Judul: Ektomikoriza Pinus merkusii di Bagian Kesatuan Pemangku Hutan (BKPH) Lembang
Abstrak: Pinus merkusii in BKPH Lembang conservation forest was associated with ectomycorrhizal fungi which produced 4 root tip morphotypes. They were irregular pinnate, dichotomous, monopodial, and coralloid. Irregular pinnate was dominant morphotype observed with occurrence frequency of 72,5%. The four morphotypes were developed by three fungal orders belong to Boletales, Russulales and Tuberales. Boletales produced two morphotypes, irregular pinnate and coralloid, whereas Russulales and Tuberales produced dichotomous and monopodial morphotypes, respectively. One ectomycorrhizal fungus was sucessfully isolated from P. merkusii ectomycorrhizal root tip. Based on morphological and molecular analysis, the isolated fungus was identified as Cenococcum geophilum. The soil properties of BKPH Lembang were acidic soil containing very low P and Ca, and low Mg and K.
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Judul: Isolasi cendawan ektomikoriza pada pinus merkusii di hutan penelitian gunung dahu, bogor
Abstrak: Pinus merkusii merupakan tumbuhan gymnospermae yang memiliki nilai ekonomi penting karena menghasilkan resin dan kayu yang baik. Selain itu p. Merkusii juga sering digunakan dalam program rebosisasi karena dapat tumbuh di lahan yang kritis. Pertumbuhan dan perkembangan p. Merkusii dipengaruhi oleh cendawan ektomikoriza yang membentuk simbiosis dengan akar tumbuhan tersebut. P. Merkusii bersimbiosis secara obligat dengan cendawan ektomikoriza. Penelitian ini bertujuan untuk menganalisis morfotipe akar, mengisolasi, dan mengkarakterisasi cendawan ektomikoriza yang bersimbiosis dengan p. Merkusii. Sebanyak 70.9% akar yang diperoleh dari 28 sampel bersimbiosis dengan cendawan ektomikoriza. Terdapat 26 morfotipe akar p. Merkusii yang terdiri atas 6 tipe ramifikasi dan 9 warna. Dikotomus cokelat merupakan morfotipe dengan frekuensi, persentase kolonisasi, dan kelimpahan relatif tertinggi. Persentase kolonisasi morfotipe dikotomus cokelat ialah 18.9% sedangkan kelimpahan relatifnya 26.7%. Terdapat 22 isolat yang berhasil diidolasi. Sebanyak 6 isolat yang terdiri dari isolat gd.151(3), gd.151(5a), gd.151(5b), gd.151(5c), gd.174(1), dan isolat gd.174(2) bukan merupakan cendawan ektomikoriza karena bersporulasi yaitu. Terdapat 3 isolat yang diduga cendawan ektomikoriza yaitu isolat gd.134(2b) dan gd.142(5) yang merupakan spesies cenococcum geophilum serta isolat gd.162(1) yang memiliki sambungan apit. Beberapa struktur yang teramati dari berbagai isolat yaitu klamidospora, blastospora, anastomosis, dan papila.
Keyword: ektomikoriza, hutan penelitian gunung dahu, morfotipe, pinus merkusii

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