Recent Talks

• Calculational Proofs for Relational Graphical Linear Algebra (english)

• Álgebra Linear Gráfica (portuguese)

• Interpretações e Visualizações de Redes Neurais (portuguese)

• Aplicações de Cálculo e Álgebra Linear para alunos do DCC (portuguese)

Publications 

Google Scholar

• Victor Ghissoni, Júlia Mota, João Paixão, Lucas Rufino. Point-free calculational proofs and program derivation in Linear Algebra using a graphical syntax. 2024  Submitted.

• Bruno Hryniewicz, Fernando França  João Paixão, Laura O. Moraes.  Biblioteca para exemplificação no ensino de Álgebra Linear  (2024).  EduComp’24 [link]

• Taina Souza, Mônica Ferreira Da Silva, João Paixão, Renato Alves, Roberta Bordalo and Waldir Siqueira Moura Computational Linear Algebra to identify potential students with ADHD: pairing data compression and K-means (2022). The 22nd IEEE International Conference on Advanced Learning Technologies.

• João Paixão, Lucas Rufino, Pawel Sobocinski (2022). High-level Axioms for Graphical Linear Algebra. Science of Computer Programming [link]

• Fabiano P. Martins; João Paixão; Claudio M. de Farias; Flávia C. Delicato (2021). Hercules: A context-aware multiple application and multisensor data fusion algorithm. [link]

• Caio Sena,  João Paixão,  José Ricardo de Almeida França (2021). A Topological Data Analysis approach for retrieving Local Climate Zones patterns in satellite data. Environmental Challenges [link]

• Thomas Lewiner, Tiago Novello, João Paixão, Carlos Tomei (2021). Discrete Gradient Line Fields on Surfaces.  Topology and Its Applications. [link]

• Joao Paixao and Pawel Sobocinski, "Calculational Proofs in Relational Graphical Linear Algebra", In 23rd Brazilian Symposium on Formal Methods (SBMF 2020), 2020 (Best paper award). [PDF]

• Daniel Vieira, Joao Paixao (2019). Vector Field Neural Networks. arXiv preprint arXiv:1905.07033.[PDF]

• Joao Paixao, Joao Lagoas, Thomas Lewiner, Tiago Novello (2018). Greedy Morse matchings and discrete smoothness. arXiv preprint arXiv:1801.10118.

• Daniel Vieira, Fabio Rangel, Fabricio Firmino, Joao Paixao (2018). Vector Field Based Neural Networks. arXiv preprint arXiv:1802.08235.

• Thomas Lewiner, Tiago Novello, João Paixão, Carlos Tomei (2017). Discrete Gradient Line Fields on Surfaces. arXiv preprint arXiv:1712.08136.

• Benjamin A Burton, Thomas Lewiner, Joao Paixao, Jonathan Spreer (2016). Parameterized complexity of discrete Morse theory. ACM Transactions on Mathematical Software (TOMS).

• João Paixão, Jonathan Spreer (2015). Random collapsibility and 3-sphere recognition. arXiv preprint arXiv:1509.07607.

• Benjamin A Burton, Joao Paixao, Jonathan Spreer (2013). Computational topology and normal surfaces: Theoretical and experimental complexity bounds. Proceedings of the Meeting on Algorithm Engineering & Experiments.

• Joao Paixao, Thomas Lewiner (2013). Discrete Morse gradient fields and stable matchings. Symposium on Computational Geometry-Young Researcher Forum.

• Thomas Lewiner, Clarissa Marques, João Paixão, Scarlett de Botton, Allyson Cabral, Renata Nascimento, Vinı́cius Mello, Adelailson Peixoto, Dimas Martinez, Thales Vieira (2011). Stereo music visualization through manifold harmonics. The Visual Computer.

• Renata Nascimento, Joao Paixao, Helio Lopes, Thomas Lewiner (2010). Topology aware vector field denoising. 2010 23rd SIBGRAPI Conference on Graphics, Patterns and Images.

• Thomas Lewiner, Thales Vieira, Alex Bordignon, Allyson Cabral, Clarissa Marques, Joao Paixao, Lis Custodio, Marcos Lage, Maria Andrade, Renata Nascimento, others (2010). Tuning manifold harmonics filters. Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI Conference on.

• João Paixão, Marcos Lage, Fabiano Petronetto, Alex Laier, Sinésio Pesco, Geovan Tavares, Thomas Lewiner, Hélio Lopes (2009). Random walks for vector field denoising. Computer Graphics and Image Processing (SIBGRAPI), 2009 XXII Brazilian Symposium on.

• Paul Baginski, Scott Thomas Chapman, Natalie Hine, João Paixão (2008). On the asymptotic behavior of unions of sets of lengths in atomic monoids. Involve. [PDF]

• Jeff Amos, ST Chapman, Natalie Hine, Joao Paixao (2007). Sets of lengths do not characterize numerical monoids. Integers.

Notes

• My Numerical Methods Blog

• Triangular Inverse

• Subsets (with Lucas Rufino)

• Inequalities (with Lucas Rufino)

• Generic (with Lucas Rufino)

• Number theory (with Lucas Rufino)

About me

Interests

• Computational Geometry

• Computational Topology

• Discrete Morse Theory

• Linear Algebra and Numerical Methods Education

• Graph Theory

• Strings Diagrams

• Graphical Linear Algebra

Education

PhD in Applied Mathematics, 2014
Pontifícia Universidade Católica do Rio de Janeiro

Masters in Applied Mathematics, 2010
Pontifícia Universidade Católica do Rio de Janeiro

BSc in Mathematics, 2007
Virginia Tech

Contact

jpaixao@dcc.ufrj.br

Links

Graphical Linear Algebra Blog 

3Blue1Brown

Students

Júlia Mota (2022).  Visual Relations: A diagrammatic language to teach relations, functions and databases to young children. PhD student. UFRJ

Lucas Rufino (2021). Calculational proofs in quantales and Normal Forms in Graphical Linear Algebra Undergraduate Student (PIBIC). UFRJ

Gabriel Ferreira (2020). Álgebra Linear com Diagramas. Undergraduate Student (PIBIC). UFRJ

Caio Atila Pereira (2020). Tracking spatio-temporal patterns in Atmospheric data through Topological Data Analysis. Masters student with José Ricardo. UFRJ

Guilherme Freire (2019). Sumarização Híbrida com Redes Pointer-Generator. Undergraduate student. UFRJ.

Victor Garritano Noronha (2019). Relacionando Geometricamente Tweets e Notícias Utilizando a Word Mover's Distance. Undergraduate student. UFRJ.

Fabiano de Paula Martins (2019). Um Algoritmo de Fusão de Dados para Ambientes Inteligentes. Undergraduate student. UFRJ.

João Vitor (2019). Generalized Eigenvalue Problems In Linear Hydrodynamic Stability. Undergraduate student with Juliana Valério. UFRJ. (SBMAC Award).

Daniel Vieira (2018). Vector Field Neural Networks. Masters student. UFRJ.

Tiago Novello (2018). Discrete Line Fields on Surfaces. PhD Student with Carlos Tomei. PUC-Rio.

Iago Leal (2017). Discrete Exterior Calculus. Undergraduate student. UFRJ.

João Lagôas (2017). Algoritmos e Triângulações para o Gradiente Discreto. Masters student. UFRJ.