A survey on abelian dynamical Galois groups

Let $K$ be a number field, $f\in K[x]$ and $\alpha\in K$. A recent conjecture of Andrews and Petsche predicts that the dynamical Galois group of the pair $(f,\alpha)$ is abelian if and only if the pair $(f,\alpha)$ is $K^{\text{ab}}$-conjugated to $(g,\beta)$, where $g$ is a power or a Chebyshev map and $\beta$ is $\zeta$ or $\zeta+\zeta^{-1}$, respectively, and $\zeta$ is a root of unity. We review three completely different approaches that allow to prove several cases of the conjecture.Comment: Rendiconti Sem. Mat. Univ. Pol. Torino Vol. 80, 2022 (2022), 41 - 5

An equivariant isomorphism theorem for mod p\mathfrak p reductions of arboreal Galois representations

Let $\phi$ be a quadratic, monic polynomial with coefficients in $\mathcal O_{F,D}[t]$, where $\mathcal O_{F,D}$ is a localization of a number ring $\mathcal O_F$. In this paper, we first prove that if $\phi$ is non-square and non-isotrivial, then there exists an absolute, effective constant $N_\phi$ with the following property: for all primes $\mathfrak p\subseteq\mathcal O_{F,D}$ such that the reduced polynomial $\phi_\mathfrak p\in (\mathcal O_{F,D}/\mathfrak p)[t][x]$ is non-square and non-isotrivial, the squarefree Zsigmondy set of $\phi_{\mathfrak p}$ is bounded by $N_\phi$. Using this result, we prove that if $\phi$ is non-isotrivial and geometrically stable then outside a finite, effective set of primes of $\mathcal O_{F,D}$ the geometric part of the arboreal representation of $\phi_{\mathfrak p}$ is isomorphic to that of $\phi$. As an application of our results we prove R. Jones' conjecture on the arboreal Galois representation attached to the polynomial $x^2+t$

On the logarithmic probability that a random integral ideal is A\mathscr A-free

This extends a theorem of Davenport and Erd\"os on sequences of rational integers to sequences of integral ideals in arbitrary number fields $K$. More precisely, we introduce a logarithmic density for sets of integral ideals in $K$ and provide a formula for the logarithmic density of the set of so-called $\mathscr A$-free ideals, i.e. integral ideals that are not multiples of any ideal from a fixed set $\mathscr A$.Comment: 9 pages, to appear in S. Ferenczi, J. Ku{\l}aga-Przymus and M. Lema\'nczyk (eds.), Chowla's conjecture: from the Liouville function to the M\"obius function, Lecture Notes in Math., Springe

Human-robot coexistence and interaction in open industrial cells

Recent research results on human\u2013robot interaction and collaborative robotics are leaving behind the traditional paradigm of robots living in a separated space inside safety cages, allowing humans and robot to work together for completing an increasing number of complex industrial tasks. In this context, safety of the human operator is a main concern. In this paper, we present a framework for ensuring human safety in a robotic cell that allows human\u2013robot coexistence and dependable interaction. The framework is based on a layered control architecture that exploits an effective algorithm for online monitoring of relative human\u2013robot distance using depth sensors. This method allows to modify in real time the robot behavior depending on the user position, without limiting the operative robot workspace in a too conservative way. In order to guarantee redundancy and diversity at the safety level, additional certified laser scanners monitor human\u2013robot proximity in the cell and safe communication protocols and logical units are used for the smooth integration with an industrial software for safe low-level robot control. The implemented concept includes a smart human-machine interface to support in-process collaborative activities and for a contactless interaction with gesture recognition of operator commands. Coexistence and interaction are illustrated and tested in an industrial cell, in which a robot moves a tool that measures the quality of a polished metallic part while the operator performs a close evaluation of the same workpiece

Perinatal S-Adenosylmethionine Supplementation Represses PSEN1 Expression by the Cellular Epigenetic Memory of CpG and Non-CpG Methylation in Adult TgCRD8 Mice

DNA methylation, the main epigenetic modification regulating gene expression, plays a role in the pathophysiology of neurodegeneration. Previous evidence indicates that 50 -flanking hypomethylation of PSEN1, a gene involved in the amyloidogenic pathway in Alzheimer’s dis- ease (AD), boosts the AD-like phenotype in transgenic TgCRND8 mice. Supplementation with S-adenosylmethionine (SAM), the methyl donor in the DNA methylation reactions, reverts the patho- logical phenotype. Several studies indicate that epigenetic signatures, driving the shift between normal and diseased aging, can be acquired during the first stages of life, even in utero, and manifest phenotypically later on in life. Therefore, we decided to test whether SAM supplementation during the perinatal period (i.e., supplementing the mothers from mating to weaning) could exert a protec- tive role towards AD-like symptom manifestation. We therefore compared the effect of post-weaning vs. perinatal SAM treatment in TgCRND8 mice by assessing PSEN1 methylation and expression and the development of amyloid plaques. We found that short-term perinatal supplementation was as effective as the longer post-weaning supplementation in repressing PSEN1 expression and amyloid deposition in adult mice. These results highlight the importance of epigenetic memory and methyl donor availability during early life to promote healthy aging and stress the functional role of non-CpG methylation

Antioxidant properties of plant polyphenols in the counteraction of alcohol-abuse induced damage: impact on the mediterranean diet

Polyphenols are antioxidants contained in plants as olive and grape. As part of the Mediterranean diet, they may decrease the risk of cancer, of chronic and neurodegenerative diseases. Alcohol consumption plays a detrimental effect on health, causing tissue damage and disrupting the metabolism of Neurotrophins (NTs). NTs are crucial proteins for the life cycle of neuronal and non-neuronal cells. Alcohol abuse elicits changes in NTs levels in the brain and in other target organs, however, it was observed minor damage in animals early exposed to red wine, probably due to the antioxidant effects of polyphenols. Indeed, data show that resveratrol or other polyphenols extracted from the olive can effectively counteract serum free radicals’ formation caused by chronic alcohol intake, contrasting also alcohol-induced NTs liver elevation. The aim of the present review is to update pieces of evidences about the antioxidant properties of polyphenols and their role in counteracting alcohol-induced damage

Spatial distribution and temporal dynamics of invasive and native mosquitoes in a large Mediterranean city

Mosquitoes, including invasive species like the Asian tiger mosquito Aedes albopictus, alongside native species Culex pipiens s.l., pose a significant nuisance to humans and serve as vectors for mosquito-borne diseases in urban areas. Under- standing the impact of water infrastructure characteristics, climatic conditions, and management strategies on mosquito oc- currence and effectiveness of control measures to assess their implications on mosquito occurrence is crucial for effective vector control. In this study, we examined data collected during the local vector control program in Barcelona, Spain, focusing on 234,225 visits to 31,334 different sewers, as well as 1817 visits to 152 fountains between 2015 and 2019. We investigated both the colonization and recolonization processes of mosquito larvae within these water infrastructures. Our findings re- vealed higher larval presence in sandbox-sewers compared to siphonic or direct sewers, and the presence of vegetation and the use of naturalized water positively influenced larval occurrence in fountains. The application of larvicidal treatment significantly reduced larvae presence; however, recolonization rates were negatively affected by the time elapsed since treat- ment. Climatic conditions played a critical role in the colonization and recolonization of sewers and urban fountains, with mosquito occurrence exhibiting non-linear patterns and, generally, increasing at intermediate temperatures and accumulated rainfall levels. This study emphasizes the importance of considering sewers and fountains characteristics and climatic condi- tions when implementing vector control programs to optimize resources and effectively reduce mosquito populations

Reproductive system and spermatozoa ultrastructure support the phylogenetic proximity of Megadasys and Crasiella (Gastrotricha, Macrodasyida)

The reproductive system and the spermatozoon of Megadasys sterreri from Lanzarote (Canary Islands, Spain) were studied at structural and ultrastructural levels. The species is a simultaneous hermaphrodite with cross-fertilization and shows paired gonads, the male anterior and the female posterior, and both gametes mature in a caudo-cephalic direction. Sperm ducts converge on the midline and open into a ventral common pore. Two sexual accessory organs are present in the caudal trunk. A pipe-like frontal organ lies between the ovaries and the caudal organ, and is composed of a long, thin region connected to a large zone containing mature and degenerating spermatozoa. The cigar-like caudal organ is elongate, bulky and is made of an anterior glandulo-muscular region and a posterior muscular one. Spermatozoa are long, filiform cells formed by an acrosome, a nucleus-mitochondrial complex, and a flagellum. The long acrosome is composed of an apical twisted region and a basal straight region. The nucleo-mitochondrial complex is formed by a spring-shaped nucleus surrounding basally the mitochondrion and apically a granular material. The flagellum has a 9x2+2 axoneme, characterized by a dense and prominent central sheath surrounding the central tubules. Megadasys sterreri (Cephalodasyidae) shows the same reproductive layout as Crasiella (Planodasyidae): paired gonads, caudo-cephalic maturation of gametes, sperm ducts converging into a common ventral pore, and two sexual accessory organs. Also the spermatozoa ultrastructure shows two similarities in the two genera: a peculiar prominent central sheath in the axoneme and a similar structure of the basal region of the acrosome. Considering the likely polyphyletic nature of the family Cephalodasyidae, and the sister- taxon relationship of Megadasys and Crasiella that emerged from a recent molecular phylogenetic study, a close relationship between the two taxa appears to be very likely; consequently, we propose to remove Megadasys from the family Cephalodasyidae and affiliate it to the family Planodasyidae