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Abstract Mode-localized sensors have attracted attention because of their high parametric sensitivity and first-order common-mode rejection to temperature drift. The high-fidelity detection of resonator amplitude is critical to determining the resolution of mode-localized sensors where the measured amplitude ratio in a system of coupled resonators represents the output metric. Operation at specific bifurcation points in a nonlinear regime can potentially improve the amplitude bias stability; however, the amplitude ratio scale factor to the input measurand in a nonlinear regime has not been fully investigated. This paper theoretically and experimentally elucidates the operation of mode-localized sensors with respect to stiffness perturbations (or an external acceleration field) in a nonlinear Duffing regime. The operation of a mode-localized accelerometer is optimized with the benefit of the insights gained from theoretical analysis with operation in the nonlinear regime close to the top critical bifurcation point. The phase portraits of the amplitudes of the two resonators under different drive forces are recorded to support the experimentally observed improvements for velocity random walk. Employing temperature control to suppress the phase and amplitude variations induced by the temperature drift, 1/f noise at the operation frequency is significantly reduced. A prototype accelerometer device demonstrates a noise floor of 95 ng/√Hz and a bias instability of 75 ng, establishing a new benchmark for accelerometers employing vibration mode localization as a sensing paradigm. A mode-localized accelerometer is first employed to record microseismic noise in a university laboratory environment.

Parkinson's disease which is the second most prevalent neurodegenerative disorder in the United States is a serious and complex disease that may progress to mild cognitive impairment and dementia. The early detection of the mild cognitive impairment and the identification of its biomarkers is crucial to support neurologists in monitoring the progression of the disease and allow an early initiation of effective therapeutic treatments that will improve the quality of life for the patients. In this paper, we propose the first deep-learning based approaches to detect mild cognitive impairment in the sleep Electroencephalography for patients with Parkinson's disease and further identify the discriminative features of the disease. The proposed frameworks start by segmenting the sleep Electroencephalography time series into three sleep stages (i.e., two non-rapid eye movement sleep-stages and one rapid eye movement sleep stage), further transforming the segmented signals in the time-frequency domain using the continuous wavelet transform and the variational mode decomposition and finally applying novel convolutional neural networks on the time-frequency representations. The gradient-weighted class activation mapping was also used to visualize the features based on which the proposed deep-learning approaches reached an accurate prediction of mild cognitive impairment in Parkinson's disease. The proposed variational mode decomposition-based model offered a superior accuracy, sensitivity, specificity, area under curve, and quadratic weighted Kappa score, all above 99% as compared with the continuous wavelet transform-based model (that achieved a performance that is almost above 92%) in differentiating mild cognitive impairment from normal cognition in sleep Electroencephalography for patients with Parkinson's disease. In addition, the features attributed to the mild cognitive impairment in Parkinson's disease were demonstrated by changes in the middle and high frequency variational mode decomposition components across the three sleep-stages. The use of the proposed model on the time-frequency representation of the sleep Electroencephalography signals will provide a promising and precise computer-aided diagnostic tool for detecting mild cognitive impairment and hence, monitoring the progression of Parkinson's disease.