Judul: Studi kerusakan anatomi daun Bauhinia purpurea L. sebagai tanaman tepi jalan di kota Bogor
Abstrak: Penelitian ini bertujuan untuk mengetahui secara mikroskopis kerusakan anatomi daun B. purpurea sebagai tanaman tepi jalan di Kota Bogor, untuk menduga adanya pengaruh emisi kendaraan bermotor. Bahan yang digunakan dalam penelitian ini adalah preparat daun pohon B. purpurea berupa daun muda dan daun tua. Dalam penelitian ini dilakukan pengamatan terhadap kerusakan bentuk, warna dan isi sel pada jaringan epidermis atas dan bawah, palisade serta bunga karang. Hasil pengamatan kerusakan dianalisis secara deskriptif. Selain itu dilakukan pula pengukuran terhadap panjang dan lebar sel masing-masing jaringan (epidermis atas dan bawah, palisade serta bunga karang) dan hasil ini dianalisis dengan menggunakan Rancangan pengamatan Percobaan Faktorial dengan dua perlakuan, yaitu umur daun dan faktor lokasi.
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Judul: Studi anatomi daun beberapa jenis anakan di beberapa lokasi di kota Bogor
Abstrak: Hasil pengamatan mikroskopis dianalisa dengan menggunakan rancangan acak faktorial 2 x 2 untuk panjang dan lebar sel masing-masing peubah dan secara deskriptif untuk kerusakan bentuk, warna dan isi sel. Dari hasil pengamatan tersebut dapat ditentukan tingkat kerusakan dan tingkat kepekaan tanaman terhadap pencemaran udara secara mikroskopis. Hasil pengamatan mikroskopis selanjutnya dibandingkan dengan hasil pengamatan secara makroskopis berupa data sekunder. Pengamatan makroskopis tersebut dapat menentukan tingkat kerusakan dan tingkat kepekaan tanaman terhadap pencemaran udara secara makroskopis. Selanjutnya gabungan pengamatan secara mikroskopis dan makroskopis dapat menentukan tingkat ketahanan jenis tanaman terhadap pencemaran udara. Hasil penelitian menunjukkan bahwa diperoleh jenis- jenis tanaman berdasarkan tingkat kerusakan anatomi daun yang tertinggi dan secara mikroskopis termasuk peka (tidak tahan) terhadap pencemaran udara yaitu: Bauhinia 2 purpurea L, Podocarpus imbricatus Bl, Agathis alba Foxw, Swietenia macrophylla King dan Bixa orellana L. Sedangkan Filicium decipiens Thw dan Myristica fragrans Houti kurang rusak anatomi daunnya jika dibandingkan dengan kelima jenis tanaman yang telah disebutkan sebelumnya dan secara mikroskopis termasuk kurang peka (agak tahan) terhadap pencemaran udara.
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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