Judul: Pengaruh Periode Penyinaran dan Temeperatur terhadap Pertumbuhan Diatom Phaeodactylum tricornutum Bohlin
Abstrak: Penelitian ini dilakukan di Sub Balai Penelitian Budidaya Pantai, Bojonegara, Serang yang dilakukan pada bulan Februari sampai Mei 1988. Penelitian ini bertujuan untuk mengetahui pola pertumbuhan dan kemampuan adaptasi dari diatom Phaeodactylum tricornutum selama penelitian. Diatom merupakan salah satu jenis makanan alami organisme seperti udang, echinodermata dan moluska. Salah satu jenis diatom laut yang banyak digunakan sebagai makanan larva mol uska adal ah Phaeodactylum tricornutum.
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Judul: Studi kelimpahan, komposisi, dan distribusi diatom (Bacillari-ophyceae) di Perairan Teluk Pelabuhan Ratu pada bulan Mei, Juli 1994
Abstrak: Plankton terutama fitoplankton merupakan mata rantai- penting dari jaringan makanan dalam suatu ekosistem per- airan di laut selain tumbuhan makro laut. ilik IPB University Diatom adalah kelompok fitoplankton yang paling besar jumlahnya dan paling sering ditemukan di perairan laut maupun tawar. Keberadaan diatom dalam suatu perairan memiliki beberapa peranan penting yaitu: (1) Diatom meru- pakan produser primer yang merupakan sumber energi bagi beberapa organisma hewani, dimana diatom merupakan maka- nan utama herbivora terpenting dilaut, yaitu kopepoda. Umumnya kopepoda selektif dalam memilih fitoplankton (60- 70%) makanan utamanya adalah diatom. (2) Diatom merupa- kan penghasil oksigen terlarut yang cukup besar diperair- an. (3) Diatom dapat digunakan sebagai petunjuk kualitas suatu perairan (perairan tercemar dan bersih). Kelimpahan, komposisi, dan distribusi diatom seperti halnya fitoplankton yang lainnya dipengaruhi oleh suhu, salinitas, pH, kecepatan arus, kecerahan, dan berbagai kandungan zat hara (fosfat, nitrat, dan silikat).
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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