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The Kepler mission has provided a treasure trove of eclipsing binaries (EBs), observed at extremely high photometric precision, nearly continuously for several years. We are carrying out a survey of ~100 of these EBs to derive dynamical…

With the unprecedented photometric precision of the Kepler Spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities,…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

This paper investigates the problem of trajectory planning for autonomous vehicles at unsignalized intersections, specifically focusing on scenarios where the vehicle lacks the right of way and yet must cross safely. To address this issue,…

This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…

Belief compression improves the tractability of large-scale partially observable Markov decision processes (POMDPs) by finding projections from high-dimensional belief space onto low-dimensional approximations, where solving to obtain…

To provide backup and augmentation to global navigation satellite system (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be employed as signals of opportunity (SOP) for position, navigation and timing (PNT). Since the…

For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…

A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order…

Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…

While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology…

Methods of the explicitly correlated F12 approach are applied to the problem of calculating the uncoupled second-order dispersion energy in symmetry-adapted perturbation theory. The accuracy of the new method is tested for noncovalently…

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 with order $1/2$ in convex domains but has a reduced…

Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has…

We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…

We used the database of eclipsing binaries detected by the OGLE microlensing project in the pencil-beam search volume toward Baade's Window to define a sample of 74 detached, equal-mass, main-sequence binary stars with short orbital periods…

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…

Detached eclipsing binary stars (dEBs) are a key source of data on fundamental stellar parameters. While there is a vast source of candidate systems in the light curve databases of survey missions such as Kepler and TESS, published…

Bayesian nonparametric regression with dependent wavelets has dual shrinkage properties: there is shrinkage through a dependent prior put on functional differences, and shrinkage through the setting of most of the wavelet coefficients to…

Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is…