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Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
In modern astronomy, the quantity of data collected has vastly exceeded the capacity for manual analysis, necessitating the use of advanced artificial intelligence (AI) techniques to assist scientists with the most labor-intensive tasks. AI…
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a…
The frequency-domain approach (FDA) to transient analysis of the boundary element method, although is appealing for engineering applications, is computationally expensive. This paper proposes a novel adaptive frequency sampling (AFS)…
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…
X-ray absorption near edge structure (XANES) spectroscopy is a powerful technique for characterizing the chemical state and symmetry of individual elements within materials, but requires collecting data at many energy points which can be…
Continuum fitting is an important aspect of Lyman-alpha forest science, since errors in the estimated optical depths scale with the fractional continuum error. However, traditional methods of estimating continua in noisy and…
In ultrasound imaging the appearance of homogeneous regions of tissue is subject to speckle, which for certain applications can make the detection of tissue irregularities difficult. To cope with this, it is common practice to apply speckle…
PAC-Bayesian algorithms and Gibbs posteriors are gaining popularity due to their robustness against model misspecification even when Bayesian inference is inconsistent. The PAC-Bayesian alpha-posterior is a generalization of the standard…
Spectral fitting of X-ray data usually involves minimizing statistics like the chi-square and the Cash statistic. Here we discuss their limitations and introduce two measures based on the cumulative sum (CuSum) of model residuals to…
This paper proposes a Chebyshev polynomial expansion framework for the recovery of a continuous angular power spectrum (APS) from channel covariance. By exploiting the orthogonality of Chebyshev polynomials in a transformed domain, we…
Technological advancement has led to improvement in the design capabilities of astronomical spectrographs, allowing for high precision spectroscopy, thereby expanding the realms of observational astronomy. High-resolution spectrographs use…
The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…
Laser frequency combs (LFCs) are an important component of Doppler radial velocity (RV) spectroscopy that pushes fractional precision to the $10^{-10}$ level, as required to identify and characterize Earth-like exoplanets. However, large…
This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based…
Most localization methods for mixed far-field (FF) and near-field (NF) sources are based on uniform linear array (ULA) rather than sparse linear array (SLA). In this paper, we propose a localization method for mixed FF and NF sources based…
In Neural Networks (NN), Adaptive Activation Functions (AAF) have parameters that control the shapes of activation functions. These parameters are trained along with other parameters in the NN. AAFs have improved performance of Neural…
We consider the application of a ubercalibration-like relative flux calibration to the grism observations of the Roman High Latitude Wide Area Survey (HLWAS). We propose a simplified model of the calibration with an independent flat field…
Polarization analysis in x-ray spectroscopy provides an orientation dependent sensitivity to local bonding environments. For a cluster of atoms, polarization sensitivity is most often discussed through the lens of point group symmetries.…