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The network approach towards the analysis of the dynamics of complex systems has been successfully applied in a multitude of studies in the neurosciences and has yielded fascinating insights. With this approach, a complex system is considered to be composed of different constituents which interact with each other. Interaction structures can be compactly represented in interaction networks. In this contribution, we present a brief overview about how interaction networks are derived from multivariate time series, about basic network characteristics, and about challenges associated with this analysis approach.
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.
Light-addressable potentiometric sensors (LAPS) are semiconductor-based potentiometric sensors, with the advantage to detect the concentration of a chemical species in a liquid solution above the sensor surface in a spatially resolved manner. The addressing is achieved by a modulated and focused light source illuminating the semiconductor and generating a concentration-depending photocurrent. This work introduces a LAPS set-up that is able to monitor the electrical impedance in addition to the photocurrent. The impedance spectra of a LAPS structure, with and without illumination, as well as the frequency behaviour of the LAPS measurement are investigated. The measurements are supported by electrical equivalent circuits to explain the impedance and the LAPS-frequency behaviour. The work investigates the influence of different parameters on the frequency behaviour of the LAPS. Furthermore, the phase shift of the photocurrent, the influence of the surface potential as well as the changes of the sensor impedance will be discussed.