Generalized vector valued almost periodic and ergodic distributions

For \Cal A\subset L^1_{loc}(\Bbb J,X) let \Cal M\Cal A consist of all $f\in L^1_{loc}$ with M_h f (\cdot):=\frac {1}{h}\int_{0}^{h}f(\cdot +s)\,ds \in \Cal A for all $h>0$. Here $X$ is a Banach space, $\Bbb J= (\alpha ,\infty), [\alpha ,\infty)$ or $\Bbb R$. Usually \Cal A\subset\Cal M\Cal A\subset \Cal M^2\Cal A\subset .... The map \Cal A \to \Cal {D}'_{\Cal A} is iteration complete, that is \Cal {D}'_{\Cal {D}'_{\Cal A}}= \Cal {D}'_{\Cal A}. Under suitable assumptions \widetilde {\Cal M}^n \Cal {A}= \Cal A + \{T^{(n)} : T \in \Cal A\}, and similarly for \Cal {M}^n \Cal A. Almost periodic $X$-valued distributions \h'_{\A} with \A = almost periodic (ap) functions are characterized in several ways. Various generalizations of the Bohl-Bohr-Kadets theorem on the almost periodicity of the indefinite integral of an ap or almost automorphic function are obtained. On \Cal {D}'_{\Cal E} , \Cal E the class of ergodic functions, a mean can be constructed which gives Fourier series. Special cases of \Cal A are the Bohr ap, Stepanoff ap, almost automorphic, asymptotically ap, Eberlein weakly ap, pseudo ap and (totally) ergodic functions (\T)\E. Then always \Cal {M}^n \Cal A is strictly contained in \Cal {M}^{n+1} \Cal A. The relations between \m^n \E, \m^n\T\E and subclasses are discussed. For many of the above results a new $(\Delta)$-condition is needed, we show that it holds for most of the \A needed in applications. Also, we obtain new tauberian theorems for $f\in L^1_{loc}(\Bbb J,X)$ to belong to a class \A which are decisive in describing the asymptotic behavior of unbounded solutions of many abstract differential-integral equations. This generalizes various recent resultsComment: 69 page

Asymmetries in Human Tolerance of Uncertainty in Interaction with Alarm Systems: Effects of Risk Perception or Evidence for a General Commission Bias?

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Providing access towards raw data is often considered to be a good solution for improving human decision making in interaction with imperfect automated decision support such as alarm systems. However, there is some evidence that such cross-checking measures are used in an asymmetric manner with respect to the amount of uncertainty involved in the decision. Namely, people seem to accept low amounts of uncertainty when complying with an alarm cue, but not when contradicting it. The current study investigates the question whether this phenomenon is limited to alarm systems and a high risk environment. Within a multi-task PC simulation participants performed a low risk monitoring task which was supported by a system neutrally framed as “assistant system”. In one group the cues emitted by the system were 90% correct, in the other 10% were correct, thus causing a 10% uncertainty about the real state in both conditions. Results show a strong asymmetry as participants in the latter condition spent a high amount of effort in reducing their uncertainty, while participants in the former condition did not. Furthermore participants’ behavior almost exactly replicates the asymmetric cross-checking pattern found in a former study which employed a comparatively high risk monitoring task supported by an “alarm system”. This supports the hypothesis that the observed commission bias represents a general phenomenon in the context of automated decision support, irrespective of the risk attributed to the environment and irrespective of whether the system represents an alarm system or not

Waveform sampling using an adiabatically driven electron ratchet in a two-dimensional electron system

We utilize a time-periodic ratchet-like potential modulation imposed onto a two-dimensional electron system inside a GaAs/Al$_x$Ga$_{1-x}$As heterostructure to evoke a net dc pumping current. The modulation is induced by two sets of interdigitated gates, interlacing off center, which can be independently addressed. When the transducers are driven by two identical but phase-shifted ac signals, a lateral dc pumping current $I(\phi)$ results, which strongly depends on both, the phase shift $\phi$ and the waveform $V(t)$ of the imposed gate voltages. We find that for different periodic signals, the phase dependence $I(\phi)$ closely resembles $V(t)$. A simple linear model of adiabatic pumping in two-dimensional electron systems is presented, which reproduces well our experimental findings.Comment: 3 figure