Time-series data dynamic density clustering

In many clustering problems, the whole data is not always static. Over time, part of it is likely to be changed, such as updated, erased, etc. Suffer this effect, the timeline can be divided into multiple time segments. And, the data at each time slice is static. Then, the data along the timeline shows a series of dynamic intermediate states. The union set of data from all time slices is called the time-series data. Obviously, the traditional clustering process does not apply directly to the time-series data. Meanwhile, repeating the clustering process at every time slices costs tremendous. In this paper, we analyze the transition rules of the data set and cluster structure when the time slice shifts to the next. We find there is a distinct correlation of data set and succession of cluster structure between two adjacent ones, which means we can use it to reduce the cost of the whole clustering process. Inspired by it, we propose a dynamic density clustering method (DDC) for time-series data. In the simulations, we choose 6 representative problems to construct the time-series data for testing DDC. The results show DDC can get high accuracy results for all 6 problems while reducing the overall cost markedly.

A rate-dependent KP modeling and direct compensation control technique for hysteresis in piezo-nanopositioning stages

This paper first presents a rate-dependent Krasnosel’skii-Pokrovskii (RKP) model to capture the hysteresis of piezo-nanopositioning stages. The dynamic density function of the RKP model is obtained via neural network with frequency behavior input signal. Under the persistently exciting condition, the convergence of the neural network with Krasnosel’skii-Pokrovskii (KP) operators is proved rigorously. In order to address the hysteresis issue, a direct compensation control (DCC) approach with the KP compensation operator is proposed, where its dynamic density function is same as that of the RKP model. Some experiments with different reference signals are conducted to verify the effectiveness of the proposed modeling and DCC method on piezo-nanopositioning stages.

Simulation of Spatial Spread of the COVID-19 Pandemic on the Basis of the Kinetic-Advection Model

A new two-parameter kinetic equation model is proposed to describe the spatial spread of the virus in the current pandemic COVID-19. The migration of infection carriers from certain foci inherent in some countries is considered. The one-dimensional model is applied to three countries: Russia, Italy, and Chile. Both their geographical location and their particular shape stretching in the direction from the centers of infection (Moscow, Lombardy, and Santiago, respectively) make it possible to use such an approximation. The dynamic density of the infected is studied. Two parameters of the model are derived from known data. The first is the value of the average spreading rate associated with the transfer of infected persons in transport vehicles. The second is the frequency of the decrease in numbers of the infected as they move around the country, associated with the arrival of passengers at their destination. An analytical solution is obtained. Simple numerical methods are also used to perform a series of calculations. Calculations us to make some predictions, for example, about the time of recovery in Russia, if the beginning of recovery in Moscow is known.