Judul: Pemanfaatan kijing taiwan (Anodonta woodiana, Lea) sebagai biofilter pada sistem budidaya ikan mas
Abstrak: Kegiatan budidaya ikan secara intensif berarti melakukan pemeliharaan ikan dengan padat penebaran yang tinggi dan pemberian pakan buatan, sehingga menghasilkan buangan limbah organik dan anorganik yang cukup besar. Hal ini akan berdampak terhadap kualitas air yang buruk, yang akan berdampak pada pertumbuhan dan kelangsungan hidup ikan. Penelitian ini bertujuan menganalisa peran kijing taiwan sebagai biofilter pada sistem budidaya ikan mas kondisi terkontrol, dan mengukur pertumbuhan serta kelangsungan hidup ikan mas (Cyprinuscarpio) dan kijing taiwan (Anodonta woodiana). Dari hasil penelitian ini diharapkan diperoleh informasi tentang kemampuan kijing taiwan (A. woodiana) sebagai biofilter pada kondisi terkontrol.
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Judul: Efektivitas kijing taiwan (Anodonta woodiana) dalam menyerap limbah organik pada budidaya ikan sistem resirkulasi
Abstrak: Penelitian berlangsung pada bulan Februari sampai April 2007 di Loka Riset Pemuliaan Budidaya Air tawar Sukamandi, Sukamandi Subang. Tujuan penelitian ini adalh mengetahui tingkat efektifitas Kijing Taiwan (Anodonta woodiana) dalam menyaring bahan organik hasil buangan kegiatan pemeliharaan ikan sistem resirkulasi. Hasil penelitian ini diharapkan dapat memmberikan informasi tentang efektifitas Kijin gTaiwan (Anodonta woodiana) dalam menyerap limbah organik dari kegiatan budidaya ikan sistem resirkulasi, sehingga dapat digunakan sebagai pertimbangan dalam pengolahan limbah budidaya secara biologis yang efektif dan ekonomis. Informasi mengenai penurunan kadar bahan organik akibat aktifitas organiisme ini (melalui mekanisme filter feeding) merupakan informasi utama dari hasil penelitian ini.
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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