Abstract-We propose an approach for verifying non-linear hybrid systems using higher-order Taylor models that are a combination of bounded degree polynomials over the initial conditions and time, bloated by an interval. Taylor models are an effective means for computing rigorous bounds on the complex time trajectories of non-linear differential equations. As a result, Taylor models have been successfully used to verify properties of non-linear continuous systems. However, the handling of discrete (controller) transitions remains a challenging problem.In this paper, we provide techniques for handling the effect of discrete transitions on Taylor model flowpipe construction. We explore various solutions based on two ideas: domain contraction and range over-approximation. Instead of explicitly computing the intersection of a Taylor model with a guard set, domain contraction makes the domain of a Taylor model smaller by cutting away parts for which the intersection is empty. It is complemented by range over-approximation that translates Taylor models into commonly used representations such as template polyhedra or zonotopes, on which intersections with guard sets have been previously studied. We provide an implementation of the techniques described in the paper and evaluate the various design choices over a set of challenging benchmarks.

For any function f from R to R, one can define a corresponding function on the space of n × n (block-diagonal) real symmetric matrices by applying f to the eigenvalues of the spectral decomposition. We show that this matrix-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as (ρ-order) semismoothness. Our analysis uses results from nonsmooth analysis as well as perturbation theory for the spectral decomposition of symmetric matrices. We also apply our results to the semidefinite complementarity problem, addressing some basic issues in the analysis of smoothing/semismooth Newton methods for solving this problem.

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The oxygen evolution reaction (OER) plays a paramount role in a variety of electrochemical energy conversion devices, and the exploration of highly active, stable, and low-cost electrocatalysts is one of the most important topics in this field. The exfoliated black phosphorus (EBP) nanosheet with a two-dimensional (2D) layered structure has high carrier mobility but is limited by excessive oxygen-containing intermediate absorption and fast deterioration in air. We here report the fabrication of nanohybrids of amorphous CoFeB nanosheets on EBP nanosheets (EBP/CoFeB). The 2D/2D heterostructure, thanks to the electronic interactions and oxygen affinity difference between EBP and CoFeB nanosheets, is capable of balancing the oxygen-containing intermediate absorption to an optimal status for facilitating the OER process. While the crystalline EBP contributes to the improved conductivity, the amorphous coating protects EBP and thus ensures the catalytic stability. The EBP/CoFeB electrocatalyst shows excellent OER performance with an ultralow overpotential of 227 mV at 10 mA cm–2 with an ultrasmall Tafel slope of 36.7 mV dec–1 with excellent stability. This study may inspire more researches to develop heterostructured nanohybrid electrocatalysts for a diversity of electrochemical reactions.

Cell wall recalcitrance is the major challenge to improving saccharification efficiency in converting lignocellulose into biofuels. However, information regarding the transcriptional regulation of secondary cell wall biogenesis remains poor in switchgrass (Panicum virgatum), which has been selected as a biofuel crop in the United States. In this study, we present a combination of computational and experimental approaches to develop gene regulatory networks for lignin formation in switchgrass. To screen transcription factors (TFs) involved in lignin biosynthesis, we developed a modified method to perform co-expression network analysis using 14 lignin biosynthesis genes as bait (target) genes. The switchgrass lignin co-expression network was further extended by adding 14 TFs identified in this study, and seven TFs identified in previous studies, as bait genes. Six TFs (PvMYB58/63, PvMYB42/85, PvMYB4, PvWRKY12, PvSND2 and PvSWN2) were targeted to generate overexpressing and/or down-regulated transgenic switchgrass lines. The alteration of lignin content, cell wall composition and/or plant growth in the transgenic plants supported the role of the TFs in controlling secondary wall formation. RNA-seq analysis of four of the transgenic switchgrass lines revealed downstream target genes of the secondary wall-related TFs and crosstalk with other biological pathways. In vitro transactivation assays further confirmed the regulation of specific lignin pathway genes by four of the TFs. Our meta-analysis provides a hierarchical network of TFs and their potential target genes for future manipulation of secondary cell wall formation for lignin modification in switchgrass.