Judul: Uji Antagonisme antara Trichoderma spp. dan Fusarium oxysporum pada berbagai pH Medium In vitro
Abstrak: Penelitian ini bertujuan untuk menginventarisasi jenis-jenis Trichoderma di beberapa lokasi pertanaman buncis (Phaseolus vulgaris). Di samping itu juga untuk mengetahui isolat Trichoderma yang menyebabkan persentase hambatan tertinggi terhadap Fusarium oxysporum yang diisolasi dari tanaman buncis pada berbagai pH medium agar. Pengambilan contoh tanah dilakukan di daerah pertanaman yang sedang atau sehabis ditanami buncis. Pada setiap petak diambil 5 contoh tanah secara acak, kemudian dikeringudarakan dan disaring dengan saringan 9 mesh. Untuk mengisolasi Trichoderma dari contoh tanah digunakan metode pengenceran. Setelah itu setiap koloni Trichoderma yang berbeda warna dan pola pertumbuhan dari setiap pengenceran yang memberikan koloni cendawan secara terpisah dan dari setiap lokasi dimurnikan pada medium Potato Dextrose Agar (PDA). Kemudian untuk mengidentifikasi cendawan digunakan medium Malt Extract Agar (MEA). ...
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Judul: Pengaruh Pemupukan NPK Terhadap peningkatan Potensi Antagonis Trichoderma Sp. pada Pythium Sp. penyebab Rebah Kecambah Mentimun
Abstrak: Percobaan ini dilakukan untuk mengetahui pengaruh pu- puk N,P,K (dengan kombinasi 15-15-15) terhadap aktivitas Trichoderma sp. sebagai agen antagonis pada Pythium sp. penyebab rebah kecambah mentimun. Percobaan dilakukan di Laboratorium cendawan patogen tumbuhan dan rumah kaca Jurusan Hama dan Penyakit Tumbuhan, Fakultas Pertanian, Institut Pertanian Bogor. Isolat Patogen yaitu Pythium sp. dan antagonis Trichoderma sp. masing-masing diisolasi dari tanah Tajur dan Darmaga kemudian dibiakan pada media PDA. Telah diidentifikasi dua isolat Trichoderma sp. yang diperoleh dari hasil isolasi. Hasil identifikasi sementara menunjukkan bahwa isolat Tri- choderma yang diperoleh adalah T. koningii dan T. harzianum. Kedua isolat tersebut dibiakan secara massal pada medium campuran dedak padi dan serbuk gergaji ( 1 : 1 dalam volume) selama 14 hari. Sedangkan pembiakan massal Pythium sp. dilakukan pada media Corn-Meal Sand selama 7 hari. ...
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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