Chance, Calculation and Life. Группа авторов
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or mathematical duality (showing the “relevance of negative results”), other times by stressing the role of randomness in the robustness or resilience of phenomena. The ways we acquire knowledge may be enlightened by this approach, also in view of the role of symmetries and invariance in mathematical modeling and of the strong connections between spontaneous symmetry breaking and random events discussed in Longo and Montévil (2015).
1.8. Acknowledgments
The authors have been supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant and have benefitted from discussions and collaboration with A. Abbott, S. Galatolo, M. Hoyrup, T. Paul and K. Svozil. We also thank the referees for their excellent comments and suggestions. We also warmly thank Springer Editions for authorizing the translation of the original article (Classical, Quantum and Biological Randomness as Relative Unpredictability. Invited Paper, special issue of Natural Computing, Volume 15, Issue 2, pp. 263–278, Springer, March 2016) and Louis Ter Ovanessian who provided the translation.
1.9. References
Abbott, A.A., Calude, C.S., Conder, J., Svozil, K. (2012). Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A, 86, 062109 [Online]. Available at: http://dx.doi.org/10.1103/PhysRevA.86.062109 [Accessed January 2021].
Abbott, A.A., Calude, C.S., Svozil, K. (2014a). Value-indefinite observables are almost everywhere. Physical Review A, 89, 032109 [Online]. Available at: http://dx.doi.org/10.1103/PhysRevA.89.032109 [Accessed January 2021].
Abbott, A.A., Calude, C.S., Svozil, K. (2014b). Value indefiniteness is almost everywhere. Physical Review A, 89(3), 032109 [Online]. Available at: http://arxiv.org/abs/1309.7188 [Accessed January 2021].
Abbott, A.A., Calude, C.S., Svozil, K. (2015a). A non-probabilistic model of relativised predictability in physics. Information, 6, 773–789.
Abbott, A.A., Calude, C.S., Svozil, K. (2015b). On the unpredictability of individual quantum measurement outcomes. In Fields of Logic and Computation II – Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday, Lecture Notes in Computer Science, Beklemishev, L.D., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds). Springer, 9300, 69–86 [Online]. Available at: http://dx.doi.org/10.1007/978-3-319-23534-9_4 [Accessed January 2021].
Anthes, G. (2011). The quest for randomness. Communications of the ACM, 54(4), 13–15. Arjun, R. and van Oudenaarden, R. (2008). Stochastic gene expression and its consequences. Cell, 135(2), 216–226.
Bailly, F. and Longo, G. (2009). Biological organization and anti-entropy. Journal of Biological Systems, 17(1), 63–96.
Ball, P. (2011). The dawn of quantum biology. Nature, 474, 272–274.
Barbara Bravi, G.L. (2015). The unconventionality of nature: Biology, from noise to functional randomness. In Unconventional Computation and Natural Computation Conference, Calude, C.S., Dinneen, M.J. (eds). Springer, LNCS 9252 [Online]. Available at: http://www.di.ens.fr/users/longo/files/CIM/Unconventional-NatureUCNC2015.pdf [Accessed January 2021].
Bell, J.S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447–452 [Online]. Available at: http://dx.doi.org/10.1103/RevModPhys.38.447.
Borel, E. (1909). Les probabilités dénombrables et leurs applications arithmétiques. Rendiconti del Circolo Matematico di Palermo (1884–1940), 27, 247–271 [Online]. Available at: http://dx.doi.org/10.1007/BF03019651 [Accessed January 2021].
Bork, P., Jensen, L.J., von Mering, C., Ramani, A.K., Lee, I., Marcotte, E.M. (2004). Protein interaction networks from yeast tohuman. Current Opinion in Structural Biology, 14, 292–299.
Born, M. (1926). Zur Quantenmechanik der Stoßvorg änge. Zeitschrift für Physik, 37, 863–867 [Online]. Available at: http://dx.doi.org/10.1007/BF01397477 [Accessed January 2021].
Born, M. (1969). Physics in my Generation, 2nd edition. Springer, New York.
Bros, J. and Iagolnitzer, D. (1973). Causality and local mathematical analyticity: Study. Ann. Inst. Henri Poincaré, 18(2), 147–184.
Buiatti, M. (2003). Functional dynamics of living systems and genetic engineering. Rivista di biologia, 97(3), 379–408.
Buiatti, M. and Longo, G. (2013). Randomness and multilevel interactions in biology. Theory Bioscience, 132, 139–158.
Calude, C. (2002). Information and Randomness – An Algorithmic Perspective, 2nd edition. Springer, Berlin.
Calude, C.S. and Staiger, L. (2018). Liouville numbers, Borel normality and algorithmic randomness. Theory of Computing Systems, 62(7), 1573–1585.
Calude, C.S. and Svozil, K. (2008). Quantum randomness and value indefiniteness. Advanced Science Letters, 1(2), 165–168 [Online]. Available at: http://dx.doi.org/10.1166/asl.2008.016.EprintarXiv:quant-ph/0611029 [Accessed January 2021].
Calude, C.S., Meyerstein, W., Salomaa, A. (2012). The universe is lawless or “pantôn chrêmatôn metron anthrôpon einai”. A Computable Universe: Understanding Computation & Exploring Nature as Computation, Zenil, H. (ed.). World Scientific, Singapore.
Champernowne, D.G. (1933). The construction of decimals normal in the scale of ten. The Journal of London Mathematical Society, 8, 254–260.
Chang, H.H., Hemberg, M., Barahona, M., Ingber, D.E., Huang, S. (2008). Transcription wide noise control lineage choice in mammalian progenitor cells. Nature, 453, 544–548.
Cooper, S.B. (2004). Computability Theory. Chapman Hall/CRC Mathematics Series, Boca Raton.
Copeland, A.H. and Erdös, P. (1946). Note on normal numbers. Bull. Amer. Math. Soc., 52, 857–860.
Cover, T.M. and Thomas, J.A. (1991). Elements of Information Theory. John Wiley & Sons, New York.
Deutsch, D. (1985). Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990), 400(1818), 97–117 [Online]. Available at: http://dx.doi.org/10.1098/rspa.1985.0070 [Accessed January 2021].
Dietrich, M. (2003). Richard Goldschmidt: Hopeful monsters and other “heresies”. Nature Reviews Genetics: Historical Article Journal Article Portraits, 4, 68–74.
Downey, R. and Hirschfeldt, D. (2010). Algorithmic Randomness and Complexity. Springer, Berlin.
Eagle, A. (2005). Randomness is unpredictability. British Journal for the Philosophy of Science, 56(4), 749–790 [Accessed January 2021].
Einstein, A., Podolsky, B., Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777–780 [Online]. Available at: http://dx.doi.org/10.1103/PhysRev.47.777 [Accessed January 2021].
Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S. (2002).