Judul: Ability of Bacillus altitudinis Bacteria in Degrading Anthracene Compound.
Abstrak: Hidrokarbon aromatik polisiklik (PAH) merupakan senyawa toksik yang bersifat karsinogenik dan mutagenik sehingga sangat berbahaya jika terdapat di lingkungan. Salah satu jenis PAH yang digunakan dalam penelitian ini adalah antrasena. Biodegradasi merupakan salah satu metode yang dapat digunakan untuk menangani PAH dengan memanfaatkan bakteri. Bakteri yang digunakan dalam penelitian adalah Bacillus altitudinis yang diisolasi dari tanah tercemari minyak bumi. Penambahan alkilbenzena sulfonat linear 0.04% dapat meningkatkan kemampuan bakteri dalam mendegradasi antrasena. Parameter yang diamati adalah rapatan optis, total plate count (TPC), pH, dan analisis menggunakan kromatografi gas-spektrometer massa (GCMS). Hasil pengamatan menunjukkan bahwa selama 28 hari kultivasi, terjadi perubahan pH dari 6 menjadi 8, larutan bertambah keruh, pertumbuhan optimum bakteri terjadi pada 0.4 satuan absorbans, nilai TPC naik dari 0.32×106 cfu/mL menjadi 1.53×106 cfu/mL, dan analisis antrasena setelah 28 hari menggunakan GCMS menunjukkan penurunan tinggi puncak dari hari ke-0 ke hari ke-28 sebesar 62.51%., Ability of Bacillus altitudinis Bacteria in Degrading Anthracene Compound.
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Judul: Perubahan Struktur Fenantrena Selama Proses Biodegradasi oleh Bakteri Bacillus altitudinis
Abstrak: Polycyclic aromatic hydrocarbons (PAHs) are toxic, mutagenic, and carcinogenic pollutants that are present in environment. Some bacterial species have ability to metabolize these compounds and use them as energy sources for their growth. Bacillus altitudinis was used to degrade phenanthrene, a three-ring aromatic PAH. The maximum degradation rate (14%) was obtained when Bacillus altitudinis was cultured for 28 days after the addition of 50 ppm phenanthrene to the liquid medium. Furthermore, the degradation was affected by addition of Tween 80 as surfactants. The observation parameters were total plate count (TPC) and pH. The value TPC increased for 28 days cultivation and pH value increased too from 6 to 8 during the 28 days cultivation. The mechanism of degradation was determined through identification of metabolites, the possible pathway of phenanthrene degradation is via phthalic acid. It has been proofed by a mass spectrum of phthalic acid at retention time of 7.607 with match quality of 72.
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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