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: Besar tubuh anak usia 4 sampai 14 tahun di wilayah Purwakarta
Abstrak: Growth is the increase of entire body size. One of the important component which help the progress of body size is fat. The body size of an adult has high correlation with the fat of their body. Older people have greater body size because of fat deposition. The body size can be determined by calculating the Body Mass Index (BMI), which is the ratio between weight (kg) and the square of height (m2). This research was conducted to determined the growht pattern of body size and fat component of children age 4 to 14 years in Pwakarta region. The percentage of fat in a girl was correlated with BMI. On the other hand,, this correlation of fat with BMI did not existed in a boy. The Body Mass index iends io be determined by weight noi by height. Tine correlation value between BMI and weight of a boy 0.813 and a girl 0.827. While, the correlation value of the BMI to the height was 0.612 for a boy and 0.559 for a girl. The growht of body size of a girl was influenced by the body fat by fat free tnass (FFM), hut the growht of a boy was much more influenced by FFM.
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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