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.
Keyword: 

Judul: Morfotipe Ektomikoriza Famili Dipterocarpaceae dengan Metode Lubang Bor di Hutan Penelitian Haurbentes, Bogor
Abstrak: In Indonesian, Dipterocarpaceae grows in nutrient-poor and acidic soils which usually characterized by low rates of organic matter decomposition, due to it’s selective advantage of ectomycorrizas association. This research aimed to study ectomycorrizal root tip morphotypes in Haurbentes conservation forest, Bogor. The root tip morphotype was determinited by observation of root branching pattern, colour, mantle, and rhizomorph. One hundred ninety one root tips from 48 core samples derived from 8 spesies of Dipterocarpaceae were observed for root colonization and morphotype. Data showed that roots of all plant species were colonized by ectomycorrizas with the average value 34.72% or 2.15 x 102 cm. They produced 12 different morphotypes. They were unramified-simple black straight, unramified-simple black bent, unramified-simple cream colored bent, monopodial pyramide brown straight, monopodial pinnate black tortuous, monopodial pinnate brown straight, monopodial pinnate brown bent, monopodial pinnate brown tortuous, irregularly pinnate black tortuous, irregularly pinnate brown tortuous, irregularly pinnate brown bent, and irregularly pinnate cream colored bent. The highest value of root colonization abundance was observed from irregularly pinnate brown morphotype (32.54 %), while the lowest was found in monopodial pinnate black tortuous (0.37 %).
Keyword: Root tips morphotype, Haurbentes conservation forest, Ectomycorrhizas, Dipterocarpaceae

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