Judul: Fraksi Ekstrak Biji Mahoni (Swietenia macrophylla) dan Studi Pustaka Antikanker Sel MCF-7, T47D, serta HCT116
Abstrak: Kanker merupakan salah satu penyakit tidak menular yang menjadi masalah kesehatan masyarakat. Pertambahan jumlah penderita kanker yang semakin banyak, mendorong dilakukannya pencarian senyawa antikanker baru. Ekstrak biji mahoni (Swietenia macrophylla) adalah produk tumbuhan yang dilaporkan memiliki aktivitas antikanker. Penelitian ini bertujuan mendapatkan fraksi aktif yang memiliki aktivitas antikanker dari spesies tersebut dan menentukan aktivitas dari ekstrak atau fraksinya terhadap sel MCF-7, T47D, dan HCT116. Fraksionasi ekstrak etil asetat menggunakan kromatografi cair vakum menghasilkan 5 fraksi dengan rendemen antara 3.73% (Fraksi 4) dan 42.22% (Fraksi 3). Hasil studi pustaka ekstrak etanol menunjukkan aktivitas antikanker terhadap sel HCT116 dan MCF-7. Ekstrak etil asetat dan fraksinya dilaporkan sitotoksik terhadap sel kanker MCF-7 dan T47D. Senyawa aktif tersebut diduga adalah golongan limonoid.
Keyword: Sel HCT116, MCF-7, T47D,, Swietenia macrophylla

Judul: Sitotoksisitas Fraksi Teraktif Biji Mahoni Berdaun Lebar (Swietenia macrophylla) terhadap Sel Kanker MCF-7
Abstrak: Tanaman mahoni (Swietenia macrophylla) memiliki aktivitas antikanker, terutama pada bagian biji. Penelitian ini bertujuan mendapatkan fraksi paling toksik terhadap larva Artemia salina pada biji mahoni, menentukan sitotoksisitasnya terhadap sel kanker payudara MCF-7, dan mengidentifikasi senyawa dugaan menggunakan liquid chromatography-mass spectrometry. Sampel dikeringudarakan dan digiling, kemudian diekstraksi dan menghasilkan ekstrak etil asetat yang mengandung golongan senyawa triterpenoid yang berperan sebagai antikanker. Ekstrak etil asetat selanjutnya difraksionasi menggunakan kromatografi cair vakum yang menghasilkan 10 fraksi. Fraksi ke-7 paling toksik terhadap A. salina dengan LC50 43.94 μg/mL. Fraksionasi kembali pada fraksi 7 menghasilkan 3 fraksi teraktif, yaitu fraksi 7a, 7b dan 7i dengan nilai LC50 berturut-turut sebesar 23.55, 34.14, dan 19.93 μg/mL. Hasil ini menunjukkan bahwa fraksi teraktif berpotensi sebagai antikanker. Fraksi 7b dengan rendemen 5.93% menunjukkan sitotoksisitas terhadap sel MCF-7 dengan persen inhibisi sebesar 76.49% pada konsentrasi 50 μg/mL. Profil kromatogram fraksi 7b diduga menunjukkan adanya golongan senyawa limonoid yang diduga berperan dalam antikanker.
Keyword: fraksionasi, sitotoksisitas, Swietenia macrophylla, toksisitas

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