Judul: Analisis Karakteristik Aerosol Optical Depth (AOD) dan Curah Hujan di DKI Jakarta (Studi Kasus: Tahun 2015)
Abstrak: Penelitian mengenai peran aerosol dalam sistem iklim telah banyak dilakukan. Aerosol dapat mempengaruhi pola presipitasi dengan cara memodifikasi distribusi ukuran tetesan awan dan umur tinggal awan. Penambahan konsentrasi aerosol yang besar ke awan tropis laut dapat menunda pembentukan hujan di awan. Penelitian ini bertujuan untuk menganalisis karakteristik serta fluktuasi nilai aerosol optical depth (AOD) dan curah hujan di DKI Jakarta pada tahun 2015. Studi kasus ini dipilih sebab fluktuasi curah hujan yang tinggi yang ditandai dengan terjadinya banjir pada tahun tersebut dan adanya perbedaan total presipitasi yang signifikan antara bulan basah dan bulan kering diharapkan mampu menggambarkan hubungan antara AOD dengan curah hujan. Hasil yang diperoleh dari penelitian ini menunjukkan bahwa nilai AOD maksimum adalah 0,994 dan nilai minimum adalah 0,017, serta curah hujan harian tertinggi sebesar 98,3 mm. Penelitian ini menggunakan nilai parameter suhu udara dan kecepatan angin sebagai faktor yang mempengaruhi terjadinya curah hujan. Hasil analisis korelasi yang diperoleh dari penelitian ini menunjukkan bahwa aerosol optical depth berkorelasi negatif dengan curah hujan dan berkorelasi positif dengan suhu udara dan kecepatan angin., There has been a lot of research about the role of aerosols in the climate system. Aerosol affect precipitation pattern by modifying the cloud drop size distribution and cloud residence time. The addition of large aerosol concentrations to marine tropical clouds can delay the formation of rain in the cloud. This study aims to analyze the characteristics and fluctuations of aerosol optical depth (AOD) and rainfall in DKI Jakarta in 2015. This case study was chosen because of the high fluctuations in rainfall which was marked by the occurrence of 2015’s floods, and the significant difference in total precipitation between wet and dry months is expected to be able to describe the relationship between AOD and rainfall. The results obtained from this study indicate that the maximum AOD value is 0.994 and the minimum value is 0.017, and the highest daily rainfall is 98.3 mm. This study uses the parameter values of air temperature and wind speed as factors that influence the occurrence of rainfall. The results of the correlation analysis obtained from this study indicate that aerosol optical depth is negatively correlated with rainfall and positively correlated with air temperature and wind speed.
Keyword: aerosol, AOD, precipitation, temperature, wind speed

Judul: Relationship Between Aerosol Optical Depth and
Particulate Concentration in Jakarta from 2020 to 2021
Abstrak: Tujuan dari penelitian ini adalah untuk menilai korelasi antara pengukuran Aerosol Optical Depth (AOD) dan konsentrasi partikulat di Jakarta selama rentang waktu 2020-2021. Hasil analisis menunjukkan adanya hubungan antara AOD dan konsentrasi PM, dengan hubungan yang lebih kuat pada PM2.5. SPKU Bundaran HI, koefisien korelasi antara AOD 500nm dan PM2.5 adalah r = 0.78, sedangkan untuk PM10 adalah r = 0.72. Koefisien korelasi antara AOD 500nm dengan PM10 di SPKU Kelapa Gading sebesar 0.65, sedangkan koefisien korelasi antara AOD 500nm dengan PM2.5 sebesar 0.70. Nilai AOD juga dipengaruhi oleh curah hujan, terlihat dari data AERONET AOD yang menunjukkan korelasi bulanan sebesar - 0.47. Analisis data MODIS mengungkapkan konsentrasi partikulat di atmosfer yang signifikan, seperti yang ditunjukkan oleh distribusi regional AOD. Selama penutupan akibat COVID-19 pada tahun 2020, terjadi penurunan Aerosol Optical Depth (AOD) di atmosfer. Namun, pada tahun 2021, terjadi peningkatan AOD. Model regresi linier antara AOD dan PM2.5 (R2 = 0.61, RMSE = 5.2) menunjukkan akurasi yang lebih unggul dalam memprediksi dibandingkan dengan PM10`(R2 = 0.52, RMSE = 8.04). Hal ini menunjukkan bahwa data AOD dapat dimanfaatkan untuk memantau kualitas udara di Jakarta., The objective of this research is to analysis the correlation between Aerosol Optical Depth (AOD) measurements and particulate concentrations in Jakarta over the period 2020-2021. The analysis findings reveal a relationship between AOD and the concentrations of PM10 and PM2.5, with a more pronounced correlation observed for PM2.5. At the Bundaran HI air quality monitoring station (SPKU), the correlation coefficient between AOD at 500nm and PM10 is 0.72, while the correlation coefficient with PM2.5 is 0.78. At the Kelapa Gading air quality monitoring station (SPKU), the correlation coefficient between AOD at 500nm and PM10 is 0.65, whereas the correlation coefficient with PM2.5 is 0.70. AOD values are also influenced by rainfall, as indicated by AERONET AOD data showing a monthly correlation of -0.47. MODIS data analysis reveals significant particulate concentrations in the atmosphere, as demonstrated by the regional distribution of AOD. During the COVID-19 lockdown in 2020, there was a decrease in Atmospheric Aerosol Optical Depth (AOD). However, in 2021, there was an increase in AOD levels. The linear regression model between AOD and PM2.5 (R2 = 0.61, RMSE = 5.2) shows superior accuracy in prediction compared to PM10 (R2 = 0.52, RMSE = 8.04). This indicates that AOD utilization can be reliably employed to monitor air quality in Jakarta.
Keyword: AOD, curah hujan, analisis lingkungan, konsentrasi partikulat, kualitas udara Jakarta

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