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2024

• Delfino, G., "Distribuição quântica de chaves: Um estudo sobre a geração quântica de chaves criptográfica clássicas", Master's thesis LNCC, 2024. In portuguese.

2023

• Gustavo A. Bezerra, Raqueline A.M. Santos, Renato Portugal, Quantum Counting on the Complete Bipartite Graph, arXiv:2310.14141, 2023.
• Pedro H.G. Lugão, Renato Portugal, Quantum search by continuous-time quantum walk on t-designs, arXiv:2310.14141, 2023.
• Gustavo A. Bezerra, Anderson F.P. Santos, Renato Portugal, Hiperwalk: Simulation of Quantum Walks with Heterogeneous High-Performance Computing, IEEE International Conference on Quantum Computing and Engineering (QCE) DOI:10.1109/QCE57702.2023.00055, 2023.
• Caue FT Silva, Daniel Posner, Renato Portugal, Walking on Vertices and Edges by Continuous-Time Quantum Walk, Quantum Inf Process 22, 93 (2023) DOI:10.1007/s11128-023-03842-4.
• Lugão, P., "Análise assintótica de passeios quânticos para algoritmos de busca com múltiplos marcados", PhD thesis LNCC, 2023. In portuguese.

2022

• Renato Portugal, Jalil Khatibi Moqadam, Implementation of Continuous-Time Quantum Walks on Quantum Computers, arXiv:2212.08889, 2022.
• Renato Portugal, Algoritmos Cuánticos Básicos. (Translation to spanish Frank Acasiete)
• Renato Portugal, Mini-course Quantum Walk and Graph Coloring, CRM Montreal.
• Pedro H. G. Lugão, Renato Portugal, Mohamed Sabri, Hajime Tanaka, Multimarked Spatial Search by Continuous-Time Quantum Walk, arXiv:2203.14384, 2022.
• Hajime Tanaka, Mohamed Sabri, Renato Portugal, Quantum Inf Process 21, 74 (2022). DOI:10.1007/s11128-022-03417-9.
• R. Portugal, Basic Quantum Algorithms, arXiv:2201.10574, 2022.
• Teixeira, C., "Caminhando em vértices e arestas com o passeio quântico contínuo no tempo", PhD thesis LNCC, 2022. In portuguese.

2021

• Hajime Tanaka, Mohamed Sabri, Renato Portugal, Spatial Search on Johnson Graphs by Discrete-Time Quantum Walk, arXiv:2112.03744, 2021.
• Alexandre Abreu, Luís Cunha, Celina Figueiredo, Franklin Marquezino, Daniel Posner, Renato Portugal, Total tessellation cover: Bounds, hardness, and applications, Discrete Applied Mathematics (2021). DOI:10.1016/j.dam.2021.09.032.
• Rafael Cação, Lucas Cortez, Ismael de Farias, Ernee Kozyreff, Jalil Khatibi Moqadam, Renato Portugal, Quantum Walk on the Generalized Birkhoff Polytope Graph, Entropy (2021). DOI:10.3390/e23101239.
• G.A. Bezerra, P.H.G. Lugão, and R. Portugal, Phys. Rev. A 103, 062202 (2021). DOI:10.1103/PhysRevA.103.062202.
• Alexandre Abreu, Luís Cunha, Celina de Figueiredo, Luis Kowada, Franklin Marquezino, Renato Portugal, Daniel Posner, A computational complexity comparative study of graph tessellation problems, Theoretical Computer Science (2021). DOI:10.1016/j.tcs.2020.11.045.
• G. Bezerra, "Algoritmo de Contagem Quântico Aplicado ao Grafo Bipartido Completo", Master's thesis LNCC, 2021. In portuguese.

2020

• Frank Acasiete, Flavia P Agostini, J Khatibi Moqadam, Renato Portugal, Implementation of quantum walks on IBM quantum computers, Quantum Inf Process 19, 426 (2020). DOI:10.1007/s11128-020-02938-5.
• Bruno Chagas, Renato Portugal, Discrete-time quantum walks on oriented graphs, arXiv:2001.04814, 2020.
• Francisco Meira, Renato Portugal, Jose Cristiano Pereira, Optimization of creep feed grinding using cbn wheels on Nickel-Based superalloys: A case study, Journal of Manufacturing Technology Research (2020) ,
• Alexandre Abreu, Luís Cunha, C de Figueiredo, L Kowada, F Marquezino, Daniel Posner, Renato Portugal, The graph tessellation cover number: Chromatic bounds, efficient algorithms and hardness, Theoretical Computer Science (2020). DOI:10.1016/j.tcs.2019.09.013.

2019

• Yusuke Higuchi, Renato Portugal, Iwao Sato, Etsuo Segawa, Eigenbasis of the evolution operator of 2-tessellable quantum walks, Linear Algebra and its Applications (2019). DOI:10.1016/j.laa.2019.08.019.
• Pedro C. S. Costa, Fernando de Melo, and Renato Portugal, Multiparticle quantum walk with a gaslike interaction, Phys. Rev. A 100, 042320 (2019). DOI:10.1103/PhysRevA.100.042320.
• Franklin de Lima Marquezino, Renato Portugal, Carlile Lavor, A Primer on Quantum Computing, SpringerBriefs in Computer Science (2019). DOI:10.1007/978-3-030-19066-8.
• Gabriel Coutinho, Renato Portugal, Discretization of continuous-time quantum walks via the staggered model with Hamiltonians, Natural Computing (2019). DOI:10.1007/s11047-018-9688-8.
• Andrés Vallejo, Alejandro Romanelli, Raúl Donangelo, Renato Portugal, Entropy production in the quantum walk, Phys. Rev. A 99, 032319 (2019). DOI:10.1103/PhysRevA.99.032319.

2018

• Daniel Posner, Cauê F Teixeira da Silva, Renato Portugal, On the characterization of 3-tessellable graphs, Proceeding Series of the Brazilian Society of Computational and Applied Mathematics (2018). DOI:10.5540/03.2018.006.02.0308.
• Cauê F. Teixeira da Silva, Daniel Posner, Renato Portugal, Staggered quantum walk on a line of diamonds, Proceeding Series of the Brazilian Society of Computational and Applied Mathematics (2018). DOI:10.5540/03.2018.006.02.0329.
• Bruno Chagas, Renato Portugal, Stefan Boettcher, and Etsuo Segawa, Staggered quantum walk on hexagonal lattices, Phys. Rev. A 98, 052310 (2018). DOI:10.1103/PhysRevA.98.052310.
• Pedro Costa, Renato Portugal, Fernando de Melo, Quantum walks via quantum cellular automata, Quantum Information Processing volume 17, Article number: 226 (2018). DOI:10.1007/s11128-018-1983-x.
• Stefan Boettcher, Shanshan Li, Tharso D Fernandes, Renato Portugal, Complexity bounds on quantum search algorithms in finite-dimensional networks, Phys. Rev. A 98, 012320 (2018). DOI:10.1103/PhysRevA.98.012320.
• Renato Portugal, Element distinctness revisited, Quantum Information Processing volume 17, Article number: 163 (2018). DOI:10.1007/s11128-018-1930-x.
• Alejandro Romanelli, Franklin de Lima Marquezino, Renato Portugal, Raul Donangelo, The energy cost of quantum information losses, Physica A: Statistical Mechanics and its Applications (2018). DOI:10.1016/j.physa.2018.01.015.
• Norio Konno, Renato Portugal, Iwao Sato, Etsuo Segawa, Partition-based discrete-time quantum walks, Quantum Information Processing volume 17, Article number: 100 (2018) . DOI:10.1007/s11128-017-1807-4.
• Chagas, B., "Caminhada Quântica Escalonada em Grade Hexagonal", PhD thesis LNCC, 2018. In portuguese.
• Vásquez, J., "Post-Quantum Cryptography: An Efficient Differential Fault Analysis Attack and a New One-Time Signature Scheme", PhD thesis LNCC, 2018. In english.
• C. Teixeira, "Standard deviation of a staggered quantum walk on a line of diamonds", Master's thesis LNCC, 2018. In english.

2017

• R. Portugal and T. D. Fernandes, Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians, Phys. Rev. A 95, 042341 (2017) . DOI:10.1103/PhysRevA.95.042341.
• J Khatibi Moqadam, Marcos Cesar de Oliveira, Renato Portugal, Staggered quantum walks with superconducting microwave resonators, Phys. Rev. B 95, 144506 (2017) . DOI:10.1103/PhysRevB.95.144506.
• Stefan Boettcher, Shanshan Li, Renato Portugal, Renormalization of the unitary evolution equation for coined quantum walks, Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 12 (2017) . DOI:10.1088/1751-8121/aa5bc1/meta.
• Renato Portugal, Marcos Cesar de Oliveira, Jalil Khatibi Moqadam, Staggered quantum walks with Hamiltonians, Phys. Rev. A 95, 012328 (2017) . DOI:10.1103/PhysRevA.95.012328.
• Renato Portugal, Etsuo Segawa, Connecting Coined Quantum Walks with Szegedy's Model, Interdisciplinary Information Sciences, p. 119-125 (2017) . DOI:10.4036/iis.2017.A.15.
• Fábio Borges, Pedro Lara, Renato Portugal, Parallel algorithms for modular multi-exponentiation, Applied Mathematics and Computation, 292 p. 406-416 (2017) . DOI:10.1016/j.amc.2016.07.036.
• Pascal Philipp, Renato Portugal, Exact simulation of coined quantum walks with the continuous-time model, Quantum Information Processing volume 16, Article number: 14 (2017) . DOI:10.1007/s11128-016-1475-9.
• Fernandes, T., "Modelo de Caminhadas Quânticas Escalonado", PhD thesis LNCC, 2017. In portuguese.

2016

• Nicolás Díaz, Raul Donangelo, Renato Portugal, and Alejandro Romanelli, Transient temperature and mixing times of quantum walks on cycles, Phys. Rev. A 94, 012305 (2016) . DOI:10.1103/PhysRevA.94.012305.
• Renato Portugal, Staggered quantum walks on graphs, Phys. Rev. A 93, 062335 (2016) . DOI:10.1103/PhysRevA.93.062335.
• Renato Portugal, Establishing the equivalence between Szegedy’s and coined quantum walks using the staggered model, Quantum Information Processing volume 15, pages 1387–1409 (2016) . DOI:10.1007/s11128-015-1230-7.
• Renato Portugal, Raqueline AM Santos, Tharso D Fernandes, Demerson N Gonçalves, The staggered quantum walk model, Quantum Information Processing volume 15, pages 85–101 (2016) . DOI:10.1007/s11128-015-1149-z.

2015

• L Tarrataca, Challenges of adiabatic quantum evaluation of NAND trees, Quantum Information Processing (2015). DOI:10.1007/s11128-015-1137-3.
• Stefan Boettcher, Shanshan Li, Real-Space Renormalization Group for Spectral Properties of Hierarchical Networks, Journal of Physics A 48, 415001 (2015).
• Jalil Khatibi Moqadam, Renato Portugal, Marcos Cesar de Oliveira, Quantum walks on a circle with optomechanical systems, Quantum Information Processing, Volume 14, Issue 10, pp 3595-3611 (2015). DOI:10.1007/s11128-015-1079-9.
• Raqueline A. M. Santos, Renato Portugal, Stefan Boettcher, Moments of coinless quantum walks on lattices, Quantum Information Processing, Volume 14, Issue 9, pp 3179-3191 (2015). DOI:10.1007/s11128-015-1042-9.
• Ambainis, A., Portugal, R., Nahimov, N., "Spatial Search on Grids with Minimum Memory". Quantum Information and Computation, vol.15 no.13&14, pp 1233-1247, 2015.
• Renato Portugal, Stefan Boettcher, Stefan Falkner, One-Dimensional Coinless Quantum Walks, Physical Review A 91, 052330 (2015),
• Juan del Carmen Grados Vasquez, Fabio Borges, Renato Portugal, Pedro Lara, An Efficient One-Bit Model for Differential Fault Analysis on Simon Family, Workshop on Fault Diagnosis and Tolerance in Cryptography (FDTC) (2015). 10.1109/FDTC.2015.18.
• Stefan Boettcher, Stefan Falkner, Renato Portugal, Relation between random walks and quantum walks, Phys. Rev. A 91, 052330 (2015). DOI:10.1103/PhysRevA.91.052330.
• Lara, P.C.S., "Global Optimization Algorithms based on Quantum Algorithms", PhD thesis LNCC. In portuguese.
• A.B. Leão, "A new HPC quantum-walk simulator", Master's thesis LNCC, 2015. In portuguese.

2014

• Stefan Falkner, Stefan Boettcher, Weak Limit of the 3-State Quantum Walk on the Line, Phys. Rev. A 90, 012307, 2014.
• Lara, P.C.S., Portugal, R., Lavor, C., "A new hybrid classical-quantum algorithm for continuous global optimization problems". Journal of Global Optimization, vol. 60, Issue 2, pp 317-331, 2014.
• Santos, R.A.M., Portugal, R., Fragoso, M.D., "Decoherence in quantum Markov chains". Quantum Information Processing, 13, 559-572, 2014.
• Santos, R.A.M., "Algoritmos Baseados em Cadeias de Markov Quânticas", PhD thesis LNCC. In portuguese.
• N. Paiva, "Análise e Conversão de Algoritmos Criptográficos para Forma Normal Conjuntiva", Master's thesis LNCC, 2014. In portuguese.
• D. Gaspar, "Passeios Aleatórios Clássicos e Quânticos em Tapetes de Sierpiński", Master's thesis LNCC, 2014. In portuguese.

2013

• L. Tarrataca, A. Wichert, Quantum Iterative Deepening with an application to the Halting problem, PloS One 8(3), e57309, 2013.
• L. Tarrataca, A. Wichert, Intricacies of quantum computational paths, Quantum information processing 12(2), 1365-1378, 2013.
• Santiago, D.F.G., Portugal, R., Melo, N., "Non-Pauli observables for CWS codes", Quantum Information Processing, 12, 1871-1884, 2013.
• Marquezino, F., Portugal, R., Boettcher, S., "Spatial search algorithms on Hanoi networks", Physical Review. A, 87, 012329, 2013.
• Moqadam, J.K., Portugal, R., Svaiter, N.F., Corrêa, G.O., "Analyzing the Toffoli gate in disordered circuit QED", Physical Review A, 87, 042324, 2013.
• Moqadam, J.K., "Analysis of the Implementation of the Toffoli Gate with Imperfections", PhD thesis LNCC. In English.
• Santiago, D.F.G., "CWS-type Quantum Error Correcting Codes", PhD thesis LNCC. In portuguese.

2012

• Abal, G., Donangelo, R., Forets, M., Portugal, R., "Spatial quantum search in a triangular network". MSCS - Mathematical Structures in Computer Science, 22, 521-531, 2012.
• J. Vásquez, "Estudo Comparativo de Algoritmos de Decodificação para Códigos de Goppa Aplicados no McEliece", Master's thesis LNCC, 2012. In portuguese.

2011

• Marquezino, F.L., Portugal, R. and Boettcher S., "Quantum search algorithms on hierarchical networks. In: IEEE Information Theory Workshop (ITW), 2011, Paraty. Proc. IEEE Information Theory Workshop, 2011. v. 1. p. 247-251. DOI: 10.1109/ITW.2011.6089429
• P. Lara, "Paralelização Eficiente para o Algoritmo de Exponenciação Modular", Master's thesis LNCC, 2011. In portuguese.
• R. Azevedo, "Cadeias de Markov Quânticas", Master's thesis LNCC, 2011. In portuguese.

2010

• Abal,G., Donangelo, R., Marquezino, F.L. and Portugal R., "Spatial search in a honeycomb network", arXiv:1001.1139, 2010. To appear in Math. Structures in Computer Science.
• Marquezino, F.L., Portugal, R. and Sasse, F.D., "Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition", arXiv:1005.3730, 2010. To appear in Journal of Computational and Applied Mathematics.
• Marquezino, F.L., "Analysis, Simulations and Algorithmic Applications of Quantum Walks", PhD thesis LNCC, 2010. In portuguese.

2009

• Gonçalves, D.N., Portugal, R. and Cosme, C.M.M., "Solutions to the Hidden Subgroup Problem on some Metacyclic Groups". In: 4th Workshop on Theory of Quantum Computation, Communication and Criptography, 2009, Waterloo. Lectures Notes in Computing Science (LNCS), 2009. v. 5906.
• Abal,G., Donangelo, R., Marquezino, F.L., Oliveira, A.C. and Portugal, R., "Decoherence in Search Algorithms". In: Proceedings of the XXIX Brazilian Computer Society Congress (SEMISH), p. 293-306, arXiv:0912.1523, 2009.
• Santos, R.A.M. and Portugal, R. "Quantum Hitting Time on the Complete Graph", arXiv:0912.1217 , 2009.
• Kempf, A. and Portugal, R. "Group Velocity of Discrete-Time Quantum Walks", Phys. Rev. A, 79, 052317(2009), arXiv:0901.4237, 2009.
• Gonçalves, D.N., "Quantum Algorithms for Problems in Computational Group Theory", PhD thesis, LNCC, 2009. In portuguese.

2008

• Marquezino, F.L., Portugal, R., Abal, G. and Donangelo, R. "Mixing Times in Quantum Walks on the Hypercube", Phys. Rev. A 77, 042312(2008), arXiv:0712.0625, 2008.
• Marquezino, F.L. and Portugal, R. "The QWalk Simulator of Quantum Walks", Computer Physics Communications 179 (5), p.359-369. arXiv:0803.3459, 2008.
• Gonçalves, D.N., Portugal, R. and Cosme, C.M.M., "Algoritmos Quânticos para uma Classe de Produtos Semidiretos de Grupos". In: Anais do XXXI Congresso de Matemática Aplicada e Computacional, v.1, p.159-163, 2008.
• E. Dalcumune, "Algoritmos Quânticos para o Problema do Isomorfismo de Grafos", Master's thesis LNCC, 2008. In portuguese.
• T. Fernandes, "Problema do subgrupo oculto em grupos nilpotentes", Master's thesis LNCC, 2008. In portuguese.

2007

• Cosme, C.M.M. and Portugal, R. " Quantum algorithm for the hidden subgroup problem on a class of semidirect product groups", arXiv:quant-ph/0703223, 2007. Submitted.
• Marquezino, F.L. and Portugal, R. "QWalk: Simulador de Caminhadas Quânticas", In Proc. of 2nd WECIQ, pages 123-132, Campina Grande, Brazil, 2007. In portuguese.
• Oliveira, A.C., Portugal, R. and Donangelo, R. "Caminhos Quânticos Passando por Fendas". In: Proc. of 2nd WECIQ, Campina Grande, Brazil, 2007. In portuguese.
• Kowada, L.A.B., Figueiredo, C.M.H., Portugal, R. and Lavor, C.C., "Aplicação do Algoritmo de Grover para Problemas NP-Completos". In: Proc. of 2nd WECIQ, Campina Grande, Brazil, 2007. In portuguese.
• Souza, M.F., Lavor, C.C., Portugal, R. and Maculan, N., "Cálculo da informação acessível via branch-and-bound e aritmética intervalar". In: Proc. of 2nd WECIQ, Campina Grande, Brazil, 2007.
• Oliveira, A.C. "Simulation of Quantum Walks in Two-Dimensional Lattices", PhD thesis LNCC, 2007. In portuguese.
• Oliveira, F.B. "Analysis of the cryptography security and steganography in images sequences", Master's thesis, LNCC, 2007. In portuguese.
• Souza, M.F., "A new approach to calculate the accessible information", Master's thesis, LNCC, 2007. In portuguese.

2006

• Kowada, L.A.B., Portugal, R. and Figueiredo, C.M.H. "Reversible Karatsuba's Algorithm", Journal of Universal Computer Science, vol. 12, no. 5, 499-511, 2006.
• Faber, J., Rosa, L.P. and Portugal, R. "Information Processing in Brain Microtubules", Biosystems, vol. 83, pages 1-9, Netherlands, 2006.
• Faber, J., Portugal, R. and Rosa, L.P. "Quantum Games in Open Systems using Biophysical Hamiltonians", 2006. Accepted for publication in Physics Letters A.
• Oliveira, A.C., Portugal, R. and Donangelo, R. "Decoherence in two-dimensional quantum walks", 2006. Accepted for publication in Physical Review A.
• Kowada, L.A.B. "Design of Reversible and Quantum Algorithms", PhD thesis, COPPE, 2006. In portuguese.
• Marquezino, F.L. "The Approximate Quantum Fourier Transform and its Simulation", Master's thesis, LNCC, 2006. In portuguese.

2005

• Portugal, R., Lavor, C.C. and Carvalho, L.M. "Quantum Algorithms for the Graph Isomorphism Problem". In: CNMAC, 2005, São Paulo.
• Carvalho, L.M., Lavor, C.C. and Portugal, R. "Representações de um q-bit: propriedades e visualização". In: XXVIII Congresso Nacional de Matemática Aplicada e Computacional, 2005, São Paulo.
• Faber, J. "Quantum Games from Biophysical Hamiltonians and a Sub-Neuronal Optimization Criterium of Information", PhD thesis LNCC, 2005. In portuguese.
• Gonçalves, D.N. "Quantum Fourier Transform in the Dihedral Group", Master's thesis LNCC, 2005. In portuguese.

2004

• Rosa, L.P. and Faber, J. "Quantum Models of Mind: Are They Compatible with Environment Decoherence?". Physical Review E - Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics, v. 70, n. 031902, 2004.
• Portugal, R., Lavor, C.C., Carvalho, L.M. and Maculan, N. "Uma Introdução à Computação Quântica", São Paulo: SBMAC, 2004. (An Introduction to Quantum Computing, book in portuguese)
• Faber, J.F.F., Rosa, L.P. and Portugal, R. "Information processing in brain microtubules". In: Proceedings of Quantum Mind 2003 - Consciousness, Quantum Physics and the Brain, 2003, Tucson.
• Lavor, C., Maculan Filho, N. and Portugal, R. "O Algoritmo de Grover". In: XXXV Simpósio Brasileiro de Pesquisa Operacional, 2003, Natal.
• Gonçalves, D.N. and Portugal, R. "Transformada de Fourier em Grupos Não-comutativos". In: XXVII Congresso Nacional de Matemática Aplicada e Computacional, 2004, Porto Alegre.
• Marquezino, F.L. and Mello Junior, R.R. "Simulation of the Quantum Fourier Transform using Distributed Computation", Monograph (BSc in Computer Science), UCP, 2004. In portuguese.
• Marquezino, F.L. and Mello Junior, R.R. "Considerations on Classical and Quantum Bits", 2004. Quantum arXiv, physics/0404133.
• Marquezino, F.L. and Mello Junior, R.R. "An Introduction to Logical Operations on Classical and Quantum Bits", 2004. Quantum arXiv, physics/0404134.
• Marquezino, F.L., Helayel-Neto, J.A. "Estudo Introdutório do Protocolo Quântico BB84 para Troca Segura de Chaves". Revista Eletrônica de Iniciação Científica, ano IV, número IV, Dezembro, 2004.
• Faber, J. "Quantum Computation on Open Systems and an Application to the Biological Model of Fröhlich", Master's thesis LNCC, 2004. In portuguese.

2003

• Manssur, L.R.U. and Portugal, R. "Stochastic Simulation of Quantum Computation". Europhysics Letters, v. 63, n. 4, p. 492-497, 2003.
• Lavor, C., Manssur, L. and Portugal, R. "Quantum Computing and Database Search". In: Proceedings Workshop on Computacional Grids and Applications, 2003, Petrópolis.
• Lavor, C., Maculan Filho, N., Portugal, R. "Shor's Algorithms and Applications to Break the Protocols of Classical Cryptography". In: XXVI Congresso Nacional de Matemática Aplicada e Computacional, 2003, São José do Rio Preto. Anais do XXVI CNMAC, 2003. v. 1. p. 1-10.
• Faber, J., Thess, R.N., Giraldi, G. "Learning Linear Operators by Genetic Algorithms". 2003.
• Faber, J., Petric, M., Rosa, L.P. "The Problems of Consciousness: A Critical Summary". In: Towards a Science of Consciousness, Praga, 2003.
• Faber, J., Rosa, L.P., Portugal, R. Information Processing in Brain Microtubules. In: Quantum Mind, Tucson, 2003.

2002

• Portugal, R., Manssur, L.R.U., Silva, R.S. and Marquezino, F.L. "Simulação de Computação Quântica". In: XXV CNMAC, 2002, Nova Friburgo.
• Faber, J., Giraldi, G. "Quantum Models of Artificial Neural Networks". In: I Meeting of Quantum Information, 2002, Belo Horizonte. I Meeting of Quantum Information, 2002.