Parrondo's paradox articles
Contents
Introduction
Below are the links to selected publications on Parrodo's paradox, and closely related phenomena, in order to get an overview of the development of the field. The wiki concept is exploited, for the purpose of quickly updating the information with ease. To return to the previous page, click the "back" button on your browser or to return to the Abbott Homepage scroll down to the links at the bottom of this page.
2013
[1] Marius-F. Danca, "Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox," Communications in Nonlinear Science and Numerical Simulation, Vol. 18, No. 3, pp. 500–510, 2013, http://dx.doi.org/10.1016/j.cnsns.2012.08.019
[2] Wayne Wah Ming Soo and Kang Hao Cheong, "Parrondo’s paradox and complementary Parrondo processes," Physica A: Statistical Mechanics and its Applications, Vol. 392, No. 1, pp. 17–26, 2013, http://dx.doi.org/10.1016/j.physa.2012.08.006
2012
[3] Wang Fulai, "Improvement and empirical research on chaos control by theory of 'chaos + chaos = order'," Chaos, Vol. 22, No. 4, Art. No. 043145, 2012, http://dx.doi.org/10.1063/1.4772966
[4] Tieyan Si, "An optical model for implementing Parrondo’s game and designing stochastic game with long-term memory," Chaos, Solitons & Fractals, Vol. 45, No. 11, pp. 1430–1436, 2012, http://dx.doi.org/10.1016/j.chaos.2012.08.004
[5] Neng-gang Xie, Jia-yi Guo, Ye Ye, Chao Wang, and Lu Wang, "The paradox of group behaviors based on Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 23, pp. 6146–6155, 2012, http://dx.doi.org/10.1016/j.physa.2012.07.024
[6] Lu Wang, Yong-fei Zhu, Ye Ye, Rui Meng, Neng-gang Xie, "The coupling effect of the process sequence and the parity of the initial capital on Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 21, pp. 5197–5207, 2012, http://dx.doi.org/10.1016/j.physa.2012.06.008
[7] Stewart N. Ethier and Jiyeon Lee, "Parrondo's paradox via redistribution of wealth," Electronic Journal of Probability, Vol. 17, pp. 1–21, 2012, http://dx.doi.org/10.1214/EJP.v17-1867
[8] Marius-F. Danca and Dejan Lai, "Parrondo's game model to find numerically stable attractors of a tumor growth model," Int. J. Bifurcation Chaos, Vol. 22, Art. No. 1250258, 2012, http://dx.doi.org/10.1142/S0218127412502586
[9] Ye Ye, Neng-Gang Xie, Lin-Gang Wang, Rui Meng, Yu-Wan Cen, "Study of biotic evolutionary mechanisms based on the multi-agent Parrondo's games," Fluctuation Noise Letters, Vol. 11, Art. No. 1250012, 2012, http://dx.doi.org/10.1142/S0219477512500125
[10] Prakash Gorroochurn, "Parrondo's perplexing paradox (1996)," Chapter 33 in Classic Problems of Probability, Wiley, 2012, http://dx.doi.org/10.1002/9781118314340.ch33
2011
[11] Paul D. Williams and Alan Hastings, "Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology," Proceedings Royal Society B, Vol. 278, No. 1710, pp. 1281–1290, 20007, http://dx.doi.org/10.1098/rspb.2010.2074
[12] Miquel Montero, "Parrondo-like behavior in continuous-time random walks with memory," Physical Review E, Vol. 84, Art. No. 051139, 2011, http://dx.doi.org/10.1103/PhysRevE.84.051139
[13] Lu Wang, Neng-gang Xie, Yong-fei Zhu, Ye Ye, and Rui Meng, "Parity effect of the initial capital based on Parrondo’s games and the quantum interpretation," Physica A: Statistical Mechanics and its Applications, Vol. 390, No. 23–24, pp. 4535–4542, 2011, http://dx.doi.org/10.1016/j.physa.2011.07.043
[14] Yong-fei Zhu, Neng-gang Xie, Ye Ye, and Fa-rui Peng, "Quantum game interpretation for a special case of Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Vol. 390, No. 4, pp. 579–586, 2011, http://dx.doi.org/10.1016/j.physa.2010.10.039
[15] Jiayi Guo, Nenggang Xie, and Ye Ye, "The theoretical analysis and computer simulation on Parrondo's history dependent games," Procedia Engineering, Vol. 15, pp. 4597–4602, 2011, http://dx.doi.org/10.1016/j.proeng.2011.08.863
[16] Steven A. Bleiler and Faisal Shah Khan, "Properly quantized history-dependent Parrondo games, Markov processes, and multiplexing circuits," Physics Letters A, Vol. 375, No. 19, pp. 1930–1943, 2011, http://dx.doi.org/10.1016/j.physleta.2011.03.051
[17] Rui Li, Yong-fei Zhu, Jia-yi Guo, Lu Wang, and Neng-gang Xie, "The quantum game interpretation for a special phenomenon of Parrondo's Paradox," Procedia Engineering, Vol. 15, pp. 3715–3722, 2011, http://dx.doi.org/10.1016/j.proeng.2011.08.696
[18] Neng-gang Xie, Yun Chen, Ye Ye, Gang Xu, Lin-gang Wang, and Chao Wang, "Theoretical analysis and numerical simulation of Parrondo’s paradox game in space," Chaos, Solitons & Fractals, Vol. 44, No. 6, pp. 401–414, 2011, http://dx.doi.org/10.1016/j.chaos.2011.01.014
[19] Antonio Di Crescenzo and Franco Pellerey, "Stochastic comparisons of series and parallel systems with randomized independent components," Operations Research Letters, Vol. 39, No. 5, pp. 380–384, 2011, http://dx.doi.org/10.1016/j.orl.2011.07.004
2010
[20] Lei Chen, Chuan-Feng Li, Ming Gong, and Guang-Can Guo, "Quantum Parrondo game based on a quantum ratchet effect," Physica A: Statistical Mechanics and its Applications, Vol. 389, No. 19, pp. 4071–4074, 2010, http://dx.doi.org/10.1016/j.physa.2010.06.011
[21] Richard A. Epstein, "Parrondo’s principle" Chapter 4 in The Theory of Gambling and Statistical Logic (Second Edition), Academic Press, pp. 74–94, 2010, http://dx.doi.org/10.1016/B978-0-12-374940-6.00004-8
[22] Derek Abbott, "Asymmetry and disorder: A decade of Parrondo's paradox," Fluctuations and Noise Letters, Vol. 9, No. 1, pp. 129–156, 2010, http://dx.doi.org/10.1142/S0219477510000010
[23] Salman Khan, M. Ramzan, and M. K. Khan, "Quantum Parrondo’s games under decoherence," International Journal of Theoretical Physics, Vol. 49, No. 1, pp 31–41, 2010, http://dx.doi.org/10.1007/s10773-009-0175-y
[24] Derek Abbott, B. R. Davis, and J. M. R. Parrondo, "The two-envelope problem revisited," Fluctuations and Noise Letters, Vol. 9, No. 1, pp. 1–8, 2010, http://dx.doi.org/10.1142/S0219477510000022
[25] E. Tahami and M. R. H. Golpaygani, "The role of three irrational numbers Pi, Neper and Feigenbaum constant as a new switching strategies in the Parrondo's paradox," Proc. Int. 2nd IEEE Conf. on Information and Financial Engineering, (ICIFE), Chongqing, China, September 17–19, 2010, pp. 291–295, http://dx.doi.org/10.1109/ICIFE.2010.5609305
[26] Michael Stutzer, "The paradox of diversification," The Journal of Investing, Vol. 19, No. 1, pp. 32–35, 2010, http://dx.doi.org/10.3905/JOI.2010.19.1.032
2009
Derek Abbott, "Developments in Parrondo’s paradox," Applications of Nonlinear Dynamics: Understanding Complex Systems, (Eds: Visarath In, Patrick Longhini, and Antonio Palacios), Springer, pp. 307–321, 2009, http://dx.doi.org/10.1016/10.1007/978-3-540-85632-0_25
[27] Stewart N. Ethier and Jiyeon Lee, "Limit theorems for Parrondo’s paradox," Electronic Journal of Probability, Vol. 14, pp. 1827–1862, 2009, http://dx.doi.org/10.1214/EJP.v14-684
[28] Daniel C. Osipovitch, Carl Barratt, and Pauline M. Schwartz, "Systems chemistry and Parrondo’s paradox: computational models of thermal cycling," New Journal of Chemistry, Vol. 33, No. 10, pp. 2022–2027, http://dx.doi.org/10.1039/B900288J
[29] C. P. Roca, J. A. Cuesta and A. Sánchez, "Imperfect imitation can enhance cooperation," Europhysics Letters, Vol. 87, No. 4, Art. No. 48005, 2009, http://dx.doi.org/10.1209/0295-5075/87/48005
[30] M. D. McDonnell and D. Abbott, "Randomized switching in the two-envelope problem," Proceedings of the Royal Society A, Vol. 465, No. 2111, pp. 3309-3322, 2009.
[31] Lawrence N. Dworsky, "Benford, Parrondo, and Simpson," Chapter 13 in Probably Not: Future Prediction Using Probability and Statistical Inference, Wiley, 2008, http://dx.doi.org/10.1002/9780470282052.ch13
2008
[32] Ehrhard Behrends,"Stochastic dynamics and Parrondo’s paradox," Physica D: Nonlinear Phenomena, Vol. 237, No. 2, pp. 198–206, 2008, http://dx.doi.org/10.1016/j.physa.2011.07.043
[33] Michael A. H. Dempster, Igor V. Evstigneev, and Klaus Reiner Schenk-Hoppé, "Financial markets. The joy of volatility," Quantitative Finance, Vol. 8, No. 1, pp. 1–3, 2008, http://dx.doi.org/10.1080/14697680701799577
[34] David Bulger, James Freckleton, and Jason Twamley, "Position-dependent and cooperative quantum Parrondo walks," New Journal of Physics, Vol. 10, Art. No. 093014, 2008, http://dx.doi.org/10.1088/1367-2630/10/9/093014
[35] Andrzej Korzeniowski, "Mean reversal for stochastic hybrid systems," Nonlinear Analysis: Hybrid Systems, Vol. 2, No. 2, pp. 613–625, 2008, http://dx.doi.org/10.1016/j.nahs.2006.09.005
2007
[36] Floyd A. Reed, "Two-locus epistasis with sexually antagonistic selection: A genetic Parrondo's paradox," Genetics, Vol. 176, No. 3, pp. 1923–1929, 2007, http://dx.doi.org/10.1534/genetics.106.069997
[37] J. Košík, J. A. Miszczak and V. Bužeka, "Quantum Parrondo's game with random strategies," Journal of Modern Optics, Vol. 54, Nos. 133–15, pp. 2275–2287, 2007, http://dx.doi.org/10.1080/09500340701408722
F. Stjernberg, "Parrondo’s paradox and epistemology—when bad things happen to good cognizers (and conversely)," in Hommage Wlodek. Philosophical Papers Dedicated to Wlodek Rabinowicz, (Eds: T. Rønnow-Rasmussen, B. Petersson, J. Josefsson and D. Egonsson), 2007, Online: http://www.fil.lu.se/hommageawlodek.
2006
[38] Jose S. Cánovas, Antonio Linero, and Daniel Peralta-Salas, "Dynamic Parrondo’s paradox," Physica D: Nonlinear Phenomena, Vol. 218, No. 2, pp. 177–184, 2006, http://dx.doi.org/10.1016/j.physd.2006.05.004
[39] Zoran Mihailović and Milan Rajković, "Cooperative Parrondo's games on a two-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Vol. 365, No. 1, pp. 244–251, 2006, http://dx.doi.org/10.1016/j.physa.2006.01.032
[40] Pau Amengual, Pascal Meurs, Bart Cleuren, and Raul Toral, "Reversals of chance in paradoxical games," Physica A: Statistical Mechanics and its Applications, Vol. 371, No. 2, pp. 641–648, 2006, http://dx.doi.org/10.1016/j.physa.2006.03.038
2005
[41] Jonas Almeida, Daniel Peralta-Salas, and Miguel Romera, "Can two chaotic systems give rise to order?" Physica D: Nonlinear Phenomena, Vol. 200, No. 1–2, pp. 124–132, 2005, http://dx.doi.org/10.1016/j.physd.2004.10.003
[42] Piotr Gawron and Jaroslaw A. Miszczak, "Quantum implementation of Parrondo's paradox," Fluctuation and Noise Letters, Vol. 5, pp. L471–L478, 2005, http://arxiv.org/pdf/quant-ph/0502185, http://dx.doi.org/10.1142/S0219477505002902
[43] Richard Spurgin and Maurry Tamarkin, "Switching investments can be a bad idea when Parrondo's paradox applies," Journal of Behavioural Finance, Vol. 6, No. 1, pp. 15–18, 2005, http://dx.doi.org/10.1207/s15427579jpfm0601_3
[44] Pau Amengual and Raul Toral, "Transfer of information in Parrondo's games," Fluctuation and Noise Letters, Vol. 5, No. 1, pp. L63–L71, 2005, http://dx.doi.org/10.1142/S0219477505002409
[45] Tian Yow Tsong and Cheng-Hung Chang, "Enzyme as catalytic wheel powered by a Markovian engine: conformational coupling and barrier surfing models," Physica A, Vol. 350, pp. 108–121, 2005, http://dx.doi.org/10.1016/j.physa.2004.11.024
[46] Denise M. Wolf, Vijay V. Vazirani, and Alan P. Arkin, "Diversity in times of adversity: probabilistic strategies in microbial survival games," Journal of Theoretical Biology, Vol. 234, pp. 227–253, 2005, http://dx.doi.org/10.1016/j.jtbi.2004.11.020
[47] Andrew Allison, Charles E. M. Pearce and Derek Abbott, "State-space visualization and fractal properties of Parrondo's games," Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control, (Eds: A.S. Nowack and K Szajowski), Birkhauser, Boston, Vol. 7, pp. 613–633, 2005, http://dx.doi.org/10.1007/0-8176-4429-6_32
[48] Gregory P. Harmer and Derek Abbott, "Parrondo's capital and history-dependent games," Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control, (Eds: A .S. Nowack and K. Szajowski), Birkhauser, Boston, Vol. 7, pp. 635–648, 2005, http://dx.doi.org/10.1007/0-8176-4429-6_33
[49] Joseph Ng and Derek Abbott, "Introduction to quantum games and a quantum Parrondo game," Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control, (Eds: A.S. Nowack and K Szajowski), Birkhauser, Boston, Vol. 7, pp. 649–665, 2005, http://dx.doi.org/10.1007/0-8176-4429-6_34
[50] Abraham Boyarsky, Paweł Góra, and Md. Shafiqul Islam, "Randomly chosen chaotic maps can give rise to nearly ordered behavior," Physica D: Nonlinear Phenomena, Vol. 210, pp. 284–294, 2005, http://dx.doi.org/10.1016/j.physd.2005.07.015
2004
[51] Luis Dinís and Juan M. R. Parrondo, "Inefficiency of voting in Parrondo games," Physica A: Statistical Mechanics and its Applications, Vol. 343, pp. 701–711, 2004, http://dx.doi.org/10.1016/j.physa.2004.06.076
P. Amengual, A. Allison, R. Toral and D. Abbott, "Discrete-time ratchets, the Fokker-Planck equation and Parrondo's paradox," Proc. Roy. Soc. London A., Vol. 460, pp. 2269-2284, 2004.
P. Amengual, and R. Toral, "Parrondo games and the zipping algorithm," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 203-212.
P. Amengual, and R. Toral, "Exact ratchet description of Parrondo's games with self-transitions," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 407-415.
E. Behrends, "The mathematical background of Parrondo's paradox," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 510-519.
F.J. Cao, L. Dinis and J.M.R. Parrondo, "Feedback control in a collective flashing ratchet," Physical Review Letters , Vol 93, No. 4, 040603, 2004.
R. Iyengar and R. Kohli, "Why Parrondo's paradox is irrelevant for utility theory, stock buying, and the emergence of life," Complexity, Vol. 9, No. 1, pp. 23-27, 2004. [Note: there are a number of very amusing basic errors in this paper. For example the authors have misunderstood what a statistical "birth-death process" is and have literally taken it to mean birth and death of humans!]
B. Cleuren and C. Van den Broeck, "Primary Parrondo paradox," Europhysics Letters., Vol. 67, No. 2, pp.151-157, 2004.
J.M.R. Parrondo and L. Dinis, "Brownian motion and gambling: from ratchets to paradoxical games," Contemporary Physics, Vol 45, pp. 147-157, 2004.
T.W. Tang, A. Allison and D. Abbott, "Parrondo's games with chaotic switching," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 520-530.
C. Van den Broeck and B. Cleuren, "Parrondo games with strategy," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 109-118.
B. Cleuren and C. Van den Broeck, "Optimizing strategies in the primary Parrondo paradox," Physical Review E, Vol. 70, 06710, 2004.
T. Platkowski, "Evolution of populations playing mixed multiplayer games," Mathematical and Computer Modelling, Vol. 39, pp. 981-989, 2004.
N. Masuda and N. Konno, "Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics," The European Physical Journal B, Vol. 40, pp. 313-319, 2004.
T.K. Philips, and A.B. Feldman, "Parrondo's Paradox is not paradoxical," 2004, http://ssrn.com/abstract=581521
L. Dinis and J.M.R. Parrondo, "Inefficiency of voting in Parrondo's games," Physica A, Vol. 343, pp. 701-711, 2004.
H. Martin and H.C. von Baeyer, "Simple games to illustrate Parrondo's paradox," American Journal of Physics, Vol. 72, No. 5, pp. 710-714, 2004.
T.W. Tang, A. Allison and D. Abbott, "Investigation of chaotic switching strategies in parrondo's games," Fluctuation and Noise Letters, Vol. 4, No. 4., pp. L585-L596, 2004.
A.P. Flitney, D. Abbott and N.F. Johnson, "Quantum walks with history dependence," J. Phys. A: Math. Gen. (IOP), Vol. 37, pp. 7581-7591, 2004.
P.C.W. Davies, "Does quantum mechanics play a non-trivial role in life?" BioSystems (Elsevier), Vol. 78, pp. 69-79, 2004.
2003
[52] A. P. Flitney and D. Abbott, "Quantum models of Parrondo's games," Physica A: Statistical Mechanics and its Applications, Vol. 324, No. 1–2, 2003, pp. 152–156, http://dx.doi.org/10.1016/S0378-4371(02)01909-X
[53] R. Toral, Pau Amengual, and Sergio Mangioni, "Parrondo's games as a discrete ratchet," Physica A: Statistical Mechanics and its Applications, Vol. 327, No. 1–2, 2003, pp. 105–110, http://dx.doi.org/10.1016/S0378-4371(03)00459-X
[54] P. Arena, S. Fazzino, L. Fortuna, and P. Maniscalco, "Game theory and non-linear dynamics: the Parrondo Paradox case study," Chaos, Solitons & Fractals, Vol. 17, No. 2–3, 2003, pp. 545–555, http://dx.doi.org/10.1016/S0960-0779(02)00397-1
P. Arena, S. Fazzino, L. Fortuna and P. Maniscalco, "Game theory and non-linear dynamics: the Parrondo's paradox case study," Chaos, Solitons and Fractals, Vol. 17, pp. 545-555, 2003.
C.H. Chang and T.Y. Tsong, "Truncation and reset process on the dynamics of Parrondo's games," Physical Review E, Vol. 67, No. 2, 025101, 2003.
L. Dinis and J.M.R. Parrondo, "Optimal strategies in collective Parrondo games," Europhysics Letters, Vol 63, No. 3, pp. 319-325, 2003.
R.J. Kay and N.F. Johnson, "Winning combinations of history-dependent games," Physical Review E, Vol. 67, No. 5, 056128, 2003.
G. Latouche and P.G. Taylor, "Drift conditions for matrix-analytic models," Mathematics of Operations Research, Vol. 28, No. 2, pp. 346-360, 2003.
Y. Lee, A. Allison, D. Abbott and H.E. Stanley, "Minimal Brownian ratchet: an exactly solvable model," Physical Review Letters, Vol. 91, No. 22, pp. 220601, 2003.
Z. Mihailovic and M. Rajkovic, "One dimensional asynchronous cooperative Parrondo's games," Fluctuation and Noise Letters, Vol. 3, No. 4, pp. L389-L398, 2003.
J.M.R. Parrondo and B.J. de Cisneros, "Paradoxical games and Brownian thermal engines," 2003. http://arxiv.org/pdf/cond-mat/0309053
Z. Mihailovic and M. Rajkovic, "Synchronous cooperative Parrondo's games," Fluctuation and Noise Letters, Vol. 3, No. 4, pp. L399-L406, 2003.
R. Toral, P. Amengual and S. Mangioni, "Parrondo's games as a discrete ratchet," Physica A, Vol. 327, pp. 105-110, 2003.
R. Toral, P. Amengual and S. Mangioni, "A Fokker-Planck description for Parrondo's games," Proceedings of SPIE, Vol. 309, No. 5114, 2003.
A.W. Ghosh and S.V. Khare, "Breaking of general rotational symmetries by multidimensional classical ratchets," Physical Review E, Vol. 67, 056110, 2003.
G.C. Berresford and A.M. Rocket, "Parrondo's Paradox," International Journal of Mathematics and Mathematical Sciences, Vol. 62, pp. 3957-3962, 2003.
E. Behrends, "Parrondos Paradoxon Ein stochastisches Perpetuum Mobile?" Mitteilungen der Deutschen Mathematiker-Verinigung, Vol. 1, pp. 5-10, 2003.
N.F. Johnson, P. Jefferies and P.M. Hui, Financial Market Complexity: What Physics Can Tell Us About Market Behaviour," Oxford University Press, 2003.
A.P. Flitney and D. Abbott, "Quantum models of Parrondo's games," Physica A, Vol. 324, pp. 152-156, 2003. top
2002
[55] A. P. Flitney, J. Ng, and D. Abbott, "Quantum Parrondo's games," Physica A: Statistical Mechanics and its Applications, Vol. 314, No. 1–4, 2002, pp. 35–42, http://dx.doi.org/10.1016/S0378-4371(02)01084-1
D. Abbott, P.C.W. Davies and C.R. Shalizi, "Order from disorder: the role of noise in creative processes. A special issue on game theory and evolutionary processes—overview," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. C1-C12, 2002.
R. Ait-Haddou and W. Herzog, "Force and motion generation of myosin motors: muscle contraction," Journal of Electromyography and Kinesiology, Vol. 12, pp. 435-445, 2002.
A. Allison and D. Abbott, "The physical basis for Parrondo's games," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L327-L341, 2002.
J. Buceta, K. Lindenberg and J.M.R. Parrondo, "Pattern formation induced by nonequilibrium global alternation of dynamics," Physical Review E, Vol. 66, pp. 036216(1)-036216(11), 2002.
J. Buceta and K. Lindenberg, "Switching-induced Turing instability," Physical Review E, Vol. 66, 046202, 2002.
J. Buceta, K. Lindenberg and J.M.R. Parrondo, "Stationary and oscillatory spatial patterns induced by global periodic switching," Physical Review Letters, Vol. 88, No. 2, 024103, 2002.
J. Buceta, K. Lindenberg and J.M.R. Parrondo, "Spatial patterns induced by random switching," Fluctuation and Noise Letters, Vol. 2, No. 1, pp. L21-L29, 2002.
M. Bucolo, R. Caponetto, L. Fortuna, M. Frasca and A. Rizzo, "Does chaos work better than noise," Circuits and Systems Magazine, IEEE, Vol. 2, No. 3, pp. 4-19, 2002.
B. Cleuren and C. Van den Broeck, "Random walks with absolute negative mobility," Physical Review E, Vol. 65, 030101, 2002.
L. Dinis and J.M.R. Parrondo, "Parrondo's paradox and the risks of short-range optimization," 2002. http://arxiv.org/pdf/cond-mat/0212358
A.P. Flitney, J. Ng and D. Abbott, "Quantum Parrondo's games," Physica A, Vol. 314, pp. 35-42, 2002.
A.P. Flitney and D. Abbott, "An introduction to quantum game theory," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. R175-R188, 2002.
G.P. Harmer and D. Abbott, "A review of Parrondo's paradox," Fluctuation and Noise Letters, Vol. 2, No. 2, pp. R71-R107, 2002.
D. Heath, D. Kinderlehrer and M. Kowalczyk, "Discrete and continuous ratchets: from coin toss to molecular motor," Discrete and Continuous Dynamical Systems-Series B, Vol. 2, No. 2, pp. 153-167, 2002.
E.S. Key, M.M. Klosek and D. Abbott, "On Parrondo's paradox: how to construct unfair games by composing fair games," 2002. http://arxiv.org/pdf/math/0206151
L. Kocarev and Z. Tasev, "Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox," Physical Review E , Vol. 65, pp. 046215(1)-046215(4), 2002.
C.F. Lee and N.F. Johnson, "Exploiting randomness in quantum information processing," Physics Letter A, Vol. 301, pp. 343-349, 2002.
C.F. Lee, N.F. Johnson, F. Rodriguez and L. Quiroga, "Quantum coherence, correlated noise and Parrondo games," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L293-L298, 2002.
D. A. Meyer and H. Blumer, "Quantum Parrondo games: biased and unbiased," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L257-L262, 2002.
D. A. Meyer and H. Blumer, "Parrondo games as lattice gas automata," Journal of Statistical Physics, Vol. 107, No. 1,2, pp. 225-239, 2002.
O.E. Percus and J.K. Percus, "Can two wrongs make a right? Coin-tossing games and Parrondo's paradox," Mathematical Intelligencer, Vol. 24, No. 3, pp. 68-72, 2002.
R. Pyke, "On random walks and diffusions related to Parrondo's games," 2002. http://arxiv.org/pdf/math.PR/0206150
L. Rasmusson and M. Boman, "Analytical expressions for Parrondo games," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L343-L348, 2002.
P. Reimann, "Brownian motors: noisy transport far from equilibrium," Physics Reports, Vol. 361, pp. 57-265, 2002.
P. Reimann and P. Hanggi, "Introduction to the physics of Brownian motors," Applied Physics A, Vol. 75, pp. 169-178, 2002.
R. Toral, "Capital redistribution brings wealth by Parrondo's paradox," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L305-L311, 2002.
A. Allison and D. Abbott, "A MEMS Brownian ratchet," Microelectronics Journal (Elsevier), Vol. 33, No. 3, pp. 235-243, Mar. 2002.
S. Rahmann, "Optimal adaptive strategies for games of the Parrondo type," 2002 (Unpublished).
2001
D. Abbott, "Overview: unsolved problems of noise and fluctuations," Chaos, Vol. 11, No. 3, pp. 526-538, 2001.
R.D. Astumian, "Making molecules into motors," Scientific American, pp. 56-64, Jul. 2001.
A. Allison and D. Abbott, "Control systems with stochastic feedback," Chaos, Vol. 11, No. 3, pp. 715-724, 2001.
A. Allison and D. Abbott, "Stochastic resonance in a Brownian ratchet," Fluctuation and Noise Letters (Elsevier), Vol. 1, No. 4, pp. L239-244, Dec. 2001.
M. Boman, S.J. Johansson and D. Lyback, "Parrondo strategies for artificial traders," Intelligent Agent Technology (Eds: N. Zhong, J. Liu, S. Ohsuga and J. Bradshaw), pp. 150-159, 2001.
G.P. Harmer, D. Abbott, P.G. Taylor and J.M.R. Parrondo, "Brownian ratchets and Parrondo's games," Chaos, Vol. 11, No. 3, pp. 705-714, 2001.
R. Toral, "Cooperative Parrondo's games," Fluctuation and Noise Letters, Vol. 1, No. 1, pp. L7-L12, 2001.
Stan Wagon and D. Velleman, "Parrondo's paradox," Mathematica in Education and Research, Vol. 9, Nos. 3-4, pp. 85-90, 2001.
2000
P.C.W. Davies, "Physics and life," The First Steps of Life in the Universe: Proceedings of the Sixth Trieste Conference on Chemical Evolution, (Ed: J. Chela-Flores, T.C. Owen and F. Raulin), Trieste, Italy, 18-22 September 2000.
G.P. Harmer, D. Abbott and P.G. Taylor, "The paradox of Parrondo's games," Proc. Royal Society London A, Vol. 456, pp. 247-259, 2000.
H. Moraal, "Counterintuitive behaviour in games based on spin models," Journal of Physics A: Math, Vol. 33, pp. L203-L206, 2000.
J.M.R. Parrondo, G.P. Harmer and D. Abbott, "New paradoxical games based on Brownian ratchets," Physical Review Letters, Vol. 85, No. 24, pp. 5226-5229, Dec. 2000.
1999
G.P. Harmer and D. Abbott, "Parrondo's paradox," Statistical Science, Vol. 14, No. 2, pp. 206-213, 1999.
G.P. Harmer and D. Abbott, "Losing strategies can win by Parrondo's paradox," Nature (London), Vol. 402, No. 6764, p. 864, Dec. 1999.
1996
Juan M. R. Parrondo, "How to cheat a bad mathematician," in EEC HC&M Network on Complexity and Chaos (#ERBCHRX-CT940546) , ISI, Torino, Italy (1996), Unpublished.
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