Judul: Daya simpan benih pepaya (Carica papaya L.) hasil ekstraksi dengan larutan kapur tohor
Abstrak: Penelitian daya simpan benih pepaya genotipe IPB I dilakukan untuk mengetahui viabilitas benih yang diekstrasi dengan larutan kapur tohor pada berbagai taraf konsentrasi selama penyimpanan dalam kondisi ruang AC maupun ruang suhu kamar.
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Judul: Evaluasi Viabilitas Benih Pepaya (Carica papaya L.) Setelah Penyimpanan pada Kondisi Kelembaban dan Suhu Kamar.
Abstrak: Penelitian ini bertujuan untuk mengevaluasi viabilitas lima varietas/genotipe benih pepaya yang telah disimpan pada periode 6 - 180 minggu dalam kondisi kamar dengan RH 55 - 77% dan suhu 25.6 - 30.90C. Benih pepaya yang diuji berasal dari Pusat Kajian Buah Tropika (PKBT) IPB, yaitu Varietas Arum Bogor, Prima, Carisya, Genotipe IPB 5 dan IPB 8. Penelitian dilakukan mulai dari Mei - November 2010, di Laboratorium Ilmu dan Teknologi Benih, Departemen Agronomi dan Hortikultura, Fakultas Pertanian IPB, Dramaga, Bogor. Penelitian terdiri atas lima percobaan terpisah yang dilakukan berdasarkan pengujian benih dari setiap varietas/genotipe pepaya. Masing-masing percobaan dilakukan dengan menggunakan analisis Rancangan Acak Lengkap (RAL) satu faktor dengan tiga unit ulangan. Faktor yang digunakan dalam penelitian ini adalah perlakuan pra perkecambahan menggunakan air murni, larutan atonik 0.5% atau larutan KNO3 10%. Uji lanjut dengan menggunakan Duncan’s Multiple Range Test (DMRT) pada taraf 5%. Benih pepaya Varietas Prima, Carisya dan Genotipe IPB 5 memiliki nilai viabilitas tinggi dengan persentase daya berkecambah (DB) dan potensi tumbuh maksimum (PTM) mencapai >75 % dalam kondisi kelembaban dan suhu kamar selama 29 minggu. Pada kondisi yang sama benih pepaya Genotipe IPB 8 mampu disimpan hingga periode penyimpanan 27 minggu, sedangkan Varietas Arum Bogor memiliki nilai viabilitas rendah (<50%) hingga periode penyimpanan 32 minggu. Perlakuan pra perkecambahan dengan larutan KNO3 10%dibandingkan dengan larutan atonik 0.5% atau air murni, dapat meningkatkan nilai vigor benih pepaya Varietas Arum Bogor, Carisya, Genotipe IPB 5 dan IPB 8, tetapi tidak mempengaruhi nilai viabilitasnya. Nilai viabilitas dan vigor benih pepaya Varietas Prima tidak dipengaruhi oleh seluruh jenis perlakuan pra perkecambahan.
Keyword: Seed viability, Duncan’s Multiple Range Test (DMRT), Genotipe IPB 8

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