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The integration of biomolecular logic principles with electronic transducers allows designing novel digital biosensors with direct electrical output, logically triggered drug-release, and closed-loop sense/act/treat systems. This opens new opportunities for advanced personalized medicine in the context of theranostics. In the present work, we will discuss selected examples of recent developments in the field of interfacing enzyme logic gates with electrodes and semiconductor field-effect devices. Special attention is given to an enzyme OR/Reset logic gate based on a capacitive field-effect electrolyte-insulator-semiconductor sensor modified with a multi-enzyme membrane. Further examples are a digital adrenaline biosensor based on an AND logic gate with binary YES/NO output and an integrated closed-loop sense/act/treat system comprising an amperometric glucose sensor, a hydrogel actuator, and an insulin (drug) sensor.
The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.