Judul: Distribusi dan struktur komunitas fitoplankton di perairan teluk jakarta dan kaitannya dengan red tide
Abstrak: Penelitian dengan judul Distribusi dan Struktur Komunitas Fitoplankton di Perairan Teluk Jakarta dan Kaitannya dengan Red Tide dilaksankan di Teluk Jakarta pada bulan Juli, Oktober dan Desember 2005. Analisis data diadakan di Laboratorium Biologi Balai Riset Perikanan Laut (BRPL) dan Laboratorium oseanografi Kimia, Ilmu Kelautan, Institut Pertanian Bogor. Pengamatan dilakukan pada 12 stasiun yang telah direncanakan.
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Judul: Kajian Terhadap Struktur Komunitas dan Sebaran Fitoplankton di Perairan Teluk Jakarta
Abstrak: Teluk Jakarta terletak dibagian utara Kota Jakarta dan merupakan daerah yang sangat penting karena berbagai fungsinya antara lain : 1. Pelabuhan barang dan penumpang ; 2. Daerah penangkapan ikan ; 3. Tempat rekreasi ; 4. 'Tempat pembuangan sampah dan limbah'. Padatnya aktivitas tersebut akan mempengaruhi komponen biotik dan abiotik yaitu fitoplankton dan parameter fisika-kimia perairan. Tujuan dari penelitian ini adalah untuk mengetahui eksistensi komunitas fitoplankton dengan tujuan melihat distribusi spasial dan perkembangan bulanan ( Juli, September dan Nopember Tahun 2001 ) serta keterkaitannya dengan parameter fisika-kimia di perairan Teluk Jakarta. Penelitian ini dilaksanakan antara bulan Juli sampai Nopember 2001 yang berlokasi di perairan Teluk Jakarta dengan 14 stasiun. Pengambilan contoh dilakukan sebanyak tiga kali dalam selang waktu dua bulan sekali. Parameter fisika-kimia perairan yang dianalisis meliputi salinitas, pH, kekeruhan, DO, suhu, kecerahan. Nilai-nilai parameter nitrat, nitrit, ammonia, fosfat, silika merupakan data sekunder hasil penelitian Damar (2001). Sampel fitoplankton dianalisis dengan metode sedimentasi yang merupakan modifikasi dari metode Utermohl. Analisis data yang dilakukan meliputi kelimpahan, indeks keanekaragaman, keseragaman, dominansi, kesamaan antar stasiun berdasarkan kelimpahan dan nilai parameter fisika-kimia. Untuk melihat hubungan kelimpahan dengan parameter fisika-kimia digunakan analisis regresi berganda.
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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