Judul: Struktur Komunitas Ikan Karang (Famili Chaetodontidae) dan Keterkaitannya dengan Persentase Penutupan Karang Hidup di Ekosistem Terumbu Karang Perairan Nusa Penida, Bali
Abstrak: Terumbu karang berfungsi sebagai daerah pelindung bagi organisme laut dan mempunyai kestabilan serta keragaman spesies yang tinggi. Ekosistem terumbu karang teradaptasi baik dengan adanya simbiose internal dan intra komunitas, tetapi rentan terhadap gangguan aktifitas manusia dan mudah sekali diserang oleh faktor-faktor perusak (ekosistem yang fragile) (Odum,1971). Salah satu biota yang menambah daya tarik ekosistem terumbu karang adalah adanya ikan karang yang memiliki corak warna yang beragam dan mempesona. Keberadaan ikan karang ini kelangsungan hidupnya tergantung sepenuhnya pada kondisi terumbu karang karena seperti ikan Chaetodontidae sebagian besar dari spesiesnya mengkonsumsi polip karang.
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Judul: Struktur Komunitas Ikan Karang Dan Keterkaitannya Dengan Persentase Penutupan Karang Hidup Dl Ekosistem Terumbu Karang Daerah Perlindungan Laut Pulau Sebesi, Lampung
Abstrak: Penelitian ini bertujuan untuk rnengetahui struktur komunitas ikan karang dan persentase penutupan karang serta hubungan antara kelimpahan, jumlah spesies, dan keanekaragarnan ikan karang dengan persen penutupan karang hidup. lkan karang di kawasan Daerah Perlindungan Laut terdiri dari 36 farnili, 59 genus, dan 136 spesies. Kondisi ikan karang di kedalaman 3 meter secara keseluruhan berada dalam keadaan yang cukup baik, terlihat dari rata-rata indeks keanekaragarnan dan keseragarnan yang tinggi (2,54 dan 0,80), serta nilai indeks dorminansi rata-rata yang rendah (0,13) rnengindikasikan hampir tidak ada jenis ikan tertentu yang rnendominansi di kedalaman ini, Kondisi ikan karang di kedalaman 6 meter secara keseluruhan berada dalam tekanan lingkungan yang kuat. Hal ini terlihat dari rata-rata nilai indeks keanekaragarnan yang rendah (2,26). Narnun demikian, komunitas berada dalam keadaan yang cukup stabil, terlihat dari nilai indeks keseragarnan rata-rata yang tinggi (0,77). Nilai indeks dominansi yang rendah (0,18) rnenunjukkan hampir tidak ada jenis ikan tertentu yang rnendorninansi di kedalarnan ini. Secara umum komunitas ikan karang di kedalarnan 3 meter lebih baik bila dibandingkan dengan komunitas ikan karang di kedalaman 6 meter. Hasil regresi polinomial mernperlihatkan hubungan yang cukup erat antara penurunan kelimpahan, keanekaragaman, dan jumlah spesies ikan karang dengan peningkatan persentase penutupan terumbu karang hidup. Peningkatan persen penutupan karang hidup merniliki pengaruh yang lebih nyata terhadap penurunan jumlah spesies ikan karang yaitu 0.7013 di kedalaman 3 meter dan 0,7183 di kedalaman 6 meter.
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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