ShantanuT01/DACTYL-Pretraining huggingface dataset:
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and interpret them in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we review three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold the best framework is the so-called third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian $3$-geometries, which turns out to be isomorphic to a (part of a) $1+5$ Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given and it is analysed the creation of the universes, their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe-antiuniverse pairs.
In this paper we study the one dimensional symmetry problem of entire solutions to the problem \[\Delta u=uv^2,\Delta v=vu^2,u,v>0 \text{in} \mathbb{R}^n,\] for all $n\geq 2$. We prove that, if a solution $(u,v)$ is a local minimizer and has linear growth at infinity, then it is one dimensional, i.e. depending only on one variable. In the proof we also obtain the global Lipschitz continuity of solutions only under the linear growth assumption.
The critical properties of the $S=1/2$ Heisenberg two-leg ladders are investigated in a magnetic field. Combining the exact diagonalization method and the finite-size-scaling analysis based on conformal field theory, we calculate the critical exponents of spin correlation functions numerically. For a strong interchain coupling, magnetization dependence of the critical exponents shows characteristic behavior depending on the sign of the interchain coupling. We also calculate the critical exponents for the $S=1/2$ Heisenberg two-leg ladder with a diagonal interaction, which is thought as a model Hamiltonian of the organic spin ladder compound ${Cu}_2({1,4-diazacycloheptane})_2{Cl}_4$. Numerical results are compared with experimental results of temperature dependence of the NMR relaxation rate $1/T_1$.
The progenitor systems for type Ia supernovae are still controversial. One of the methods to test the proposed scenario for the progenitor systems is to identify companions that are supposed to survive according to the so-called single degenerate scenario. These companions might be affected by supernova ejecta. We present several numerical simulations of surviving red-giant companions whose envelopes were stripped and heated. We find that red-giants with less-massive helium cores ($\lesssim0.30\,M_{\odot}$) can be so faint after the supernovae that we cannot detect them. In addition, we apply the results to the case of SNR 0509-67.5, and put constraints on the helium core mass, envelope stripping, and energy injection under the single degenerate scenario for type Ia supernovae.
Strain engineering can effectively tune the electronic, topological and piezoelectric properties of materials. In this work, the small strain (-4\% to 4\%) effects on piezoelectric properties of $\alpha$-AsP monolayer are studied by density functional theory (DFT). The piezoelectric stress tensors $e_{ij}$ and elastic stiffness tensors $C_{ij}$ are reported by using density functional perturbation theory (DFPT) and finite difference method (FDM). It is found that the Young's modulus of $\alpha$-AsP monolayer shows very strong anisotropy, and the armchair direction is very softer than zigzag direction, which provides possibility for tuning easily piezoelectric coefficients along the armchair direction. In considered strain range, uniaxial compressive (tensile) strain along the armchair (zigzag) direction is found to raise observably both the $e_{22}$ and $d_{22}$ (absolute value). In fact, both compressive strain along the armchair direction and tensile strain along the zigzag direction essentially reduce the lattice constants along the armchair direction, which can enhance the piezoelectric coefficients. The $e_{ij}$ of $\beta$-AsP monolayer as a function of strain is also studied to illustrate the importance of particular puckered structure of $\alpha$-AsP in enhancing the piezoelectric coefficients. A classic SnSe monolayer with puckered structure is used to further declare that small strain along the armchair direction can effectively improve the piezoelectric coefficients. For example, the $d_{22}$ of SnSe monolayer at -3.5\% strain is up to 628.8 pm/V from unstrained 175.3 pm/V. For SnSe monolayer, a large peak is observed for $e_{22}$, which is due to a structural phase transition. For $e_{16}$ of SnSe monolayer, a large peak is also observed due to the cross of lattice constants $a$ along the zigzag direction and $b$ along the armchair direction.
In the pursuit of achieving ever-increasing accuracy, large and complex neural networks are usually developed. Such models demand high computational resources and therefore cannot be deployed on edge devices. It is of great interest to build resource-efficient general purpose networks due to their usefulness in several application areas. In this work, we strive to effectively combine the strengths of both CNN and Transformer models and propose a new efficient hybrid architecture EdgeNeXt. Specifically in EdgeNeXt, we introduce split depth-wise transpose attention (STDA) encoder that splits input tensors into multiple channel groups and utilizes depth-wise convolution along with self-attention across channel dimensions to implicitly increase the receptive field and encode multi-scale features. Our extensive experiments on classification, detection and segmentation tasks, reveal the merits of the proposed approach, outperforming state-of-the-art methods with comparatively lower compute requirements. Our EdgeNeXt model with 1.3M parameters achieves 71.2% top-1 accuracy on ImageNet-1K, outperforming MobileViT with an absolute gain of 2.2% with 28% reduction in FLOPs. Further, our EdgeNeXt model with 5.6M parameters achieves 79.4% top-1 accuracy on ImageNet-1K. The code and models are available at https://t.ly/_Vu9.
Prior to the last decade, most observations of roAp stars have concerned the light variations. Recently some new, striking results of spectroscopic observations with high time resolution, high spectral dispersion, and a high signal-to-noise ratio became available. Since the oscillations found in roAp stars are high overtones, the vertical wavelengths of the oscillations are so short that the amplitude and phase of the variation of each spectroscopic line are highly dependent on the level of the line profile. Hence, analyses of the variation of the spectroscopic lines of roAp stars potentially provide us with new information about the vertical structure of the atmosphere of these stars. In order to extract such information, a numerical simulation of the line-profile variation beyond a single-surface approximation is necessary. We carried out a numerical simulation of line-profile variation by taking account of the finite thickness of the line forming layer. We demonstrated how effective this treatment is, by comparing the simulation with the observed line profiles.
We study the influence of energy levels broadening and electron subsystem overheating in island electrode (cluster) on current-voltage characteristics of three-electrode structure. A calculation scheme for broadening effect in one-dimensional case is suggested. Estimation of broadening is performed for electron levels in disc-like and spherical gold clusters. Within the two-temperature model of metallic cluster and by using a size dependence of the Debye frequency the effective electron temperature as a function of bias voltage is found approximately. We suggest that the effects of broadening and electron overheating are responsible for the strong smoothing of current-voltage curves, which is observed experimentally at low temperatures in structures based on clusters consisting of accountable number of atoms.
In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The difficulty, and hence the contribution, of the paper lie in three aspects, which include rough initial conditions, degenerate diffusion coefficient, and weakest possible assumptions on the correlation function of the noise. In particular, our results cover the parabolic Anderson model starting from a Dirac delta initial measure.
In a previous paper of Winter and the author the Law of Large Numbers for the local mass of certain superdiffusions was proved under a spectral theoretical assumption, which is equivalent to the ergodicity (positive recurrence) of the motion component of an $H$-transformed (or weighted) superprocess. In fact the assumption is also equivalent to the property that the scaling for the expectation of the local mass is pure exponential.   In this paper we go beyond ergodicity, that is we consider cases when the scaling is not purely exponential. Inter alia, we prove the analog of the Watanabe-Biggins Law of Large Numbers for super-Brownian motion (SBM).   We will also prove another Law of Large Numbers for a bounded set moving with subcritical speed, provided the variance term decays sufficiently fast.
Self-supervised representation learning is a fundamental problem in computer vision with many useful applications (e.g., image search, instance level recognition, copy detection). In this paper we present a new contrastive self-supervised representation learning algorithm in the context of Copy Detection in the 2021 Image Similarity Challenge hosted by Facebook AI Research. Previous work in contrastive self-supervised learning has identified the importance of being able to optimize representations while ``pushing'' against a large number of negative examples. Representative previous solutions either use large batches enabled by modern distributed training systems or maintain queues or memory banks holding recently evaluated representations while relaxing some consistency properties. We approach this problem from a new angle: We directly learn a query model and a key model jointly and push representations against a very large number (e.g., 1 million) of negative representations in each SGD step. We achieve this by freezing the backbone on one side and by alternating between a Q-optimization step and a K-optimization step. During the competition timeframe, our algorithms achieved a micro-AP score of 0.3401 on the Phase 1 leaderboard, significantly improving over the baseline $\mu$AP of 0.1556. On the final Phase 2 leaderboard, our model scored 0.1919, while the baseline scored 0.0526. Continued training yielded further improvement. We conducted an empirical study to compare the proposed approach with a SimCLR style strategy where the negative examples are taken from the batch only. We found that our method ($\mu$AP of 0.3403) significantly outperforms this SimCLR-style baseline ($\mu$AP of 0.2001).
Prior research on self-supervised learning has led to considerable progress on image classification, but often with degraded transfer performance on object detection. The objective of this paper is to advance self-supervised pretrained models specifically for object detection. Based on the inherent difference between classification and detection, we propose a new self-supervised pretext task, called instance localization. Image instances are pasted at various locations and scales onto background images. The pretext task is to predict the instance category given the composited images as well as the foreground bounding boxes. We show that integration of bounding boxes into pretraining promotes better task alignment and architecture alignment for transfer learning. In addition, we propose an augmentation method on the bounding boxes to further enhance the feature alignment. As a result, our model becomes weaker at Imagenet semantic classification but stronger at image patch localization, with an overall stronger pretrained model for object detection. Experimental results demonstrate that our approach yields state-of-the-art transfer learning results for object detection on PASCAL VOC and MSCOCO.
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
We derive scaling limits for integral functionals of It\^o processes with fast nonlinear mean-reversion speed. We show that in these limits, the fast mean-reverting process is "averaged out" by integrating against its invariant measure. These convergence results hold uniformly in probability and, under mild integrability conditions, also in $\mathcal{S}^p$. They are a crucial building block for the analysis of portfolio choice models with small superlinear transaction costs, carried out in the companion paper of the present study.
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining "toric" roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more efficient approach which works directly with the variables and their inverse. We show that the commutation relations and the inversion relations characterize toric border bases. We explicitly describe the first syzygy module associated to a toric border basis in terms of these relations. Finally, a new border basis algorithm for Laurent polynomials is described and a proof of its termination is given for zero-dimensional toric ideals.
It is well known that, for pressureless matter, Newtonian and relativistic cosmologies are equivalent. We show that this equivalence breaks down in the quantum level. In addition, we find some cases for which quantum Newtonian cosmology can be related to quantum cosmology in (2+1) dimensions. Two exact solutions for the wave function of the Newtonian universe are also obtained.
The stability and properties of the monovacancy and the divacancy in single-walled carbon nanotubes (CNTs) are addressed by spin-density functional calculations. We study these defects in four nanotubes, the armchair (6,6) and (8,8) and the zigzag (10,0) and (14,0), which have diameters of about 8 and 11 \AA, respectively. We also study different defect concentrations along the tube axis by increasing the supercell in this direction in order to have one defect every 13 and 26 \AA of CNT length. Our results show that in the equilibrium geometry CNTs with a monovacancy exhibit ferromagnetism with magnetic moments ranging from 0.3 to 0.8 $\mu_{\rm B}$. On the other hand, CNTs with a divacancy do not exhibit magnetism due to the full reconstruction around the defect where all C atoms are three coordinated. We observe that the presence of a monovacancy does not change drastically the CNT electronic properties, preserving their corresponding metallic or semiconducting character. However, for the divacancy both armchair and zigzag CNT become semiconductors exhibiting a energy gap of about 0.15 eV.
The spatial dependence of the superfluid density is calculated for the Kosterlitz-Thouless transition in the presence of hard-wall boundaries, for the case of a single wall bounding the half-infinite plane, and for a superfluid strip bounded by two walls. The boundaries induce additional vortices that cause the superfluid density to become anisotropic, with the tensor component perpendicular to the wall falling to zero at the wall, whereas the component parallel to the wall remains finite. The effects of the boundaries are found to extend over all measured length scales, since the correlation length is infinite in the superfluid phase.
We present a numerical model to study the behavior of thermonuclear flames in the discontinuity approximation. This model is applied to investigate the Landau-Darrieus instability under conditions found in Type Ia supernova explosions of Chandrasekhar mass white dwarfs. This is a first step to explore the flame microstructure in these events. The model reproduces Landau's linearized stability analysis in early stages of the flame evolution and the stabilization in a cellular flame structure in the nonlinear stage.
Context. The properties of hydrogenated amorphous carbon (a-C:H) dust evolve in response to the local radiation field in the interstellar medium and the evolution of these properties is particularly dependent upon the particle size. Aims. A model for finite-sized, low-temperature amorphous hydrocarbon particles, based on the microphysical properties of random and defected networks of carbon and hydrogen atoms, with surfaces passivated by hydrogen atoms, has been developed. Methods. The eRCN/DG and the optEC(s) models have been combined, adapted and extended into a new optEC(s)(a) model that is used to calculate the optical properties of hydrocarbon grain materials down into the sub-nanometre size regime, where the particles contain only a few tens of carbon atoms. Results. The optEC(s)(a) model predicts a continuity in properties from large to small (sub-nm) carbonaceous grains. Tabulated data of the size-dependent optical constants (from EUV to cm wavelengths) for a-C:H (nano-)particles as a function of the bulk material band gap [Eg(bulk)], or equivalently the hydrogen content, are provided. The effective band gap [Eg(eff.)] is found to be significantly larger than Eg(bulk) for hydrogen-poor a-C(:H) nano-particles and their predicted long-wavelength ({\lambda} > 30{\mu}m) optical properties differ from those derived for interstellar polycyclic aromatic hydrocarbons (PAHs). Conclusions. The optEC(s)(a) model is used to investigate the size-dependent structural and spectral evolution of a-C(:H) materials under ISM conditions, including: the IR-FUV extinction, the 217 nm bump and the infrared emission bands. The model makes several predictions that can be tested against observations.
We investigate the spin-stripe mechanism responsible for the peculiar nanometer modulation of the incommensurate magnetic order that emerges between the vector-chiral and the spin-density-wave phase in the frustrated zigzag spin-1/2 chain compound $\beta$-TeVO$_4$. A combination of magnetic-torque, neutron-diffraction and spherical-neutron-polarimetry measurements is employed to determine the complex magnetic structures of all three ordered phases. Based on these results, we develop a simple phenomenological model, which exposes the exchange anisotropy as the key ingredient for the spin-stripe formation in frustrated spin systems.
Time-resolved spectra of six short gamma-ray bursts (sGRBs), measured by the {\em Swift} telescope, are used to estimate the parameters of a plerion-like model of the X-ray afterglow. The unshrouded, optically thin component of the afterglow is modelled as emanating from an expanding bubble of relativistic, shock-accelerated electrons fuelled by a central object. The electrons are injected with a power-law distribution and cool mainly by synchrotron losses. We compute posteriors for model parameters describing the central engine (e.g. spin frequency at birth, magnetic field strength) and shock acceleration (e.g. power-law index, minimum injection energy). It is found that the central engine is compatible with a millisecond magnetar, and the shock physics is compatible with what occurs in Galactic supernova remnants, assuming standard magnetic field models for the magnetar wind. Separately, we allow the magnetic field to vary arbitrarily and infer that it is roughly constant and lower in magnitude than the wind-borne extension of the inferred magnetar field. This may be due to the expansion history of the bubble, or the magnetization of the circumstellar environment of the sGRB progenitor.
Since the early 1990s Gamma Ray Bursts have been accepted to be of extra-galactic origin due to the isotropic distribution observed by BATSE and the redshifts observed via absorption line spectroscopy. Nevertheless, upon further examination at least one case turned out to be of galactic origin. This particular event presented a Fast Rise, Exponential Decay (FRED) structure which leads us to believe that other FRED sources might also be Galactic. This study was set out to estimate the most probable degree of contamination by galactic sources that certain samples of FREDs have. In order to quantify the degree of anisotropy the average dipolar and quadripolar moments of each sample of GRBs with respect to the galactic plane were calculated. This was then compared to the probability distribution of simulated samples comprised of a combination of isotropically generated sources and galactic sources. We observe that the dipolar and quadripolar moments of the selected subsamples of FREDs are found more than two standard deviations outside those of random isotropically generated samples.The most probable degree of contamination by galactic sources for the FRED GRBs of the Swift catalog detected until February 2011 that do not have a known redshift is about 21 out of 77 sources which is roughly equal to 27%. Furthermore we observe, that by removing from this sample those bursts that may have any type of indirect redshift indicator and multiple peaks gives the most probable contamination increases up to 34% (17 out of 49 sources). It is probable that a high degree of contamination by galactic sources occurs among the single peak FREDs observed by Swift.
Using the publicly available Quijote simulations, we present the first measurements of the assembly bias of dark matter halos in N-body simulations which include massive neutrinos. We focus on the dependence of the linear bias $b_1$ on three halo properties: 1) concentration $c$, 2) spin $\lambda$, and 3) ellipticity $s$. Although these simulations cover a large volume, superior to any future surveys, we do not detect any effect of neutrinos on the relations $b_1(c)$, $b_1(\lambda)$ and $b_1(s)$ at fixed halo mass. We further study the dependence of halo properties and environment on neutrinos, finding these quantities to be impacted by neutrino masses at the same level as assembly bias. We find that the effect of neutrinos on spin and shape can be largely attributed to the change in the cold dark matter $\sigma_8$ in neutrinos simulations, which is not the case for concentration.
New models of rotating and non-rotating stars are computed for initial masses between 25 and 120 Msun and for metallicities Z = 0.004, 0.008, 0.020 and 0.040 with the aim of reexamining the wind contribution of Wolf-Rayet (WR) stars to the F19 enrichment of the interstellar medium. Models with an initial rotation velocity vini = 300 km/s are found to globally eject less F19 than the non-rotating models. We compare our new predictions with those of Meynet & Arnould (2000), and demonstrate that the F19 yields are very sensitive to the still uncertain F19(alpha,p)Ne22 rate and to the adopted mass loss rates. Using the recommended mass loss rate values that take into account the clumping of the WR wind and the NACRE reaction rates when available, we obtain WR F19 yields that are significantly lower than predicted by Meynet & Arnould (2000), and that would make WR stars non-important contributors to the galactic F19 budget. In view, however, of the large nuclear and mass loss rate uncertainties, we consider that the question of the WR contribution to the galactic F19 remains quite largely open.