Judul: Analisis kestabilan model populasi plankton pada fenomena red tide
Abstrak: Keistimewaan dari suatu populasi plankton adalah pada saat terjadinya ledakan populasi yang sangat cepat. Fenomena ini dibagi menjadi dua tipe, yaitu spring bloonzs dan red tide. Spring blooms seperli namanya, terjadi pada musim-mush tertentu dan disebabkan oleh perubahan temperatur ataupun ketersediaan nutrisi. Sedangkan red tide merupakan suatu fenomena diiana ledakan populasi fitoplankton menyebabkan permukaan air laut menjadi berwarna merah dan mengandung racun yang diproduksi oleh alga jenis dinorr~ustigates( yang hanya hidup di air asin dan temperatur yang rendah). Racun ini dapat membunuh ikan serta invertebrala yang ada di laut sehiiga dapat mempengarnhi proses rantai makanan di laut.
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Judul: Analisis model Phytoplankton, Toxic Phytoplankton, dan Zooplankton pada Lingkungan Perairan
Abstrak: Pada perairan terdapat berbagai macam organisme, salah satunya adalah plankton. Plankton merupakan organisme tingkat pertama yang berfungsi sebagai produsen atau penyedia energi bagi organisme lain. Plankton terdiri atas dua macam, yaitu phytoplankton dan zooplankton. Phytoplankton merupakan kelompok plankton yang bersifat seperti tumbuhan, sedangkan zooplankton merupakan anggota plankton yang bersifat hewani. Berlebihnya phytoplankton pada lingkungan perairan dapat menimbulkan fenomena blooming yang ditandai dengan berubahnya warna air laut yang dikenal dengan brown tides. Istilah yang saat ini sering digunakan di dunia Internasional adalah Harmful Algae Blooms atau HABs. HABs adalah suatu fenomena blooming toxic-phytoplankton di suatu perairan yang dapat menyebabkan kematian biota lain. Karya ilmiah ini membahas model phytoplankton, toxic-phytoplankton, dan zooplankton yang diambil dari Banarjee & Ezio (2011). Berdasarkan model tersebut dilakukan simulasi analisis kestabilan dan nilai parameter. Hasil simulasi menunjukkan bahwa jika tingkat kematian populasi pyhtoplankton meningkat maka populasi toxic-phytoplankton akan meningkat pula. Jika tingkat kematian populasi phytoplankton rendah, maka populasi toxic-phytoplankton juga rendah. Agar kondisi HABs tidak terjadi dalam suatu lingkungan perairan, populasi phytoplankton harus ditingkatkan.
Keyword: Plankton, Model, Stability, Harmful Algae Blooms, Plankton, Kestabilan, Model matematika, Analisis model, Simulasi komputasi

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