Judul: Penelaahan Beberapa Karakteristik Biologi Populasi Ikan Botia (Botia macracanthus Bleeker) di Sungai Batanghari dan Sungai Kapuas
Abstrak: Peningkatan aktivitas manusia dalam mengeksploitasi sumberdaya alam seringkali memmpengaruhi keanekaragaman hayati dan kestabilan ekologis yang meliputi seluruh karakter komunitas organisme perairan dari ekosistem yang berbeda beserta kerumitan dan keterkaitannya, hingga aspek genetik dari varietas dalam satu spesies. Adanya penangkapan ikan-ikan ekonomis seperti ikan botia, maupun perubahan habitat karena adanya peningkatan aktivitas manusia di sekitar sungai juga terjadi di DAS Batanghari dan Kapuas.
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Judul: Biologi reproduksi Ikan Botia (Botia macracanthus Bleeker) di Sungai Batanghari, Propinsi Jambi
Abstrak: Ikan botia (Botia macracanthus Blkr) merupakan salah satu ikan hias air tawar ekonomis penting, yang berasal dari Sumatera dan Kalimantan. Keberadaannya di alam sangat ter- batas, dan sampai sekarang belum dapat dibudidayakan secara intensif, sehingga produksi ikan tersebut sepenuhnya berasal dari usaha penangkapan dari alam. Dengan demikian, perlu diadakan usaha domestikasi . Tujuan dari penelitian ini, yaitu mengetahui aspek biologi reproduksi ikan botia, antara lain mengenai TKG, fekunditas, diameter telur, dan pola migrasi. Adapun manfaatnya, diharapkan dapat memberikan informasi untuk penge- lolaan sumberdaya ikan tersebut, yang berorientasi kepada upaya domestikasi, sehingga keberadaan populasinya di alam dapat dipertahankan. Metoda pengambilan sampel ikan dilakukan dari dua wilayah, yaitu di Sungai Batanghari dan danau-danau sekitarnya. Sampel yang diambil dari sungai berasal dari 3 stasiun, yaitu Hilir (I), Tengah (II), dan Hulu sungai (III). masing- masing stasiun dibagi menjadi 2 sub-stasiun sebagai ulangannya. Sedangkan sampel yang berasal dari danau, meliputi Danau Teluk, dan Danau Sipin yang terletak di bagian hilir sungai; dan Danau Baru yang terletak di bagian hulu. Pengambilan sampel ini dilakukan 1 minggu sekali, pada setiap stasiun. Pengambilan sampel untuk parameter fisika kimia air dilakukan pada stasiun yang telah ditetapkan untuk pengambilan sampel ikan, namun waktu pengambilannya dilakukan 2 minggu sekali…dst
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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