Randomized QuickSort and the Entropy of the Random Source

The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from $nlog n$ to $n^2$, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution

Randomized Quicksort and the Entropy of the Random Source

Abstract. The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from n log n to n 2, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution. Keywords. QuickSort, Randomized Algorithms, Entropy.

Electronic Colloquium on Computational Complexity, Report No. 59 (2004) Randomized Quicksort and the Entropy of the Random Number Generator

The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from n log n to n 2, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy, the geometrical distribution and the δ-random source.

Quality of drainage blood: Survival of red cells after re-transfusion and content of free hemoglobin and potassium

AbstractRe-transfusion of drainage blood is widely used in orthopedic surgery, but objective evidence of the efficacy of re-transfusion of drainage blood in view of post-transfusion survival of RBC has not been given so far. With this study we wanted to evaluate the efficacy and safety of transfusion of drainage blood collected with HandyVac® autotransfusion system. In 7 patients red cells in drainage blood were labeled with biotin and percentage of labeled red cells in circulation were determined immediately after re-transfusion, and during 10 days after surgery. To assess further unwanted side-effects of re-transfusion of drainage blood potassium and free hemoglobin were determined in the collected blood. Ten days after re-transfusion at mean 78.9% of drainage-blood derived RBC were found in circulation. Free hemoglobin in drainage blood ranged from 16.8 to 59.2mg/dL; potassium in drainage blood ranged from 3.84 to 4.52mmol/L. Our results suggest that re-transfusion of drainage blood collected with HandyVac® autotransfusion system is an efficient procedure that seems to be safe in view of free hemoglobin and potassium in the product

Mutations of the myeloid transcription factor CEBPA are not associated with the blast crisis of chronic myeloid leukaemia

The transcription factor CEBPA is crucial for normal myeloid differentiation. CEBPA gene mutations have been reported in patients with acute myeloid leukaemia. The inevitable evolution of chronic myeloid leukaemia (CML) in chronic phase (CP) to a fatal blast crisis (BC) is assumed to result from the acquisition of additional genetic changes in the leukaemic clone. Gain of CEBPA mutations might represent a key event causing the differentiation block observed in myeloid CML-BC, but not in CML-CP. Here, no CEBPA mutation in 95 CML-BC patients was found, suggesting a limited role, if any, of CEBPA mutations in this disorder