Inverse M-matrix, a new characterization Dellacherie, Claude; Martínez, Servet; San Martín, Jaime
Linear algebra and its applications,
06/2020, Volume:
595
Journal Article
Peer reviewed
Open access
In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity ...of certain inner products.
We report the discovery of distant RR Lyrae stars, including the most distant known in the Milky Way, using data taken in the g-band with the Dark Energy Camera as part of the High cadence Transient ...Survey (HiTS; 2014 campaign). We detect a total of 173 RR Lyrae stars over a ∼120 deg2 area, including both known RR Lyrae and new detections. The heliocentric distances dH of the full sample range from 9 to >200 kpc, with 18 of them beyond 90 kpc. We identify three sub-groups of RR Lyrae as members of known systems: the Sextans dwarf spheroidal galaxy, for which we report 46 new discoveries, and the ultra-faint dwarf galaxies Leo IV and Leo V. Following an MCMC methodology, we fit spherical and ellipsoidal profiles of the form (R) ∼ Rn to the radial density distribution of RR Lyrae in the Galactic halo. The best fit corresponds to the spherical case, for which we obtain a simple power-law index of , consistent with recent studies made with samples covering shorter distances. The pulsational properties of the outermost RR Lyrae in the sample (dH > 90 kpc) differ from the ones in the halo population at closer distances. The distribution of the stars in a period-amplitude diagram suggest they belong to Oosterhoff-intermediate or Oosterhoff II groups, similar to what is found in the ultra-faint dwarf satellites around the Milky Way. The new distant stars discovered represent an important addition to the few existing tracers of the Milky Way potential in the outer halo.
CONVERGENCE TO THE MEAN FIELD GAME LIMIT Nutz, Marcel; San Martin, Jaime; Tan, Xiaowei
The Annals of applied probability,
02/2020, Volume:
30, Issue:
1
Journal Article
Peer reviewed
Open access
We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n → ∞. ...However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as “large n” equilibria.
Coronavirus disease 2019 (COVID-19) is an infectious disease caused by a group of viruses that provoke illnesses ranging from the common cold to more serious illnesses such as pneumonia. COVID-19 ...started in China and spread rapidly from a single city to an entire country in just 30 days and to the rest of the world in no more than 3 months. Several studies have tried to model the behavior of COVID-19 in diverse regions, based on differential equations of the SIR and stochastic SIR type, and their extensions. In this article, a statistical analysis of daily confirmed COVID-19 cases reported in eleven different cities in Europe and America is conducted. Log-linear models are proposed to model the rise or drop in the number of positive cases reported daily. A classification analysis of the estimated slopes is performed, allowing a comparison of the eleven cities at different epidemic peaks. By rescaling the curves, similar behaviors among rises and drops in different cities are found, independent of socioeconomic conditions, type of quarantine measures taken, whether more or less restrictive. The log-linear model appears to be suitable for modeling the incidence of COVID-19 both in rises and drops.
Chile rapidly implemented an extensive COVID-19 vaccination campaign, deploying a diversity of vaccines with a strategy that prioritized the elderly and individuals with comorbidities. This study ...aims to assess the direct impact of vaccination on the number of COVID-19 related cases, hospital admissions, ICU admissions and deaths averted during the first year and a half of the campaign.
Via Chile's transparency law, we obtained access to weekly event counts categorized by vaccination status and age. Integrating this data with publicly available census and vaccination coverage information, we conducted a comparative analysis of weekly incidence rates between vaccinated and unvaccinated groups from December 20, 2020 to July 2, 2022 to estimate the direct impact of vaccination in terms of the number of cases, hospitalizations, ICU admissions and deaths averted, using an approach that avoids the need to explicitly specify the effectiveness of each vaccine deployed.
We estimated that, from December 20, 2020 to July 2, 2022 the vaccination campaign directly prevented 1,030,648 (95% Confidence Interval: 1,016,975-1,044,321) cases, 268,784 (95% CI: 264,524-273,045) hospitalizations, 85,830 (95% CI: 83,466-88,194) ICU admissions and 75,968 (95% CI: 73,909-78,028) deaths related to COVID-19 among individuals aged 16 years and older. This corresponds to a reduction of 26% of cases, 66% of hospital admissions, 70% of ICU admissions and 67% of deaths compared to a scenario without vaccination. Individuals 55 years old or older represented 67% of hospitalizations, 73% of ICU admissions and 89% of deaths related to COVID-19 prevented.
This study highlights the role of Chile's vaccination campaign in reducing COVID-19 disease burden, with the most substantial reductions observed in severe outcomes.
The High Cadence Transient Survey (HiTS) aims to discover and study transient objects with characteristic timescales between hours and days, such as pulsating, eclipsing, and exploding stars. This ...survey represents a unique laboratory to explore large etendue observations from cadences of about 0.1 days and test new computational tools for the analysis of large data. This work follows a fully data science approach, from the raw data to the analysis and classification of variable sources. We compile a catalog of ∼15 million object detections and a catalog of ∼2.5 million light curves classified by variability. The typical depth of the survey is 24.2, 24.3, 24.1, and 23.8 in the u, g, r, and i bands, respectively. We classified all point-like nonmoving sources by first extracting features from their light curves and then applying a random forest classifier. For the classification, we used a training set constructed using a combination of cross-matched catalogs, visual inspection, transfer/active learning, and data augmentation. The classification model consists of several random forest classifiers organized in a hierarchical scheme. The classifier accuracy estimated on a test set is approximately 97%. In the unlabeled data, 3485 sources were classified as variables, of which 1321 were classified as periodic. Among the periodic classes, we discovered with high confidence one δ Scuti, 39 eclipsing binaries, 48 rotational variables, and 90 RR Lyrae, and for the nonperiodic classes, we discovered one cataclysmic variable, 630 QSOs, and one supernova candidate. The first data release can be accessed in the project archive of HiTS (http://astro.cmm.uchile.cl/HiTS/).
In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to -∞ at the origin, and the diffusion to have an entrance ...boundary at +∞. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth-death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with probability 1. An important example is the logistic Feller diffusion. We give sufficient conditions on the drift near 0 and near +∞ for the existence of quasi-stationary distributions, as well as rate of convergence in the Yaglom limit and existence of the Q-process. We also show that, under these conditions, there is exactly one quasi-stationary distribution, and that this distribution attracts all initial distributions under the conditional evolution, if and only if +∞ is an entrance boundary. In particular, this gives a sufficient condition for the uniqueness of quasi-stationary distributions. In the proofs spectral theory plays an important role on L² of the reference measure for the killed process.
Bisexual Galton-Watson processes are discrete Markov chains where reproduction events are due to mating of males and females. Owing to this interaction, the standard branching property of ...Galton-Watson processes is lost. We prove tightness for conveniently rescaled bisexual Galton-Watson processes, based on recent techniques developed in V. Bansaye, M.E. Caballero, and S. Méléard, Scaling limits of population and evolution processes in random environment, Electron. J. Probab. 24(19) (2019), pp. 1-38. We also identify the possible limits of these rescaled processes as solutions of a stochastic system, coupling two equations through singular coefficients in Poisson terms added to square roots as coefficients of Brownian motions. Under some additional integrability assumptions, pathwise uniqueness of this limiting system of stochastic differential equations and convergence of the rescaled processes are obtained. Two examples corresponding to mutual fidelity are considered.
During the analysis of RR Lyrae stars (RRLs) discovered in the High Cadence Transient Survey (HiTS) taken with the Dark Energy Camera at the 4 m telescope at Cerro Tololo Inter-American Observatory, ...we found a group of three very distant, fundamental mode pulsator RR Lyrae (type ab). The location of these stars agrees with them belonging to the Leo V ultra-faint satellite galaxy, for which no variable stars have been reported to date. The heliocentric distance derived for Leo V based on these stars is 173 5 kpc. The pulsational properties (amplitudes and periods) of these stars locate them within the locus of the Oosterhoff II group, similar to most other ultra-faint galaxies with known RRLs. This serendipitous discovery shows that distant RRLs may be used to search for unknown faint stellar systems in the outskirts of the Milky Way.
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