On the Tropicalization of the Hilbert Scheme

In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is currently considered.Comment: 19 page

On a theorem of Faltings on formal functions

In 1980, Faltings proved, by deep local algebra methods, a local result regarding formal functions which has the following global geometric fact as a consequence. Theorem: Let k be an algebraically closed field (of any characteristic). Let Y be a closed subvariety of a projective irreducible variety X defined over k. Assume that X \subseteq P^n, dim(X)=d>2 and Y is the intersection of X with r hyperplanes of P^n, with r \le d-1. Then, every formal rational function on X along Y can be (uniquely) extended to a rational function on X. Due to its importance, the aim of this paper is to provide two elementary global geometric proofs of this theorem.Comment: 9 page

On the tropicalization of the Hilbert scheme

International audienceIn this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is usually considered

ARCHEOLOGIA DEI PAESAGGI NELLA VALLE DEL MISA (MARCHE, ITALIA): NUOVI DATI DALLA LETTURA INTEGRATA DEL TERRITORIO

The paper presents an integrated and multidisciplinary study carried out in the Misa River valley (Marche, Italy), through the combination of geomorphological, historical and archaeological data, with the goal to underline the most relevant changes occurred in this territory between the Roman Age and the Middle Age. Particular focus is reserved to the analysis of the relationship between human presence and physical geography, and to their reciprocal influences. A specific attention is dedicated to the new useful data for the geomorphological reconstruction of the watercourse configuration\u2019s changes in the area of the Roman town of Ostra, after the Roman period

ARCHEOLOGIA DEI PAESAGGI NELLA VALLE DEL MISA (MARCHE, ITALIA): NUOVI DATI DALLA LETTURA INTEGRATA DEL TERRITORIO

The paper presents an integrated and multidisciplinary study carried out in the Misa River valley (Marche, Italy), through the combination of geomorphological, historical and archaeological data, with the goal to underline the most relevant changes occurred in this territory between the Roman Age and the Middle Age. Particular focus is reserved to the analysis of the relationship between human presence and physical geography, and to their reciprocal influences. A specific attention is dedicated to the new useful data for the geomorphological reconstruction of the watercourse configuration’s changes in the area of the Roman town of Ostra, after the Roman period

DESIGN OF A MOTORCYCLE ENGINE CONTROL UNIT USING AN INTEGRATED CONTROL-IMPLEMENTATION APPROACH ⋆

Abstract: The design of automotive control systems is becoming increasingly complex as the level of performance required by car manufactures grows continuously and the constraints on cost and development time imposed by the market become tighter. A successful design, without costly and time consuming re-design cycles, can be achieved only by using an efficient design methodology that allows for component re-use and evaluation of platform requirements at the early stages of the design flow. In this paper, we illustrate the application of an integrated control-implementation design methodology, recently proposed by our group, to the development of the top few layers of abstraction in the design flow of an engine control system for motorcycles

Ancient landscape changes in the North Marche region : an archaeological and geomorphological appraisal in the Cesano valley

il contributo prende in analisi il rapporto tra il popolamento antio della valle del cesano e l'evoluzione della geografia fisica, allo scopo di ricostruire le variazioni del paesaggio legate in particolare alle vicende della citt\ue0 romana di suas

Distinctive Role of the Systemic Inflammatory Profile in Non-Small-Cell Lung Cancer Younger and Elderly Patients Treated with a PD-1 Immune Checkpoint Blockade: A Real-World Retrospective Multi-Institutional Analysis

An immune checkpoint blockade with mAbs to PD-1 and PD-L1 is an expanding therapeutic option for mNSCLC patients. This treatment strategy is based on the use of mAbs able to restore the anti-tumor activity of intratumoral T cells inhibited by PD-1 binding to PD-L1/2 on tumor and inflammatory cells. It has been speculated that a chronic status of systemic inflammation as well as the immunosenescence physiologically occurring in elderly patients may affect the efficacy of the treatment and the occurrence of irAEs. We performed a multi-institutional retrospective study aimed at evaluating the effects of these mAbs (nivolumab or atezolizumab) in 117 mNSCLC patients younger (90 cases) and older (27 cases) than 75 years in correlation with multiple inflammatory parameters (NLR, CRP, ESR, LDH and PCT). No differences were observed when the cohorts were compared in terms of the frequency of PFS, OS, inflammatory markers and immune-related adverse events (irAEs). Similarly, the occurrence of irAEs was strictly correlated with a prolonged OS survival in both groups. On the contrary, a negative correlation between the high baseline levels of inflammatory markers and OS could be demonstrated in the younger cohort only. Overall, PD-1/PD-L1-blocking mAbs were equally effective in young and elderly mNSCLC patients; however, the detrimental influence of a systemic inflammation at the baseline was only observed in young patients, suggesting different aging-related inflammation immunoregulative effects