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In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three ...
Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear eleme ...
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...
When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...
Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions. Complex ne ...
Three-component ParABS systems are widely distributed factors for plasmid partitioning and chromosome segregation in bacteria. ParB acts as adaptor protein between the 16-base pair centromeric parS DNA sequences and the DNA segregation proteins ParA and Sm ...
