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Inertial Frames of Reference01:03

Inertial Frames of Reference

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Newton’s first law is usually considered to be a statement about reference frames. It provides a method for identifying a special type of reference frame: the inertial reference frame. In principle, we can make the net force on a body zero. If its velocity relative to a given frame is constant, then that frame is said to be inertial. So, by definition, an inertial reference frame is a reference frame where Newton's first law holds valid. Newton's first law applies to objects with...
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A reference frame accelerating or decelerating relative to an inertial frame is a non-inertial frame. To help understand this, consider what taking off in an airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone all have in common. All these systems are accelerating, decelerating, or rotating relative to the Earth; hence, they all are non-inertial frames. All these systems exhibit inertial forces, which merely seem to arise from motion,...
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In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
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On comparing the reactivity of silver and lead, it is observed that the two ionic species, Ag+ (aq) and Pb2+ (aq), show a difference in their redox reactivity towards copper: the silver ion undergoes spontaneous reduction, while the lead ion does not. This relative redox activity can be easily quantified in electrochemical cells by a property called cell potential. This property is commonly known as cell voltage in electrochemistry, and it is a measure of the energy which accompanies the charge...
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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Unified Bayesian Estimator of EEG Reference at Infinity: rREST (Regularized Reference Electrode Standardization

Shiang Hu1, Dezhong Yao1, Pedro A Valdes-Sosa1,2

  • 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for NeuroInformation, University of Electronic Science and Technology of China, Chengdu, China.

Frontiers in Neuroscience
|May 22, 2018
PubMed
Summary

Resolving the electroencephalogram (EEG) reference problem, this study unifies average reference (AR) and REST methods within a Bayesian framework. The regularized REST (rREST) method demonstrated superior accuracy in estimating EEG potentials.

Keywords:
EEG referenceinverse problemregularizationrelative errorunified estimatorvolume conduction

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Area of Science:

  • Neuroscience
  • Biophysics
  • Signal Processing

Background:

  • The selection of a reference electrode in electroencephalogram (EEG) recordings remains a significant challenge, leading to inconsistencies in data analysis and interpretation.
  • Current primary methods, Average Reference (AR) and Reference Electrode Standardization Technique (REST), are often considered incompatible.
  • A unified theoretical framework is needed to reconcile these differing approaches to EEG referencing.

Purpose of the Study:

  • To propose a unified Bayesian linear inverse problem framework for estimating potentials at infinity and determining the EEG reference.
  • To develop regularized versions of AR and REST (rAR and rREST) for simultaneous denoising and reference estimation.
  • To evaluate the performance of traditional and novel EEG reference estimators using simulations and real-world EEG data.

Main Methods:

  • Formulation of EEG reference estimation as a unified Bayesian linear inverse problem solvable by maximum a posteriori estimation.
  • Development of regularized AR (rAR) and rREST methods incorporating a noise-to-signal variance ratio regularization parameter.
  • Validation using simulated EEG data with known ground truth and analysis of resting-state EEG data from 89 subjects (Cuban Human Brain Mapping Project).

Main Results:

  • The unified framework shows AR and REST as specific cases, with REST utilizing a prior based on the EEG generative model.
  • Simulations indicate rREST achieves the lowest relative error in estimating EEG potentials at infinity, outperforming AR and standard REST.
  • Realistic volume conductor models and Generalized Cross-Validation (GCV) for regularization parameter selection improve performance, with rREST consistently yielding the lowest GCV on real EEG data.

Conclusions:

  • The proposed unified Bayesian inverse problem framework offers a novel perspective for resolving the EEG reference issue.
  • Regularized REST (rREST) provides a robust and accurate method for EEG reference estimation and signal denoising.
  • This framework facilitates principled theoretical advancements and numerical evaluations for EEG reference techniques.