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To assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
We have developed a scanning photoluminescence technique that can directly map out the local two-dimensional electron density with a relative accuracy of $\sim2.2\times10^8$ cm$^{-2}$. The validity of this approach is confirmed by the…
Gravitational wave detectors like the Einstein Telescope and LISA generate long multivariate time series, which pose significant challenges in spectral density estimation due to a number of overlapping signals as well as the presence of…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Two-dimensional spectroscopy (2DS) is a powerful ultrafast technique for probing electronic and vibrational dynamics in complex microscopic systems. Extracting detailed information on system dynamics and system-bath interactions from 2DS…
Multidimensional spectroscopy has a long history originating from nuclear magnetic resonance, and has now found widespread application at infrared and optical frequencies as well. However, the energy scales of traditional multidimensional…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
We have proposed and developed a method to utilize attosecond pulses in diffraction imaging techniques applied to complex samples. In this study, the effects of the broadband properties of the wavefield owing to attosecond pulses are…
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
Two-dimensional coherent spectroscopy (2DCS) with terahertz radiation offers a promising new avenue for the exploration of many-body phenomena in quantum magnets. This includes the potential diagnosis of fractionalized excitations, for…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
This article introduces a method of evaluating subsamples until any prescribed level of classification accuracy is attained, thus obtaining arbitrary accuracy. A logarithmic reduction in error rate is obtained with a linear increase in…
We investigate three-point statistics in weak lensing convergence, through the integrated bispectrum. This statistic involves measuring power spectra in patches, and is thus easy to measure, and avoids the complexity of estimating the very…
In this paper, we investigate a non-iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and/or magnetic permeability…
Two-dimensional (2D) spectroscopy combines high temporal and spectral resolution, allowing the observation of ultrafast energy transfer and the separation of homogeneous and inhomogeneous broadening. Typically, 2D spectroscopy is dominated…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying…