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Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations. This is especially an issue when applying Gaussian process models to multiple functions simultaneously in various applications of functional data analysis. We consider a multi-level Gaussian process regression model where a common mean function and individual subject-specific deviations are modeled simultaneously as latent Gaussian processes. We derive exact analytic and computationally efficient expressions for the log-likelihood function and the posterior distributions in the case where the observations are sampled on either a completely or partially regular grid. This enables us to fit the model to large data sets that are currently computationally inaccessible using a standard implementation. We show through a simulation study that our analytic expressions are several orders of magnitude faster compared to a standard implementation, and we provide an implementation in the probabilistic programming language Stan., Comment: 48 pages, 3 figures; Figure 1 corrected

A common property of globular clusters (GC) is to host multiple populations characterized by peculiar chemical abundances. Recent photometric studies suggest that the He content could vary between the populations of a GC by up to $\Delta$He $\sim$ 0.13, in mass fraction. The initial He content impacts the evolution of low-mass stars by ultimately modifying their lifetimes, luminosity, temperatures, and, more generally, the morphology of post-RGB evolutionary tracks in the Hertzsprung-Russell diagram. We present new physically accurate isochrones with different initial He-enrichments and metallicities, with a focus on the methods implemented to deal with the post-RGB phases. The isochrones are based on tracks computed with the stellar evolution code STAREVOL for different metallicities (Z = 0.0002, 0.0009, 0.002, and 0.008) and with different He-enrichment (from 0.25 to 0.6 in mass fraction). We describe the effect of He-enrichment on the morphology of the isochrones and test these by comparing the predicted number counts of HB and AGB stars with those of selected GCs. Comparing the number ratios, we find that our new theoretical ones agree with the observed values within $1\sigma$ in most cases. The work presented here sets the ground for future studies on stellar populations in globular clusters, in which the abundances of light elements in He-enhanced models will rely on different assumptions for the causes of this enrichment. The developed methodology permits the computation of isochrones from new stellar tracks with non-canonical stellar processes. The checked number counts ensure that, at least in this reference set, the contribution of the luminous late stages of stellar evolution to the integrated light of a GC is represented adequately., Comment: 15 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

The first stars might have been fast rotators. This would have important consequences for their radiative, mechanical and chemical feedback. We discuss the impact of fast initial rotation on the evolution of massive Population III models and on their nitrogen and oxygen stellar yields. We explore the evolution of Population III stars with initial masses in the range of 9Msol < Mini < 120Msol starting with an initial rotation on the Zero Age Main Sequence equal to 70% of the critical one. We find that with the physics of rotation considered here, our rapidly-rotating Population III stellar models do not follow a homogeneous evolution. They lose very little mass in case mechanical winds are switched on when the surface rotation becomes equal or larger than the critical velocity. Impact on the ionising flux appears modest when compared to moderately-rotating models. Fast rotation favours, in models with initial masses above ~20Msol, the appearance of a very extended intermediate convective zone around the H-burning shell during the core He-burning phase. This shell has important consequences on the sizes of the He- and CO-cores and thus impacts the final fate of stars. Moreover, it has a strong impact on nucleosynthesis boosting the production of primary 14N. Fast initial rotation impacts significantly the chemical feedback of Population III stars. Observations of extremely metal-poor stars and/or starbursting regions are essential to provide constraints on the properties of the first stars., Comment: Accepted in A&A. Pages 17. Figures 15. Tables 2

Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider multiple, mostly conflicting objectives, such as cost and quality. We present a variational quantum optimization algorithm to solve discrete multi-objective optimization problems on quantum computers. The proposed quantum multi-objective optimization (QMOO) algorithm incorporates all cost Hamiltonians representing the classical objective functions in the quantum circuit and produces a quantum state consisting of Pareto-optimal solutions in superposition. From this state we retrieve a set of solutions and utilize the widely applied hypervolume indicator to determine its quality as an approximation to the Pareto-front. The variational parameters of the QMOO circuit are tuned by maximizing the hypervolume indicator in a quantum-classical hybrid fashion. We show the effectiveness of the proposed algorithm on several benchmark problems with up to five objectives. We investigate the influence of the classical optimizer, the circuit depth and compare to results from classical optimization algorithms. We find that the algorithm is robust to shot noise and produces good results with as low as 128 measurement shots in each iteration. These promising result open the perspective to run the algorithm on near-term quantum hardware., Comment: revision of text, added shot noise analysis

We present evolutionary models of massive, accreting population III stars with constant and variable accretion rates until the end of silicon burning, with final masses of 1000 - 3000 Msol. In all our models, after the core-hydrogen-burning phase, the star expands towards the red side of the Hertzsprung-Russell diagram is where it spends the rest of its evolution. During core helium burning, the models exhibit an outer convective envelope as well as many large intermediate convective zones.These intermediate zones allow for strong internal mixing to occur which enriches the surface in helium. The effect of increasing metallicity at a constant accretion rate of 10^{-3} Msol/yr shows an increase in the lifetime, final mass and distribution of helium in the envelope. Our fiducial model with mass of 3000 Msol has a final surface helium abundance of 0.74 and 9% of its total mass or 50% of the core mass, has a value of Gamma1 < 4/3 at the end of core silicon burning. If the collapse of the core is accompanied by the ejection of the envelope above the carbon-oxygen core, this could have a significant impact on the chemical evolution of the surroundings and subsequent stellar generations. The model has a final log(N/O) ~ 0.45, above the lower limit in the recently detected high-redshift galaxy GN-z11. We discuss the impact of a single 3000 Msol star on chemical, mechanical and radiative feedback, and present directions for future work., Comment: Accepted for publication in A&A

Mass-loss in red supergiants (RSGs) is generally recognized to be episodic, but mass-loss prescriptions fail to reflect this. Evolutionary models show that the total amount of mass lost during this phase determines if these stars evolve to warmer temperatures before undergoing core collapse. The current Geneva evolutionary models mimic episodic mass loss by enhancing the quiescent prescription rates whenever the star's outer layers exceed the Eddington luminosity by a large factor. This results in a 20 solar-mass model undergoing significantly more mass loss during the RSG phase than it would have otherwise, but has little effect on models of lower masses. We can test the validity of this approach observationally by measuring the proportion of high-luminosity RSGs to that predicted by the models. To do this, we use our recent luminosity-limited census of RSGs in M31 and M33, making modest improvements to membership, and adopting extinctions based on the recent panchromatic M31 and M33 Hubble surveys. We then compare the proportions of the highest luminosity RSGs found to that predicted by published Geneva models, as well as to a special set of models computed without the enhanced rates. We find good agreement with the models which include the supra-Eddington enhanced mass loss. The models with lower mass-loss rates predict a larger fraction of high-luminosity RSGs than observed, and thus can be ruled out. We also use these improved data to confirm that the upper luminosity limit of RSGs is log L/Lo~5.4, regardless of metallicity, using our improved data on M31 and M33 plus previous results on the Magellanic Clouds., Comment: Accepted for publication in the Astrophysical Journal. Revised version includes an additional reference

Causal inference can estimate causal effects, but unless data are collected experimentally, statistical analyses must rely on pre-specified causal models. Causal discovery algorithms are empirical methods for constructing such causal models from data. Several asymptotically correct methods already exist, but they generally struggle on smaller samples. Moreover, most methods focus on very sparse causal models, which may not always be a realistic representation of real-life data generating mechanisms. Finally, while causal relationships suggested by the methods often hold true, their claims about causal non-relatedness have high error rates. This non-conservative error tradeoff is not ideal for observational sciences, where the resulting model is directly used to inform causal inference: A causal model with many missing causal relations entails too strong assumptions and may lead to biased effect estimates. We propose a new causal discovery method that addresses these three shortcomings: Supervised learning discovery (SLdisco). SLdisco uses supervised machine learning to obtain a mapping from observational data to equivalence classes of causal models. We evaluate SLdisco in a large simulation study based on Gaussian data and we consider several choices of model size and sample size. We find that SLdisco is more conservative, only moderately less informative and less sensitive towards sample size than existing procedures. We furthermore provide a real epidemiological data application. We use random subsampling to investigate real data performance on small samples and again find that SLdisco is less sensitive towards sample size and hence seems to better utilize the information available in small datasets.

Sigma Ori E, a massive helium B-type star, shows a high surface rotation and a strong surface magnetic field potentially challenging the process of wind magnetic braking. The Gaia satellite provides an accurate distance to that star and confirms its membership to the sigma Ori cluster. We account for these two key pieces of information to investigate whether single star models can reproduce the observed properties of sigma Ori E and provide new estimates for its metallicity, mass, and age. We compute rotating stellar models accounting for wind magnetic braking and magnetic quenching of the mass loss. We obtain that sigma Ori E is a very young star (age less than 1 Myr) with an initial mass around 9 Msol, a surface equatorial magnetic field around 7 kG and having a metallicity Z (mass fraction of heavy elements) around 0.020. No solution is obtained with the present models for a metallicity Z=0.014. The initial rotation of the models fitting sigma Ori E is not much constrained and can be anywhere in the range studied in the present work. Because of its very young age, models predict no observable changes of the surface abundances due to rotational mixing. The simultaneous high surface rotation and high surface magnetic field of sigma Ori E may simply be a consequence of its young age. This young age implies that the processes responsible for producing the chemical inhomogeneities that are observed at its surface should be rapid. Thus for explaining the properties of sigma Ori E, there is no necessity to invoke a merging event although such a scenario cannot be discarded. Other stars (HR 5907, HR 7355, HR 345439, HD 2347, CPD -50^{o}3509$) showing similar properties as sigma Ori E (fast rotation and strong surface magnetic field) may also be very young stars, although determination of the braking timescales is needed to confirm such a conclusion., Comment: 13 pages, 8 figures, paper accepted for publication in Astronomy and Astrophysics

In this paper we present a data-adaptive estimation procedure for estimation of average treatment effects in a time-to-event setting based on generalized random forests. In these kinds of settings, the definition of causal effect parameters are complicated by competing risks; here we distinguish between treatment effects on the crude and the net probabilities, respectively. To handle right-censoring, and to switch between crude and net probabilities, we propose a two-step procedure for estimation, applying inverse probability weighting to construct time-point specific weighted outcomes as input for the forest. The forest adaptively handles confounding of the treatment assigned by applying a splitting rule that targets a causal parameter. We demonstrate that our method is effective for a causal search through a list of treatments to be ranked according to the magnitude of their effect. We further apply our method to a dataset from the Danish health registries where it is of interest to discover drugs with an unexpected protective effect against relapse of severe depression.

Many popular sports involve matches between two teams or players where each team have the possibility of scoring points throughout the match. While the overall match winner and result is interesting, it conveys little information about the underlying scoring trends throughout the match. Modeling approaches that accommodate a finer granularity of the score difference throughout the match is needed to evaluate in-game strategies, discuss scoring streaks, teams strengths, and other aspects of the game. We propose a latent Gaussian process to model the score difference between two teams and introduce the Trend Direction Index as an easily interpretable probabilistic measure of the current trend in the match as well as a measure of post-game trend evaluation. In addition we propose the Excitement Trend Index - the expected number of monotonicity changes in the running score difference - as a measure of overall game excitement. Our proposed methodology is applied to all 1143 matches from the 2019-2020 National Basketball Association (NBA) season. We show how the trends can be interpreted in individual games and how the excitement score can be used to cluster teams according to how exciting they are to watch.

Understanding the nature of the first stars is key to understanding the early universe. With new facilities such as JWST we may soon have the first observations of the earliest stellar populations, but to understand these observations we require detailed theoretical models. Here we compute a grid of stellar evolution models using the Geneva code with the aim to improve our understanding of the evolution of zero-metallicity stars, with particular interest in how rotation affects surface properties, interior structure, and metal enrichment. We produce a range of models of initial masses (Mini) from 1.7 Msun to 120 Msun, focusing on massive models of 9 Msun < Mini < 120 Msun. Our grid includes models with and without rotation, with rotating models having an initial velocity of 40% of the critical velocity. We find that rotation strongly impacts the evolution of the first stars, mainly through increased core size and stronger H-burning shells during core He-burning. Without radiative mass loss, angular momentum builds at the surface in rotating models, thus models of initial masses Mini > 60 Msun reach critical rotation on the main sequence and experience mass loss. We find that rotational mixing strongly affects metal enrichment, but does not always increase metal production as we see at higher metallicities. This is because rotation leads to an earlier CNO boost to the H shell during He-burning, which may hinder metal enrichment depending on initial mass and rotational velocity. Electronic tables of this new grid of Population III models are publicly available., Comment: 20 pages, 15 figures. Accepted for publication in MNRAS

We study the Wiener disorder detection problem where each observation is associated with a positive cost. In this setting, a strategy is a pair consisting of a sequence of observation times and a stopping time corresponding to the declaration of disorder. We characterize the minimal cost of the disorder problem with costly observations as the unique fix-point of a certain jump operator, and we determine the optimal strategy., Comment: To appear in Journal of/Advances in Applied Probability

News media often report that the trend of some public health outcome has changed. These statements are frequently based on longitudinal data, and the change in trend is typically found to have occurred at the most recent data collection time point - if no change had occurred the story is less likely to be reported. Such claims may potentially influence public health decisions on a national level. We propose two measures for quantifying the trendiness of trends. Assuming that reality evolves in continuous time we define what constitutes a trend and a change in trend, and introduce a probabilistic Trend Direction Index. This index has the interpretation of the probability that a latent characteristic has changed monotonicity at any given time conditional on observed data. We also define an index of Expected Trend Instability quantifying the expected number of changes in trend on an interval. Using a latent Gaussian Process model we show how the Trend Direction Index and the Expected Trend Instability can be estimated in a Bayesian framework and use the methods to analyze the proportion of smokers in Denmark during the last 20 years, and the development of new COVID-19 cases in Italy from February 24th onwards.

We introduce the Tournament Rank Probability Score (TRPS) as a measure to evaluate and compare pre-tournament predictions, where predictions of the full tournament results are required to be available before the tournament begins. The TRPS handles partial ranking of teams, gives credit to predictions that are only slightly wrong, and can be modified with weights to stress the importance of particular features of the tournament prediction. Thus, the Tournament Rank Prediction Score is more flexible than the commonly preferred log loss score for such tasks. In addition, we show how predictions from historic tournaments can be optimally combined into ensemble predictions in order to maximize the TRPS for a new tournament., Comment: 11 pages, 2 figures

The mass-loss rates of red supergiant stars (RSGs) are poorly constrained by direct measurements, and yet the subsequent evolution of these stars depends critically on how much mass is lost during the RSG phase. In 2012 the Geneva evolutionary group updated their mass-loss prescription for RSGs with the result that a 20 solar mass star now loses 10x more mass during the RSG phase than in the older models. Thus, higher mass RSGs evolve back through a second yellow supergiant phase rather than exploding as Type II-P supernovae, in accord with recent observations (the so-called "RSG Problem"). Still, even much larger mass-loss rates during the RSG phase cannot be ruled out by direct measurements of their current dust-production rates, as such mass-loss is episodic. Here we test the models by deriving a luminosity function for RSGs in the nearby spiral galaxy M31 which is sensitive to the total mass loss during the RSG phase. We carefully separate RSGs from asymptotic giant branch stars in the color-magnitude diagram following the recent method exploited by Yang and collaborators in their Small Magellanic Cloud studies. Comparing our resulting luminosity function to that predicted by the evolutionary models shows that the new prescription for RSG mass-loss does an excellent job of matching the observations, and we can readily rule out significantly larger values., Comment: ApJ, accepted

The Asymptotic Giant Branch (AGB) scenario ascribes the multiple populations in old Galactic Globular Clusters (GGC) to episodes of star formation in the gas contaminated by the ejecta of massive AGBs and super-AGBs of a first stellar population. The mass of these AGBs (4-8Msun) today populate the Young Massive Clusters (YMC) of the Magellanic Clouds, where rapid rotation and its slowing down play an important role in shaping the color magnitude diagram features. Consequently, we must reconsider whether the rotational evolution of these masses affects the yields, and whether the resulting abundances are compatible with the chemical patterns observed in GGC. We show the first results of a differential analysis, by computing the hot bottom burning evolution of non rotating models with increased CNO-Na abundances at the 2DU, following the results of MESA rotational models., Comment: 4 pages, in "Why Galaxies care about AGB stars: a continuing challenge through cosmic time" Proceedings IAU Symposium No. 343, 2018 F. Kerschbaum, M. Groenewegen, and H. Olofsson, eds

Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture components. In particular, only the average regression model for one of the components in the mixture model is needed and no requirements on the distributions. The consistency and asymptotic distribution of the estimators is derived and the proposed method is validated through a series of simulation studies and is shown to be highly accurate. We illustrate the use of the moment-based mixture of regression models with an application to wine quality data., Comment: 17 pages, 3 figures

In this work, amorphous thin films in Mg-Si-O-N system were prepared in order to investigate the dependence of optical and mechanical properties on Mg composition. Reactive RF magnetron co-sputtering from magnesium and silicon targets were used for the deposition of Mg-Si-O-N thin films. Films were deposited on float glass, silica wafers and sapphire substrates in an Ar, N2 and O2 gas mixture. X-ray photoelectron spectroscopy, atomic force microscopy, scanning electron microscopy, spectroscopic ellipsometry, and nanoindentation were employed to characterize the composition, surface morphology, and properties of the films.