21 citations · 47 across the 9 of their papers we have counts for
10 papers
Probing the interference between non-linear, axionic and space-time-anisotropy effects in the QED vacuum
J. M. A. Paixão, L. P. R. Ospedal, M. J. Neves +1
We pursue the investigation of a generic non-linear extension of axionic electrodynamics in a Carroll-Field-Jackiw (CFJ) scenario that implements Lorentz-symmetry violation (LSV).…
The axion-photon mixing in non-linear electrodynamic scenarios
J. M. A. Paixão, L. P. R. Ospedal, M. J. Neves +1
In this contribution, we re-assess some aspects of axionic electrodynamics by coupling non-linear electromagnetic effects to axion physics. We present a number of motivations to ju…
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…
Random collapsibility and 3-sphere recognition
João Paixão, Jonathan Spreer
A triangulation of a -manifold can be shown to be homeomorphic to the -sphere by describing a discrete Morse function on it with only two critical faces, that is, a sequence…
Parameterized Complexity of Discrete Morse Theory
Benjamin A. Burton, Thomas Lewiner, João Paixão +1
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. Howeve…
Computational topology and normal surfaces: Theoretical and experimental complexity bounds
Benjamin A. Burton, João Paixão, Jonathan Spreer
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to expone…