ShantanuT01/DACTYL-Pretraining huggingface dataset:
The formation of massive stars exceeding 10 solar masses usually results in large-scale molecular outflows. Numerical simulations, including ionization, of the formation of such stars show evidence for ionization-driven molecular outflows. We here examine whether the outflows seen in these models reproduce the observations. We compute synthetic ALMA and CARMA maps of CO emission lines of the outflows, and compare their signatures to existing single-dish and interferometric data. We find that the ionization-driven models can only reproduce weak outflows around high-mass star-forming regions. We argue that expanding H II regions probably do not represent the dominant mechanism for driving observed outflows. We suggest instead that observed outflows are driven by the collective action of the outflows from the many lower-mass stars that inevitably form around young massive stars in a cluster.
Given a curve over a finite field, we compute the number of stable bundles of not necessarily coprime rank and degree over it. We apply this result to compute the virtual Poincare polynomials of the moduli spaces of stable bundles over a curve. A similar formula for the virtual Hodge polynomials and motives is conjectured.
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of measure inequality for the marginals of the bridge of a gradient diffusion and refined large deviation expansions for the tails of a random walk on a graph are derived. In contrast with the existing literature about bridges, all the estimates we obtain hold for non asymptotic time scales. New concentration of measure inequalities for pinned Poisson random vectors are also established. The quantities expressing our conditions are the so called \textit{reciprocal characteristics} associated with the Markov generator.
The final stage in the formation of terrestrial planets consists of the accumulation of ~1000-km ``planetary embryos'' and a swarm of billions of 1-10 km ``planetesimals.'' During this process, water-rich material is accreted by the terrestrial planets via impacts of water-rich bodies from beyond roughly 2.5 AU. We present results from five high-resolution dynamical simulations. These start from 1000-2000 embryos and planetesimals, roughly 5-10 times more particles than in previous simulations.   Each simulation formed 2-4 terrestrial planets with masses between 0.4 and 2.6 Earth masses. The eccentricities of most planets were ~0.05, lower than in previous simulations, but still higher than for Venus, Earth and Mars. Each planet accreted at least the Earth's current water budget.   We demonstrate several new aspects of the accretion process: 1) The feeding zones of terrestrial planets change in time, widening and moving outward. Even in the presence of Jupiter, water-rich material from beyond 2.5 AU is not accreted for several millions of years. 2) Even in the absence of secular resonances, the asteroid belt is cleared of >99% of its original mass by self-scattering of bodies into resonances with Jupiter. 3) If planetary embryos form relatively slowly, following the models of Kokubo & Ida, then the formation of embryos in the asteroid belt may have been stunted by the presence of Jupiter. 4) Self-interacting planetesimals feel dynamical friction from other small bodies, which has important effects on the eccentricity evolution and outcome of a simulation.
We present our second paper on the Allen Telescope Array Twenty-centimeter Survey (ATATS), a multi-epoch, ~700 sq. deg. radio image and catalog at 1.4 GHz. The survey is designed to detect rare, bright transients as well as to commission the ATA's wide-field survey capabilities. ATATS explores the challenges of multi-epoch transient and variable source surveys in the domain of dynamic range limits and changing (u,v) coverage.   Here we present images made using data from the individual epochs, as well as a revised image combining data from all ATATS epochs. The combined image has RMS noise 3.96 mJy / beam, with a circular beam of 150 arcsec FWHM. The catalog, generated using a false detection rate algorithm, contains 4984 sources, and is >90% complete to 37.9 mJy. The catalogs generated from snapshot images of the individual epochs contain between 1170 and 2019 sources over the 564 sq. deg. area in common to all epochs. The 90% completeness limits of the single epoch catalogs range from 98.6 to 232 mJy.   We compare the catalog generated from the combined image to those from individual epochs, and from the NRAO VLA Sky Survey (NVSS), a legacy survey at the same frequency. We are able to place new constraints on the transient population: fewer than 6e-4 transients / sq. deg., for transients brighter than 350 mJy with characteristic timescales of minutes to days. This strongly rules out an astronomical origin for the ~1 Jy sources reported by Matsumura et al. (2009), based on their stated rate of 3.1e-3 / sq. deg.
We find two natural spherical functors associated to the Kummer surface and analyse how their induced twists fit with Bridgeland's conjecture on the derived autoequivalence group of a complex algebraic K3 surface.
In this manuscript we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower order term depending on $x$, $u$ and $\nabla u$. More precisely, we prove that any locally bounded viscosity solution constitutes a weak solution, extending previous results by Juutinen, Lindqvist and Manfredi on the homogeneous case, and Julin and Juutinen for a linear right hand side. Moreover, we provide a converse statement in the full case under extra assumptions on the regularity of the solutions.
Turbulence significantly influences the dynamics of flame in SNIa. The large Reynolds number makes impossible the direct numerical simulations of turbulence, and different models of turbulence have to be used. Here we present the simulations with the $k$-$\epsilon$ model. The turbulence is generated by the RTL instability and crucially influences flame front velocity, resulting in $v_{\rm flame}\sim 300$ km/s. The model reproduces turbulent properties in low-dimensional simulations and can be used for the low-cost studies.
Experiments show that macroscopic systems in a stationary nonequilibrium state exhibit long range correlations of the local thermodynamic variables. In previous papers we proposed a Hamilton-Jacobi equation for the nonequilibrium free energy as a basic principle of nonequilibrium thermodynamics. We show here how an equation for the two point correlations can be derived from the Hamilton-Jacobi equation for arbitrary transport coefficients for dynamics with both external fields and boundary reservoirs. In contrast with fluctuating hydrodynamics, this approach can be used to derive equations for correlations of any order. Generically, the solutions of the equation for the correlation functions are non-trivial and show that long range correlations are indeed a common feature of nonequilibrium systems. Finally, we establish a criterion to determine whether the local thermodynamic variables are positively or negatively correlated in terms of properties of the transport coefficients.
We present macroscopic and neutron diffraction data on multiferroic lightly Co-doped Ni$_3$V$_2$O$_8$. Doping Co into the parent compound suppresses the sequence of four magnetic phase transitions and only two magnetically ordered phases, the paraelectric high temperature incommensurate (HTI) and ferroelectric low temperature incommensurate (LTI), can be observed. Interestingly, the LTI multiferroic phase with a spiral (cycloidal) magnetic structure is stabilized down to at least 1.8 K, which could be revealed by measurements of the electric polarization and confirmed by neutron diffraction on single crystal samples. The extracted magnetic moments of the LTI phase contain besides the main exchange also fine components of the cycloid allowed by symmetry which result in a small amplitude variation of the magnetic moments along the cycloid propagation due to the site-dependent symmetry properties of the mixed representations. In the HTI phase a finite imaginary part of the spine magnetic moment could be deduced yielding a spin cycloid instead of a purely sinusoidal structure with an opposite spin chirality for different spine spin chains. The magnetic ordering of the cross-tie sites in both phases is different in comparison to the respective ones in the pure Ni compound. A wider temperature stability range of the HTI phase has been observed in comparison to Ni$_3$V$_2$O$_8$ which can be explained by an additional single-ion easy-axis anisotropy due to Co-doping. The larger incommensurability of the Co-doped compounds yields a larger ratio between the competing next-nearest neighbour and nearest neighbour interaction, which is $J_2/J_1$=0.43 (0.47) for a doping level of 7% (10%) Co compared to 0.39 in the parent compound.
In the present paper, our objective is to treat a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Dedekind-type sums with weight in connection with modified q-Genocchi polynomials with weight alpha by using p-adic invariant q-integral on Zp.
We consider $S=1$ triangular lattice Heisenberg antiferromagnets with a strong single-ion anisotropy $D$ that dominates over the nearest-neighbour antiferromagnetic exchange $J$. In this limit of small $J/D$, we study low temperature ($T \sim J \ll D$) properties of such magnets by employing a low-energy description in terms of hard-core bosons with nearest neighbour repulsion $V \approx 4J + J^2/D$ and nearest neighbour unfrustrated hopping $t \approx J^2/2D$. Using a cluster Stochastic Series Expansion (SSE) algorithm to perform sign-problem-free quantum Monte Carlo (QMC) simulations of this effective model, we establish that the ground-state three-sublattice order of the easy-axis spin-density $S^z(\vec{r})$ melts in zero field ($B=0$) in a {\em two-step} manner via an intermediate temperature phase characterized by power-law three-sublattice order with a temperature dependent exponent $\eta(T) \in [\frac{1}{9}, \frac{1}{4}]$. For $\eta(T) < \frac{2}{9}$ in this phase, we find that the uniform easy-axis susceptibility of an $L \times L$ sample diverges as $\chi_L \sim L^{2-9 \eta}$ at $B=0$, consistent with a recent prediction that the thermodynamic susceptibility to a uniform field $B$ along the easy axis diverges at small $B$ as $\chi_{\rm easy-axis}(B) \sim B^{-\frac{4-18\eta}{4-9\eta}}$ in this regime.
Training state-of-the-art models for human pose estimation in videos requires datasets with annotations that are really hard and expensive to obtain. Although transformers have been recently utilized for body pose sequence modeling, related methods rely on pseudo-ground truth to augment the currently limited training data available for learning such models. In this paper, we introduce PoseBERT, a transformer module that is fully trained on 3D Motion Capture (MoCap) data via masked modeling. It is simple, generic and versatile, as it can be plugged on top of any image-based model to transform it in a video-based model leveraging temporal information. We showcase variants of PoseBERT with different inputs varying from 3D skeleton keypoints to rotations of a 3D parametric model for either the full body (SMPL) or just the hands (MANO). Since PoseBERT training is task agnostic, the model can be applied to several tasks such as pose refinement, future pose prediction or motion completion without finetuning. Our experimental results validate that adding PoseBERT on top of various state-of-the-art pose estimation methods consistently improves their performances, while its low computational cost allows us to use it in a real-time demo for smoothly animating a robotic hand via a webcam. Test code and models are available at https://github.com/naver/posebert.
Let $\mathbb{F}_q$ be the finite field of characteristic $p$ with $q$ elements and $\mathbb{F}_{q^n}$ its extension of degree $n$. The conjecture of Morgan and Mullen asserts the existence of primitive and completely normal elements (PCN elements) for the extension $\mathbb{F}_{q^n}/\mathbb{F}_q$ for any $q$ and $n$. It is known that the conjecture holds for $n \leq q$. In this work we prove the conjecture for a larger range of exponents. In particular, we give sharper bounds for the number of completely normal elements and use them to prove asymptotic and effective existence results for $q\leq n\leq O(q^\epsilon)$, where $\epsilon=2$ for the asymptotic results and $\epsilon=1.25$ for the effective ones. For $n$ even we need to assume that $q-1\nmid n$.
We examine the singularities of the wave fronts of null geodesics from point sources in the Kerr Metric. We find that the wave fronts develop a tube like structure that collapses non-symmetrically, leading to cusp features in the wave front singularities. As the wave front advances, the cusps trace out an astroidal shaped caustic tube, which had been discovered previously using lens mapping and geodesic deviation methods. Thus, the wave front approach in this study helps to complete a picture of caustics and gravitational lensing in the Kerr geometry.
A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable characteristics of the Archimedean generator, the upper and lower tails of the copula are classified into one of three classes each, one corresponding to asymptotic dependence and the other two to asymptotic independence. For a long list of single-parameter families, the relevant tail quantities are computed so that the corresponding classes in the decision tree can easily be determined. In addition, new models with tailor-made upper and lower tails can be constructed via a number of transformation methods. The frequently occurring category of asymptotic independence turns out to conceal a surprisingly rich variety of tail dependence structures.
We present the first absolute proper motion measurement of Leo I, based on two epochs of HST ACS/WFC images separated by ~5 years. The average shift of Leo I stars with respect to ~100 background galaxies implies a proper motion of (mu_W, mu_N) = (0.1140 +/- 0.0295, -0.1256 +/- 0.0293) mas/yr. The implied Galactocentric velocity vector, corrected for the reflex motion of the Sun, has radial and tangential components V_rad = 167.9 +/- 2.8 km/s and V_tan = 101.0 +/- 34.4 km/s, respectively. We study the detailed orbital history of Leo I by solving its equations of motion backward in time for a range of plausible mass models for the Milky Way and its surrounding galaxies. Leo I entered the Milky Way virial radius 2.33 +/- 0.21 Gyr ago, most likely on its first infall. It had a pericentric approach 1.05 +/- 0.09 Gyr ago at a Galactocentric distance of 91 +/- 36 kpc. We associate these time scales with characteristic time scales in Leo I's star formation history, which shows an enhanced star formation activity ~2 Gyr ago and quenching ~1 Gyr ago. There is no indication from our calculations that other galaxies have significantly influenced Leo I's orbit, although there is a small probability that it may have interacted with either Ursa Minor or Leo II within the last ~1 Gyr. For most plausible Milky Way masses, the observed velocity implies that Leo I is bound to the Milky Way. However, it may not be appropriate to include it in models of the Milky Way satellite population that assume dynamical equilibrium, given its recent infall. Solution of the complete (non-radial) timing equations for the Leo I orbit implies a Milky Way mass M_MW,vir = 3.15 (-1.36, +1.58) x 10^12 Msun, with the large uncertainty dominated by cosmic scatter. In a companion paper, we compare the new observations to the properties of Leo I subhalo analogs extracted from cosmological simulations.
The Boolean lattice $2^{[n]}$ is the family of all subsets of $[n]=\{1,\dots,n\}$ ordered by inclusion, and a chain is a family of pairwise comparable elements of $2^{[n]}$. Let $s=2^{n}/\binom{n}{\lfloor n/2\rfloor}$, which is the average size of a chain in a minimal chain decomposition of $2^{[n]}$. We prove that $2^{[n]}$ can be partitioned into $\binom{n}{\lfloor n/2\rfloor}$ chains such that all but at most $o(1)$ proportion of the chains have size $s(1+o(1))$. This asymptotically proves a conjecture of F\"uredi from 1985. Our proof is based on probabilistic arguments. To analyze our random partition we develop a weighted variant of the graph container method. Using this result, we also answer a Kalai-type question raised recently by Das, Lamaison and Tran. What is the minimum number of forbidden comparable pairs forcing that the largest subfamily of $2^{[n]}$ not containing any of them has size at most $\binom{n}{\lfloor n/2\rfloor}$? We show that the answer is $(\sqrt{\frac{\pi}{8}}+o(1))2^{n}\sqrt{n}$. Finally, we discuss how these uniform chain decompositions can be used to optimize and simplify various results in extremal set theory.
The fluctuations of massless Dirac fermion can not only turn a first-order bosonic phase transition (in the Landau sense) to a quantum critical point, but also work reversely to enhance the first-order transition itself, depending on the implementation of finite size effects in the coupling corrections. Here, we report a case study of the latter by employing quantum Monte Carlo simulation upon a lattice model in which the bosonic part featuring the Landau-Devonshire first-order phase transition and Yukawa coupled to the Dirac fermions. We find that the parameter range for the first-order phase transition becomes larger as the Yukawa coupling increases and the microscopic mechanism of this phenomena is revealed, at a quantitative level, as the interplay between the critical fluctuations and the finite-size effects. Moreover, the scaling behavior at the separation point between the first-order and the continuous phase transitions is found to belong to the chiral tricritical Gross-Neveu universality. Our result demonstrates that the interplay of massless Dirac fermions, critical fluctuations and the finite size effects could trigger a plethora of interesting phenomena and therefore great care is called for when making generalizations.
We compare data from the Diffuse InfraRed Background Experiment (DIRBE) on the Cosmic Background Explorer (COBE) satellite to the the Wainscoat et al. (1992) model of the infrared sky. The model is first compared with broadband K (2.2 microns) star counts. Its success at K gives credence to its physical approach which is extrapolated to the L band (3.5 microns). We have analyzed the histograms of the pixel by pixel intensities in the 2.2 and 3.5 micron maps from DIRBE after subtracting the zodiacal light. The shape of these histograms agrees quite well with the histogram shape predicted using the Wainscoat et al. model of the infrared sky, but the predicted histograms must be displaced by a constant intensity in order to match the data. This shift is the cosmic infrared background, which is 16.9+/-4.4 kJy/sr or 23.1+/-5.9 nW/m^2/sr at 2.2 microns, and 14.4+/-3.7 kJy/sr or 12.4+/-3.2 nW/m^2/sr at 3.5 microns.
Neural network classifiers have become the de-facto choice for current "pre-train then fine-tune" paradigms of visual classification. In this paper, we investigate k-Nearest-Neighbor (k-NN) classifiers, a classical model-free learning method from the pre-deep learning era, as an augmentation to modern neural network based approaches. As a lazy learning method, k-NN simply aggregates the distance between the test image and top-k neighbors in a training set. We adopt k-NN with pre-trained visual representations produced by either supervised or self-supervised methods in two steps: (1) Leverage k-NN predicted probabilities as indications for easy vs. hard examples during training. (2) Linearly interpolate the k-NN predicted distribution with that of the augmented classifier. Via extensive experiments on a wide range of classification tasks, our study reveals the generality and flexibility of k-NN integration with additional insights: (1) k-NN achieves competitive results, sometimes even outperforming a standard linear classifier. (2) Incorporating k-NN is especially beneficial for tasks where parametric classifiers perform poorly and / or in low-data regimes. We hope these discoveries will encourage people to rethink the role of pre-deep learning, classical methods in computer vision. Our code is available at: https://github.com/KMnP/nn-revisit.
The progenitors of low-luminosity Type II-Plateau supernovae (SNe II-P) are believed to be red supergiant (RSG) stars, but there is much disparity in the literature concerning their mass at core collapse and therefore on the main sequence. Here, we model the SN radiation arising from the low-energy explosion of RSG stars of 12, 25, and 27 M$_{\odot}$ on the main sequence and formed through single star evolution. Despite the narrow range in ejecta kinetic energy (2.5$-$4.2$\times$10$^{50}$ erg) in our model set, the SN observables from our three models are significantly distinct, reflecting the differences in progenitor structure (e.g., surface radius, H-rich envelope mass, He-core mass). Our higher mass RSG stars give rise to Type II SNe that tend to have bluer colors at early times, a shorter photospheric phase, and a faster declining $V$-band light curve (LC) more typical of Type II-linear SNe, in conflict with the LC plateau observed for low-luminosity SNe II. The complete fallback of the CO core in the low-energy explosions of our high mass RSG stars prevents the ejection of any ${}^{56}$Ni (nor any core O or Si), in contrast to low-luminosity SNe II-P, which eject at least 0.001 M$_{\odot}$ of ${}^{56}$Ni. In contrast to observations, type II SN models from higher mass RSGs tend to show an H$\alpha$ absorption that remains broad at late times (due to a larger velocity at the base of the H-rich envelope). In agreement with the analyses of pre-explosion photometry, we conclude that low-luminosity SNe II-P likely arise from low-mass rather than high-mass RSG stars.
Bridges form dynamically in granular media as a result of spatiotemporal inhomogeneities. We classify bridges as linear and complex, and analyse their geometrical characteristics. In particular, we find that the length distribution of linear bridges is exponential. We then turn to the analysis of the orientational distribution of linear bridges and find that, in three dimensions, they are {\it vertically diffusive but horizontally superdiffusive}; thus, when they exist, long linear bridges form `domes'. Our results are in good accord with Monte Carlo simulations of bridge structure; we make predictions for quantities that are experimentally accessible, and suggest that bridges are very closely related to force chains.
The object of study is the group of units O^\ast(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite cyclic cover of a rational variety. On a cyclic cover X \rightarrow A^m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that O^\ast(X) is equal to k^\ast, the nonzero scalars. The same conclusion holds, if X is a sufficiently general affine hyperelliptic curve. If X has a projective completion such that the divisor at infinity has r components, then sufficient conditions are given for O^\ast(X)/k^\ast to be isomorphic to Z^(r-1).
For a wave equation with pure delay, we study an inhomogeneous initial-boundary value problem in a bounded 1D domain. Under smoothness assumptions, we prove unique existence of classical solutions for any given finite time horizon and give their explicit representation. Continuous dependence on the data in a weak extrapolated norm is also shown.