Tyler McMillen

Publications

• A. Bourget, A. Loya and T. McMillen. Spectral asymptotics for Kac-Murdock-Szegő matrices, Japanese Journal of Mathematics (2018)

• A. Bourget and T. McMillen. Asymptotics of determinants of discrete Schrödinger operators. Journal of Spectral Theory (2018)

• A. Bourget and T. McMillen. A First Szegő’s Limit Theorem for a class of non-Toeplitz matrices. Constructive Approximation (2017)

• T. McMillen, J. Xin, Y. Yu and A. Zlatos. Ballistic orbits and front speed enhancement for ABC flows. SIAM Journal on Applied Dynamical Systems,  (2016)

• T. Williams and T. McMillen. Strategies for swimming: explorations of the behavior of a neuro-musculo-mechanical model of the lamprey. Biology Open, 4, pp 253-258 (2015)

• C. Diekman, M. Golubitsky, T. McMillen and Y. Wang. Reduction and dynamics of a generalized rivalry network with two learned patterns. SIAM Journal on Applied Dynamical Systems, 11, pp 1270-1309 (2012)

• T. McMillen, P. Simen and S. Behseta. Hebbian learning in linear-nonlinear networks with tuning curves leads to near-optimal multi-alternative decision making. Neural Networks, 24, pp 417-426 (2011)

• A. Bourget and T. McMillen. On the distribution and interlacing of the zeros of Stieltjes polynomials. Proceedings of the American Mathematical Society, 138, pp 3267-3275 (2010) 

• T. McMillen and S. Behseta. On the effects of signal acuity in a multi-alternative model of decision making. Neural Computation, 22, pp 539-580 (2010)

• T. McMillen. On the eigenvalues of double band matrices. Linear Algebra and its Applications, 431, pp 1890-1897 (2009)

• A. Bourget and T. McMillen. Spectral inequalities for the quantum asymmetrical top. Journal of Physics A: Mathematical and Theoretical, 42, no. 9 (2009) 

• A. Bourget, T. McMillen and A. Vargas. Interlacing and non-orthogonality of spectral polynomials for the Lamé operator. Proceedings of the American Mathematical Society, 137, pp 1699-1710 (2009). 

• T. McMillen, A. Bourget and A. Agnew. On the zeros of complex Van Vleck polynomials. Journal of Computational and Applied Mathematics, 223, pp 862-871 (2009)

• T. McMillen, T. Williams and P. Holmes. Nonlinear muscles, passive viscoelasticity and body taper conspire to create curvature waves in anguilliform swimmers. PLoS Computational Biology, 4(8): e1000157 (2008) 

• T. McMillen and P. Holmes. An elastic rod model for anguilliform swimming. Journal of Mathematical Biology, 53, pp 843-886 (2006)

• T. McMillen and P. Holmes. The dynamics of choice among multiple alternatives. Journal of  Mathematical Psychology, 50, pp 30-57 (2006)

• T. McMillen and A. Goriely. Whip waves. Physica D, 184, pp 192-225 (2003)

• A. Goriely and T. McMillen. The shape of a cracking whip. Physical Review Letters, 88(244301) (2002)

• T. McMillen and A. Goriely. Tendril perversion in intrinsically curved rods. Journal of Nonlinear Science, 12, pp 241-281 (2002)

• J. Powell, T. McMillen, and P. White. Connecting a chemotactic model for mass action to a rapid integro-difference emulation strategy. SIAM Journal on Applied Mathematics, 59, pp 547-572 (1999)