Judul: Penelitian penyebab penyakit kerdil pada tanaman pisang (Musa spp.) di Jawa Barat
Abstrak: Tujuan penelitian ini ialah mengetahui penyebab dan cara penularan penyakit kerdil pisang, Di samping itu dilakukan pula peninjauan lapang untuk mengetahui adanya penyakit tersebut di beberapa kabupaten di Jawa Barat. Tanaman pisang yang memperlihatkan gejala penyakit kerdil diperoleh dari Kecamatan Cimahi Utara, Kabupaten Bandung. Dari hasil pengujian ternyata penyakit tersebut tidak disebabkan oleh Fgsarium sp., Rhizoctonia sp. ataupun suatu isolat bakteri. Ketiga isolat jasad renik ini di isolasi dari akar tanaman pisang Ambon Jepang yang menunjukkan gejala penyakit kerdil. Pada akar tersebut tidak dijumpai adanya nematoda, Pengamatan dengan mikroskop elektron tidak memperlihatkan adanya partikel virus atau mikroorganisme pada cairan atau jaringan daun tanaman sakit. Preparat yang diamati dengan mikroskop elektron dibuat dengan metode celup dan irisan halus. Penyebab penyakit kerdil pisang dapat ditularkan pada tanaman pisang Ambon Jepang melalui kutudaun pisang Petalonia nigronervosa dengan cara penularan untuk virus persisten, tetapi tidak dengan cara penularan untuk virus nonpersisten atau secara mekanik dengan ekstrak daun tanaman sakit.
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Judul: Pemanfaatan rizobakteri pemacu pertumbuhan tanaman (RPPT) untuk menegndalikan penyakit kerdil pisang (Banana Bunchy Top)
Abstrak: Pisang merupakan salah satu komoditi hortikultura yang merupakan tanaman asli Indonesia. Penyakit kerdil pisang merupakan penyakit paling penting pada tanaman pisang di Indonesia. Virus ini menyerang tanaman pisang secara sistemik sehingga sulit untuk dikendalikan secara langsung. Beberapa cara yang digunakan dalam pengendalian penyakit ini diantaranya dengan penanaman bibit yang sehat, pembongkaran tanaman sakit, pengendalian vektor, dan penggunaan kultivar yang tahan. Beberapa tahun terakhir banyak dilaporkan keberhasilan pengendalian penyakit tanaman menggunakan rizobakteri pemacu pertumhuhan tanaman (RPPT) yang dalam bahasa inggris disebut Plant Growth Promoting Rhizobacteria (PGPR). Penelitian dilaksanakan di Laboratorium Mikologi Tumbuban, Laboratorium Virologi Tumbuhan, dan Rumah Kaca Cikabayan, Departemen Proteksi Tanaman, Fakultas Pertanian, Institut Pertanian Bogor pada bulan Desember 2005 sampai Juni 2006.
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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