ShantanuT01/DACTYL-Pretraining huggingface dataset:
Working over the complex field and formalizing and sharpening approaches introduced by several authors, we give a method for verifying when a divisor on a blow up of P^2 at general points is nef. The method is useful both theoretically and when doing computer computations. The main application is to obtain significantly improved explicit lower bounds for multipoint Seshadri constants on P^2.
[Abridged] We present a new approach to investigate the content and spatial distribution of dust in structurally unresolved star-forming galaxies from the observed dependence of integrated spectral properties on galaxy inclination. We develop an innovative combination of generic models of radiative transfer (RT) in dusty media with a prescription for the spectral evolution of galaxies, via the association of different geometric components of galaxies with stars in different age ranges. We show that a wide range of RT models all predict a quasi-universal relation between slope of the attenuation curve at any wavelength and V-band attenuation optical depth in the diffuse interstellar medium (ISM), at all galaxy inclinations. This relation predicts steeper (shallower) dust attenuation curves than both the Calzetti and MW curves at small (large) attenuation optical depths, which implies that geometry and orientation effects have a stronger influence on the shape of the attenuation curve than changes in the optical properties of dust grains. We use our combined RT and spectral evolution model to interpret the observed dependence of the H\alpha/H\beta\ ratio and ugrizYJH attenuation curve on inclination in a sample of ~23 000 nearby star-forming galaxies. From a Bayesian MCMC fit, we measure the central face-on B-band optical depth of this sample to be tau_B\perp~1.8\pm0.2. We also quantify the enhanced optical depth towards newly formed stars in their birth clouds, finding this to be significantly larger in galaxies with bulges than in disc-dominated galaxies, while tau_B\perp is roughly similar in both cases. Finally, we show that neglecting the effect of geometry and orientation on attenuation can severely bias the interpretation of galaxy spectral energy distributions, as the impact on broadband colours can reach up to 0.3-0.4 mag at optical wavelengths and 0.1 mag at near-infrared ones.
In this paper we study the sum of powers in the Gaussian integers $\mathbf{G}_k(n):=\sum_{a,b \in [1,n]} (a+b i)^k$. We give an explicit formula for $\mathbf{G}_k(n) \pmod n $ in terms of the prime numbers $p \equiv 3 \pmod 4$ with $p \mid \mid n$ and $p-1 \mid k$, similar to the well known one due to von Staudt for $\sum_{i=1}^n i^k \pmod n$. We apply this formula to study the set of integers $n$ which divide $\mathbf{G}_n(n)$ and compute its asymptotic density with six exact digits: $0.971000\ldots$.
Recognizing text in natural images is a challenging task with many unsolved problems. Different from those in documents, words in natural images often possess irregular shapes, which are caused by perspective distortion, curved character placement, etc. We propose RARE (Robust text recognizer with Automatic REctification), a recognition model that is robust to irregular text. RARE is a specially-designed deep neural network, which consists of a Spatial Transformer Network (STN) and a Sequence Recognition Network (SRN). In testing, an image is firstly rectified via a predicted Thin-Plate-Spline (TPS) transformation, into a more "readable" image for the following SRN, which recognizes text through a sequence recognition approach. We show that the model is able to recognize several types of irregular text, including perspective text and curved text. RARE is end-to-end trainable, requiring only images and associated text labels, making it convenient to train and deploy the model in practical systems. State-of-the-art or highly-competitive performance achieved on several benchmarks well demonstrates the effectiveness of the proposed model.
Single-view depth prediction is a fundamental problem in computer vision. Recently, deep learning methods have led to significant progress, but such methods are limited by the available training data. Current datasets based on 3D sensors have key limitations, including indoor-only images (NYU), small numbers of training examples (Make3D), and sparse sampling (KITTI). We propose to use multi-view Internet photo collections, a virtually unlimited data source, to generate training data via modern structure-from-motion and multi-view stereo (MVS) methods, and present a large depth dataset called MegaDepth based on this idea. Data derived from MVS comes with its own challenges, including noise and unreconstructable objects. We address these challenges with new data cleaning methods, as well as automatically augmenting our data with ordinal depth relations generated using semantic segmentation. We validate the use of large amounts of Internet data by showing that models trained on MegaDepth exhibit strong generalization-not only to novel scenes, but also to other diverse datasets including Make3D, KITTI, and DIW, even when no images from those datasets are seen during training.
While the Band function or other phenomenological functions are commonly used to fit GRB prompt emission spectra, we propose a new parametric function that is inspired by an internal shock physical model. We use this function as a proxy of the model to confront it easily to GRB observations. We built a parametric function that represents the spectral form of the synthetic bursts provided by our internal shock synchrotron model (ISSM). We simulated the response of the Fermi instruments to the synthetic bursts and fitted the obtained count spectra to validate the ISSM function. Then, we applied this function to a sample of 74 bright GRBs detected by the Fermi/GBM, and we computed the width of their spectral energy distributions around their peak energy. For comparison, we fitted also the phenomenological functions that are commonly used in the literature. Finally, we performed a time-resolved analysis of the broadband spectrum of GRB 090926A, which was jointly detected by the Fermi GBM and LAT. The ISSM function reproduces 81% of the spectra in the GBM bright GRB sample, versus 59% for the Band function, for the same number of parameters. It gives also relatively good fits to the GRB 090926A spectra. The width of the MeV spectral component that is obtained from the fits of the ISSM function is slightly larger than the width from the Band fits, but it is smaller when observed over a wider energy range. Moreover, all of the 74 analysed spectra are found to be significantly wider than the synthetic synchrotron spectra. We discuss possible solutions to reconcile the observations with the internal shock synchrotron model, such as an improved modeling of the shock micro-physics or more accurate spectral measurements at MeV energies.
Observations of globular clusters in dwarf galaxies can be used to study a variety of topics, including the structure of dark matter halos and the history of vigorous star formation in low-mass galaxies. We report on the properties of the faint globular cluster (M_V ~ -3.4) in the M31 dwarf galaxy Andromeda I. This object adds to the growing population of low-luminosity Local Group galaxies that host single globular clusters.
In this paper, we clarify the mistakes made in the former article entitled "Vanishing Theorems on Toric Varieties in Positive Characteristic". On the other hand, we use the positive characteristic method to reprove the Bott vanishing theorem, the degeneration of the Hodge to de Rham spectral sequence and the Kawamata-Viehweg vanishing theorem for log pairs on toric varieties over a field of arbitrary characteristic, where concerned Weil divisors are torus invariant.
We present a series of monitoring observations of the Crab Nebula with the Chandra X-ray Observatory, focusing on the temporal evolution of the structure. This series of 8 observations, spanning a period of approximately six months, shows the dynamic nature of the inner X-ray structures. We detected outward moving ``wisps'' from the recently discovered inner ring seen in optical observations. We also find that the inner ring itself shows temporal variations in structure. The torus also appears to be expanding. Such temporal variations generally match the canonical scenario that an expanding synchrotron nebula injected from the pulsar is confined by the supernova ejecta.
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when they reach diameter at least N was studied in earlier papers. Using volume as a way to measure the size of a cluster - instead of diameter - leads, for large N, to a quite different behavior (contrary to what happens on the binary tree, where the volume model and the diameter model are "asymptotically the same"). In particular, we show the existence of a sequence of "exceptional" length scales.
The continuum resonance spectrum of $^5$H ($^3$H+$n$+$n$) is investigated by use of the complex scaled hyperspherical adiabatic expansion method. The crucial $^3$H-neutron potential is obtained by switching off the Coulomb part from successful fits to $^3$He-proton experimental data. These two-body potentials must be expressed exclusively by operators conserving the nucleon-core mean field angular momentum quantum numbers. The energies $E_R$ and widths $\Gamma_R$ of the $1/2^+$ ground-state resonance and the lowest two excited $5/2^+$ and $3/2^+$-resonances are found to be $(1.6,1.5)$ MeV, $(2.8,2.5)$ MeV and $(3.2,3.9)$ MeV, respectively. These results agree with most of the experimental data. The energy distributions of the fragments after decay of the resonances are predicted.
The generalized Cauchy-Riemann equations (GCRE) in biquaternion algebra appear to be Lorentz-invariant. The Laplace equation is in this case replaced by a nonlinear (complexified) eikonal equation. GCRE contain the 2-spinor and the gauge structures, and their integrability conditions take the form of free-source Maxwell and Yang-Mills equations. For the value of electric charge from GCRE only the quantization rule follows, as well as the treatment of Coulomb law as a stereographic map. The equivalent geometrodynamics in a Weyl-Cartan affine space and the conjecture of a complex-quaternion structure of space-time are discussed.
The large N_f self-consistency programme is reviewed. As an application the QCD beta-function is computed at O(1/N_f) and the anomalous dimensions of polarized twist-2 singlet operators are determined at the same order.
We revisit the color-magnitude relation (CMR) of the Virgo cluster early-type galaxies in order to explore its alleged non-linearity. To this aim, we reanalyze the relation already published from data obtained within the ACS Virgo Cluster Survey of the Hubble Space Telescope, and perform our own photometry and analysis of the images of the 100 early-type galaxies observed as part of this survey. In addition, we compare our results with those reported in the literature from data of the Sloan Digital Sky Survey. We have found that when the brightest galaxies and untypical systems are excluded from the sample, a linear relation arises in agreement with what is observed in other groups and clusters. The central regions of the brightest galaxies also follow this relation. In addition, we notice that Virgo contains at least four compact elliptical galaxies besides the well known object VCC 1297 (NGC 4486B). Their locations in the <mueff>-luminosity diagram define a different trend to that followed by normal early-type dwarf galaxies, setting an upper limit in effective surface brightness and a lower limit in effective radius for their luminosities. Based on the distribution of different galaxy sub-samples in the color-magnitude and <mueff>-luminosity diagrams we draw some conclusions on their formation and the history of their evolution.
Null and timelike equatorial orbits are investigated in a family of hairy black holes in the cubic Galileon theory. These include rotating generalizations of static black hole metrics supporting a time-dependent scalar field. Depending on the coupling and rotation, the properties of the geodesics expectedly deviate from general relativity. In particular, it is found that stable circular geodesics only exist below a critical coupling, which is related to the existence of an outermost stable circular orbit. Focusing on the strong-field region, images of an accretion disk are also produced to highlight tendencies that would constrain the model given further accurate observations of supermassive black holes.
The interstellar medium (ISM) is constantly evolving due to unremitting injection of energy in various forms. Energetic radiation transfers energy to the ISM: from the UV photons, emitted by the massive stars, to X- and $\gamma$-ray ones. Cosmic rays are another source of energy. Finally, mechanical energy is injected through shocks or turbulence. Shocks are ubiquitous in the interstellar medium of galaxies. They are associated to star formation (through jets and bipolar outflows), life (via stellar winds), and death (in AGB stellar winds or supernovae explosion). The dynamical processes leading to the formation of molecular clouds also generate shocks where flows of interstellar matter collide. Because of their ubiquity, the study of interstellar shocks is also a useful probe to the other mechanisms of energy injection in the ISM. This study must be conducted in order to understand the evolution of the ISM as a whole, and to address various questions: what is the peculiar chemistry associated to shocks, and what is their contribution to the cycle of matter in galaxies ? What is the energetic impact of shocks on their surroundings on various scales, and hence what is the feedback of stars on the galaxies ? What are the scenarios of star formation, whether this star formation leads to the propagation of shocks, or whether it is triggered by shock propagation ? What is the role of shocks in the acceleration of cosmic rays ? Can they shed light on their composition and diffusion processes ? In order to progress on these questions, it is paramount to interpret the most precise observations with the most precise models of shocks. From the observational point of view, the James Webb Space Telescope represents a powerful tool to better address the above questions, as it will allow to observe numerous shock tracers in the infrared range at an unprecedented spatial and spectral resolution.
In this paper, our aim is to investigate necessary conditions for optimal investment. We model the wealth process by Backward differential stochastic equations (shortly for BSDE) with or without constraints on wealth and portfolio process. The constraints can be very general thanks the non-smooth analysis method we adopted.
In this article we shall derive functional limit theorems for the multi-dimensional elephant random walk (MERW) and thus extend the results provided for the one-dimensional marginal by Bercu and Laulin (2019). The MERW is a non-Markovian discrete time-random walk on $\mathbb{Z}^d$ which has a complete memory of its whole past, in allusion to the traditional saying that an elephant never forgets. As the name suggests, the MERW is a $d$-dimensional generalisation of the elephant random walk (ERW), the latter was first introduced by Sch\"utz and Trimper in 2004. We measure the influence of the elephant's memory by a so-called memory parameter $p$ between zero and one. A striking feature that has been observed by Sch\"utz and Trimper is that the long-time behaviour of the ERW exhibits a phase transition at some critical memory parameter $p_c$. We investigate the asymptotic behaviour of the MERW in all memory regimes by exploiting a connection between the MERW and P\'olya urns, following similar ideas as in the work by Baur and Bertoin for the ERW.
Correlations of two like charged pions emitted from a hot and charged spherically expanding nuclear system are investigated. The motion of the pions is described quantum mechanically using the Klein-Gordon equation which includes Coulomb field and pion absorption. Flow modifies the radial distribution of the source function and rescales the pion wave functions. The radii extracted from the correlation functions are calculated in sideward and outward direction as a function of the pair momentum. Comparison with recent measurements at SIS and AGS energies is made.
The primordial CMB $B$-mode search is on the spotlight of the scientific community due to the large amount of cosmological information that is encoded in the primeval signal. However, the detection of this signal is challenging from the data analysis point of view, due to the relative low amplitude compared to the foregrounds, the lensing contamination coming from the leakage of $E$-modes, and the instrumental noise. Here, we studied the viability of the detection of the primordial polarization $B$-mode with a ground-based telescope operating in the microwave low-frequency regime (i.e., from 10GHz-120GHz) in a handful of different scenarios: i. the instrument's channels distribution and noise, ii. the tensor-to-scalar ratio ($r$) detectability considering different possible $r$ values and degrees of delensing, iii. the effect of including a possible source of polarized anomalous microwave emission (AME), iv. the strengths and weaknesses of different observational strategies and, v. the atmospheric and systematic noise impact on the recovery. We focused mainly on the removal of galactic foregrounds as well as noise contamination by applying a full-parametric pixel-based maximum likelihood component separation technique. Moreover, we developed a numerical methodology to estimate the residuals power spectrum left after component separation, which allow us to mitigate possible biases introduced in the primordial $B$-mode power spectrum reconstruction. Among many other results, we found that this sort of experiment is capable of detecting Starobinsky's $r$ even when no delensing is performed or, a possible polarized AME contribution is taken into account. Besides, we showed that this experiment is a powerful complement to other on-ground or satellite missions, such as LiteBIRD, since it can help significantly with the low-frequency foregrounds characterization.
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.
We report on recent improvements to our non-perturbative calculation of the positronium spectrum. Our Hamiltonian is a two-body effective interaction which incorporates one-photon exchange terms, but neglects fermion self-energy effects. This effective Hamiltonian is diagonalized numerically in a harmonic oscillator basis at strong coupling ($\alpha=0.3$) to obtain the mass eigenvalues. We find that the mass spectrum compares favorably to the Bohr spectrum of non-relativistic quantum mechanics evaluated at this unphysical coupling.
Hybrid magnonics has recently attracted intensive attentions as a promising platform for coherent information processing. In spite of its rapid development, on-demand control over the interaction of magnons with other information carriers, in particular microwave photons in electromagnonic systems, has been long missing, significantly limiting the broad applications of hybrid magnonics. Here, we show that by introducing Floquet engineering into cavity electromagnonics, coherent control on the magnon-microwave photon coupling can be realized. Leveraging the periodic temporal modulation from a Floquet drive, our first-of-its-kind Floquet cavity electromagnonic system can manipulate the interaction between hybridized cavity electromagnonic modes on demand. Moreover, we demonstrate a new coupling regime in such systems: the Floquet ultrastrong coupling, where the Floquet splitting is comparable with or even larger than the level spacing of the two interacting modes, resulting in the breakdown of the rotating wave approximation. Our findings open up new directions for magnon-based coherent signal processing.
This work is devoted to study the existence of infinitely many weak solutions to nonlocal equations involving a general integrodifferential operator of fractional type. These equations have a variational structure and we find a sequence of nontrivial weak solutions for them exploiting the ${\mathbb{Z}}_2$-symmetric version of the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. As a particular case, we derive an existence theorem for the fractional Laplacian, finding nontrivial solutions of the equation $$ \left\{\begin{array}{ll} (-\Delta)^s u=f(x,u) & {\mbox{in}} \Omega\\ u=0 & {\mbox{in}} \erre^n\setminus \Omega. \end{array} \right. $$ As far as we know, all these results are new and represent a fractional version of classical theorems obtained working with Laplacian equations.
Using growth diagrams, we define a skew domino Schensted correspondence which is a domino analogue of the skew Robinson-Schensted correspondence due to Sagan and Stanley. The color-to-spin property of Shimozono and White is extended. As an application, we give a simple generating function for the weighted sum of skew domino tableaux, which is a generalization of Stanley's sign-imbalance formula. The generating function gives a method to calculate the generalized sign-imbalance formula. We also extend Sj{\"o}strand's theorems on sign-imbalance of skew shapes.
Compressibility of boron subarsenide B12As2 has been studied by synchrotron X-ray diffraction up to 47 GPa at room temperature in a diamond anvil cell using Ne pressure transmitting medium. A fit of experimental p-V data by Vinet equation of state yielded the bulk modulus of 150(4) GPa and its first pressure derivative of 6.4(3). No pressure-induced phase transitions have been observed.
Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is possible from these rules to select a new algorithm which performs significantly better than the standard loop algorithm in strong magnetic fields at low temperatures.
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as "spherical" representations consisting of a dense map of essentially ray-traced samples of the object from all directions. These representations offer trade-offs in terms of what object information is captured and to what degree of detail it is captured, but it is not clear how to measure these information trade-offs since the two types of representations are so different. We demonstrate that both types of representations in fact exist at two extremes of a common representational continuum, essentially choosing to prioritize either the number of views of an object or the pixels (i.e., field of view) allotted per view. We identify interesting intermediate representations that lie at points in between these two extremes, and we show, through systematic empirical experiments, how accuracy varies along this continuum as a function of input information as well as the particular deep learning architecture that is used.