Judul: Analisis enzim fosfomonoesterase tanah dari berbagai tingkat kebakaran hutan Taman Nasional Bukit Bangkirai Kalimantan Timur
Abstrak: Tanah merupakan sumber daya alrun sebagai penyedia prulgan dan papan bagi manusia selta media tumbuh dan penyedia hara bagi tanamrul. Di dalam tanah banyak terjadi proses kompleks seperti pengambilan hara oleh tanaman dan aktivitas mikroorganisme tanah. Enzim yang dihasilkal1 mikroorganisme trulall merupakan pengurai berbagai substrat di dalam tanah.
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Judul: Hubungan Respirasi Mikrob Dengan Aktivitas Fosfomonoesterase Dan Karboksimetilselulase Tanah Pada Berbagai Tingkat Kebakaran Hutan
Abstrak: Tingkat kebakaran hutan mempengaruld aktivitas respirasi tanall dan aktivitas enzim fosfomonoesterase (PMEase) dan karboksilnetilselulase (CMCase). Dalaln penelitian ini, analisis respirasi tanah dilakukan secara titrimetri terhadap larutan basa yang telah menangkap COz selama inkubasi tanah dengan dan tanpa induksi glukosa. Aktivitas enzim ditentukan secara spektrofotometri melalui pengukuran produk basil reaksi enzimatik. Respirasi basal rata-rata tertinggi terdapat pada salnpel tanah Ilutan alami diikuti oleh hutan terbakar, hutan sangat terbakar, dan hutan alang-alang. Penamballan glukosa tela11 meningkatkan aktivitas respirasi tanall hutan alang-alang relatif terlladap hutan sangat terbakar. Dari pengamatan diketallui bahwa dengan se~nakin tinggi nilai aktivitas respirasi maka makin tinggi pula aktivitas enzim PMEase dan CMCase. Artinya bahwa dalam ha1 ini mikrob penghasil enzim tersebut dapat berkurang aktivitasnya atau populasinya seandainya dalam ekosisteln tanah hutan telnpat hidupnya tejadi kerusakan akibat kebakaran lrutan. Parameter kinetik menunjukkan nilai K, tertinggi diperoleh dari enziln yang diekstraksi dari tanali hutan sangat terbakar. Ini ~nenandakan bahwa kebakaran hutan dapat menurunkan afinitas enzim PhEase dan CMCase terlradap substrat. Urutan peilingkatan afinitas enzim PMEase terhadap substrat adalah hutan alami>l~utant erbakar>l~utana lang-alang>hutan sangat terbakar, sedangkan untuk enziln CMCase urutanllya adalah liutan alami>l~utan alang-alang>lutan terbakar>hutan sangat terbakar. Adapun untuk nilai V& bagi enzim PMEase dan CMCase urutannya hutan alami>hutan alangalangzhutan terbakar;.l~utan sangai terbakar. Aktivitas PMEase dan CMCase tertinggi adalah pad2 tanah hutan alami dan terendah pada hutan sangat terbakar.
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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