Silhueta de pessoa indiferenciada

Daniel Graça

Professor associado com agregação
Faculdade de Ciências e Tecnologia
Centro de Estudos e de Desenvolvimento da Matemática no Ensino Superior
Subsistema
Docentes Universitário
Unidade ID
Centro de Estudos e de Desenvolvimento da Matemática no Ensino Superior
Unidade ID externa
Instituto de Telecomunicações (IT)
Regime
Exclusividade
Vínculo
CT em Funções Públicas por tempo indeterminado
Daniel Graça. Concluiu o Título de Agregado em Matemática em 2018/06/08 pela Universidade de Lisboa - Instituto Superior Técnico, Doutoramento em Matemática em 2007/09/05 pela Universidade de Lisboa - Instituto Superior Técnico, Mestrado em Matemática Aplicada em 2002/09/06 pela Universidade de Lisboa - Instituto Superior Técnico e Licenciatura em Matemática em 2000/07/07 pela Universidade do Algarve. É Investigador no Instituto de Telecomunicações, Professor Associado na Universidade do Algarve e Investigador na Universidade de Aveiro - Centro de Investigação e Desenvolvimento em Matemática e Aplicações. Publicou 31 artigos em revistas especializadas. Possui 4 capítulos de livros. Recebeu 3 prémios e/ou homenagens. Participa e/ou participou como Investigador em 1 projeto. Atua na área de Ciências Exatas com ênfase em Matemática. No seu currículo Ciência Vitae os termos mais frequentes na contextualização da produção científica, tecnológica e artístico-cultural são: Computational models which use real numbers; Computation with dynamical systems; Computability theory; Computational complexity; .

Atividades

Atividades
Membro de associação. Association Computability in Europe. Member of the Council.

Projetos

Projetos
2017/04/01 - 2023/03/31. Computing with Infinite Data, H2020: MSCA-RISE - Research and Innovation Staff Exchange. Investigador. Universidade do Algarve.

Produções

Daniel Graça; Cristóbal Rojas; Ning Zhong. 2018. "Computing geometric Lorenz attractors with arbitrary precision". Transactions of the American Mathematical Society, 370 (-): 2955-2970. https://doi.org/10.1090/tran/7228
Daniel S. Graça; Ning Zhong. 2018. Computability of Ordinary Differential Equations. https://doi.org/10.1007/978-3-319-94418-0_21
Olivier Bournez; Daniel Graça; Amaury Pouly. 2017. "Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length". Journal of the ACM, 64 (6): Article no. 38-Article no. 38. https://doi.org/10.1145/3127496
Olivier Bournez; Daniel Graça; Amaury Pouly. 2017. "On the Functions Generated by the General Purpose Analog Computer". Information and Computation, To appear (To appear): To appear-To appear. https://doi.org/10.1016/j.ic.2017.09.015
Olivier Bournez; Daniel Graça; Amaury Pouly. 2016. "Computing with polynomial ordinary differential equations". Journal of Complexity, 36 (-): 106-140. https://doi.org/10.1016/j.jco.2016.05.002
Amaury Pouly; Daniel Graça. 2016. "Computational complexity of solving polynomial differential equations over unbounded domains". Theoretical Computer Science, 626 (2): 67-82. https://doi.org/10.1016/j.tcs.2016.02.002
Graça, Daniel. 2016. "Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length - The General Purpose Analog Computer and Computable Analysis are two efficiently equivalent models of computations". https://doi.org/10.4230/LIPIcs.ICALP.2016.109
Daniel Graça; Ning Zhong. 2015. "An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable". Theory of Computing Systems, 57 (2): 478-520. https://doi.org/10.1007/s00224-015-9609-5
Graça, Daniel. 2015. "Rigorous numerical computation of polynomial differential equations over unbounded domains". 469-473. Vol. 9582. https://doi.org/10.1007/978-3-319-32859-1
Graça, Daniel. 2013. "Turing machines can be efficiently simulated by the General Purpose Analog Computer". https://doi.org/10.1007/978-3-642-38236-9_16
Bournez, O.; Graça, D.S.; Pouly, A.; Zhong, N.. 2013. "Computability and computational complexity of the evolution of nonlinear dynamical systems". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7921 LNCS: 12-21. https://doi.org/10.1007/978-3-642-39053-1_2
Bournez, O.; Graça, D.S.; Hainry, E.. 2013. "Computation with perturbed dynamical systems". Journal of Computer and System Sciences, 79 (5): 714-724. https://doi.org/10.1016/j.jcss.2013.01.025
Bournez, O.; Graça, D.S.; Pouly, A.. 2012. "On the complexity of solving initial value problems". Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 115-121. https://doi.org/10.1145/2442829.2442849
Graça, D.S.; Zhong, N.; Buescu, J.. 2012. "Computability, noncomputability, and hyperbolic systems". Applied Mathematics and Computation, 219 (6): 3039-3054. https://doi.org/10.1016/j.amc.2012.09.031
Graa, D.S.; Zhong, N.; Dumas, H.S.. 2012. "The connection between computability of a nonlinear problem and its linearization: The HartmanGrobman theorem revisited". Theoretical Computer Science, 457: 101-110. https://doi.org/10.1016/j.tcs.2012.07.013
Graça, D.S.. 2012. "Noncomputability, unpredictability, and financial markets". Complexity, 17 (6): 24-30. https://doi.org/10.1002/cplx.21395
Graça, D.; Zhong, N.. 2011. "Computability in planar dynamical systems". Natural Computing, 10 (4): 1295-1312. https://doi.org/10.1007/s11047-010-9230-0
Bournez, O.; Graça, D.S.; Pouly, A.. 2011. "Solving analytic differential equations in polynomial time over unbounded domains". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6907 LNCS: 170-181. https://doi.org/10.1007/978-3-642-22993-0_18
Graça, Daniel. 2011. "Computability and Dynamical Systems". https://doi.org/10.1007/978-3-642-11456-4_11
Bournez, O.; Graça, D.S.; Hainry, E.. 2010. "Robust computations with dynamical systems". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6281 LNCS: 198-208. https://doi.org/10.1007/978-3-642-15155-2_19
Graça, D.S.; Zhong, N.. 2009. "Computing domains of attraction for planar dynamics". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5715 LNCS: 179-190. https://doi.org/10.1007/978-3-642-03745-0_22
Graa, D.S.; Buescu, J.; Campagnolo, M.L.. 2009. "Computational bounds on polynomial differential equations". Applied Mathematics and Computation, 215 (4): 1375-1385. https://doi.org/10.1016/j.amc.2009.04.055
Collins, P.; Graça, D.S.. 2009. "Effective computability of solutions of differential inclusions the ten thousand monkeys approach". Journal of Universal Computer Science, 15 (6): 1162-1185. http://www.scopus.com/inward/record.url?eid=2-s2.0-67650731821&partnerID=MN8TOARS
Graça, D.S.; Zhong, N.; Buescu, J.. 2009. "Computability, noncomputability and undecidability of maximal intervals of IVPS". Transactions of the American Mathematical Society, 361 (6): 2913-2927. https://doi.org/10.1090/S0002-9947-09-04929-0
Collins, P.; Graça, D.S.. 2008. "Effective Computability of Solutions of Ordinary Differential Equations The Thousand Monkeys Approach". Electronic Notes in Theoretical Computer Science, 221 (C): 103-114. https://doi.org/10.1016/j.entcs.2008.12.010
Graça, D.S.; Buescu, J.; Campagnolo, M.L.. 2008. "Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs". Electronic Notes in Theoretical Computer Science, 202 (C): 49-57. https://doi.org/10.1016/j.entcs.2008.03.007
Graça, D.S.; Campagnolo, M.L.; Buescu, J.. 2008. "Computability with polynomial differential equations". Advances in Applied Mathematics, 40 (3): 330-349. https://doi.org/10.1016/j.aam.2007.02.003
Bournez, O.; Campagnolo, M.L.; Graça, D.S.; Hainry, E.. 2007. "Polynomial differential equations compute all real computable functions on computable compact intervals". Journal of Complexity, 23 (3): 317-335. https://doi.org/10.1016/j.jco.2006.12.005
Bournez, O.; Campagnolo, M.L.; Graça, D.S.; Hainry, E.. 2006. "The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3959 LNCS: 631-643. https://doi.org/10.1007/11750321_60
Graça, D.S.; Campagnolo, M.L.; Buescu, J.. 2005. "Robust simulations of Turing machines with analytic maps and flows". Lecture Notes in Computer Science, 3526: 169-179. http://www.scopus.com/inward/record.url?eid=2-s2.0-26444476497&partnerID=MN8TOARS
Graça, D.S.. 2004. "Some recent developments on Shannon's General Purpose Analog Computer". Mathematical Logic Quarterly, 50 (4-5): 473-485. https://doi.org/10.1002/malq.200310113
Graça, Daniel; Ning Zhong. 2021. "Computability of Differential Equations". Em Handbook of Computability and Complexity in Analysis, editado por Vasco Brattka; Peter Hertling. Springer. https://www.springer.com/gp/book/9783030592332
Daniel S. Graça; Ning Zhong. 2021. "Computability of Limit Sets for Two-Dimensional Flows". 494-503. Springer International Publishing. https://doi.org/10.1007/978-3-030-80049-9_48
Daniel S. Graça; Ning Zhong. 2022. "Computing the exact number of periodic orbits for planar flows". Transactions of the American Mathematical Society. https://doi.org/10.1090/tran/8644
Graça, Daniel; Zhong, Ning. 2021. "The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable". Theoretical Computer Science, 895: 48-54. https://doi.org/10.1016/j.tcs.2021.09.028
Olivier Bournez; Riccardo Gozzi; Daniel S. Graça; Amaury Pouly. 2023. "A continuous characterization of PSPACE using polynomial ordinary differential equations". Journal of Complexity, 77: 101755-101755. https://doi.org/10.1016/j.jco.2023.101755
Riccardo Gozzi; Daniel Graça. 2023. "Characterizing time computational complexity classes with polynomial differential equations". Computability, 12 (1): 23-57. https://doi.org/10.3233/com-210384
Daniel Graça; Ning Zhong. 2023. "Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines". Computability, 117-144. https://doi.org/10.3233/com-210381
 

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