Miracle-dz/UniFAR-FTUs huggingface dataset:
Sliced Inverse Regression: application to fundamental stellar parameters

Abstract We present a method for deriving the stellar fundamental parameters. It is based on a regularized sliced inverse regression (RSIR). We first tested it on noisy synthetic spectra of A, F, G, and K-type stars, and inverted simultaneously their atmospheric fundamental parameters: Teff. , log g, [M/H] and v sin i. Different learning databases were calculated using a range of sampling in Teff. , log g, v sin i, and [M/H]. Combined with a principal component analysis (PCA) nearest neighbors (NN) search, the size of the learning database is reduced. A Tikhonov regularization is applied, given the ill-conditioning of SIR. For all spectral types, decreasing the size of the learning database allowed us to reach internal accuracies better than PCA-based NN-search using larger learning databases. For each analyzed parameter, we have reached internal errors that are smaller than the sampling step of the parameter. We have also applied the technique to a sample of observed FGK and A stars. For a selection of well-studied stars, the inverted parameters are in agreement with the ones derived in previous studies. The RSIR inversion technique, complemented with PCA pre-processing proves to be efficient in estimating stellar parameters of A, F, G, and K-type stars.
Non-commutative Desingularization of Determinantal Varieties, II: Arbitrary Minors

The first author was partly supported by NSERC grant 3-642-114-80. The second author was partly supported by National Science Foundation grant DMS 0902119 and National Security Agency grant H98230-05-1-0032. The third author is director of research at the FWO. Part of this research was supported through the program "Research in Pairs" by the Mathematisches Forschungsinstitut Oberwolfach in 2012, and part was carried out at the Mathematical Sciences Research Institute in 2013 with the support of the National Science Foundation under Grant No. 0932078 000. We thank both institutes for their hospitality.
Integral points on the complement of the branch locus of projections from hypersurfaces

We study the integral points on $\mathbb P_ n\setminus D$, where $D$ is the branch locus of a projection from an hypersurface in $\mathbb P_{n+1}$ to a hyperplane $H\simeq\mathbb P_n$. In doing that we follow the approach proposed in a paper by Zannier but we prove a more general result that also gives a sharper bound that may lead to prove the finiteness of integral points and has more applications. The proofs we present in this paper are effective and they provide a way to actually construct a set containing all the integral points in question. Our results find a concrete application to Diophantine equations, more specifically to the problem of finding integral solutions to equations $F(x_0,\dots,x_n)=c$, where $c$ is a given nonzero value and $F$ is a homogeneous form defining the branch locus $D$.
Quantum State Reduction

We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schrodinger equation, and have introduced the density matrix as the expectation of the random pure projection operator associated with the evolving state vector. After working out properties of the reduction process we construct a general solution to the energy-driven stochastic master equation. The solution is obtained by the use of nonlinear filtering theory and takes the form of a completely positive stochastic map.
Linear bias forecasts for emission line cosmological surveys

We forecast the linear bias for Hα-emitting galaxies at high redshift. To simulate a Euclid-like and a WFIRST-like survey, we place galaxies into a large-volume dark matter halo lightcone by sampling a library of luminosity-dependent halo occupation distributions (HODs), which is constructed using a physically motivated galaxy formation model. We calibrate the dust attenuation in the lightcones such that they are able to reproduce the Hα luminosity function or the Hα cumulative number counts. The angle-averaged galaxy correlation function is computed for each survey in redshift slices of width Δ z = 0.2. In each redshift bin the linear bias can be fitted with a single, scale-independent value that increases with increasing redshift. Fitting for the evolution of linear bias with redshift, we find that our Euclid-like and WFIRST-like surveys are both consistent within error with the relation b(z) = 0.7z + 0.7. Our bias forecasts are consistent with bias measurements from the HiZELS survey. We find that the Euclid-like and WFIRST-like surveys yield linear biases that are broadly consistent within error, most likely due to the HOD for the WFIRST-like survey having a steeper power-law slope towards larger halo masses.
Molecular Hydrogen Excitation around Active Galactic Nuclei

We report R ~ 3000 Very Large Telescope ISAAC K-band spectroscopy of the nuclei (i.e., central 100-300 pc) of nine galaxies hosting an active galactic nucleus. For five of these we also present spectra of the circumnuclear region out to 1 kpc. We have measured a number of molecular hydrogen lines in the ν = 1-0, 2-1, and 3-2 vibrational transitions, as well as the Brγ and He I recombination lines and the Na I stellar absorption feature. Although only three of the galaxies are classified as type 1 Seyfert galaxies in the literature, broad Brγ (FWHM ≳ 1000 km s-1) is seen in seven of the objects. The ν = 1-0 emission appears thermalized at temperatures T ~ 1000 K. However, the ν = 2-1 and ν = 3-2 emission show evidence of being radiatively excited by far-ultraviolet photons. The photodissociation region models that fit the data best are, as for the ultraluminous infrared galaxies in Davies et al., those for which the H2 emission arises in dense clouds illuminated by intense far-ultraviolet radiation. The Na I stellar absorption line is clearly seen in six of the nuclear spectra of these AGNs, indicating the presence of a significant population of late-type stars. It is possible that these stars are a result of the same episode of star formation that gave rise to the stars heating the photodissociation regions. It seems unlikely that the AGN is the dominant source of excitation for the near-infrared H2 emission: in two of the nuclear spectra H2 was not detected at all, and in general we find no evidence of suppression of the 2-1 S(3) line, which may occur in X-ray-irradiated gas. Our data do not reveal any significant difference between the nuclear and circumnuclear line ratios, suggesting that the physical conditions of the dominant excitation mechanism are similar both near the AGN and in the larger scale environment around it, and that star formation is an important process even in the central 100 pc around AGNs.
On applications of Razborov's flag algebra calculus to extremal 3-graph theory

In this paper, we prove several new Turan density results for 3-graphs with independent neighbourhoods. We show: \pi(K_4^-, C_5, F_{3,2})=12/49, \pi(K_4^-, F_{3,2})=5/18, and \pi(J_4, F_{3,2})=\pi(J_5, F_{3,2})=3/8, where J_t is the 3-graph consisting of a single vertex x together with a disjoint set A of size t and all $\binom{|A|}{2}$ 3-edges containing x. We also prove two Turan density results where we forbid certain induced subgraphs: \pi(F_{3,2}, induced K_4^-)=3/8 and \pi(K_5, 5-set spanning 8 edges)=3/4. The latter result is an analogue for K_5 of Razborov's result that \pi(K_4, 4-set spanning 1 edge)=5/9. We give several new constructions, conjectures and bounds for Turan densities of 3-graphs which should be of interest to researchers in the area. Our main tool is `Flagmatic', an implementation of Razborov's flag algebra calculus, which we are making publicly available. In a bid to make the power of Razborov's method more widely accessible, we have tried to make Flagmatic as user-friendly as possible, hoping to remove thereby the major hurdle that needs to be cleared before using the flag algebra calculus. Finally, we spend some time reflecting on the limitations of our approach, and in particular on which problems we may be unable to solve. Our discussion of the `complexity barrier' for the flag algebra calculus may be of general interest.
White Dwarfs in Globular Clusters: Hubble Space Telescope Observations of M4

Using WFPC2 on the Hubble Space Telescope, we have isolated a sample of 258 white dwarfs (WDs) in the Galactic globular cluster M4. Fields at three radial distances from the cluster center were observed, and sizable WD populations were found in all three. The location of these WDs in the color-magnitude diagram, their mean mass of 0.51(±0.03) M☉, and their luminosity function confirm basic tenets of stellar evolution theory and support the results from current WD cooling theory. The WDs are used to extend the cluster main-sequence mass function upward to stars that have already completed their nuclear evolution. The WD/red dwarf binary frequency in M4 is investigated and is found to be at most a few percent of all the main-sequence stars. The most ancient WDs found are ~9 Gyr old, a level that is set solely by the photometric limits of our data. Even though this is less than the age of M4, we discuss how these cooling WDs can eventually be used to check the turnoff ages of globular clusters and hence constrain the age of the universe.
New high-dimensional examples of ballistic random walks in random environment

We give new criteria for ballistic behavior of random walks in random environment which are perturbations of the simple symmetric random walk on $\mathbb Z^d$ in dimensions $d\ge 4$. Our results extend those of Sznitman [Ann. Probab. 31, no. 1, 285-322 (2003)] and the recent ones of Ram\'irez and Saglietti [Preprint, arXiv:1808.01523], and allow us to exhibit new examples in dimensions $d\ge 4$ of ballistic random walks which do not satisfy Kalikow's condition. Our criteria implies ballisticity whenever the average of the local drift of the walk is not too small compared with an appropriate moment of the centered environment. The proof relies on a concentration inequality of Boucheron et al. [Ann. Probab. 33, no. 2, 514-560 (2005)].
How nucleation and luminosity shape faint dwarf galaxies

We study the intrinsic shapes of a sample of over 400 quiescent galaxies in the cores of the Virgo and Fornax clusters with luminosities $10^{6} \leq L_{g}/L_{\odot} \leq 10^{8}$. Similar to satellites of the Local Group and Centaurus A, these faint, low surface brightness cluster galaxies are best described as a family of thick ($C/A > 0.5$), oblate-triaxial spheroids. However, the large sample size allows us to show that the flattening of their stellar distributions depends both on luminosity and on the presence of a nuclear star cluster. Nucleated satellites are thicker at all luminosities compared to their non-nucleated counterparts, and fainter galaxies are systematically thicker as well, regardless of nucleation. Once nucleation is accounted for, we find no evidence that the environment the satellites live in plays a relevant role in setting their three-dimensional structure. We interpret both the presence of stellar nuclei and the associated thicker shapes as the result of preferential early and rapid formation, effectively making these faint nucleated galaxies the first generation of cluster satellites.
Physical conditions in regions of star formation

▪ Abstract The physical conditions in molecular clouds control the nature and rate of star formation, with consequences for planet formation and galaxy evolution. The focus of this review is on the conditions that characterize regions of star formation in our Galaxy. A review of the tools and tracers for probing physical conditions includes summaries of generally applicable results. Further discussion distinguishes between the formation of low-mass stars in relative isolation and formation in a clustered environment. Evolutionary scenarios and theoretical predictions are more developed for isolated star formation, and observational tests are beginning to interact strongly with the theory. Observers have identified dense cores collapsing to form individual stars or binaries, and analysis of some of these cores support theoretical models of collapse. Stars of both low and high mass form in clustered environments, but massive stars form almost exclusively in clusters. The theoretical understanding of such re.
Surface defects as transfer matrices

The supersymmetric index of the 4d $\mathcal{N} = 1$ theory realized by a brane tiling coincides with the partition function of an integrable 2d lattice model. We argue that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defects in theories with $\mathrm{SU}(2)$ flavor groups, we identify the relevant L-operator as that discovered by Sklyanin in the context of the eight-vertex model. We verify this identification by computing the indices of class-$\mathcal{S}$ and -$\mathcal{S}_k$ theories in the presence of the surface defects.
Asymptotic properties of solutions of the fractional diffusion-wave equation

For the fractional diffusion-wave equation with the Caputo-Djrbashian fractional derivative of order α ∈ (1, 2) with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave equation and some other hyperbolic equations) and a pointwise stabilization property of solutions (similar to a well-known property of the heat equation and some other parabolic equations).
Traffic and related self-driven many-particle systems

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by “phantom traffic jams” even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems “freeze by heating”? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.
Keck HIRES Observations of the QSO FIRST J104459.6+365605: Evidence for a Large-Scale Outflow

This paper presents an analysis of a Keck HIRES spectrum of the QSO FIRST J104459.6+365605, covering the rest wavelength range from 2260 to 2900 Å. The line of sight toward the QSO contains two clusters of outflowing clouds that give rise to broad blue-shifted absorption lines. The outflow velocities of the clouds range from -200 to -1200 km s-1 and from -3400 to -5200 km s-1, respectively. The width of the individual absorption lines ranges from 50 to more than 1000 km s-1. The most prominent absorption lines are those of Mg II, Mg I, and Fe II, and Mn II is also present. The low-ionization absorption lines occur at the same velocities as the most saturated Mg II lines, showing that the Fe II, Mg I, and Mg II line-forming regions must be closely associated. Many absorption lines from excited states of Fe II are present, allowing a determination of the population of several low-lying energy levels. The populations of the excited levels are found to be considerably smaller than expected for LTE and imply an electron density in the Fe II line-forming regions of ne ~ 4 × 103 cm-3. Modeling the ionization state of the absorbing gas with this value of the electron density as a constraint, we find that the distance between the Fe II and Mg I line-forming region and the continuum source is ~7 × 102 pc. From the correspondence in velocity between the Fe II, Mg I, and Mg II lines we infer that the Mg II lines must be formed at the same distance. The Mg II absorption fulfills the criteria for broad absorption lines defined by Weymann and coworkers. Therefore, the distance we find between the Mg II line-forming region and the continuum source is surprising, since BALs are generally thought to be formed in outflows at a much smaller distance from the nucleus.
Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VIII. Structure of the Broad-line Region and Mass of the Central Black Hole in Mrk 142

This is the eighth in a series of papers reporting on a large reverberation mapping (RM) campaign to measure black hole (BH) mass in active galactic nuclei with high accretion rates. We employ the recently developed dynamical modeling approach for broad-line regions (BLRs) based on the method of Pancoast et al. to analyze the RM data set of Mrk 142 observed in the first monitoring season. In this approach, continuum variations are reconstructed using a damped random walk process, and BLR structure is delineated using a flexible disk-like geometry, in which BLR clouds move around the central BH with Keplerian orbits or inflow/outflow motion. The approach also includes the possibilities of anisotropic emission from BLR clouds, nonlinear response of the line emission to the continuum, and different long-term trends in the continuum and emission-line variations. We implement the approach in a Bayesian framework that is apt for parallel computation and use a Markov chain Monte Carlo technique to recover the parameters and uncertainties for the modeling, including the mass of the central BH. We apply three BLR models with different prescriptions of BLR cloud distributions and find that the best model for fitting the data of Mrk 142 is a two-zone BLR model, consistent with the theoretical BLR model surrounding slim accretion disks. The best model yields a BH mass of , resulting in a virial factor of for the full width at half maximum of the Hβ line measured from the mean spectrum. The virial factors for the other measures of the Hβ line width are also presented.
Properties and Occurrence Rates for Kepler Exoplanet Candidates as a Function of Host Star Metallicity from the DR25 Catalog

Correlations between the occurrence rate of exoplanets and their host star properties provide important clues about the planet formation process. We studied the dependence of the observed properties of exoplanets (radius, mass, and orbital period) as a function of their host star metallicity. We analyzed the planetary radii and orbital periods of over 2800 Kepler candidates from the latest Kepler data release, DR25 (Q1–Q17), with revised planetary radii based on Gaia DR2 as a function of host star metallicity (from the Q1–Q17 (DR25) stellar and planet catalog). With a much larger sample and improved radius measurements, we are able to reconfirm previous results in the literature. We show that the average metallicity of the host star increases as the radius of the planet increases. We demonstrate this by first calculating the average host star metallicity for different radius bins and then supplementing these results by calculating the occurrence rate as a function of planetary radius and host star metallicity. We find a similar trend between host star metallicity and planet mass: the average host star metallicity increases with increasing planet mass. This trend, however, reverses for masses >4.0 MJ: host star metallicity drops with increasing planetary mass. We further examined the correlation between the host star metallicity and the orbital period of the planet. We find that for planets with orbital periods less than 10 days, the average metallicity of the host star is higher than that for planets with periods greater than 10 days.
Stringent limits on the masses of the supermassive black holes in seven nearby galaxies

We present new stringent limits on the mass $M_{bh}$ of the central supermassive black hole for a sample of 7 nearby galaxies. Our $M_{bh}$ estimates are based on the dynamical modeling of the central width of the nebular emission lines measured over subarcsecond apertures with the Hubble Space Telescope. The central stellar velocity dispersion $\sigma_c$ of the sample galaxies is derived from new long-slit spectra from ground-based observations and the bulge effective radius is obtained from a two-dimensional photometric decomposition of the i-band images from the Sloan Digital Sky Survey. The derived stringent $M_{bh}$ limits run parallel and above the $M_{bh}-\sigma_c$ relation with no systematic trend depending on the galaxy distance or morphology. This gives further support to previous findings suggesting that the nuclear gravitational potential is remarkably well traced by the width of the nebular lines when the gas is centrally peaked. With our investigation, the number of galaxies with stringent $M_{bh}$ limits obtained from nebular-line width increases to 114 and can be used for studying the scaling relations between $M_{bh}$ and properties of their host galaxies.