Related papers: Efficient Detection of Borromean Linking in Ellips…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
We construct an algorithm to decide whether two given Legendrian or transverse links are equivalent. In general, the complexity of the algorithm is too high for practical implementation. However, in many cases, when the symmetry group of…
In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…
A formalism is proposed to study the electron tunneling between extended states, based on the spin-boson Hamiltonian previously used in two-level systems. It is applied to analyze the out--of--plane tunneling in layered metals considering…
An exact conservative remapping scheme requires overlaps between two meshes and a reconstruction scheme on the old cells (Lagrangian mesh). While the are intensive discussion on reconstruction schemes, there are relative sparse discussion…
We develop a minimal system to study the stochastic formation of Borromean links within topologically entangled networks without requiring the use of knot invariants. Borromean linkages may form in entangled solutions of open polymer chains…
We describe a criterion for the detection of entanglement between two multi-boson systems. The criterion is based on calculating correlations of Gell-Mann matrices with a fixed boson number on each subsystem. This applies naturally to…
A set of n segments in the plane may form a Euclidean TSP tour, a tree, or a matching, among others. Optimal TSP tours as well as minimum spanning trees and perfect matchings have no crossing segments, but several heuristics and…
The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of $\mathcal{M}_g$. This new proof exhibits a new beautiful tautological relation that stems from the…
This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…
Recent advances in the field of strongly correlated electron systems allow to access the entanglement properties of interacting fermionic models, by means of Monte Carlo simulations. We briefly review the techniques used in this context to…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
The list of knots with up to 10 crossings is commonly referred to as the Rolfsen Table. This paper presents a way to generate the Rolfsen table in a simple, clear, and reproducible manner. The methods we use are similar to those used by J.…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
In this paper we promote a method for the evaluation of a surface topography which we call the correlogram correlation method. Employing a theoretical analysis as well as numerical simulations the method is proven to be the most accurate…
In stellar interferometry, image quality improves significantly with the inclusion of more telescopes and the use of phase closure. We demonstrate, using first coherent and then partially coherent white light, a compact and efficient…
A novel iterative algorithm for the efficient computation of the intersection areas of an arbitrary number of circles is presented. The algorithm, based on a trellis-structure, hinges on two geometric results which allow the existence-check…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Two trapped ions that are kilometers apart can be entangled by the joint detection of two photons, each coming from one of the ions, in a basis of entangled states. Such a detection is possible with linear optical elements. The use of…
Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with…