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Being inspired by phasor analysis in linear circuit theory, and its algebraic counterpart - the AC-(operational)-calculus for sinusoids developed by W. Marten and W. Mathis - we define a complex structure on several spaces of real-valued…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography…
We propose a precise and efficient normal estimation method that can deal with noise and nonuniform density for unstructured 3D point clouds. Unlike existing approaches that directly take patches and ignore the local neighborhood…
The masked projection techniques are popular in the area of non-linear model reduction. Quantifying and minimizing the error in model reduction, particularly from masked projections, is important. The exact error expressions are often…
Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate…
We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…
In the mean-median-mode triad of univariate centrality measures, the mode has been overlooked for estimating the center of symmetry in continuous and unimodal settings. This paper expands on the connection between kernel mode estimators and…
The paper investigates the sensitivity of the inverse problem of recovering the velocity field in a bounded domain from the boundary dynamic Dirichlet-to-Neumann map (DDtN) for the wave equation. Three main results are obtained: (1)…
This paper introduces a shape optimisation framework for achieving desired mutual inductances (MIs) among coils in 3D space. Utilising a wire modelling approach, the coils are discretised using B-spline curves, with control points (CPs)…
We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
We introduce a shape-sensitive loss function for catheter and guidewire segmentation and utilize it in a vision transformer network to establish a new state-of-the-art result on a large-scale X-ray images dataset. We transform…
We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and…
Coherent, continuous spatial representations are critical for synthesizing physical and perceptual phenomena into a single representational space. Radial basis kernels provide a path forward for this type of distributed representation. In…
In industrial and environmental monitoring, achieving real-time and precise fluid flow measurement remains a critical challenge. This study applies linear quantization in FPGA-based soft sensors for fluid flow estimation, significantly…
We compute f-mode sensitivity kernels for flows. Using a two-dimensional model, the scattered wavefield is calculated in the first Born approximation. We test the correctness of the kernels by comparing an exact solution (constant flow), a…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
Multi-modal systems have the capacity of producing more reliable results than systems with a single modality in road detection due to perceiving different aspects of the scene. We focus on using raw sensor inputs instead of, as it is…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…