Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Reservoir characterization of the Cardium Formation in the Ferrier Oilfield, west-central Alberta, Canada.

This thesis has the main aim of defining the lithostratigraphy, depositional architecture, post-depositional modifications and reservoir characteristics of the Cardium Formation in the Ferrier Oilfield, and how these characteristics can have great impact over production rates, GOR and produced fluid discrimination. In the Ferrier area, the Cardium Formation is composed by a NE prograding clastic sequence made up of offshore to shoreface deposits sealed by marine shales. The main reservoir is composed by sandstones and conglomerates interpreted to have deposited in a shoreface depositional environment. Lithofacies and net reservoir thickness mapping led to more detailed understanding of the 3D reservoir architecture, and cross-sections shed light on the Cardium depositional architecture and post-deposition sediment erosion in the Ferrier area. Detailed core logging, thin section, SEM and CL analyses were used to study the mineralogy, texture and pore characterization of the Cardium reservoir, and three main compartments have been identified based on production data and reservoir characteristics. Finally, two situations showing odd production behaviour of the Cardium were resolved. This shed light on the effect of structural features and reservoir quality and thickness over hydrocarbon migration pathways. The Ferrier example offers a unique case of fluid discrimination in clastic reservoirs due both to depositional and post-depositional factors, and could be used as analogue for similar situations in the Western Canadian Sedimentary Basin.

Knowledge-based Chord Embeddings

This thesis develops AI methods as a contribution to computational musicology, an interdisciplinary field that studies music with computers. In systematic musicology a composition is defined as the combination of harmony, melody and rhythm. According to de La Borde, harmony alone "merits the name of composition". This thesis focuses on analysing the harmony from a computational perspective. We concentrate on symbolic music representation and address the problem of formally representing chord progressions in western music compositions. Informally, chords are sets of pitches played simultaneously, and chord progressions constitute the harmony of a composition. Our approach combines ML techniques with knowledge-based techniques. We design and implement the Modal Harmony ontology (MHO), using OWL. It formalises one of the most important theories in western music: the Modal Harmony Theory. We propose and experiment with different types of embedding methods to encode chords, inspired by NLP and adapted to the music domain, using both statistical (extensional) knowledge by relying on a huge dataset of chord annotations (ChoCo), intensional knowledge by relying on MHO and a combination of the two. The methods are evaluated on two musicologically relevant tasks: chord classification and music structure segmentation. The former is verified by comparing the results of the Odd One Out algorithm to the classification obtained with MHO. Good performances (accuracy: 0.86) are achieved. We feed a RNN for the latter, using our embeddings. Results show that the best performance (F1: 0.6) is achieved with embeddings that combine both approaches. Our method outpeforms the state of the art (F1 = 0.42) for symbolic music structure segmentation. It is worth noticing that embeddings based only on MHO almost equal the best performance (F1 = 0.58). We remark that those embeddings only require the ontology as an input as opposed to other approaches that rely on large datasets.