International audienceWe describe a general framework for realistic analysis of sorting algorithms, and we applyit to the average-case analysis of three basic sorting algorithms (QuickSort, InsertionSort,BubbleSort). Usually the analysis deals with the mean number of key comparisons, buthere we view keys as words produced by the same source, which are compared via theirsymbols in lexicographic order. The ‘realistic’ cost of the algorithm is now the total numberof symbol comparisons performed by the algorithm, and, in this context, the average-caseanalysis aims to provide estimates for the mean number of symbol comparisons used by thealgorithm. For sorting algorithms, and with respect to key comparisons, the average-casecomplexity of QuickSort is asymptotic to 2n log n, InsertionSort to n^2/4 and BubbleSort ton^2/2. With respect to symbol comparisons, we prove that their average-case complexitybecomes Θ(n log_2 n), Θ(n^2), Θ(n^2 log n). In these three cases, we describe the dominantconstants which exhibit the probabilistic behaviour of the source (namely entropy andcoincidence) with respect to the algorithm

We revisit the analysis of the classical QuickSelect algorithm. Usually, the analysis deals with the mean number of key comparisons, but here we view keys as words produced by a source, and words are compared via their symbols in lexicographic order. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independentsymbols) and Markov sources, as well as many unbounded-correlation sources. The "realistic" cost of the algorithm is here the total number of symbol comparisons performed by the algorithm, and, in this context, the average-case analysis aims to provide estimates for the mean number of symbol comparisons. For the QuickSort algorithm, known average-case complexity results are of Θpn log nq in the case of key comparisons, and Θpn log 2 nq for symbol comparisons. For QuickSelect algorithms, and with respect to key comparisons, the average-case complexity is Θpnq. In this present article, we prove that, with respect to symbol comparisons, QuickSelect's average-case complexity remains Θpnq. In each case, we provide explicit expressions for the dominant constants, closely related to the probabilistic behaviour of the source.We began investigating this research topic with Philippe Flajolet, and the short version of the present paper (the ICALP'2009 paper) was written with him. As usual, Philippe played a central role, notably on the following points: introduction of the QuickVal algorithm, tameness of sources, and use of the Rice's method. He also made many experiments exhibiting the asymptotic slope ρpαq and plotted nice graphs, which are reproduced in this paper. Even though the extended abstract does not provide any proof of the analysis of the algorithm QuickQuant, Philippe also devised with us a precise plan for this proof which has now completely been written. For all these reasons, we could have added (and certainly would have liked to add) Philippe as a co-author of this paper. On the other hand, Philippe was extremely exacting of how his papers were to be written and organised, and we cannot be sure that he would have liked or validated our editing choices. In the end, this is why we have decided not to include him as a co-author, but instead, to dedicate, with deference and affection, this paper to his memory. Thank you, Philippe!

This study developed a simple two-step procedure to produce isomaltooligosaccharides (IMOs) from low-cost sweet potato starch (SPS). Effect of various reaction parameters on the steps of the synthesis process of IMOs was systematically investigated. The results show that Spezyme Xtra enzyme was the most suitable for the liquefaction step. The oligosaccharide components’ contents, including G1–G10 and G2–G6, reached 73.95 ± 0.02% and 49.24 ± 3.19%, respectively, after liquefaction. The simultaneous saccharification and transglycosylation (SST) reaction of SPS followed the liquefaction after the α-amylase activity was deactivated. This reaction was simultaneously treated by β-amylase, pullulanase, and α-transglucosidase. The effect of various reaction parameters, consisting of solution pH, reaction temperature, enzyme dosage, and reaction time, on the SST reaction to synthesize IMOs from SPS was fully studied. The results showed that the highest concentration of IMOs (IG234) reached 68.85 ± 1.82 g/L at the optimal condition. The purification of pristine IMO was performed by adding Saccharomyces cerevisiae var. diastaticus BE 134 yeast cells at the final step of the procedure. In particular, the SST reaction for the synthesis of IMOs from SPS shortened SST reaction time by three times compared with other three-step synthesis procedures of IMOs. These findings show that the SPS-derived IMOs can be applied as a novel and inexpensive prebiotic healthcare product for human gastrointestinal health, dieters, and diabetics.

The assessment of the bacteriological quality among 390 samples of bottled drinking water was studied. The samples were tested for Escherichia coli, Clostridia, total Coliform, Streptococci feacal and Pseudomonas aeruginosa. The rates of microbial contamination in bottled drinking water were of 56.7% (2017) and 50.7% (2018). The samples failed to meet QCVN drinking water standard of acceptable limits of bacterial presence including Pseudomonas aeruginosa (41.5%), total Coliform (11.8%), Clostridia (4.6%); Escherichia coli (4.9%) and Streptococcifeacal (1.3%). It is necessary to strengthen the inspection, supervision, propagation, and education that give warnings, ensure water quality and raise the awareness of producers, traders and consumers.