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Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…
We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to…
In adaptive control theory, the dynamic regressor extension and mixing (DREM) procedure has become widespread as it allows one to describe major of adaptive control problems in unified terms of the parameter estimation problem of a…
This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing…
We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and…
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…
The methods for determination of the characteristics of the extrema are discussed with an application to irregularly spaced data, which are characteristic for photometrical observations of variable stars. We introduce new special functions,…
This study examines the characterization of binary star systems using Spectral Energy Distributions (SEDs), a technique increasingly essential with the rise of large-scale astronomical surveys. Binaries can emit flux at different regions of…
In the last couple of decades, tremendous progress has been achieved in developing robotic telescopes and, as a result, sky surveys (both terrestrial and space) have become the source of a substantial amount of new observational data. These…
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…
Recent developments in computational power and machine learning techniques motivate their use in many different astrophysical research areas. Consequently, many machine learning models have been trained to classify exoplanet transit signals…
Exoplanetary atmospheric observations require an exquisite precision in the measurement of the relative flux among wavelengths. In this paper, we aim to provide a new adaptive method to treat light curves before fitting transit parameters…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and…
We review the method NAV (New Algol Variable) first introduced in 2012Ap.....55..536A, which uses the locally-dependent shapes of eclipses in an addition to the trigonometric polynomial of the second order (which typically describes the…
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(\Omega)$-norm with order $1/2$ in convex…
We present an automated classification of 2165 \textit{Kepler} eclipsing binary (EB) light curves that accompanied the second \textit{Kepler} data release. The light curves are classified using Locally Linear Embedding, a general nonlinear…