🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.013412s)
  1. Unsupervised Topological Learning for Identification of Atomic Structures (2022)

    Sébastien Becker, Emilie Devijver, Rémi Molinier, Noël Jakse
    Abstract We propose an unsupervised learning methodology with descriptors based on topological data analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a priori knowledge, our method allows for an autonomous identification of clusters of atomic structures through a Gaussian mixture model. We apply successfully this approach to the analysis of elemental Zr in the crystalline and liquid states as well as homogeneous nucleation events under deep undercooling conditions. This opens the way to deeper and autonomous study of complex phenomena in materials at the atomic scale.
  2. Unveiling Patterns of International Communities in a Global City Using Mobile Phone Data (2015)

    Paolo Bajardi, Matteo Delfino, André Panisson, Giovanni Petri, Michele Tizzoni
    Abstract We analyse a large mobile phone activity dataset provided by Telecom Italia for the Telecom Big Data Challenge contest. The dataset reports the international country codes of every call/SMS made and received by mobile phone users in Milan, Italy, between November and December 2013, with a spatial resolution of about 200 meters. We first show that the observed spatial distribution of international codes well matches the distribution of international communities reported by official statistics, confirming the value of mobile phone data for demographic research. Next, we define an entropy function to measure the heterogeneity of the international phone activity in space and time. By comparing the entropy function to empirical data, we show that it can be used to identify the city’s hotspots, defined by the presence of points of interests. Eventually, we use the entropy function to characterize the spatial distribution of international communities in the city. Adopting a topological data analysis approach, we find that international mobile phone users exhibit some robust clustering patterns that correlate with basic socio-economic variables. Our results suggest that mobile phone records can be used in conjunction with topological data analysis tools to study the geography of migrant communities in a global city.