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Singularity theory and its applications to differential geometry, differential equations and computer vision

Grant number: 19/07316-0
Support Opportunities:Research Projects - Thematic Grants
Duration: August 01, 2019 - July 31, 2025
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Farid Tari
Grantee:Farid Tari
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Pesquisadores principais:
João Do Espirito Santo Batista Neto ; João Nivaldo Tomazella ; Moacir Antonelli Ponti
Associated researchers:Ana Claudia Nabarro ; Antonio Castelo Filho ; Bruna Orefice Okamoto ; Daiane Alice Henrique Ament ; Débora Lopes da Silva ; Douglas Hilário da Cruz ; Fabio Scalco Dias ; Francisco Braun ; James William Bruce ; Jaume Llibre Salo ; Jorge Luiz Deolindo Silva ; Lakehal Belarbi ; Leandro Nery de Oliveira ; Luciana de Fátima Martins ; Luis Fernando de Osório Mello ; Marcelo Escudeiro Hernandes ; Maria Elenice Rodrigues Hernandes ; Míriam Garcia Manoel ; Mostafa Salarinoghabi ; Ronaldo Alves Garcia
Associated scholarship(s):23/17907-0 - Curvature Estimation Using Machine Learning Algorithms, BP.IC
23/11669-0 - Multi-local singularities of k-folding maps on curves and surfaces., BP.DR
23/15751-3 - 3D Reconstruction of Human Faces: a Laplacian Approach, BP.IC
+ associated scholarships 23/09684-1 - Topology of polynomial maps through their bifurcation locus, BP.DR
23/09727-2 - Invariants of singular germs and Newton polyedra, BP.MS
23/10748-4 - Gröbner Bases: A first contact, BP.IC
23/10828-8 - Singularities of germs of smooth functions, BP.IC
22/10370-9 - On the geometry of singular surfaces, BP.PD
22/10661-3 - Discrete differential geometry from a singularity theory view point, BP.IC
22/06325-8 - Geometric deformations of singularities, BP.PD
22/00133-0 - Geometric bifurcations of singular plane curves, BP.MS
22/01501-2 - Algebraic theory of graphs and neural networks, BP.IC
21/08895-3 - Qualitative theory of differential equations in the plane: topological classification results, BP.MS
21/02932-4 - On k-folding map-germs and hidden symmetries of curves in the Euclidean plane, BP.MS
21/03830-0 - Deep multi-domain representations for analyzing social media posts, BP.IC
21/02923-5 - Discrete differential geometry of plane curves from a singularity theory viewpoint, BP.IC
20/16475-1 - Mapping representations between different domains and subspaces using geometric deep learning, BP.IC
20/10888-2 - Equisingularity of families of surfaces with non-isolated singularities, BP.PD
20/07224-5 - Image curves reconstruction by means of robust features, BP.IC
20/04143-4 - Dynamics of piecewise smooth functions on the interval, BP.IC
19/19714-0 - Apparent contour of surfaces in R3 and extensions of Koenderink's formula, BP.MS - associated scholarships

Abstract

Singularity theory deals with the study of singular varieties and mappings. It is a well established theory and gained wide interestdue to its applications to various areas of science and its interaction with several areas of mathematics. It has applications to, among others, optics, robotics and computer vision. The project has four central research directions: one deals with problems in singularity theory proper, and the other three consider applications of this theory to differential geometry, differential equations, computer vision and image analysis. The project will continue the work of the team in these area of research and will start two new lines of research on the study of vector fields from an infinitesimal point of view and recognition of images using a geometric approach. The problems are challenging, ambitious and innovative, both from a theoretical point of view and applications. The team, formed by internationally renowned researchers and with its extensive and varied experience, is well prepared to face the challenges of the project. It is worth emphasising that a part of the project is multi-disciplinary an envolves mathematicians as well as computer scientists. In addition to the expected scientific results, the team will contribute to the training of human resources through the supervision of undergraduate, doctoral and post-doctoral students, and dissemination of scientific knowledge. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (30)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
LIMA-PEREIRA, B. K.; NUNO-BALLESTEROS, J. J.; OREFICE-OKAMOTO, B.; TOMAZELLA, J. N.. THE RELATIVE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A HYPERSURFACE. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 64, n. 3, p. 662-674, . (19/07316-0)
MANOEL, MIRIAM; OLIVEIRA, LEANDRO N.. EQUIVARIANT MAPPINGS AND INVARIANT SETS ON MINKOWSKI SPACE. Colloquium Mathematicum, v. 167, n. 1, . (19/07316-0)
IZUMIYA, SHYUICHI; NABARRO, ANA CLAUDIA; SACRAMENTO, ANDREA DE JESUS. CURVES IN A SPACELIKE HYPERSURFACE IN MINKOWSKI SPACE-TIME. OSAKA JOURNAL OF MATHEMATICS, v. 58, n. 4, p. 947-966, . (19/07316-0, 16/19139-7)
FERRAZ RIBEIRO, LEO SAMPAIO; BUI, TU; COLLOMOSSE, JOHN; PONTI, MOACIR; IEEE COMP SOC. Scene Designer: a Unified Model for Scene Search and Synthesis from Sketch. 2021 IEEE/CVF INTERNATIONAL CONFERENCE ON COMPUTER VISION WORKSHOPS (ICCVW 2021), v. N/A, p. 10-pg., . (19/02808-1, 17/22366-8, 19/07316-0)
DOS SANTOS, FERNANDO PEREIRA; THUME, GABRIELA SALVADOR; PONTI, MOACIR ANTONELLI; IEEE COMP SOC. Data Augmentation Guidelines for Cross-Dataset Transfer Learning and Pseudo Labeling. 2021 34TH SIBGRAPI CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI 2021), v. N/A, p. 8-pg., . (19/07316-0)
BRAUN, FRANCISCO; FERNANDES, FILIPE. On Reeb components of nonsingular polynomial differential systems on the real plane. Journal of Differential Equations, v. 320, p. 10-pg., . (19/07316-0, 20/14498-4)
CASTELO, ANTONIO; BUENO, LUCAS MOUTINHO; GAMEIRO, MARCIO. A combinatorial marching hypercubes algorithm. COMPUTERS & GRAPHICS-UK, v. 102, p. 67-77, . (13/07375-0, 19/06249-7, 19/07316-0, 17/25631-4)
BRAGA, DENIS DE CARVALHO; DA FONSECA, ALEXANDER FERNANDES; MELLO, LUIS FERNANDO; RIBEIRO, RONISIO MOISES; PESSOA, CLAUDIO GOMES. Crossing Limit Cycles Bifurcating from Two or Three Period Annuli in Discontinuous Planar Piecewise Linear Hamiltonian Differential Systems with Three Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 33, n. 10, p. 17-pg., . (19/10269-3, 19/07316-0, 23/04061-6)
CAVALLARI, GABRIEL B.; PONTI, MOACIR A.; IEEE COMP SOC. Semi-supervised siamese network using self-supervision under scarce annotation improves class separability and robustness to attack. 2021 34TH SIBGRAPI CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI 2021), v. N/A, p. 8-pg., . (19/07316-0, 19/02033-0)
CASTRO, AUGUSTO R.; GRASSI JR, VALDIR; PONTI, MOACIR A.; FARINELLA, GM; RADEVA, P; BOUATOUCH, K. Deep Depth Completion of Low-cost Sensor Indoor RGB-D using Euclidean Distance-based Weighted Loss and Edge-aware Refinement. PROCEEDINGS OF THE 17TH INTERNATIONAL JOINT CONFERENCE ON COMPUTER VISION, IMAGING AND COMPUTER GRAPHICS THEORY AND APPLICATIONS (VISAPP), VOL 4, v. N/A, p. 9-pg., . (19/07316-0)
BRANDER, DAVID; TARI, FARID. Wave maps and constant curvature surfaces: singularities and bifurcations. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, v. 23, n. 1, p. 37-pg., . (19/07316-0)
DOS SANTOS, FERNANDO P.; ZOR, CEMRE; KITTLER, JOSEF; PONTI, MOACIR A.. Learning image features with fewer labels using a semi-supervised deep convolutional network. NEURAL NETWORKS, v. 132, p. 131-143, . (19/07316-0, 18/22482-0)
DO COUTO FERNANDES, MARCO ANTONIO; TARI, FARID. ON THE MULTIPLICITY OF UMBILIC POINTS. PACIFIC JOURNAL OF MATHEMATICS, v. 319, n. 1, p. 29-pg., . (19/07316-0)
BRAUN, FRANCISCO; FERNANDES, FILIPE. Very degenerate polynomial submersions and counterexamples to the real Jacobian conjecture. Journal of Pure and Applied Algebra, v. 227, n. 8, p. 10-pg., . (20/14498-4, 19/07316-0)
SAMPAIO FERRAZ RIBEIRO, LEO; BUI, TU; COLLOMOSSE, JOHN; PONTI, MOACIR. Scene designer: compositional sketch-based image retrieval with contrastive learning and an auxiliary synthesis task. MULTIMEDIA TOOLS AND APPLICATIONS, v. N/A, p. 23-pg., . (19/02808-1, 17/22366-8, 19/07316-0)
CASTELO, SONIA; PONTI, MOACIR; MINGHIM, ROSANE. A Visual Mining Approach to Improved Multiple- Instance Learning. ALGORITHMS, v. 14, n. 12, . (19/07316-0, 13/25055-2)
OLIVEIRA DE RESENDE, DAMARES CRYSTINA; PONTI, MOACIR ANTONELLI. obust image features for classification and zero-shot tasks by merging visual and semantic attribute. NEURAL COMPUTING & APPLICATIONS, v. 34, n. 6, . (18/22482-0, 19/07316-0)
DIAS, FABIO SCALCO; MELLO, LUIS FERNANDO; VALLS, CLAUDIA. Kukles Systems of Degree Three with Global Centers. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 54, n. 4, p. 15-pg., . (19/07316-0)
BRAUN, FRANCISCO; GONCALVES DIAS, LUIS RENATO; SANTOS, JEAN VENATO. ON GLOBAL INVERTIBILITY OF SEMI-ALGEBRAIC LOCAL DIFFEOMORPHISMS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 58, n. 2, p. 713-730, . (17/00136-0, 19/07316-0)
DIAS, FABIO SCALCO; MELLO, LUIS FERNANDO. Globally Asymptotically Stable Equilibrium Points in Kukles Systems. Qualitative Theory of Dynamical Systems, v. 19, n. 3, p. 7-pg., . (19/07316-0)
PONTI, MOACIR A.; DOS SANTOS, FERNANDO P.; RIBEIRO, LEO S. F.; CAVALLARI, GABRIEL B.; IEEE COMP SOC. Training Deep Networks from Zero to Hero: avoiding pitfalls and going beyond. 2021 34TH SIBGRAPI CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI 2021), v. N/A, p. 8-pg., . (19/07316-0, 17/22366-8, 19/02033-0)
DIAS, FABIO FELIX; PONTI, MOACIR ANTONELLI; MINGHIM, ROSANE. classification and quantification approach to generate features in soundscape ecology using neural network. NEURAL COMPUTING & APPLICATIONS, v. 34, n. 3, SI, . (19/07316-0)
DIAS, FABIO SCALCO; RIBEIRO, RONISIO MOISES; VALLS, CLAUDIA. Global Phase Portraits for the Kukles Systems of Degree 3 with Z(2)-Reversible Symmetries. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 31, n. 06, . (19/07316-0)
ALVES, ALEXANDRE; SALARINOGHABI, MOSTAFA. ON THE FAMILY OF CUBIC PARABOLIC POLYNOMIALS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. N/A, p. 14-pg., . (19/07316-0)
DIAS, FABIO SCALCO; MELLO, LUIS FERNANDO. Polynomial Vector Fields on Algebraic Surfaces of Revolution. Results in Mathematics, v. 76, n. 1, . (19/07316-0)
CASANOVA, EDRESSON; WEBER, JULIAN; SHULBY, CHRISTOPHER; CANDIDO JUNIOR, ARNALDO; GOELGE, EREN; PONTI, MOACIR ANTONELLI; CHAUDHURI, K; JEGELKA, S; SONG, L; SZEPESVARI, C; et al. YourTTS: Towards Zero-Shot Multi-Speaker TTS and Zero-Shot Voice Conversion for Everyone. INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 162, v. N/A, p. 12-pg., . (19/07316-0)
SANCHIS, GUILLERMO PENAFORT; TARI, FARID. On k-folding map-germs and hidden symmetries of surfaces in the Euclidean 3-space. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 45-pg., . (19/07316-0)
BRAGA, DENIS DE CARVALHO; DIAS, FABIO SCALCO; LLIBRE, JAUME; MELLO, LUIS FERNANDO. The discontinuous matching of two globally asymptotically stable crossing piecewise smooth systems in the plane do not produce in general a piecewise differential system globally asymptotically stable. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. N/A, p. 8-pg., . (19/07316-0)
CANDIDO, DOUGLAS MODESTO; DIAS, FABIO SCALCO; MELLO, LUIS FERNANDO. Global Phase Portraits of Ordinary Differential Equations Modeling the Acute Promyelocytic Leukemia. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, v. N/A, p. 18-pg., . (19/07316-0)
BRAUN, FRANCISCO; MEZA-SARMIENTO, INGRID S.. Topological equivalence of submersion functions and topological equivalence of their foliations on the plane: The linear-like case. Journal of Mathematical Analysis and Applications, v. 521, n. 2, p. 25-pg., . (20/14498-4, 19/07316-0)

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