Judul: Analisis dan Pemodelan Dampak ENSO dan IOD Terhadap Hotspot di Papua
Abstrak: Curah hujan dan anomalinya merupakan salah satu pemicu kemunculan hotspot. ENSO dan IOD memiliki dampak pada peningkatan dan penurunan curah hujan di Indonesia. Penelitian ini memodelkan dampak IOD dan ENSO terhadap hotspot di Papua. Dampak tersebut dimodelkan menggunakan optimasi tanpa kendala dengan fungsi tujuan meningkatkan korelasi antara data iklim (dryspell dan anomali curah hujan) dan data hotspot dan variabel keputusan adalah koefisien model. Koefisien merepresentasikan dampak IOD, ENSO, dan kombinasi keduanya terhadap hotspot. Pembobotan dryspell dan anomali curah hujan dengan ENSO dan IOD memberikan peningkatan korelasi terhadap hotspot dibanding sebelum diboboti. Analisis HCM juga menunjukkan pembobotan tersebut memberikan penguatan asosiasi secara spasial. ENSO menjadi indikator yang lebih besar dampaknya terhadap hotspot di Papua dibanding IOD., Total precipitation dan its anomalies are the triggers for the emergence of hotspot. ENSO and IOD have impacts on increasing and decreasing total precipitation in Indonesia. This study modeled the impact of IOD and ENSO on hotspot in Papua. The impact is modeled using unconstraint optimization with the objective function maximizing the correlation between climate data (dryspell and precipitation anomaly) and hotspot data and the decision variable is the model coefficient. The coefficients represent the impact of IOD, ENSO, and combination of them on hotspots. Weighting with ENSO and IOD on dryspell and precipitation anomaly improves correlation to hotspots compared before weighting. HCM analysis also showed the weighting improved spatial associations. ENSO is an indicator of its greater impact on hotspot in Papua than IOD.
Keyword: anomali curah hujan, dryspell, ENSO, IOD, HCM, hotspot, hujan

Judul: The Global Climate Prediction Data Association Analysis for Hotspots Using the Combined Empirical Orthogonal Function (CEOF)
Abstrak: Iklim global yang terdiri dari El Nino-Southern Oscillation (ENSO) dan Indian Ocean Dipole (IOD) memiliki dampak pada penurunan curah hujan di wilayah Indonesia. Penelitian sebelumnya menemukan bahwa ENSO dan IOD yang berasal dari dataset OISST memiliki keterkaitan dengan hotspot di Indonesia, khususnya di Sumatera bagian selatan dan Kalimantan. Namun hasil korelasinya terlalu kecil sehingga penelitian sebelumnya tidak difokuskan pada menganalisis kekuatan korelasi antar wilayah. Oleh karena itu, studi ini menghitung asosiasi estimasi ENSO dan IOD yang berasal dari dataset ERA5 pada hotspot di Indonesia berdasarkan Heterogeneous Correlation Map (HCM) dan menganalisis kekuatan korelasi antar wilayah di Indonesia. ERA5 merupakan data estimasi yang sering digunakan untuk analisis prakiraan cuaca. Hasil penelitian menunjukkan bahwa ENSO lebih berasosiasi dengan titik api di Papua dan Kalimantan. Sebaliknya, IOD lebih dikaitkan dengan titik api di Sumatera bagian selatan. Selain itu, berdasarkan varians yang dijelaskan dan kekuatan korelasinya, hotspot di Indonesia lebih sensitif terhadap ENSO dan IOD yang berasal dari ERA5 daripada OISST., The global climate consisting of the El Nino-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) has an impact on reducing rainfall in Indonesia. Previous researches have found that ENSO and IOD derived from the OISST dataset are correlated to hotspots in Indonesia, particularly in southern Sumatra and Kalimantan. However, their correlation is too small so that previous research was not focused on analyzing the strength of the correlation between regions. Therefore, this study calculates the association of ENSO and IOD estimation derived from the ERA5 dataset of hotspots in Indonesia based on the Heterogeneous Correlation Map (HCM) and analyzes the strength of the correlation among regions in Indonesia. Apart from OISST, ERA5 is an estimated data which is often used for weather forecast analysis. The result of the study shows that ENSO is more associated with hotspots in Papua and Kalimantan. In contrast, IOD is more associated with hotspots in southern Sumatra. In addition, based on the variance described and the strength of the correlation, hotspots in Indonesia are more sensitive to ENSO and IOD originating from ERA5 than OISST’s.
Keyword: ENSO, Heterogeneous correlation map, Hotspot, IOD, SVD

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