We report on the automatic alignment of a transmission electron microscope equipped with an orbital angular momentum sorter using a convolutional neural network. The neural network is able to control all relevant parameters of both the electron-optical setup of the microscope and the external voltage source of the sorter without input from the user. It can compensate for mechanical and optical misalignments of the sorter, in order to optimize its spectral resolution. The alignment is completed over a few frames and can be kept stable by making use of the fast fitting time of the neural network.

A reformulated implementation of single-sideband ptychography enables analysis and display of live detector data streams in 4D scanning transmission electron microscopy (STEM) using the LiberTEM open-source platform. This is combined with live first moment and further virtual STEM detector analysis. Processing of both real experimental and simulated data shows the characteristics of this method when data are processed progressively, as opposed to the usual offline processing of a complete data set. In particular, the single-sideband method is compared with other techniques such as the enhanced ptychographic engine in order to ascertain its capability for structural imaging at increased specimen thickness. Qualitatively interpretable live results are obtained also if the sample is moved, or magnification is changed during the analysis. This allows live optimization of instrument as well as specimen parameters during the analysis. The methodology is especially expected to improve contrast- and dose-efficient in situ imaging of weakly scattering specimens, where fast live feedback during the experiment is required.

The question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees’ risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.