The bisymplectomorphism group of a bounded symmetric domain

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. It has been shown in arXiv:math.DG/0603141 that there exists a diffeomorphism from the domain to the ambient vector space which puts in correspondence the above pair of forms. This phenomenon is called symplectic duality for Hermitian non compact symmetric spaces. In this article, we first give a different and simpler proof of this fact. Then, in order to measure the non uniqueness of this symplectic duality map, we determine the group of bisymplectomorphisms of a bounded symmetric domain, that is, the group of diffeomorphisms which preserve simultaneously the hyperbolic and the flat symplectic form. This group is the direct product of the compact Lie group of linear automorphisms with an infinite-dimensional Abelian group. This result appears as a kind of Schwarz lemma.Comment: 19 pages. Version 2: minor correction

NEW PERSPECTIVES FOR MAPPING ALTERATIONS IN HBIM IN CONSERVATION PROJECTS

Historic Building Information Modelling (HBIM) finds one of its most interesting applications in conservation design. The HBIM approach did not originate as a simple data archive method but as an information tool to help the designer at all stages of the building process. Turning to the field of preservation, a lot of information about the building is represented by thematic maps. They make it possible to get a graphic representation of the state of conservation of a facade or to understand the structural situation of a building. This research, experimented on the Arch of Augustus in Aosta, starts from the large amount of data acquired by the RAVA Laboratory of the Superintendence of Aosta over a long period. These data allowed for testing different approaches to thematic mapping, depending on the specific themes to be represented. In any case, even this experimentation required theoretical reasoning that preceded the operational phases. The question, which this article wants only to start to address, concerns the role of thematic mappings in the preservation project carried out with an HBIM approach, their necessity, and their implementation towards truly threedimensional data, which therefore maintains all the information that is directly acquired in three dimensions

NEWPERS PECTIVES FOR MAPPING ALTERATIONS IN HBIMIN CONSERVATION PROJECTS

Historic Building Information Modelling (HBIM) finds one of its most interesting applications in conservation design. The HBIMapproachdid not originate as a simple data archive method but as an information tool to help the designer at all stages of the building process. Turning to the field of preservation, a lot of information about the building is represented by thematic maps. They makeit possible to get a graphic representation of the state of conservation of a facade or to understand the structural situation of a building. This research, experimented on the Arch of Augustus in Aosta, starts from the large amount of data acquired by the RAVA Laboratory of the Superintendence of Aosta over a long period. These data allowed for testing different approaches to thematic mapping, depending on the specific themes to be represented. In any case, even this experimentation required theoretical reasoning that preceded the operational phases. The question, which this article wants only to start to address, concerns the role of thematic mappings in the preservation project carried out with an HBIM approach, their necessity, and their implementation towards truly threedimensional data, which therefore maintains all the information that is directly acquired in three dimensions

Riemannian geometry of Hartogs domains

Let D_F = \{(z_0, z) \in {\C}^{n} | |z_0|^2 < b, \|z\|^2 < F(|z_0|^2) \} be a strongly pseudoconvex Hartogs domain endowed with the \K metric $g_F$ associated to the \K form $\omega_F = -\frac{i}{2} \partial \bar{\partial} \log (F(|z_0|^2) - \|z\|^2)$. This paper contains several results on the Riemannian geometry of these domains. In the first one we prove that if $D_F$ admits a non special geodesic (see definition below) through the origin whose trace is a straight line then $D_F$ is holomorphically isometric to an open subset of the complex hyperbolic space. In the second theorem we prove that all the geodesics through the origin of $D_F$ do not self-intersect, we find necessary and sufficient conditions on $F$ for $D_F$ to be geodesically complete and we prove that $D_F$ is locally irreducible as a Riemannian manifold. Finally, we compare the Bergman metric $g_B$ and the metric $g_F$ in a bounded Hartogs domain and we prove that if $g_B$ is a multiple of $g_F$, namely $g_B=\lambda g_F$, for some $\lambda\in \R^+$, then $D_F$ is holomorphically isometric to an open subset of the complex hyperbolic space.Comment: to appear in International Journal of Mathematic

PopRank: Ranking pages' impact and users' engagement on Facebook

Users online tend to acquire information adhering to their system of beliefs and to ignore dissenting information. Such dynamics might affect page popularity. In this paper we introduce an algorithm, that we call PopRank, to assess both the Impact of Facebook pages as well as users' Engagement on the basis of their mutual interactions. The ideas behind the PopRank are that i) high impact pages attract many users with a low engagement, which means that they receive comments from users that rarely comment, and ii) high engagement users interact with high impact pages, that is they mostly comment pages with a high popularity. The resulting ranking of pages can predict the number of comments a page will receive and the number of its posts. Pages impact turns out to be slightly dependent on pages' informative content (e.g., science vs conspiracy) but independent of users' polarization.Comment: 10 pages, 5 figure

THE ARCH OF AUGUSTUS IN AOSTA: DATA AND ANALYSIS REUSE FOR A CONSERVATION PROJECT

The paper proposes a path for the management of the Arch of Augustus in Aosta to exploit the potential of Historic Building Information Modelling (HBIM). The HBIM system acts both as a place where to georeference the available data and as a tool for the elaboration of the conservation project in all its aspects. The system deals with different data from the survey of geometries to that of materials and alterations, up to the conservation project (mainly focused on the surfaces, with the aim of traceability of the events that the monument has lived, lives, and will live). The challenges in this research concern several aspects. First, it will be necessary to adapt the regular geometry of the BIM approach to the complex shapes necessary for the reproduction of surface alterations in the Puddinga stone. In addition, even more important, the ability to manage the monitoring data distributed at different times, comparing and making them available to current and future restorers (and other operators involved in the preservation). These tasks will be fixed by drawing up a dynamic conservation project, i.e. one that can make use of the available data at any time and all those that will become available during the work. Attempts of data digitization to give a shared value to the conservation activities had already been proposed in the past. The new research now starts from the reconnaissance of the weaknesses of the previous proposals, mainly related to the use of tailor-made systems (software) that are difficult to maintain, to implement and use in a very heterogeneous team of operators (architects, archaeologists, engineers, topographers, chemists, historians…

Per una migliore comprensione dei rapporti storici tra sinto piemontese di Piemonte e sinto piemontese di Francia: alcune considerazioni a partire da evidenze morfologiche e lessicali

In Piemonte (Italia) e nella Francia meridionale vivono due comunità sinte che definiscono se stesse come “piemontesi”. Le relazioni storiche tra queste due comunità non sono note, ma la loro comune auto-denominazione suggerisce come prima ipotesi un’origine comune e in particolare che i sinti piemontesi di Francia siano un gruppo di sinti piemontesi del Piemonte migrato dalle originarie sedi italiane. L’esame dei dialetti romaní delle due comunità mostra tuttavia come questa ricostruzione appaia un poco semplicistica, soprattutto perché la varietà di romaní parlata dai sinti piemontesi di Francia condivide un certo numero di tratti morfologici e lessicali con il sinto lombardo, un’altra varietà di romaní parlata nell’Italia settentrionale. L’articolo discute alcune caratteristiche di questi dialetti sinti e propone l’ipotesi che i sinti piemontesi di Francia siano i discendenti di una comunità originariamente insediata in un’area intermedia tra quelle storicamente occupate dai sinti piemontesi di Piemonte e i sinti lombardi

GEOMETRY AND INFORMATION FOR THE PRESERVATION OF A ROMAN MOSAIC THROUGH A HBIM APPROACH

Abstract. The archaeological site is a mine of data and information that helps to deepen the knowledge of its origin, history, and structure. This virtuous approach becomes even more effective when these data, properly processed and structured, form the basis for a project of conservation and enhancement of the cultural asset.The Roman mosaics dug in Castiglione delle Stiviere in 1995 represent an interesting case in which all the archaeological information, made available by the Superintendence, was used through an HBIM (Historical Building Information Modeling) approach for the conservation project. The Stratigraphic Units (US) of the findings have identified the strategy for the geometric and informative modeling of the BIM (Building Information Modeling) model and have also been exploited in the design phase for the project of the new roof structure and especially for the cost analysis. The structuring of the data by stratigraphic units was also used in the drafting of the preventive and planned conservation, necessary to enhance and prolong the state of good health of the property.This work has been developed in the internship activity within a training course on HBIM, in collaboration with the Diocese of Mantua, owner of the property