Judul: Struktur komunitas mkrozoobenthos dan kaitannya dengan kandungan logam berat (Pb, Cu, dan Cd) pada air dan sedimen di waduk Cirata, Jawa Barat
Abstrak: Waduk Cirata merupakan salah satu waduk yang dibangun di DAS Citarum. Kandungan logam berat dalam perairan akan berpengaruh terhadap makhluk hidup di dalamnya, termasuk makrozoobenthos.
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Judul: Pengaruh Logam Berat Cd, Pb dan Cu pada Sedimen Terhadap Struktur Komunitas Makrozoobenthos di Waduk Saguling, Jawa Barat
Abstrak: Salah satu dampak negatif dari berkembangnya aktivitas antropogenik di DAS Citarum Hulu adalah peningkatan konsentrasi logam berat yang masuk ke dalam Waduk Saguling. Logam berat mampu berikatan dengan bahan partikulat maupun tersuspensi yang selanjutnya akan mengendap di dasar perairan sebagai sedimen. Logam berat sebagai polutan toksik berdampak negatif terhadap struktur komunitas makrozoobenthos Tujuan penelitian ini adalah: (1) mengetahui struktur komunitas makrozoobenthos yang hidup di Waduk Saguling; (2) mengkaji kemungkinann adanya pengelompokkan habitat berdasarkan kesamaan struktur komunitas makrozoobenthos; (3) mengkaji hubungan keberadaan logam berat Cd, Pb dan Cu terhadap struktur komunitas makrozoobenthos di Waduk Saguling. Pengelompokkan habitat berdasarkan kesamaan struktur komunitas makrozoobenthos menggunakan similaritas Sorensen dengan analisis statistik Non Metric Dimentional Scaling (NMDS) dengan software Comunity Analysis Package versi 2.1. Untuk melihat pengaruh logam berat Cd, Pb dan Cu pada sedimen terhadap struktur komunitas makrozoobenthos, dilakukan korelasi parametrik Pearson Product Moment dengan atribut biologi yaitu: Kekayaan Taksa, Indeks Diversitas, Keseragaman, dan Biological Monitoring Working Party serta korelasi nonmetrik Rank Spearman Correlation dengan kepadatan gastropoda. Makrozoobenthos yang ditemukan di Waduk Saguling terdiri dari 34 jenis yang dapat digolongkan kedalam lima filum yaitu Moluska, Uniramia, Annelida, Platyhelminthes dan Crustacea. Cacing Limnodrilus dari filum Annelida kelas Oligochaeta merupakan jenis yang paling banyak ditemukan dengan total kepadatan 63.293 individu/m2. Hasil ordinasi NMDS menunjukkna tiga pengelompokkan habitat. Kelompok pertama Stasiun Gunung Wayang dengan kondisi tercemar ringan, kelompok kedua yaitu Stasiun Nanjung dengan kondisi tercemar berat dan kelompok ketiga terdiri dari sepuluh stasiun yang berada di Waduk Saguling dengan kondisi tercemar sedang. Hubungan antara konsentrasi logam berat pada sedimen dengan atribut biologi menunjukkan nilai korelasi yang negatif. Pada Selang Kepercayaan 95% tingkat sensitifitas struktur komunitas makrozoobenthos di Waduk Saguling terhadap logam berat menunjukkan pola hierarki Pb>Cu>Cd.
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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