ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let D(m,n) be the set of all the integer points in the m-dilate of the Birkhoff polytope of doubly-stochastic n by n matrices. In this paper we find the sharp upper bound on the tropical determinant over the set D(m,n). We define a version of the tropical determinant where the maximum over all the transversals in a matrix is replaced with the minimum and then find the sharp lower bound on thus defined tropical determinant over D(m,n).
We present a supersymmetric non-linear $\s$-model built up in the $N=1$ superspace of Atiyah-Ward space-time. A manifold of the K\"ahler type comes out that is restricted by a particular decomposition of the K\"ahler potential. The gauging of the $\s$-model isometries is also accomplished in superspace.
We introduce the concept of initial-phase spectroscopy as a control of the dynamics of entangled states encoded into a two-atom system interacting with a broadband squeezed vacuum field. We illustrate our considerations by examining the transient spectrum of the field emitted by two systems, the small sample (Dicke) and the spatially extended (non-Dicke) models. It is found that the shape of the spectral components depends crucially on the relative phase between the initial entangled state and the squeezed field. We follow the temporal evolution of the spectrum and show that depending on the relative phase a hole burning can occur in one of the two spectral lines. We compare the transient behavior of the spectrum with the time evolution of the initial entanglement and find that the hole burning can be interpreted as a manifestation of the phenomenon of entanglement sudden death. In addition, we find that in the case of the non-Dicke model, the collective damping rate may act like an artificial tweezer that rotates the phase of the squeezed field.
We have investigated STM images of the (110) cross-sectional surface of Mn-doped GaAs using first principles total-energy pseudopotential calculations. We focus on configurations with Mn interstitial in the uppermost surface layers. In particular, we have found that Mn impurities, surrounded by Ga or As atoms, introduce in both cases strong local distortions in the GaAs(110) surface, with bond length variations up to 8 % on surface and non-negligible relaxations effects propagating up to the third sub-surface layer. In both cases interstitial Mn induces a spin-polarization on its nearest neighbors, giving rise to a ferromagnetic Mn-As and to antiferromagnetic Mn-Ga configuration.
We give an interpretation of the temperature in de Sitter universe in terms of a dynamical Unruh effect associated with the Hubble sphere. As with the quantum noise perceived by a uniformly accelerated observer in static space-times, observers endowed with a proper motion can in principle detect the effect. In particular, we study a "Kodama observer" as a two-field Unruh detector for which we show the effect is approximately thermal. We also estimate the back-reaction of the emitted radiation and find trajectories associated with the Kodama vector fields are stable.
In this letter, we study the late-time evolution of a torsion cosmology only with the spin-$0^+$ mode. We find three kinds of analytical solutions with a constant affine scalar curvature. In the first case, it is not physical because the matter density will be negative. In the second case, it shows that the dark energy can be mimicked in the torsion cosmological model. In the third case, the characteristic of late-time evolution is similar to that of the universe of matter dominant. And we also find a kind of expression with the non-constant curvature that the periodic character of numerical calculation is only the reflection of solution in a specific period of evolution. Using these expressions, we shall be able to predict the evolution over the late-time. From this prediction, we know the fate of universe that the universe would expand forever, slowly asymtotically to a halt.
We present the 100 strongest 1.4 GHz point sources from a new mosaic image in the direction of the Large Magellanic Cloud (LMC). The observations making up the mosaic were made over a ten year period and were combined with Parkes single dish data at 1.4 GHz to complete the image for short spacing. An initial list of co-identifications within 10" at 0.843, 4.8 and 8.6 GHz consisted of 2682 sources. Elimination of extended objects and artifact noise allowed the creation of a refined list containing 1988 point sources. Most of these are presumed to be background objects seen through the LMC; a small portion may represent compact H II regions, young SNRs and radio planetary nebulae. For the 1988 point sources we find a preliminary average spectral index of -0.53 and present a 1.4 GHz image showing source location in the direction of the LMC.
It is shown that new leading ($\al'$) as well as all-order solutions of String theory can be obtained by taking appropriate singular limits of the known solutions. We give several leading order solutions for the bosonic as well as the heterotic string. We then present all-order forms of the previously known two dimensional cosmological solutions. An all-order form for the cosmological solution in three dimensions is also predicted. The physical implications of our results are discussed.
We theoretically examine the validity of Matthiessen's rule caused by strong dislocation-dislocation interaction using a fully quantized dislocation field, where its degree of deviation is quantified at arbitrary electron energy, dislocation-electron and dislocation-dislocation distances and interaction strengths. Contrary to intuition, we show that the electron relaxation rate deviates from the Matthiessen's rule in an oscillatory way as a function of inter-dislocation distance, instead of monotonically. This study could serve as a computational tool to investigate the electronic behavior of a highly-dislocated system at a full quantum field theoretical level.
Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work we inspect the capacity for correlated many body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a non-classical phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.
Warps in the outer gaseous disks of galaxies are a ubiquitous phenomenon, but it is unclear what generates them. One theory is that warps are generated internally through spontaneous bending instabilities. Other theories suggest that they result from the interaction of the outer disk with accreting extragalactic material. In this case, we expect to find cases where the circular velocity of the warp gas is poorly correlated with the rotational velocity of the galaxy disk at the same radius. Optical spectroscopy presents itself as an interesting alternative to 21-cm observations for testing this prediction, because (i) separating the kinematics of the warp from those of the disk requires a spatial resolution that is higher than what is achieved at 21 cm at low HI column density; (ii) optical spectroscopy also provides important information on star formation rates, gas excitation, and chemical abundances, which provide clues to the origin of the gas in warps. We present here preliminary results of a study of the kinematics of gas in the outer-disk warps of seven edge-on galaxies, using multi-hour VLT/FORS2 spectroscopy.
Generative adversarial networks (GANs) have been trained to be professional artists able to create stunning artworks such as face generation and image style transfer. In this paper, we focus on a realistic business scenario: automated generation of customizable icons given desired mobile applications and theme styles. We first introduce a theme-application icon dataset, termed AppIcon, where each icon has two orthogonal theme and app labels. By investigating a strong baseline StyleGAN2, we observe mode collapse caused by the entanglement of the orthogonal labels. To solve this challenge, we propose IconGAN composed of a conditional generator and dual discriminators with orthogonal augmentations, and a contrastive feature disentanglement strategy is further designed to regularize the feature space of the two discriminators. Compared with other approaches, IconGAN indicates a superior advantage on the AppIcon benchmark. Further analysis also justifies the effectiveness of disentangling app and theme representations. Our project will be released at: https://github.com/architect-road/IconGAN.
We verify Green's conjecture for a generic $k$-gonal curve of genus $g$, for $g\geq k(k-1)/2$.
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on graphs, and its non-commutative dual is realized in three different ways, in particular as the Grossman-Larson algebra of heap ordered trees.   Extensions to endofunctions, parking functions, set compositions, set partitions, planar binary trees and rooted forests are discussed. Finally, we introduce one-parameter families interpolating between different structures constructed on the same combinatorial objects.
In ten space-time dimensions the number of Majorana-Weyl fermions is not conserved, not only during the time evolution, but also by rotations. As a consequence the empty Fock state is not rotationally symmetric. We construct explicitly the simplest singlet state which provides the starting point for building up invariant SO(9) subspaces. The state has non-zero fermion number and is a complicated combination of the 1360 elementary, gauge invariant, gluinoless Fock states with twelve fermions. Fermionic structure of higher irreps of SO(9) is also briefly outlined.
We investigate weak convergence of finite-dimensional distributions of a renewal shot noise process $(Y(t))_{t\geq 0}$ with deterministic response function $h$ and the shots occurring at the times $0 = S_0 < S_1 < S_2<\ldots$, where $(S_n)$ is a random walk with i.i.d.\ jumps. There has been an outbreak of recent activity around this topic. We are interested in one out of few cases which remained open: $h$ is regularly varying at $\infty$ of index $-1/2$ and the integral of $h^2$ is infinite. Assuming that $S_1$ has a moment of order $r>2$ we use a strong approximation argument to show that the random fluctuations of $Y(s)$ occur on the scale $s=t+g(t,u)$ for $u\in [0,1]$, as $t\to\infty$, and, on the level of finite-dimensional distributions, are well approximated by the sum of a Brownian motion and a Gaussian process with independent values (the two processes being independent). The scaling function $g$ above depends on the slowly varying factor of $h$. If, for instance, $\lim_{t\to\infty}t^{1/2}h(t)\in (0,\infty)$, then $g(t,u)=t^u$.
The intrinsic anisotropy delta and flattening epsilon of simulated merger remnants is compared with elliptical galaxies that have been observed by the SAURON collaboration, and that were analysed using axisymmetric Schwarzschild models. Collisionless binary mergers of stellar disks and disk mergers with an additional isothermal gas component, neglecting star formation cannot reproduce the observed trend delta = 0.55 epsilon (SAURON relationship). An excellent fit of the SAURON relationship for flattened ellipticals with epsilon >= 0.25 is however found for merger simulations of disks with gas fractions >= 20%, including star formation and stellar energy feedback. Massive black hole feedback does not strongly affect this result. Subsequent dry merging of merger remnants however does not generate the slowly-rotating SAURON ellipticals which are characterized by low ellipticities epsilon < 0.25 and low anisotropies. This indicates that at least some ellipticals on the red galaxy sequence did not form by binary mergers of disks or early-type galaxies. We show that stellar spheroids resulting from multiple, hierarchical mergers of star-bursting subunits in a cosmological context are in excellent agreement with the low ellipticities and anisotropies of the slowly rotating SAURON ellipticals and their observed trend of delta with epsilon. The numerical simulations indicate that the SAURON relation might be a result of strong violent relaxation and phase mixing of multiple, kinematically cold stellar subunits with the angular momentum of the system determining its location on the relation.
Diagonal and off-diagonal flavor and conserved charge susceptibilities reveal the prevalent degrees of freedom of heated strongly interacting matter. Results obtained from lattice simulations are compared with various model estimates in an effort to weed down various possible pictures of a quark gluon plasma. We argue that the vanishing of the off-diagonal quark flavor susceptibilities and its derivatives with respect to chemical potential, at temperatures above 1.5Tc, can only be understood in a picture of a gas or liquid composed of quasi-particles which carry the same quantum numbers as quarks and antiquarks. A potential new observable, blind to neutral and non-strange particles, is introduced and related via isospin symmetry to the ratio of susceptibilities of baryonic strangeness to strangeness generated in the excited matter created at RHIC.
We study the mass distribution in the late-type dwarf galaxy NGC 2976 through stellar kinematics obtained with the VIRUS-P integral-field spectrograph and anisotropic Jeans models as a test of cosmological simulations and baryonic processes that putatively alter small-scale structure. Previous measurements of the H-alpha emission-line kinematics have determined that the dark matter halo of NGC 2976 is most consistent with a cored density profile. We find that the stellar kinematics are best fit with a cuspy halo. Cored dark matter halo fits are only consistent with the stellar kinematics if the stellar mass-to-light ratio is significantly larger than that derived from stellar population synthesis, while the best-fitting cuspy model has no such conflict. The inferred mass distribution from a harmonic decomposition of the gaseous kinematics is inconsistent with that of the stellar kinematics. This difference is likely due to the gas disk not meeting the assumptions that underlie the analysis such as no pressure support, a constant kinematic axis, and planar orbits. By relaxing some of these assumptions, in particular the form of the kinematic axis with radius, the gas-derived solution can be made consistent with the stellar kinematic models. A strong kinematic twist in the gas of NGC 2976's center suggests caution, and we advance the mass model based on the stellar kinematics as more reliable. The analysis of this first galaxy shows promising evidence that dark matter halos in late-type dwarfs may in fact be more consistent with cuspy dark matter distributions than earlier work has claimed.
Recovering the latent photorealistic faces from their artistic portraits aids human perception and facial analysis. However, a recovery process that can preserve identity is challenging because the fine details of real faces can be distorted or lost in stylized images. In this paper, we present a new Identity-preserving Face Recovery from Portraits (IFRP) to recover latent photorealistic faces from unaligned stylized portraits. Our IFRP method consists of two components: Style Removal Network (SRN) and Discriminative Network (DN). The SRN is designed to transfer feature maps of stylized images to the feature maps of the corresponding photorealistic faces. By embedding spatial transformer networks into the SRN, our method can compensate for misalignments of stylized faces automatically and output aligned realistic face images. The role of the DN is to enforce recovered faces to be similar to authentic faces. To ensure the identity preservation, we promote the recovered and ground-truth faces to share similar visual features via a distance measure which compares features of recovered and ground-truth faces extracted from a pre-trained VGG network. We evaluate our method on a large-scale synthesized dataset of real and stylized face pairs and attain state of the art results. In addition, our method can recover photorealistic faces from previously unseen stylized portraits, original paintings and human-drawn sketches.
We report the synthesis of SrMnO$_{3-{\delta}}$F$_{{\gamma}}$ perovskite oxyfluoride thin films using a vapor transport method to fluorinate as-grown SrMnO$_{2.5}$ epitaxial thin films. The influence of the fluoropolymer, which acts as a fluorine vapor source, was investigated by utilizing polyvinyl fluoride (PVF), polyvinylidene difluoride (PVDF) and polytetrafluoroethylene (PTFE) in the reaction. The same process was carried out with polyethylene (PE) to isolate the role of carbon in the vapor transport process. The F distribution was probed by X-ray photoemission spectroscopy, which confirmed the incorporation of F into the films and revealed higher F concentrations in films exposed to PVF and PVDF compared to PTFE. The c-axis parameter expands after fluorination, a result consistent with density functional theory calculations that attribute the volume expansion to elongated Mn-F bonds compared to shorter Mn-O bonds. Using X-ray absorption spectroscopy, we show that the fluorination process reduces the nominal Mn oxidation state suggesting that F substitutes on O sites in the lattice as opposed to filling anion vacancy sites, a finding further supported by calculated formation energies of different F site occupancies. These results provide new insights into topochemical fluorination of perovskite oxides, which should enable future synthesis and design efforts focused on oxyfluoride heterostructures.
Let $E$ be an elliptic curve with good reduction at a fixed odd prime $p$ and $K$ an imaginary quadratic field where $p$ splits. We give a growth estimate for the Mordell-Weil rank of $E$ over finite extensions inside the $\mathbb{Z}_p^2$-extension of $K$.
We present the first data release of the Survey on extragALactic magnetiSm with SOFIA (SALSA Legacy Program) with a set of 14 nearby ($<20$ Mpc) galaxies with resolved imaging polarimetric observations using HAWC+ from $53$ to $214$ $\mu$m at a resolution of $5-18$" ($90$ pc $-$ $1$ kpc). We introduce the definitions and background on extragalactic magnetism, and present the scientific motivation and sample selection of the program. Here, we focus on the general trends in the emissive polarization fraction. Far-infrared polarimetric observations trace the thermal polarized emission of magnetically aligned dust grains across the galaxy disks with polarization fractions of $P=0-15$% in the cold, $T_{\rm d} = [19,48]$ K, and dense, $\log_{10}(N_{\rm HI+H_{2}}) = [19.96,22.91]$, interstellar medium. The spiral galaxies show a median $\langle P_{154\mu m} \rangle = 3.3\pm0.9 $% across the disks. We report the first polarized spectrum of starburst galaxies showing a minimum within $89-154$ $\mu$m. The falling $53-154$ $\mu$m polarized spectrum may be due to a decrease in the dust grain alignment efficiency produced by variations in dust temperatures along the line-of-sight in the galactic outflow. We find that the starburst galaxies and the star-forming regions within normal galaxies have the lowest polarization fractions. We find that 50% (7 out of 14) of the galaxies require a broken power-law in the $P-N_{HI+H_{2}}$ and $P-T_{d}$ relations with three different trends. Group 1 has a relative increase of anisotropic random B-fields produced by compression or shear of B-fields in the galactic outflows, starburst rings, and inner-bar of galaxies; and Groups 2 and 3 have a relative increase of isotropic random B-fields driven by star-forming regions in the spiral arms, and/or an increase of dust grain alignment efficiency caused by shock-driven regions or evolutionary stages of a galaxy.
In this paper, we develop a full statistical method for the pairwise velocity estimator previously proposed, and apply Cosmicflows-2 catalogue to this method to constrain cosmology. We first calculate the covariance matrix for line-of-sight velocities for a given catalogue, and then simulate the mock full-sky surveys from it, and then calculate the variance for the pairwise velocity field. By applying the $8315$ independent galaxy samples and compressed $5224$ group samples from Cosmicflows-2 catalogue to this statistical method, we find that the joint constraint on $\Omega^{0.6}_{\rm m}h$ and $\sigma_{8}$ is completely consistent with the WMAP 9-year and Planck 2015 best-fitting cosmology. Currently, there is no evidence for the modified gravity models or any dynamic dark energy models from this practice, and the error-bars need to be reduced in order to provide any concrete evidence against/to support $\Lambda$CDM cosmology.
We study resonant tunneling through an interacting quantum dot coupled to normal metallic and superconducting leads. We show that large Coulomb interaction gives rise to novel effects in Andreev transport. Adopting an exact relation for the Green's function, we find that at zero temperature, the linear response conductance is enhanced due to Kondo-Andreev resonance in the Kondo limit, while it is suppressed in the empty site limit. In the Coulomb blockaded region, on the other hand, the conductance is reduced more than the corresponding conductance with normal leads because large charging energy suppresses Andreev reflection.
Solutions of the undeformed IKKT matrix model with structure R^{3,1} x K are presented, where the noncommutativity relates the compact with the non-compact space. The extra dimensions are stabilized by angular momentum, and the scales of K are generic moduli of the solutions. Explicit solutions are given for K= T^2, K= T^4, K = S^2 x T^2 and K = S^2 x S^2. Infinite towers of Kaluza-Klein modes may arise in some directions, along with an effective UV cutoff on the non-compact space. Deformations of these solutions carry NC gauge theory coupled to (emergent) gravity. Analogous solutions of the BFSS model are also given.
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. The trace norm is just one of the Ky Fan k-norms, given by the sum of the k largest singular values, which are studied more generally in the present paper. Several relations to chromatic number, spectral radius, spread, and to other fundamental parameters are outlined. Some results are extended to more general matrices.