Judul: Fluktuasi dan Serapan Populasi Musiman Heleopeltis antonii Signoret (Hemiptera : Miridae) pada Tanaman Cokelat di Kebun Kalibakar (PT Perkebuan XXIII) Dampit, Malang
Abstrak: Penelitian ini telah dilakukan di kebun cokelat Kalibakar (PT Perkebunan XXIII) Dampit, Malang, bertujuan mengatahui pola fluktuasi dan sebaran populasi H. antonii. Penelitian berlangsung dari bulan April 1982 sampai bulan Mei 1984. Kebun coklat terisolasi dan tiap-tiap tahun mengalami serangan H. antonii ditetapkan sebagai tempat percobaan. Petak percobaan seluas 9 ha ditetapkan pada tempat percobaan dan dibebaskan dari pengendalian jasad pengganggu yang menggunakan pestisida.
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Judul: Hubungan timbal balik antara Heleopeltis antonii sign. (Hemiptera : miridae)
Abstrak: Penelitian dilakukan di dua kebun percobaan yaitu yang ada di Balai Penelitian Perkebunan (BPP) Jember den di BPP Bogor, dan berlangsung mulai bulan Oktober 1985 sampai dengan September 1988. Populasi Helopeltis diketahui berfluktuasi sepanjang tahun menurut pola tertentu, sejalan dengan tersedianya buah di pertanaman kakao. Disamping menyerang buah. Helopeltis sp. juga diketahui menyerang pucuk kakao. Kualitas buah atau pucuk sebagai sumber nutrisi bagi Helopeltis diperkirakan mempengaruhi perkembangan serangga tersebut. Komposisi senyawa nutrisi pada buah diduga berbeda- beda, tergantung dari umur buah, jarak tanam, tipe tanaman dan aplikasi senyawa kimia pada tanaman atau langsung pada buah kakao. Disamping itu kornposisi nutrisi antara buah dan pucuk kakao di perkirakan juga berbeda-beda. Perbedaan komposisi senyawa nutrisi yang terkandung dalam sumber makanan akan berikan pengaruh yang berbeda terhadap perkembangan H. antonii.
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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