Judul: IPB (Bogor Agricultural University)
Abstrak: Logam berat IIg dan Cd diketahui sebagai unsur kelumit yang bukan saja tidak esensial, namun juga bersifat racun baik bagi tumbuhan maupun hewan air. Logam berat tersebut yang terdapat dalam air akan mudah diabsorpsi dan terakumulasi pada tubuh organisme air. Perilaku Hg dan Cd yang terakumulasi pada jaringan tubuh ikan khususnya yang hidup dalam air mengandung kadar Hg dan Cd almi yang rendah, masih sangat sedikit disingkapkan., In the aquatic environtment both Mercury (Hg) and Cadmium (Cd) are heavy metals found as trace elements which are non-essential for aquatic plant and animal organisms, but are, however, potentially toxic for these organisms. These heavy metals are readily absorbed and subsequently accumulated in the bodies of aquatic organisms. Presently, information concerning the behaviour of Hg and Cd accumulated in fish living in aquatic environments with low concentrations of Hg and Cd is scarce.
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Judul: IPB (Bogor Agricultural University)
Abstrak: Cakung Dalam river has received pollutants discharged by industries, including heavy metals. Hg, Cd, and Pb are heavy metals which very toxic in the world and their impact from generation to generation. The research was aimed : to determine the distribution level of heavy metals (Hg, Cd, and Pb); to developed distribution model of heavy metals; to calculate water economic value ; and to developed evolution model of water economic value . The distribution level of heavy metals were compared with standard values; the water economic value was determined by total economic valuation; the distribution model of Hg, Cd, and Pb, and the evolution model of water economic value were developed using Powersim 2.5c, MS. Exce l, SPSS 10.05, and Minitab. Validation of the models carried out by implementing theoritical test, structure stability test, consistency test, AME test, AVE test, Kalman filter test, U-Thelil’s test, and DW test. In 2003, the distribution level of heavy metals in river water, ground water, paddy, rice, and fishes are sign that Hg of river water was above standard value of group-C water (PP RI No. 82, 2001). It is not suitable to support fisheries and poultry. The distribution model of heavy metals showed increasing trend in the second half year in river water and ground water, and every half year in paddy, rice, and fishes. Over a 50 year period, the Hg, Cd, and Pb are predicted to increase by 0,012 ppm, 0,0029 ppm, and 0,0013 ppm in river water respectively; 0,01808 ppm, 0,08771 ppm, and 0,19150 ppm in ground water respectively; 0,0072 ppm, 0,0041 ppm, and 0,0069 ppm in paddy respectively; 0,0041 ppm, 0,0042 ppm, and 0,0084 ppm in rice respectively; and 0,0079 ppm, 0,0097 ppm, and 0,0056 ppm in fishes respectively. The water economic value in 2003 without heavy metals input was Rp 1.094.961.301,52. The evolution model of water economic value is predicted to decrease gradually : for 2003-2010, due to toxicity crustacea by Hg on river water; in 2010, due to Cd on ground water was above standard value of cleaning water; in 2028, due to Hg on river water was above standard value on agricultural water; and since 2032, due to river sedimentation. The water economic value by 2050 (January) is predicted Rp 337.336.753,73.
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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