Judul: Optimization of Fuzzy C-Means Performance using Particle Swarm Optimization on the ASEAN Food Security Index
Abstrak: Ketahanan pangan yang tidak merata di negara-negara ASEAN dapat ditangani dengan analisis gerombol. Penelitian ini bertujuan menggerombolkan negara-negara ASEAN berdasarkan faktor-faktor yang memengaruhi indeks ketahanan pangan menggunakan 14 peubah. Data yang digunakan bersumber dari ASEAN Publication, World Bank, dan Asian Development Bank. Metode yang digunakan adalah Fuzzy C-Means (FCM) dengan Particle Swarm Optimization (PSO). FCM dipilih karena kemampuannya menangani data berdimensi tinggi, sedangkan PSO digunakan untuk mengoptimalkan parameter secara global. Hasil optimasi PSO menunjukkan jumlah gerombol terbaik adalah empat (?? = 4) dan parameter fuzzy (?? = 1,5). Parameter dengan tiga dan dua gerombol juga diuji untuk perbandingan. Evaluasi penggerombolan menggunakan Silhouette Coefficient, Partition Coefficient, dan Xie-Beni Index menunjukkan bahwa FCM yang dioptimalkan dengan PSO memiliki indeks validitas terbaik. Gerombol 1 terdiri dari empat negara dengan ketahanan pangan kurang baik, gerombol 2 terdiri dari dua negara dengan ketahanan pangan cukup baik, gerombol 3 terdiri dari tiga negara yang paling rentan, dan gerombol 4 hanya beranggotakan Singapura dengan ketahanan pangan terbaik. Singapura dapat menjadi contoh bagi negara-negara ASEAN lainnya karena memiliki nilai indikator penyusun indeks ketahanan pangan yang sangat baik., Unequal food security in ASEAN countries can be handled using cluster analysis. This research aimed to group ASEAN countries based on factors that influence the food security index using 14 variables. The data was obtained from the ASEAN Publication, World Bank, and Asian Development Bank. The method used was Fuzzy C-Means (FCM) with Particle Swarm Optimization (PSO). FCM was chosen because of its ability to handle high-dimensional data, while PSO was used to optimize global parameters. PSO optimization results showed that the best number of clusters is four (?? = 4) and fuzzy parameters (?? = 1.5). Parameters with three and two clusters were also tested for comparison. Clustering evaluation using the Silhouette Coefficient, Partition Coefficient, and Xie-Beni Index showed that FCM optimized with PSO had the best validity index. Cluster 1 consisted of four countries with poor food security, cluster 2 consisted of two countries with reasonably good food security, cluster 3 consisted of the three most vulnerable countries, and cluster 4 only consisted of Singapore with the best food security. Singapore could be an example for other ASEAN countries because it has excellent indicators that make up the food security index.
Keyword: ASEAN, ketahanan pangan, fuzzy c-means, particle swarm optimization

Judul: Modeling the Diversity of Food Security Index in Indonesia with Spatial Approach, Efficiency Analysis, and Clustering
Abstrak: Ketahanan pangan yang digambarkan oleh ukuran Indeks Ketahanan Pangan (IKP) umumnya memiliki variasi permasalahan regional antar wilayahnya dan cenderung berfluktuasi antar tahunnya, sehingga diperlukan pendekatan penanganan yang disesuaikan dengan kondisi masing-masing wilayah. Penelitian ini menggunakan pendekatan geographically temporally weighted regression yang memungkinkan untuk memodelkan keragaman spasial dan temporal dalam data, dan sesuai dengan sifat data ketahanan pangan yaitu cenderung bervariasi antar wilayah dan tahun. Selanjutnya output analisis tersebut diperdalam dengan data envelopment analysis untuk menilai efisiensi pemanfaatan sumber daya terhadap kondisi ketahanan pangan antar wilayah dan menggunakan penggerombolan k-medoid untuk melakukan perbandingan kondisi pangan antar kelompok wilayah. Seluruh wilayah di Indonesia menjadi objek penelitian ini, yaitu sebanyak 514 kabupaten/kota selama tahun 2020-2022. Hasil dari penelitian menunjukkan bahwa peubah angka harapan hidup, laju pertumbuhan penduduk, persentase penduduk miskin, produksi tanaman pangan, dan pengeluaran per kapita berpengaruh pada taraf nyata 5% terhadap nilai IKP di sebagian besar wilayah, dengan nilai Pseudo R^2 sebesar 91.2%. Hasil analisis DEA menunjukkan terdapat dua puluh tujuh daerah di Indonesia yang selalu konsisten dengan tingkat efisiensi ketahanan pangan maksimum. Namun secara keseluruhan, kemampuan efisiensi mengalami penurunan yang cukup signifikan pada tahun 2022. Hal ini diperkuat dengan hasil analisis gerombol k-medoid bahwa dari tiga gerombol yang terbentuk (gerombol dengan IKP cenderung tinggi, sedang, dan rendah), gerombol dengan tingkat ketahanan pangan rendah mengalami peningkatan sebesar 9% dari tahun 2020 ke tahun 2022 yang perlu diperhatikan., Food security, which is represented by the Food Security Index (FSI) measure, generally has regional variations between regions and tends to fluctuate between years, so a handling approach that is tailored to the conditions of each region is needed. This study uses a geographically temporally weighted regression approach that allows to model spatial and temporal variability in the data, which is in accordance with the nature of food security data, which tends to vary between regions and years. Then the output of the analysis is deepened with data envelopment analysis to assess the efficiency of resource utilization towards food security conditions between regions and using k-medoid clustering to compare food conditions between regional groups. All regions in Indonesia became the object of this research, namely 514 districts/cities during 2020-2022. The results of the study indicated that the variables of life expectancy, population growth rate, percentage of poor people, food crop production, and per capita expenditure have a significant effect on the FSI value in most regions, with a Pseudo R^2 value of 91.2%. The results of DEA analysis showed that there are twenty seven regions in Indonesia that are always consistent with the maximum level of food security efficiency. But overall, the efficiency ability has decreased significantly in 2022. This is reinforced by the results of the k-medoid clustering analysis that of the three clusters formed (clusters with IKP tending to be high, medium, and low), the cluster with a low level of food security has increased by 9% from 2020 to 2022, which needs more attention.
Keyword: data envelopment analysis, food security index, geographically temporally weighted regression, k-medoid clustering

Judul: Hamiltonian formulation for linear waves motion in two layers fluid
Abstrak: The surface wave could be considered as a wave that separates two fluids, namely water and air. Based on this assumption, it is introduced the interfacial wave, a wave between two layers of fluid with different density. The formulation of interfacial waves motion begins with deriving the base equation of irrotational ideal fluid. Furthermore, according to irrotational fluid assumption, the base equation can be stated in velocity potential. In this derivation, the fluids domain is assumed to be restricted by rigid lid boundary conditions, both at the upper and lower limit. Therefore, the interfacial waves motion can be explained in a hamiltonian formulation. In the hamiltonian formulation, total energy is defined as the sum of kinetic and potential energy. The hamiltonian system is obtained from reduction of kinetic energy by using the Dirichlet Neumann Operator. The resulted kinetic energy equation is nonlinear. Therefore, this form is linearized by first part of the Taylor expansion. This linearization gives a dispersion relation of linear wave. Based on this dispersion relation, the phase speed of the linear wave depends on the density ratio of the two layers fluid.
Keyword: