The problem is considered of the optimal choice of moving sensor trajectories from the viewpoint of distributed-parameter system identification accuracy. The determinant of the information matrix of parameter estimates is taken as a measure of identification accuracy. Necessary and sufficient conditions for the trajectories to be optimal are derived. It is shown that the optimum trajectories can be found by solving a sequence of optimal sensor allocation problems. A number of examples illustrates the proposed approach.

On the basis of a semi-realistic SIR microsimulation for Germany and Poland, we show that the R ₀ parameter interval for which the COVID-19 epidemic stays overcritical but below the capacity limit of the health care system to reach herd immunity is so narrow that a successful implementation of this strategy is likely to fail, which is in contrast to results obtained from classical differential equation models. Our microsimulation is based on official census data and involves household composition and age distribution as the main population structure variables. Outside household contacts are characterised by an out-reproduction number R ^* which is the only free parameter of the model. For a subcritical domain we compute the time till extinction and prevalence as a function of the initial number of infected individuals and R ^* . For the Polish city of Wrocław we also discuss the combined impact of testing coverage and contact reduction. For both countries we estimate R ^* for disease progression until 20th of March 2020.

The problem of optimal design of experiments for identification of distributed systems described by a linear, parabolic partial differential equation is considered. Conditions of an experiment, which consists of the spectral density of a stochastic input signal and a probability measure corresponding to positions of sensors, are chosen such as to maximize the accuracy of a finite number of the system's eigenvalue estimates. Conditions for optimality of the experiment design are derived. In particular, it is shown that the optimal input consists of a finite number sinusoids and optimal positions of the sensors can be found analytically in some eases, Application of the results is illustrated in case of a vibrating system.

This paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions. A nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box. As such, it will be coined as the Vertical Box Control Chart (V-Box Chart). Its implementation requires merely to count the number of data points which fall into the box attached to the last available observation. No a priori knowledge of data distributions is required and proper tuning of the box size provides a quick detection technique. This is supported by establishing statistical properties of the method which explain the role of the tuning parameters used in the V-Box Chart. These theoretical results are verified by simulation studies which indicate that the V-Box Chart may provide quick detection with zero delay for jumps of moderate sizes. Its averaged run length to detection is more favorable than the one for the classical EWMA method. By comparison with the classical Shewhart chart, which was optimized for normal errors, our method provides comparable or better performance.