ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\goth E(\goth p)$ denote the Eisenstein ideal in the Hecke algebra $\Bbb T(\goth p)$ of the Drinfeld modular curve $X_0(\goth p)$ parameterizing Drinfeld modules of rank two over $\Bbb F_q[T]$ of general characteristic with Hecke level $\goth p$-structure, where $\goth p\triangleleft\Bbb F_q[T]$ is a non-zero prime ideal. We prove that the characteristic $p$ of the field $\Bbb F_q$ does not divide the order of the quotient $\Bbb T(\goth p)/\goth E(\goth p)$ and the Eisenstein ideal $\goth E(\goth p)$ is locally principal.
A large number of publications are available for the Optical Character Recognition (OCR). Significant researches, as well as articles are present for the Latin, Chinese and Japanese scripts. Arabic script is also one of mature script from OCR perspective. The adaptive languages which share Arabic script or its extended characters; still lacking the OCRs for their language. In this paper we present the efforts of researchers on Arabic and its related and adapted languages. This survey is organized in different sections, in which introduction is followed by properties of Sindhi Language. OCR process techniques and methods used by various researchers are presented. The last section is dedicated for future work and conclusion is also discussed.
We develop a method by which vacuum transitions may be included in light-front calculations. This allows tadpole contributions which are important for symmetry-breaking effects and yet are missing from standard light-front calculations. These transitions also dictate a nontrivial vacuum and contributions from vacuum bubbles to physical states. In nonperturbative calculations these separate classes of contributions (tadpoles and bubbles) cannot be filtered; instead, we regulate the bubbles and subtract the vacuum energy from the eigenenergy of physical states. The key is replacement of momentum-conserving delta functions with model functions of finite width; the width becomes the regulator and is removed after subtractions. The approach is illustrated in free scalar theory, quenched scalar Yukawa theory, and in a limited Fock-space truncation of $\phi^4$ theory.
Membranes of carbon allotropes comprised solely of densely packed pentagonal rings, known as pentagraphene, exhibit negative Poisson's ratio (auxetic behavior) and a bandgap of $3.2$ eV. In this work, we investigated the structural stability, mechanical and fracture properties of nanotubes formed by rolling up pentagraphene membranes, the so-called pentagraphene nanotubes (PGNTs). Single-walled PGNT of three distinct configurations: zigzag, $\alpha$-armchair, and $\beta$-armchair were studied combining first-principles calculations and reactive molecular dynamics simulations. Our results showed Young's modulus values of $680-800 GPa$, critical strain of $18-21\%$, and ultimate tensile stress of $85-110 GPa$. We also observed auxetic behavior. During stretching at room temperature, we observed a transition between $\beta$-armchair to $\alpha$-armchair PGNT close to the critical strain. With relation to fracture patterns, we observed that mechanical failure starts at bonds mostly aligned to the stretching direction and after tube radial collapse.
Existing alignment-based methods have to employ the pretrained human parsing models to achieve the pixel-level alignment, and cannot identify the personal belongings (e.g., backpacks and reticule) which are crucial to person re-ID. In this paper, we propose the identity-guided human semantic parsing approach (ISP) to locate both the human body parts and personal belongings at pixel-level for aligned person re-ID only with person identity labels. We design the cascaded clustering on feature maps to generate the pseudo-labels of human parts. Specifically, for the pixels of all images of a person, we first group them to foreground or background and then group the foreground pixels to human parts. The cluster assignments are subsequently used as pseudo-labels of human parts to supervise the part estimation and ISP iteratively learns the feature maps and groups them. Finally, local features of both human body parts and personal belongings are obtained according to the selflearned part estimation, and only features of visible parts are utilized for the retrieval. Extensive experiments on three widely used datasets validate the superiority of ISP over lots of state-of-the-art methods. Our code is available at https://github.com/CASIA-IVA-Lab/ISP-reID.
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.
The aberrated radiation pressure at the inner edge of the accretion disk around an astrophysical black hole imparts a relative azimuthal velocity on the electrons with respect to the ions which gives rise to a ring electric current that generates large scale poloidal magnetic field loops. This is the Cosmic Battery established by Contopoulos and Kazanas in 1998. In the present work we perform realistic numerical simulations of this important astrophysical mechanism in advection-dominated accretion flows-ADAF. We confirm the original prediction that the inner parts of the loops are continuously advected toward the central black hole and contribute to the growth of the large scale magnetic field, whereas the outer parts of the loops are continuously diffusing outward through the turbulent accretion flow. This process of inward advection of the axial field and outward diffusion of the return field proceeds all the way to equipartition, thus generating astrophysically significant magnetic fields on astrophysically relevant timescales. We confirm that there exists a critical value of the magnetic Prandtl number between unity and 10 in the outer disk above which the Cosmic Battery mechanism is suppressed.
An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so as to be able to weigh any integer weight l < m with as few weights as possible and only one scale pan.   We show that the number of parts of an M-partition is a log-linear function of m and the M-partitions of m correspond to lattice points in a polytope. We exhibit a recurrence relation for counting the number of M-partitions of m and, for ``half'' of the positive integers, this recurrence relation will have a generating function. The generating function will be, in some sense, the same as the generating function for counting the number of distinct binary partitions for a given integer.
Organic charge-transfer complexes (CTCs) formed by strong electron acceptor and strong electron donor molecules are known to exhibit exotic effects such as superconductivity and charge density waves. We present a low-temperature scanning tunneling microscopy and spectroscopy (LT-STM/STS) study of a two-dimensional (2D) monolayer CTC of tetrathiafulvalene (TTF) and fluorinated tetracyanoquinodimethane (F4TCNQ), self-assembled on the surface of oxygen-intercalated epitaxial graphene on Ir(111) (G/O/Ir(111)). We confirm the formation of the charge-transfer complex by dI/dV spectroscopy and direct imaging of the singly-occupied molecular orbitals. High-resolution spectroscopy reveals a gap at zero bias, suggesting the formation of a correlated ground state at low temperatures. These results point to the possibility to realize and study correlated ground states in charge-transfer complex monolayers on weakly interacting surfaces.
The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends also to its inverted counterpart, in which the oscillator frequency is analytically continued to pure imaginary values. In this article we probe the inverted harmonic oscillator (IHO) with recently developed quantum chaos diagnostics such as the out-of-time-order correlator (OTOC) and the circuit complexity. In particular, we study the OTOC for the displacement operator of the IHO with and without a non-Gaussian cubic perturbation to explore genuine and quasi scrambling respectively. In addition, we compute the full quantum Lyapunov spectrum for the inverted oscillator, finding a paired structure among the Lyapunov exponents. We also use the Heisenberg group to compute the complexity for the time evolved displacement operator, which displays chaotic behaviour. Finally, we extended our analysis to N-inverted harmonic oscillators to study the behaviour of complexity at the different timescales encoded in dissipation, scrambling and asymptotic regimes.
The common-envelope (CE) phase is an important stage in the evolution of binary stellar populations. The most common way to compute the change in orbital period during a CE is to relate the binding energy of the envelope of the Roche-lobe filling giant to the change in orbital energy. Especially in population-synthesis codes, where the evolution of millions of stars must be computed and detailed evolutionary models are too expensive computationally, simple approximations are made for the envelope binding energy. In this study, we present accurate analytic prescriptions based on detailed stellar-evolution models that provide the envelope binding energy for giants with metallicities between Z = 10-4 and Z = 0.03 and masses between 0.8 Msun and 100 Msun, as a function of the metallicity, mass, radius and evolutionary phase of the star. Our results are also presented in the form of electronic data tables and Fortran routines that use them. We find that the accuracy of our fits is better than 15% for 90% of our model data points in all cases, and better than 10% for 90% of our data points in all cases except the asymptotic giant branches for three of the six metallicities we consider. For very massive stars (M > 50 Msun), when stars lose more than ~20% of their initial mass due to stellar winds, our fits do not describe the models as accurately. Our results are more widely applicable - covering wider ranges of metallicity and mass - and are of higher accuracy than those of previous studies.
We present some (unfortunately not all) known properties on the Cremona group; when it's possible we mentioned links with the most known group of polynomial automorphisms of the affine plane. The mentioned properties are essentially algebraic properties: generators, relations, finite subgroups, subgroups of finite type, automorphisms of the Cremona group, Tits alternative... but also dynamical properties: classification of birational maps, centralizer, dynamic of an Heisenberg subgroup... We deal with the construction of entropic automorphisms on rational surfaces.
We present a simple modification of the Altarelli-Feruglio $A_4$ flavor symmetry model using a minimal number of parameters congruous with the symmetries of the original theory. The resulting model is consistent with all presently known data on neutrino masses and mixings. Furthermore, it makes testable tight predictions for future experiments aimed at improving the measurements of $\sin^2\theta_{12}$, $\sin^2\theta_{13}$, $\delta_{\rm CP}$ and the neutrinoless double-beta decay parameter $|m_{ee}|$. Our model exploits the unique possibility of multiple allowed, yet qualitatively different, contractions of fields charged under the $A_4$ discrete symmetry.
We investigate the three-point correlation between the Lyman-$\alpha$ forest and the CMB weak lensing ($\delta_F \delta_F \kappa$) expressed as the cross-correlation between the CMB weak lensing field and local variations in the forest power spectrum. In addition to the standard gravitational bispectrum term, we note the existence of a non-standard systematic term coming from mis-estimation of the mean flux over the finite length of Lyman-$\alpha$ skewers. We numerically calculate the angular cross-power spectrum and discuss its features. We integrate it into zero-lag correlation function and compare our predictions with recent results by Doux et al.. We find that our predictions are statistically consistent with the measurement, and including the systematic term improves the agreement with the measurement. We comment on the implication of the response of the Lyman-$\alpha$ forest power spectrum to the long-wavelength density perturbations.
We discuss electron-positron pair-production by super-intense, short laser pulses off the physical vacuum state locally deformed by (stripped) nuclei with large nuclear charges. Consequences of non-perturbative vacuum polarisation resulting from such a deformation are shortly broached. Production probabilities per pulse are calculated.
The ~1700 year old PSR B0540-69 in the LMC is considered the twin of the Crab pulsar because of its similar spin parameters, magnetic field, and energetics. Its optical spectrum is fit by a power-law, ascribed to synchrotron radiation, like for the young Crab and Vela pulsars. nIR observations, never performed for PSR B0540-69, are crucial to determine whether the optical power-law spectrum extends to longer wavelengths or a new break occurs, like it happens for both the Crab and Vela pulsars in the mIR, hinting at an even more complex particle energy and density distribution in the pulsar magnetosphere. We observed PSR B0540-69 in the J, H, and Ks bands with the VLT to detect it, for the first time, in the nIR and characterise its optical-to-nIR spectrum. To disentangle the pulsar emission from that of its pulsar wind nebula (PWN), we obtained high-spatial resolution adaptive optics images with NACO. We could clearly identify PSR B0540-69 in our J, H, and Ks-band images and measure its flux (J=20.14, H=19.33, Ks=18.55, with an overall error of +/- 0.1 magnitudes in each band). The joint fit to the available optical and nIR photometry with a power-law spectrum gives a spectral index alpha=0.70 +/-0.04. The comparison between our NACO images and HST optical ones does not reveal any apparent difference in the PWN morphology as a function of wavelength. The PWN optical-to-nIR spectrum is also fit by a single power-law, with spectral index alpha=0.56+/- 0.03, slightly flatter than the pulsar's. Using NACO at the VLT, we obtained the first detection of PSR B0540-69 and its PWN in the nIR. Due to the small angular scale of the PWN (~4") only the spatial resolution of the JWST will make it possible to extend the study of the pulsar and PWN spectrum towards the mid-IR.
A composition analysis of KASCADE air shower data is performed by means of unfolding the two-dimensional frequency spectrum of electron and muon numbers. Aim of the analysis is the determination of energy spectra for elemental groups representing the chemical composition of primary cosmic rays. Since such an analysis depends crucially on simulations of air showers the two different hadronic interaction models QGSJet and SIBYLL are used for their generation. The resulting primary energy spectra show that the knee in the all particle spectrum is due to a steepening of the spectra of light elements but, also, that neither of the two simulation sets is able to describe the measured data consistently over the whole energy range with discrepancies appearing in different energy regions.
Based on over 5400 BV images of 47 Tuc collected between 1998 and 2010 we obtained light curves of 65 variables, 21 of which are newly detected objects. New variables are located mostly just outside of the core in a region poorly studied by earlier surveys of the cluster. Among them there are four detached eclipsing binaries and five likely optical counterparts of X-ray sources. Two detached systems are promising targets for follow-up observations. We briefly discuss properties of the most interesting new variables.
The role of slight changes of the chemical composition on antiferromagnetic ordering of Cr in rare-earth orthochoromites was investigated on a series of ceramic solid-solutions Ce$_{1-x}$Eu${_x}$O$_3$ where x varied from 0 to 1. Gradual replacement of Ce with Eu reduces the cell volume and acts equivalently to applying external pressure. Full replacement of Ce by Eu, on the other hand, reduces the N\'{e}el temperature from 260 K for CeCrO$_3$ to 178 K for EuCrO$_3$ as established by magnetization, heat capacity and neutron powder diffraction measurements. High resolution x-ray powder diffraction measurements on Ce$_{1-x}$Eu${_x}$O$_3$ and neutron powder diffraction studies on CeCrO$_3$ enable to correlate the magnetic properties of the Cr magnetic subsystem with the size of the lattice and minute changes of the bonding and torsion angles within and between the CrO$_6$ octahedra. We find that the sizes and the shapes of the CrO$6$ octahedra remain essentially unchanged as the size of the rare-earth cations is reduced whereas decreasing Cr - O - Cr bonding angles and increasing inclination of neighboring octahedra enable to compensate for the decreasing lattice size.
We present inelastic neutron scattering data on the quantum paramagnet AgVOAsO4 that establish the system is a S=1/2 alternating spin chain compound and provide a direct measurement of the spin gap. We also present experimental evidence for two different types of field-induced magnetic order between mu_0H_c1 = 8.4T and mu_0H_c2 = 48.9T, which may be related to Bose-Einstein condensation (BEC) of triplons. Thermodynamic measurements in magnetic fields up to 60T and temperatures down to 0.1K reveal a H-T phase diagram consisting of a dome encapsulating two ordered phases with maximum ordering temperatures of 3.8K and 5.3K respectively. This complex phase diagram is not expected for a single-Q BEC system and therefore establishes AgVOAsO4 as a promising multi-Q BEC candidate capable of hosting exotic vortex phases.
We analyze the evolution of shock waves in high-resolution 3D radiative MHD simulations of the quiet Sun and their synthetic emission characteristics. The simulations model the dynamics of a 12.8x12.8x15.2 Mm quiet-Sun region (including a 5.2 Mm layer of the upper convection zone and a 10 Mm atmosphere from the photosphere to corona) with an initially uniform vertical magnetic field of 10 G, naturally driven by convective flows. We synthesize the Mg II and C II spectral lines observed by the IRIS satellite and EUV emission observed by the SDO/AIA telescope. Synthetic observations are obtained using the RH1.5D radiative transfer code and temperature response functions at both the numerical and instrumental resolutions. We found that the Doppler velocity jumps of the C II 1334.5 A IRIS line and a relative enhancement of the emission in the 335 A SDO/AIA channel are the best proxies for the enthalpy deposited by shock waves into the corona (with Kendall's $\tau$ correlation coefficients of 0.59 and 0.38, respectively). The synthetic emission of the lines and extreme ultraviolet passbands are correlated with each other during the shock wave propagation. All studied shocks are mostly hydrodynamic (i.e., the magnetic energy carried by horizontal fields is $\leq{}$2.6% of the enthalpy for all events) and have Mach numbers > 1.0-1.2 in the low corona. The study reveals the possibility of diagnosing energy transport by shock waves into the solar corona, as well as their other properties, by using IRIS and SDO/AIA sensing observations.
Ordinary baryonic particles (such as protons and neutrons) account for only one-sixth of the total matter in the Universe. The remainder is a mysterious "dark matter" component, which does not interact via the electromagnetic force and thus neither emits nor reflects light. However, evidence is mounting for its gravitational influence. The past few years have seen particular progress in observations of weak gravitational lensing, the slight deflection of light from distant galaxies due to the curvature of space around foreground mass. Recent surveys from the Hubble Space Telescope have provided direct proof for dark matter, and the first measurements of its properties. We review recent results, then prospects and challenges for future gravitational lensing surveys.
The redshift of $z\sim1.5$ is the transition epoch of protoclusters (PCs) from the star-forming phase into the quenching phase, and hence an appropriate era to investigate the build up of the quenched population. We define a `core' as the most massive halo in a given PC, where environmental effects are likely to work most effectively, and search for cores at $1<z<1.5$. We use a photometric redshift catalogue of a wide (effective area of $\sim22.2\,\mathrm{deg}^{2}$) and deep ($i\sim26.8\,\mathrm{mag}$) optical survey with Subaru Hyper-Suprime Cam. Regarding galaxies with $\log(M_{*}/M_{\odot})>11.3$ as the central galaxies of PC cores, we estimate their average halo mass by clustering analysis and find it to be $\log(M_\mathrm{h}/M_{\odot})\sim13.7$. An expected mass growth by the IllustrisTNG simulation and the observed overdensities around them suggest that the PC cores we find are progenitors of present-day clusters. Classifying our galaxy sample into red and blue galaxies, we calculate the stellar mass function (SMF) and the red galaxy fraction. The SMFs in the PC cores are more-top heavy than field, implying early high-mass galaxy formation and disruption of low-mass galaxies. We also find that the red fraction increases with stellar mass, consistent with stellar-mass dependent environmental quenching recently found at $z>1$. Interestingly, although the cores with red and blue centrals have similar halo masses, only those with red centrals show a significant red fraction excess compared to the field, suggesting a conformity effect. Some observational features of PC cores may imply that the conformity is caused by assembly bias.
Let $X$ be a ringed space together with the data $M$ of a set $M_x$ of prime ideals of $\O_{X,x}$ for each point $x \in X$. We introduce the localization of $(X,M)$, which is a locally ringed space $Y$ and a map of ringed spaces $Y \to X$ enjoying a universal property similar to the localization of a ring at a prime ideal. We use this to prove that the category of locally ringed spaces has all inverse limits, to compare them to the inverse limit in ringed spaces, and to construct a very general $\Spec$ functor. We conclude with a discussion of relative schemes.
We consider a class of interaction terms that describes correlated tunneling of composite fermions between effective Landau levels. Despite being generic and of similar strength to that of the usual density-density couplings, these terms are not included in the accepted theory of the edges of fractional quantum Hall systems. Here we show that they may lead to an instability of the edge towards a new reconstructed state with additional channels, and thereby demonstrate the incompleteness of the traditional edge theory.
Both lattice simulations and theoretical studies show that the spectral function of the gluon propagator of QCD (in various gauges, as well as for the gauge-invariant Pinch Technique, or PT, propagator) is not non-negative everywhere, although it should be if it has a physical interpretation as in QED. Theory says moreover that the non-positive spectral function of the Landau-gauge or of the PT gluon propagator is further constrained to obey a superconvergence relation (the integral of the spectral function vanishes). We review the theoretical and lattice evidence for violation of positivity as well as various interpretations of this violation, and consider methods for checking superconvergence on the lattice (so far undone). The most common interpretation is that positivity violation implies confinement of gluons, so the gluon propagator does not describe processes with physical gluons. Another more direct and gauge-invariant interpretation arises from the PT: Asymptotic freedom alone demands non-positivity and superconvergence.