scholarly journals Understanding Harmonic Structures Through Instantaneous Frequency

2021 ◽  
Author(s):  
Marco S Fabus ◽  
Mark W Woolrich ◽  
Catherine E Warnaby ◽  
Andrew J Quinn
Keyword(s):  
Instantaneous Frequency ◽  
Field Potential ◽  
Analytic Number Theory ◽  
Real Data ◽  
Clear Understanding ◽  
Mode Decomposition ◽  
Sinusoidal Waveform ◽  
Neurophysiological Data ◽  
Definition Of ◽  
Hippocampal Theta

The analysis of harmonics and non-sinusoidal waveform shape in neurophysiological data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonics structure in the FitzHugh-Nagumo model and the non-sinusoidal hippocampal theta oscillation in rat local field potential data. We further discuss how our definition helps to address mode splitting in EMD. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional and clinical roles of non-sinusoidal neural oscillations.

scholarly journals Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics

2021 ◽  
Author(s):  
Andrew J. Quinn ◽  
Vítor Lopes-dos-Santos ◽  
Norden Huang ◽  
Wei-Kuang Liang ◽  
Chi-Hung Juan ◽  
...  
Keyword(s):  
Instantaneous Frequency ◽  
Animal Movement ◽  
Field Potential ◽  
Real Data ◽  
Analytical Framework ◽  
Movement Speed ◽  
High Temporal Resolution ◽  
Cycle Duration ◽  
Neuronal Oscillations ◽  
Phase Alignment

AbstractNon-sinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time-series using masked Empirical Mode Decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency and phase) using instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase-grid space, makes it possible to compare cycles of different durations and shapes. ‘Normalised shapes’ can then be constructed with high temporal detail whilst accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks non-sinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average, yet exhibiting high variability on a cycle-by-cycle basis. We show how Principal Components Analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of enquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.

scholarly journals Numerical and Experimental Investigation on Parameter Identification of Time-Varying Dynamical System Using Hilbert Transform and Empirical Mode Decomposition

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Jun Chen ◽  
Guanyu Zhao
Keyword(s):  
Free Vibration ◽  
Empirical Mode Decomposition ◽  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Structural Parameters ◽  
Damping Ratio ◽  
Modal Parameters ◽  
Time Varying ◽  
Mode Decomposition ◽  
Definition Of

This paper proposes an approach to identifying time-varying structural modal parameters using the Hilbert transform and empirical mode decomposition. Definition of instantaneous frequency and instantaneous damping ratio based on Hilbert transform for single-degree-of-freedom (SDOF) system is first introduced. The following is the definition of Hilbert damping spectrum from which the time-varying damping ratio of multi-degree-of-freedom (MDOF) system can be calculated. Identification procedures for both instantaneous frequency and damping ratios based on their definition are then introduced. Applicability of the proposed identification algorithm has been validated through several numerical examples. The instantaneous frequency and damping ratios of SDOF system under free vibration and under sinusoidal and white noise excitation have been identified. The proposed method is also applied to MDOF system with slow and sudden changing structural parameters. The results demonstrate that when the system modal parameters are slowly changing, the instantaneous frequency could be easily and well identified with satisfied accuracy for all cases. However, the instantaneous damping ratio could be extracted only when the system is lightly damped. The damping results are better for free vibration situation than for the forced vibration cases. It is also shown that the suggested method can easily track the abrupt change of system modal parameter under free vibration. The proposed method is then applied to a 12-story short-lag shear wall structure model tested on a shaking table. The instantaneous dynamic properties of the structure were identified and were then introduced as known parameters into a finite element model. Comparisons with the numerical results using constant structural parameters demonstrate that the calculated structural responses using the identified time-varying parameters are much closer to the experimental results.

scholarly journals Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics

2021 ◽  
Author(s):  
Andrew J Quinn ◽  
Vitor Lopes-dos-Santos ◽  
Norden Huang ◽  
Wei-Kuang Liang ◽  
Chi-hung Juan ◽  
...  
Keyword(s):  
Instantaneous Frequency ◽  
Animal Movement ◽  
Field Potential ◽  
Real Data ◽  
Analytical Framework ◽  
Movement Speed ◽  
High Temporal Resolution ◽  
Cycle Duration ◽  
Neuronal Oscillations ◽  
Phase Alignment

Non-sinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time-series using masked Empirical Mode Decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency and phase) using instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase-grid space, makes it possible to compare cycles of different durations and shapes. 'Normalised shapes' can then be constructed with high temporal detail whilst accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks non-sinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average, yet exhibiting high variability on a cycle-by-cycle basis. We show how Principal Components Analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of enquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.

The first flush in sewer systems

1996 ◽  
Vol 33 (9) ◽  
pp. 101-108 ◽  
Author(s):  
Agnès Saget ◽  
Ghassan Chebbo ◽  
Jean-Luc Bertrand-Krajewski
Keyword(s):  
Treatment Strategy ◽  
Real Data ◽  
First Flush ◽  
Clear Definition ◽  
Controversial Subject ◽  
Sewer Systems ◽  
Wet Weather ◽  
Definition Of ◽  
Appearance Frequency

The first flush phenomenon of urban wet weather discharges is presently a controversial subject. Scientists do not agree with its reality, nor with its influences on the size of treatment works. Those disagreements mainly result from the unclear definition of the phenomenon. The objective of this article is first to provide a simple and clear definition of the first flush and then to apply it to real data and to obtain results about its appearance frequency. The data originate from the French database based on the quality of urban wet weather discharges. We use 80 events from 7 separately sewered basins, and 117 events from 7 combined sewered basins. The main result is that the first flush phenomenon is very scarce, anyway too scarce to be used to elaborate a treatment strategy against pollution generated by urban wet weather discharges.

Misconceptions of Metrology and Calibration

2021 ◽  
Author(s):  
Christopher Herrmann ◽  
Keyword(s):  
Metrological Traceability ◽  
The Other ◽  
Clear Understanding ◽  
New Meanings ◽  
The World ◽  
Definition Of

In today’s world of manufacturing, R&D, and testing across diverse industries, the definition of Metrology and calibration has taken on new meanings, whether it is right or wrong. With the evolving requirements for defining traceability, which is impacted through ISO/IEC 17025: 2017 as well as the NIST’s definition of Metrological Traceability, we must step back and truly understand what the differences are between these 2 terms. In this paper, we will evaluate the definitions of Metrology and calibration. We will also look at the importance of each and how one affects the other. While both terms are important, as liaisons within the Science of Measurement, we need to be able to articulate the differences between both terms to assist in bringing the representatives working in various industries to a clear understanding of how calibration is an action within the world of Metrology.

Assessment of Damage Progression in Automotive Electronics Assemblies Subjected to Temperature and Vibration

2018 ◽  
Author(s):  
Pradeep Lall ◽  
Tony Thomas
Keyword(s):  
Instantaneous Frequency ◽  
Low Frequency ◽  
Principal Component ◽  
Large Data ◽  
Data Sets ◽  
Automotive Electronics ◽  
Damage Progression ◽  
Mode Decomposition ◽  
Electronic Assemblies ◽  
Strain Signal

Electronics in automotive underhood environments is used for a number of safety critical functions. Reliable continued operation of electronic safety systems without catastrophic failure is important for safe operation of the vehicle. There is need for prognostication methods, which can be integrated, with on-board sensors for assessment of accrued damage and impending failure. In this paper, leadfree electronic assemblies consisting of daisy-chained parts have been subjected to high temperature vibration at 5g and 155°C. Spectrogram has been used to identify the emergence of new low frequency components with damage progression in electronic assemblies. Principal component analysis has been used to reduce the dimensionality of large data-sets and identify patterns without the loss of features that signify damage progression and impending failure. Variance of the principal components of the instantaneous frequency has been shown to exhibit an increasing trend during the initial damage progression, attaining a maximum value and decreasing prior to failure. The unique behavior of the instantaneous frequency over the period of vibration can be used as a health-monitoring feature for identifying the impending failures in automotive electronics. Further, damage progression has been studied using Empirical Mode Decomposition (EMD) technique in order to decompose the signals into Independent Mode Functions (IMF). The IMF’s were investigated based on their kurtosis values and a reconstructed strain signal was formulated with all IMF’s greater than a kurtosis value of three. PCA analysis on the reconstructed strain signal gave better patterns that can be used for prognostication of the life of the components.

scholarly journals Trivariate Empirical Mode Decomposition via Convex Optimization for Rolling Bearing Condition Identification

Sensors ◽  
2018 ◽  
Vol 18 (7) ◽  
pp. 2325 ◽  
Author(s):  
Yong Lv ◽  
Houzhuang Zhang ◽  
Cancan Yi
Keyword(s):  
Convex Optimization ◽  
Empirical Mode Decomposition ◽  
Dimensional Space ◽  
Real Data ◽  
Rolling Bearing ◽  
Low Rank ◽  
Data Matrix ◽  
Mode Decomposition ◽  
Uniform Sample ◽  
Local Mean

As a multichannel signal processing method based on data-driven, multivariate empirical mode decomposition (MEMD) has attracted much attention due to its potential ability in self-adaption and multi-scale decomposition for multivariate data. Commonly, the uniform projection scheme on a hypersphere is used to estimate the local mean. However, the unbalanced data distribution in high-dimensional space often conflicts with the uniform samples and its performance is sensitive to the noise components. Considering the common fact that the vibration signal is generated by three sensors located in different measuring positions in the domain of the structural health monitoring for the key equipment, thus a novel trivariate empirical mode decomposition via convex optimization was proposed for rolling bearing condition identification in this paper. For the trivariate data matrix, the low-rank matrix approximation via convex optimization was firstly conducted to achieve the denoising. It is worthy to note that the non-convex penalty function as a regularization term is introduced to enhance the performance. Moreover, the non-uniform sample scheme was determined by applying singular value decomposition (SVD) to the obtained low-rank trivariate data and then the approach used in conventional MEMD algorithm was employed to estimate the local mean. Numerical examples of synthetic defined by the fault model and real data generated by the fault rolling bearing on the experimental bench are provided to demonstrate the fruitful applications of the proposed method.

scholarly journals Stochastic Non-Pharmaceutical Optimal Control Strategies to Mitigate COVID-19

2021 ◽  
Author(s):  
Paolo Scarabaggio ◽  
Raffaele Carli ◽  
Graziana Cavone ◽  
Nicola Epicoco ◽  
Mariagrazia Dotoli
Keyword(s):  
Control Strategies ◽  
Optimal Strategies ◽  
Real Data ◽  
Chance Constraint ◽  
Control Actions ◽  
Regional Strategies ◽  
Italian Regions ◽  
Predictive Controller ◽  
Definition Of ◽  
Constraint Approach

This paper proposes a stochastic non-linear model predictive controller to support policy-makers in determining robust optimal strategies to tackle the COVID-19 secondary waves. First, a time-varying <i>SIRCQTHE </i>epidemiological model (considering Susceptible, Infected, Removed, Contagious, Quarantined, Threatened, Healed, and Extinct compartments of individuals) is defined to get reliable predictions on the pandemic dynamics on a regional basis. A stochastic Model Predictive Control problem is then formulated to select the necessary control actions to minimize the arising socio-economic costs. <br>In particular, considering the unavoidable uncertainty characterizing this decision-making process, we ensure that the capacity of the network of regional healthcare systems is not violated in accordance with a chance constraint approach.<br>Furthermore, since the infection rate depends on people’s mobility, differently from the related literature, we model the control actions as interventions affecting the mobility levels associated to different socio-economic categories.<br><div>The effectiveness of the presented method in properly supporting the definition of diversified regional strategies for tackling the COVID-19 spread is tested on the network of Italian regions using real data from the Italian Civil Protection Department. However, provided the availability of reliable data, the proposed approach can be easily extended to cope with other countries' characteristics and different levels of the spatial scale.</div><div><br></div><div>Preprint of paper submitted to IEEE Transactions on Automation Science and Engineering (<em>T-ASE</em>)</div>

scholarly journals Optogenetic activation of SST-positive interneurons restores hippocampal theta oscillation impairment induced by soluble amyloid beta oligomersin vivo

2018 ◽  
Author(s):  
Hyowon Chung ◽  
Kyerl Park ◽  
Hyun Jae Jang ◽  
Michael M Kohl ◽  
Jeehyun Kwag
Keyword(s):  
Learning And Memory ◽  
Peak Power ◽  
Pyramidal Neurons ◽  
Hippocampal Slices ◽  
Field Potential ◽  
Theta Oscillations ◽  
Ca1 Pyramidal Neurons ◽  
Theta Frequency ◽  
Hippocampal Theta

AbstractAbnormal accumulation of amyloid β oligomers (AβO) is a hallmark of Alzheimer’s disease (AD), which leads to learning and memory deficits. Hippocampal theta oscillations that are critical in spatial navigation, learning and memory are impaired in AD. Since GABAergic interneurons, such as somatostatin-positive (SST+) and parvalbumin-positive (PV+) interneurons, are believed to play key roles in the hippocampal oscillogenesis, we asked whether AβO selectively impairs these SST+ and PV+ interneurons. To selectively manipulate SST+ or PV+ interneuron activity in mice with AβO pathologyin vivo, we co-injected AβO and adeno-associated virus (AAV) for expressing floxed channelrhodopsin-2 (ChR2) into the hippocampus of SST-Cre or PV-Cre mice. Local field potential (LFP) recordingsin vivoin these AβO–injected mice showed a reduction in the peak power of theta oscillations and desynchronization of spikes from CA1 pyramidal neurons relative to theta oscillations compared to those in control mice. Optogenetic-activation of SST+ but not PV+ interneurons in AβO–injected mice fully restored the peak power of theta oscillations and resynchronized the theta spike phases to a level observed in control mice.In vitrowhole-cell voltage-clamp recordings in CA1 pyramidal neurons in hippocampal slices treated with AβO revealed that short-term plasticity of SST+ interneuron inhibitory inputs to CA1 pyramidal neurons at theta frequency were selectively disrupted while that of PV+ interneuron inputs were unaffected. Together, our results suggest that dysfunction in inputs from SST+ interneurons to CA1 pyramidal neurons may underlie the impairment of theta oscillations observed in AβO-injected micein vivo.Our findings identify SST+ interneurons as a target for restoring theta-frequency oscillations in early AD.

The Place of Concerns for Posterity in the Global Education for Sustainable Development Agenda

2017 ◽  
pp. 1433-1453
Author(s):  
Katia Vladimirova
Keyword(s):  
Sustainable Development ◽  
Environmental Ethics ◽  
Global Education ◽  
Education For Sustainable Development ◽  
Future Generations ◽  
Clear Understanding ◽  
Education Philosophy ◽  
Development Agenda ◽  
Definition Of ◽  
Conceptual Foundations

Education is a powerful tool to alter unsustainable values and mindsets. But in order for it to be used most efficiently it is crucial to have a clear understanding of what values should be advanced, changed, or developed. This chapter aims to clarify some conceptual difficulties with the value of future generations in education for sustainable development. Future generations are embedded in the definition of sustainable development and can be reasonably expected to be at the heart of education for sustainable development. This chapter explores this assumption and analyzes how future-oriented concerns are formulated and advanced in the global educational agenda put forward during the Decade of Education for Sustainable Development (2005-2014) led by UNESCO. This analysis compares conceptual foundations of ESD against key developments in climate and environmental ethics on the treatment of posterity. This chapter can contribute to the disciplines of environmental education, philosophy of education, and to climate ethics.

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