Asymptotic properties of free monoid morphisms

Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word $w =g(f^\omega(a))$ is the image of a fixed point of a morphism $f$ under another morphism $g$, then there exist a non-erasing morphism $\sigma$ and a coding $\tau$ such that $w =\tau(\sigma^\omega(b))$. Based on the Perron theorem about asymptotic properties of powers of non-negative matrices, our main contribution is an in-depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non-erasing ones. We also explicitly provide an algorithm computing $\sigma$ and $\tau$ from $f$ and $g$.Comment: 25 page

Behavior of digital sequences through exotic numeration systems

peer reviewedMany digital functions studied in the literature, e.g., the summatory function of the base-k sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic number theory or linear algebra. In this paper we develop a method based on exotic numeration systems and we apply it on two examples motivated by the study of generalized Pascal triangles and binomial coefficients of words

SURFACE ENGINEERING FOR PARTS MADE BY ADDITIVE MANUFACTURING

peer reviewedthe surface preparation of metal parts made by additive manufacturing (AM). AM is a technology of choice for manufacturing of parts with complex shapes (heat exchangers, RF supports, optical parts…) and integrated functions such as conformal cooling channels, clips, hinges, etc. This opens the door for lightweight parts which are of prime importance for space applications. The potential of the AM technologies is however impeded by the quite rough surface finish that is observed on the as-manufactured parts. It is known that such a finish is likely to impact the performance of the parts. Several post-treatment techniques can be applied to improve the surface condition of the AM parts. However, so far, the influence of the successive post-processing steps on the final properties is not well established. Therefore, a better understanding of the impact of surface characteristics on the material behaviour is needed to expand the use of AM for high performance parts. The objective of this study, supported by ESA, is to propose and evaluate various surface finishing techniques for parts made by the AM technologies, in order to check their compatibility, evaluate their properties and derive guidelines for future applications. CRM is the prime proposer of this study and is in charge of the surface treatment and characterisations. Sirris additive manufacturing facilities are used to produce the parts. Thales Alenia Space and Walopt are included into the industrial team to provide concrete application cases. The study focuses on metals. Two metals under study are presented here: AlSi10Mg and Ti6Al4V. This paper is devoted to the early results of the first steps of surface preparation, namely material removal from the surface of the produced parts in order to improve their surface properties. As a first phase, tribo-finishing (TF) is tested on prototype parts to check its capabilities. Surface and volume parameters are analyzed, namely achieved roughness, material removal rate, location of removed material. The limitations in terms of geometry and applicability are discussed as well. These first observations should serve as guidelines for further application of AM for the design of parts used in space industry

Autoantibodies neutralizing type I IFNs are present in ~4% of uninfected individuals over 70 years old and account for ~20% of COVID-19 deaths

Publisher Copyright: © 2021 The Authors, some rights reserved.Circulating autoantibodies (auto-Abs) neutralizing high concentrations (10 ng/ml; in plasma diluted 1:10) of IFN-alpha and/or IFN-omega are found in about 10% of patients with critical COVID-19 (coronavirus disease 2019) pneumonia but not in individuals with asymptomatic infections. We detect auto-Abs neutralizing 100-fold lower, more physiological, concentrations of IFN-alpha and/or IFN-omega (100 pg/ml; in 1:10 dilutions of plasma) in 13.6% of 3595 patients with critical COVID-19, including 21% of 374 patients >80 years, and 6.5% of 522 patients with severe COVID-19. These antibodies are also detected in 18% of the 1124 deceased patients (aged 20 days to 99 years; mean: 70 years). Moreover, another 1.3% of patients with critical COVID-19 and 0.9% of the deceased patients have auto-Abs neutralizing high concentrations of IFN-beta. We also show, in a sample of 34,159 uninfected individuals from the general population, that auto-Abs neutralizing high concentrations of IFN-alpha and/or IFN-omega are present in 0.18% of individuals between 18 and 69 years, 1.1% between 70 and 79 years, and 3.4% >80 years. Moreover, the proportion of individuals carrying auto-Abs neutralizing lower concentrations is greater in a subsample of 10,778 uninfected individuals: 1% of individuals 80 years. By contrast, auto-Abs neutralizing IFN-beta do not become more frequent with age. Auto-Abs neutralizing type I IFNs predate SARS-CoV-2 infection and sharply increase in prevalence after the age of 70 years. They account for about 20% of both critical COVID-19 cases in the over 80s and total fatal COVID-19 cases.Peer reviewe

Vaccine breakthrough hypoxemic COVID-19 pneumonia in patients with auto-Abs neutralizing type I IFNs

Life-threatening `breakthrough' cases of critical COVID-19 are attributed to poor or waning antibody response to the SARS- CoV-2 vaccine in individuals already at risk. Pre-existing autoantibodies (auto-Abs) neutralizing type I IFNs underlie at least 15% of critical COVID-19 pneumonia cases in unvaccinated individuals; however, their contribution to hypoxemic breakthrough cases in vaccinated people remains unknown. Here, we studied a cohort of 48 individuals ( age 20-86 years) who received 2 doses of an mRNA vaccine and developed a breakthrough infection with hypoxemic COVID-19 pneumonia 2 weeks to 4 months later. Antibody levels to the vaccine, neutralization of the virus, and auto- Abs to type I IFNs were measured in the plasma. Forty-two individuals had no known deficiency of B cell immunity and a normal antibody response to the vaccine. Among them, ten (24%) had auto-Abs neutralizing type I IFNs (aged 43-86 years). Eight of these ten patients had auto-Abs neutralizing both IFN-a2 and IFN-., while two neutralized IFN-omega only. No patient neutralized IFN-ss. Seven neutralized 10 ng/mL of type I IFNs, and three 100 pg/mL only. Seven patients neutralized SARS-CoV-2 D614G and the Delta variant (B.1.617.2) efficiently, while one patient neutralized Delta slightly less efficiently. Two of the three patients neutralizing only 100 pg/mL of type I IFNs neutralized both D61G and Delta less efficiently. Despite two mRNA vaccine inoculations and the presence of circulating antibodies capable of neutralizing SARS-CoV-2, auto-Abs neutralizing type I IFNs may underlie a significant proportion of hypoxemic COVID-19 pneumonia cases, highlighting the importance of this particularly vulnerable population