Исследование методов оценивания стабильности взаимного поведения стохастических процессов

The sensitivity of some methods for estimating the mutual dynamic stability of stochastic processes with given correlative properties was studied in relation to the phase detuning between the processes. Two classes of normally distributed random stochastic processes are considered: the processes with short-term correlation and the processes with a long-term correlation, characterized by the specified Hurst coefficients.На примере тестовых процессов с заданными корреляционными свойствами исследована чувствительность методов оценивания стабильности взаимной динамики стохастических процессов к фазовой расстройке между ними. Рассмотрены два класса нормально распределенных стохастических случайных процессов: процессы с кратковременной зависимостью и процессы с долговременной зависимостью, характеризующиеся заданным показателем Херста

Исследование методов оценивания стабильности взаимного поведения стохастических процессов

The sensitivity of some methods for estimating the mutual dynamic stability of stochastic processes with given correlative properties was studied in relation to the phase detuning between the processes. Two classes of normally distributed random stochastic processes are considered: the processes with short-term correlation and the processes with a long-term correlation, characterized by the specified Hurst coefficients.На примере тестовых процессов с заданными корреляционными свойствами исследована чувствительность методов оценивания стабильности взаимной динамики стохастических процессов к фазовой расстройке между ними. Рассмотрены два класса нормально распределенных стохастических случайных процессов: процессы с кратковременной зависимостью и процессы с долговременной зависимостью, характеризующиеся заданным показателем Херста

Improved online event detection and differentiation by a simple gradient-based nonlinear transformation: Implications for the biomedical signal and image analysis

Despite recent success in advanced signal analysis technologies, simple and universal methods are still of interest in a variety of applications. Wearable devices including biomedical monitoring and diagnostic systems suitable for long-term operation are prominent examples, where simple online signal analysis and early event detection algorithms are required. Here we suggest a simple and universal approach to the online detection of events represented by abrupt bursts in long-term observational data series. We show that simple gradient-based transformations obtained as a product of the signal and its derivative lead to the improved accuracy of the online detection of any significant bursts in the observational data series irrespective of their particular shapes. We provide explicit analytical expressions characterizing the performance of the suggested approach in comparison with the conventional solutions optimized for particular theoretical scenarios and widely utilized in various signal analysis applications. Moreover, we estimate the accuracy of the gradient-based approach in the exact positioning of single ECG cycles, where it outperforms the conventional Pan-Tompkins algorithm in its original formulation, while exhibiting comparable detection effectiveness. Finally, we show that our approach is also applicable to the comparative analysis of lanes in electrophoretic gel images widely used in life sciences and molecular diagnostics like restriction fragment length polymorphism (RFLP) and variable number tandem repeats (VNTR) methods. A simple software tool for the semi-automated electrophoretic gel image analysis based on the proposed gradient based methodology is freely available online at https://bitbucket.org/rogex/sds-page-image-analyzer/downloads/

Investigation of Some Methods for Estimating the Mutual Dynamic Stability of Stochastic Processes

The sensitivity of some methods for estimating the mutual dynamic stability of stochastic processes with given correlative properties was studied in relation to the phase detuning between the processes. Two classes of normally distributed random stochastic processes are considered: the processes with short-term correlation and the processes with a long-term correlation, characterized by the specified Hurst coefficients