Judul: Struktur komunitas makrozoobenthos dan parameter fisika & kimia untuk menduga kualitas perairan di Sungai Cihideung, Kabupaten Bogor, Jawa Barat
Abstrak: Sungai Cihideung merupakan salah satu sungai yang mengalir sepanjang Kabupaten Bogor. Hulu sungai terletak di Gunung Salak dan bermuara di Sungai Cisadane. Sungai Cihideung saat ini dimanfaatkan oleh masyarakat sekitar untuk berbagai keperluan. Tanpa adanya pengawasan, berbagai aktivitas tersebut berpotensi menurunkan kualitas perairan Sungai Cihideung.
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Judul: Kualitas fisika-kimia perairan dan struktur komunitas makrozoobentos di sungai Ciliwung, Bogor
Abstrak: Sungai Ciliwung merupakan salah satu sungai di Jawa barat, yang mengalir di wilayah Kabupaten Bogor, Kotamadya Bogor dan DKI Jakarta. Sehubungan dengan meningkatnya kegiatan-kegiatan di sepanjang DAS Ciliwung maka dikhawatirkan kualitas air Sungai Ciliwung akan mengalami penurunan. Organisme yang akan merasakan langsung dampak dari perubahan lingkungan sungai adalah makrozoobentos yang mempunyai daya adaptasi yang berbeda terhadap bahan pencemar. Penelitian ini bertujuan untuk mengetahui kualitas fisika-kimia air dan struktur komunitas makrozoobentos di Sungai Ciliwung, Bogor serta melihat tingkat pengaruh masukan bahan pencemar dengan menggunakan analisis kurva ABC. Penelitian ini dilakukan di Sungai Ciliwung, Jawa Barat bersama Tim PROKASIH Bogor. Penelitian ini dilaksanakan pada tanggal 3 Desember 1998 dan 3 Maret 1999. Lokasi penelitian meliputi Sungai Ciliwung yang termasuk dalam Kabupten Bogor. Lokasi penelitian di bagi menjadi 3 stasiun pengamatan. Setiap stasiun dilakukan 2 kali pengamatan dengan selang waktu 3 bulan. Untuk mengetahui struktur komunitas mekrozoobentos dilakukan analisis kepadatan, indeks keanekaragaman, indeks keseragaman, indeks dominansi, dan indeks penyebaran Morisita. Salah satu cara untuk mengetahui tingkat pencemaran sungai adalah dengan menggunakan kurva ABC. Makrozoobentos yang ditemukan terdiri dari 6 kelas, yaitu Kelas Oligochaeta, Gastropoda, Hirudinea, Pterygota, Pelecypoda dan Malacostraca. Berdasarkan 2 kali pengamatan, Stasiun 2 memiliki kepadatan terbesar. Indeks keanekaragaman dari 2 kali pengamatan tergolong rendah. Pada pengamatan pertama, indeks keanekaragaman berkisar antara 2,303,10. Pada pengamatan kedua berkisar antara 2,542,70. Indeks keseragaman tergolong tinggi, yaitu berkisar antara 0,660,9....
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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