M\'ethode de Mahler: relations lin\'eaires, transcendance et applications aux nombres automatiques

This paper is concerned with Mahler's method. We study in detail the structure of linear relations between values of Mahler functions at algebraic points. In particular, given a field ${\bf k}$, a Mahler function $f(z)\in{\bf k}\{z\}$, and an algebraic number $\alpha$, $0<\vert \alpha\vert <1$, that is not a pole for $f$, we show that one can always determined whether the number $f(\alpha)$ is transcendental or not. In the latter case, we obtain that $f(\alpha)$ belong to the number fields ${\bf k}(\alpha)$. We also consider some consequences of such results to a classical number theoretical problem: the study of sequences of digits of algebraic numbers in an integer (or, more generally, algebraic) base. Our results are based on a theorem of Philippon [31] that we refine. We also simplify his proof.Comment: 46 pp, in Frenc

MÉTHODE DE MAHLER : RELATIONS LINÉAIRES, TRANSCENDANCE ET APPLICATIONS AUX NOMBRES AUTOMATIQUES

— Cet article est consacré à la méthode de Mahler. Nous décrivons en détail la structure des relations de dépendance linéaire entre les valeurs aux points algébriques de fonctions mahlériennes. Étant donnés un corps de nombres k, une fonction mahlérienne f (z) ∈ k{z} et α un nombre algébrique, 0 < |α| < 1, qui n'est pas un pôle de f , nous montrons notamment que l'on peut toujours déterminer si le nombre f (α) est transcendant ou non. Dans ce dernier cas, nous obtenons que f (α) appartient nécessairement à l'extension k(α). Nous considérons également les conséquences remarquables de cette théorie concernant un problème arithmétique classique : l'étude de la suite des chiffres des nombres algébriques dans une base entière ou, plus généralement, algébrique. Nos résultats sont obtenus à partir d'un théorème récent de Philippon [31] que nous raffinons et dont nous simplifions la démonstration

Plague risk in the western United States over seven decades of environmental change

After several pandemics over the last two millennia, the wildlife reservoirs of plague (Yersinia pestis) now persist around the world, including in the western United States. Routine surveillance in this region has generated comprehensive records of human cases and animal seroprevalence, creating a unique opportunity to test how plague reservoirs are responding to environmental change. Here, we test whether animal and human data suggest that plague reservoirs and spillover risk have shifted since 1950. To do so, we develop a new method for detecting the impact of climate change on infectious disease distributions, capable of disentangling long-term trends (signal) and interannual variation in both weather and sampling (noise). We find that plague foci are associated with high-elevation rodent communities, and soil biochemistry may play a key role in the geography of long-term persistence. In addition, we find that human cases are concentrated only in a small subset of endemic areas, and that spillover events are driven by higher rodent species richness (the amplification hypothesis) and climatic anomalies (the trophic cascade hypothesis). Using our detection model, we find that due to the changing climate, rodent communities at high elevations have become more conducive to the establishment of plague reservoirs—with suitability increasing up to 40% in some places—and that spillover risk to humans at mid-elevations has increased as well, although more gradually. These results highlight opportunities for deeper investigation of plague ecology, the value of integrative surveillance for infectious disease geography, and the need for further research into ongoing climate change impacts

Constraining the galaxy-halo connection of infrared-selected unWISE galaxies with galaxy clustering and galaxy-CMB lensing power spectra

We present the first detailed analysis of the connection between galaxies and their dark matter halos for the unWISE galaxy catalog -- a full-sky, infrared-selected sample built from WISE data, containing over 500 million galaxies. Using unWISE galaxy-galaxy auto-correlation and Planck CMB lensing-galaxy cross-correlation measurements down to 10 arcmin angular scales, we constrain the halo occupation distribution (HOD), a model describing how central and satellite galaxies are distributed within dark matter halos, for three unWISE} galaxy samples at mean redshifts $\bar{z} \approx 0.6$, $1.1$, and $1.5$. We constrain the characteristic minimum halo mass to host a central galaxy, $M_\mathrm{min}^\mathrm{HOD} = 1.83^{+0.41}_{-1.63} \times 10^{12} M_\odot/h$, $5.22^{+0.34}_{-4.80} \times 10^{12} M_\odot/h$, $6.60 ^{+0.30}_{-1.11} \times 10^{13} M_\odot/h$ for the unWISE samples at $\bar{z}\approx 0.6$, $1.1$, and $1.5$, respectively. We find that all three samples are dominated by central galaxies, rather than satellites. Using our constrained HOD models, we infer the effective linear galaxy bias for each unWISE sample, and find that it does not evolve as steeply with redshift as found in previous perturbation-theory-based analyses of these galaxies. We discuss possible sources of systematic uncertainty in our results, the most significant of which is the uncertainty on the galaxy redshift distribution. Our HOD constraints provide a detailed, quantitative understanding of how the unWISE galaxies populate the underlying dark matter halo distribution. These constraints will have a direct impact on future studies employing the unWISE galaxies as a cosmological and astrophysical probe, including measurements of ionized gas thermodynamics and dark matter profiles via Sunyaev-Zel'dovich and lensing cross-correlations

A genetic algorithm approach to the minimum cost design of reinforced concrete flanged beams under multiple loading conditions

This paper presents results of the application of genetic algorithms to the minimum cost design of continuous beams cast in situ with reinforced concrete slabs to form an integral structure. A practical “problem-seeks-optimum design” approach requires full consideration of these rigidly jointed beam-and-slab connections, together with realistic multiple loading conditions and limit states as embodied in British and European Codes of Practice. The fitness function includes the cost of concrete, longitudinal and shear reinforcement, and the cost of formwork and labour. Results obtained so far have shown that genetic algorithms can be successfully applied to the minimum cost design of flanged beams, overcoming the difficulties associated with the discontinuity of the design equations and their complex inter-relationship with the design variables