We note that by combining the techniques in [15] and [16], one can get an explicit binary code that corrects k block transpositions with O( √ kn) redundant bits. However to our knowledge this result has not appeared anywhere in the literature, and moreover it requires at least Ω( √ n) redundant bits even to correct one block transposition.
Paeonia ostii is a traditional medicinal plant popularly used in China. This study intended to evaluate the antioxidant properties and the chemical components of the flavonoid-rich extracts from the flowers of P. ostii. The results showed that the flavonoid-rich extracts from the flowers of P. ostii had strong scavenging capacities on 2,2′-Azinobis-(3-ethylbenzthiazoline-6-sulphonate) (ABTS), hydroxyls, superoxide anions, and 1,1-diphenyl-2-picrylhydrazyl (DPPH) radicals in a dose-dependent manner. Five flavonoids, dihydrokaempferol (1), apigenin-7-O-β-d-glucoside (2), apigenin-7-O-β-d-neohesperidoside (3), kaempferol-7-O-β-d-glucopyranoside (4), and kaempferol-3-O-β-d-glucopyranosyl-7-O-β-d-glucopyranoside (5), were isolated from the flavonoid-rich extracts of the flowers of P. ostii. High-performance liquid chromatography (HPLC) analysis revealed that compounds 3 and 4 were abundant in the P. ostii flower and in flavonoid-rich extracts. The main components of the flower of P. ostii are flavonoids. The high antioxidant activity of the flavonoid-rich extracts may be attributed to the high content of flavonoids. The five isolated flavonoids were the primary antioxidant ingredients, and may play important roles in the strong antioxidant activities of this flower. Based on the obtained results, the flower of P. ostii could be a potential source of natural antioxidants in food and pharmaceutical applications.
Synchronization strings are recently introduced by Haeupler and Shahrasbi [15] in the study of codes for correcting insertion and deletion errors (insdel codes). A synchronization string is an encoding of the indices of the symbols in a string, and together with an appropriate decoding algorithm it can transform insertion and deletion errors into standard symbol erasures and corruptions. This reduces the problem of constructing insdel codes to the problem of constructing standard error correcting codes, which is much better understood. Besides this, synchronization strings are also useful in other applications such as synchronization sequences and interactive coding schemes. For all such applications, synchronization strings are desired to be over alphabets that are as small as possible, since a larger alphabet size corresponds to more redundant information added.Haeupler and Shahrasbi [15] showed that for any parameter ε > 0, synchronization strings of arbitrary length exist over an alphabet whose size depends only on ε. Specifically, [15] obtained an alphabet size of O(ε −4 ), which left an open question on where the minimal size of such alphabets lies between Ω(ε −1 ) and O(ε −4 ). In this work, we partially bridge this gap by providing an improved lower bound of Ω ε −3/2 , and an improved upper bound of O ε −2 . We also provide fast explicit constructions of synchronization strings over small alphabets.Further, along the lines of previous work on similar combinatorial objects, we study the extremal question of the smallest possible alphabet size over which synchronization strings can exist for some constant ε < 1. We show that one can construct ε-synchronization strings over alphabets of size four while no such string exists over binary alphabets. This reduces the extremal question to whether synchronization strings exist over ternary alphabets.
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