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Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…
The Least Absolute Shrinkage and Selection Operator (LASSO) has gained attention in a wide class of continuous parametric estimation problems with promising results. It has been a subject of research for more than a decade. Due to the…
Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…
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…
To extract useful information about quantum effects in cold atom experiments, one central task is to identify the intrinsic quantum fluctuation from extrinsic system noises of various kinds. As a data processing method, principal component…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…
We propose a scheme utilizing ideas from infinite dimensional compressed sensing for thermal source localization. Using the soft recovery framework of one of the authors, we provide rigorous theoretical guarantees for the recovery…
We apply the compressive sensing lattice dynamics (CSLD) method to calculate phonon dispersion for crystalline solids. While existing methods such as frozen phonon, small displacement, and linear response are routinely applied for phonon…
We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
Many astrophysical sources, especially compact accreting sources, show strong, random brightness fluctuations with broad power spectra in addition to periodic or quasi-periodic oscillations (QPOs) that have narrower spectra. The random…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
This paper proposes an adaptive near-field beam training method to enhance performance in multi-user and multipath environments. The approach identifies multiple strongest beams through beam sweeping and linearly combines their received…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
Inverse scattering from discrete targets with the single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) measurements is analyzed by compressed sensing theory with and without the…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…