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.
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Judul: Diversity and Ecology of Begonia in the Nirmala Tea Plantation, Mount Halimun Salak National Park
Abstrak: Begonia merupakan salah satu dari enam marga tumbuhan berbunga terbesar yang tersebar dari daerah tropik hingga daerah sub tropik. Begonia mampu tumbuh dalam berbagai relung ekologi, dari dataran rendah sampai hutan pegunungan. Jenis tertentu dari marga Begonia dapat tumbuh di kebun teh sebagai tumbuhan bawah. Penelitian ini bertujuan mengidentifikasi keanekaragaman Begonia dan menganalisis hubungan faktor abiotik terhadap persebaran Begonia di Perkebunan Teh Nirmala. Pengambilan sampel dilakukan di Perkebunan Teh Nirmala, Taman Nasional Gunung Halimun Salak (TNGHS) dengan metode purposive sampling pada ketinggian 1070 dan 1500 m dpl. Sampel yang ditemukan di lapangan dibuat herbarium kering, kemudian diamati ciri morfologi dan diidentifikasi dengan mengacu pada hasil penelitian sebelumnya. Data ekologi yang diukur di lapangan dianalisis menggunakan Canonical Correspondence Analysis (CCA) untuk mengetahui pengaruh faktor-faktor lingkungan terhadap keberadaan Begonia. Begonia yang ditemukan pada penelitian ini hanya satu jenis, yaitu Begonia cucullata dengan tiga varian dan ditemukan dengan dua cara hidup yang berbeda, yaitu hidup terestrial dan epifit. Ketiga varian berbeda pada warna batang, warna daun permukaan adaksial dan abaksial, bulu pada tepi daun, ada tidaknya daun pelindung, dan tipe tepi daun. Sebaran Begonia cucullata dipengaruhi oleh suhu udara dan kecepatan angin. Begonia cucullata varian 1 terestrial memiliki indeks nilai penting dan dominasi tertinggi di dua ketinggian lokasi penelitian, Begonia is one of the six largest flowering plant genera that spread from the tropics to the sub-tropics. Begonia is able to grow in a variety of ecological niches, from lowlands to mountain forests. Some species of begonias can grow in tea gardens as an understorey. This study aims to identify Begonia diversity and analyze the relationship between abiotic factors and the distribution of Begonia in Nirmala Tea Plantation. Sampling was carried out at the Nirmala Tea Plantation, Gunung Halimun Salak National Park (TNGHS) with a purposive sampling method at altitudes of 1070 and 1500 m above sea level. The samples found in the field were made herbarium, then observed morphological characteristics and were identified by referring to the results of previous studies. Ecological data measured in the field were analyzed using Canonical Correspondence Analysis (CCA) to determine the effect of environmental factors to the existence of Begonia. Begonia found in this study is only one species, namely Begonia cucullata with three variants and found with two different habitats, namely terrestrials and epiphytes. The three variants differ in the color of the stem, the color of the adaxial and abaxial leaves, the indumenta on the leaf margin, the presence or absence of the stipula, and the type of leaf margin. The distribution of Begonia cucullata is influenced by air temperature and wind speed. Terrestrial Begonia cucullata variant 1 has the highest importance and dominance index at the two study sites.
Keyword: altitude, Begonia cucullata, environmental factors, three variants

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