ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use a new method to model fluctuations of the Lyman-Werner (LW) and Lyman-alpha radiation backgrounds at high redshift. At these early epochs the backgrounds are symptoms of a universe newly lit with its first stars. LW photons (11.5-13.6 eV) are of particular interest because they dissociate molecular hydrogen, the primary coolant in the first minihalos. By using a variation of the halo model, we efficiently generate power spectra for any choice of radiation background. We find that the LW power spectrum typically traces the matter power spectrum at large scales but turns over at the scale corresponding to the effective `horizon' of LW photons (~100 comoving Mpc), unless the sources are extremely rare. The series of horizons that characterize the Lyman-alpha flux profile shape the fluctuations of that background in a similar fashion, though those imprints are washed out once one considers fluctuations in the brightness temperature of the 21-cm signal. The Lyman-alpha background strongly affects the redshifted 21-cm signal at just about the time the LW background begins to dissociate molecular hydrogen, so measuring that background's properties will reveal important information about the transition from early Population III stars to more normal stars. Around this time we find that fluctuations in the LW background are weak; the fractional standard deviation is less than ~0.5 on scales > 10 cMpc, only rising to be of order unity on scales < 1 cMpc. This should not lead to substantial spatial fluctuations in molecular hydrogen content, except at the earliest times. Even then, most halos form far from other sources, so the transition from star formation in low-mass to high-mass halos is rather homogeneous across the universe.
We propose a scheme for measuring the Berry phase in the vibrational degree of freedom of a trapped ion. Starting from the ion in a vibrational coherent state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the internal degrees of freedom of the ion. Our method can be applied to preparation of Schr\"odinger cat states.
Perturbative aspects of ultraviolet and infrared dynamics of noncommutative quantum field theory is examined in detail. It is observed that high loop momentum contribution to the nonplanar diagram develops a new infrared singularity with respect to the external momentum. This singular behavior is closely related to that of ultraviolet divergence of planar diagram. It is also shown that such a relation is precise in noncommutative Yang-Mills theory, but the same feature does not persist in noncommutative generalization of QED.
First-principles calculations using the plane-wave pseudopotential method within the generalized gradient approximation method were performed to study the pressure dependence of the structural, elastic, electronic and optical properties for the half-Heusler compounds ScPtSb and YPtSb in a cubic MgAgAs-type structure. The calculations were performed with the inclusion of spin-orbit coupling. The calculated equilibrium lattice parameters are in good agreement with the available experimental and theoretical values. The crystal rigidity and mechanical stability were discussed using the elastic constants and related parameters, namely bulk modulus, shear modulus, Debye temperature, Poisson's coefficient, Young's modulus and isotropic sound velocities. The calculated electronic band structures show that ScPtSb has an indirect gap of $\Gamma-X $ type, whereas YPtSb has a direct band gap of $\Gamma -\Gamma $ type. Furthermore, the effect of pressure on the optical properties, namely the dielectric function, absorption spectrum, refractive index, extinction coefficient, reflectivity and energy-loss spectrum is investigated for both compounds ScPtSb and YPtSb.
Grid-based magnetohydrodynamic (MHD) simulations have proven invaluable for the study of astrophysical accretion disks. However, the fact that angular momentum transport in disks is mediated by MHD turbulence (with structure down to very small scales) raises the concern that the properties of the modeled accretion disks are affected by the finite numerical resolution of the simulation. By implementing an orbital advection algorithm into the Athena code in cylindrical geometry, we have performed a set of global (but unstratified) Newtonian disk simulations extending up to resolutions previously unattained. We study the convergence of these models as a function of spatial resolution and initial magnetic field geometry. The usual viscosity parameter ($\alpha$) or the ratio of thermal-to-magnetic pressure ($\beta$) are found to be poor diagnostics of convergence, whereas the average tilt angle of the magnetic field in the $(r,\phi)$-plane is a very good diagnostic of convergence. We suggest that this is related to the saturation of the MHD turbulence via parasitic modes of the magnetorotational instability. Even in the case of zero-net magnetic flux, we conclude that our highest resolution simulations (with 32-zones and 64-zones per vertical scale height) have achieved convergence.   Our global simulations reach resolutions comparable to those used in local, shearing box models of MHD disk turbulence. We find that the saturation predictors derived from local simulations correspond well to the instantaneous correlations between local flux and stress found in our global simulations. However, the conservation of magnetic flux implicit in local models is not realized in our global disks. Thus, the magnetic connectivity of an accretion disk represents physics that is truly global and cannot be captured in any ab-initio local model.
Squashed entanglement and entanglement of purification are quantum mechanical correlation measures and defined as certain minimisations of entropic quantities. We present the first non-trivial calculations of both quantities. Our results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost. This property is known as "locking" and has previously been observed for other correlation measures, such as the accessible information, entanglement cost and the logarithmic negativity.   In the case of squashed entanglement, the results are obtained with the help of an inequality that can be understood as a quantum channel analogue of well-known entropic uncertainty relations. This inequality may prove a useful tool in quantum information theory.   The regularised entanglement of purification is known to equal the entanglement needed to prepare a many copies of quantum state by local operations and a sublinear amount of communication. Here, monogamy of quantum entanglement (i.e., the impossibility of a system being maximally entangled with two others at the same time) leads to an exact calculation for all quantum states that are supported either on the symmetric or on the antisymmetric subspace of a dxd-dimensional system.
We have analysed the kinematics of a sample of 114 hot subdwarf stars, for 2/3 of which we present new proper motions, spectroscopic and photometric data. The vast majority of the stars show a kinematic behaviour that is similar to that of Thick Disk stars. Some stars have velocities rather fitting to solar, i.e. Thin Disk, kinematics. 16 objects have orbital velocities which differ considerably from those of Disk stars. These are members of the Galactic Halo. We analysed the velocity dispersions and calculated orbits. Most stars feature orbits with disk character (eccentricity <= 0.5), a few reach far above the Galactic plane and have very eccentric orbits (ecc >= 0.7). The intermediate eccentricity range is poorly populated. This indicates that the (Thick) Disk and the Halo are kinematically disjunct. Plotting a histogram of the orbit data points along z leads to the z-distance probability distribution of the star; doing this for all stars leads to the z-distance probability distribution of the sample. The logarithmic histogram shows two slopes, each representing the scale height of a population. The disk component has a scale height of 0.9 (0.1) kpc, which is consistent with earlier results and is similar to that of the Thick Disk. The other slope represents a component with a scale height ~7 kpc, a much flatter gradient than for the disk component. This shows that the vast majority of the sdBs are Disk stars, but a Halo minority is present, too. The kinematic history and population membership of the sdB stars on the whole is different from that of the cooler HBA stars, which are predominantly or even exclusively Halo objects. This leads to the question, whether the Halo sdB stars are of similar origin as the HBAs, or whether their kinematical behaviour possibly represents another origin, such as infalling stellar aggregates.
Recent studies of FeSi$_{(1-x)}$Ge$_x$, which found a transition from an insulating to a magnetic metallic state near $x$=0.25, have revived the discussion about the role of strong correlation in these systems. Here are spin polarized band calculations made for 64-atom supercells of FeSi$_{(1-x)}$Ge$_x$ for different $x$ and different volumes for large $x$. The results show that the small band gap in FeSi is closed for $x \geq 0.3$, because of both substitutional disorder and increased volume. Ferromagnetism appears near this composition and becomes enforced for increasing $x$. The $x$-dependence of the electronic specific heat can be understood from the exchange splitting of the density-of-states near the gap. Strong volume dependencies for the properties of FeGe suggest experiments using pressure instead of $x$ for investigations of the gap.
We investigate the kinematics of neutral gas in the Small Magellanic Cloud (SMC) and test the hypothesis that it is rotating in a disk. To trace the 3D motions of the neutral gas distribution, we identify a sample of young, massive stars embedded within it. These are stars with radial velocity measurements from spectroscopic surveys and proper motion measurements from Gaia, whose radial velocities match with dominant HI components. We compare the observed radial and tangential velocities of these stars with predictions from the state-of-the-art rotating disk model based on high-resolution 21 cm observations of the SMC from the Australian Square Kilometer Array Pathfinder telescope. We find that the observed kinematics of gas-tracing stars are inconsistent with disk rotation. We conclude that the kinematics of gas in the SMC are more complex than can be inferred from the integrated radial velocity field. As a result of violent tidal interactions with the LMC, non-rotational motions are prevalent throughout the SMC, and it is likely composed of distinct sub-structures overlapping along the line of sight.
We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with a complex geometry. In particular we describe how to reduce ($2n$+$1$)-dimensional complex matrices to {\em overlapping\/} ($n$+$1$)-dimensional quaternionic matrices with generalized quaternionic elements. This step resolves an outstanding difficulty with reduction of purely complex matrix groups within quaternionic QM and avoids {\em anomalous} eigenstates. As a result we present a more complete translation from CQM to QQM and viceversa.
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider encodings of $d$-level (i.e. qudit) quantum operators into multi-qubit operators, studying resource requirements for approximating operator exponentials by Trotterization. We primarily focus on spin-$s$ and truncated bosonic operators in second quantization, observing desirable properties for approaches based on the Gray code, which to our knowledge has not been used in this context previously. After outlining a methodology for implementing an arbitrary encoding, we investigate the interplay between Hamming distances, sparsity patterns, bosonic truncation, and other properties of local operators. Finally, we obtain resource counts for five common Hamiltonian classes used in physics and chemistry, while modeling the possibility of converting between encodings within a Trotter step. The most efficient encoding choice is heavily dependent on the application and highly sensitive to $d$, although clear trends are present. These operation count reductions are relevant for running algorithms on near-term quantum hardware because the savings effectively decrease the required circuit depth. Results and procedures outlined in this work may be useful for simulating a broad class of Hamiltonians on qubit-based digital quantum computers.
The original Fujita approximation theorem states that the volume of a big divisor $D$ on a projective variety $X$ can always be approximated arbitrarily closely by the self-intersection number of an ample divisor on a birational modification of $X$. One can also formulate it in terms of graded linear series as follows: let $W_{\bullet} = \{W_k \}$ be the complete graded linear series associated to a big divisor $D$: \[   W_k = H^0\big(X,\mathcal{O}_X(kD)\big). \] For each fixed positive integer $p$, define $W^{(p)}_{\bullet}$ to be the graded linear subseries of $W_{\bullet}$ generated by $W_p$: \[   W^{(p)}_{m}={cases}   0, &\text{if $p\nmid m$;}   \mathrm{Image} \big(S^k W_p \rightarrow W_{kp} \big), &\text{if $m=kp$.}   {cases} \] Then the volume of $W^{(p)}_{\bullet}$ approaches the volume of $W_{\bullet}$ as $p\to\infty$. We will show that, under this formulation, the Fujita approximation theorem can be generalized to the case of multigraded linear series.
Current advances in technology have highlighted the importance of video analysis in the domain of computer vision. However, video analysis has considerably high computational costs with traditional artificial neural networks (ANNs). Spiking neural networks (SNNs) are third generation biologically plausible models that process the information in the form of spikes. Unsupervised learning with SNNs using the spike timing dependent plasticity (STDP) rule has the potential to overcome some bottlenecks of regular artificial neural networks, but STDP-based SNNs are still immature and their performance is far behind that of ANNs. In this work, we study the performance of SNNs when challenged with the task of human action recognition, because this task has many real-time applications in computer vision, such as video surveillance. In this paper we introduce a multi-layered 3D convolutional SNN model trained with unsupervised STDP. We compare the performance of this model to those of a 2D STDP-based SNN when challenged with the KTH and Weizmann datasets. We also compare single-layer and multi-layer versions of these models in order to get an accurate assessment of their performance. We show that STDP-based convolutional SNNs can learn motion patterns using 3D kernels, thus enabling motion-based recognition from videos. Finally, we give evidence that 3D convolution is superior to 2D convolution with STDP-based SNNs, especially when dealing with long video sequences.
We present 7 mm lambda VLBA observations of the compact nonthermal radio source in the Galactic Center, Sgr A*. These observations confirm the hypothesis that the image of Sgr A* is a resolved elliptical Gaussian caused by the scattering of an intervening thermal plasma. The measured major axis of Sgr A* is 0.76 \pm 0.04 mas, consistent with the predicted scattering size of 0.67 \pm 0.03. We find an axial ratio of 0.73 \pm 0.10 and a position angle of 77.0 \pm 7.4 deg. These results are fully consistent with VLBI observations at longer wavelengths and at 3 mm lambda. We find no evidence for any additional compact structure to a limit of 35 mJy.   The underlying radio source must be smaller than 4.1 AU for a galactocentric distance of 8.5 kpc. This result is consistent with the conclusion that the radio emission from Sgr A* results from synchrotron or cyclo-synchrotron radiation of gas in the vicinity of a black hole with a mass near 10^6 M_sun.
We investigate the impact of 3D hydrodynamical model atmospheres of red giant stars at different metallicities on the formation of spectral lines of a number of ions and molecules. We carry out realistic 3D simulations of surface convection in red giant stars with varying stellar parameters. We use the simulations as time-dependent hydrodynamical model stellar atmospheres to compute atomic (Li, O, Na, Mg, Ca, Fe) and molecular (CH, NH, OH) spectral lines under the assumption of local thermodynamic equilibrium (LTE). We compare the line strengths computed in 3D with the results of analogous line formation calculations for 1D, hydrostatic, plane-parallel MARCS model atmospheres in order to estimate the impact of 3D models on the derivation of elemental abundances. The temperature and density inhomogeneities and correlated velocities in 3D models, as well as the differences between the 1D and mean 3D structures significantly affect the predicted line strengths. Under the assumption of LTE, the low atmospheric temperatures of very metal-poor 3D model atmospheres cause the lines from neutral species and molecules to appear stronger than in 1D. Therefore, elemental abundances derived from these lines using 3D models are significantly lower than according to 1D analyses. Differences between 3D and 1D abundances of C, N, and O derived from CH, NH, and OH weak low-excitation lines are found to be in the range -0.5 dex to -1.0 dex for the the red giant stars at [Fe/H]=-3 considered here. At this metallicity, large negative corrections (about -0.8 dex) are also found for weak low-excitation Fe I lines. We caution, however, that departures from LTE might be significant for these and other elements and comparable to the effects due to stellar granulation.
We prove that a two-variable p-adic l_q-function has the series p-adic expansion which interpolates a linear combinations of terms of the generalized q-Euler polynomials at non positive integers. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given this note is due to Washington
Within the modified potential cluster model with forbidden states effectively taking into account the Pauli Exclusion Principle the astrophysical S-factor of radiative p14N capture to 15O ground state has been calculated. The calculation was performed at the proton energy up to 5 MeV in the center of mass system (c.m.) with taking into account broad resonances up to 3.4 MeV in c.m. To explain reasonably the available experimental data it is required to admit the existence of 14N cluster in excited state 14N* with the excitation energy equal to 5.69 MeV and momentum JP = 1-. It is assumed that in this case the 4D1/2 state wave function of the p14N* clusters relative motion may be used. There was shown that it is succeeded to describe the S-factor of p14N capture in the resonance region only under the assumption that all low-lying resonances at 260(1/2+), 987(3/2+), 1447(1/2+), 2187(3/2+), and 3211(3/2+) keV in c.m. are the 4D1/2 and 4D3/2 scattering waves.
We show that a dispiration (a disclination plus a screw dislocation) polarizes the vacuum of a scalar field giving rise to an energy momentum tensor which, as seen from a local inertial frame, presents non vanishing off-diagonal components. The results may have applications in cosmology (chiral cosmic strings) and condensed matter physics (materials with linear defects).
It is well known that in an exact covering system in $\mathbb{Z}$, the biggest modulus must be repeated. Very recently, Kim gave an analogous result for certain quadratic fields, and Kim also conjectured that it must hold in any algebraic number field. In this paper, we prove Kim's conjecture. In other words, we prove that exact covering systems in any algebraic number field must have repeated moduli.
We perform photometric analyses for a bright early-type galaxy (ETG) sample with 2949 galaxies ($M_{\rm r}<-22.5$ mag) in the redshift range of 0.05 to 0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo 1. We measure the Petrosian and isophotal magnitudes, as well as the corresponding half-light radius for each galaxy. We find that for brightest galaxies ($M_{\rm r}<-23$ mag), our Petrosian magnitudes, and isophotal magnitudes to 25 ${\rm mag/arcsec^2}$ and 1\% of the sky brightness are on average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian values, respectively. In the first case the underestimations are caused by overestimations in the sky background by the SDSS PHOTO algorithm, while the latter two are also due to deeper photometry. Similarly, the typical half-light radii ($r_{50}$) measured by the SDSS algorithm are smaller than our measurements. As a result, the bright-end of the $r$-band luminosity function is found to decline more slowly than previous works. Our measured luminosity densities at the bright end are more than one order of magnitude higher than those of Blanton et al. (2003), and the stellar mass densities at $M_{\ast}\sim 5\times10^{11} M_{\odot}$ and $M_{\ast}\sim 10^{12} M_{\odot}$ are a few tenths and a factor of few higher than those of Bernardi et al. (2010). These results may significantly alleviate the tension in the assembly of massive galaxies between observations and predictions of the hierarchical structure formation model.
We study the time-variable linear polarisation of Sgr A* during a bright NIR flare observed with the GRAVITY instrument on July 28, 2018. Motivated by the time evolution of both the observed astrometric and polarimetric signatures, we interpret the data in terms of the polarised emission of a compact region ('hotspot') orbiting a black hole in a fixed, background magnetic field geometry. We calculated a grid of general relativistic ray-tracing models, created mock observations by simulating the instrumental response, and compared predicted polarimetric quantities directly to the measurements. We take into account an improved instrument calibration that now includes the instrument's response as a function of time, and we explore a variety of idealised magnetic field configurations. We find that the linear polarisation angle rotates during the flare, which is consistent with previous results. The hotspot model can explain the observed evolution of the linear polarisation. In order to match the astrometric period of this flare, the near horizon magnetic field is required to have a significant poloidal component, which is associated with strong and dynamically important fields. The observed linear polarisation fraction of $\simeq 30\%$ is smaller than the one predicted by our model ($\simeq 50\%$). The emission is likely beam depolarised, indicating that the flaring emission region resolves the magnetic field structure close to the black hole.
Within all approaches to quantum gravity small violations of the Einstein Equivalence Principle are expected. This includes violations of Lorentz invariance. While usually violations of Lorentz invariance are introduced through the coupling to additional tensor fields, here a Finslerian approach is employed where violations of Lorentz invariance are incorporated as an integral part of the space-time metrics. Within such a Finslerian framework a modified dispersion relation is derived which is confronted with current high precision experiments. As a result, Finsler type deviations from the Minkowskian metric are excluded with an accuracy of 10^{-16}.
We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety.