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Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as cost functions using STL's robust semantics, transforming the synthesis problem into an optimization problem. Unfortunately, these cost functions are non-smooth and non-convex, and exact solutions using mixed-integer programming do not scale well. Recent work has focused on using smooth approximations of robustness, which enable faster gradient-based methods to find local maxima, at the expense of soundness and/or completeness. We propose a novel robustness approximation that is smooth everywhere, sound, and asymptotically complete. Our approach combines the benefits of existing approximations, while enabling an explicit tradeoff between conservativeness and completeness.

Nanostructures fabricated with DNA are emerging as a practical approach for applications ranging from advanced manufacturing to therapeutics. To support the strides made in improving accessibility and facilitating commercialization of DNA nanostructure applications, we identify the need for a rapid characterization approach that aids nanostructure production. In our work, we introduce a low-fidelity characterization approach that provides an interdependent assessment of DNA origami formation, concentration and morphology using capacitance sensing. Change in charge is one of the transduction methods to determine capacitive loading on a substrate. It is known that cations in the solution stabilize DNA origami nanostructures. So, we hypothesized that the presence of cations and nanostructures in a buffer solution can induce capacitance change that is distinctive of the nanostructure present. In this study we were able to detect a change in the capacitance when the nanostructure solution was deposited on our capacitance sensor, and we could distinguish between pre-annealed and annealed structures at concentrations less than 15 nM. The capacitance measurements were affected by the concentration of Mg2+ions in the solution, the staple-to-scaffold stoichiometric ratio of the nanostructure and the nanostructure morphology. Maintaining a 12.5 mM Mg2+concentration in the nanostructure buffer, we discover a linear relationship between the relative capacitance change and the nanostructure concentration from 5 nM to 20 nM, which we call the characteristic curve. We find distinct characteristic curves for our three nanostructures with distinct morphologies but similar molecular weight - a rectangular plate, a sphere and a rod. Given that we can distinguish nanostructure formation, concentration and morphology, we expect that capacitance measurement will emerge as an affordable and rapid approach for quality control for nanostructure production.

We report on the use of a lab-on-CMOS biosensor platform for quantitatively tracking the proliferation of RAW 264.7 murine Balb/c macrophages. We show that macrophage proliferation correlates linearly with an average capacitance growth factor resulting from capacitance measurements at a plurality of electrodes dispersed in a sensing area of interest. We further show a temporal model that captures the cell number evolution in the area over long periods (e.g., 30 h). The model links the cell numbers and the average capacitance growth factor to describe the observed cell proliferation.

We report on the use of a lab-on-CMOS biosensor platform for quantitatively tracking the growth of RAW 264.7 murine Balb/c macrophages. We show that macrophage growth over a wide sensing area correlates linearly with an average capacitance growth factor resulting from capacitance measurements at a plurality of electrodes dispersed in the sensing area. We further show a temporal model that captures the cell evolution in the area of interest over long periods (e.g., 30 hours). The model links the cell numbers and the average capacitance growth factor associated with the sensing area to describe the observed growth kinetics.