Recent zbMATH articles in MSC 06E30https://www.zbmath.org/atom/cc/06E302022-05-16T20:40:13.078697ZWerkzeugBoolean function metrics can assist modelers to check and choose logical ruleshttps://www.zbmath.org/1483.920712022-05-16T20:40:13.078697Z"Zobolas, John"https://www.zbmath.org/authors/?q=ai:zobolas.john"Monteiro, Pedro T."https://www.zbmath.org/authors/?q=ai:monteiro.pedro-t"Kuiper, Martin"https://www.zbmath.org/authors/?q=ai:kuiper.martin"Flobak, Åsmund"https://www.zbmath.org/authors/?q=ai:flobak.asmundSummary: Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and interpretation of those systems. Defining rules that determine how the output activity of biological entities is regulated by their respective inputs has proven to be challenging. Partly this is because of the inherent noise in data that allows multiple model parameterizations to fit the experimental observations, but some of it is also due to the fact that models become increasingly larger, making the use of automated tools to assemble the underlying rules indispensable. We present several Boolean function metrics that provide modelers with the appropriate framework to analyze the impact of a particular model parameterization. We demonstrate the link between a semantic characterization of a Boolean function and its consistency with the model's underlying regulatory structure. We further define the properties that outline such consistency and show that several of the Boolean functions under study violate them, questioning their biological plausibility and subsequent use. We also illustrate that regulatory functions can have major differences with regard to their asymptotic output behavior, with some of them being biased towards specific Boolean outcomes when others are dependent on the ratio between activating and inhibitory regulators. Application results show that in a specific signaling cancer network, the function bias can be used to guide the choice of logical operators for a model that matches data observations. Moreover, graph analysis indicates that commonly used Boolean functions become more biased with increasing numbers of regulators, supporting the idea that rule specification can effectively determine regulatory outcome despite the complex dynamics of biological networks.The number of almost perfect nonlinear functions grows exponentiallyhttps://www.zbmath.org/1483.940812022-05-16T20:40:13.078697Z"Kaspers, Christian"https://www.zbmath.org/authors/?q=ai:kaspers.christian"Zhou, Yue"https://www.zbmath.org/authors/?q=ai:zhou.yue.1|zhou.yueSummary: Almost perfect nonlinear (APN) functions play an important role in the design of block ciphers as they offer the strongest resistance against differential cryptanalysis. Despite more than 25 years of research, only a limited number of APN functions are known. In this paper, we show that a recent construction by \textit{H. Taniguchi} [Des. Codes Cryptography 87, No. 9, 1973--1983 (2019; Zbl 1419.11138)] provides at least \(\frac{\varphi(m)}{2}\left\lceil\frac{2^m+1}{3m}\right\rceil\) inequivalent APN functions on the finite field with \({2^{2m}}\) elements, where \(\varphi\) denotes Euler's totient function. This is a great improvement of previous results: for even \(m\), the best known lower bound has been \(\frac{\varphi(m)}{2}\left(\lfloor\frac{m}{4}\rfloor+1\right)\); for odd \(m\), there has been no such lower bound at all. Moreover, we determine the automorphism group of Taniguchi's APN functions.