[1]
Ali, I., Brunner, H. and Tang, T., A spectral method for pantograph-type delay differential equations and its convergence analysis, J. Comput Math., 27 (2009), pp. 254–265.

[2]
Back, Joakim, Nobile, Fabio, Tamellini, Lorenzo and Tempone, Raul, Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison, Hesthaven, J. S. and Ronquist, E. M. eds., Lecture Notes in Computational Science and Engineering, 76 (Springer, 2011) 43–62, Selected papers from the ICOSAHOM '09 conference.

[3]
Brunner, H., Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge University Press, Cambridge, 2004.

[4]
Campbell, S. A., Edwards, R. and Van Den Driessche, P., Delayed coupling between two neural network loops, SIAM J. Appl. Math., 65(1) (2004), pp. 316–335.

[5]
Clenshaw, C. W. and Curtis, A. R., A method for numerical integration on an automatic computer, Numer. Math., 2 (1960), pp. 197–205.

[6]
Fishman, G., Monte Carlo: Concepts, Algorithms, and Applications, Springer-Verlag, New York, 1996.

[7]
Gao, Z. and Zhou, T., On the choice of design points for least square polynomial approximations with application to uncertainty quantification, Commun. Comput. Phys., accepted, 2014.

[8]
Ghanem, R. and Spanos, P., Stochastic Finite Elements: A Spectral Approach, SpringerVerlag, New York, 1991.

[9]
Hoang, V. H. and Schwab, C., Sparse tensor Galerkin discretizations for parametric and random parabolic PDEs: I. Analytic regularity and gPC-approximation, Report 2010-11, Seminar for Applied Mathematics, ETH Zurich, 2010.

[10]
Hoang, V. H. and Schwab, C., Analytic regularity and gPC approximation for parametric and random 2nd order hyperbolic PDEs, Report 2010-19, Seminar for Applied Mathematics, ETH Zurich, 2010.

[11]
Lotka, A., Elements of Physical Biology, Williams and Wilkins, Baltimore, 1925.

[12]
Migliorati, G., Nobile, F., Schwerin, E. and Tempone, R., Analysis of the discrete L2 projection on polynomial spaces with random evaluations, Found. Comput. Math., D0I:10.1007/s10208-013-9186-4, 2014.

[13]
Nobile, F., Tempone, R. and Webster, C., A sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal., 46/5 (2008), pp. 2309–2345.

[14]
Nobile, F., Tempone, R. and Webster, C., An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal., 46/5 (2008), pp. 2411–2442.

[15]
Novak, E. and Ritter, K., High dimensional integration of smooth functions over cubes, Numer. Math., 75 (1996), pp. 79–97.

[16]
Novak, E. and Ritter, K., Simple cubature formulas with high polynomial exactness, Constructive Approx., 15 (1999), pp. 499–522.

[17]
Palanisamy, K. R., Balachandran, K. and Ramasamy, S.R., Optimal control of linear time-varying delay systems via single-term Walsh series, Proc. IEEE, 135 (1988), 332.

[18]
Poleszczuk, Jan, Delayed differential equations in description of biochemical reactions channels, XXI Congress of Differential Equations and Applications XI Congress of Applied Mathematics Ciudad Real, 21-25 September 2009 (pp. 1–8).

[19]
Ruiz-Herrera, A., Chaos in delay differential equations with applications in population dynamics, Discrete Contin. Dyn. Syst. 33(4) (2013), pp. 1633–1644.

[20]
Smolyak, S., Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl., 4 (1963), pp. 240–243.

[21]
Tang, T. and Zhou, T., Convergence analysis for stochastic collocation methods to scalar hyperbolic equations with a random wave speed, Commun. Comput. Phys., 8 (2010), pp. 226–248.

[22]
Trefethen, L. N., Is Gauss quadrature better than Clenshaw-Curtis?, SIAM Rev., 2006.

[23]
Villasana, M. and Radunskaya, A., A delay differential equation model for tumor growth, J. Math. Biol., 47(3) (2003), pp. 270–294.

[24]
Volterra, V., Varizioni e fluttuazioni del numero d’individui in specie animali conviventi, Mem. R. Acad. Naz. dei Lincei (ser. 6), 2 (1926), pp. 31–113.

[25]
Wang, Z. Q. and Wang, L. L., A Legendre-Gauss collocation method for nonlinear delay differ-ential equations, Dis. Cont. Dyn. Sys. B, 13(3) (2010), pp. 685–708.

[26]
Xiu, D., Efficient collocational approach for parametric uncertainty analysis, Commun. Comput. Phys., 2 (2007), pp. 293–309.

[27]
Xiu, D. and Hesthaven, J. S., High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., 27 (2005), pp. 1118–1139.

[28]
Xiu, D. and Karniadakis, G. E., Modeling uncertainty inflow simulations via generalized polynomial chaos, J. Comput. Phys., 187 (2003). pp. 137–167.

[29]
Xiu, D. and Karniadakis, G. E., The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24(2), pp. 619–644.

[30]
Zhou, T., Narayan, A. and Xu, Z., Multivariate discrete least-squares approximations with a new type of collocation grid, available online: http://arxiv.org/abs/1401.0894, January 2014.
[31]
Zhou, T. and Tang, T., Galerkin methods for stochastic hyperbolic problems using bi-orthogonal polynomials, J. Sci. Comput., 51 (2012), pp. 274–292.

[32]
Zhou, T. and Tang, T., Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed, J. Comput. Math., 30(6) (2012), pp. 643–656.

[33]
Zhou, T., Stochastic Galerkin methods for elliptic interface problems with random input, J. Comput. App. Math., 236 (2011), pp. 782–792.