Abstract Piecewise-linear models constitute an attractive alternative to construct a function whose graph fits a finite set of discrete points. These models are preferably selected over other approximation strategies like polynomials or splines. Although there are several piecewise-linear models reported in literature, the so-called High Level Canonical has the remarkable advantage of emerging from a well-structured algorithmic methodology to efficiently determine the parameters of any given piecewise-linear function. However, as it happens in all other piecewise-linear models, it also has the problem of lack of differentiability at the breakpoints. In order to solve this problem, an approach based on an exponential approximation of the basis-function is proposed as a strategy to transform the High Level Canonical piecewise-linear model into a smooth-piecewise one. This mathematical transformation ensures the existence and continuity of the nth-order derivatives of the resulting smooth model. Besides of this, it is observed that by applying the piecewise-linear to smooth transformation, the number of terms of the resulting smooth representation can significantly be reduced due to a great number of them can be approximated by a line equation. In order to verify the effectiveness of this proposal, numerical simulations performed on one-dimensional and two-dimensional functions are reported.

The nutritional information of cooked food is useful for the dietary planning of individuals, which includes calculating diets more attached to everyday life, providing adequate dietary guidance, developing new products, giving information to consumers as well as various aspects of food health regulation. The aim of this study was to determine the chemical composition (moisture, ash, crude protein, ether extract, crude fiber, carbohydrates, Na, K, Ca, Fe, Zn, Mg and Cu), vitamins (riboflavin and thiamine) and the energy supply of typical cooked foods of the states of Puebla and Tlaxcala, Mexico. Cooked foods were collected from restaurants, taverns or markets and grouped into: 1) Snacks, 2) stews, and 3) moles. Analyses were performed with the official methods of AOAC and AACC. The energy supply was calculated using Atwater factors. Significant differences (p≤0.05) of nutrients between groups were detected with the Kruskal-Wallis test; and differences between values were detected with the Wilcoxon-Mann-Whitney test. The results showed that the snack group provides the greatest contribution of energy (850 kJ), Ca and Cu per 100 g compared to other groups. But some cooked foods were out of the confidence interval of each group in relation to other nutrients, which may be caused by using traditional ingredients or certain cooking techniques. An example is the meat undergoing a process of salting for preservation, known as cecina.

La información nutrimental de los alimentos cocinados es útil para la planificación dietética de los individuos, la cual incluye calcular dietas más apegadas a la vida cotidiana, ofrecer orientación alimentaria adecuada, desarrollar nuevos productos, informar al consumidor y aspectos diversos de la regulación sanitaria de los alimentos. El objetivo de este estudio fue determinar la composición química (humedad, cenizas, proteína cruda, extracto etéreo, fibra cruda, hidratos de carbono, Na, K, Ca, Fe, Zn, Mg y Cu), vitaminas (riboflavina y tiamina) y el aporte energético de alimentos cocinados, típicos de los estados de Puebla y Tlaxcala, México. Los alimentos cocinados se obtuvieron de restaurantes, fondas o mercados y se agruparon en: 1) Antojitos, 2) guisos y, 3) moles. Los análisis se realizaron con los métodos oficiales de la AOAC y la AACC. El aporte energético se calculó con los factores de Atwater. Las diferencias significativas (p≤0.05) de los nutrimentos entre grupos se detectaron con la prueba de Kruskal-Wallis; y las diferencias entre los valores se detectaron con la prueba de Wilcoxon-Mann-Whitney. Los resultados mostraron que el grupo de antojitos ofrece el aporte mayor de energía (850 kJ), Ca y Cu por cada 100 g, respecto al resto de los grupos. Pero hubo alimentos que estuvieron fuera del intervalo de confianza de cada grupo en los demás nutrimentos, lo cual pudo deberse al uso de ingredientes tradicionales o técnicas culinarias. Un ejemplo es la carne sometida a un procedimiento de salazón para su conservación, que se conoce como cecina.