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Goldsborough, Andrew M.; Rautu, Stefan Alexandru; Roemer, Rudolf A. (2015)
Publisher: IOP Publishing Ltd.
Languages: English
Types: Article
Subjects: Q1, QA, QC

Classified by OpenAIRE into

arxiv: Quantitative Biology::Tissues and Organs
We study the leaf-to-leaf distances on full and complete m-ary graphs\ud using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [2] H. Wiener, J. Am. Chem. Soc. 69, 17 (1947).
    • [3] M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Boulder, CO, 1995).
    • [4] K. H. Rosen, Discrete Mathematics and Its Applications, 7th ed. (McGraw Hill, New York, NY, 2012).
    • [5] K. Leckey, R. Neininger, and W. Szpankowski, Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA) (SIAM, Philadelphia, 2013).
    • [6] L. A. Szekely, H. Wang, and T. Wu, Discrete Math. 311, 1197 (2011).
    • [7] H. Wang, ICA Bulletin 60, 62 (2010).
    • [8] P. Jacquet and M. Regnier, Normal Limiting Distribution for the Size and the External Path Length of Tries, Tech. Rep. RR-0827 (INRIA, 1988).
    • [9] P. Kirschenhofer, H. Prodinger, and W. Szpankowski, Theor. Comput. Sci. 68, 1 (1989).
    • [10] P. Kirschenhofer, H. Prodinger, and W. Szpankowski, SIAM J. Comput. 23, 598 (1994).
    • [11] U. Schollwo¨ck, Ann. Phys. 326, 96 (2011).
    • [12] A. M. Goldsborough and R. A. Ro¨mer, Phys. Rev. B 89, 214203 (2014).
    • [13] G. Evenbly and G. Vidal, J. Stat. Phys. 145, 891 (2011).
    • [14] P. Silvi, V. Giovannetti, S. Montangero, M. Rizzi, J. I. Cirac, and R. Fazio, Phys. Rev. A 81, 062335 (2010).
    • [15] M. Gerster, P. Silvi, M. Rizzi, R. Fazio, T. Calarco, and S. Montangero, Phys. Rev. B 90, 125154 (2014).
    • [16] This is the information needed by the holography methods used in Ref. [12].
    • [17] S. Kanemitsu, M. Katsurada, and M. Yoshimoto, Aequationes Math. 59, 1 (2000).
    • [18] H. Srivastava, in Essays in Mathematics and its Applications, edited by P. M. Pardalos and T. M. Rassias (Springer, Berlin/Heidelberg, 2012), p. 431.
    • [19] J. Guillera and J. Sondow, Ramanujan J. 16, 247 (2008).
    • [20] Wolfram Research Inc., Mathematica Version 9.0 (Champaign, IL, 2012).
    • [21] Y.-Y. Shi, L.-M. Duan, and G. Vidal, Phys. Rev. A 74, 022320 (2006).
    • [22] L. Tagliacozzo, G. Evenbly, and G. Vidal, Phys. Rev. B 80, 235127 (2009).
    • [23] F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006).
    • [24] M. M. Wolf, G. Ortiz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 97, 110403 (2006).
    • [25] G. Evenbly and G. Vidal, Phys. Rev. B 79, 144108 (2009).
    • [26] We emphasize that this definition of random trees is different from the definition of so-called Catalan tree graphs [1], as the number of unique graphs is given by the Catalan number Cn and does not double count the degenerate graphs as shown in the center of the n = 3 case of Fig. 6(b).
    • [27] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, London, 1994).
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