We introduce a method for training neural networks to perform image or volume
segmentation in which prior knowledge about the topology of the segmented object can be …

Topological data analysis refers to approaches for systematically and reliably computing
abstract 'shapes' of complex data sets. There are various applications of topological data …

Graph theory is now becoming a standard tool in system-level neuroscience. However,
endowing observed brain anatomy and dynamics with a complex network structure does not …

The increasing amount of data in biomechanics research has greatly increased the
importance of develo** advanced multivariate analysis and machine learning techniques …

Propelled by a fast evolving landscape of techniques and datasets, data science is growing
rapidly. Against this background, topological data analysis (TDA) has carved itself a niche …

Persistence diagrams are one of the main tools in the field of Topological Data Analysis
(TDA). They contain fruitful information about the shape of data. The use of machine learning …

Persistence landscapes map persistence diagrams into a function space, which may often
be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map …

Functional brain networks are often constructed by quantifying correlations between time
series of activity of brain regions. Their topological structure includes nodes, edges …

We use persistent homology and persistence images as an observable of three variants of
the two-dimensional XY model to identify and study their phase transitions. We examine …

We apply modern methods in computational topology to the task of discovering and
characterizing phase transitions. As illustrations, we apply our method to four two …