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We propose novel non-linear graph-based analog codes that directly encode k real-valued source samples into n real-valued samples by using (non-linear) sample-by-sample soft quantization of the input samples followed by a linear transformation on the soft-quantized values. Different from existing analog coding schemes, the proposed analog codes are able to produce additional output symbols in a rateless manner and can be decoded utilizing message passing algorithms dealing with real-valued nodes, achieving a performance close to the theoretical limits. 

Several previous studies on targeted food items using carbon and nitrogen stable isotope ratios in Brazil have revealed that many of the items investigated are adulterated; mislabeled or even fraud. Here, we present the first Brazilian isotopic baseline assessment that can be used not only in future forensic cases involving food authenticity, but also in human forensic anthropology studies. The δ13C and δ15N were determined in 1245 food items and 374 beverages; most of them made in Brazil. The average δ13C and δ15N of C3 plants were −26.7 ± 1.5‰, and 3.9 ± 3.9‰, respectively, while the average δ13C and δ15N of C4 plants were −11.5 ± 0.8‰ and 4.6 ± 2.6‰, respectively. The δ13C and δ15N of plant-based processed foods were −21.8 ± 4.8‰ and 3.9 ± 2.7‰, respectively. The average δ13C and δ15N of meat, including beef, poultry, pork and lamb were -16.6 ± 4.7‰, and 5.2 ± 2.6‰, respectively, while the δ13C and δ15N of animal-based processed foods were −17.9 ± 3.3‰ and 3.3 ± 3.5‰, respectively. The average δ13C of beverages, including beer and wine was −22.5 ± 3.1‰. We verified that C-C4 constitutes a large proportion of fresh meat, dairy products, as well as animal and plant-based processed foods. The reasons behind this high proportion will be addressed in this study.