Judul: Aktivitas Antibakteri dan Antioksidan Ekstrak Air, Etanol, dan N- heksana Sayur Hitam (Asystasia sp.) Asal Kabupaten Dogiyai-Papua.
Abstrak: The black vegetable (Asystasia sp.) plants has been used by people in Papuan as vegetable and has been known to heal wounds. The purpose of this study was to identify the content of phytochemicals, antibacterial and antioxidant from black vegetable. The black vegetable extracted with water, 70% ethanol, and n-hexane solvent. Antioxidant activity of black vegetable extracts were determined by DPPH method and antibacterial activity tested by paper disc method against Escherichia coli (Gram negative) and Staphylococcus aureus (Gram positive). The result phytochemicals showed that the black vegetable by water, ethanol 70% and n-hexane extracts contained flavonoid, saponin, tannin and steroids. Antibacterial test results showed that the extract do not have any antibacterial activity against E.coli and S. aureus. The analysis of antioxidant activity showed that the IC50 value of boiling (water), heating (water), n-hexane, without heating (water) and ethanol 70%, respectively for 1286.894 ppm, 3391.667 ppm, 1098.667 ppm, 228 842 ppm and 263.117 ppm. The conclusion, black vegetable is do not have antibacterial activity and has a weak antioxidant activity.
Keyword: E. coli. S. aureus, black vegetable, antioxidant, antibacterial

Judul: Aktivitas Antioksidan dan Sitotoksisitas Ekstrak Bawang Hitam (Allium sativum)
Abstrak: Bawang hitam adalah hasil dari proses pemanasan dan pencoklatan bawang putih, dan merupakan salah satu dari bahan olahan di Indonesia yang dapat dimanfaatkan sebagai sumber antioksidan untuk mengatasi penyakit degeneratif. Penelitian ini bertujuan melakukan ekstraksi bawang hitam yang dikeringkan untuk selanjutnya diuji aktivitas antioksidan dan sitotoksisitasnya. Bawang hitam dikeringkan dan diekstraksi dengan menggunakan 4 jenis pelarut yaitu etanol 30%, 70%, 96% dan akuades. Uji kadar air dan penghitungan rendemen dilakukan untuk mengetahui kualitas sampel. Aktivitas antioksidan ekstrak ditentukan menggunakan uji DPPH dengan vitamin C sebagai kontrol positif, dan sitotoksisitas ditentukan menggunakan uji BSLT. Hasil uji menunjukkan bawang hitam memiliki kadar air sebesar 9.16% dengan rendemen terendah dari pelarut etanol 96% sebesar 22.79 % dan rendemen tertinggi dari pelarut etanol 70% sebesar 45.34%. Ekstrak bawang hitam dengan pelarut akuades memiliki nilai IC50 dan LC50 terendah dibandingkan dengan ekstrak lainnya, dengan nilai IC50 sebesar 4.58 ppm dan nilai LC50 sebesar 758.57 ppm.
Keyword: antioksidan, bawang hitam, ekstrak, sitotoksisitas

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