A Java High Performance Tool For Topological Data Analysis
From algebraic topology a new set of algorithms have been derived. These algorithms are identified with “computational topology” or often pointed out as Topological Data Analysis (TDA) and are used for investigating high-dimensional data in a quantitative manner. TDA is largely used for the analysis of complex systems; for instance Ibekwe et al.  used TDA for reconstructing the relationship structure of E. coli O157 and the authors proved that the non-O157 is in 32 soils (16 organic and 16 conventionally managed soils). TDA was also used by De Silva  for the analysis of sensor networks and it was successfully applied to the study of viral evolution in biological complex systems . Petri et al.  used a homological approach for studying the characteristics of functional brain networks at the mesoscopic level. Computational topology algorithms can be divided in two families: topological data compression and topological data completion. Algorithms for topological data compression aims to represent a collection of higher dimensional data points through a graph, the main algorithm is known as Mapper . Topological data completion, conversely, completes data to more complex structures, i.e. simplicial complexes, that can be easiest analyzed. This subset of algorithms is based on Persistent Homology .
In Topology we established the basics of computational topology. In the following we would like to highlight a set of instances of topological data analysis. The following examples can be used by the reader as signpost in his or her personal quest to perform a convenient topological data analysis.
 A M IBEKWE, J MA, D E CROWLEY, C-H YANG, A M JOHNSON, T C PETROSSIAN, AND P Y LUM. Topological data analysis of Escherichia coli O157: H7 and non-O157 survival in soils. Frontiers in cellular and infection microbiology, 4, 2014.
 V DE SILVA AND R GHRIST. Coverage in sensor networks via persistent homology. Algebraic & Geometric Topology, 7(339-358):24, 2007
 J-M CHAN, G CARLSSON, AND R RABADAN. Topology of viral evolution. Proceedings of the National Academy of Sciences, 110(46):18566–18571, 2013.
 G PETRI, P EXPERT, F TURKHEIMER, R CARHART-HARRIS, D NUTT, P J HELLYER, AND F VACCARINO. Homological scaffolds of brain functional networks. Journal of The Royal Society Interface, 11(101):20140873, 2014.
 F MEMOLI, G SINGH AND G CARLSSON. Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. 2007.
 H EDELSBRUNNER AND J HARER. Computational topology: an introduction. American Mathematical Soc., 2010.