Moduli spaces of abstract and embedded Kummer varieties

In this paper, we investigate the construction of two moduli stacks of Kummer varieties. The first one is the stack $\mathcal K^{\text{abs}}_g$ of abstract Kummer varieties and the second one is the stack $\mathcal K^{\text{em}}_g$ of embedded Kummer varieties. We will prove that $\mathcal K^{\text{abs}}_g$ is a Deligne-Mumford stack and its coarse moduli space is isomorphic to $\boldsymbol A_g$, the coarse moduli space of principally polarized abelian varieties of dimension $g$. On the other hand we give a modular family $\mathcal W_g\to U$ of embedded Kummer varieties embedded in $\mathbb P^{2^g-1}\times\mathbb P^{2^g-1}$, meaning that every geometric fiber of this family is an embedded Kummer variety and every isomorphic class of such varieties appears at least once as the class of a fiber. As a consequence, we construct the coarse moduli space $\boldsymbol{\mathsf K}^{\text{em}}_2$ of embedded Kummer surfaces and prove that it is obtained from $\boldsymbol A_2$ by contracting a particular curve inside this space. We conjecture that this is a general fact: $\boldsymbol{\mathsf K}^{\text{em}}_g$ could be obtained from $\boldsymbol A_g$ via a contraction for all $g>1$.Comment: 31 page

A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation

International audienceWe consider the capacity formulation of the Robust Network Loading Problem. The aim of the paper is to study what happens from the theoretical and from the computational point of view when the routing policy (or scheme) changes. The theoretical results consider static, volume, affine and dynamic routing, along with splittable and unsplittable flows. Our polyhedral study provides evidence that some well-known valid inequalities (the robust cutset inequalities) are facets for all the considered routing/flows policies under the same assumptions. We also introduce a new class of valid inequalities, the robust 3-partition inequalities, showing that, instead, they are facets in some settings, but not in others. A branch-and-cut algorithm is also proposed and tested. The computational experiments refer to the problem with splittable flows and the budgeted uncertainty set. We report results on several instances coming from real-life networks, also including historical traffic data, as well as on randomly generated instances. Our results show that the problem with static and volume routing can be solved quite efficiently in practice and that, in many cases, volume routing is cheaper than static routing, thus possibly representing the best compromise between cost and computing time. Moreover, unlikely from what one may expect, the problem with dynamic routing is easier to solve than the one with affine routing, which is hardly tractable, even using decomposition methods

Free global DSM assessment on large scale areas exploiting the potentialities of the innovative google earth engine platform

The high-performance cloud-computing platform Google Earth Engine has been developed for global-scale analysis based on the Earth observation data. In particular, in this work, the geometric accuracy of the two most used nearly-global free DSMs (SRTM and ASTER) has been evaluated on the territories of four American States (Colorado, Michigan, Nevada, Utah) and one Italian Region (Trentino Alto-Adige, Northern Italy) exploiting the potentiality of this platform. These are large areas characterized by different terrain morphology, land covers and slopes. The assessment has been performed using two different reference DSMs: the USGS National Elevation Dataset (NED) and a LiDAR acquisition. The DSMs accuracy has been evaluated through computation of standard statistic parameters, both at global scale (considering the whole State/Region) and in function of the terrain morphology using several slope classes. The geometric accuracy in terms of Standard deviation and NMAD, for SRTM range from 2-3 meters in the first slope class to about 45 meters in the last one, whereas for ASTER, the values range from 5-6 to 30 meters. In general, the performed analysis shows a better accuracy for the SRTM in the flat areas whereas the ASTER GDEM is more reliable in the steep areas, where the slopes increase. These preliminary results highlight the GEE potentialities to perform DSM assessment on a global scale

A geometric analysis of the SIRS compartmental model with fast information and misinformation spreading

We propose an SIRS compartmental model with demography and fast information and misinformation spreading in the population. The analysis of the complete 6-dimensional system shows the existence of seven equilibrium points. Since under our assumptions the system evolves on two time scales, we completely characterize the possible asymptotic behaviours with techniques of Geometric Singular Perturbation Theory (GSPT). During our analysis of the fast dynamics, we identify three branches of the critical manifold, which exist under determined conditions. We perform a theoretical bifurcation analysis of the fast system to understand the relation between these three equilibria when varying specific parameters of the fast system. We then observed a delayed loss of stability on the various branches of the critical manifold, as the slow dynamics may cause the branches to lose their hyperbolicity. We emphasise how the inclusion of (mis)information spreading, even in low dimensional compartmental models, can radically alter the asymptotic behaviour of the epidemic. We conclude with numerical simulations of various remarkable scenarios.Comment: 27 pages, 8 figures, 1 tabl

A survey on Lyapunov functions for epidemic compartmental models

In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, and provide a commentary on their use. Our aim is to provide a comprehensive starting point to readers who are attempting to prove global stability of systems of ODEs. The focus is on mathematical epidemiology, however some of the functions and strategies presented in this paper can be adapted to a wider variety of models, such as prey–predator or rumor spreading

Reconstructing eruptive source parameters from tephra deposit: a numerical study of medium-sized explosive eruptions at Etna volcano

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A geometric analysis of the SIRS model with secondary infections

We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0 < 1$. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis, to complement our analytical results.Comment: 31 pages, 9 figure

Museos virtuales y entorno construido: narrativas y experiencias inmersivas vía centros de geodatos multitemporales

[EN] Our built environment is nowadays considered as a dynamic complex, stretching and transforming across space and time, with the interaction of human, social and economic dimensions. It needs to be safeguarded as living places for the future taking into account such complexity. The general aim of this work is to contribute to the comprehension of landscape values, enhancing participation processes by tourists and local communities, considering the built environment as a system: the sum of natural transformation, ancient artefacts stratification and human activities, partially covering the tangible traces, and functioning as a vehicle for the comprehension of intangible values. Multi-temporal, multi-scale and geospatial datasets can play an important role in such knowledge transfer processes by means of narratives and immersive experiences in a multimedia museum approach. In particular, the cartographic heritage, in the form of metric and non-metric maps, can be progressively used as a source of information for innovative narratives. Virtual Museums (VMs)are additional "channels" to disseminate content and to provide knowledge about cultural heritage; they have emerged from the crossbreeding process between museums and digital technologies. Investigating how digital storytelling may support communication and understanding of complex systems, such as the built environment and landscape, it is relevant because cultural awareness may foster the sense of belonging and identity construction of which Europe is thirsty, contributing to the safeguarding of fragile sites. The paper provides useful information for museums that would like to follow this pathway. It retraces the main steps of storytelling production and presents interesting examples of immersive narrative models based on geospatial data and a virtual hub, helping people to retrieve and access information and to recognize places of memory mostly unknown. Moreover, it offers an evaluation of existing tools that can be adopted for this purpose. Eventually, by virtue of the research carried out for the case study of the Virtual Museum of Como Lake Landscape, the paper aims at ascertaining which kind of stories and experiences can be designed, the potential of these tools and possible weaknesses or constraints that deserve future researches.[ES] El entorno construido se considera hoy en día como un complejo dinámico, que se extiende y transforma a través del espacio y el tiempo, con interacción de dimensiones humanas, sociales y económicas. Debe salvaguardarse como lugares donde vivir el futuro teniendo en cuenta tal complejidad. El objetivo general de este trabajo es contribuir a la comprensión de los valores paisajísticos, potenciando los procesos de participación de los turistas y de los autóctonos, considerando el entorno construido como un sistema: suma de la transformación natural, de la estratificación de artefactos antiguos y de actividades humanas, cubriendo parcialmente los rastros tangibles, y vehículo de comprensión de valores intangibles. Los conjuntos de datos multitemporales, a multi-escala y geoespaciales pueden desempeñar un papel importante en dicho proceso de transferencia de conocimiento a través de narrativas y experiencias inmersivas en el enfoque de un museo multimedia. En particular, el patrimonio cartográfico, en forma de mapas métricos y mapas no métricos, puede utilizarse progresivamente como fuente de información para narrativas innovadoras. Los Museos Virtuales (VM) son “canales” adicionales que permiten difundir contenido y proporcionar conocimiento sobre el patrimonio cultural; surgen del proceso de mestizaje entre museos y tecnologías digitales. Investigar cómo la narración digital puede apoyar la comunicación y la comprensión de sistemas complejos, como el entorno construido y el paisaje, es relevante porque la conciencia cultural puede fomentar el sentido de pertenencia y la construcción de identidad de los que Europa tiene sed, contribuyendo a la protección de sitios frágiles. El artículo proporciona información útil para los museos que deseen seguir este camino. Describe los principales pasos que deberían considerarse a la hora de producir narrativas y pone ejemplos interesantes de modelos narrativos inmersivos basados en datos geoespaciales y centros virtuales, que ayudan a las personas a recuperar y acceder a información, y a reconocer lugares desconocidos o vagamente retenidos en la memoria. Además, ofrece una evaluación de las herramientas existentes que se pueden adoptar con este propósito. El objetivo es aclarar, finalmente, en virtud dela investigación desarrollada en el caso de estudio del Museo Virtual del Paisaje del Lago di Como, qué tipo de historias y experiencias se pueden diseñar, el potencial de estas herramientas y las posibles debilidades o limitaciones que merecen futuras investigaciones.We thank Stefano Della Torre (Head of Polimi dABC) as Sc. Responsible of the Advisory within the PORL FESR 2007/2013 ‘Multimedia system for the presentation and participated recognizing of the environmental values of the landscape of the Lake of Como’; and Leoni Marco (Director of the Museum of Como Lake Landscape) for the concession of museum’s data and his support in developing the PhD research of which this paper presents a summary of preliminary findings.The research leading to the results of this paper is partially funded under the ICT Policy Support Programme (ICT PSP) as part of the Competitiveness and Innovation Framework Programme by the European Community (CIP) GA no. 620400.Brumana, R.; Oreni, D.; Caspani, S.; Previtali, M. (2018). Virtual museums and built environment: narratives and immersive experience via multi-temporal geodata hub. Virtual Archaeology Review. 9(19):34-49. https://doi.org/10.4995/var.2018.9918SWORD3449919Bedford, L. (2001). Storytelling: The real work of museums. 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A geo-swot chart, using a values centered approach and multi temporal-maps for landscape assessment and multimedia ecomuseum. In ICOMOS International Symposium "Heritage and Landscape as Human Values", Theme 1"Sharing and experiencing the identity of communities through tourism and interpretation" (pp. 186-191). Florence, Italy.Brumana, R., Santana Quintero, M., Barazzetti, L., Previtali, M., Banfi, F., Oreni, D., Roels D., & Roncoroni, F. (2015b). Towards a virtual hub approach for landscape assessment and multimedia ecomuseum using multi temporal-maps. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XL-5/W7, 49-56. https://doi.org/10.5194/isprsarchives-XL-5-W7-49-2015Bruner, J. (1991). The Narrative Construction of Reality. Critical Inquiry, 18 (1), 1-21. https://doi.org/10.1086/448619Caquard, S. (2013). Mapping narrative cartography. 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Perspectives on the 3-D analysis through the cadastral map series (XVIII -XX sec.) and the first geodetic large scale map of Milan realized by the 'Astronomidi Brera' (Astronomers of Brera): toward an advanced portal. E-PERIMETRON, 4(2), 86-100.Nativi, S., Craglia, M., & Pearlman, J. (2013). Earth science infrastructures interoperability: the brokering approach. IEEE Journal of Selected Topics. Applied Earth Observations and Remote Sensing, 6(3), 1118-1129. https://doi.org/10.1109/JSTARS.2013.2243113Pierdicca, R., Malinverni, E., Frontoni, E., Colosi, F., & Orazi, R. (2016). 3D visualization tools to explore ancient architectures in South America. Virtual Archaeology Review, 7(15), 44-53.https://doi.org/10.4995/var.2016.5904Pini, L. (2003). Tremezzo il paese dove fioriscono I limoni. Tremezzo: Silvana Editoriale.Previtali, M. (2017). Geopan atl@s: A brokering based gateway to georeferenced historical maps for risk analysis. 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Retrieved October25, 2017, from http://www.v-must.net/sites/default/files/D2.3d_StateArt_VirtualMuseums_2015.pdfWong, A. (2015). The whole story, and then some: 'digital storytelling' in evolving museum practice. In MW2015: Museums and the Web 2015, Chicago, United States. Retrieved October25, 2017, from http://mw2015.museumsandtheweb.com/paper/the-whole-story-and-then-some-digital-storytelling-in-evolving-museum-practice