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Walczak Z, Bauer JH. Noise-induced Parrondo's paradox in discrete-time quantum walks. Phys Rev E 2023; 108:044212. [PMID: 37978709 DOI: 10.1103/physreve.108.044212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 09/14/2023] [Indexed: 11/19/2023]
Abstract
Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. We show that noise can induce Parrondo's paradox in one-dimensional discrete-time quantum walks with deterministic periodic as well as aperiodic sequences of two-state quantum coins where this paradox does not occur in the absence of noise. Moreover, we show how the noise-induced Parrondo's paradox affects the time evolution of quantum entanglement for such quantum walks.
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Affiliation(s)
- Zbigniew Walczak
- Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland
| | - Jarosław H Bauer
- Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland
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2
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Gokhale CS, Sharma N. Optimizing crop rotations via Parrondo's paradox for sustainable agriculture. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221401. [PMID: 37206968 PMCID: PMC10189593 DOI: 10.1098/rsos.221401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 04/25/2023] [Indexed: 05/21/2023]
Abstract
Crop rotation, a sustainable agricultural technique, has been at humanity's disposal since time immemorial and is practised globally. Switching between cover crops and cash crops helps avoid the adverse effects of intensive farming. Determining the optimum cash-cover rotation schedule for maximizing yield has been tackled on multiple fronts by agricultural scientists, economists, biologists and computer scientists, to name a few. However, considering the uncertainty due to diseases, pests, droughts, floods and impending effects of climate change is essential when designing rotation strategies. Analysing this time-tested technique of crop rotations with a new lens of Parrondo's paradox allows us to optimally use the rotation technique in synchrony with uncertainty. While previous approaches are reactive to the diversity of crop types and environmental uncertainties, we make use of the said uncertainties to enhance crop rotation schedules. We calculate optimum switching probabilities in a randomized cropping sequence and suggest optimum deterministic sequences and judicious use of fertilizers. Our methods demonstrate strategies to enhance crop yield and the eventual profit margins for farmers. Conforming to translational biology, we extend Parrondo's paradox, where two losing situations can be combined eventually into a winning scenario, to agriculture.
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Affiliation(s)
- Chaitanya S. Gokhale
- Center for Computational and Theoretical Biology (CCTB), University of Würzburg, Würzburg, Germany
- Research Group for Theoretical Models of Eco-evolutionary Dynamics, Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany
| | - Nikhil Sharma
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany
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Walczak Z, Bauer JH. Parrondo's paradox in quantum walks with three coins. Phys Rev E 2022; 105:064211. [PMID: 35854503 DOI: 10.1103/physreve.105.064211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 06/03/2022] [Indexed: 06/15/2023]
Abstract
Parrondo's paradox refers to the apparently paradoxical effect whereby a certain combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's paradox can occur not only in the case of one-dimensional discrete-time quantum walks with a deterministic sequence of two quantum coins but also in the case of one-dimensional discrete-time quantum walks with a deterministic sequence of three quantum coins. Moreover, we show how Parrondo's paradox affects the time evolution of quantum entanglement for such quantum walks.
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Affiliation(s)
- Zbigniew Walczak
- Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland
| | - Jarosław H Bauer
- Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland
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4
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Walczak Z, Bauer JH. Parrondo's paradox in quantum walks with deterministic aperiodic sequence of coins. Phys Rev E 2021; 104:064209. [PMID: 35030945 DOI: 10.1103/physreve.104.064209] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 12/07/2021] [Indexed: 11/07/2022]
Abstract
Parrondo's effect is a well-known apparent paradox where a combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's effect can occur not only in the case of one-dimensional discrete quantum walks with random or deterministic periodic sequence of two- or multistate quantum coins but also in the case of one-dimensional discrete quantum walks with deterministic aperiodic sequence of two-state quantum coins. Moreover, we show how Parrondo's effect affects the time evolution of the walker-coin quantum entanglement.
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Affiliation(s)
- Zbigniew Walczak
- Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland
| | - Jarosław H Bauer
- Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland
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Wen T, Koonin EV, Cheong KH. An alternating active-dormitive strategy enables disadvantaged prey to outcompete the perennially active prey through Parrondo's paradox. BMC Biol 2021; 19:168. [PMID: 34425802 PMCID: PMC8383410 DOI: 10.1186/s12915-021-01097-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 07/14/2021] [Indexed: 12/13/2022] Open
Abstract
BACKGROUND Dormancy is widespread in nature, but while it can be an effective adaptive strategy in fluctuating environments, the dormant forms are costly due to the inability to breed and the relatively high energy consumption. We explore mathematical models of predator-prey systems, in order to assess whether dormancy can be an effective adaptive strategy to outcompete perennially active (PA) prey, even when both forms of the dormitive prey (active and dormant) are individually disadvantaged. RESULTS We develop a dynamic population model by introducing an additional dormitive prey population to the existing predator-prey model which can be active (active form) and enter dormancy (dormant form). In this model, both forms of the dormitive prey are individually at a disadvantage compared to the PA prey and thus would go extinct due to their low growth rate, energy waste on the production of dormant prey, and the inability of the latter to grow autonomously. However, the dormitive prey can paradoxically outcompete the PA prey with superior traits and even cause its extinction by alternating between the two losing strategies. We observed higher fitness of the dormitive prey in rich environments because a large predator population in a rich environment cannot be supported by the prey without adopting an evasive strategy, that is, dormancy. In such environments, populations experience large-scale fluctuations, which can be survived by dormitive but not by PA prey. CONCLUSION We show that dormancy can be an effective adaptive strategy to outcompete superior prey, recapitulating the game-theoretic Parrondo's paradox, where two losing strategies combine to achieve a winning outcome. We suggest that the species with the ability to switch between the active and dormant forms can dominate communities via competitive exclusion.
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Affiliation(s)
- Tao Wen
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design (SUTD), 8 Somapah Road, S487372, Singapore, Singapore
| | - Eugene V Koonin
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD, 20894, USA
| | - Kang Hao Cheong
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design (SUTD), 8 Somapah Road, S487372, Singapore, Singapore.
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6
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Edhan O, Hellman Z, Nehama I. Making the most of potential: potential games and genotypic convergence. ROYAL SOCIETY OPEN SCIENCE 2021; 8:210309. [PMID: 34457339 PMCID: PMC8385380 DOI: 10.1098/rsos.210309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 08/02/2021] [Indexed: 06/13/2023]
Abstract
We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum-Eagon Theorem. To analyse varying environments, we introduce the concept of 'virtual convergence', under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.
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Affiliation(s)
- Omer Edhan
- Department of Economics, University of Manchester, Manchester, UK
| | - Ziv Hellman
- Department of Economics, Bar-Ilan University, Ramat Gan, Israel
| | - Ilan Nehama
- Department of Economics, Bar-Ilan University, Ramat Gan, Israel
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7
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Does Cancer Biology Rely on Parrondo's Principles? Cancers (Basel) 2021; 13:cancers13092197. [PMID: 34063648 PMCID: PMC8125342 DOI: 10.3390/cancers13092197] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Revised: 04/29/2021] [Accepted: 04/29/2021] [Indexed: 12/17/2022] Open
Abstract
Simple Summary Parrondo’s paradox, whereby losing strategies or deleterious effects can combine to provide a winning outcome, has been increasingly applied by biologists to explain complex adaptations in many living systems. Here, we suggest that considering this paradox in oncology, particularly in relation to the phenotypic diversity of malignant cells, could also be a promising approach to understand several puzzling aspects of cancer biology. For example, the high genetic and epigenetic instability of cancer cells, their metastatic behavior and their capacity to enter dormancy could be explained by Parrondo’s theory. We also discuss the relevance of Parrondo’s paradox in a therapeutical framework using different examples. This work provides a compelling argument that the traditional separation between medicine and other disciplines remains a fundamental limitation that needs to be overcome if complex processes, such as oncogenesis, are to be completely understood. Abstract Many aspects of cancer biology remain puzzling, including the proliferative and survival success of malignant cells in spite of their high genetic and epigenetic instability as well as their ability to express migrating phenotypes and/or enter dormancy despite possible fitness loss. Understanding the potential adaptive value of these phenotypic traits is confounded by the fact that, when considered separately, they seem to be rather detrimental at the cell level, at least in the short term. Here, we argue that cancer’s biology and success could frequently be governed by processes underlying Parrondo’s paradox, whereby combinations of intrinsically losing strategies may result in winning outcomes. Oncogenic selection would favor Parrondo’s dynamics because, given the environmental adversity in which malignant cells emerge and evolve, alternating between various less optimal strategies would represent the sole viable option to counteract the changing and deleterious environments cells are exposed to during tumorigenesis. We suggest that malignant processes could be viewed through this lens, and we discuss how Parrondo’s principles are also important when designing therapies against cancer.
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Koh JM, Cheong KH. Generalized Solutions of Parrondo's Games. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2020; 7:2001126. [PMID: 33344113 PMCID: PMC7740106 DOI: 10.1002/advs.202001126] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 06/18/2020] [Indexed: 05/04/2023]
Abstract
In game theory, Parrondo's paradox describes the possibility of achieving winning outcomes by alternating between losing strategies. The framework had been conceptualized from a physical phenomenon termed flashing Brownian ratchets, but has since been useful in understanding a broad range of phenomena in the physical and life sciences, including the behavior of ecological systems and evolutionary trends. A minimal representation of the paradox is that of a pair of games played in random order; unfortunately, closed-form solutions general in all parameters remain elusive. Here, we present explicit solutions for capital statistics and outcome conditions for a generalized game pair. The methodology is general and can be applied to the development of analytical methods across ratchet-type models, and of Parrondo's paradox in general, which have wide-ranging applications across physical and biological systems.
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Affiliation(s)
- Jin Ming Koh
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design (SUTD)8 Somapah RdSingaporeS487372Singapore
- California Institute of TechnologyPasadenaCA91125USA
| | - Kang Hao Cheong
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design (SUTD)8 Somapah RdSingaporeS487372Singapore
- SUTD‐Massachusetts Institute of Technology International Design Centre8 Somapah RdSingaporeS487372Singapore
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9
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Babajanyan SG, Lin W, Cheong KH. Cooperate or Not Cooperate in Predictable but Periodically Varying Situations? Cooperation in Fast Oscillating Environment. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2020; 7:2001995. [PMID: 33173734 PMCID: PMC7610311 DOI: 10.1002/advs.202001995] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Revised: 07/03/2020] [Accepted: 07/07/2020] [Indexed: 05/02/2023]
Abstract
In this work, the cooperation problem between two populations in a periodically varying environment is discussed. In particular, the two-population prisoner's dilemma game with periodically oscillating payoffs is discussed, such that the time-average of these oscillations over the period of environmental variations vanishes. The possible overlaps of these oscillations generate completely new dynamical effects that drastically change the phase space structure of the two-population evolutionary dynamics. Due to these effects, the emergence of some level of cooperators in both populations is possible under certain conditions on the environmental variations. In the domain of stable coexistence the dynamics of cooperators in each population form stable cycles. Thus, the cooperators in each population promote the existence of cooperators in the other population. However, the survival of cooperators in both populations is not guaranteed by a large initial fraction of them.
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Affiliation(s)
- S. G. Babajanyan
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design8 Somapah Road S487372Singapore
| | - Wayne Lin
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design8 Somapah Road S487372Singapore
| | - Kang Hao Cheong
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design8 Somapah Road S487372Singapore
- SUTD‐Massachusetts Institute of Technology International Design CentreS487372Singapore
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10
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Lai JW, Cheong KH. Parrondo effect in quantum coin-toss simulations. Phys Rev E 2020; 101:052212. [PMID: 32575251 DOI: 10.1103/physreve.101.052212] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Accepted: 04/28/2020] [Indexed: 12/30/2022]
Abstract
Game A + Game B = Game C. Parrondo's games follow this basic structure where A and B are losing games and C is a winning game-a phenomenon called Parrondo's paradox. These games can take on a wider class of definitions and exhibit these paradoxical results. In this paper, we show three paradoxical cases. (i) The successive "tossing" of a single fair quantum coin gives a biased result, a previously known result. (ii) The random tossing of two quantum coins, each with successive biased expectations, gives an average random walk position of approximately zero. (iii) The sequential periodic tossing of two quantum coins, each with successive negative biased expectations, gives an average random walk with positive expectation. Using these results, we then propose a protocol for identifying and classifying quantum operations that span the same Hilbert space for a two-level quantum system.
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Affiliation(s)
- Joel Weijia Lai
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore S487372
| | - Kang Hao Cheong
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore S487372 and SUTD-Massachusetts Institute of Technology International Design Centre, Singapore S487372
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11
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Cheong KH, Koh JM, Jones MC. Paradoxical Survival: Examining the Parrondo Effect across Biology. Bioessays 2020; 41:e1900027. [PMID: 31132170 DOI: 10.1002/bies.201900027] [Citation(s) in RCA: 55] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Revised: 03/26/2019] [Indexed: 01/17/2023]
Abstract
Parrondo's paradox, in which losing strategies can be combined to produce winning outcomes, has received much attention in mathematics and the physical sciences; a plethora of exciting applications has also been found in biology at an astounding pace. In this review paper, the authors examine a large range of recent developments of Parrondo's paradox in biology, across ecology and evolution, genetics, social and behavioral systems, cellular processes, and disease. Intriguing connections between numerous works are identified and analyzed, culminating in an emergent pattern of nested recurrent mechanics that appear to span the entire biological gamut, from the smallest of spatial and temporal scales to the largest-from the subcellular to the complete biosphere. In analyzing the macro perspective, the pivotal role that the paradox plays in the shaping of biological life becomes apparent, and its identity as a potential universal principle underlying biological diversity and persistence is uncovered. Directions for future research are also discussed in light of this new perspective.
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Affiliation(s)
- Kang Hao Cheong
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore, Singapore
| | - Jin Ming Koh
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore, Singapore
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12
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Tan Z, Koh JM, Koonin EV, Cheong KH. Predator Dormancy is a Stable Adaptive Strategy due to Parrondo's Paradox. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2020; 7:1901559. [PMID: 32042555 PMCID: PMC7001654 DOI: 10.1002/advs.201901559] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Revised: 08/09/2019] [Indexed: 05/20/2023]
Abstract
Many predators produce dormant offspring to escape harsh environmental conditions, but the evolutionary stability of this adaptation has not been fully explored. Like seed banks in plants, dormancy provides a stable competitive advantage when seasonal variations occur, because the persistence of dormant forms under harsh conditions compensates for the increased cost of producing dormant offspring. However, dormancy also exists in environments with minimal abiotic variation-an observation not accounted for by existing theory. Here it is demonstrated that dormancy can out-compete perennial activity under conditions of extensive prey density fluctuation caused by overpredation. It is shown that at a critical level of prey density fluctuations, dormancy becomes an evolutionarily stable strategy. This is interpreted as a manifestation of Parrondo's paradox: although neither the active nor dormant forms of a dormancy-capable predator can individually out-compete a perennially active predator, alternating between these two losing strategies can paradoxically result in a winning strategy. Parrondo's paradox may thus explain the widespread success of quiescent behavioral strategies such as dormancy, suggesting that dormancy emerges as a natural evolutionary response to the self-destructive tendencies of overpredation and related biological phenomena.
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Affiliation(s)
- Zhi‐Xuan Tan
- Science and Math ClusterSingapore University of Technology and Design (SUTD)SingaporeS487372Singapore
| | - Jin Ming Koh
- Science and Math ClusterSingapore University of Technology and Design (SUTD)SingaporeS487372Singapore
| | - Eugene V. Koonin
- National Center for Biotechnology InformationNational Library of MedicineNational Institutes of HealthBethesdaMD20894USA
| | - Kang Hao Cheong
- Science and Math ClusterSingapore University of Technology and Design (SUTD)SingaporeS487372Singapore
- SUTD‐Massachusetts Institute of Technology International Design CentreSingaporeS487372Singapore
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13
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Saakian DB, Cheong KH, Koh JM. Solution of the Crow-Kimura model with changing population size and Allee effect. Phys Rev E 2018; 98:012405. [PMID: 30110762 DOI: 10.1103/physreve.98.012405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Indexed: 11/07/2022]
Abstract
The Crow-Kimura model is commonly used in the modeling of genetic evolution in the presence of mutations and associated selection pressures. We consider a modified version of the Crow-Kimura model, in which population sizes are not fixed and Allee saturation effects are present. We demonstrate the evolutionary dynamics in this system through an analytical approach, examining both symmetric and single-peak fitness landscape cases. Especially interesting are the dynamics of the populations near extinction. A special version of the model with saturation and degradation on the single-peak fitness landscape is investigated as a candidate of the Allee effect in evolution, revealing reduction tendencies of excessively large populations, and extinction tendencies for small populations. The analytical solutions for these dynamics are presented with accuracy O(1/N), where N is the number of nucleotides in the genome.
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Affiliation(s)
- David B Saakian
- Theoretical Physics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam.,Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam.,A. I. Alikhanyan National Science Laboratory (Yerevan PhysicsInstitute) Foundation, 2 Alikhanian Brothers Street, Yerevan 375036, Armenia
| | - Kang Hao Cheong
- Engineering Cluster, Singapore Institute of Technology, 10 Dover Drive, Singapore 138683, Singapore
| | - Jin Ming Koh
- Engineering Cluster, Singapore Institute of Technology, 10 Dover Drive, Singapore 138683, Singapore
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14
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Reply to Cheong et al.: Unicellular survival precludes Parrondo's paradox. Proc Natl Acad Sci U S A 2018; 115:E5260. [PMID: 29752383 DOI: 10.1073/pnas.1806709115] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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15
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Cheong KH, Saakian DB, Zadourian R. Allison mixture and the two-envelope problem. Phys Rev E 2017; 96:062303. [PMID: 29347428 DOI: 10.1103/physreve.96.062303] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Indexed: 06/07/2023]
Abstract
In the present study, we have investigated the Allison mixture, a variant of the Parrondo's games where random mixing of two random sequences creates autocorrelation. We have obtained the autocorrelation function and mutual entropy of two elements. Our analysis shows that the mutual information is nonzero even if two distributions have identical average values. We have also considered the two-envelope problem and solved for its exact probability distribution.
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Affiliation(s)
- Kang Hao Cheong
- Engineering Cluster, Singapore Institute of Technology, 10 Dover Drive, Singapore 138683, Singapore
| | - David B Saakian
- Theoretical Physics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
- Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam
- A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, 2 Alikhanian Brothers Street, Yerevan 375036, Armenia
| | - Rubina Zadourian
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
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16
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Tan ZX, Cheong KH. Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction. eLife 2017; 6. [PMID: 28084993 PMCID: PMC5319843 DOI: 10.7554/elife.21673] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2016] [Accepted: 01/11/2017] [Indexed: 11/13/2022] Open
Abstract
Organisms often exhibit behavioral or phenotypic diversity to improve population fitness in the face of environmental variability. When each behavior or phenotype is individually maladaptive, alternating between these losing strategies can counter-intuitively result in population persistence-an outcome similar to the Parrondo's paradox. Instead of the capital or history dependence that characterize traditional Parrondo games, most ecological models which exhibit such paradoxical behavior depend on the presence of exogenous environmental variation. Here we present a population model that exhibits Parrondo's paradox through capital and history-dependent dynamics. Two sub-populations comprise our model: nomads, who live independently without competition or cooperation, and colonists, who engage in competition, cooperation, and long-term habitat destruction. Nomads and colonists may alternate behaviors in response to changes in the colonial habitat. Even when nomadism and colonialism individually lead to extinction, switching between these strategies at the appropriate moments can paradoxically enable both population persistence and long-term growth.
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Affiliation(s)
| | - Kang Hao Cheong
- Engineering Cluster, Singapore Institute of Technology, , Singapore
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17
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Ye Y, Cheong KH, Cen YW, Xie NG. Effects of behavioral patterns and network topology structures on Parrondo's paradox. Sci Rep 2016; 6:37028. [PMID: 27845430 PMCID: PMC5109481 DOI: 10.1038/srep37028] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2016] [Accepted: 10/24/2016] [Indexed: 11/09/2022] Open
Abstract
A multi-agent Parrondo's model based on complex networks is used in the current study. For Parrondo's game A, the individual interaction can be categorized into five types of behavioral patterns: the Matthew effect, harmony, cooperation, poor-competition-rich-cooperation and a random mode. The parameter space of Parrondo's paradox pertaining to each behavioral pattern, and the gradual change of the parameter space from a two-dimensional lattice to a random network and from a random network to a scale-free network was analyzed. The simulation results suggest that the size of the region of the parameter space that elicits Parrondo's paradox is positively correlated with the heterogeneity of the degree distribution of the network. For two distinct sets of probability parameters, the microcosmic reasons underlying the occurrence of the paradox under the scale-free network are elaborated. Common interaction mechanisms of the asymmetric structure of game B, behavioral patterns and network topology are also revealed.
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Affiliation(s)
- Ye Ye
- Department of Mechanical Engineering, Anhui University of Technology, Anhui Ma'anshan 243002, China
| | - Kang Hao Cheong
- Engineering Cluster, Singapore Institute of Technology, 10 Dover Drive, Singapore 138683, Singapore
| | - Yu-Wan Cen
- Department of Mechanical Engineering, Anhui University of Technology, Anhui Ma'anshan 243002, China
| | - Neng-Gang Xie
- Department of Mechanical Engineering, Anhui University of Technology, Anhui Ma'anshan 243002, China
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