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1. Modified Arcsine Law for One-Bit Sampled Stationary Signals with Time-Varying Thresholds

   Eamaz, A; Yeganegi, F.; Soltanalian, M. (January 2021, Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing)

   null (Ed.)

   One-bit quantization has attracted considerable attention in signal processing for communications and sensing. The arcsine law is a useful relation often used to estimate the normalized covariance matrix of zero-mean stationary input signals when they are sampled by one-bit analog-to-digital converters (ADCs)---practically comparing the signals with a given threshold level. This relation, however, only considers a zero threshold which can cause a remarkable information loss. For the first time in the literature, this paper introduces an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds. In particular, the proposed method is shown to accurately recover the variance and autocorrelation of the stationary signals of interest. 

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2. One-bit digital radar

   https://doi.org/10.1109/ACSSC.2017.8335529  

   Ren, Jiaying; Li, Jian (October 2017, Signals, Systems, and Computers, 2017 51st Asilomar Conference on)

   This paper introduces a one-bit digital radar involving direct one-bit sampling with unknown dithering of the received radio frequency (RF) signal. Due to avoiding the analog mixer and the down-conversion of the RF signal, the digital radar can be energy-efficient and low-priced. The use of unknown dithering allows for the one-bit samples to be processed efficiently using conventional algorithms. A computationally efficient range-Doppler estimation method based on fractional Fourier transform (FRFT) and fast Fourier transform (FFT) is used for linear frequency modulated continuous wave (LFMCW) transmissions, and the CLEAN algorithm is used for target parameter estimation. 

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3. Hesitant adaptive search with estimation and quantile adaptive search for global optimization with noise

   https://doi.org/10.1007/s10898-023-01307-7  

   Zabinsky, Zelda B; Linz, David D (September 2023, Journal of Global Optimization)

   Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that the objective function can be observed directly. We consider the case where the objective function must be estimated, often using a noisy function, as in simulation. We present a finite-time analysis of algorithm performance that combines estimation with a sampling distribution. We present a framework called Hesitant Adaptive Search with Estimation, and derive an upper bound on function evaluations that is cubic in dimension, under certain conditions. We extend the framework to Quantile Adaptive Search with Estimation, which focuses sampling points from a series of nested quantile level sets. The analyses suggest that computational effort is better expended on sampling improving points than refining estimates of objective function values during the progress of an adaptive search algorithm. 

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4. Non-invasive identification of swallows via deep learning in high resolution cervical auscultation recordings

   https://doi.org/10.1038/s41598-020-65492-1  

   Khalifa, Yassin; Coyle, James L.; Sejdić, Ervin (December 2020, Scientific Reports)

   Abstract High resolution cervical auscultation is a very promising noninvasive method for dysphagia screening and aspiration detection, as it does not involve the use of harmful ionizing radiation approaches. Automatic extraction of swallowing events in cervical auscultation is a key step for swallowing analysis to be clinically effective. Using time-varying spectral estimation of swallowing signals and deep feed forward neural networks, we propose an automatic segmentation algorithm for swallowing accelerometry and sounds that works directly on the raw swallowing signals in an online fashion. The algorithm was validated qualitatively and quantitatively using the swallowing data collected from 248 patients, yielding over 3000 swallows manually labeled by experienced speech language pathologists. With a detection accuracy that exceeded 95%, the algorithm has shown superior performance in comparison to the existing algorithms and demonstrated its generalizability when tested over 76 completely unseen swallows from a different population. The proposed method is not only of great importance to any subsequent swallowing signal analysis steps, but also provides an evidence that such signals can capture the physiological signature of the swallowing process. 

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5. Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization

   Dey, Papri; Kannan, Ravi; Ryder, Nick; Srivastava, Nikhil (January 2023, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023))

   We study the bit complexity of two related fundamental computational problems in linear algebra and control theory. Our results are: (1) An Õ(n^{ω+3}a+n⁴a²+n^ωlog(1/ε)) time algorithm for finding an ε-approximation to the Jordan Normal form of an integer matrix with a-bit entries, where ω is the exponent of matrix multiplication. (2) An Õ(n⁶d⁶a+n⁴d⁴a²+n³d³log(1/ε)) time algorithm for ε-approximately computing the spectral factorization P(x) = Q^*(x)Q(x) of a given monic n× n rational matrix polynomial of degree 2d with rational a-bit coefficients having a-bit common denominators, which satisfies P(x)⪰0 for all real x. The first algorithm is used as a subroutine in the second one. Despite its being of central importance, polynomial complexity bounds were not previously known for spectral factorization, and for Jordan form the best previous best running time was an unspecified polynomial in n of degree at least twelve [Cai, 1994]. Our algorithms are simple and judiciously combine techniques from numerical and symbolic computation, yielding significant advantages over either approach by itself. 

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