ShantanuT01/DACTYL-Pretraining huggingface dataset:
The {\it Far Ultraviolet Spectroscopic Explorer} ({\it FUSE}) has allowed precise determinations of the column densities of molecular hydrogen ($\Hmol$) in Galactic lines of sight with a wide range of pathlengths and extinction properties. However, survey studies of lines of sight with greater extinction have been mostly restricted to the low-$J$ states (lower total angular momentum) in which most molecular hydrogen is observed. This paper presents a survey of column densities for the molecular hydrogen in states of greater rotational excitation ($J \geq 2$) in Galactic lines of sight with $\log{\NHmol} \gtrsim 20$. This study is comprehensive through the highest excited state detectable in each line of sight. J=5 is observed in every line of sight, and we detect J=7 in four lines of sight, J=8 in one line of sight, and vibrationally excited $\Hmol$ in two lines of sight. We compared the apparent $b$-values and velocity offsets of the higher-$J$ states relative to the dominant low-$J$ states and we found no evidence of any trends that might provide insight into the formation of higher-$J$ $\Hmol$, although these results are the most affected by the limits of the {\it FUSE} resolution. We also derive excitation temperatures based on the column densities of the different states. We confirm that at least two distinct temperatures are necessary to adequately describe these lines of sight, and that more temperatures are probably necessary. Total $\Hmol$ column density is known to be correlated with other molecules; we explore if correlations vary as a function of $J$ for several molecules, most importantly CH and CH$^+$. Finally, we briefly discuss interpretations of selected lines of sight by comparing them to models computed using the Meudon PDR code.
We study the conductivity, density of states, and magnetic correlations of a two dimensional, two band fermion Hubbard model using determinant Quantum Monte Carlo (DQMC) simulations. We show that an orbitally selective Mott transition (OSMT) occurs in which the more weakly interacting band can be metallic despite complete localization of the strongly interacting band. The DQMC method allows us to test the validity of the use of a momentum independent self-energy which has been a central approximation in previous OSMT studies. In addition, we show that long range antiferromagnetic order (LRAFO) is established in the insulating phase, similar to the single band, square lattice Hubbard Hamiltonian. Because the critical interaction strengths for the onset of insulating behavior are much less than the bandwidth of the itinerant orbital, we suggest that the development of LRAFO plays a key role in the transitions.
We have performed simulations to investigate the dynamics of the M dwarf star GJ 876 in an attempt to reveal any stabilizing mechanism for sustaining the system.We simulated different coplanar and noncoplanar configurations of two-planet systems and other cases.From the simulations,we found that the 2 :1 mean-motion resonance between two planets can act as an effective mechanism for maintaining the stability of the system.This result is explained by a proposed analytical model.Using this model,we studied the region of motion of the inner planet by varying the parameters of the system,and we detected that the analytical results are well consistent with the numerical simulations.
In this note we prove Poincar\'e type inequalities for a family of kinetic equations. We apply this inequality to the variational solution of a linear kinetic model.
We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard Laplacian case, where the stable state invades the unstable one at constant speed, we prove here that invasion holds at an exponential in time velocity. These results provide a mathematically rigorous justification of numerous heuristics about this model.
We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence properties. We consider algorithms in the spirit of Monte-Carlo Tree Search, to estimate at best the minimax value of a given position: it consists in simulating, successively, $n$ well-chosen matches, starting from this position. We build an algorithm, which is optimal, step by step, in some sense: once the $n$ first matches are simulated, the algorithm decides from the statistics furnished by the $n$ first matches (and the a priori we have on the game) how to simulate the $(n+1)$-th match in such a way that the increase of information concerning the minimax value of the position under study is maximal. This algorithm is remarkably quick. We prove that our step by step optimal algorithm is not globally optimal and that it always converges in a finite number of steps, even if the a priori we have on the game is completely irrelevant. We finally test our algorithm, against MCTS, on Pearl's game and, with a very simple and universal a priori, on the games Connect Four and some variants. The numerical results are rather disappointing. We however exhibit some situations in which our algorithm seems efficient.
We present an analysis of the galaxy-scale gaseous outflows from the FIRE (Feedback in Realistic Environments) simulations. This suite of hydrodynamic cosmological zoom simulations resolves formation of star-forming giant molecular clouds to $z=0$, and features an explicit stellar feedback model on small scales. Our simulations reveal that high redshift galaxies undergo bursts of star formation followed by powerful gusts of galactic outflows that eject much of the ISM and temporarily suppress star formation. At low redshift, however, sufficiently massive galaxies corresponding to L*-progenitors develop stable disks and switch into a continuous and quiescent mode of star formation that does not drive outflows far into the halo. Mass-loading factors for winds in L*-progenitors are $\eta \approx 10$ at high redshift, but decrease to $\eta \ll 1$ at low redshift. Although lower values of $\eta$ are expected as halos grow in mass over time, we show that the strong suppression of outflows with decreasing redshift cannot be explained by mass evolution alone. Circumgalactic outflow velocities are variable and broadly distributed, but typically range between one and three times the circular velocity of the halo. Much of the ejected material builds a reservoir of enriched gas within the circumgalactic medium, some of which could be later recycled to fuel further star formation. However, a fraction of the gas that leaves the virial radius through galactic winds is never regained, causing most halos with mass $M_h \le 10^{12} M_{\odot}$ to be deficient in baryons compared to the cosmic mean by $z=0$.
We study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration $p$ of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong bond disorder. Using the standard Monte Carlo simulation and the powerful Wang-Landau flat-histogram method, we carry out in this work intensive simulations over the whole range of $p$. We show that the first-order transition disappears with a tiny amount of ferromagnetic bonds, namely $p\sim 0.01$, in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small $p$ ($\simeq 5%$). With increasing $p$, the system changes into a spin glass and then to a ferromagnetic phase when $p>0.65$. The phase diagram in the space ($T_c,p$) shows an asymmetry, unlike the case of the $\pm J$ Ising spin glass on the simple cubic lattice. We calculate the relaxation time around the spin-glass transition temperature and we show that the spin autocorrelation follows a stretched exponential relaxation law where the factor $b$ is equal to $\simeq 1/3$ at the transition as suggested by the percolation-based theory. This value is in agreement with experiments performed on various spin glasses and with Monte Carlo simulations on different SG models.
We show how the multiplicative structure on Pythagorean triples defined by Beauregard--Suryanarayan arises from automorphisms of the hyperbolic plane, and how the structure theorem of this product follow naturally from this connection. We also show how the natural involution on Pythagorean triples is related to Pell's equation with the parameter 2, and prove a generalization of this phenomenon.
Various methods have been proposed to search for extrasolar planets. Compared to the other methods, microlensing has unique applicabilities to the detections of Earth-mass and free-floating planets. However, the microlensing method is seriously flawed by the fact that the masses of the detected planets cannot be uniquely determined. Recently, Gould, Gaudi, & Han introduced an observational setup that enables one to resolve the mass degeneracy of the Earth-mass planets. The setup requires a modest adjustment to the orbit of an already proposed Microlensing planet-finder satellite combined with ground-based observations. In this paper, we show that a similar observational setup can also be used for the mass determinations of free-floating planets with masses ranging from ~0.1 M_J to several Jupiter masses. If the proposed observational setup is realized, the future lensing surveys will play important roles in the studies of Earth-mass and free-floating planets, which are the populations of planets that have not been previously probed.
A maximum likelihood type estimation of the drift and volatility coefficient parameters in the CIR type model driven by $\alpha$-stable noises is studied when the dispersion parameter $\varepsilon\to0$ and the discrete observations frequency $n\to\infty$ simultaneously.
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen internal degree of freedom, the so called internal clock. We investigate the way in which the choice of internal clock determines the quantum dynamics and how much different quantum dynamics induced by different clocks are. We develop our method of comparison by extending the Hamilton-Jacobi theory of contact transformations to include a new type of transformations which transform both the canonical variables and the internal clock. We employ our method to study the quantum dynamics of the Friedmann-Lemaitre model and obtain semiclassical corrections to the classical dynamics, which depend on the choice of internal clock. For a unique quantisation map we find the abundance of inequivalent semiclassical corrections induced by quantum dynamics taking place in different internal clocks. It follows that the concepts like minimal volume, maximal curvature and the number of quantum bounces, often used to describe quantum effects in cosmological models, depend on the choice of internal clock.
The masses of central supermassive black holes in a soft X-ray selected sample of the narrow-line Seyfert 1 galaxies (NLS1s) are estimated by some different methods to test their theoretical models. Apart from the methods using the H$\beta$ linewidth and the [O III] linewidth, soft X-ray excess as a prominent character of NLS1s is used to estimate the black hole masses. The virial mass derived from the H$\beta$ linewidth assuming random orbits of broad-line reigns (BLRs) is consistent with that from the soft X-ray bump luminosity for NLS1s but with a larger scatter. The virial black hole masses showed that most of NLS1s are in the super-Eddington accretion state while most of broad-line Seyfert 1 galaxies (BLS1s) are not. We found that the black hole mass estimated from [O III] linewidth is not in agreement with above two methods. Using the Eddington limit relation for the super-Eddington accretion suggested by Wang (2004), we found that there are 16 NLS1s satisfied with this Eddington limit relation. The masses of these 16 NLS1s derived from X-ray luminosity are systematically larger than that from H$\beta$ linewidth assuming random BLRs orbits. If the mass derived from X-ray luminosity is true, the mean disk inclination to the line of sight in these 16 NLS1s is about $17^{\circ}$, which provided new support for the pole-on orientation effect in NLS1s.
Understanding causes and effects in mechanical systems is an essential component of reasoning in the physical world. This work poses a new problem of counterfactual learning of object mechanics from visual input. We develop the CoPhy benchmark to assess the capacity of the state-of-the-art models for causal physical reasoning in a synthetic 3D environment and propose a model for learning the physical dynamics in a counterfactual setting. Having observed a mechanical experiment that involves, for example, a falling tower of blocks, a set of bouncing balls or colliding objects, we learn to predict how its outcome is affected by an arbitrary intervention on its initial conditions, such as displacing one of the objects in the scene. The alternative future is predicted given the altered past and a latent representation of the confounders learned by the model in an end-to-end fashion with no supervision. We compare against feedforward video prediction baselines and show how observing alternative experiences allows the network to capture latent physical properties of the environment, which results in significantly more accurate predictions at the level of super human performance.
We study the phase space of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein-Gauss- Bonnet action. We show the existence of solutions with nonflat asymptotic behavior.
A direct observation of the spiral structure of the Galaxy is hindered by our position in the middle of the Galactic plane. We propose a method based on the analysis of the birthplaces of high Galactic latitude runaway stars to map the spiral arms and determine their dynamics. As a proof of concept, the method is applied to a local sample of early-type stars and a sample of runaways stars to obtain estimates of the pattern speed and the spiral arm's phase angle. We also estimate the performance of this method once the data gathered by Gaia, in particular for runaway stars observed on the other side of the Galaxy, is available.
Verlinde bundles are vector bundles $V_k$ arising as the direct image $\pi_*(\mathcal L^{\otimes k})$ of polarizations of a proper family of schemes $\pi\colon \mathfrak X \to S$. We study the splitting behavior of Verlinde bundles in the case where $\pi$ is the universal family $\mathfrak X \to |\mathcal O(d)|$ of hypersurfaces of degree $d$ in $\mathbb P^n$ and calculate the cohomology class of the locus of jumping lines of the Verlinde bundles $V_{d+1}$ in the cases $n=2,3$.
In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous (with respect to the Lebesgue measure on the real line). The distribution is identified through the form of the density with respect to a measure which is a sum of the bivariate Lebesgue measure on $\R^2$ and the univariate Lebesgue measure on the diagonal $\{(x,x):\,x\in\R\}$.   We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample. Nevertheless the general question of identifiability of the parent distribution by regression of order statistics from overlapping samples remains open.
This paper considers various formulations of the sum-product problem. It is shown that, for a finite set $A\subset{\mathbb{R}}$, $$|A(A+A)|\gg{|A|^{\frac{3}{2}+\frac{1}{178}}},$$ giving a partial answer to a conjecture of Balog. In a similar spirit, it is established that $$|A(A+A+A+A)|\gg{\frac{|A|^2}{\log{|A|}}},$$ a bound which is optimal up to constant and logarithmic factors. We also prove several new results concerning sum-product estimates and expanders, for example, showing that $$|A(A+a)|\gg{|A|^{3/2}}$$ holds for a typical element of $A$.
The 3-arc graph of a digraph $D$ is defined to have vertices the arcs of $D$ such that two arcs $uv, xy$ are adjacent if and only if $uv$ and $xy$ are distinct arcs of $D$ with $v\ne x$, $y\ne u$ and $u,x$ adjacent.   We prove that Hadwiger's conjecture holds for 3-arc graphs.
We attempt to solve the Einstein equations for string dust and null flowing radiation for the general axially symmetric metric, which we believe is being done for the first time. We obtain the string-dust and radiating generalizations of the Kerr and the NUT solutions. There also occurs an interesting case of radiating string-dust which arises from string-dust generalization of Vaidya's solution of a radiating star.
The paper deals with the nonequilibrium two-lead Anderson model, considered as an adequate description for transport through a d-c biased quantum dot. Using a self-consistent equation-of-motion method generalized out of equilibrium, we calculate a fourth-order decoherence rate $\gamma^{(4)}$ induced by a bias voltage $V$. This decoherence rate provides a cut-off to the infrared divergences of the self-energy showing up in the Kondo regime. At low temperature, the Kondo peak in the density of states is split into two peaks pinned at the chemical potential of the two leads. The height of these peaks is controlled by $\gamma^{(4)}$. The voltage dependence of the differential conductance exhibits a zero-bias peak followed by a broad Coulomb peak at large $V$, reflecting charge fluctuations inside the dot. The low-bias differential conductance is found to be a universal function of the normalized bias voltage $V/T_K$, where $T_K$ is the Kondo temperature. The universal scaling with a single energy scale $T_K$ at low bias voltages is also observed for the renormalized decoherence rate $\gamma^{(4)}/T_K$. We discuss the effect of $\gamma^{(4)}$ on the crossover from strong to weak coupling regime when either the temperature or the bias voltage is increased.
Our understanding of strong gravity near supermassive compact objects has recently improved thanks to the measurements made by the Event Horizon Telescope (EHT). We use here the M87* shadow size to infer constraints on the physical charges of a large variety of nonrotating or rotating black holes. For example, we show that the quality of the measurements is already sufficient to rule out that M87* is a highly charged dilaton black hole. Similarly, when considering black holes with two physical and independent charges, we are able to exclude considerable regions of the space of parameters for the doubly-charged dilaton and the Sen black holes.
Intermediate polars are members of the cataclysmic variable binary stars. They are characterized by a moderately magnetized white dwarf accreting matter from a cool main-sequence companion star. In many cases, this accretion gives rise to a detectable $X$-ray emission. VZ Sex is an interesting $X$-ray source whose nature needs a robust confirmation. Here, we used archive $XMM$-Newton observation to assign the source to the intermediate polar class. We applied the Lomb-Scargle periodogram method to detect any relevant periodic feature in the $0.1$--$10$ keV light curve and performed a spectral fitting of the $X$-ray spectrum in order to get information on the on-going accretion mechanism. By inspecting the periodogram, we detected a clear periodic feature at $\simeq 20.3$ minutes that we interpret as the spin period of the white dwarf. We additionally found the typical side bands expected as the consequence of the beat between the spin and the orbital period of $\simeq 3.581$ hours. The source is characterized by a unabsorbed flux of $\simeq 2.98\times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ corresponding to an intrinsic luminosity {of $\simeq 7 \times 10^{31}$ erg s$^{-1}$ } {for a distance of $\simeq 433$ pc}. The existence of such features allow us to classify VZ Sex as a clear member of the intermediate polar class. Furthermore, with the estimated WD spin, the ratio $P_{spin}/P_{orb}$ is $\simeq 0.09$, i.e. consistent with that expected for a typical IP system above the period gap. In addition, the estimated intrinsic luminosity opens the possibility that a bridge linking the normally bright IPs to the faint population of sources does exist.
In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where $X=\{X(t)\}$ is a spectrally positive L\'evy process and $c\in\RL$. As an example we investigate the inverse Gaussian L\'evy process.
We initiate the study of simultaneous core multipartitions, generalising simultaneous core partitions, which have been studied extensively in the recent literature. Given a multipartition datum (s|c), which consists of a non-negative integer s and an l-tuple c of integers, we introduce the notion of an (s|c)-core multipartition. Given an arbitrary set of multicore data, we give necessary and sufficient conditions for the corresponding set of simultaneous core multipartitions to be finite. We then study the special case of simultaneous core bipartitions, giving exact enumerative results in some special subcases.
The stellar mass, size and rotational velocity of galactic disks all grow from redshift ~2 to the present by amounts that are estimated from observationally derived scaling relations. The product of these three quantities, the angular momentum of stellar disks, is then estimated to grow by a remarkably large factor, between ~20 and ~50, whereas other evidences suggest a more moderate increase. This requires that the specific angular momentum of the accreted gas should systematically increase with time while remaining co-rotational with the disk over most of the last ~10 Gyr. Thus, the baryonic gas vorticity of the circumgalactic medium appears to emerge as a major driver in galaxy evolution, and this paper is meant to attract attention on the sheer size of the angular momentum increase and on the need to explore to which extent this can be observed in nature and/or in simulations.
In order to find the conditions which determine whether X-Ray hot gas in galaxy groups (intragroup gas; IGG) is heated externally or internally, we investigate the evolution of blast waves in galaxy groups growing on a hierarchical clustering scenario. We find that the blast waves driven by quasars are confined in groups and heat the IGG internally at z<~ 1. However, at z>~ 1, they expel the IGG from groups; the expelled gas may fall back into the groups later as externally heated gas. Moreover, this may explain the observed low metal abundance of IGG. For blast waves driven by strong starbursts, the shift of the fate of blast waves occurs at z~ 3. On the other hand, although blast waves driven by weak starbursts do not expel IGG from groups, the heating efficiency decreases at z>~ 3 because of radiative cooling. It will be useful to compare these results with XMM-Newton observations.