ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a set of solar neighborhood ($d < 3$ kpc) stars from Gaia Data Release 2 to determine azimuthal star count differences, i.e., left and right of the line from the Galactic center through the sun - and compare these differences north and south. In this companion paper to Gardner et al. (2020), we delineate our procedures to remove false asymmetries from sampling effects, incompleteness, and/or interloper populations, as this is crucial to tests of axisymmetry. Particularly, we have taken care to make appropriate selections of magnitude, color, in-plane Galactocentric radius and Galactic $|b|$ and $|z|$. We find that requiring parallax determinations of high precision induces sampling biases, so that we eschew such requirements and exclude, e.g., regions around the lines of sight to the Magellanic clouds, along with their mirror-image lines of sight, to ensure well-matched data sets. After making conservative cuts, we demonstrate the existence of azimuthal asymmetries, and find differences in those, north and south. These asymmetries give key insights into the nature and origins of the perturbations on Galactic matter, allowing us to assess the relative influence of the Magellanic Clouds (LMC & SMC), the Galactic bar, and other masses on the Galactic mass distribution, as described in Gardner et al. (2020). The asymmetry's radial dependence reveals variations that we attribute to the Galactic bar, and it changes sign at a radius of $(0.95 \pm 0.03) R_0$, with $R_0$ the Sun-Galactic-Center (GC) distance, to give us the first direct assessment of the outer Lindblad resonant radius.
We consider the effects of the Faddeev-Popov determinant in the Coulomb gauge on the confinement properties of the QCD vacuum. We show that the the determinant is needed to regularize the otherwise divergent functional integrals near the Gribov horizon but still enables large field configurations to generate IR enhanced running coupling. The physical gluon propagator is found to be strongly suppressed in the   IR consistent with expectations from lattice gauge calculations.
In this paper we study smooth projective rational surfaces, defined over an algebraically closed field of any characteristic, with pseudo-effective anticanonical divisor. We provide a necessary and sufficient condition in order for any nef divisor to be semiample. We adopt our criterion to investigate Mori dream surfaces in the complex case.
We carried out a target survey for Lyman break galaxies (LBGs) and Lyman alpha emitters (LAEs) around QSO SDSS J0211-0009 at z=4.87. The deep and wide broadband and narrowband imaging simultaneously revealed the perspective structure of these two high-z populations. The LBGs without Ly-alpha emission form a filamentary structure including the QSO, while the LAEs are distributed around the QSO but avoid it within a distance of ~4.5Mpc. On the other hand, we serendipitously discovered a protocluster with a significant concentration of LBGs and LAEs where no strongly UV ionizing source such as a QSO or radio galaxy is known to exist. In this cluster field, two populations are spatially cross-correlated with each other. The relative spatial distribution of LAEs to LBGs is in stark contrast between the QSO and the cluster fields. We also found a weak trend showing that the number counts based on Ly-alpha and UV continuum fluxes of LAEs in the QSO field are slightly lower than in the cluster field, whereas the number counts of LBGs are almost consistent with each other. The LAEs avoid the nearby region around the QSO where the local UV background radiation could be ~100 times stronger than the average for the epoch. The clustering segregation between LBGs and LAEs seen in the QSO field could be due to either enhanced early galaxy formation in an overdense environment having caused all the LAEs to evolve into LBGs, or local photoionization due to the strong UV radiation from the QSO effectively causing a deficit in low-mass galaxies like LAEs.
Besides various asymptotic results on the concept of sum-product bases in $\mathbb{N}_0$, we consider by probabilistic arguments the existence of thin sets $A,A'$ of integers such that $AA+A=\mathbb{N}_0$ and $A'A'+A'A'=\mathbb{N}_0$.
We consider the numerical evolution of black hole initial data sets, consisting of single black holes distorted by strong gravitational waves, with a full 3D, nonlinear evolution code. These data sets mimic the late stages of coalescing black holes. We compare various aspects of the evolution of axisymmetric initial data sets, obtained with this 3D code, to results obtained from a well established axisymmetric code. In both codes we examine and compare the behavior of metric functions, apparent horizon properties, and waveforms, and show that these dynamic black holes can be accurately evolved in 3D. In particular we show that with present computational resources and techniques, the process of excitation and ringdown of the black hole can be evolved, and one can now extract accurately the gravitational waves emitted from the 3D Cartesian metric functions, even when they carry away only a small fraction ($<< 1%$) of the rest mass energy of the system. Waveforms for both the $\ell=2$ and the much more difficult $\ell=4$ and $\ell=6$ modes are computed and compared with axisymmetric calculations. In addition to exploring the physics of distorted black hole data sets, and showing the extent to which the waves can be accurately extracted, these results also provide important testbeds for all fully nonlinear numerical codes designed to evolve black hole spacetimes in 3D, whether they use singularity avoiding slicings, apparent horizon boundary conditions, or other evolution methods.
In this paper, we study relative deformations of maps into a family of K\"ahler manifolds whose images are divisors. We show that if the map satisfies a condition called semiregularity, then it allows relative deformations if and only if the cycle class of the image remains Hodge in the family. This gives a refinement of the so-called variational Hodge conjecture. We also show that the semiregularity of maps is related to classical notions such as Cayley-Bacharach conditions and d-semistability.
In this article we consider a linearized Calder\'on problem for polyharmonic operators of order $2m\ (m\ge 2)$ in the spirit of Calder\'on's original work [Cal80]. We give a uniqueness result for determining coefficients of order $\leq 2m-1$ up to gauge, based on inverting momentum ray transforms.
Let $b\ge 2$ be a given integer. In this paper, we show that there only finitely many positive integers $d$ which are not squares, such that the Pell equation $X^2-dY^2=1$ has two positive integer solutions $(X,Y)$ with the property that their $X$-coordinates are base $b$-repdigits. Recall that a base $b$-repdigit is a positive integer all whose digits have the same value when written in base $b$. We also give an upper bound on the largest such $d$ in terms of $b$.
The natural excitations of an interacting one-dimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analysed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to non-linear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.
In this paper, we propose an unified hyperspectral image classification method which takes three-dimensional hyperspectral data cube as an input and produces a classification map. In the proposed method, a deep neural network which uses spectral and spatial information together with residual connections, and pixel affinity network based segmentation-aware superpixels are used together. In the architecture, segmentation-aware superpixels run on the initial classification map of deep residual network, and apply majority voting on obtained results. Experimental results show that our propoped method yields state-of-the-art results in two benchmark datasets. Moreover, we also show that the segmentation-aware superpixels have great contribution to the success of hyperspectral image classification methods in cases where training data is insufficient.
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
We present the results of a new HI, optical, and H-alpha interferometric study of the nearby spiral galaxy NGC 157. Our combined C- and D-array observations with the VLA show a large-scale, ring-like structure in the neutral hydrogen underlying the optical disk, together with an extended, low surface density component going out to nearly twice the Holmberg radius. Beginning just inside the edge of the star-forming disk, the line of nodes in the gas disk commences a 60 degree warp, while at the same time, the rotation velocity drops by almost half its peak value of 200 km/s, before leveling off again in the outer parts. While a flat rotation curve in NGC 157 cannot be ruled out, supportive evidence for an abrupt decline comes from the ionised gas kinematics, the optical surface photometry, and the global HI profile. A standard `maximum-disk' mass model predicts comparable amounts of dark and luminous matter within NGC 157. Alternatively, a model employing a disk truncated at 2 disk scale lengths could equally well account for the unusual form of the rotation curve in NGC 157.
We discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubed\'{a}t decorations. We then consider a 1-parameter family generalization of the Villain's fully frustrated model, which interpolates between Onsager's 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions \textit{a l\'{a} Bethe}.
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy minimization and growth dynamics. By introducing a regularization in the model, we prove that solutions can be obtained as limits of time-discrete solutions, built by means of an exponential-update scheme. By further allowing the dependence of growth dynamics on an additional scalar field, to be interpreted as a nutrient or inhibitor, we formulate an optimal control problem and prove existence of optimal controls and states. Eventually, we tackle the existence of coupled morphoelastic and nutrient solutions, when the latter is allowed to diffuse and interact with the growing body.
The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This correspondence is used for characterising the probability distribution which governs the number of factors in a randomly selected factorisation of an asymptotically large N. Asymptotic upper bounds on both the skewness and the excess of this distribution, and on the total number of factorisations, are conjectured. The asymptotic formulas are checked against exact numerical data obtained with the help of recursion relations. It is also demonstrated that for large numbers which are the product of different primes the probability distribution approaches a Gaussian, while identical prime factors give rise to non-Gaussian statistics.
Problem 10 of the Landelijke Interuniversitaire Mathematische Olympiade 2010 asks for a proof that all matrices in a certain family are nilpotent. Both model solutions prove this using the Cayley-Hamilton theorem. I give a purely combinatorial proof.
Star clusters are studied widely both as benchmarks for stellar evolution models and in their own right. Cluster age and mass distributions within galaxies are probes of star formation histories, and of cluster formation and disruption processes. The vast majority of clusters in the Universe is small, and it is well known that the integrated fluxes and colors have broad probability distributions, due to small numbers of bright stars. This paper goes beyond the description of predicted probability distributions, and presents results of the analysis of cluster energy distributions in an explicitly stochastic context. The method developed is Bayesian. It provides posterior probability distributions in the age-mass-extinction space, using multi-wavelength photometric observations and a large collection of Monte-Carlo simulations of clusters of finite stellar masses. Both UBVI and UBVIK datasets are considered, and the study conducted in this paper is restricted to the solar metallicity. We first reassess and explain errors arising from the use of standard analysis methods, which are based on continuous population synthesis models: systematic errors on ages and random errors on masses are large, while systematic errors on masses tend to be smaller. The age-mass distributions obtained after analysis of a synthetic sample are very similar to those found for real galaxies in the literature. The Bayesian approach on the other hand, is very successful in recovering the input ages and masses. Taking stochastic effects into account is important, more important for instance than the choice of adding or removing near-IR data in many cases. We found no immediately obvious reason to reject priors inspired by previous (standard) analyses of cluster populations in galaxies, i.e. cluster distributions that scale with mass as M^-2 and are uniform on a logarithmic age scale.
We present a search for CO(3-2) emission in SDF-26821, a BzK-selected star-forming galaxy (sBzK) at z = 2.044, using the 45-m telescope of the Nobeyama Radio Observatory and the Nobeyama Millimeter Array. We do not detect significant emission and derive 2 \sigma limits: the CO luminosity of L'CO < 3.1 x 10^10 K km s^{-1} pc^{-2}, the ratio of far-infrared luminosity to CO luminosity of L_FIR/L'CO > 57 Lsun (K km s^{-1} pc^{-2})^{-1}, and the molecular gas mass of M_H2 < 2.5 x 10^10 Msun, assuming a velocity width of 200 km s^{-1} and a CO-to-H2 conversion factor of alpha_CO=0.8 Msun (K km s^{-1} pc^{-2})^{-1}. The ratio of L_FIR/L'CO, a measure of star formation efficiency (SFE), is comparable to or higher than the two z ~ 1.5 sBzKs detected in CO(2-1) previously, suggesting that sBzKs can have a wide range of SFEs. Comparisons of far-infrared luminosity, gas mass, and stellar mass among the sBzKs suggest that SDF-26821 is at an earlier stage of forming stars with a similar SFE and/or more efficiently forming stars than the two z ~ 1.5 sBzKs. The higher SFEs and specific star formation rates of the sBzKs compared to local spirals are indicative of the difference in star formation modes between these systems, suggesting that sBzKs are not just scaled-up versions of local spirals.
We present an X-ray timing analysis of the transient X-ray binary MXB 1658-298, using data obtained from the RXTE and XMM-Newton observatories. We have made 27 new mid eclipse time measurements from observations made during the two outbursts of the source. These new measurements have been combined with the previously known values to study long term changes in orbital period of the binary system. We have found that the mid-eclipse timing record of MXB 1658-298 is quite unusual. The long term evolution of mid-eclipse times indicates an overall orbital period decay with a time scale of -- 6.5(7) x 10^7 year. Over and above this orbital period decay, the O-C residual curve also shows a periodic residual on shorter timescales. This sinusoidal variation has an amplitude of ~9 lt-sec and a period of ~760 d. This is indicative of presence of a third body around the compact X-ray binary. The mass and orbital radius of the third body are estimated to lie in the range, 20.5-26.9 Jupiter mass and 750-860 lt-sec, respectively. If true, then it will be the most massive circumbinary planet and also the smallest period binary known to host a planet.
Lithium abundances are presented for 91 dwarf and subgiant stars in the Galactic bulge. The analysis is based on line synthesis of the 7Li line at 6707 {\AA} in high-resolution spectra obtained during gravitational microlensing events, when the brightnesses of the targets were highly magnified. Our main finding is that the bulge stars at sub-solar metallicities, and that are older than about eight billion years, does not show any sign of Li production, that is, the Li trend with metallicity is flat (or even slightly declining). This indicates that no lithium was produced during the first few billion years in the history of the bulge. This finding is essentially identical to what is seen for the (old) thick disk stars in the Solar neighbourhood, and adds another piece of evidence for a tight connection between the metal-poor bulge and the Galactic thick disk. For the bulge stars younger than about eight billion years, the sample contains a group of stars at very high metallicities at [Fe/H]~+0.4 that have lithium abundances in the range A(Li)=2.6-2.8. In the Solar neighbourhood the lithium abundances have been found to peak at a A(Li)~3.3 at [Fe/H]~ +0.1 and then decrease by 0.4-0.5 dex when reaching [Fe/H]~+0.4. The few bulge stars that we have at these metallicities, seem to support this declining A(Li) trend. This could indeed support the recent claim that the low A(Li) abundances at the highest metallicities seen in the Solar neighbourhood could be due to stars from the inner disk, or the bulge region, that have migrated to the Solar neighbourhood.
We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and for exponential or subexponential convergence to the equilibrium. The obtained conditions extend Veretennikov--Khasminskii conditions for SDEs and are optimal in a certain sense.
We show that systems with negative specific heat can violate the zeroth law of thermodynamics. By both numerical simulations and by using exact expressions for free energy and microcanonical entropy it is shown that if two systems with the same intensive parameters but with negative specific heat are thermally coupled, they undergo a process in which the total entropy increases irreversibly. The final equilibrium is such that two phases appear, that is, the subsystems have different magnetizations and internal energies at temperatures which are equal in both systems, but that can be different from the initial temperature.
We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class of nonlinear partial differential equations, including some of the most famous model equations for water waves. A detailed analysis is given for weak solutions of the Camassa-Holm equation. In addition, we establish the existence of nonsymmetric linear rotational waves for the Euler equations.
Let S be a K3 surface and S^[n] the Hilbert scheme of length n subschemes of S. Over the cartesian square of S^[n] there exists a natural reflexive rank 2n-2 coherent sheaf E, which is locally free away from the diagonal. The fiber of E, over a pair of ideal sheaves of distinct subschemes, is the vector space of extensions of the first ideal sheaf by the second. We prove that E is slope stable if the rank of the Picard group of S is less than or equal to 19. The Chern classes of End(E) are known to be monodromy invariant. Consequently, the sheaf End(E) is polystable-hyperholomorphic.
We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 seconds. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.
Prior plays an important role in providing the plausible constraint on human motion. Previous works design motion priors following a variety of paradigms under different circumstances, leading to the lack of versatility. In this paper, we first summarize the indispensable properties of the motion prior, and accordingly, design a framework to learn the versatile motion prior, which models the inherent probability distribution of human motions. Specifically, for efficient prior representation learning, we propose a global orientation normalization to remove redundant environment information in the original motion data space. Also, a two-level, sequence-based and segment-based, frequency guidance is introduced into the encoding stage. Then, we adopt a denoising training scheme to disentangle the environment information from input motion data in a learnable way, so as to generate consistent and distinguishable representation. Embedding our motion prior into prevailing backbones on three different tasks, we conduct extensive experiments, and both quantitative and qualitative results demonstrate the versatility and effectiveness of our motion prior. Our model and code are available at https://github.com/JchenXu/human-motion-prior.
In \cite{st2017}, the authors introduced the so-called \emph{general divide and color models}. One of the most well-known examples of such a model is the Ising model with external field $h = 0$, which has a color representation given by the random cluster model. In this paper, we give necessary and sufficient conditions for this color representation to be unique. We also show that if one considers the Ising model on a complete graph, then for many $h > 0$, there is no color representation. This shows in particular that any generalization of the random cluster model which provides color representations of Ising models with external fields cannot, in general, be a generalized divide and color models. Furthermore, we show that there can be at most finitely many $\beta > 0$ at which the random cluster model can be continuously extended to a color representation for $h \not = 0$.