Judul: Kajian aktivitas antimikroba buah andalehat (Chrysophyllum roxburghii G. Don) dan mobe (Ficus sp)
Abstrak: Andalehat (Chrysopyhllum roxburghii G.Don.) dan mobe (Ficus sp.) adalah jenis rempah yang sering digunakan pada masakan khas Sumetera Utara, contohnya gulai ikan mas arsik, naniura dan tinombur. Penggunaan andalehat dan mobe semakin menurun, karena upacara adat yang dianggap tidak atau kurang praktis menjadi jarang dipenuhi dengan lengkap. Bahkan dikhawatirkan rempah andalehat dan mobe terancam punah jika tidak dipertahankan penggunaannya. Tujuan penelitian adalah mempelajari daya antimikroba terhadap bakteri patogen dan perusak makanan dari buah andalehat dan mobe. Diharapkan andalehat dan mobe dapat digunakan sebagai sumber alternatif senyawa antimikroba yang dapat diaplikasikan pada produk pangan secara luas, sekaligus menghindari kepunahannya...
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Judul: Kajian Aktivitas Antimikroba Buah Andaliman (Zanthoxylum acanthopodicum) dan Antarasa (Litsea cubeba)
Abstrak: Indonesia dikenal sebagai salah satu negara pusat keraganlan genetika dari tumbuhan rempah-renlpah. Rempah-rempah selain digunakan sebagai obat-obatan tradisional, juga digunakan sebagai bumbu masakan untuk memberikan citarasa dan nlembangkitkan selera makan. Buah andaliman dan antarasa adalah rempah-rempah khas Sumatera Utara. Buah andaliman sering digunakan oleh suku Batak sebagai bulnbu campuran rnasakan atau campuran bumbu samba1 khas untuk berbagai jenis makanan, seperti ikan mas arsik, naniura dan natinombur. Buah antarasa mempunyai rasa dan buah mirip andaliman, serta belum banyak dibudidayakan.
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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