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We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…

We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a…

For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…

Classical high-order weighted essentially non-oscillatory (WENO) schemes are designed to achieve optimal convergence order for smooth solutions and to maintain non-oscillatory behaviors for discontinuities. However, their spectral…

The unique functionalities of antiferromagnets offer promising routes to advance information technology. Their compensated magnetic order leads to spin resonances in the THz-regime, which suggest the possibility to coherently control…

Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…

This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…

We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that data from a head-neck position tracking system, one of biomechanical models, show…

The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet…

This paper deals with the estimation of hidden periodicities in a non-linear regression model with stationary noise displaying cyclical dependence. Consistency and asymptotic normality are established for the least-squares estimates.

The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…

Hyperspectral unmixing (HU) is a critical yet challenging task in remote sensing. However, existing nonnegative matrix factorization (NMF) methods with graph learning mostly focus on first-order or second-order nearest neighbor…

This paper considers the problem of frequency estimation for a multi-sinusoidal signal consisting of n sinuses in finite-time. The parameterization approach based on applying delay operators to a measurable signal is used. The result is the…

Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this, however identification and tracking of relevant turbulent…

We propose a new algorithm for time stretching music signals based on the theory of nonstationary Gabor frames (NSGFs). The algorithm extends the techniques of the classical phase vocoder (PV) by incorporating adaptive time-frequency (TF)…

Most adaptive optics (AO) systems using pyramid wavefront sensors (PyWFS) to estimate the phase of the pupil field use mechanical modulation of the beam in order to increase the dynamic range in low-order modes so the PyWFS can usefully…

This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes,…

We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST) to model and analyze oscillatory physiological signals. To…