Judul: Kajian Paparan Logam Berat dari Pangan di Indonesia
Abstrak: Cemaran logam berat dapat masuk dalam makanan dari air (air laut, air irigasi, air baku), tanah pertanian dan udara. Lembanga pangan dunia CODEX dan Badan Pengawasan Obat dan Makanan Indonesia telah menetapkan batas maksimum untuk 5 jenis logam yaitu timbal, merkuri, kadmium, timah dan arsen. Kajian paparan dilakukan untuk menduga tingkat paparan logam berat tersebut di Indonesia. Dalam melakukan kajian paparan diperlukan dua data yaitu data konsentrasi logam berat dan data konsumsi pangan di Indonesia. Data konsentrasi logam berat (timbal, merkuri, kadmium, timah dan arsen) pada pangan menggunakan data sekunder yang dikumpulkan dari pencarian online pada beberapa sumber ilmiah online dengan kata kunci “logam berat pada pangan, cemaran logam berat”. Data tingkat konsumsi diambil dari Laporan Survey Konsumsi Makanan Individu (SKMI) 2014 yang mengkategorikan konsumen dan makanan dalam enam kelompok usia dan 17 kelompok pangan. Tingkat paparan logam beratdihitung dengan pendekatan deterministik yang menggunakan data konsentrasi logam berat pada pangan (minimum, maksimum dan rerata berdasarkan perhitungan data pustaka) dan batas maksimum logam berat pada pangan dari regulasi serta rerata tingkat konsumsi. Karakterisasi risiko dilakukan dengan membandingkan tingkat paparan dengan Provisional Tolerable Weekly Intake (PTWI). Karakterisasi risiko dilakukan dengan membandingkan tingkat paparan logam berat dengan Provisional Tolerable Weekly Intake (PTWI) dan Provisional Tolerable Monthly Intake (PTMI). Pustaka terbanyak diperoleh untuk logam timbal dan kelompok ikan, hasil laut dan olahannya. Kadar rerata merkuri, kadmium dan timah tertinggi terdapat pada kelompok ikan, hasil laut dan olahannya. Kelompok minuman merupakan kelompok pangan dengan rerata timbal pustaka tertinggi sedangkan untuk logam arsen, kadar rerata tertinggi terdapat pada kelompok sayuran dan olahannya. Hasil penelitian menunjukkan kelompok balita (0-59 bulan) memiliki nilai paparan logam berat tertinggi. Nilai paparan logam berat berdasarkan batas maksimum regulasi lebih tinggi dibandingkan nilai paparan logam berat berdasarkan kadar rerata pustaka. Hasil karakterisasi risiko menunjukkan nilai risiko paparan timbal dan kadmium dari kadar rerata pustaka berisiko tinggi (>100% PTWI) pada semua kelompok usia. Pada logam merkuri nilai risiko paparan berdasarkan kadar rerata pustaka berisiko tinggi pada kelompok balita (0-59 bulan) dan anak-anak (5-12 tahun), sedangkan nilai risiko paparan timah dan arsen dari kadar pustaka berisiko rendah pada semua kelompok usia. Kelompok pangan yang paling berkontribusi pada paparan timbal, merkuri dan timah adalah kelompok ikan, hasil laut dan olahannya, sedangkan paparan kadmium kelompok pangan yang paling berkontribusi adalah air minum dan pada paparan arsen, sayur dan olahannya sebagai kontributor utama. Hasil kajian ini dapat digunakan untuk prediksi awal tingkat risiko kesehatan masyarakat Indonesia terhadap paparan logam berat dari pangan. Verifikasi hasil kajian ini masih diperlukan dengan kajian paparan yang menggunakan pendekatan probabilistik dengan ketepatan hasil yang lebih baik.
Keyword: Kajian paparan, deterministik, logam berat, Survey Konsumsi Makanan Individu (SKMI)

Judul: Kajian Paparan Logam Berat Timbal (Pb) dari Air Minum pada Anak Balita di Indonesia
Abstrak: Stunting in children is still occuring in Indonesia, which becomes a shared responsibility of several stakeholders to overcome it. Lead (Pb) is a heavy metal which interferes calcium metabolism causing inneffective development of bones and teeth thus, Pb is a risk factor for stunting. Drinking water contributes the highest exposure to Pb, it is necessary to determine the risk characterization of Pb from the water. Exposure assessment were conducted by sampling, obtaining Pb concentrations, extracting data from the Individual Food Consumption Survey and Basic Health Research, calculating Pb exposure, risk characterizing of Pb and predicting the correlation of Pb exposure to the nutritional status of PB/U or TB/U children aged 0-47 month. Pb exposure was obtained by multiplying the consumption data with predicted levels of Pb in drinking water and divided by body weight. Lead risk characterization was calculated using Margin of Exposure (MoE) approach by comparing Pb benchmark dose lowerbound and exposure. The correlation of Pb exposure with nutritional status was also calculated by Pearson analysis. Samples were taken from 34 provinces in Indonesia, there were 25 provinces (75,8%) with Pb levels less than LoD and 8 provinces (24,2%) with Pb levels more than LoD. The average percentage of children in Indonesia aged 0-47 months who consume less drinking water is 76,81%. The average exposure and risk characterization of Pb ranged from 0,026-0,082 μg/kg body weight per day and 28,05-8,79, respectively, suggesting low risk of Pb exposure from drinking water. Stronger correlation of Pb exposure with nutritional status was observed in province with Pb level above Limit of Detection (LoD) than those of below LoD with correlation values (r) of children aged 0-11 months; 12-23 months; and 36-47 months; 36-47 months is r 0,004; r -0,038; r -0,109; r -0,231. The result showed that the higher Pb exposure, the lower the nutritional status, although the correlation is weak. Pb exposure from drinking water does not cause stunting in toddlers.
Keyword: drinking water, exposure assessment, lead, stunting, toddler

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