1 citations · 1 across the 3 of their papers we have counts for
5 papers
Discrete Line Fields on Surfaces
Tiago Novello, João Paixão, Carlos Tomei +1
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their…
Vector Field Neural Networks
Daniel Vieira, Joao Paixao
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting p…
Vector Field Based Neural Networks
Daniel Vieira, Fabio Rangel, Fabricio Firmino +1
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data…
Greedy Morse matchings and discrete smoothness
Joao Paixao, Joao Lagoas, Thomas Lewiner +1
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a comp…
Discrete Gradient Line Fields on Surfaces
Thomas Lewiner, Tiago Novello, Joao Paixao +1
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector…