This paper shows an image/video application using topological invariants for human gait recognition. Using a background subtraction approach, a stack of silhouettes is extracted from a subsequence and glued through their gravity centers, forming a 3D digital image I . From this 3D representation, the border simplicial complex ∂K(I) is obtained. We order the triangles of ∂K(I) obtaining a sequen...

Persistent homology is a novel multi-scale topological method that is gaining popularity in data analysis. It has proven effective in revealing nonlinear patterns of high-dimensional imaging data that are otherwise undetected by existing mono-scale techniques. Among several descriptors of persistent homology, the recently proposed PL possess many desirable properties for rigorous statistical in...

References Books [1] H. Edelsbrunner and J. Harer Computational topology: An introduction, AMS (2009). (pdf) [2] A. Zomorodian Topology for computing Cambridge Monographs on Applied and Computational Mathematics (No. 16), (2009). (pdf) [3] T. Kaczynski et al. Computational homology Springer (2004). [4] V . Pascucci et al. Topological Methods in Data Analysis and Visualization: Theory, Algorithm...

A recent advance in computational homology gives an order-of-magnitude improvement in applications to neural coding analysis.

The genetic basis for chronic persistence of Brucella abortus in lymphoid organs of mice, cows, and humans is currently unknown. We identified B. abortus genes involved in chronic infection, by assessing the ability of 178 signature-tagged mutants to establish and maintain persistent infection in mice. Each mutant was screened for its ability to colonize the spleens of mice at 2 and 8 weeks aft...

Persistent homology is a powerful notion rooted in topological data analysis which allows for retrieving the essential topological features of an object. The attention on persistent homology is constantly growing in a large number of application domains, such as biology and chemistry, astrophysics, automatic classification of images, sensor and social network analysis. Thus, an increasing numbe...

Technological advances in the past few decades have fueled the exponential growth of “omic” data in biology. Understanding the rules of life from existing omic data sets, which offer unprecedented opportunities for mathematicians, remains an important mission of the field. Biomolecular structurefunction relationship is a major rule of life, and recognizing this relationship is the holy grail of...

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...