Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

The spatial association of numbers and mathematical symbols

The "SNARC effect" refers to the finding that people respond faster to small numbers with the left hand and to large numbers with the right hand. This effect is often explained by hypothesizing that numbers are represented from left to right in ascending order (Mental Number Line). However, the SNARC effect may not depend on quantitative information, but on other factors such as the order in which numbers are often represented from left to right in our culture. Four experiments were performed to test this hypothesis. In the first experiment, the concept of spatial association was extended to nonnumeric mathematical symbols: the minus and plus symbols. These symbols were presented as fixation points in a spatial compatibility paradigm. The results demonstrated an opposite influence of the two symbols on the target stimulus: the minus symbol tends to favor the target presented on the left, while the plus symbol the target presented on the right, demonstrating that spatial association can emerge in the absence of a numerical context. In the last three experiments, the relationship between quantity and order was evaluated using normal numbers and mirror numbers. Although mirror numbers denote quantity, they are not encountered in a left-to-right spatial organization. In Experiments 1 and 2, participants performed a magnitude classification task with mirror and normal numbers presented together (Experiment 1) or separately (Experiment 2). In Experiment 3, participants performed a new task in which quantity information processing was not required: the mirror judgment task. The results show that participants access the quantity of both normal and mirror numbers, but only the normal numbers are spatially organized from left to right. In addition, the physical similarity between the numbers, used as a predictor variable in the last three experiments, showed that the physical characteristics of numbers influenced participants' reaction times.

The Hitchin map for one-nodal base curves of compact type

Studying moduli spaces of semistable Higgs bundles (E, \phi) of rank n on a smooth curve C, a key role is played by the spectral curve X (Hitchin), because an important result by Beauville-Narasimhan-Ramanan allows us to study isomorphism classes of such Higgs bundles in terms of isomorphism classes of rank-1 torsion-free sheaves on X. This way, the generic fibre of the Hitchin map, which associates to any semistable Higgs bundle the coefficients of the characteristic polynomial of \phi, is isomorphic to the Jacobian of X. Focusing on rank-2 Higgs data, this construction was extended by Barik to the case in which the curve C is reducible, one-nodal, having two smooth components. Such curve is called of compact type because its Picard group is compact. In this work, we describe and clarify the main points of the construction by Barik and we give examples, especially concerning generic fibres of the Hitchin map. Referring to Hausel-Pauly, we consider the case of SL(2,C)-Higgs bundles on a smooth base curve, which are such that the generic fibre of the Hitchin map is a subvariety of the Jacobian of X, the Prym variety. We recall the description of special loci, called endoscopic loci, such that the associated Prym variety is not connected. Then, letting G be an affine reductive group having underlying Lie algebra so(4,C), we consider G-Higgs bundles on a smooth base curve. Starting from the construction by Bradlow-Schaposnik, we discuss the associated endoscopic loci. By adapting these studies to a one-nodal base curve of compact type, we describe the fibre of the SL(2,C)-Hitchin map and of the G-Hitchin map, together with endoscopic loci. In the Appendix, we give an interpretation of generic spectral curves in terms of families of double covers.

Locating the source of volcanic tremor at stromboli volcano, italy

We have developed a method for locating sources of volcanic tremor and applied it to a dataset recorded on Stromboli volcano before and after the onset of the February 27th 2007 effusive eruption. Volcanic tremor has attracted considerable attention by seismologists because of its potential value as a tool for forecasting eruptions and for better understanding the physical processes that occur inside active volcanoes. Commonly used methods to locate volcanic tremor sources are: 1) array techniques, 2) semblance based methods, 3) calculation of wave field amplitude. We have choosen the third approach, using a quantitative modeling of the seismic wavefield. For this purpose, we have calculated the Green Functions (GF) in the frequency domain with the Finite Element Method (FEM). We have used this method because it is well suited to solve elliptic problems, as the elastodynamics in the Fourier domain. The volcanic tremor source is located by determining the source function over a regular grid of points. The best fit point is choosen as the tremor source location. The source inversion is performed in the frequency domain, using only the wavefield amplitudes. We illustrate the method and its validation over a synthetic dataset. We show some preliminary results on the Stromboli dataset, evidencing temporal variations of the volcanic tremor sources.

Pues no soy mujer. The Upheaval of Singularity in Sor Juana Inés de la Cruz.

This thesis titled Pues no soy mujer: The Upheaval of Singularity in Sor Juana Inés de la Cruz centers on the revolution that sor Juana (San Miguel Nepantla 1648?- Mexico City 1695) started in the debate about singularity, sexedness, and in-betweenness—not only in the field of literary studies and literary criticism, but also in the broad landscape of feminist and gender studies. By defining herself neither as a woman, nor as a stable subject belonging to a fixed homogeneous group or genre, sor Juana opens an interesting debate about difference and non-binarism. In sor Juana’s literary corpus identities are endless and impossible to grasp in their ultimate meaning. They remain forever impossible to place, neither fully present nor fully absent. They exist in a dangerous balance between (nepantla) life and death, dancing and moving, following the chaotic geometry of points, folding the ordinate symmetry of lines, and subverting the hegemonic order of the patriarchal and colonial world.

Estimating crustal deformation from geodetic data

By the end of the 19th century, geodesy has contributed greatly to the knowledge of regional tectonics and fault movement through its ability to measure, at sub-centimetre precision, the relative positions of points on the Earth’s surface. Nowadays the systematic analysis of geodetic measurements in active deformation regions represents therefore one of the most important tool in the study of crustal deformation over different temporal scales [e.g., Dixon, 1991]. This dissertation focuses on motion that can be observed geodetically with classical terrestrial position measurements, particularly triangulation and leveling observations. The work is divided into two sections: an overview of the principal methods for estimating longterm accumulation of elastic strain from terrestrial observations, and an overview of the principal methods for rigorously inverting surface coseismic deformation fields for source geometry with tests on synthetic deformation data sets and applications in two different tectonically active regions of the Italian peninsula. For the long-term accumulation of elastic strain analysis, triangulation data were available from a geodetic network across the Messina Straits area (southern Italy) for the period 1971 – 2004. From resulting angle changes, the shear strain rates as well as the orientation of the principal axes of the strain rate tensor were estimated. The computed average annual shear strain rates for the time period between 1971 and 2004 are γ˙1 = 113.89 ± 54.96 nanostrain/yr and γ˙2 = -23.38 ± 48.71 nanostrain/yr, with the orientation of the most extensional strain (θ) at N140.80° ± 19.55°E. These results suggests that the first-order strain field of the area is dominated by extension in the direction perpendicular to the trend of the Straits, sustaining the hypothesis that the Messina Straits could represents an area of active concentrated deformation. The orientation of θ agree well with GPS deformation estimates, calculated over shorter time interval, and is consistent with previous preliminary GPS estimates [D’Agostino and Selvaggi, 2004; Serpelloni et al., 2005] and is also similar to the direction of the 1908 (MW 7.1) earthquake slip vector [e.g., Boschi et al., 1989; Valensise and Pantosti, 1992; Pino et al., 2000; Amoruso et al., 2002]. Thus, the measured strain rate can be attributed to an active extension across the Messina Straits, corresponding to a relative extension rate ranges between < 1mm/yr and up to ~ 2 mm/yr, within the portion of the Straits covered by the triangulation network. These results are consistent with the hypothesis that the Messina Straits is an important active geological boundary between the Sicilian and the Calabrian domains and support previous preliminary GPS-based estimates of strain rates across the Straits, which show that the active deformation is distributed along a greater area. Finally, the preliminary dislocation modelling has shown that, although the current geodetic measurements do not resolve the geometry of the dislocation models, they solve well the rate of interseismic strain accumulation across the Messina Straits and give useful information about the locking the depth of the shear zone. Geodetic data, triangulation and leveling measurements of the 1976 Friuli (NE Italy) earthquake, were available for the inversion of coseismic source parameters. From observed angle and elevation changes, the source parameters of the seismic sequence were estimated in a join inversion using an algorithm called “simulated annealing”. The computed optimal uniform–slip elastic dislocation model consists of a 30° north-dipping shallow (depth 1.30 ± 0.75 km) fault plane with azimuth of 273° and accommodating reverse dextral slip of about 1.8 m. The hypocentral location and inferred fault plane of the main event are then consistent with the activation of Periadriatic overthrusts or other related thrust faults as the Gemona- Kobarid thrust. Then, the geodetic data set exclude the source solution of Aoudia et al. [2000], Peruzza et al. [2002] and Poli et al. [2002] that considers the Susans-Tricesimo thrust as the May 6 event. The best-fit source model is then more consistent with the solution of Pondrelli et al. [2001], which proposed the activation of other thrusts located more to the North of the Susans-Tricesimo thrust, probably on Periadriatic related thrust faults. The main characteristics of the leveling and triangulation data are then fit by the optimal single fault model, that is, these results are consistent with a first-order rupture process characterized by a progressive rupture of a single fault system. A single uniform-slip fault model seems to not reproduce some minor complexities of the observations, and some residual signals that are not modelled by the optimal single-fault plane solution, were observed. In fact, the single fault plane model does not reproduce some minor features of the leveling deformation field along the route 36 south of the main uplift peak, that is, a second fault seems to be necessary to reproduce these residual signals. By assuming movements along some mapped thrust located southward of the inferred optimal single-plane solution, the residual signal has been successfully modelled. In summary, the inversion results presented in this Thesis, are consistent with the activation of some Periadriatic related thrust for the main events of the sequence, and with a minor importance of the southward thrust systems of the middle Tagliamento plain.

Magnetohydrodynamic Effects On Mixed Convection Flows In Channels And Ducts

This work focuses on magnetohydrodynamic (MHD) mixed convection flow of electrically conducting fluids enclosed in simple 1D and 2D geometries in steady periodic regime. In particular, in Chapter one a short overview is given about the history of MHD, with reference to papers available in literature, and a listing of some of its most common technological applications, whereas Chapter two deals with the analytical formulation of the MHD problem, starting from the fluid dynamic and energy equations and adding the effects of an external imposed magnetic field using the Ohm's law and the definition of the Lorentz force. Moreover a description of the various kinds of boundary conditions is given, with particular emphasis given to their practical realization. Chapter three, four and five describe the solution procedure of mixed convective flows with MHD effects. In all cases a uniform parallel magnetic field is supposed to be present in the whole fluid domain transverse with respect to the velocity field. The steady-periodic regime will be analyzed, where the periodicity is induced by wall temperature boundary conditions, which vary in time with a sinusoidal law. Local balance equations of momentum, energy and charge will be solved analytically and numerically using as parameters either geometrical ratios or material properties. In particular, in Chapter three the solution method for the mixed convective flow in a 1D vertical parallel channel with MHD effects is illustrated. The influence of a transverse magnetic field will be studied in the steady periodic regime induced by an oscillating wall temperature. Analytical and numerical solutions will be provided in terms of velocity and temperature profiles, wall friction factors and average heat fluxes for several values of the governing parameters. In Chapter four the 2D problem of the mixed convective flow in a vertical round pipe with MHD effects is analyzed. Again, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the wall. A numerical solution is presented, obtained using a finite element approach, and as a result velocity and temperature profiles, wall friction factors and average heat fluxes are derived for several values of the Hartmann and Prandtl numbers. In Chapter five the 2D problem of the mixed convective flow in a vertical rectangular duct with MHD effects is discussed. As seen in the previous chapters, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the four walls. The numerical solution obtained using a finite element approach is presented, and a collection of results, including velocity and temperature profiles, wall friction factors and average heat fluxes, is provided for several values of, among other parameters, the duct aspect ratio. A comparison with analytical solutions is also provided, as a proof of the validity of the numerical method. Chapter six is the concluding chapter, where some reflections on the MHD effects on mixed convection flow will be made, in agreement with the experience and the results gathered in the analyses presented in the previous chapters. In the appendices special auxiliary functions and FORTRAN program listings are reported, to support the formulations used in the solution chapters.

L' "opera mondo" di Paolo Volponi fra satira e morale

Nella mia tesi di dottorato mi propongo di indagare la metamorfosi del romanzo nella letteratura italiana contemporanea attraverso il lavoro di Paolo Volponi, che può essere descritto come un’«opera mondo», in accordo con la formula critica coniata da Franco Moretti. Volponi intende superare il divario fra l’io e il mondo e ricomporre il corpo come una mediazione umanistica di ragione e sensi. La sua opera può essere definita ‘epica’ perché recupera la tradizione del romanzo cavalleresco e la parodia esercitata su questa tradizione letteraria da Cervantes nel Don Chisciotte. Ma, come l’Ulysses di Joyce, è un’epica «moderna» perché fondata su una totalità disgiunta e sul conflitto dialogico, in una linea che accomuna la moltiplicazione dei punti di vista, propria del romanzo polifonico secondo Bachtin, alla pluralità di prospettive del discorso scientifico. Dopo un primo capitolo teorico, nel secondo e nel terzo capitolo della tesi i romanzi di Volponi vengono studiati in rapporto al filone dell’«epica moderna» e al genere satirico, che ha un suo modello fondativo nell’opera di Giacomo Leopardi. Il quarto capitolo si focalizza sulle ultime raccolte poetiche, che mostrano la tendenza a recuperare il linguaggio formulare e la matrice orale della poesia delle origini, servendosene per rappresentare in funzione contrappuntistica l’universo globale dell’età contemporanea.

Comparing Different Approaches for Clustering Categorical Data

There are different ways to do cluster analysis of categorical data in the literature and the choice among them is strongly related to the aim of the researcher, if we do not take into account time and economical constraints. Main approaches for clustering are usually distinguished into model-based and distance-based methods: the former assume that objects belonging to the same class are similar in the sense that their observed values come from the same probability distribution, whose parameters are unknown and need to be estimated; the latter evaluate distances among objects by a defined dissimilarity measure and, basing on it, allocate units to the closest group. In clustering, one may be interested in the classification of similar objects into groups, and one may be interested in finding observations that come from the same true homogeneous distribution. But do both of these aims lead to the same clustering? And how good are clustering methods designed to fulfil one of these aims in terms of the other? In order to answer, two approaches, namely a latent class model (mixture of multinomial distributions) and a partition around medoids one, are evaluated and compared by Adjusted Rand Index, Average Silhouette Width and Pearson-Gamma indexes in a fairly wide simulation study. Simulation outcomes are plotted in bi-dimensional graphs via Multidimensional Scaling; size of points is proportional to the number of points that overlap and different colours are used according to the cluster membership.

Advanced spectroscopic techniques and chemometric analysis for atmospheric organic aerosol characterization and source apportionment

Atmospheric aerosol particles directly impact air quality and participate in controlling the climate system. Organic Aerosol (OA) in general accounts for a large fraction (10–90%) of the global submicron (PM1) particulate mass. Chemometric methods for source identification are used in many disciplines, but methods relying on the analysis of NMR datasets are rarely used in atmospheric sciences. This thesis provides an original application of NMR-based chemometric methods to atmospheric OA source apportionment. The method was tested on chemical composition databases obtained from samples collected at different environments in Europe, hence exploring the impact of a great diversity of natural and anthropogenic sources. We focused on sources of water-soluble OA (WSOA), for which NMR analysis provides substantial advantages compared to alternative methods. Different factor analysis techniques are applied independently to NMR datasets from nine field campaigns of the project EUCAARI and allowed the identification of recurrent source contributions to WSOA in European background troposphere: 1) Marine SOA; 2) Aliphatic amines from ground sources (agricultural activities, etc.); 3) Biomass burning POA; 4) Biogenic SOA from terpene oxidation; 5) “Aged” SOAs, including humic-like substances (HULIS); 6) Other factors possibly including contributions from Primary Biological Aerosol Particles, and products of cooking activities. Biomass burning POA accounted for more than 50% of WSOC in winter months. Aged SOA associated with HULIS was predominant (> 75%) during the spring-summer, suggesting that secondary sources and transboundary transport become more important in spring and summer. Complex aerosol measurements carried out, involving several foreign research groups, provided the opportunity to compare source apportionment results obtained by NMR analysis with those provided by more widespread Aerodyne aerosol mass spectrometers (AMS) techniques that now provided categorization schemes of OA which are becoming a standard for atmospheric chemists. Results emerging from this thesis partly confirm AMS classification and partly challenge it.

Servizi di posizionamento e potenzialità degli atti di aggiornamento cartografico in coordinate assolute ETRF2000

Il contesto nazionale è cambiato recentemente per l’introduzione del nuovo Sistema Geodetico coincidente con quello Europeo (ETRS89, frame ETRF00) e realizzato dalle stazioni della Rete Dinamica Nazionale. Sistema geodetico, associato al cartografico UTM_ETRF00, divenuto per decreto obbligatorio nelle Pubbliche Amministrazioni. Questo cambiamento ha consentito di ottenere rilevamenti dei dati cartografici in coordinate assolute ETRF00 molto più accurate. Quando i dati così rilevati vengono utilizzati per aggiornamenti cartografici perdono le coordinate originarie e vengono adattati a particolari cartografici circostanti. Per progettare una modernizzazione delle mappe catastali e delle carte tecniche finalizzata a consentire l’introduzione degli aggiornamenti senza modificarne le coordinate assolute originarie, lo studio è iniziato valutando come utilizzare sviluppi di strutturazione dei dati topografici presenti nel Database Geotopografico, modellizzazioni 3D di fabbricati nelle esperienze catastali INSPIRE, integrazioni in ambito MUDE tra progetti edilizi e loro realizzazioni. Lo studio è proseguito valutando i servizi di posizionamento in tempo reale NRTK presenti in Italia. Inoltre sono state effettuate sperimentazioni per verificare anche in sede locale la precisione e l’affidabilità dei servizi di posizionamento presenti. La criticità della cartografia catastale deriva sostanzialmente dal due fatti: che originariamente fu inquadrata in 850 Sistemi e successivamente fu trasformata in Roma40 con una esigua densità di punti rimisurati; che fino al 1988 fu aggiornata con modalità non rigorose di bassa qualità. Per risolvere tali criticità si è quindi ipotizzato di sfruttare le modalità di rilevamento NRTK per aumentare localmente la densità dei punti rimisurati e reinquadrare le mappe catastali. Il test, realizzato a Bologna, ha comportato un’analisi preliminare per individuare quali Punti Fiduciali considerare coerenti con le specifiche cartografiche per poi utilizzarli e aumentare localmente la densità dei punti rimisurati. La sperimentazione ha consentito la realizzazione del progetto e di inserire quindi i prossimi aggiornamenti senza modificarne le coordinate ETRF00 ottenute dal servizio di posizionamento.

A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Criteri e strumenti per l'applicazione dell'H-BIM. La gestione digitalizzata dei processi tra teoria e prassi

La ricerca si pone l’obiettivo di analizzare strumenti e metodi per l’applicazione dell’H-BIM comprendendone le criticità e fornendo soluzioni utili in questo campo. Al contempo la finalità non è circoscrivibile alla semplice produzione di modelli 3D semanticamente strutturati e parametrici a partire da una nuvola di punti ottenuta con un rilievo digitale, ma si propone di definire i criteri e le metodiche di applicazione delle H-BIM all’interno dell’intero processo. L’impostazione metodologica scelta prevede un processo che parte dalla conoscenza dello stato dell’arte in tema di H-BIM con lo studio dell’attuale normativa in materia e i casi studio di maggior rilevanza. Si è condotta una revisione critica completa della letteratura in merito alla tecnologia BIM e H-BIM, analizzando esperienze di utilizzo della tecnologia BIM nel settore edile globale. Inoltre, al fine di promuovere soluzioni intelligenti all’interno del Facility Management è stato necessario analizzare le criticità presenti nelle procedure, rivedere i processi e i metodi per raccogliere e gestire i dati, nonché individuare le procedure adeguate per garantire il successo dell’implementazione. Sono state evidenziate le potenzialità procedurali e operative legate all’uso sistematico delle innovazioni digitali nell’ottica del Facility Management, oltre che allo studio degli strumenti di acquisizione ed elaborazione dei dati e di post-produzione. Si è proceduto al testing su casi specifici per l’analisi della fase di Scan-to-BIM, differenziati per tipologia di utilizzo, data di costruzione, proprietà e localizzazione. Il percorso seguito ha permesso di porre in luce il significato e le implicazioni dell’utilizzo del BIM nell’ambito del Facility Management, sulla base di una differenziazione delle applicazioni del modello BIM al variare delle condizioni in essere. Infine, sono state definite le conclusioni e formulate raccomandazioni riguardo al futuro utilizzo della tecnologia H-BIM nel settore delle costruzioni. In particolare, definendo l’emergente frontiera del Digital Twin, quale veicolo necessario nel futuro della Costruzione 4.0.