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Fuzzy Hypercubes and their time-like evolution

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Abstract

The concept of Fuzzy Hypercube is defined as a simple trigonometric extension of the binary structure of an N-dimensional Boolean hypercube. Moreover, in the present study, there is a discussion on the possibility of defining Fuzzy Hypercubes as a set of \( 2^{N} \) vertices, which remain Stationary or might undergo Synchronous or Asynchronous evolution. Finally, the connection of Fuzzy Hypercubes with multivariate discrete probability distributions is also considered.

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Notes

  1. Such a time-dependent probability choice looks like a not so common situation. In a bivariate case would appear as if a coin toss probability could evolve with each observation, which is not a usual studied phenomenon. However, it appears very similar to the possible evolution of a quantum spin system.

References

  1. K. Balasubramanian, J. Math. Chem. 56, 2707–2723 (2018)

    Article  CAS  Google Scholar 

  2. K. Balasubramanian, J. Math. Chem. 57, 665–689 (2019)

    Article  Google Scholar 

  3. R. Carbó-Dorca, J. Math. Chem. 22, 143–147 (1997)

    Article  Google Scholar 

  4. R. Carbó, B. Calabuig, Molecular similarity and quantum chemistry, in Concepts and Applications of Molecular Similarity, ed. by M.A. Johnson, G.M. Maggiora (Wiley, New York, 1990), pp. 147–171

    Google Scholar 

  5. R. Carbó, B. Calabuig, Intl. J. Quant. Chem. 42, 1695–1709 (1992)

    Article  Google Scholar 

  6. R. Carbó-Dorca, J. Math. Chem. 54, 1213–1220 (2016)

    Article  Google Scholar 

  7. R. Carbó-Dorca, J. Math. Chem. 55, 914–940 (2017)

    Article  Google Scholar 

  8. R. Carbó-Dorca, J. Math. Chem. 56, 1349–1352 (2018)

    Article  Google Scholar 

  9. R. Carbó-Dorca, J. Math. Chem. 56, 1353–1356 (2018)

    Article  Google Scholar 

  10. R. Carbó-Dorca, J. Math. Sci. Model. (JMSM) 1, 1–14 (2018)

    Google Scholar 

  11. R. Carbó-Dorca, J. Math. Chem. 57, 694–696 (2019)

    Article  Google Scholar 

  12. R. Carbó-Dorca, J. Math. Chem. 57, 697–700 (2019)

    Article  Google Scholar 

  13. R. Carbó-Dorca, T. Chakraborty, J. Comput. Chem. 40, 2653 (2019)

    Article  Google Scholar 

  14. R. Carbó-Dorca, T. Chakraborty, J. Math. Chem. 57, 2182–2194 (2019)

    Article  Google Scholar 

  15. R. Carbó-Dorca, J. Math. Chem. 58, 1–5 (2020)

    Article  Google Scholar 

  16. L. Cardelli, M. Kwiatkowska, M. Whitby, Nat. Comput. 17, 109–130 (2018)

    Article  CAS  Google Scholar 

  17. J. Olejarz, K. Kaveh, C. Veller, M.A. Novak, J. Theor. Biol. 457, 170–179 (2018)

    Article  Google Scholar 

  18. R. Carbó-Dorca, J. Math. Chem. 30, 227–245 (2001)

    Article  Google Scholar 

  19. R. Carbó-Dorca, J. Math. Chem. 36, 75–81 (2004)

    Article  Google Scholar 

  20. R. Carbó-Dorca, J. Math. Chem. 54, 1751–1757 (2016)

    Article  Google Scholar 

  21. R. Carbó-Dorca, C. Muñoz-Caro, A. Niño, S. Reyes, J. Math. Chem. 55, 1869–1877 (2017)

    Article  Google Scholar 

  22. S. Kais (ed.), Quantum Information and Computation for Chemistry (Advances in Chemical Physics, vol. 54), S.A. Rice, A.R. Dinner (Series Editors) (2014)

  23. F. Arute, K. Arya, R. Babbush, D. Bacon, J.C. Bardin, R. Barends, R. Biswas, S. Boixo, F.G.S.L. Brandao, D.A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M.P. Harrigan, M.J. Hartmann, A. Ho, M. Hoffmann, T. Huang, T.S. Humble, S.V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P.V. Klimov, S. Knysh, A. Korotkov, F. Kostritsa, D. Landhuis, M. Lindmark, E. Lucero, D. Lyakh, S. Mandrà, J.R. McClean, M. McEwen, A. Megrant, X. Mi, K. Michielsen, M. Mohseni, J. Mutus, O. Naaman, M. Neeley, Ch. Neill, M.Y. Niu, E. Ostby, A. Petukhov, J.C. Platt, Ch. Quintana, E.G. Rieffel, P. Roushan, N.C. Rubin, D. Sank, K.J. Satzinger, V. Smelyanskiy, K.J. Sung, M.D. Trevithick, A. Vainsencher, B. Villalonga, T. White, Z.J. Yao, P. Yeh, A. Zalcman, H. Neven, J.M. Martinis, Nature 574, 505–511 (2019)

    Article  CAS  Google Scholar 

  24. E. Pednault, J. A. Gunnels, G. Nannicini, L. Horesh, R. Wisnieff. arxiv preprint, arXiv:1910.09534 v2 (2019)

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Authors and Affiliations

  1. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 2V4, Canada

    Jing Chang

  2. Institut de Química, Computacional i Catàlisi, Universitat de Girona, 17071, Girona, Catalonia, Spain

    Ramon Carbó-Dorca

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  1. Jing Chang
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  2. Ramon Carbó-Dorca
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Correspondence to Ramon Carbó-Dorca.

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Chang, J., Carbó-Dorca, R. Fuzzy Hypercubes and their time-like evolution. J Math Chem 58, 1337–1344 (2020). https://doi.org/10.1007/s10910-020-01137-y

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