ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $n\geq 2$ and $r\in \{1, \cdots, n-1\}$ be integers, $M$ be a compact smooth K\''ahler manifold of complex dimension $n$, $E$ be a holomorphic vector bundle with complex rank $r$ and equipped with an hermitian metric $h_E$, and $L$ be an ample holomorphic line bundle over $M$ equipped with a metric $h$ with positive curvature form. For any $d\in \mathbb{N}$ large enough, we endorse the space of holomorphic sections $H^0(M,E\otimes L^d)$ with the natural Gaussian measure associated to $h_E$ , $h$ and its curvature form. Let $U\subset M$ be an open subset with smooth boundary. We prove that the average of the $(n-r)$-th Betti number of the vanishing locus in $U$ of a random section $s$ of $H^0(M,E\otimes L^d)$ is asymptotic to ${n-1 \choose r-1} d^n\int_U c_1(L)^n$ for large $d$. On the other hand, the average of the other Betti numbers are $o(d^n)$. The first asymptotic recovers the classical deterministic global algebraic computation. Moreover, such a discrepancy in the order of growth of these averages is new and constrasts with all known other smooth Gaussian models, in particular the real algebraic one. We prove a similar result for the affine complex Bargmann-Fock model.
We study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem and tested it with mock data based on N-body simulations.
We consider the non Abelian sandpile model introduced by Y.-C. Zhang on a two-dimensional square lattice. The static and dynamical properties of the model are investigated and compared to the Abelian sandpile model of Bak, Tang and Wiesenfeld. A detailed analysis which takes the finite size effects into account yields that the exponents of the avalanche probability distribution are the same as in the Abelian model.
The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence technique. It is shown that the macro-thermo-poro-elasticity model with double porosity/diffusivity contains in particular some extra terms accounting for the micro-heterogeneities and imperfect contact at the local scale. Finally, a corrector result is given under more regularity assumptions on the data.
Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the Vlasov-Maxwell system in a two-dimensional annulus when a huge (but finite-in-time) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The authors hope that this work is a step towards a more generalized work on the three-dimensional Tokamak structure. The highlight of this work is the physical assumptions on the external magnetic potential well which remains finite within a finite time interval and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the Vlasov-Maxwell system.
We present high-precision multi-band photometry for the globular cluster (GC) M2. We combine the analysis of the photometric data obtained from the Hubble Space Telescope UV Legacy Survey of Galactic GCs GO-13297, with chemical abundances by Yong et al.(2014), and compare the photometry with models in order to analyze the multiple stellar sequences we identified in the color-magnitude diagram (CMD). We find three main stellar components, composed of metal-poor, metal-intermediate, and metal-rich stars (hereafter referred to as population A, B, and C, respectively). The components A and B include stars with different $s$-process element abundances. They host six sub-populations with different light-element abundances, and exhibit an internal variation in helium up to Delta Y~0.07 dex. In contrast with M22, another cluster characterized by the presence of populations with different metallicities, M2 contains a third stellar component, C, which shows neither evidence for sub-populations nor an internal spread in light-elements. Population C does not exhibit the typical photometric signatures that are associated with abundance variations of light elements produced by hydrogen burning at hot temperatures. We compare M2 with other GCs with intrinsic heavy-element variations and conclude that M2 resembles M22, but it includes an additional stellar component that makes it more similar to the central region of the Sagittarius galaxy, which hosts a GC (M54) and the nucleus of the Sagittarius galaxy itself.
Two new sufficient conditions for generalized cycles (including Hamilton and dominating cycles as special cases) in an arbitrary k-connected graph (k=1,2,...) are derived, which prove the truth of Bondy's (1980) famous conjecture for some variants significantly improving the result expected by the given hypothesis. Similarly, two new lower bounds for the circumference (the length of a longest cycle) are established for the reverse hypothesis proposed by Jung (2001).
Describing long-ranged electrostatics using short-ranged pair potentials is appealing since the computational complexity scales linearly with the number of particles. The foundation of this approach is to mimic the long-ranged medium response by cancelling electric multipoles within a small cutoff sphere. We propose a rigorous and formally exact new method that cancels up to infinitely many multipole moments and is free of operational damping parameters often required in existing theories. Using molecular dynamics simulations of water with and without added salt, we discuss radial distribution functions, Kirkwood-Buff integrals, dielectrics, diffusion coefficients, and angular correlations in relation to existing electrostatic models. We find that the proposed method is an efficient and accurate alternative for handling long-ranged electrostatics as compared to Ewald summation schemes. The methodology and proposed parameterization is applicable also for dipole-dipole interactions.
The curvaton reheating mechanism in a Scale Invariant Two Measures Theory defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold which are metric independent is studied. The model involves two scalar matter fields, a dilaton, that transforms under scale transformations and it will be used also as the inflaton of the model and another scalar, which does not transform under scale transformations and which will play the role of a curvaton field. Potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry are introduced. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) For given value of the curvaton field an effective potential for the scalar field with two flat regions for the dilaton which allows for a unified description of both early universe inflation as well as of present dark energy epoch;(iii) In the phase corresponding to the early universe, the curvaton has a constant mass and can oscillate decoupled from the dilaton and that can be responsible for both reheating and perturbations in the theory. In this framework, we obtain some interesting constraints on different parameters that appear in our model;   (iii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase. Finally we discuss generalizations of the model, through the effect of higher curvature terms, where inflaton and curvaton can have coupled oscillations.
We investigate the relationship between global offensive $k$-alliances and some characteristic sets of a graph including $r$-dependent sets and $\tau$-dominating sets. As a consequence of the study, we obtain bounds on the global offensive $k$-alliance number in terms of several parameters of the graph.
This article consists of a detailed geometric study of the one-dimensional vorticity model equation $$\omega_{t} + u\omega_{x} + 2\omega u_{x} = 0, \qquad \omega = H u_{x}, \qquad t\in\mathbb{R},\; x\in S^{1}\,,$$ which is a particular case of the generalized Constantin-Lax-Majda equation. Wunsch showed that this equation is the Euler-Arnold equation on $\operatorname{Diff}(S^{1})$ when the latter is endowed with the right-invariant homogeneous $\dot{H}^{1/2}$-metric. In this article we prove that the exponential map of this Riemannian metric is not Fredholm and that the sectional curvature is locally unbounded. Furthermore, we prove a Beale-Kato-Majda-type blow-up criterion, which we then use to demonstrate a link to our non-Fredholmness result. Finally, we extend a blow-up result of Castro-C\'ordoba to the periodic case and to a much wider class of initial conditions, using a new generalization of an inequality for Hilbert transforms due to C\'ordoba-C\'ordoba.
We apply the equal load-sharing fiber bundle model of fracture failure in composite materials to model the traffic failure in a system of parallel road network in a city. For some special distributions of traffic handling capacities (thresholds) of the roads, the critical behavior of the jamming transition can be studied analytically. This has been compared with that for the asymmetric simple exclusion process in a single channel or road.
This paper proposes a novel image set classification technique based on the concept of linear regression. Unlike most other approaches, the proposed technique does not involve any training or feature extraction. The gallery image sets are represented as subspaces in a high dimensional space. Class specific gallery subspaces are used to estimate regression models for each image of the test image set. Images of the test set are then projected on the gallery subspaces. Residuals, calculated using the Euclidean distance between the original and the projected test images, are used as the distance metric. Three different strategies are devised to decide on the final class of the test image set. We performed extensive evaluations of the proposed technique under the challenges of low resolution, noise and less gallery data for the tasks of surveillance, video-based face recognition and object recognition. Experiments show that the proposed technique achieves a better classification accuracy and a faster execution time compared to existing techniques especially under the challenging conditions of low resolution and small gallery and test data.
We analyze the effect of the phonon dynamics on a recently proposed model for the uniform-incommensurate transition seen in TiOX compounds. The study is based on a recently developed formalism for nonadiabatic spin-Peierls systems based on bosonization and a mean field RPA approximation for the interchain coupling. To reproduce the measured low temperature spin gap, a spin-phonon coupling quite bigger than the one predicted from an adiabatic approach is required. This high value is compatible with the renormalization of the phonons in the high temperature phase seen in inelastic x-ray experiments. Our theory accounts for the temperature of the incommensurate transition and the value of the incommensurate wave vector at the transition point.
Beta-decay properties of neutron-rich Zr and Mo isotopes are investigated within a microscopic theoretical approach based on the proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual separable particle-hole and particle-particle forces are also included in the formalism. The structural evolution in these isotopic chains including both even and odd isotopes is analyzed in terms of the equilibrium deformed shapes. Gamow-Teller strength distributions, beta-decay half-lives, and beta-delayed neutron-emission probabilities are studied, stressing their relevance to describe the path of the nucleosynthesis rapid neutron capture process.
We report the detection of a very short time scale flare in the radio-loud narrow line quasars PKS 0558-504 by using ASCA. The X-ray count rates increased and decreased by a factor of two in 33 minutes, and possibly by 40% in as short as two minutes during this flare, confirming that such flare event does occur in this object with imaging detectors. The implied largest rate of change in luminosity in 0.8-10 keV alone, dL/dt=(1.8+/-0.4) 10^{42} ergs s^-2, is several times higher than the limit sets for the isotropic emitting plasma around a Kerr black hole. Either emission from a relativistic boosting jet or a magnetic heated corona may explain such high radiative efficiency. Magnetic field with a strength of at least a few 10^4 Gauss is required in the latter case. The spectrum during this flare is significant harder than the average one. Three radio loud narrow line active galactic nuclei (AGN) possess considerably smaller black holes than in radio loud AGN in bright quasar survey, indicating they are still in a phase of the rapid growth of the black hole by accretion.
We derive the leading contribution to the four-nucleon force within the framework of chiral effective field theory. It is governed by the exchange of pions and the lowest-order nucleon-nucleon contact interaction and includes effects due to the nonlinear pion-nucleon couplings and the pion self interactions constrained by the chiral symmetry of QCD. The resulting four-nucleon force does not contain any unknown parameters and can be tested in few- and many-nucleon studies.
Effective Hamiltonians are often used in quantum physics, both in time dependent and time independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian.
The luminosity function of galaxies of the Early Data Release of the Sloan Digital Sky Survey (SDSS) and the Las Campanas Redshift Survey (LCRS) is calculated. The luminosity function depends on redshift, density of the environment and is different for the Norther and Southern slice of SDSS. Luminosity functions is used to derive the number and luminosity density fields of galaxies of the SDSS and LCRS surveys with a grid size of 1 h^{-1} Mpc for flat cosmological models with \Omega_m=0.3 and \Omega_\Lambda =0.7. We find that the luminosity function depends on the density of the environment: in high-density regions brightest galaxies are more luminous than in low-density regions by a factor up to 5.
Total hip replacement is the most effective treatment for late stage osteoarthritis. However, adverse local tissue reactions (ALTRs) associated with fretting corrosion have been observed in patients with modular total hip implants. The purpose of this study is to increase the fretting corrosion resistance of the CoCrMo alloy and the associated metal ion release by applying hard coatings to the surface. Cathodic arc evaporation technique (arc-PVD) was used to deposit TiSiN and ZrN hard coatings on to CoCrMo substrates. The morphology, chemical composition, crystal structures and residual stress of the coatings were characterized by scanning electron microscopy, energy dispersive x-ray spectroscopy, and X-ray diffractometry. Hardness, elastic modulus, and adhesion of the coatings were measured by nano-indentation, nano-scratch test, and the Rockwell C test. Fretting corrosion resistance tests of coated and uncoated CoCrMo discs against Ti6Al4V spheres were conducted on a four-station fretting testing machine in simulated body fluid at 1Hz for 1 million cycles. Post-fretting samples were analyzed for morphological changes, volume loss and metal ion release. Our analyses showed better surface finish and lower residual stress for ZrN coating, but higher hardness and better scratch resistance for TiSiN coating. Fretting results demonstrated substantial improvement in fretting corrosion resistance of CoCrMo with both coatings. ZrN and TiSiN decreased fretting volume loss by more than 10 times and 1000 times, respectively. Both coatings showed close to 90% decrease of Co ion release during fretting corrosion tests. Our results suggest that hard coating deposition on CoCrMo alloy can significantly improve its fretting corrosion resistance and could thus potentially alleviate ALTRs in metal hip implants.
Big neural networks trained on large datasets have advanced the state-of-the-art for a large variety of challenging problems, improving performance by a large margin. However, under low memory and limited computational power constraints, the accuracy on the same problems drops considerable. In this paper, we propose a series of techniques that significantly improve the accuracy of binarized neural networks (i.e networks where both the features and the weights are binary). We evaluate the proposed improvements on two diverse tasks: fine-grained recognition (human pose estimation) and large-scale image recognition (ImageNet classification). Specifically, we introduce a series of novel methodological changes including: (a) more appropriate activation functions, (b) reverse-order initialization, (c) progressive quantization, and (d) network stacking and show that these additions improve existing state-of-the-art network binarization techniques, significantly. Additionally, for the first time, we also investigate the extent to which network binarization and knowledge distillation can be combined. When tested on the challenging MPII dataset, our method shows a performance improvement of more than 4% in absolute terms. Finally, we further validate our findings by applying the proposed techniques for large-scale object recognition on the Imagenet dataset, on which we report a reduction of error rate by 4%.
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
A non-perturbative (np) method of Field Correlators (FCM) was applied to study QCD at temperatures above the deconfinement transition ($1<T/T_c<3,~T_c\sim0.16~GeV$) and nonzero baryon densities (baryon chemical potential $\mu_B<0.5~GeV$) in an external uniform magnetic field ($eB<0.5~GeV^2$). Within FCM, the np high-temperature dynamics is embodied in the Polyakov loop and in the Debye mass due to the Color-Magnetic Confinement. Analytic expressions for quark pressure and magnetic susceptibility were obtained. The expressions were represented as series and in integral form. Magnetic susceptibility was found to increase rapidly with temperature and slowly with density. The results at the zero density limit are in agreement with lattice data.
By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Levy noise. After shortly review recent results obtained with different approaches on the time characteristics of the barrier crossing, we derive a general differential equation useful to calculate the nonlinear relaxation time. We obtain analytically the nonlinear relaxation time for free Levy flights and a closed expression in quadrature of the same characteristics for cubic potential.
We present a new framework for semantic segmentation without annotations via clustering. Off-the-shelf clustering methods are limited to curated, single-label, and object-centric images yet real-world data are dominantly uncurated, multi-label, and scene-centric. We extend clustering from images to pixels and assign separate cluster membership to different instances within each image. However, solely relying on pixel-wise feature similarity fails to learn high-level semantic concepts and overfits to low-level visual cues. We propose a method to incorporate geometric consistency as an inductive bias to learn invariance and equivariance for photometric and geometric variations. With our novel learning objective, our framework can learn high-level semantic concepts. Our method, PiCIE (Pixel-level feature Clustering using Invariance and Equivariance), is the first method capable of segmenting both things and stuff categories without any hyperparameter tuning or task-specific pre-processing. Our method largely outperforms existing baselines on COCO and Cityscapes with +17.5 Acc. and +4.5 mIoU. We show that PiCIE gives a better initialization for standard supervised training. The code is available at https://github.com/janghyuncho/PiCIE.
We give the construction modulo normalization of a new state sum model for lorentzian quantum general relativity, using the construction of Dirac's expansors to include quantum operators corresponding to edge lengths as well as the quantum bivectors of the Barrett-Crane model, and discuss the problem of its normalization. The new model gives rise to a new picture of quantum geometry in which lengths come in a discrete spectrum, while areas have a continuum of values.
We explore flat {\Lambda}CDM models with bulk viscosity, and study the role of the bulk viscosity in the evolution of these universe models. The dynamical equations for these models are obtained and solved for some cases of bulk viscosity. We obtain differential equations for the Hubble parameter H and the energy density of dark matter {\rho}, for which we give analytical solutions for some cases and for the general case we give a numerical solution. Also we calculate the statefinder parameters for this model and display them in the s-r-plane.
We describe a geometric triangulation technique, based on time-elongation maps constructed from imaging observations, to track coronal mass ejections (CMEs) continuously in the heliosphere and predict their impact on the Earth. Taking advantage of stereoscopic imaging observations from STEREO, this technique can determine the propagation direction and radial distance of CMEs from their birth in the corona all the way to 1 AU. The efficacy of the method is demonstrated by its application to the 2008 December 12 CME, which manifests as a magnetic cloud (MC) from in situ measurements at the Earth. The predicted arrival time and radial velocity at the Earth are well confirmed by the in situ observations around the MC. Our method reveals non-radial motions and velocity changes of the CME over large distances in the heliosphere. It also associates the flux-rope structure measured in situ with the dark cavity of the CME in imaging observations. Implementation of the technique, which is expected to be a routine possibility in the future, may indicate a substantial advance in CME studies as well as space weather forecasting.
Cosmic objects emit throughout the electro-magnetic spectrum, from radio waves to very high-energy gamma rays. Some spectral regions can be observed from the ground, but space instrumentation is needed for most of them. Some spectral regions are particularly difficult, for example hard X-rays and MeV gamma rays. For one thing, in this spectral region photons interact least with matter. Moreover, no focussing optics was available until very recently. INTEGRAL, the gamma ray observatory mission led by ESA, was designed to observe the sky in this very domain.