Judul: Konservasi sumberdaya alam di Taman Nasional Gunung Merapi: analisis ekologi politik
Abstrak: Gunung Merapi terletak di Pulau Jawa bagian tengah, secara admistratif berada di wilayah Propinsi Daerah Istimewa Yogyakarta dan Propinsi Jawa Tengah. Semenjak tanggal 4 Mei 2004 melaiG SK Menhut 13412004, kawasan ini telah ditetapkan menjadi Taman Nasional Gunung Merapi (TNGM). Pro-kontra terhadap penetapan TNGM muncul sebelum keluarnya SK penetapan, bahkan pro-kontra tersebut masih terus berlangsung sampai sekarang.
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Judul: Fungsi Ekologis Lahan Pasca Erupsi Gunung Merapi
Abstrak: Kawasan hutan Gunung Merapi telah ditetapkan sebagai Taman Nasional Gunung Merapi (TNGM) sejak tahun 2004. Keberadaan ekosistem hutan di TNGM ialah sebagai resapan air bagi kabupaten yang berada di sekitarnya. Citra satelit menunjukkan terdapat 3 tingkat kerusakan ekosistem hutan di TNGM, yaitu kerusakan ringan, sedang, dan berat. Penelitian ini bertujuan untuk mengetahui kemajuan fungsi lanskap pada beberapa wilayah yang mengalami kerusakan ekosistem hutan akibat erupsi Gunung Merapi. Metode penelitian ini terdiri atas: (1) Penentuan lokasi penelitian, (2) Pengukuran mikroklimat, (3) Pengukuran karakteristik tanah, dan (4) Analisis fungsi lanskap: karakterisasi organisasi lanskap dan penilaian permukaan tanah. Nilai stabilitas lahan pada zona kerusakan ringan, sedang, dan berat secara berturut-turut ialah: 48.0, 52.9, dan 45.5%. Nilai infiltrasi air pada zona kerusakan ringan, sedang, dan berat secara berturut-turut ialah: 26.5, 28.4, dan 29.7%. Nilai siklus nutrisi lahan pada zona kerusakan ringan, sedang, dan berat secara berturut-turut ialah: 20.8, 23.6, dan 16.3%. Kemajuan fungsi ekologis lahan zona kerusakan sedang lebih baik pada stablitas lahan dan siklus nutrisi lahan, sedangkan infiltrasi air lebih baik pada zona kerusakan berat.
Keyword: analisis fungsi lanskap, Gunung Merapi, restorasi, penilaian permukaan tanah, suksesi

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