If a d-dimensional integral involves an integrand ofthe functional form F (II (x I) + f2(X2) + ... ), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates XI to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and pr...

We continue our study of contour deformation as a practical tool for dealing with the sign problem using $d$-dimensional Bose gas non-zero chemical potential toy model. derive explicit expressions contours up to second order respect natural small parameter and generalise these an ansatz which evaluation Jacobian is fast ($O(1)$). examine behaviour various proposed function space-time dimensiona...

The efficient construction of higher-order interlaced polynomial lattice rules introduced recently in [6] is considered and the computational performance of these higher-order QMC rules is investigated on a suite of parametric, highdimensional test integrand functions. After reviewing the principles of their construction by the “fast component-by-component” (CBC) algorithm due to Nuyens and Coo...

Within the framework of Taylor models, no fundamental difference exists between the antiderivation and the more standard elementary operations. Indeed, a Taylor model for the antiderivative of another Taylor model is straightforward to compute and trivially satisfies inclusion monotonicity. This observation leads to the possibility of treating implicit ODEs and, more importantly, DAEs within a ...