Finiteness of rank invariants of multidimensional persistent homology groups

Rank invariants are a parametrized version of Betti numbers of a space multi-filtered by a continuous vector-valued function. In this note we give a sufficient condition for their finiteness. This condition is sharp for spaces embeddable in R^n

Pimsner algebras and Gysin sequences from principal circle actions

A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O_E is then the total space algebra of a noncommutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O_E and of B. Interesting examples come from O_E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.Comment: 29 pages. v2: Scientific content unchanged. Exposition improved. Added references. To appear in the JNc

Pimsner algebras and circle bundles

We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with the examples of quantum weighted projective and lens spaces and theta-deformations.Comment: 24 pages. v3: Updated title. No changes in the scientific content and result

The Gysin Sequence for Quantum Lens Spaces

We define quantum lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as `line bundles' over quantum lens spaces and generically define `torsion classes'. We work out explicit examples of these classes.Comment: 27 pages. v2: No changes in the scientific content and results. Section 5 completely re-written and a final section added; suppressed two appendices; added references; minor changes throughout the paper. To appear in the JNc

Da Altopascio a San Miniato: Cartografia, GIS e Virtual Landscaping

L’analisi del tratto di 30 Km di via Francigena compreso tra San Miniato ed Altopascio risulta scientificamente interessante per il notevole valore storico e culturale dei paesaggi che attraversa. L’itinerario proposto ne “ripercorre” virtualmente il percorso, rivelando, attraverso uno studio degli usi e delle coperture del suolo, l’aspetto del territorio durante il XIX secolo, poco prima delle grandi trasformazioni novecentesche. Riscopriamo così la città di Fucecchio affiancata dall’omonimo Padule, il bellissimo Ponte a Cappiano che regolava il flusso delle acque palustri, l’area boschiva delle Cerbaie e la struttura di assistenza dello Spedale di Altopascio. Grazie all’utilizzo combinato di fonti storiche cartografiche di alta qualità (Catasto Leopoldino) e di strumenti informatici tipici della moderna analisi geografica (GIS, globi virtuali, software per la modellizzazione 3D), si è cercato così di favorire una conoscenza del territorio che tenga conto delle dinamiche e dei valori storici sedimentati nelle forme attuali di questa parte preziosa del palinsesto paesaggistico toscano.The analysis of the 30 km stretch of theVia Francigena between San Miniato and Altopascio is scientifically interesting for the remarkable historical and cultural value of the landscapes it passes through. The proposed route will virtually “retrace” its trails and, through a study of the uses and coverings of the soil, will display the appearance of the area during the 19th century, shortly before the profound transformations which occurred in the Twentieth century. Thus, the city of Fucecchio and the Padule (marshes) by the same name nearby, the beautiful Ponte a Cappiano, which regulated the flow of the marsh waters, the woodlands of Cerbaie, and the charitable institution of the Spedale (ospice) in Altopascio will be rediscovered. Thanks to the combined use of historical high-quality cartographic sources (Catasto Leopoldino) and modern analytic equipment (GIS, virtual globes, 3D modeling software), we tried to promote a knowledge of the area which took into account the dynamics and historical values ​​which underlie in the present forms of this valuable part of the Tuscan landscape heritage

GPCE-based stochastic inverse methods: A benchmark study from a civil engineer’s perspective

In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems

Climate Change: impact on snow loads on structures

A general procedure to evaluate future trends in snow loads on structures is illustrated aiming to study influences of climate change at European scale, to assess its impact on the design of new structures as well as on the reliability levels of existing ones, also in view of the next revision of the Eurocodes. Analysing high quality registered meteorological data of daily temperatures, rain and snow precipitations in nine Italian weather stations, conditional probability functions of occurrence of snow precipitation, accumulation and melting have been preliminarily determined as functions of daily air temperatures. By means of Monte Carlo simulations and based upon daily output of climate models (daily max. and min. temperatures and water precipitation) yearly maxima of snow loads for various time intervals of 40 years in the period 1980-2100 have been simulated, deriving, via the extreme value theory, the characteristic ground snow loads at the sites. Then, the proposed procedure has been implemented in a more general methodology for snow map updating, in such a way that the influence of gridded data of precipitation, predicted by global climate models, on extreme values of snow loads is duly assessed. Preliminary results demonstrate that the outlined procedure is very promising and allows to estimate the evolution of characteristic ground snow loads and to define updated ground snow load maps for different climate models and scenarios

Embedding sustainability in risk management: The impact of environmental, social, and governance ratings on corporate financial risk

This study investigates the effect of corporate social and environmental evaluation on investors’ risk perception to explore the potential market risk for public companies that adopt a sustainable and responsible corporate strategy. We referred to the triple corporate assessment according to environmental, social, and governance (ESG) criteria to check whether ESG factors—meant to direct firms toward social and environmental needs—improve corporate market performance or trigger, among investors, a perception of “window dressing.” In doing so, we tested the impact of corporate social performance—proxied by an ESG assessment—on corporate financial risk using double risk measurement. We conducted a five-year longitudinal study (fiscal years 2014–2018) of 222 companies listed on the Standard & Poor’s index. The empirical findings show higher investor uncertainty regarding corporate sustainability performance, probably due to the misalignment of objectives between investors and investees. Indeed, an overall ESG assessment corresponds to higher systematic risk for firms, and a corporate environmental rating has an upward effect on the same risk dimension