Renormalization

This chapter describes in detail the general concept of renormalization. It starts with a discussion of the regularization of Feynman diagrams. After that, the subtraction procedure is explained in detail, followed by an introduction to the notion of a superficial degree of divergence of the diagram. On this basis, the models of quantum field theory are classified as renormalizable or non-renormalizable theories. The main arbitrariness of the subtraction procedure is fixed by imposing renormalization conditions. Special sections of this chapter are devoted to renormalization in dimensional regularization and renormalization group equations.

Power-line Interference Removal from High Sampled ECG Signals Using Modified Version of the Subtraction Procedure

The acquired ECG signals are often contaminated by residual Power-line Interference (PLI). A lot of methods, algorithms and techniques for PLI reduction have been published over the last few decades. The so called subtraction procedure is known to eliminate almost totally the interference without affecting the signal spectrum. The goal of our research was to develop a heuristic version of the procedure intended for ECG signals with high Sampling Rate (SR) up to 128 kHz. The PLI is extracted from the corrupted signal by technique similar to second order band-pass filter but with practically zero phase error. The sample number as well as the left and right parts outside the samples belonging to a current sine wave, which is extracted from the contaminated signal, are counted and measured. They are used to compensate the error arising with the shift between the moving averaged free of PLI signal samples and their real position along the linear segments (usually PQ and TP intervals having frequency band near to zero). The here calculated PLI components are appropriately interpolated to ‘clean’ the dynamically changed in amplitude and position contaminated samples within the non-linear segments (QRS complexes and high T waves). The reported version of the subtraction procedure is tested with 5 and 128 kHz sampled ECG signals. The maximum absolute error is about 20 μV except for the ends of the recordings. Finally, an approach to PLI elimination from paced ECG signals is proposed. It includes pace pulse extraction, signal re-sampling down to 4 kHz and subtraction procedure implementation followed by adding back the removed pace pulses.

Artefacts Removal from ECG Signal: Dragonfly Optimization-based Learning Algorithm for Neural Network-enhanced Adaptive Filtering

Electrocardiogram (ECG) artefact removal is the major research topic as the pure ECG signals are an essential part of diagnosing heart-related problems. ECG signals are highly prominent to the interaction with the other signals like the Electromyography (EMG), Electroencephalography (EEG), and Electrooculography (EOG) signals and the interference mainly occurs at the time of recording. The removal of the artefacts from the ECG signal is a hectic challenge, for which, a novel algorithm is proposed in this work. The proposed method utilizes the adaptive filter termed as the (Dragonfly optimization + Levenberg Marqueret learning algorithm) DLM-based Nonlinear Autoregressive with eXogenous input (NARX) neural network for the removal of the artefacts from the ECG signals. Once the artefact signal is identified using the adaptive filter, the identified signal is subtracted from the primary signal that is composed of the ECG signal and the artefacts through an adaptive subtraction procedure. The clean signal thus obtained is used for effective diagnosis purposes, and the experimentation performed to prove the effectiveness of the proposed method proves that the proposed method obtained a maximum Signal-to-noise ratio (SNR) of 52.8789 dB, a minimum error of 0.1832, and minimum error of 0.428.

Power-Line Interference Removal from High Sampled ECG Signals Using Modified Version of the Subtraction Procedure

BackgroundThe acquired ECG signals are often contaminated by residual Power-Line Interference (PLI). A lot of methods, algorithms and techniques for PLI reduction have been published over the last few decades. The so called subtraction procedure is known to eliminate almost totally the interference without affecting the signal spectrum. The goal of our research was to develop a heuristic version of the procedure intended for ECG signals with high SR up to 128 kHz.ResultsThe PLI is extracted from the corrupted signal by technique similar to second order band-pass filter but with practically zero phase error. The sample number as well as the left and right parts outside the samples belonging to a current sine wave are counted and measured. They are used to compensate the error arising with the shift between the moving averaged free of PLI signal samples and their real position along the linear segments (usually PQ and TP intervals having frequency band near to zero). The here calculated PLI components are appropriately interpolated to ‘clean’ the dynamically changed in amplitude and position contaminated samples within the non-linear segments (QRS complexes and high T waves).ConclusionsThe reported version of the subtraction procedure is tested with 5 and 128 kHz sampled ECG signals. The maximum absolute error is about 20 μV except for the edges of the recordings. Finally, an approach to PLI elimination from paced ECG signals is proposed. It includes pace pulse elimination, signal re-sampling down to 4 kHz and subtraction procedure implementation followed by adding back the pace pulses.

IMPROVEMENT OF GAMMA-RAY SUBTRACTION PROCEDURE FOR A CURRENT-MODE NEUTRON DETECTOR WITH A PAIR OF 6Li- AND 7Li-GLASS SCINTILLATORS

A current-mode neutron detector with a pair of 6Li- and 7Li-glass scintillators has been developed to measure high-flux neutrons in a boron neutron capture therapy field. Neutrons are basically measured by subtracting gamma-ray component using current outputs from the 7Li-glass scintillator. In the present study, the difference in the gamma-ray sensitivity between the 6Li- and 7Li-glass scintillators and the neutron sensitivity for the 7Li-glass scintillator due to the 6Li contamination were also considered to improve the gamma-ray subtraction precision. The gamma-ray subtraction procedure was experimentally investigated in thermal neutron fields with 252Cf and 241Am-Be neutron sources, which have different gamma-ray intensities per unit neutron fluence. A linear relation between neutron fluence and current output was obtained for the neutron detector in the two types of thermal neutron fields with different gamma-ray intensities. It was found that the gamma-ray subtraction procedure is useful for current-mode neutron detectors.

Recent applications of the subtracted SRPA approximation

The Second Random Phase Approximation (SRPA) is a natural extension of the Random Phase Approximation obtained by introducing more general excitation operators where two particle-two hole configurations, in addition to the one particle-one hole ones, are considered. Only in the last years, large-scale SRPA calculations, without usually employed approximations have been performed. The SRPA model corrected by a subtraction procedure designed to cure double counting issues and the related instabilities has been recently implemented and applied in the study of different physical cases. We report here on some of the most recent results obtained by using this model. In particular, results on the dipole strength 48Ca and on a systematic study of the isoscalar giant quadrupole resonance in spherical nuclei will be shown and discussed.

A Method for Reducing the Effects of Motion Contamination in Arterial Spin Labeling Magnetic Resonance Imaging

Arterial spin labeling (ASL) is a noninvasive method to measure cerebral blood flow (CBF). Arterial spin labeling is susceptible to artifact generated by head motion; this artifact is propagated through the subtraction procedure required to calculate CBF. We introduce a novel strategy for mitigating this artifact based on weighting tag/control volumes according to a noise estimate. We evaluated this strategy (DVARS weighting) in application to both pulsed ASL (PASL) and pseudo-continuous ASL (pCASL) in a cohort of normal adults (N = 57). Application of DVARS weighting significantly improved test-retest repeatability as assessed by the intra-class correlation coefficient. Before the application of DVARS weighting, mean gray matter intra-class correlation (ICC) between subsequent ASL runs was 0.48 and 0.51 in PASL and pCASL, respectively. With weighting, ICC was significantly improved to 0.63 and 0.58.