Search results for “group theory”

A proof of Raynaud's theorem: every finite flat commutative group scheme over a locally noetherian base embeds, Zariski-locally, as a closed subgroup of an abelian scheme.

Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.

With the increasing popularity of cashless payment methods for everyday, seasonal and special expenses popular banks accumulate huge amount of data about customer operations. In the article, we report a successful application of topic modelling to extract behaviour patterns from the data. The resulting models are built with BigARTM framework: flexible and efficient tool for topic modelling. The framework allows us to experiment with various models including PLSA, LDA and beyond. Results demonstrate ability of the approach to aggregate information about behaviour patterns of different customer groups. The results analysis allows to see the topics of such people clusters varying from travellers to mortgage holders. Moreover, low-dementional embeddings of the customers, which was given with topic model, were studied. We display that the client vector representations store demographic information as well as source data. We also test for a best way of preparing data for the model with metric above in mind.