Two articles were published as a result of the COPROLOGS project. The paper "Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functions" by Balázs Csáji Csanád and Bálint Horváth was published in IEEE Control Systems Letters, while the article "Joint replenishment meets scheduling" by Péter Györgyi, Tamás Kis, Tímea Tamási and József Békési was published in the Journal of Scheduling.
„This letter introduces a method to construct confidence bands for bounded, band-limited functions based on a finite sample of input-output pairs. The approach is distribution-free w.r.t. the observation noises and only the knowledge of the input distribution is assumed. It is nonparametric, that is, it does not require a parametric model of the regression function and the regions have non-asymptotic guarantees. The algorithm is based on the theory of Paley-Wiener reproducing kernel Hilbert spaces. This letter first studies the fully observable variant, when there are no noises on the observations and only the inputs are random; then it generalizes the ideas to the noisy case using gradient-perturbation methods. Finally, numerical experiments demonstrating both cases are presented” – explains the first paper's abstract.
The article "Joint replenishment meets scheduling" by Péter Györgyi, Tamás Kis, Tímea Tamási and József Békési is published in the Journal of Scheduling. According to the abstract, they investigated the combination of the joint replenishment problem (JRP) and single-machine scheduling with release dates.
„In this paper, we consider a combination of the joint replenishment problem (JRP) and single-machine scheduling with release dates. There is a single machine and one or more item types. Each job has a release date, a positive processing time, and it requires a subset of items. A job can be started at time t only if all the required item types were replenished between the release date of the job and time point t. The ordering of item types for distinct jobs can be combined. The objective is to minimize the total ordering cost plus a scheduling criterion, such as total weighted completion time or maximum flow time, where the cost of ordering a subset of items simultaneously is the sum of a joint ordering cost, and an additional item ordering cost for each item type in the subset. We provide several complexity results for the offline problem, and competitive analysis for online variants with min–sum and min–max criteria, respectively” – reads the abstract.