Judul: Total Produksi Gas dan Degradasi Bahan Kering Hijauan Tropis Pada Media Cairan Rumen Domba yang Diberi Pakan Mengandung Tanin Kajian: In Vitro dan In Sacco.
Abstrak: Hijauan tropis merupakan salah satu bahan yang banyak dimanfaatkan sebagai pakan ternak. Kendala yang dimiliki hijauan tropis sebagai bahan pakan yaitu terkait dengan kadar serat dan anti nutrisi yang cukup tinggi. Salah satu anti nutrisi yang dapat mengikat protein dan mineral adalah tanin. Oleh sebab itu, perlu dilakukan evaluasi nilai degradasi bahan pakan asal hijauan tropis pada media cairan rumen yang hewannya diberi pakan mengandung tanin secara in vitro dan in sacco.
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Judul: Total  Produksi Gas  dan   Degradasi  Bahan Kering Hijauan Tropis Pada Media Cairan Rumen Domba  yang  Diberi Pakan Mengandung Tanin Kajian: In Vitro dan In Sacco. Skripsi
Abstrak: This research was aimed to determine total gas production and dry matter degradation of fermented tropical browse plants in sheep rumen fluid containing tannins as in vitro and in sacco methods. There were nine types of tropical browse plants, such as Pennisetum purpureum, Brachiaria decumbens, Ciiperus kyllinga, Leucaena leucocephala, Artocarpus heterophyllus , Musa sapientum, Dilenia suffruticosa, Melastoma malabathricum, Sapium baccatum. This research was design using Randomized Completely Block Design Factorial. In vitro experiment and total gas production with 3 factors (9 x 3 x 2) treatment 9 type of tropical browse plants (A), three source of rumen fluids medium (B) such as B1 was control feed, B2 was condenseed tannin treatment and B3 was hydrolizable tannin treatment and with and without Polyethilene Glycol (PEG). In sacco experiment, the design was same with in vitro experiment. Data were analized by analysis of variance (ANOVA) and the differences among treatments were tested by Duncan multiple range test. The parameters observed were total gas production and dry matter degradation. Result showed that Artocarpus heterophyllus has the highest total gas production and dry matter degradation, rumen fluid with contained hydrolizable tannin has the highest total gas production and rumen fluid control has the highest dry matter degradation through in vitro technique and in sacco. There was interaction between rumen fluid with contained hydrolizable tannin with Artocarpus heterophyllus in total gas production and dry matter degradation through in vitro technique and in sacco. Polyethilene Glycol addition caused increasing of total gas production and dry matter degradation through in vitro technique.
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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