Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrative and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper.

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The oxygen reduction reaction (ORR) is of significant importance in the development of fuel cells. Now, cobalt-nitrogen-doped chiral carbonaceous nanotubes (l/d-CCNTs-Co) are presented as efficient electrocatalysts for ORR. The chiral template, N-stearyl-l/d-glutamic acid, induces the self-assembly of well-arranged polypyrrole and the formation of ordered graphene carbon with helical structures at the molecular level after the pyrolysis process. Co was subsequently introduced through the post-synthesis method. The obtained l/d-CCNTs-Co exhibits superior ORR performance, including long-term stability and better methanol tolerance compared to achiral Co-doped carbon materials and commercial Pt/C. DFT calculations demonstrate that the charges on the twisted surface of l/d-CCNTs are widely separated; as a result the Co atoms are more exposed on the chiral CCNTs. This work gives us a new understanding of the effects of helical structures in electrocatalysis.

A high cycling stability of dual‐ion batteries is greatly challenging, as the size required for inserting anions matches only insufficiently with the interlayer spacing of graphite which is often used as positive electrode. Herein, an activated expanded graphite (AEG) electrode is successfully prepared via KOH treatment. The loose structure of AEG accommodates the volume expansion caused by anion intercalation, and the large specific surface area facilitates the immersion of electrolyte ions to afford more energy density. Thus, the cycling stability is largely enhanced without losing capacity. Matching with activated carbon as negative electrode and an ionic liquid electrolyte, the assembled dual‐ion battery achieves an energy density of 43 Wh kg−1 at the power density of 756 W kg−1 within a working window of 0–3.6 V. Specifically, the energy density retains 83 % after 50 cycles. Such effective and low‐cost electrode optimization opens up a new route toward full enhancement on the cycling performance of positive electrodes for dual‐ion batteries.