Smooth monotonous functions reconstruction

We consider the problem of smooth monotonous function reconstruction on the basis of it (exact or approached) values in some points We offer a variant of accurate statement of the problem and methods of its exact and approached solution in spreadsheets Examples show that existing methods of reconstruction not always provide monotonicity of the reconstructed functionFunction of one variable; smoothness; monotonicity; reconstruction; random errors

Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behaviour, and dissipative spin dynamics in the spin boson modelComment: 4 pages, 4 figures, revised version accepted for publication in PR

Universal linear relations between susceptibility and Tc in cuprates

We developed an experimental method for measuring the intrinsic susceptibility \chi of powder of cuprate superconductors in the zero field limit using a DC-magnetometer. The method is tested with lead spheres. Using this method we determine \chi for a number of cuprate families as a function of doping. A universal linear (and not proportionality) relation between Tc and \chi is found. We suggest possible explanations for this phenomenon.Comment: Accepted for publication in PR

Tractability of multivariate problems for standard and linear information in the worst case setting: part II

We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproducing kernel Hilbert space so that function values are well defined. We prove QPT for algorithms that use only function values under the three assumptions: 1) the minimal errors for the univariate case decay polynomially fast to zero, 2) the largest singular value for the univariate case is simple and 3) the eigenfunction corresponding to the largest singular value is a multiple of the function value at some point. The first two assumptions are necessary for QPT. The third assumption is necessary for QPT for some Hilbert spaces

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Accepted versio

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner