Judul: Spatio-Temporal Distribution of Particulate Inorganic Carbon (PIC) in Musi River Estuary and Its Surrounding Using MODIS Satellite Data
Abstrak: Particulate Inorganic Carbon (PIC) atau karbon anorganik partikulat adalah komponen utama dari karbon laut global. Sekitar ¼ sedimen laut yang berada di seluruh pesisir dan samudera diwakilkan oleh PIC. Tujuan dari penelitian ini adalah untuk mengidentifikasi spasio-temporal sebaran PIC di Muara Sungai Musi dan sekitarnya. Penelitian ini menggunakan data citra Aqua MODIS, data angin permukaan bulanan dari Copernicus dan data curah hujan bulanan dari BMKG. Data pendukung berupa indeks El Nino Southern Oscillation (ENSO) bulanan diperoleh dari National Oceanic and Atmospheric Administration (NOAA) dan Dipole Mode Index (DMI) bulanan diperoleh dari Japan Agency for Marine-Earth Science and Technology (JAMSTEC). Hasil penelitian menunjukkan bahwa PIC di daerah penelitian selama 20 tahun (2002 – 2021) berada pada kisaran 1,78 – 18,06 mmol/m3 dengan rata-rata 5,24 mmol/m3 pada Musim Barat dan Musim Peralihan 1 serta 3,28 – 11,36 mmol/m3 dengan rata-rata 6,8 mmol/m3 pada Musim Timur dan Musim Peralihan 1. PIC yang lebih tinggi terdapat pada Musim Barat dan Musim Timur, sementara nilai yang lebih rendah ditemui pada Musim Peralihan 1 dan Musim Peralihan 2. Variabilitas nilai PIC dipengaruhi oleh pola angin musiman, curah hujan serta fenomena ENSO dan IOD. Fenomena IOD lebih dominan memengaruhi konsentrasi PIC di Muara Sungai Musi daripada ENSO. IOD negatif akan mengakibatkan konsentrasi PIC di Muara Sungai Musi menurun sedangkan IOD positif akan mengakibatkan peningkatan konsentrasi PIC. Saat terjadi El Nino, nilai PIC menjadi lebih tinggi dari biasanya dan kecepatan angin yang lebih kuat dari biasanya. Saat terjadi La Nina, nilai PIC cenderung lebih rendah dari biasanya dan kecepatan angin lebih lemah dari biasanya.
Keyword: ENSO, IOD, Muara Sungai Musi, PIC

Judul: Spatial-Temporal Distribution of Particulate Inorganic Carbon (PIC) in Thousand Islands Waters and surrounding Using MODIS Satellite Data
Abstrak: Particulate Inorganic Carbon adalah karbon anorganik yang terdiri dari partikel kalsium karbonat, yang dihasilkan oleh fitoplankton, diendapkan secara anorganik, atau sebagai sedimen karbonat. Tujuan penelitian adalah untuk mengetahui dan memetakan variabilitas PIC secara spasial dan temporal di Perairan Kepulauan Seribu dan sekitarnya berdasarkan data satelit. Nilai konsentrasi PIC di Perairan Kepulauan Seribu dan sekitarnya selama periode 20 tahun (2002 – 2021) pada musim barat dan musim peralihan 1 berkisar antara 0,05 - 11,56 mmol/m3 dengan rata-rata 1,91 mmol/m3 dan pada musim timur dan musim peralihan 2 berkisar antara 0,05 - 20 mmol/m3 dengan rata-rata 2,81 mmol/m3. Nilai rata-rata bulanan PIC meningkat pada musim barat dan musim timur dimana nilai PIC maksimum terjadi pada musim timur dengan nilai 4,43 mmol/m3. Nilai rata rata bulanan PIC menurun pada musim peralihan 1 dan musim peralihan 2 dengan nilai minimum terjadi pada musim peralihan 1 dengan nilai 0,58 mmol/m3. Variabilitas nilai PIC dipengaruhi oleh arah dan kecepatan angin dan tidak berhubungan nyata terhadap fenomena IOD dan ENSO. Akan tetapi, pada saat terjadi fenomena IOD positif bersamaan dengan fenomena El Nino nilai PIC secara umum meningkat dari kondisi sebelumnya dan hal ini berkaitan dengan peningkatan kecepatan angin yang meningkat secara nyata sehingga dapat mengakibatkan vertikal mixing., Particulate Inorganic Carbon consists of calcium carbonate particles, either produced by phytoplankton, deposited inorganically, or as carbonate sediments. The purpose of this study was to determine and map the spatial and temporal variability of PIC in the Seribu Islands Waters and its surroundings based on the satellite data. The value of PIC concentrations during the 20-years period (2002-2021) in the west season and transition season 1 were 0.05-11.56 mmol/m3 with average of 1.91 mmol/m3 and in the east season and transition season 2 were 0.05-20 mmol/m3 with average of 2.81 mmol/m3. The monthly average value of PIC increased in the west and east seasons where the maximum PIC value occurred in the east season with the value of 4,43 mmol/m3. The monthly mean value of PIC decreased in the transition season 1 and transition season 2 with the minimum value occurred in transition season 1 with the value of 0,58 mmol/m3. The variability of PIC was affected by wind speed and direction and was not significantly related to the IOD and ENSO. However, PIC increased when there was a positive IOD occurred along with the El Nino that associated with the increased of wind speed that caused a vertical mixing.
Keyword: El Nino, IOD, Thousand Islands Waters, PIC, Wind

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