Monday, January 24, 2022

 I have recently uploaded 2 python modules to pypi:

  1. OEISsequences: Python functions to generate The On-Line Encyclopedia of Integer Sequences (OEIS) sequences. Available at: OEISsequences · PyPI. Functions are available to compute the n-th term of a sequence or generate subsequence terms (and sometimes both) depending on what is more efficient.

  2. algebraic-connectivity-directed: Python functions to compute various notions of algebraic connectivity of directed graphs. Available at: algebraic-connectivity-directed · PyPI. I defined an extension of Fiedler's seminal algebraic connectivity concept (1973) to directed graphs in a 2005 Linear and Multilinear Algebra paper and have refined the concept in subsequent papers over the years to better capture the connectivity of directed graphs especially when they are "far" from being undirected. More information on these various notions of algebraic connectivity of directed graphs can be found in the following references:

    1. C. W. Wu, "Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling", IEEE Transactions on Circuits and Systems-I, vol. 50, no. 2, pp. 294-297, 2003.

    2. C. W. Wu, "Algebraic connecivity of directed graphs", Linear and Multilinear Algebra, vol. 53, no. 3, pp. 203-223, 2005.

    3. C. W. Wu, "On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs", Linear Algebra and its applications, vol. 402, pp. 207-227, 2005.

    4. C. W. Wu, "Synchronization in networks of nonlinear dynamical systems coupled via a directed graph", Nonlinearity, vol. 18, pp. 1057-1064, 2005.

    5. C. W. Wu, "Synchronization in Complex Networks of Nonlinear Dynamical Systems", World Scientific, 2007.

    6. C. W. Wu, "Synchronization in dynamical systems coupled via multiple directed networks," IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 68, no. 5, pp. 1660-1664, 2021.