| Topic | People | Description |
|---|---|---|
| MSC 60L10 - Signatures and data streams |
Guido Gazzani
Sara Svaluto Ferro |
The field of Signatures and data streams in Rough Analysis focuses on mathematical structures that efficiently capture the information contained in signals or temporal data. Signatures are fundamental tools in Rough Path Theory providing a compact and information-rich numerical representation of data trajectories regardless of their irregularity. By using signatures one can characterize the temporal evolution of a signal without losing essential information facilitating analysis prediction and machine learning on continuous data streams. This approach has applications in finance (for price modeling) natural language processing biomedicine and many other areas where data are sequential or temporal in nature. |
| MSC 60L70 - Algebraic structures and computation |
Sara Svaluto Ferro
|
The field of Algebraic structures and computation in Rough Analysis explores the algebraic structures underlying irregular stochastic processes and develops computational methods for their analysis and application. A central role is played by signature algebras which provide an efficient representation of data trajectories via series of characteristic functions and Hopf algebras fundamental for the symbolic manipulation of series expansions in rough models. This research area has direct implications for numerical computations in rough path theory machine learning on sequential data and the development of efficient algorithms for analyzing complex signals in finance biology and physics. |
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