RESUMO
We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.
RESUMO
Gene networks can often be interpreted as computational circuits. This article investigates the computational properties of gene regulatory networks defined in terms of the speed and the accuracy of the output of a gene network. It will be shown that there is no single optimal set of parameters, but instead, there is a trade-off between speed and accuracy. Using the trade-off it will also be shown how systems with various parameters can be ranked with respect to their computational efficiency. Numerical analysis suggests that the trade-off can be improved when the output gene is repressing itself, even though the accuracy or the speed of the auto-regulated system may be worse than the unregulated system.
Assuntos
Algoritmos , Redes Reguladoras de Genes/genética , Modelos Genéticos , Animais , Biologia Computacional/métodos , Regulação da Expressão Gênica , HumanosRESUMO
Starting with the numbers 1,2,7,42,429,7436, what is the next term in the sequence? This question arose in the area of mathematics called algebraic combinatorics, which deals with the precise counting of sets of objects, but it goes back to Lewis Carroll's work on determinants. The resolution of the problem was only achieved at the end of the last century, and with two completely different approaches: the first involved extensive verification by computer algebra and a huge posse of referees, while the second relied on an unexpected connection with the theory of 'square ice' in statistical physics. This paper, aimed at a general scientific audience, explains the background to this problem and how subsequent developments are leading to a fruitful interplay between algebraic combinatorics, mathematical physics and number theory.