Bounded Height in Pencils of Finitely Generated Subgroups

We prove height bounds concerning intersections of finitely generated subgroups in a torus with algebraic subvarieties, all varying in a pencil. This vastly extends the previously treated constant case and involves entirely different, and more delicate, techniques

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

Autonomy in Weapons Systems. The Military Application of Artificial Intelligence as a Litmus Test for Germany’s New Foreign and Security Policy

The future international security landscape will be critically impacted by the military use of artificial intelligence (AI) and robotics. With the advent of autonomous weapon systems (AWS) and a currently unfolding transformation of warfare, we have reached a turning point and are facing a number of grave new legal, ethical and political concerns. In light of this, the Task Force on Disruptive Technologies and 21st Century Warfare, deployed by the Heinrich Böll Foundation, argues that meaningful human control over weapon systems and the use of force must be retained. In their report, the task force authors offer recommendations to the German government and the German armed forces to that effect

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