in the increasing probability of successful inter-block communication as we increase the number of optical modes operated on by our elementary entangling operations.
We present a retuning of the IllustrisTNG baryonic physics model which can be used to run large-box realistic cosmological simulations with a lower resolution. This new model employs a lowered gas density threshold for star formation and reduced energy releases by stellar and black hole feedback. These changes ensure that our simulations can produce sufficient star formation to closely match the observed stellar and gas properties of galaxies and galaxy clusters, despite having $\sim$160 times lower mass resolution than the simulations used to tune the fiducial IllustrisTNG model. Using the retuned model, we have simulated Hu-Sawicki $f(R)$ gravity within a $301.75h^{-1}{\rm Mpc}$ box. This is, to date, the largest simulation that incorporates both screened modified gravity and full baryonic physics, offering a large sample ($\sim$500) of galaxy clusters and $\sim$8000 galaxy groups. We have reanalysed the effects of the $f(R)$ fifth force on the scaling relations between the cluster mass and four observable proxies: the mass-weighted gas temperature, the Compton $Y$-parameter of the thermal Sunyaev-Zel'dovich effect, the X-ray analogue of the $Y$-parameter, and the X-ray luminosity. We show that a set of mappings between the $f(R)$ scaling relations and their $\Lambda$CDM counterpart, which have been tested in a previous work using a much smaller cosmological volume, are accurate to within a few percent for the $Y$-parameters and $\lesssim7\%$ for the gas temperature for cluster-sized haloes ($10^{14}M_{\odot}\lesssim M_{500}\lesssim10^{15}M_{\odot}$). These mappings will be important for unbiased constraints of gravity using the data from ongoing and upcoming cluster surveys.
This paper is a survey of various results and techniques in first passage percolation, a random process modeling a spreading fluid on an infinite graph. The latter half of the paper focuses on the connection between first passage percolation and a certain class of stochastic growth and competition models.