We study how the stationary measure associated to analytic contractions on the unit interval behaves under changes in the contractions and the weights. Firstly we give a simple proof of the fact that the integrals of analytic functions with respect to the stationary measure vary analytically if we perturb the contractions and the weights analytically. Secondly, we consider the special case of affine contractions and we prove a conjecture of J. Fraser in on the Kantorovich–Wasserstein distance between two stationary measures associated to affine contractions on the unit interval with different rates of contraction.

Effective computational methods are important for practitioners and researchers working in strategic underground mine planning. We consider a class of problems that can be modeled as a resource-constrained project scheduling problem with optional activities; the objective maximizes net present value. We provide a computational review of math programming and constraint programming techniques for this problem, describe and implement novel problem-size reductions, and introduce an aggregated linear program that guides a list scheduling algorithm running over unaggregated instances. Practical, large-scale planning problems cannot be processed using standard optimization approaches. However, our strategies allow us to solve them to within about 5% of optimality in several hours, even for the most difficult instances.

We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the iterated function system and on the function that is being integrated. We apply this technique to estimate Hausdorff moments, Wasserstein distances and Lyapunov exponents of stationary probability measures.

This paper is devoted to the study of how thermodynamic formalism properties vary for time changes of suspension flows defined over countable Markov shifts. We prove that in general no property is preserved. We also make a topological description of the space of suspension flows according to certain thermodynamic features. For example, we show that the set of suspension flows defined over the full shift on a countable alphabet having finite entropy is open. Of independent interest might be a set of analytic tools we use to construct examples with prescribed thermodynamic behavior.