Judul: Autecology of Begonia spp. (BEGONIACEAE) and their utilities by arfak tribe in Mokwam Manokwari)
Abstrak: Begonia merupakan anggota famili Begoniaceae yang memiliki penyebaran cukup luas di Indonesia, termasuk di Papua. Kerusakan alam sebagai akibat meningkatnya kebutuhan manusia akan ruang dan kebutuhan lainnya berdarnpak pada kerusakan ekosistem, termasuk habitat alami Begonia. Tujuan penelitian adalah mendokumentasikan jenis Begonia pada hutan pegunungan di daerah Mokwam, autekologi dan manfaat jenis tersebut bagi suku Arfak di daerah Mokwam sebagai upaya menuju pelestarian sumberdaya alam hayati secara umum dimasa akan datang.
Keyword: 

Judul: Autecology of Begonia spp. (Begoniaceae) in Mount Nokilalaki, Lore Lindu National Park, Central Sulawesi
Abstrak: Begonia merupakan salah satu tanaman yang berpotensi sebagai tanaman hias yang memiliki bentuk daun asimetris, batang berair, dan bunga majemuk.Indonesia memiliki lebih dari 200 jenis Begonia yang telah teridentifikasi. 47 jenis Begonia telah terungkap di Sulawesi. Namun demikian, data ekologinya belum tersedia. Penelitian ini bertujuan untuk mengetahui distribusi, faktor abiotik dan asosiasi antar tumbuhan. Pengamatan dilakukan di gunung Nokilalaki Taman Nasional Lore Lindu, Sulawesi Tengah dengan metode ekplorasi. Analisis vegetasi tumbuhan di sekitar Begonia dilakukan dengan menggunakan plot 1×1 m. Faktor abiotik dihitung menggunakan Analisis Komponen Utama (PCA) dan rumus Morishita untuk mengetahui pola distribusi tumbuhan, asosiasi tumbuhan Begonia spp dengan tumbuhan lain di analisis dengan PCA pada software ekologi PRIMER 7. Hasil penelitian menunjukkan 2 spesies dan 1 varian Begonia ditemukan di Gunung Nokilalaki. suhu, kelembaban dan intensitas cahaya merupakan faktor abiotik yang paling berpengaruh terhadap persebaran Begonia, ditemukan di ketinggian 1100- 1800 mdpl. Hasil pengujian asosiasi Begonia spp dengan tumbuhan lainnya menunjukkan tidak adanya asosiasi.
Keyword: autekologi, Begonia aptera, Begonia celebica, distribusi, asosiasi intraspesifik

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