Effect of optimal filtering parameters for autoregressive model AR(p) on motor unit action potential signal

Error is one element of the autoregressive (AR) model, which is supposed to be white noise. Correspondingly assumption that white noise error is a normal distribution in electromyography (EMG) estimation is one of the common causes for error maximization. This paper presents the effect of a suitable choice of filtering function based on the non-invasive analysis properties of motor unit action potential signal, extracted from a non-invasive method-the high spatial resolution (HSR) electromyography (EMG), recorded during low-level isometric muscle contractions. The final prediction error procedure is used to find the number of parameters in the model. The error signal parameter, the simulated deviation from the actual signals, is suitably filtered to obtain optimally appropriate estimates of the parameters of the automatic regression model. It is filtered to acquire optimally appropriate estimates of the parameters of the automatic regression model. Then appropriate estimates of spectral power shapes are obtained with a high degree of efficiency compared with the robust method under investigation. Extensive experiment results for the proposed technique have shown that it provides a robust and reliable calculation of model parameters. Moreover, estimates of power spectral profiles were evaluated efficiently.

Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.

Over-whitening or Pre-whitening in Hydro-climatological Trend Analysis?

To meet the basic assumption of classical Mann-Kendall (MK) trend analysis, which requires serially independent time series, a pre-whitening (PW) procedure is proposed to alleviate the serial correlation structure of a given hydro-meteorological time series records for application. The procedure is simply to take the lagged differences in a given time series in the hope that the new time series will have an independent serial correlation coefficient. The whole idea was originally based on the first-order autoregressive AR (1) process, but such a procedure has been documented to damage the trend component in the original time series. On the other hand, the over-whitening procedure (OW) proposes a white noise process superposition of the same length with zero mean and some standard deviation on the original time series to convert it into serially independent series without any damage to the trend component. The stationary white noise addition does not have any trend components. For trend identification, annual average temperature records in New Jersey and Istanbul are presented to show the difference between PW and OW procedures. It turned out that the OW procedure was superior to the PW procedure, which did not cause a loss in the original trend component.

Peramalan Indeks Saham LQ45 pada Masa Pandemi COVID-19 Menggunakan Analisis Intervensi

Analisis intervensi merupakan metode pemodelan deret waktu yang dipengaruhi oleh suatu peristiwa yang menyebabkan data deret waktu mengalami fluktuatif. Metode analisis intervensi memiliki tujuan untuk mengukur besar dan lamanya efek dari suatu intervensi pada data deret waktu. Terdapat dua jenis variabel analisis intervensi, yaitu fungsi step dan fungsi pulse. Tujuan penelitian ini untuk memodelkan dan meramalkan model intervensi fungsi step pada indeks saham LQ45 dengan waktu intervensi yang diketahui. Deret waktu LQ45 dipengaruhi oleh suatu intervensi, yaitu pandemi COVID-19. Prosedur dalam melakukan metode analisis intervensi diawali dengan mengelompokkan data menjadi dua kelompok, yaitu data sebelum intervensi dan data saat intervensi sampai data terakhir. Data sebelum intervensi digunakan untuk pemodelan ARIMA. Model ARIMA yang didapatkan dari data sebelum terjadinya intervensi digunakan sebagai informasi untuk melakukan identifikasi orde intervensi. Selanjutnya dilakukan estimasi parameter dan pemeriksaan uji asumsi white noise serta uji asumsi berdistribusi normal. Model intervensi yang telah memenuhi kedua asumsi tersebut dapat digunakan untuk peramalan. Peramalan dari indeks saham LQ45 menghasilkan nilai indeks saham LQ45 yang cenderung konstan dan berkisar pada level indeks saham sebesar 883 – 884. Hasil peramalan indeks saham LQ45 sudah sangat baik dengan nilai galat sebesar 7%.

On the Bogolyubov endomorphisms of the renormalized square of white noise algebra

We introduce the quadratic analogue of the Bogolyubov endomorphisms of the canonical commutation relations (CCR) associated with the re-normalized square of white noise algebra (RSWN-algebra). We focus on the structure of a subclass of these endomorphisms: each of them is uniquely determined by a quadruple [Formula: see text], where [Formula: see text] are linear transformations from a test-function space [Formula: see text] into itself, while [Formula: see text] is anti-linear on [Formula: see text] and [Formula: see text] is real. Precisely, we prove that [Formula: see text] and [Formula: see text] are uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text], into itself. Under some additional analytic conditions on [Formula: see text] and [Formula: see text], we discover that we have only two equivalent classes of Bogolyubov endomorphisms, one of them corresponds to the case [Formula: see text] and the other corresponds to the case [Formula: see text]. Finally, we close the paper by building some examples in one and multi-dimensional cases.