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Statistical Analysis of Topological Descriptors

Student: Demidova Darya

Supervisor: Alexey Naumov

Faculty: Faculty of Computer Science

Educational Programme: Statistical Learning Theory (Master)

Year of Graduation: 2019

Topological data analysis is an actively developing area. In the past five years it has been applied to solving a wide range of problems. This has happened due to the statistical results obtained for the persistent diagrams space, the main object of the TDA. One of the significant areas of TDA application is biological tasks. In this paper, we solved the problem of restoring the topology of a room using neural signals from place cells encoding a spatial location. We developed a method that allows the stable separation of significant topological characteristics of the internal structure of the neural signal. This method can be used to restore the topology of space of any complexity.

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