Judul: Perawakan Anak Umur 4-19 Tahun di Kota Bandung
Abstrak: Somatotype in Indonesia had not been studied in Bandung City. The study aims to determine the physique of children aged 4-19 years in Bandung City and to see the physique development of children in each age class. It is carried out in girls and boys age 4-19 years old in Bandung City by Heath-Carter method. Girls had more endomorph component, while boys had more ectomorph component. Somatotype component of children aged 4-6 years both girls and boys are endomorphic-mesomorph. The correlation of Body Mass Index (BMI) to endomorph was higher in girls than in boys. Somatotype of girls and boys changed with age. Endomorph component in girls and ectomorph component in boys increased, but mesomorph component in both sexes decreased until the age of 19 years.
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Judul: Somatotypes of Bekasi Children and Adolescent Aged 3-20 Years
Abstrak: Salah satu metode kuantitatif untuk mendeskripsikan bentuk dan komposisi tubuh adalah somatotipe. Somatotipe dinyatakan dalam tiga urutan angka yang masing-masing mewakili endomorf, mesomorf, dan ektomorf. Indonesia memiliki suku, sosiokultur, dan latar belakang sosio-ekonomi yang beragam sehingga penting untuk mempelajari variasi bentuk dan komposisi tubuh menggunakan metode kuantitatif di setiap kotanya. Tujuan penelitian ini adalah menjelaskan somatotipe anak dan remaja usia 3-20 tahun di Bekasi. Pengukuran somatotipe menggunakan metode yang diperkenalkan Carter dan Heath. Komponen somatotipe berubah seiring pertambahan usia. Pada usia 3 tahun perempuan memiliki somatotipe mesomorf-endomorf. Somatotipe berubah dari endomorf menjadi mesomorf dan ektomorf yang seimbang setelah usia 12 tahun. Somatotipe laki-laki pada usia 3 tahun adalah mesomorf-ektomorf. Somatotipe lalu berubah menjadi endomorf berimbang pada usia 13 tahun. Pada usia 20 tahun, somatotipenya tetap endomorf berimbang. Secara umum, komponen endomorf perempuan naik sedangkan laki-laki turun. Komponen mesomorf dan ektomorf laki-laki lebih tinggi daripada perempuan di setiap tingkat usia.
Keyword: anak dan remaja, Bekasi, somatotipe

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