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Consider a time series of signal measurements $x(t)$, having components $x_k \mbox{ for } k = 1,2, \ldots ,N$. This paper shows how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or…
Mass spectrometry, especially so-called tandem mass spectrometry, is commonly used to assess the chemical diversity of samples. The resulting mass fragmentation spectra are representations of molecules of which the structure may have not…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
We present a method to calculate the frequency components of a pump waveform driving a parametric oscillator, which realizes a desired frequency mixing or scattering between modes. The method is validated by numerical analysis and we study…
This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers,…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives,…
We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…
The CEEMDAN algorithm is one of the modern methods used in the analysis of non-stationary signals. This research presents a study of the effectiveness of this method in audio source separation to know the limits of its work. It concluded…
This paper proposes a determined blind source separation method using Bayesian non-parametric modelling of sources. Conventionally source signals are separated from a given set of mixture signals by modelling them using non-negative matrix…
This paper introduces new techniques for estimating, identifying and simulating mixed causal-noncausal invertible-noninvertible models. We propose a framework that integrates high-order cumulants, merging both the spectrum and bispectrum…
The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce an approach based on quantum tracking control that…
We propose a novel hyperspectral (HS) anomaly detection method that is robust to various types of noise. Most existing HS anomaly detection methods are designed without explicit consideration of noise or are based on the assumption of…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…