Judul: Inventarisasi keanekaragaman jenis tumbuhan di Kawasan Taman Nasional Gunung Merapi
Abstrak: Gunung Merapi National Park (TNGM) is a nature conservation area which has a native ecosystem in the form of blend with the forest ecosystem volcanic highland area of ± 6410 ha. The interaction that exists between communities and national park should be developed to support the preservation of national park and fully bring prosperity to the local community. The existence of national park should be able to provide benefits, not only to preserve natural resources, but also prosperity for local communities. In this regard, research is needed in providing inputs to the park managers and communities in the management TNGM. This study aimed to describe the general condition of the area, inventory and analyze the wealth and diversity of plant species and identify the medicinal uses of plants into different groups in the region TNGM usefulness. The research was done in merapi mount national park in 3 (three) month from June to August 2010. It was used some equipment such as : compass Brunton, GPS, diameter measuring tool, trash bag and digital camera. The research was used a secondary data of research location general condition and primary data which are covering : various kind of species, amount and diameter of poles and tree stages; various kind of species and amount of herb, undershrub, shrub, epiphyte and liana habitus. The primary data were collected by field orientation, vegetation analyzing with nested line transect method and herbarium making. The data were analyzed to find out the importance value, index of species richness, index of species diversity, pattern of plants spread and the use of plant species. Total plant species found in the region TNGM 108 species from 52 families, with most of the family Euphorbiaceae and Fabaceae (7 species). The highest species richness and diversity found in jungle zones in mountain forest ecosystem types and the lowest was found in the core zone of an upper mountain forest ecosystem types. The pattern of distribution plants on average tend to be clumped. Plant species are found grouped into 11 groups of usability. Usefulness of the most widely plant can be utilized is for producing food that is as many as 32 species from 24 families. Advice needs to be done in this study include: rehabilitation of forest areas damaged by the eruption TNGM needs to be done by planting local native species in rehabilitation zone, further research needs to be done after the eruption of an inventory of plants and the manager needs to conduct training activities, counseling and assistance to the people involved in providing useful knowledge about plants in TNGM.
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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