相关论文: The ideal trefoil knot
Using exact continuous quantum Monte Carlo techniques, we study the zero and finite temperature properties of a system of harmonically trapped one dimensional spin 1/2 fermions with short range interactions. Motivated by experimental…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly…
Two distinct knots are said to be friends if their complements, filled along the 0-slope, produce diffeomorphic 3-manifolds. In this article, we develop a practical algorithm, implemented using SnapPy and Regina, to search for a friend of a…
The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out the knot in three dimensional space without self-overlap, colloquially the minimum amount of rope needed to tie a given knot. Theoretical upper…
Knot theory is the Mathematical study of knots. In this paper we have studied the Composition of two knots. Knot theory belongs to Mathematical field of Topology, where the topological concepts such as topological spaces, homeomorphisms,…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications. Existing unsupervised network alignment methods find suboptimal alignments that break up node…
Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…
The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real space renormalization group (RG) scheme. Numerically approximate…
A theoretical description of the radial density profile for charged particles with Yukawa interaction in a harmonic trap is described. At strong Coulomb coupling shell structure is observed in both computer simulations and experiments.…
The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory…
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…
One of the purposes in this paper is to provide a better understanding of the alternance property which occurs in Chebyshev polynomial approximation and piecewise polynomial approximation problems. In the first part of this paper, we…
Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…
We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
The trunk of a knot in $S^3$, defined by Makoto Ozawa, is a measure of geometric complexity similar to the bridge number or width of a knot. We prove that for any two knots $K_1$ and $K_2$, we have $tr(K_1 \# K_2) =…