The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data

We develop of a line of work initiated by Curto and Itskov towards understanding the amount of information contained in the spike trains of hippocampal place cells via topology considerations. Previously, it was established that simply knowing which groups of place cells fire together in an animal's hippocampus is sufficient to extract the global topology of the animal's physical environment. We model a system where collections of place cells group and ungroup according to short-term plasticity rules. In particular, we obtain the surprising result that in experiments with spurious firing, the accuracy of the extracted topological information decreases with the persistence (beyond a certain regime) of the cell groups. This suggests that synaptic transience, or forgetting, is a mechanism by which the brain counteracts the effects of spurious place cell activity

The Morse theory of \v{C}ech and Delaunay complexes

Given a finite set of points in $\mathbb R^n$ and a radius parameter, we study the \v{C}ech, Delaunay-\v{C}ech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the \v{C}ech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field.Comment: 21 pages, 2 figures, improved expositio

Topological Data Analysis in ATM: the shape of big flight data sets

Flight trajectory data sets are difficult to analyse due to several reasons, from the high interconnectedness of all their factors to the high dimensionality of the data. In this paper we introduce Topological Data Analysis (TDA) and some of its techniques to extract some useful conclusions concerning ATM data. We will show how topology encodes useful information regarding airport analysis using the set of Spanish' airports in the Summer Season of 2018. Finally, we present some conclusions, and some guidelines in order to face new challenges in the ATM area.Comment: 31 page

Persistent homology to analyse 3D faces and assess body weight gain

In this paper, we analyse patterns in face shape variation due to weight gain. We propose the use of persistent homology descriptors to get geometric and topological information about the configuration of anthropometric 3D face landmarks. In this way, evaluating face changes boils down to comparing the descriptors computed on 3D face scans taken at different times. By applying dimensionality reduction techniques to the dissimilarity matrix of descriptors, we get a space in which each face is a point and face shape variations are encoded as trajectories in that space. Our results show that persistent homology is able to identify features which are well related to overweight and may help assessing individual weight trends. The research was carried out in the context of the European project SEMEOTICONS, which developed a multisensory platform which detects and monitors over time facial signs of cardio-metabolic risk