Judul: Identifikasi Struktur Anatomi Daun Angsana dan Beringin Akibat Pengaruh Gas dan Materi Vulkanik Pasca Erupsi Gunung Merapi
Abstrak: Mount Merapi eruption occurred on Tuesday October 26, 2010. The eruption discharged various types of gases and materials consisted of sulfur dioxide (SO2), hydrogen sulfide (H2S), nitrogen dioxide (NO2), and dust particles (Total Suspended Particulates or Particulate Matter). Air pollutant particularly Merapi, gas and volcanic material can cause damage to the anatomical structure of plants around them (Wilson et al. 2007). Therefore research on the influence of gas and volcanic material on anatomical structure of urban plants in Yogyakarta city is nedeed. The aim of the research was to identify the influence of gas and volcanic material on leafs anatomical structure in two species of urban plants, namely Burmese rosewood and Banyan. This research was expected to provide consideration as input in the selection of urban vegetation to improve environmental conditions after the eruption of the Mount Merapi in Yogyakarta city. The research was carried out in Yogyakarta as a relatively polluted area, and Solo as the location of less polluted area or control, and microscopic leaf anatomical preparations were carried out in the Laboratory of Plant Anatomy, Department of Biology, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University. The research was conducted from June until August 2011. Types of data and information collected in this study consists of primary and secondary data. Primary data was taken from the results of observation on the leaf anatomical paradermal and transversal section each leaf in two cities. Secondary data on air quality data was obtained from The Environmental Bureau of each city. Data were analysed using t-student test to test the difference between plants in the relatively polluted area with the less polluted area. Observation results of leaf anatomical paradermal and transversal section of Burmese rosewood were undamaged, but which showed influence by gas and volcanic material were the decline of density and index stomata, the raise length stomatal, and the thicken of palisade tissues. Observation result of leaf anatomical paradermal and transversal section of Banyan were also undamagade and all the parameters were not significant statistically. The research had showed that Burmese rosewood and Banyan could cope up with pollutants from Mount Merapi eruption. Therefore, both species were appropriate to be planted in the Yogyakarta city.
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Judul: Keanekaragaman Tumbuhan Bawah Pasca Erupsi Merapi di Taman Nasional Gunung Merapi, Yogyakarta
Abstrak: The eruption of Merapi Volcano in 2010 caused a great damage to the surrounding ecosystem. The recovery of surrounding ecosystem was done through succesional process. Organisms occur during early succesional stage are understory plants, thus they could be used as indicator of early stage succesion of damaged vegetation in Mount Merapi. The objective of this research was to describe and compare the diversity of understory plants after the eruption of Merapi Volcano in 2010 in Mount Merapi National Park, Sleman Region, Yogyakarta in two locations namely Gandok and Kaliurang Recreational Park. Gandok was categorized as high damaged location, while Kaliurang Recreational Park represented low damaged location. Vegetation was analyzed using quadratic method. Plants sample was identified in laboratory. Vegetation analysis generated the value of Significant Value Index (SVI), Diversity Index (H’), and Similarity Index (IS). Results showed that understory plant diversity of Gandok consist of 74 species and 63 genera, while Kaliurang Recreational Park consist of 49 species and 44 genera. The highest SVI was obtained by Digitaria nuda in Gandok and Brachiaria reptans in Kaliurang Recrational Park. Gandok and Kaliurang Recreational Park have a low similarity of understory community. Both location were categorized in medium diversity level.
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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