Judul: Aktivitas Antioksidan Ekstrak Buah dan Daun Mengkudu
Abstrak: Different parts of noni (Morinda citrifolia) plant including fruit and leaf exhibited antioxidant activity. This study was conducted to investigate the antioxidant activity, total phenol, and antioxidant compound group of Noni`s leaf and fruit extracts fractions. This fruit and leaf ethyl acetate extracts were fractionated by column chromatography, yielded 4 and 7 fractions based on the identical thin layer chromatography (TLC) profile. Antioxidant activities of extracts fractions were determined by radical scavenging assay using 2,2-diphenyl-1- picrylhydrazyl (DPPH) radical and the total phenolic contents were measured using Folin-Ciocalteau method. Fraction 1 (IC50 38.18 ppm) of 4 fruit extract fractions and fraction 5 (IC50 85.86 ppm) of 7 leaf extract fractions revealed the highest antioxidant activity, though lower than vitamin C (IC50 3.85 ppm). The total phenolic contents varied from 0.40 mg of gallic acid equivalent/gram dry fruit and 1.15 mg of gallic acid equivalent/gram dry leaf. The result of phytochemical analysis confirmed the responsible antioxidant compounds present in fruit and leaf were considered as alkaloid and flavonoid. In addition, nonphenol compounds had a role as antioxidant acitivity in fruit.
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Judul: Aktivitas Antioksidan Fraksi Teraktif Buah dan Daun Asam
Abstrak: Tamarind plant (Tamarindus indica) contain tannins, flavonoids, and saponins which are usually have antioxidant activity. The purpose of this study was to determine antioxidant activity and total phenolic content of the most active fraction of tamarind fruits and leaves. Antioxidant activity was determined by 1,1-diphenyl-2-picrylhydrazyl (DPPH) free radical scavenging method and total phenolic content by Folin-Ciocalteu method. The result showed that the most active fraction of tamarind fruits and leaves had IC50 value of 293.22 mg/L and 57.89 mg/L, respectively. These results were higher compared to ascorbic acid as positive control which was 2.12 mg/L. Total phenolic content of the most active fraction of tamarind fruits and leaves was 100.48 mg gallic acid equivalent/100 g dry fruits and 107.44 mg gallic acid equivalent/100 g dry leaves, respectively. The most active fraction of tamarind leaves had higher antioxidant activity compared to its fruit, however both fractions were lower compared to ascorbic acid.
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Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm