Coherence Function in Noisy Linear System

Thomas, Cecil W.

doi:10.11648/j.ijbse.20150302.13

Cited by 9 publications

(10 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although, in principle, correlation functions in the time and frequency domains provide equivalent information, the frequency domain is more useful for identifying properties of linear systems. ,,,, Underlying mathematical issues of working in the time domain are discussed at length in ref . The frequency domain is useful because it is based on the eigenfunctions of linear systems, namely, sinusoids.…”

Section: Theorymentioning

confidence: 99%

“…Other methods may improve on classical engineering approaches, but it is unrealistic to expect them to be available, validated, and documented for some time. In fact, most recent reviews use classical methods in single input–output systems like ours. , Relevant promising approaches in two (and three) dimensions are described in refs. ,,,,, ,,,,, …”

Section: Theorymentioning

confidence: 99%

“…Specifically, the frequency response function should be estimated by Ĥ ( f ) = Ĝ italicxy ( f ) Ĝ italicxx ( f ) and the coherence function by Ĉ italicxy ( f ) = false| Ĝ italicxy ( f ) false| 2 Ĝ italicxx ( f ) Ĝ italicyy ( f ) While it may seem reasonable to estimate the frequency function using Y ( f )/ X ( f ) instead of the ratio of powers shown in eq , such estimators are known to produce serious artifacts; they are known to be so sensitive to contaminating noise that even the roundoff error of modern floating-point arithmetic can produce significant problems; see Ch. 6, particularly Section 6.14 of ref and more recent references. , These artifacts may be difficult to diagnose. For example, as observed in earlier work, ,,, the variance of the incorrect estimates can be independent of contaminating noise while the mean of the incorrect estimates can depend on the contaminating noise.…”

Section: Theorymentioning

confidence: 99%

“…Use of the coherence function is well established in engineering. Estimators of coherence are described in classic literature , and are used with little change in modern literature. − One of us (Eisenberg) has used these methods in physiology to analyze the electrical structure of cells and tissues, , as has been reviewed. − …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

H-Bonds in Crambin: Coherence in an α-Helix

Minh

Eisenberg

2023

ACS Omega

View full text Add to dashboard Cite

We applied coherence analysis�used by engineers to identify linear interactions in stochastic systems�to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the Hbonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.

show abstract

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

H-Bonds in Crambin: Coherence in an α-Helix

Minh

Eisenberg

2023

ACS Omega

View full text Add to dashboard Cite

show abstract

“…7 Frequency dependence of the spatial propagation of the LFP Coherence (Thomas, 2015;Nunez, 1981) between the LFP signals computed at different electrode locations may result from passive propagation of the LFP in the resistive extracellular medium, or from spatial correlations in the membrane currents (through the spatial extension of the dendrite, shared external inputs, or circuit-driven synchronization). We used the three different models to examine these mechanisms.…”

Section: Currents Underlying the Lfp Signalmentioning

confidence: 99%

An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials

Maex

2018

Neural Computation

View full text Add to dashboard Cite

Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood.In the present computational study, we show that a model circuit of interneurons, coupled via both GABA A receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/f power scaling at low (< 15 Hz) frequencies, power accumulation in the γ-frequency band (30-100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplification of single-neuron spectral properties, owing to the refractory period, by parameters that favour neuronal synchrony, such as delayed inhibition. The present study also confirms that both synaptic and voltage-gated membrane currents substantially contribute to the LFP, and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.

show abstract