Faced with the increasing need for correctly designed hybrid and cyber-physical systems today, the problem of including provision for continuously varying behaviour as well as the usual discrete changes of state is considered in the context of Event-B. An extension of Event-B called Hybrid Event-B is presented, that accommodates continuous behaviours (called pliant events) in between familiar discrete transitions (called mode events in this context). The continuous state change can be specified by a combination of indirect specification via ordinary differential equations, or direct specification via assignment of variables to values that depend on time, or indirect specification by demanding that behaviour obeys a time dependent predicate. The syntactic elements of the extension are discussed, and the semantics is described in terms of the properties of time dependent valuations of variables. Refinement is examined in detail, with reference to the notion of refinement inherited from discrete Event-B. A full suite of proof obligations is presented, covering all aspects of the new framework. A selection of examples and case studies is presented. A particular challenge -bearing in mind the desirability of conforming to existing intuitions about discrete Event-B, and the impact on tool support (as embodied in tools for discrete Event-B like Rodin)-is to design the whole framework so as to disturb as little as possible the existing structures for handling discrete Event-B.

Microcapsules are a key class of microscale materials with applications in areas ranging from personal care to biomedicine, and with increasing potential to act as extracellular matrix (ECM) models of hollow organs or tissues. Such capsules are conventionally generated from non-ECM materials including synthetic polymers. Here, we fabricated robust microcapsules with controllable shell thickness from physically-and enzymatically-crosslinked gelatin and achieved a core-shell architecture by exploiting a liquid-liquid phase separated aqueous dispersed phase system in a one-step microfluidic process. Microfluidic mechanical testing revealed that the mechanical robustness of thicker-shell capsules could be controlled through modulation of the shell thickness. Furthermore, the microcapsules demonstrated environmentally-responsive deformation, including buckling by osmosis and external mechanical forces. Finally, a sequential release of cargo species was obtained through the degradation of the capsules. Stability measurements showed the capsules were stable at 37 • C for more than two weeks. These smart capsules are promising models of hollow biostructures, microscale drug carriers, and building blocks or compartments for active soft materials and robots.

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Liquid–liquid phase‐separated biomolecular systems are increasingly recognized as key components in the intracellular milieu where they provide spatial organization to the cytoplasm and the nucleoplasm. The widespread use of phase‐separated systems by nature has given rise to the inspiration of engineering such functional systems in the laboratory. In particular, reversible gelation of liquid–liquid phase‐separated systems could confer functional advantages to the generation of new soft materials. Such gelation processes of biomolecular condensates have been extensively studied due to their links with disease. However, the inverse process, the gel–sol transition, has been less explored. Here, a thermoresponsive gel–sol transition of an extracellular protein in microgel form is explored, resulting in an all‐aqueous liquid–liquid phase‐separated system with high homogeneity. During this gel–sol transition, elongated gelatin microgels are demonstrated to be converted to a spherical geometry due to interfacial tension becoming the dominant energetic contribution as elasticity diminishes. The phase‐separated system is further explored with respect to the diffusion of small particles for drug‐release scenarios. Together, this all‐aqueous system opens up a route toward size‐tunable and monodisperse synthetic biomolecular condensates and controlled liquid–liquid interfaces, offering possibilities for applications in bioengineering and biomedicine.

This report summarises the background and recent progress in the research of its co-authors. It is aimed at the construction of links between algebraic presentations of the principles of programming and the exploitation of concurrency in modern programming practice. The signature and laws of a Concurrent Kleene Algebra (CKA) largely overlap with those of a Regular Algebra, with the addition of concurrent composition and a few simple laws for it. They are re-interpreted here in application to computer programs. The inclusion relation for regular expressions is re-interpreted as a refinement ordering, which supports a stepwise contractual approach to software system design and to program debugging.The laws are supported by a hierarchy of models, applicable and adaptable to a range of different purposes and to a range of different programming languages. The algebra is presented in three tiers. The bottom tier defines traces of program execution, represented as sets of events that have occurred in a particular run of a program; the middle tier defines a program as the set of traces of all its possible behaviours. The top tier introduces additional incomputable operators, which are useful for describing the desired or undesired properties of computer program behaviour. The final sections outline directions in which further research is needed.

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The emerging applications of hydrogel materials at different length scales, in areas ranging from sustainability to health, have driven the progress in the design and manufacturing of microgels. Microgels can provide miniaturized, monodisperse, and regulatable compartments, which can be spatially separated or interconnected. These microscopic materials provide novel opportunities for generating biomimetic cell culture environments and are thus key to the advances of modern biomedical research. The evolution of the physical and chemical properties has, furthermore, highlighted the potentials of microgels in the context of materials science and bioengineering. This review describes the recent research progress in the fabrication, characterization, and applications of microgels generated from biomolecular building blocks. A key enabling technology allowing the tailoring of the properties of microgels is their synthesis through microfluidic technologies, and this paper highlights recent advances in these areas and their impact on expanding the physicochemical parameter space accessible using microgels. This review finally discusses the emerging roles that microgels play in liquid–liquid phase separation, micromechanics, biosensors, and regenerative medicine.

Micron-scale soft materials are finding a wide range of applications in bioengineering and molecular medicine, while also increasingly emerging as useful components for consumer products. The mechanical characterization of such microscale soft objects is conventionally performed with techniques such as atomic force microscopy or micropipette aspiration that measure the local properties of micron scale objects in a serial manner. To permit scalable characterization of the global mechanical properties of soft microscale objects, we developed and describe here a microfluidic platform that can be used for performing parallelized integrated measurements of the shear modulus of individual microscale particles. We demonstrate the effectiveness of this approach by characterizing the mechanical properties of multiple protein microgels in parallel, and show that the obtained values are in good agreement with conventional serial measurements. This platform allows parallelized in situ measurements of the mechanical properties of soft deformable micron-scale particles, and builds on scalable single-layer soft-photolithography fabrication, making the measurement system readily adaptable for a range of potential applications. Graphical Abstract