7,744 research outputs found
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 when the base field is a
number field and is Galois. Our second result
establishes an explicit height bound for any non-zero element which is
not a root of unity in a Galois extension , depending on
the degree of and the number of conjugates of
which are multiplicatively independent over . As a consequence, we
obtain a height bound for such 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
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