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The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…
Powder X-ray Diffraction (PXRD) and Pair Distribution Function (PDF) analysis are well-established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In PXRD…
Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by finding an approximate solution to the many-body Schr\"odinger equation. However, the cost of these…
In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…
Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive…
Vision transformers (ViT) have recently attracted considerable attentions, but the huge computational cost remains an issue for practical deployment. Previous ViT pruning methods tend to prune the model along one dimension solely, which may…
This study introduces a systematic and optimised methodology for designing Linear Variable Differential Transformer (LVDT) sensors and Voice Coil (VC) actuators, tailored for high-precision applications such as gravitational wave detectors…
We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by residue calculus. The computational test reveals that with only $16$ summation terms this approximation provides average accuracy…
This paper presents an adjoint-assisted, topology-optimization-inspired approach for analyzing topological sensitivities in fluid domains based on porous media formulations -- without directly utilizing the porosity field as a design…
Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Ito process. This work…
This paper introduces a new approach to extract and analyze vector data from technical drawings in PDF format. Our method involves converting PDF files into SVG format and creating a feature-rich graph representation, which captures the…
While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…
We derive the full expression for the shape of the charge spectrum that results from the illumination of a photo-multiplier tube. The derivation is for low intensity illumination with constant gain, a common condition for most nuclear and…
We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions…
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
Density functional theory (DFT) is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, etc. In this paper, we suggest a method for obtaining the equilibrium…
The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining probability density function and its derivatives, and mainly for fitting stochastic model with the fundamental probabilistic relationships of…