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Parameter-free stochastic gradient descent (PFSGD) algorithms do not require setting learning rates while achieving optimal theoretical performance. In practical applications, however, there remains an empirical gap between tuned stochastic…

There is a need for fast adaptation in spike sorting algorithms to implement brain-machine interface (BMIs) in different applications. Learning and adapting the functionality of the sorting process in real-time can significantly improve the…

Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…

This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD), a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both spatiotemporal and purely temporal data. By incorporating…

This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…

The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gammachirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates…

There has been significant attention devoted to the effectiveness of various domains, such as semi-supervised learning, contrastive learning, and meta-learning, in enhancing the performance of methods for noisy label learning (NLL) tasks.…

Point spread function (PSF) engineering is vital for precisely controlling the focus of light in computational imaging, with applications in neural imaging, fluorescence microscopy, and biophotonics. The PSF is derived from the magnitude of…

A sensorless speed, average temperature and resistance estimation technique based on Neural Network (NN) for brushed DC machines is proposed in this paper. The literature on parameters and state spaces estimations of the Brushed DC…

We investigate a data-driven approach for tuning the filtered spherical harmonics method (\fpn) when solving the radiation transport equation (RTE). The \fpn method extends the classical spherical harmonics approach (\pn) by introducing…

In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is based on a concept called GSLLN (Generalized Strong Law of…

Sparse adaptive filtering has gained much attention due to its wide applicability in the field of signal processing. Among the main algorithm families, sparse norm constraint adaptive filters develop rapidly in recent years. However, when…

Spike sorting is a crucial step in decoding multichannel extracellular neural signals, enabling the identification of individual neuronal activity. A key challenge in brain-machine interfaces (BMIs) is achieving real-time, low-power spike…

This paper investigates typical behaviors like damped oscillations in fractional order (FO) dynamical systems. Such response occurs due to the presence of, what is conceived as, pseudo-damping and meta-damping in some special class of FO…

The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal…

We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise…

The stochastic parallel gradient descent (SPGD) algorithm is usually employed as the control strategy for phase-locking in fiber laser phased array systems. However, the convergence speed of the SPGD algorithm will slow down as the number…

This paper presents the Universal Software Radio Peripheral (USRP) experimental results of the Max-Min signal to noise ratio (SNR) Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks which is recently proposed in…

Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. One fast…