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The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…
This paper focuses on computing the directional extremal boundary of a union of equal-radius circles. We introduce an efficient algorithm that accurately determines this boundary by analyzing the intersections and dominant relationships…
We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
Optical fluorescence imaging is capable of measuring both the spatial and rotational dynamics of single molecules. However, unavoidable measurement noise will result in inaccurate estimates of rotational dynamics, causing a molecule to…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large…
Cross sections for proton inelastic collision with different nuclei are described within the Glauber approximation. The significant difference between approximate ``Glauber'' formula and exact calculations with geometrical scaling…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…
High-precision surface roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and only can achieve the precision of 0.1 nm with white light interferometer.…
We discuss the computational performance of the adaptive resolution technique in molecular simulation when it is compared with equivalent full coarse-grained and full atomistic simulations. We show that an estimate of its efficiency, within…
Accurate monocular depth estimation is crucial for 3D scene understanding, but existing methods often blur depth at object boundaries, introducing spurious intermediate 3D points. While achieving sharp edges usually requires very…
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…
When solving partial differential equations on scattered nodes using the Radial Basis Function-generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs…
Directional couplers are a fundamental building block in integrated photonics, particularly in quantum applications and optimization-based design where precision is critical. Accurate functionality is crucial to ensure reliable operation…
Numerical relativity simulations provide a full description of the dynamics of binary systems, including gravitational radiation. The waveforms produced by these simulations have a number of applications in gravitational-wave detection and…
We use a simple, collision-based, discrete, random abrasion model to compute the profiles for the stoss faces in a bedrock abrasion process. The model is the discrete equivalent of the generalized version of a classical, collision based…
We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel space. A kernel typically…
Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we…