Lower Bounds for Heights in Relative Galois Extensions

The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\alpha$ when the base field $\mathbb{K}$ is a number field and $\mathbb{K}(\alpha)/\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\alpha$ which is not a root of unity in a Galois extension $\mathbb{F}/\mathbb{K}$, depending on the degree of $\mathbb{K}/\mathbb{Q}$ and the number of conjugates of $\alpha$ which are multiplicatively independent over $\mathbb{K}$. As a consequence, we obtain a height bound for such $\alpha$ that is independent of the multiplicative independence condition

Cellular automata on regular rooted trees

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts

The Role of Gut Microbiota Biomodulators on Mucosal Immunity and Intestinal Inflammation

Alterations of the gut microbiota may cause dysregulated mucosal immune responses leading to the onset of inflammatory bowel diseases (IBD) in genetically susceptible hosts. Restoring immune homeostasis through the normalization of the gut microbiota is now considered a valuable therapeutic approach to treat IBD patients. The customization of microbe-targeted therapies, including antibiotics, prebiotics, live biotherapeutics and faecal microbiota transplantation, is therefore considered to support current therapies in IBD management. In this review, we will discuss recent advancements in the understanding of host-microbe interactions in IBD and the basis to promote homeostatic immune responses through microbe-targeted therapies. By considering gut microbiota dysbiosis as a key feature for the establishment of chronic inflammatory events, in the near future it will be suitable to design new cost-effective, physiologic, and patient-oriented therapeutic strategies for the treatment of IBD that can be applied in a personalized manner

Economic Interplay Forecasting Business Success

A startup ecosystem is a dynamic environment in which several actors, such as investors, venture capitalists, angels, and facilitators, are the protagonists of a complex interplay. Most of these interactions involve the flow of capital whose size and direction help to map the intricate system of relationships. This quantity is also considered a good proxy of economic success. Given the complexity of such systems, it would be more desirable to supplement this information with other informative features, and a natural choice is to adopt mathematical measures. In this work, we will specifically consider network centrality measures, borrowed by network theory. In particular, using the largest publicly available dataset for startups, the Crunchbase dataset, we show how centrality measures highlight the importance of particular players, such as angels and accelerators, whose role could be underestimated by focusing on collected funds only. We also provide a quantitative criterion to establish which firms should be considered strategic and rank them. Finally, as funding is a widespread measure for success in economic settings, we investigate to which extent this measure is in agreement with network metrics; the model accurately forecasts which firms will receive the highest funding in future years

Antiviral Property of the Fungal Metabolite 3-O-Methylfunicone in Bovine Herpesvirus 1 Infection

Bovine herpesvirus type-1 (BoHV-1) is a widespread pathogen that provokes infectious rhinotracheitis and polymicrobial infections in cattle, resulting in serious economic losses to the farm animal industry and trade restrictions. To date, non-toxic active drugs against BoHV-1 are not available. The exploitation of bioactive properties of microbial products is of great pharmaceutical interest. In fact, fungi are a promising source of novel drugs with a broad spectrum of activities and functions, including antiviral properties. Hence, the potential antiviral properties of 3-O-methylfunicone (OMF), a secondary metabolite produced by Talaromyces pinophilus, were evaluated on BoHV-1. In this study, during BoHV-1 infection in bovine cells (MDBK), the non-toxic concentration of 5 µM OMF considerably reduced signs of cell death and increased cell proliferation. Furthermore, OMF significantly decreased the virus titer as well as the cytopathic effect and strongly inhibited the expression of bICP0, the major regulatory protein in the BoHV-1 lytic cycle. These findings were accompanied by a considerable up-regulation in the expression of the aryl hydrocarbon receptor (AhR), a multifunctional transcription factor also linked to the host’s response to a herpesvirus infection. Overall, our results suggest that by involving AhR, OMF shows potential against a BoHV-1 infection