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We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
Many robotics applications require alignment and fusion of observations obtained at multiple views to form a global model of the environment. Multi-way data association methods provide a mechanism to improve alignment accuracy of pairwise…
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…
Linear mixed-effects models are a central analytical tool for modeling hierarchical and longitudinal data, as they allow simultaneous representation of fixed and random sources of variation. In practice, inference for such models is most…
Balancing the distributions of the confounders across the exposure levels in an observational study through matching or weighting is an accepted method to control for confounding due to these variables when estimating the association…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
The coherent radiation emitted by an electron bunch provides a diagnostic signal that can be used to estimate its longitudinal distribution. Commonly only the amplitude of the intensity spectrum can be measured and the associated phase must…
We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum,…
We analyze the problem of resolving two point-sources in the case of mutually coherent sources with arbitrary quantum statistics, mutual phase, relative and absolute intensity. We use a sensitivity measure based on the method of moments and…
We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie-Gr\"uneisen equations of state, which are widely used in practical applications. The solver provides the interface…
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to…
Fitting mixture distributions is needed in applications where data belongs to inhomogeneous populations comprising homogeneous sub-populations. The mixing proportions of the sub populations are in general unknown and need to be estimated as…
We address the relation between quantum metrological resolution and coherence. We examine this dependence in two manners: we develop a quantum Wiener-Kintchine theorem for a suitable model of quantum ruler, and we compute the Fisher…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the highest multiplicity. This leads to a complete classification of blow-up profiles in…
The general form of solutions for parameters of interfering Breit-Wigner resonances is found. The number of solutions is determined by the properties of roots of corresponding characteristic equation and does not exceed $2^{N-1}$, where $N$…
In this article, we study a double-phase variable-exponent Kirchhoff problem and show the existence of at least three solutions. The proposed model, as a generalization of the Kirchhoff equation, is interesting since it is driven by a…
The properties of symmetric nuclear matter are investigated within the Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The…
Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we…
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…