The Zariski-Riemann space of valuation domains associated to pseudo-convergent sequences

Let $V$ be a valuation domain with quotient field $K$. Given a pseudo-convergent sequence $E$ in $K$, we study two constructions associating to $E$ a valuation domain of $K(X)$ lying over $V$, especially when $V$ has rank one. The first one has been introduced by Ostrowski, the second one more recently by Loper and Werner. We describe the main properties of these valuation domains, and we give a notion of equivalence on the set of pseudo-convergent sequences of $K$ characterizing when the associated valuation domains are equal. Then, we analyze the topological properties of the Zariski-Riemann spaces formed by these valuation domains.Comment: any comment is welcome! Trans. Amer. Math. Soc. 373 (2020), no. 11, 7959-799

Extending valuations to the field of rational functions using pseudo-monotone sequences

Let $V$ be a valuation domain with quotient field $K$. We show how to describe all extensions of $V$ to $K(X)$ when the $V$-adic completion $\widehat{K}$ is algebraically closed, generalizing a similar result obtained by Ostrowski in the case of one-dimensional valuation domains. This is accomplished by realizing such extensions by means of pseudo-monotone sequences, a generalization of pseudo-convergent sequences introduced by Chabert. We also show that the valuation rings associated to pseudo-convergent and pseudo-divergent sequences (two classes of pseudo-monotone sequences) roughly correspond, respectively, to the closed and the open balls of $K$ in the topology induced by $V$.Comment: all comments are welcome!

Metrizability of spaces of valuation domains associated to pseudo-convergent sequences

Let $V$ be a valuation domain of rank one with quotient field $K$. We study the set of extensions of $V$ to the field of rational functions $K(X)$ induced by pseudo-convergent sequences of $K$ from a topological point of view, endowing this set either with the Zariski or with the constructible topology. In particular, we consider the two subspaces induced by sequences with a prescribed breadth or with a prescribed pseudo-limit. We give some necessary conditions for the Zariski space to be metrizable (under the constructible topology) in terms of the value group and the residue field of $V$.Comment: pp. 1-22, final version, to appear in J. Algebra Appl. (2021). arXiv admin note: substantial text overlap with arXiv:1809.0953

The polynomial closure is not topological

We characterize the polynomial closure of a pseudo-convergent sequence in a valuation domain $V$ of arbitrary rank, and then we use this result to show that the polynomial closure is never topological when $V$ has rank at least $2$

Characterization of the Pall Celeris system as a point-of-care device for therapeutic angiogenesis

Abstract Background aims The Pall Celeris system is a filtration-based point-of-care device designed to obtain a high concentrate of peripheral blood total nucleated cells (PB-TNCs). We have characterized the Pall Celeris–derived TNCs for their in vitro and in vivo angiogenic potency. Methods PB-TNCs isolated from healthy donors were characterized through the use of flow cytometry and functional assays, aiming to assess migratory capacity, ability to form capillary-like structures, endothelial trans-differentiation and paracrine factor secretion. In a hind limb ischemia mouse model, we evaluated perfusion immediately and 7 days after surgery, along with capillary, arteriole and regenerative fiber density and local bio-distribution. Results Human PB-TNCs isolated by use of the Pall Celeris filtration system were shown to secrete a panel of angiogenic factors and migrate in response to vascular endothelial growth factor and stromal-derived factor-1 stimuli. Moreover, after injection in a mouse model of hind limb ischemia, PB-TNCs induced neovascularization by increasing capillary, arteriole and regenerative fiber numbers, with human cells detected in murine tissue up to 7 days after ischemia. Conclusions The Pall Celeris system may represent a novel, effective and reliable point-of-care device to obtain a PB-derived cell product with adequate potency for therapeutic angiogenesis

The Future of Cities

This report is an initiative of the Joint Research Centre (JRC), the science and knowledge service of the European Commission (EC), and supported by the Commission's Directorate-General for Regional and Urban Policy (DG REGIO). It highlights drivers shaping the urban future, identifying both the key challenges cities will have to address and the strengths they can capitalise on to proactively build their desired futures. The main aim of this report is to raise open questions and steer discussions on what the future of cities can, and should be, both within the science and policymaker communities. While addressing mainly European cities, examples from other world regions are also given since many challenges and solutions have a global relevance. The report is particularly novel in two ways. First, it was developed in an inclusive manner – close collaboration with the EC’s Community of Practice on Cities (CoP-CITIES) provided insights from the broader research community and city networks, including individual municipalities, as well as Commission services and international organisations. It was also extensively reviewed by an Editorial Board. Secondly, the report is supported by an online ‘living’ platform which will host future updates, including additional analyses, discussions, case studies, comments and interactive maps that go beyond the scope of the current version of the report. Steered by the JRC, the platform will offer a permanent virtual space to the research, practice and policymaking community for sharing and accumulating knowledge on the future of cities. This report is produced in the framework of the EC Knowledge Centre for Territorial Policies and is part of a wider series of flagship Science for Policy reports by the JRC, investigating future perspectives concerning Artificial Intelligence, the Future of Road Transport, Resilience, Cybersecurity and Fairness Interactive online platform : https://urban.jrc.ec.europa.eu/thefutureofcitiesJRC.B.3-Territorial Developmen

The polynomial closure is not topological

We characterize the polynomial closure of a pseudo-convergent sequence in a valuation domain $V$ of arbitrary rank, and then we use this result to show that the polynomial closure is never topological when $V$ has rank at least $2$

Metrizability of spaces of valuation domains associated to pseudo-convergent sequences

Let V be a valuation domain of rank one with quotient field K. We study the set of extensions of V to the field of rational functions K(X) induced by pseudo-convergent sequences of K from a topological point of view, endowing this set either with the Zariski or with the constructible topology. In particular, we consider the two subspaces induced by sequences with a prescribed breadth or with a prescribed pseudo-limit. We give some necessary conditions for the Zariski space to be metrizable (under the constructible topology) in terms of the value group and the residue field of V