Unique Characterization of Spatiotemporal Neuronal Network Activity

We apply the Triple Correlation Uniqueness (TCU) theorem to the most basic representation of network spiking activity, the raster, to prove that third-order (triple) correlation uniquely characterizes spiking activity in the brain. As a consequence, the three-node (triple) motifs comprising the triple correlation are fundamental building blocks of neuronal activity. By analysing the putative flow of information in these motifs, we group all possible motifs into fourteen motif-classes. These motif-classes embody well-known and well-studied properties in neuroscience, e.g. spike rate, local dynamics, synchrony, feedback, feedforward, convergence, and divergence. We show that motifs with some of these properties---divergence, convergence, and feedforward---are far more prevalent in the triple correlation; and thus, these properties contribute more to characterizing neural activity than do the other properties. In the frequency domain, the triple correlation is the bispectrum, which characterizes the phase-relationship between spike trains and the relationships between frequency bands. We apply these analyses to example rasters to illustrate the dependence of our characterization on the firing patterns underlying neural activity.

A Triple-Correlation Framework for Demonstrating an Innovative Gas Warning System: A Case Study in China

This research aims to develop an innovative gas warning system for improving production safety in the underground coal mining industry. Coal mining is an important sector for China’s economic development; gas monitoring systems are widely adopted as almost 60% of coal mining accidents are caused by gas. Existing gas monitoring systems mainly focus on simply detecting real-time data obtained from gas sensors. The literature review did not find gas monitoring systems that provide alarms or warnings from the correlation of gas with data from other sensors. This research aims to fill this gap to uncover hidden patterns and correlations between gas and temperature, wind, and dust, and incorporate data analytics into developing an innovative, integrated gas warning system. Correlational research was adopted using 328,320 data outputs obtained from ZhongXing Co. Ltd in Dec 2019. The study found strong relations between gas and temperature, wind, and dust. A Triple-Correlation Theoretical Framework and a Unified Modeling Language (UML) model were developed for an innovative gas warning system. As a result of this research, the ZhongXing Innovative Gas Warning System was developed and deployed for user acceptance testing on 28 Aug 2020.

Novel Fault Identification for Electromechanical Systems via Spectral Technique and Electrical Data Processing

It is proposed, developed, investigated, and validated by experiments and modelling for the first time in worldwide terms new data processing technologies, higher order spectral multiple correlation technologies for fault identification for electromechanical systems via electrical data processing. Investigation of the higher order spectral triple correlation technology via modelling has shown that the proposed data processing technology effectively detects component faults. The higher order spectral triple correlation technology successfully applied for rolling bearing fault identification. Experimental investigation of the technology has shown, that the technology effectively identifies rolling bearing fault by electrical data processing at very early stage of fault development. Novel technology comparisons via modelling and experiments of the proposed higher order spectral triple correlation technology and the higher order spectra technology show the higher fault identification effectiveness of the proposed technology over the bicoherence technology.

On triple correlations of Fourier coefficients of cusp forms. II

The triple correlation [Formula: see text] for arbitrary coefficients [Formula: see text] is estimated on average over [Formula: see text] in some short intervals. By introducing a device of short intervals, we are able to reduce this problem to uniform oscillations of one of the three coefficients, say [Formula: see text], against additive characters of [Formula: see text] over short intervals. The argument is simple, but refines previous arguments in certain cases. More precise estimates are also obtained by taking [Formula: see text] to be Fourier coefficients of cusp forms and Möbius functions, which substantially improve previous results.