The Price of Anarchy for Minsum Related Machine Scheduling

We address the classical uniformly related machine scheduling problem with minsum objective. The problem is solvable in polynomial time by the algorithm of Horowitz and Sahni. In that solution, each machine sequences its jobs shortest first. However when jobs may choose the machine on which they are processed, while keeping the same sequencing rule per machine, the resulting Nash equilibria are in general not optimal. The price of anarchy measures this optimality gap. By means of a new characterization of the optimal solution, we show that the price of anarchy in this setting is bounded from above by 2. We also give a lower bound of e/(e-1). This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem, where the price of anarchy equals 4. Interestingly, as Nash equilibria coincide with shortest processing time first (SPT) schedules, the same bounds hold for SPT schedules. Thereby, our work also fills a gap in the literature

Artificial Intelligence techniques to support cognitive rehabilitation

In recent years, the Guttmann Institute has incorporated an intelligent assistant as a predicted and personalized decision support system (PPDSS). This PPDSS helps plan rehabilitation sessions for patients suffering from acquired brain injury (ABI). Results show questionable planning when comparing patient profiles and their assigned tasks. The distribution of percentage of effort does not perfectly match the distribution of the cognitive profile. This paper provides a thorough analysis of the patient profiles, showing that a patient’s initial profile and the task execution scores during their first few sessions can be used to better predict their final improvement, to a certain degree of accuracy. Furthermore, results show that more executions of tasks does not automatically lead to improvement. Practice does not seem to make perfect. The proposed technique involves the incorporation of task-weights in the new scheduler

Kunstmestvervangers onderzocht; Monitoring installaties

Onderzoek naar installaties die worden ingezet bij de verwerking van mes

SUPERSET: A (Super)Natural Variant of the Card Game SET

We consider Superset, a lesser-known yet interesting variant of the famous card game Set. Here, players look for Supersets instead of Sets, that is, the symmetric difference of two Sets that intersect in exactly one card. In this paper, we pose questions that have been previously posed for Set and provide answers to them; we also show relations between Set and Superset. For the regular Set deck, which can be identified with F^3_4, we give a proof for the fact that the maximum number of cards that can be on the table without having a Superset is 9. This solves an open question posed by McMahon et al. in 2016. For the deck corresponding to F^3_d, we show that this number is Omega(1.442^d) and O(1.733^d). We also compute probabilities of the presence of a superset in a collection of cards drawn uniformly at random. Finally, we consider the computational complexity of deciding whether a multi-value version of Set or Superset is contained in a given set of cards, and show an FPT-reduction from the problem for Set to that for Superset, implying W[1]-hardness of the problem for Superset

Grenswaarden voor het N- en P-gehalte in vaste mest

The variation and limiting values of the N and P content of solid livestock manure were determined from the composition of manure that was transported from 2008 to 2010 as registered by the Dutch Regulation Service. The realibility of the data was evaluated on the basis of N- and P excreted by livestock and manure volumes