ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper establishes the global existence and regularity for a system of the two-dimensional (2D) magnetohydrodynamic (MHD) equations with only directional hyperresistivity. More precisely, the equation of $b_1$ (the horizontal component of the magnetic field) involves only vertical hyperdiffusion (given by $\Lambda_2^{2\beta} b_1$) while the equation of $b_2$ (the vertical component) has only horizontal hyperdiffusion (given by $\Lambda_1^{2\beta} b_2$), where $\Lambda_1$ and $\Lambda_2$ are directional Fourier multiplier operators with the symbols being $|\xi_1|$ and $|\xi_2|$, respectively. We prove that, for $\beta>1$, this system always possesses a unique global-in-time classical solution when the initial data is sufficiently smooth. The model concerned here is rooted in the MHD equations with only magnetic diffusion, which play a significant role in the study of magnetic reconnection and magnetic turbulence. In certain physical regimes and under suitable scaling, the magnetic diffusion becomes partial (given by part of the Laplacian operator). There have been considerable recent developments on the fundamental issue of whether classical solutions of these equations remain smooth for all time. The papers of Cao-Wu-Yuan \cite{CaoWuYuan} and of Jiu-Zhao \cite{JiuZhao2} obtained the global regularity when the magnetic diffusion is given by the full fractional Laplacian $(-\Delta)^\beta$ with $\beta>1$. The main result presented in this paper requires only directional fractional diffusion and yet we prove the regularization in all directions. The proof makes use of a key observation on the structure of the nonlinearity in the MHD equations and technical tools on Fourier multiplier operators such as the H\"{o}rmander-Mikhlin multiplier theorem. The result presented here appears to be the sharpest for the 2D MHD equations with partial magnetic diffusion.
Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydro- dynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations.   Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion).   Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case.   Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi- layered prominences.   Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper.
Crowd counting is a challenging task due to the issues such as scale variation and perspective variation in real crowd scenes. In this paper, we propose a novel Cascaded Residual Density Network (CRDNet) in a coarse-to-fine approach to generate the high-quality density map for crowd counting more accurately. (1) We estimate the residual density maps by multi-scale pyramidal features through cascaded residual density modules. It can improve the quality of density map layer by layer effectively. (2) A novel additional local count loss is presented to refine the accuracy of crowd counting, which reduces the errors of pixel-wise Euclidean loss by restricting the number of people in the local crowd areas. Experiments on two public benchmark datasets show that the proposed method achieves effective improvement compared with the state-of-the-art methods.
A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal vertex called the root. The pebbling number of a graph $\pi(G)$ is the minimum number of pebbles needed so every distribution of $\pi(G)$ pebbles can reach every choice of the root. We introduce a new variant of graph pebbling, a game between two players. One player aims to move a pebble to the root and the other player aims to prevent this. We show configurations of various classes of graphs for which each player has a winning strategy. We will characterize the winning player for a specific class of diameter two graphs.
We study a hole-doped two-leg ladder system including metal ions, oxygen, and electron-lattice interaction, as a model for Sr_{14-x}Ca_xCu_{24}O_{41-\delta}. Single- and bi-polaronic states at 1/4-hole doping are modeled as functions of pressure by applying an unrestricted Hartree-Fock approximation to a multiband Peierls-Hubbard Hamiltonian. We find evidence for a pressure-induced phase transition between single-polaron and bi-polaron states. The electronic and phononic excitations in those states, including distinctive local lattice vibrational modes, are calculated by means of a direct-space Random Phase approximation. Finally, as a function of pressure, we identify a transition between site- and bond-centered bi-polarons, accompanied by a soft mode and a low-energy charge-sliding mode. We suggest comparisons with available experimented data.
The "Universality Theorem" for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R)=R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R' inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f(R') theories so defined are dynamically equivalent to the corresponding metric-affine f(R) theory. In particular for the function f(R)=R the standard equivalence between GR and Holst Lagrangian is obtained.
Numerous scene text detection methods have been proposed in recent years. Most of them declare they have achieved state-of-the-art performances. However, the performance comparison is unfair, due to lots of inconsistent settings (e.g., training data, backbone network, multi-scale feature fusion, evaluation protocols, etc.). These various settings would dissemble the pros and cons of the proposed core techniques. In this paper, we carefully examine and analyze the inconsistent settings, and propose a unified framework for the bottom-up based scene text detection methods. Under the unified framework, we ensure the consistent settings for non-core modules, and mainly investigate the representations of describing arbitrary-shape scene texts, e.g., regressing points on text contours, clustering pixels with predicted auxiliary information, grouping connected components with learned linkages, etc. With the comprehensive investigations and elaborate analyses, it not only cleans up the obstacle of understanding the performance differences between existing methods but also reveals the advantages and disadvantages of previous models under fair comparisons.
Using the correlated signal and idler photon pairs generated in a dispersion shifted fiber by a pulsed pump, we measure the quantum efficiency of a InGaAs/InP avalanche photodiode-based single photon detector. Since the collection efficiency of photon pairs is a key parameter to correctly deduce the quantum efficiency, we carefully characterize the collection efficiency by studying correlation dependence of photon pairs upon the spectra of pump, signal and idler photons. This study allows us to obtain quantum efficiency of the single photon detector by using photon pairs with various kinds of bandwidths.
Here we explore the radiation features of optical nanoantennas, analyzing the concepts of input impedance, optical radiation resistance, impedance matching and loading of plasmonic nanodipoles. We discuss how the concept of antenna impedance may be applied to optical frequencies, and how its quantity may be properly defined and evaluated. We exploit these concepts in optimization of nanoantenna loading by optical nanocircuit elements, extending classic concepts of radio-frequency antenna theory to the visible regime for the proper design and matching of plasmonic nanoantennas.
This paper examines a pair of bent functions on $\mathbb{Z}_2^{2m}$ and their relationship to a necessary condition for the existence of an automorphism of an edge-coloured graph whose colours are defined by the properties of a canonical basis for the real representation of the Clifford algebra $\mathbb{R}_{m,m}.$ Some other necessary conditions are also briefly examined.
The long-period ($P = 1091$ s) of the recently discovered pulsar GLEAM-X J162759.5-523504.3 can be attained by neutron stars evolving with fallback discs and magnetic dipole moments of a few $10^{30}$ G cm$^3$ at ages greater than $\sim 2 \times 10^5$ yr consistently with the observational upper limits to the period derivative, $\dot{P}$, and the X-ray luminosity, $L_X$, of the source. The current upper limits for $\dot{P}$ allow two alternative present states: (1) The disc is still active with ongoing accretion at a low rate such that the accretion luminosity is much less than the neutron star's cooling luminosity, which in turn is below the upper limit for $L_X$. In this scenario the spin-down will continue at $\dot{P} \sim 10^{-10}$ s s$^{-1}$ until the disc becomes inactive; the final period will be $P \sim$ a few $10^3$ s. (2) The disc is already inactive, there is no accretion. In this case the period evolution has leveled off to the observed value in the final period range. The remaining, very weak, dipole torque sustaining asymptotic spin-down at $\dot{P} \sim 4 \times 10^{-18}$ s s$^{-1}$. Long periods $P \sim$ a few $10^3$ s were predicted for the final states of soft gamma repeaters and anomalous X-ray pulsars with relatively strong dipole fields in earlier work with the fallback disc model.
The response of a nucleus composed of nucleons and confined quarks is calculated in a non-relativistic cluster model and is shown to be a convolution of responses of, respectively, a nucleus with interacting point-nucleons and of a nucleon composed of quarks. We further show that the apparent off-shell energy in the expression for the nucleon structure function in Impulse Approximation does not constitue a real problem. We conjecture a generalization to the relativistic regime.
Cosmography, the study and making of maps of the universe or cosmos, is a field where visual representation benefits from modern three-dimensional visualization techniques and media. At the extragalactic distance scales, visualization is contributing in understanding the complex structure of the local universe, in terms of spatial distribution and flows of galaxies and dark matter. In this paper, we report advances in the field of extragalactic cosmography obtained using the SDvision visualization software in the context of the Cosmicflows Project. Here, multiple visualization techniques are applied to a variety of data products: catalogs of galaxy positions and galaxy peculiar velocities, reconstructed velocity field, density field, gravitational potential field, velocity shear tensor viewed in terms of its eigenvalues and eigenvectors, envelope surfaces enclosing basins of attraction. These visualizations, implemented as high-resolution images, videos, and interactive viewers, have contributed to a number of studies: the cosmography of the local part of the universe, the nature of the Great Attractor, the discovery of the boundaries of our home supercluster of galaxies Laniakea, the mapping of the cosmic web, the study of attractors and repellers.
We introduce a new descriptor of the weblike pattern in the distribution of galaxies and matter: the scale dependent Betti numbers which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic used in earlier analyses of cosmological models. The richer information content of Betti numbers goes along with the availability of fast algorithms to compute them. When measured as a function of scale they provide a "Betti signature" for a point distribution that is a sensitive yet robust discriminator of structure. The signature is highly effective in revealing differences in structure arising in different cosmological models, and is exploited towards distinguishing between different dark energy models and may likewise be used to trace primordial non-Gaussianities.   In this study we demonstrate the potential of Betti numbers by studying their behaviour in simulations of cosmologies differing in the nature of their dark energy.
In this paper, we describe the set of all solutions of monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, as an application of the result, we study several perturbations of the considered equation over $p$-adic field.
Dark energy equation of state can be effectively described by that of a barotropic fluid. The barotropic fluid model describes the background evolution and the functional form of the equation of state parameter is well constrained by the observations. Equally viable explanations of dark energy are via scalar field models, both canonical and non-canonical; these scalar field models being low energy descriptions of an underlying high energy theory. In this paper, we attempt to reconcile the two approaches to dark energy by way of reconstructing the evolution of the scalar field potential. For this analysis, we consider canonical quintessence scalar field and the phantom field for this reconstruction. We attempt to understand the analytical or semi-analytical forms of scalar field potentials corresponding to typical well behaved parameterisations of dark energy using the constraints from recent observations.
Recent progress in the field of multiferroics led to the discovery of many new materials in which ferroelectricity is induced by cycloidal spiral orders. The direction of the electric polarization is typically constrained by spin anisotropies and magnetic field. Here, we report that the mixed rare-earth manganite, Gd$_{0.5}$Dy$_{0.5}$MnO$_3$, exhibits a spontaneous electric polarization along a general direction in the crystallographic ac-plane, which is suppressed below 10 K but re-emerges in an applied magnetic field. Neutron diffraction measurements show that the polarization direction results from a large tilt of the spiral plane with respect to the crystallographic axes and that the suppression of ferroelectricity is caused by the transformation of a cycloidal spiral into a helical one, a unique property of this rare-earth manganite. The freedom in the orientation of the spiral plane allows for a fine magnetic control of ferroelectricity, i.e. a rotation as well as a strong enhancement of the polarization depending on the magnetic field direction. We show that this unusual behavior originates from the coupling between the transition metal and rare-earth magnetic subsystems.
Recently released Planck data favor a lower value of the Hubble constant and a higher value of the fraction matter density in the standard $\Lambda$CDM model, which are discrepant with some of the low-redshift measurements. Within the context of this cosmology, we examine the consistency of the estimated values for the Hubble constant and fraction matter density with redshift tomography. Using the SNe Ia, Hubble parameter, BAO and CMB data, which are divided into three bins, we find no statistical evidence for any tension in the three redshift bins, although there exists a 1.4$\sigma$ deviation of the Hubble constant in the middle redshift from the one in the high redshift bin.
In this paper, the asymptotic behavior of sequences of successive Steiner and Minkowski symmetrizations is investigated. We state an equivalence result between the convergences of those sequences for Minkowski and Steiner. Moreover, in the case of independent (and not necessarily identically distributed) directions, we prove the almost sure convergence of successive symmetrizations at rate exponential for Minkowski, and at rate $e^{-c\sqrt{n}}$, with $c>0$, for Steiner.
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a particular case of the reduced system are shown to coincide, in essence, with the statistical sum of the well-known (inhomogeneous) 2-dimensional dimer model (the statistical sum is here a function of two parameters). Possible generalizations of the system are examined.
We construct a supermanifold ST which turns to be an open subset of a superquadric Q(5|6) subset P^{3|3}times P^{3|3}. The Dolbeault algebra Omega^{0*}(ST) is quasiisomorphic to N=3, D=4 YM algebra in Batalin-Vilkovisky formulation. We construct a dbar-closed functional tr:Omega^{0*}(ST)=>C. We conjecture that Chern-Simons theory associated with a triple Omega^{0*}(ST)\otimes Mat_n,dbar,tr tr_{Mat_n}) is equivalent to N=3, D=4 YM theory with gauge group U_n in euclidean signature.
Climate change is a pressing issue that is currently affecting and will affect every part of our lives. It's becoming incredibly vital we, as a society, address the climate crisis as a universal effort, including those in the Computer Vision (CV) community. In this work, we analyze the total cost of CO2 emissions by breaking it into (1) the architecture creation cost and (2) the life-time evaluation cost. We show that over time, these costs are non-negligible and are having a direct impact on our future. Importantly, we conduct an ethical analysis of how the CV-community is unintentionally overlooking its own ethical AI principles by emitting this level of CO2. To address these concerns, we propose adding "enforcement" as a pillar of ethical AI and provide some recommendations for how architecture designers and broader CV community can curb the climate crisis.
We propose a refinement of the notion of blow-Nash equivalence between Nash function germs, which is an analog in the Nash setting of the blow-analytic equivalence defined by T.-C. Kuo. The new definition is more natural and geometric. Moreover, this equivalence relation still does not admit moduli for a Nash family of isolated singularities. Some previous invariants are no longer invariants for this new relation, however, thanks to a Denef & Loeser formula coming from motivic integration in a Nash setting, we managed to derive new invariants for this equivalence relation.
In this paper we address the problem of systems under an external feedback. This is performed using a large deviation approach and rate distortion from information theory. In particular we define a lower boundary for the maximum entropy reduction that can be obtained using a feedback apparatus with a well defined accuracy in terms of measurement of the state of the system. The large deviation approach allows also to define a new set of potentials, including information, which similarly to more conventional thermodynamic potentials can define the state with optimal use of the information given the accuracy of the feedback apparatus.
We explore geometrical properties of fermionic vertex operators for a NSR superstring in order to establish connection between worldsheet and target space supersymmetries. The mechanism of picture-changing is obtained as a result of imposing certain constraints on a world-sheet gauge group of the NSR theory. It is found that picture-changing operators of various integer ghost numbers form a polynomial ring. By using properties of the picture-changing formalism we establish connection between the NSR and GS superstring theories. We explore the properties of the $\kappa$-symmetry in the NSR formalism and show that it leads to some new identities between correlation functions.
The electronic structure of the recently synthesised (3x3) reconstructed silicene on (4x4) Ag(111) is investigated by first-principles calculations. New states emerge due to the strong hybridization between silicene and Ag. Analyzing the nature and composition of these hybridized states, we show that i) it is possible to clearly distinguish them from states coming from the Dirac cone of free-standing silicene or from the sp-bands of bulk Ag and ii) assign their contribution to the description of the linearly dispersing band observed in photoemission. Furthermore, we show that silicene atoms contribute to the Fermi level, which leads to similar STM patterns as observed below or above the Fermi level. Our findings are crucial for the proper interpretation of experimental observations.
Long ago, Argyres and Douglas discovered a particularly simple interacting 4D $\mathcal{N}=2$ superconformal field theory (SCFT) on the Coulomb branch of $SU(3)$ $\mathcal{N}=2$ super Yang-Mills. Further hints of the theory's simplicity arise due to the fact that it has the smallest possible value of the $c$ central charge among unitary interacting $\mathcal{N}=2$ SCFTs. A main purpose of this note is to uncover additional aspects of this minimal Argyres-Douglas (MAD) theory's simplicity. In particular, we argue that: (1) the MAD theory shares an infinite set of large spin thresholds in part of its operator spectrum with the free $\mathcal{N}=2$ Maxwell theory (this data is therefore invariant under generic $\mathcal{N}=2$-preserving renormalization group flows to the IR) and (2) the MAD theory has, at every order in the natural grading, the smallest number of "Schur" operators of any unitary $\mathcal{N}=2$ theory (interacting or free). We then show that property (1) has a suitable generalization for all $(A_1, A_{2k})$ cousins of the MAD theory. In particular, the corresponding large spin thresholds encode generic renormalization group flows within this class. This construction therefore gives a different handle on these flows from the one provided by the Seiberg-Witten description. To emphasize the importance of these spin thresholds, we abstractly study theories with "enough matter" to form Higgs branches and argue that infinitely many spin thresholds are small or vanishing.
We consider the ADM formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond General Relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the universe following the spirit of Weyl's postulate, has been fixed, $f$ theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation, i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued $f$ functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected Loop Quantum Cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.