Judul: Aktivitas Penghambatan Ekstrak Sirih Merah Piper crocatum terhadap Pembentukan Malondialdehida (MDA) dan Enzim Tirosinase
Abstrak: Piper crocatum leave bark is a medicinal plant. It contains antioxidant compounds. The objectives of this research was to determine the antioxidant activity and inhibitory activity to tyrosinase of P. crocatum extract. Extraction process of Piper crocatum was conducted separately by using the solvent ethanol 70% and n-hexane. Determination of antioxidant activity was conducted with Thiobarbituric acid method (TBA) and for tyrosinase inhibitory activity using microplate reader. The results showed that the ethanol extract at concentration of 200 ppm higher (α>0.05), inhibitory effects than vitamin E on the formation malondialdehida. n-hexane extract at concentration of 200 ppm higher (α>0.05). Tyrosinase inhibition activity test showed the ethanol extract has IC50 1655 ppm, n-hexane extract has IC50 3090.56 ppm. Ethanol extract has inhibitory MDA and enzyme tyrosinase than n-hexane extract.
Keyword: Piper crocatum, Tyrosinase, Antioxidative activity

Judul: Aktivitas Antioksidasi Campuran Ekstrak Daun Sirih Merah dan Kulit Kayu Manis
Abstrak: Piper crocatum leaves and Cinnamomum burmanii bark are medicinal plants. The plants compounds as antioxidant. The objectives of this research are to determine the antioxidant activity of the extract mixture P. crocatum and C. burmanii with Thiobarbituric acid method (TBA) and 1,1-diphenyl-2-picrylhydrazyl method (DPPH). Extraction process of P. crocatum and C. burmanii was conducted separately by using the solvent water. P. crocatum extract mixed with extract of C. burmanii with a ratio of 5:0, 4:1, 3:2, 2.5:2.5, 0:5. The results showed that the 3:2 concentration 200 ppm (61%) had the same inhibitory activity as vitamin E against malondialdehida formation. Meanwhile, formula 2.5:2.5 concentration 25 ppm (59%) had the same inhibitory activity as vitamin E against DPPH radical inhibition
Keyword: Cinnamomum burmanii., Piper crocatum, antioxidative activity

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