Judul: Uji ketahanan padi varietas semeru dan batangpane terhadap virus tungro
Abstrak: Penelitian ini bertujuan mengetahui ketahanan padi varistas Semeru dan Batangpane terhadap serangan virus tungro melalui vektor wereng hijau (Nephotettix virescens Distant.). Pengujian dilakukan di rumah kaca bagian Fisiologi Tumbuhan dan rumah kaca bagian Virologi Tumbuhan, Fakultas Pertanian, Institut Pertanian Bogor. Penelitian ini menggunakan Rancangan Acak Lengkap dengan enam perlakuan dan 10 ulangan. Tanaman uji dari masing-masing varietas diinokulasi dengan tiga imago wereng hijau betina yang sebelumnya telah diberi makan akuisisi pada tanaman padi varietas TN-1 yang terinfeksi tungro selama 24 jam. Periode makan inokulasi pada masing-masing tanaman uji selama 24 jam. Tanaman kontrol dari masing-masing varietas diinokulasi dengan tiga imago wereng hijau yang bebas virus tungro. Tanaman uji dari varietas TN-1, Semeru dan Batangpane menunjukkan perubahan warna daun yang berkisar dari kuning sampai jingga. Pada daun yang tua, terdapat bercak-bercak merah kecoklatan dengan bentuk dan ukuran yang bermacam- macam.
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Judul: Pengujian Ketahanan Varietas Padi IR 56 Terhadap Penyakit Tungro
Abstrak: Penelitian ini dilakukan sejak awal November sampai akhir Desember 1983, yang bertujuan untuk mengetahui derajat ketahanan varietas terhadap virus tungro dan untuk mengetahui pengaruh penyakit terhadap pertumbuhan. Pengujian merupakan percobaan pot dengan inokulasi buatan menggunakan metode kurungan milar plastik. Derajat ketahanan varietas ditentukan berdasarkan persentase tanaman yang terinfeksi setelah inokulasi. Pengaruh penyakit terhadap pertumbuhan ditentukan dengan membadingkan tinggi tanaman, berat kering total, dan berat kering akar tanaman yang terinfeksi dengan tanaman sehat (kontrol). Hasil pengujian menunjukkan bahwa varietas pada IR 56 digolongkan tahan terhadap virus tungro. Perbandingan tinggi dan berat kering antara tanaman sakit dan sehat pada varietas IR 56 tidak berbeda nyata, sedangkan pada varietas TN1 berbeda nyata.
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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