ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we consider diffusion semigroups generated by second order differential operators of degenerate type. The operators that we consider do not, in general, satisfy the Hormander condition and are not hypoelliptic. In particular, instead of working under the Hormander paradigm, we consider the so-called UFG condition, introduced by Kusuoka and Strook in the eighties. The UFG condition is weaker than the uniform Hormander condition, the smoothing effect taking place only in certain directions (rather than in every direction, as it is the case when the Hormander condition is assumed). Under the UFG condition, Kusuoka and Strook deduced sharp small time asymptotic bounds for the derivatives of the semigroup in the directions where smoothing occurs. In this paper, we study the large time asymptotics for the gradients of the diffusion semigroup in the same set of directions and under the same UFG condition. In particular, we identify conditions under which the derivatives of the diffusion semigroup in the smoothing directions decay exponentially in time. This paper constitutes therefore a stepping stone in the analysis of the long time behaviour of diffusions which do not satisfy the Hormander condition.
We have embarked upon a project to model the UV spectra of BALQSOs using a Monte Carlo radiative transfer code previously validated through modelling of the winds of cataclysmic variable stars (e.g. Noebauer et al. 2010). We intend to use the simulations to investigate the plausibility of geometric unification (e.g. Elvis 2000) of the different classes of QSO. Here we introduce the code, and present some initial results. These demonstrate that for reasonable geometries and mass loss rates we are able to produce synthetic spectra which reproduce the important features of observed BALQSO spectra.
Graph energy and Domination in graphs are most studied areas of graph theory. In this paper we made an attempt to connect these two areas of graph theory by introducing c-dominating energy of a graph $G$. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.
Ratchet effect -- a {\it dc} current induced by the electromagnetic wave impinging on the spatially modulated two-dimensional (2D) electron liquid -- occurs when the wave amplitude is spatially modulated with the same wave vector as the 2D liquid but is shifted in phase. The analysis within the framework of the hydrodynamic model shows that the ratchet current is dramatically enhanced in the vicinity of the plasmonic resonances and has nontrivial polarization dependence. In particular, for circular polarization, the current component, perpendicular to the modulation direction, changes sign with the inversion of the radiation helicity. Remarkably, in the high-mobility structures, this component might be much larger than the the current component in the modulation direction. We also discuss the non-resonant regime realized in dirty systems, where the plasma resonances are suppressed, and demonstrate that the non-resonant ratchet current is controlled by the Maxwell relaxation in the 2D liquid.
One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.
Context. The precise determinations of stellar mass at $\sim$1% provide important constraints on stellar evolution models. Accurate parallax measurements can also serve as independent benchmarks for the next Gaia data release. Aims. We aim at measuring the masses and distance of binary systems with a precision level better than 1% using a fully geometrical and empirical method. Methods. We obtained the first interferometric observations for the eclipsing systems AI Phe, AL Dor, KW Hya, NN Del, $\psi$ Cen and V4090 Sgr with the VLTI/PIONIER combiner, which we combined with radial velocity measurements to derive their three-dimensional orbit, masses, and distance. Results. We determined very precise stellar masses for all systems, ranging from 0.04% to 3.3 % precision level. We combined these measurements with stellar effective temperature and linear radius to fit stellar isochrones models and determined the age of the systems. We also derived the distance to the systems with a precision level as high as 0.4%. Conclusions. The comparison of theoretical models with stellar parameters shows that stellar models are still deficient in simultaneously fitting the stellar parameters (Teff , R and M) with such level of precision on individual masses. This stresses the importance of precisely measuring the stellar parameters to better calibrate stellar evolution models. The precision of our model-independent orbital parallaxes varies from 24$\mu$as as to 70$\mu$as and they provide a unique opportunity to check on the future Gaia measurements for possible systematic errors.
The Hilbert class polynomial $H_{\mathcal{O}}(x)\in \mathbb{Z}[x]$ attached to an order $\mathcal{O}$ in an imaginary quadratic field $K$ is the monic polynomial whose roots are precisely the distinct $j$-invariants of elliptic curves over $\mathbb{C}$ with complex multiplication by $\mathcal{O}$. Let $p$ be a prime inert in $K$ and strictly greater than $|\operatorname{disc}(\mathcal{O})|$. We show that the number of $\mathbb{F}_p$-roots of $H_\mathcal{O}(x)\!\! \pmod{p}$ is either zero or $|\operatorname{Pic}(\mathcal{O})[2]|$ by exhibiting a free and transitive action of $\operatorname{Pic}(\mathcal{O})[2]$ on the set of $\mathbb{F}_p$-roots of $H_\mathcal{O}(x)\!\! \pmod p$ whenever it is nonempty. We also provide a concrete criterion for the nonemptiness of the set of $\mathbb{F}_p$-roots. A similar result was first obtained by Xiao et al.~[Int. J. Number Theory, DOI: 10.1142/S1793042122500555] and generalized much further by Li et al.~[arXiv:2108.00168] (that covers the current result) with a different approach.
The vulnerability of face recognition systems to presentation attacks has limited their application in security-critical scenarios. Automatic methods of detecting such malicious attempts are essential for the safe use of facial recognition technology. Although various methods have been suggested for detecting such attacks, most of them over-fit the training set and fail in generalizing to unseen attacks and environments. In this work, we use transfer learning from the vision transformer model for the zero-shot anti-spoofing task. The effectiveness of the proposed approach is demonstrated through experiments in publicly available datasets. The proposed approach outperforms the state-of-the-art methods in the zero-shot protocols in the HQ-WMCA and SiW-M datasets by a large margin. Besides, the model achieves a significant boost in cross-database performance as well.
Numerical results for the Directed Polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for system size considerably larger than that considered previously. For the extreme strong disorder case (Min-Max system), associated with the Directed Percolation model, the expected value of the meandering exponent, zeta = 0.5 is clearly revealed, with very week finite size effects. For the week disorder case, associated with the KPZ equation, finite size effects are stronger, but the value of seta is clearly seen in the vicinity of 0.57. In systems with "strong disorder" it is expected that the system will cross over sharply from Min-Max behavior at short chains to weak disorder behavior at long chains. This is indeed what we find. These results indicate that 1+4 is not the Upper Critical Dimension (UCD) in the week disorder case, and thus 4+1 does not seem to be the upper critical dimension for the KPZ equation.
The model dependence of the predictions of nucleon resonances with hidden charm is investigated. We consider several coupled-channel models which are derived from relativistic quantum field theory by using (1) a unitary transformation method, and (2) the three-dimensional reductions of Bethe-Salpeter Equation. With the same vector meson exchange mechanism, we find that all models give very narrow molecular-like nucleon resonances with hidden charm in the mass range of 4.3 GeV $ < M_R < $ 4.5 GeV, in consistent with the previous predictions.
When asymptotically analysing the summatory function of a $q$-regular sequence in the sense of Allouche and Shallit, the eigenvalues of the sum of matrices of the linear representation of the sequence determine the "shape" (in particular the growth) of the asymptotic formula. Existing general results for determining the precise behavior (including the Fourier coefficients of the appearing fluctuations) have previously been restricted by a technical condition on these eigenvalues.   The aim of this work is to lift these restrictions by providing a insightful proof based on generating functions for the main pseudo Tauberian theorem for all cases simultaneously. (This theorem is the key ingredient for overcoming convergence problems in Mellin--Perron summation in the asymptotic analysis.)   One example is discussed in more detail: A precise asymptotic formula for the amount of esthetic numbers in the first~$N$ natural numbers is presented. Prior to this only the asymptotic amount of these numbers with a given digit-length was known.
We investigate the effect of hydrogen on the mobility of a screw dislocation in body-centered cubic (bcc) iron using first-principles calculations, and show that an increase of screw dislocation velocity is expected for a limited temperature range. The interaction energy between a screw dislocation and hydrogen atoms is calculated for various hydrogen positions and dislocation configurations with careful estimations of the finite size effects, and the strongest binding energy of a hydrogen atom to the stable screw dislocation configuration is estimated to be $256\pm32$ meV. These results are incorporated into a line tension model of a curved dislocation line to elucidate the effect of hydrogen on the dislocation migration process. Both the softening and hardening effect of hydrogen, caused by the reduction of kink nucleation enthalpy and kink trapping, respectively, are evaluated. A clear transition between softening and hardening behavior at the lower critical temperature is predicted, which is in qualitative agreement with the experimental observation.
We present source code for the computer algebra system Mathematica that analyzes the distribution of nearby Galaxies using SDSS data. Download instructions are given, thus within 10 minutes, the reader can verify that galaxies are distributed in an essentially non-homogeneous manner and cluster on 2-dimensional structures. The short code uses a simple method inspired by Minkowski functionals: the distances to the next neighbors are calculated and compared to random distributions in three and two dimensions. The observed distance distribution corresponds clearly to the latter case. The paper may also be helpful for nonexpert scientists to get started with SDSS data analysis.
In this study, hysteresis characteristics of the generalized spin-S binary alloy represented by the formula $A_c B_{1-c}$ have been investigated within the framework of effective field approximation. The binary system consists of type A (spin-S) and type B (spin-S) atoms which are randomly distributed on a honeycomb lattice. Both integer and half-integer spin models of two magnetic atom types are examined. By detailed investigation on hysteresis loops, multiple hysteresis behaviors are obtained for a given set of Hamiltonian parameters. Besides, the quantities of hysteresis characteristics as the hysteresis loop area, remanent magnetization, and coercive field have been investigated as functions of concentration.
Quantum well states (QWSs) can form at the surface or interfaces of materials with confinement potential. They have broad applications in electronic and optical devices such as high mobility electron transistor, photodetector and quantum well laser. The properties of the QWSs are usually the key factors for the performance of the devices. However, direct visualization and manipulation of such states are in general challenging. In this work, by using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy/spectroscopy (STM/STS), we directly probe the QWSs generated on the vacuum interface of a narrow band gap semiconductor Nb2SiTe4. Interestingly, the position and splitting of QWSs could be easily manipulated via potassium (K) dosage onto the sample surface. Our results suggest Nb2SiTe4 to be an intriguing semiconductor system to study and engineer the QWSs, which has great potential in device applications.
We study the non-trivial phase of the two-dimensional breathing kagome lattice, displaying both edge and corner modes. The corner localized modes of a two-dimensional flake were initially identified as a signature of a higher-order topological phase but later shown to be trivial for perturbations that were thought to protect them. Using various theoretical and simulation techniques, we confirm that it does not display higher-order topology: the corner modes are of trivial nature. Nevertheless, they might be protected. First, we show a set of perturbations within a tight-binding model that can move the corner modes away from zero energy, also repeat some perturbations that were used to show that the modes are trivial. In addition, we analyze the protection of the corner modes in more detail and find that only perturbations respecting the sublattice or generalized chiral and crystalline symmetries, and the lattice connectivity, pin the corner modes to zero energy robustly. A destructive interference model corroborates the results. Finally, we analyze a muffin-tin model for the bulk breathing kagome lattice. Using topological and symmetry markers, such as Wilson loops and Topological Quantum Chemistry, we identify the two breathing phases as adiabatically disconnected different obstructed atomic limits.
Due to their ability to recognize complex patterns, neural networks can drive a paradigm shift in the analysis of materials science data. Here, we introduce ARISE, a crystal-structure identification method based on Bayesian deep learning. As a major step forward, ARISE is robust to structural noise and can treat more than 100 crystal structures, a number that can be extended on demand. While being trained on ideal structures only, ARISE correctly characterizes strongly perturbed single- and polycrystalline systems, from both synthetic and experimental resources. The probabilistic nature of the Bayesian-deep-learning model allows to obtain principled uncertainty estimates, which are found to be correlated with crystalline order of metallic nanoparticles in electron tomography experiments. Applying unsupervised learning to the internal neural-network representations reveals grain boundaries and (unapparent) structural regions sharing easily interpretable geometrical properties. This work enables the hitherto hindered analysis of noisy atomic structural data from computations or experiments.
The Linnik phenomenon concerning the repelling effect of Siegel's zeros is extended to L-functions in a family wider than hitherto considered.
The formation of globular clusters (GC), with their multiple stellar generations, is still an unsolved puzzle. Thus, interest is rising on the possibility to detect their precursors at high redshift, hence directly witnessing their formation. A simple set of assumptions are empirically justified and then used to predict how many such precursors formed between redshift 3 and 10 could actually be detected by the NIRCam instrument on board of JWST. It is shown that the near power-law shape of the rest-frame UV continuum of young globular cluster precursors (GCP) implies that both colours and luminosities in NIRCam long-wavelength passbands depend remarkably weakly on formation redshift. Thus, the predicted number counts depend only little on the actual formation redshifts in the mentioned range, with the exception of the bluest passbands for which counts can be strongly suppressed by intergalactic absorption along the line of sight. Instead, counts depend strongly on the actual mass of GCPs, in such a way that one NIRCam pointing should detect of the order of 10 GCPs to mag$\sim 30$ if their mass distribution was the same of today GCs, or over 1,000 if their mass was 10 times higher. Therefore, GCP number counts will set fairly tight constraints on the initial mass of GCs. An encouraging agreement with the number density of candidate GCPs at $z=6-8$, revealed by the Hubble Frontier Fields (HFF) program, suggests that their initial mass could be at least 4 times higher than that of their local descendants if all were to end up as GCs.
In this paper we present the analytical expression for the neutron scattering law for an isotropic source of neutrons, obtained within the framework of the gas model with the temperature of the moderating medium as a parameter. The obtained scattering law is based on the solution of the kinematic problem of elastic scattering of neutrons on nuclei in the L-system in the general case. I.e. both the neutron and the nucleus possess the arbitrary velocity vectors in the L-system. For the new scattering law the flux densities and neutron moderation spectra depending on the temperature are obtained for the reactor fissile medium. The expressions for the moderating neutrons spectra allow reinterpreting the physical nature of the underlying processes in the thermal region.
Conducting steady-states of doped bilayer graphene have a non-zero sublattice pseudospin polarization. Electron-electron interactions renormalize this polarization even at zero temperature, when the phase space for electron-electron scattering vanishes. We show that because of the strength of interlayer tunneling, electron-electron interactions nevertheless have a negligible influence on the conductivity which vanishes as the carrier number density goes to zero. The influence of interactions is qualitatively weaker than in the comparable cases of single-layer graphene or topological insulators, because the momentum-space layer pseudospin vorticity is 2 rather than 1. Our study relies on the quantum Liouville equation in the first Born approximation with respect to the scattering potential, with electron-electron interactions taken into account self-consistently in the Hartree-Fock approximation and screening in the random phase approximation. Within this framework the result we obtain is exact.
This study aims to assess the properties and classification of 62 variable stars in Cygnus, little studied since their discovery and originally reported in the Information Bulletin on Variable Stars (IBVS) 1302. Using data from previous studies and several astronomical databases, we performed our analysis mainly utilizing a period analysis software and comparing the photometric characteristics of the variables in a Colour-Absolute Magnitude Diagram. For all stars, the variability is confirmed. We discovered new significant results for the period and/or type of 17 variables and highlighted incorrect cross-reference names on astronomical databases for 23 stars. For 3 stars, whose original type was unknown, we propose a new type. We calculated an epoch of a minimum or a maximum for 24 stars; for 3 of them, the epoch has been defined for the first time. This assessment also identifies some cases for which results from the ASAS-SN Catalog of Variable Stars are not consistent with results from Gaia DR2 and/or our analysis.
Instance segmentation requires a large number of training samples to achieve satisfactory performance and benefits from proper data augmentation. To enlarge the training set and increase the diversity, previous methods have investigated using data annotation from other domain (e.g. bbox, point) in a weakly supervised mechanism. In this paper, we present a simple, efficient and effective method to augment the training set using the existing instance mask annotations. Exploiting the pixel redundancy of the background, we are able to improve the performance of Mask R-CNN for 1.7 mAP on COCO dataset and 3.3 mAP on Pascal VOC dataset by simply introducing random jittering to objects. Furthermore, we propose a location probability map based approach to explore the feasible locations that objects can be placed based on local appearance similarity. With the guidance of such map, we boost the performance of R101-Mask R-CNN on instance segmentation from 35.7 mAP to 37.9 mAP without modifying the backbone or network structure. Our method is simple to implement and does not increase the computational complexity. It can be integrated into the training pipeline of any instance segmentation model without affecting the training and inference efficiency. Our code and models have been released at https://github.com/GothicAi/InstaBoost
Infrared and visible image fusion (IVIF) expects to obtain images that retain thermal radiation information from infrared images and texture details from visible images. In this paper, a model-based convolutional neural network (CNN) model, referred to as Algorithm Unrolling Image Fusion (AUIF), is proposed to overcome the shortcomings of traditional CNN-based IVIF models. The proposed AUIF model starts with the iterative formulas of two traditional optimization models, which are established to accomplish two-scale decomposition, i.e., separating low-frequency base information and high-frequency detail information from source images. Then the algorithm unrolling is implemented where each iteration is mapped to a CNN layer and each optimization model is transformed into a trainable neural network. Compared with the general network architectures, the proposed framework combines the model-based prior information and is designed more reasonably. After the unrolling operation, our model contains two decomposers (encoders) and an additional reconstructor (decoder). In the training phase, this network is trained to reconstruct the input image. While in the test phase, the base (or detail) decomposed feature maps of infrared/visible images are merged respectively by an extra fusion layer, and then the decoder outputs the fusion image. Qualitative and quantitative comparisons demonstrate the superiority of our model, which can robustly generate fusion images containing highlight targets and legible details, exceeding the state-of-the-art methods. Furthermore, our network has fewer weights and faster speed.