Judul: Pengaruh Bintik Putih pada Buah, KAdar Air Awal dan Kondisi Simpan terhadap Viabilitas Benih Mahoni (Swietenia macrophylla King)
Abstrak: Tujuan penelitian ini adalah untuk mengamati pengaruh tingkat cernbentukan bintik putih pada buah, kadar air anal dan Bondisi simpan terhadap viabilitas benih mahoni serta menpelajari sifat fisiologisnya dalam penyimpanan. Penelitian ini dilaksanakan di Laboratorium Balai Teknologi Perbenihan Kehutanan Bogor. Penelitian dimulai pada bulan Agustus 1986 sampai bulan Pebruari 1987. Bahan yang digunakan adalah buah mahoni dengan dua tingkat pembentukan bintik putih pada buah yaitu buah dengan bintik putih kurang dari 50 persen (A1) dan lebih dari 50 persen (A2) luas permukaan buah.
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Judul: Pengaruh tingkat masak, kadar air awal dan periode simpan terhadap viabilitas benih mengkudu (Morinda citrifolia L.)
Abstrak: Penelitian ini bertujuan untuk mengetahui pengaruh tingkat masak, kadar air awal dan periode simpan terhadap viabilitas benih mengkudu (Morinda citrifolia L.). Penelitian ini menggunakan Rancangan Kelompok Lengkap Teracak (RKLT) yang disusun secara faktorial menggunakan tiga faktor. Faktor pertama adalah tingkat masak benih dengan dua taraf yaitu benih yang berasal dari buah berwarna kuning (M₁) dan buah berwarna putih (M2). Faktor kedua adalah kadar air awal benih dengan taraf 9-13% (A₁), 18-22% (A2) dan 58-62% (A3). Faktor ke tiga adalah periode simpan benih, yaitu 0 minggu (S₁), 2 minggu (S2), 4 minggu (S3), 6 minggu (S4), 8 minggu (S3), 10 minggu (S6) dan 12 minggu (S7). Benih yang telah mencapai kadar air yang diharapkan disimpan dalam ruang penyimpanan AC yang berbeda berdasarkan pengelompokan ruang simpan. Ruang I dengan suhu rata-rata 21.05°C dan kelembaban rata-rata 64.53%. Ruang II dengan suhu rata-rata 22.55°C dan kelembaban rata-rata 70.89 %. Ruang III dengan suhu rata-rata 25.28°C dan kelembaban rata-rata 45.69 %. Setiap perlakuan diulang sebanyak tiga kali. Parameter yang diamati yaitu Viabilitas Potensial dengan tolok ukur Daya Berkecambah (DB) dan Berat Kering Kecambah Normal (BKKN), Viabilitas Total dengan tolok ukur Potensi Tumbuh Maksimum (PTM), Vigor Kekuatan Tumbuh dengan tolok ukur Kecepatan Tumbuh (KCT), Kadar Air dan Bobot 1000 butir. Hasil penelitian menunjukkan tingkat masak sebagai faktor tunggal tidak berpengaruh nyata terhadap semua parameter yang diamati. Faktor tunggal kadar air benih tidak berpengaruh nyata terhadap parameter viabilitas potensial, viabilitas total, dan vigor kekuatan tumbuh tetapi berpengarüh sangat nyata terhadap parameter kadar air benih. Sedangkan periode simpan berpengaruh sangat nyata terhadap semua parameter yang diamati. ...
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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