ShantanuT01/DACTYL-Pretraining huggingface dataset:
The non-relativistic scattering of a spin-1/2 particle off a self-dual monopole reduces, for large distances, to the dyon problem, studied previously by D'Hoker and Vinet. The S matrix (calculated by Zwanziger's algebraic method based on the o(3,1)\oplus o(3) dynamical symmetry, discovered by D'Hoker and Vinet) is shown to factorize into the product of the spinless S-matrix, S_0, with a spin-dependent factor. The total cross-section is identical to the one found in the spinless case.
Many studies have shown that there are clear sequences in the period-luminosity relationship (PLR) for Mira variables and semiregular variables (SRVs) in the Large Magellanic Cloud (LMC). To investigate the PLR for SRVs in our galaxy, we examined the annual parallax measurement and conducted K'-band photometric monitoring of an SRV star SV Pegasus (SV Peg). We measured the position change of the associating H$_2$O maser spots by phase-referencing VLBI observations with VERA at 22 GHz, spanning approximately 3 yr, and detected an annual parallax of $\pi = 3.00 \pm 0.06$ mas, corresponding to a distance of $D=333 \pm 7$ pc. This result is in good agreement with the Hipparcos parallax and improves the accuracy of the distance from 35 $\%$ to 2 $\%$. However, the GAIA DR2 catalog gave a parallax of $\pi=1.12\pm0.28$ mas for SV Peg. This indicates that the GAIA result might be blurred by the effect of the stellar size because the estimated stellar radius was $\sim 5$ mas, which is comparable to the parallax. We obtained a K'-band mean magnitude of $m_{K'} = -0.48$ mag and a period of $P=177$ days from our photometric monitoring with a 1-m telescope. Using the trigonometric distance, we derived an absolute magnitude of $M_{K'}=-8.09 \pm 0.05$ mag. This result shows that the position of SV Peg in the PLR falls on the C' sequence found in the PLR in the LMC, which is similar to other SRVs in our galaxy.
Researchers have developed excellent feed-forward models that learn to map images to desired outputs, such as to the images' latent factors, or to other images, using supervised learning. Learning such mappings from unlabelled data, or improving upon supervised models by exploiting unlabelled data, remains elusive. We argue that there are two important parts to learning without annotations: (i) matching the predictions to the input observations, and (ii) matching the predictions to known priors. We propose Adversarial Inverse Graphics networks (AIGNs): weakly supervised neural network models that combine feedback from rendering their predictions, with distribution matching between their predictions and a collection of ground-truth factors. We apply AIGNs to 3D human pose estimation and 3D structure and egomotion estimation, and outperform models supervised by only paired annotations. We further apply AIGNs to facial image transformation using super-resolution and inpainting renderers, while deliberately adding biases in the ground-truth datasets. Our model seamlessly incorporates such biases, rendering input faces towards young, old, feminine, masculine or Tom Cruise-like equivalents (depending on the chosen bias), or adding lip and nose augmentations while inpainting concealed lips and noses.
Final-state interactions in (e,e'n) knockout reactions in the quasi-free region are studied by considering the multistep direct scattering of the ejectile nucleon. Primary and multiple particle emission are included within the same model and are found to become important with increasing excitation energy. Charge-exchange effects taken into account through the two-step (e,e'p)(p,n) and three-step (e,e'p)(p,N)(N,n) processes are also found to increase with energy. A comparison with the results obtained with an isospin-dependent optical potential at small excitation energies is presented.
In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, with right hand side bounded away from zero and infinity, is $W_{\rm loc}^{2,1}$. This is obtained by showing higher integrability a-priori estimates for $D^2 u$, namely $D^2 u \in L\log^k L$ for any $k\in \mathbb N$.
We investigate the possibility that present-day galaxies and their dark matter haloes contain a population of massive black holes (MBHs) that form by hierarchical merging of the black hole remnants of the first stars in the Universe. Some of the MBHs may be large enough or close enough to the centre of the galactic host that they merge within a Hubble time. We estimate to what extent this process could contribute to the mass of the super-massive black holes (SMBHs) observed in galactic centres today. The relation between SMBH and galactic bulge mass in our model displays the same slope as that found in observations. Many MBHs will not reach the centre of the host halo, however, but continue to orbit within it. In doing so MBHs may remain associated with remnants of the satellite halo systems of which they were previously a part. Using a semi-analytical approach that explicitly accounts for dynamical friction, tidal disruption and encounters with galactic disks, we follow the hierarchical merging of MBH systems and their subsequent dynamical evolution inside the respective host haloes. We predict the mass and abundance of MBHs in present-day galactic haloes, and also estimate the MBH mass accretion rates as well as bolometric luminosities for two different accretion scenarios. MBHs that have not undergone recent merging will retain associated dark matter cusps that were enhanced by black hole accretion growth, and may be possible sources of gamma rays via neutralino annihilations.
The expected hitting time of discrete quantum walks on a hypercube (HC) is numerically known to be exponentially shorter than that of their classical analogs in terms of the scaling with the HC dimension. Recent numerical analyses illustrated that this scaling exists not only on the bare HC, but also when the HC graph is symmetrically and locally embedded into larger graphs. The present work investigates the necessity of symmetry and locality for the speed-up by considering embeddings that are nonsymmetric or nonlocal. We provide numerical evidence that the exponential speed-up survives also in these cases. Furthermore, our numerical simulations demonstrate that removing a single edge from the HC also does not destroy the exponential speed-up. In the nonlocal embedding of the HC we encounter dark states, which we analyze. We provide a general and detailed presentation of the mapping that reduces the exponentially large Hilbert space of the quantum walk to an effective subspace of polynomial scaling. This mapping is our essential tool to numerically study quantum walks in such high-dimensional structures.
We investigate the viability of the magnetorotational instability (MRI) in accretion disks around both solar-type stars and very low mass stars. In particular, we determine the disk regions where the MRI can be shut off either by Ohmic resistivity (the so-called Dead and Undead Zones) or by ampipolar diffusion (a region we term the Zombie Zone). We consider 2 stellar masses: Mstar = 0.7 and 0.1 Msun. In each case, we assume that: the disk surface density profile is that of a scaled Minimum Mass Solar Nebula, with Mdisk/Mstar ~ 0.01 as currently estimated; disk ionisation is driven primarily by stellar X-rays, complemented by cosmic rays and radionuclides; and the stellar X-ray luminosity scales with bolometric luminosity as Lx/Lstar ~ 10^-3.5, as observed. Ionization rates are calculated with the MOCCASIN code, and ionisation balance determined using a simplified chemical network, including well-mixed 0.1 um grains at various levels of depletion. We find that (1) ambipolar diffusion is the primary factor controlling MRI activity in disks around both solar-type and very low mass stars. Assuming that the MRI yields the maximum possible field strength at each radius, we further find that: (2) the MRI-active layer constitutes only ~ 5-10% of the total disk mass; (3) the accretion rate (Mdot) varies radially in both magnitude and sign (inward or outward), implying time-variable accretion as well as the creation of disk gaps and overdensities, with consequences for planet formation and migration; (4) achieving the empirical accretion rates in solar-type and very low mass stars requires a depletion of well-mixed small grains by a factor of 10-1000 relative to the standard dust-to-gas mass ratio of 10^-2; and (5) the current non-detection of polarized emission from field-aligned grains in the outer disk regions is consistent with active MRI at those radii.
In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between the Euler numbers and the second kind stirling numbers.
We determine, for an elliptic curve $E/\mathbb Q$ and for all $p$, all the possible torsion groups $E(\mathbb Q_{\infty, p})_{tors}$, where $\mathbb Q_{\infty, p}$ is the $\mathbb Z_p$-extension of $\mathbb Q$.
OSIRIS is a Day One instrument that will be available at the 10m GTC telescope which is being built at La Palma observatory in the Canary Islands. This optical instrument is designed to obtain wide-field narrow-band images using tunable filters and to do low-resolution spectroscopy in both long-slit and multislit modes. For the multislit spectroscopy mode, we have developed a software to assist the observers to design focal plane masks. In this paper we describe the characteristics of this Mask Designer tool. We discuss the main design concepts, the functionality and particular features of the software.
We aim to constrain the properties and evolutionary status of early and mid-spectral type supergiants (from O4 to O7.5). These posses the highest mass-loss rates among the O stars, and exhibit conspicuous wind profiles. Using the non-LTE wind code CMFGEN, we simultaneously analyzed the FUV-UV and optical spectral range to determine the photospheric properties and wind parameters. We derived effective temperatures, luminosities, surface gravities, surface abundances, mass-loss rates, wind terminal velocities, and clumping filling factors. The supergiants define a very clear evolutionary sequence, in terms of ages and masses, from younger and more massive stars to older stars with lower initial masses. O4 supergiants cluster around the 3 Myr isochrone and are more massive than 60 Msun, while the O5 to O7.5 stars have masses in the range 50 - 40 Msun and are 4 +/- 0.3 Myr old. The surface chemical composition is typical of evolved O supergiants (nitrogen-rich, carbon- and oxygen-poor). While the observed ranges of carbon and nitrogen mass-fractions are compatible with those expected from evolutionary models for the measured stellar masses, the N/C ratios as a function of age are inconsistent with the theoretical predictions for the four earliest (O4 spectral type) stars of the sample. We question the efficiency of rotational mixing as a function of age for these stars and suggest that another mechanism may be needed to explain the observed abundance patterns. Mass-loss rates derived with clumped-models range within a factor of three of the theoretical mass-loss rates. The corresponding volume-filling factors associated with small-scale clumping are 0.05 +/- 0.02. Clumping is found to start close to the photosphere for all but three stars, two of which are fast rotators.
Given a quartic Galois extension $L/\mathbb{Q}$ of number fields and a Hopf-Galois structure $H$ on $L/\mathbb{Q}$, we study the freeness of the ring of integers $\mathcal{O}_L$ as module over the associated order $\mathfrak{A}_H$ in $H$. For the classical Galois structure $H_c$, we know by Leopoldt's theorem that $\mathcal{O}_L$ is $\mathfrak{A}_{H_c}$-free. If $L/\mathbb{Q}$ is cyclic, it admits a unique non-classical Hopf-Galois structure, whereas if it is biquadratic, it admits three such Hopf-Galois structures. In both cases, we obtain that freeness depends on the solvability in $\mathbb{Z}$ of certain generalized Pell equations. We shall translate some results on Pell equations into results on the $\mathfrak{A}_H$-freeness of $\mathcal{O}_L$.
In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained result generalizes a corresponding one proved by Horodecki [Acta Phys. Slov. 48, 141 (1998).]. But, for the entanglement cost it requires certain conditions for holding the decomposition, and the distillable entanglement only has a week result as inequality. Finally, we presented an example to show that the conditions of our conclusions are existence.
This basic introduction to tropical geometry is hopefully accessible to a first years student in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking.   I tried as much as possible to illustrate each new definition with concrete examples and nice pictures.   As the title suggests, this text is in French. A Portuguese (Brazil) version, as well as correction of exercises, can be found at http://people.math.jussieu.fr/~brugalle/largerpubli.html
We construct and study a natural compactification $\overline{M}^r(N)$ of the moduli scheme $M^r(N)$ for rank-$r$ Drinfeld $\F_q[T]$-modules with a structure of level $N \in \F_q[T]$. Namely, $\overline{M}^r(N) = {\rm Proj}\,{\bf Eis}(N)$, the projective variety associated with the graded ring ${\bf Eis}(N)$ generated by the Eisenstein series of rank $r$ and level $N$. We use this to define the ring ${\bf Mod}(N)$ of all modular forms of rank $r$ and level $N$. It equals the integral closure of ${\bf Eis}(N)$ in their common quotient field $\widetilde{\MF}_r(N)$. Modular forms are characterized as those holomorphic functions on the Drinfeld space $\Om^r$ with the right transformation behavior under the congruence subgroup $\Ga(N)$ of $\Ga = {\rm GL}(r,\F_q[T])$ ("weak modular forms") which, along with all their conjugates under $\Ga/\Ga(N)$, are bounded on the natural fundamental domain $\BF$ for $\Ga$ on $\Om^r$.
The de-excited energy of electron capture (EC) induced by magnetic field decay may be a new source for heating magnetar crust, so we do a quantitative calculation on the EC process near the outer crust and analyze their influence on persistent X-ray radiation of magnetars, adopting the experimental data or the results of theoretical model (including the large-scale shell model and quasi-particle random phase approximation).
Electron Spin Resonance (ESR) can microscopically probe both conduction electrons (ce) and local moment (LM) spin systems in different materials. A ce spin resonance (CESR) is observed in metallic systems based on light elements or with enhanced Pauli susceptibility. LM ESR is frequently seen in compounds with paramagnetic ions and localized d or f electrons. Here we report a remarkable and unprecedented ESR signal in the heavy fermion (HF) superconductor beta-YbAlB4[1] which behaves as a CESR at high temperatures and acquires characteristics of the Yb3+ LM ESR at low temperature. This dual behavior in same ESR spectra strikes as an in situ unique observation of the Kondo quasiparticles giving rise to a new ESR response called Kondo coupled resonant mode (KCRM). The proximity to a quantum critical point (QCP) may favor the observation of a KCRM and its dual character in beta-YbAlB4 may unveil the 4f-electrons nature at the QCP.
The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more detrimental and hard to analyze compared to those ideal stochastic errors. In this paper, we study the independent coherent error due to the imperfect unitary rotation on each physical qubit of the toric code. We find that the surface code under coherent error satisfies generalized Knill-Laflamme (K-L) criterion and falls into the category of approximate QEC. The extra term in the generalized K-L criterion corresponds to the coherent part of the error channel at logical level, and then show that the generalized K-L criterion approaches the normal K-L criterion when the code distance becomes large. In addition, we also find that if the code with a fixed distance d is $\epsilon$-correctable, the value of $\epsilon$ describing the accuracy of the approximate QEC cannot be smaller than a lower bound. We then study the success probability of QEC under such coherent errors, and confirm that the exact success probability under coherent error is smaller than the results using Pauli twirling approximation at physical level.
We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover all the cases.
Stellar bars are a common morphological feature of spiral galaxies. While it is known that they can form in isolation, or be induced tidally, few studies have explored the production of stellar bars in galaxy merging. We look to investigate bar formation in galaxy merging using methods from deep learning to analyse our N-body simulations. The primary aim is to determine the constraints on the mass ratio and orientations of merging galaxies that are most conducive to bar formation. We further aim to explore whether it is possible to classify simulated barred spiral galaxies based on the mechanism of their formation. We test the feasibility of this new classification schema with simulated galaxies. Using a set of 29,400 images obtained from our simulations, we first trained a convolutional neural network to distinguish between barred and non-barred galaxies. We then tested the network on simulations with different mass ratios and spin angles. We adapted the core neural network architecture for use with our additional aims. We find that a strong inverse relationship between mass ratio and the number of bars produced. We also identify two distinct phases in the bar formation process; (1) the initial, tidally induced formation pre-merger, and (2) the destruction and/or regeneration of the during and after the merger. Mergers with low mass ratios and closely-aligned orientations are considerably more conducive to bar formation compared to equal-mass mergers. We demonstrate the flexibility of our deep learning approach by showing it is feasible to classify bars based on their formation mechanism.
We present the results of the analysis of Type II and anomalous Cepheids using the data from the Kepler K2 mission. The precise light curves of these pulsating variable stars are the key to study the details of their pulsation, such as the period-doubling effect or the presence of additional modes. We applied the Automated Extended Aperture Photometry (autoEAP) to obtain the light curves of the targeted variable stars which were observed. The light curves were Fourier analyzed. We investigated twelve stars observed by the K2 mission, seven Type II and five anomalous Cepheids. Among the Type II Cepheids EPIC 210622262 shows period-doubling, and four stars have modulation present in their light curves which are different from the period-doubling effect. We calculated the high-order Fourier parameters for the short-period Cepheids. We also determined physical parameters by fitting model atmospheres to the spectral energy distributions. The determined distances using the parallaxes measured by the Gaia space telescope have limited precision below 16 mag for these types of pulsating stars, regardless if the inverse method is used or the statistical method to calculate the distances. The BaSTI evolutionary models were compared to the luminosities and effective temperatures. Most of the Type II Cepheids are modeled with low metallicity models, but for a few of them solar-like metallicity ([Fe/H]=0.06) model is required. The anomalous Cepheids are compared to low-metallicity single stellar models. We do not see signs of binarity among our sample stars.
A good edge-labelling of a simple graph is a labelling of its edges with real numbers such that, for any ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. Say a graph is good if it admits a good edge-labelling, and is bad otherwise. Our main result is that any good n-vertex graph whose maximum degree is within a constant factor of its average degree (in particular, any good regular graph) has at most n^{1+o(1)} edges. As a corollary, we show that there are bad graphs with arbitrarily large girth, answering a question of Bode, Farzad and Theis. We also prove that for any Delta, there is a g such that any graph with maximum degree at most Delta and girth at least g is good.
We describe an implementation of the structure functions of Babul \& Starkman, in order to quantify the ``sheet-like'' nature of a distribution of matter. We test this statistic on a toy model describing cosmic string wakes, and show that it does a better job than other statistics which have been proposed for distinguishing non-Gaussianity in the form of sheets. We conclude that the most favoured cosmic string model is unlikely to produce a significant increase in the sheet-like nature of the matter distribution beyond that which occurs in Gaussian models (with the same power spectrum) due to the formation of Zeldovich pancakes. Although the statistic was developed in the context of cosmic string wake formation, we expect it to be useful for comparing the observed galaxy distribution with a wide range of theoretical models with different power spectra.
We propose that the euclidean bilocal collective field theory of critical large-N vector models provides a complete definition of the proposed dual theory of higher spin fields in anti de-Sitter spaces. We show how this bilocal field can be decomposed into an infinite number of even spin fields in one more dimension. The collective field has a nontrivial classical solution which leads to a O(N) thermodynamic entropy characteristic of the lower dimensional theory, as required by general considerations of holography. A subtle cancellation of the entropy coming from the bulk fields in one higher dimension with O(1) contributions from the classical solution ensures that the subleading terms in thermodynamic quantities are of the expected form. While the spin components of the collective field transform properly under dilatational, translational and rotational isometries of $AdS$, special conformal transformations mix fields of different spins indicating a need for a nonlocal map between the two sets of fields. We discuss the nature of the propagating degrees of freedom through a hamiltonian form of collective field theory and argue that nonsinglet states which are present in an euclidean version are related to nontrivial backgrounds.
We discuss phantom metrics admitting Killing spinors in fake N=2, D=4 supergravity coupled to vector multiplets. The Abelian U(1) gauge fields in the fake theory have kinetic terms with the wrong sign. We solve the Killing spinor equations for the standard and fake theories in a unified fashion by introducing a parameter which distinguishes between the two theories. The solutions found are fully determined in terms of algebraic conditions, the so-called stabilisation equations, in which the symplectic sections are related to a set of functions. These functions are harmonic in the case of the standard supergravity theory and satisfy the wave-equation in flat (2+1)-space-time in the fake theory. Explicit examples are given for the minimal models with quadratic prepotentials.