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We present an approach in the framework of abstract interpretation to analyze list-manipulating programs by combining shape and numerical abstractions. The analysis automatically divides a list into non-overlapping list segments according to the reachability property of pointer variables to list nodes. The list nodes in each segment are abstracted by a bit-vector wherein each bit corresponds to a pointer variable and indicates whether the nodes can be reached by that pointer variable. Moreover, for each bit-vector, we introduce an auxiliary integer variable, namely a counter variable, to record the number of nodes in the segment abstracted by that bit-vector. On this basis, we leverage the power of numerical abstractions to discover numerical relations among counter variables, so as to infer relational length properties among list segments. Furthermore, we show how our approach works for circular lists. Our approach stands out in its ability to find intricate properties that involve both shape and numerical information, which are important for checking program properties such as memory safety. A prototype is implemented and preliminary experimental results are encouraging. [ABSTRACT FROM AUTHOR]

• In situ large-scale 3D visualization of membrane fouling by LSFM. • An inner concentrated DEX layer was observed in hydrophilic membrane. • Foulant distribution and penetration shown correlations with membrane fouling. Membrane fouling restricts the wide applications of membrane technology and therefore, it is essential to develop novel analytical techniques to characterize membrane fouling and to further understand the mechanism behind it. In this work, we demonstrate a capability of high-resolution large-scale 3D visualization and quantification of the foulants on/in membranes during fouling process based on light sheet fluorescence microscopy as a noninvasive reproducible optical approach. The adsorption processes of dextran (DEX) on/in two polyvinylidene fluoride membranes with similar pore structure but distinct surface hydrophilicity were clearly observed. For a hydrophilic polyvinylidene fluoride (PVDF) membrane, the diffusion and adsorption of the DEX in membrane matrix were much slower compared to that for a hydrophobic membrane. A concentrated foulant layer was observed in the superficial potion of the hydrophilic membrane matrix while the foulants were observed quickly penetrating across the overall hydrophobic PVDF membrane during a short adsorption process. Both the inner concentrated fouling layer (in membrane superficial portion) and the foulant penetration (in membrane asymmetric structure) presented correlations with membrane fouling irreversibility, which could elucidate the microscopic events of hydrophilic membrane in resisting fouling. In addition, the imaging results could be correlated with the XDLVO analysis, suggesting how the membrane-foulant and foulant-foulant interfacial interactions resulted in a time-dependent membrane fouling process. This work provides a fast, highly-sensitive and noninvasive imaging platform for in situ characterization of membrane fouling evolution and should be useful for a wide range of membrane-based process explorations. Image, graphical abstract [ABSTRACT FROM AUTHOR]