相关论文: Circle arrangements of link projections

We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation $I$-bundles over closed but not necessarily orientable surfaces. We call these twisted links, and show that they subsume the…

For a fixed radius $r$ and a point $o$ in the curve complex of a surface, we define the sphere of radius $r$ to be the induced subgraph on the set of vertices of distance $r$ from $o$. We show that these spheres are almost simply connected…

We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of…

This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…

From classical knot theory we know that every knot in $S^3$ is the boundary of an oriented, embedded surface. A standard demonstration of this fact achieved by elementary technique comes from taking a regular projection of any knot and…

We give a shorter and simpler proof of the result of [2], which gives a necessary and sufficient condition for when a lattice diagram is the projection of a lattice link.

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…

We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if $p$ is a positive contraction in an operator system $V$ which satisfies certain…

The double orthogonal projection of the 4-space onto two mutually perpendicular 3-spaces is a method of visualization of four-dimensional objects in a three-dimensional space. We present an interactive animation of the stereographic…

Link prediction is a paradigmatic problem in network science, which aims at estimating the existence likelihoods of nonobserved links, based on known topology. After a brief introduction of the standard problem and metrics of link…

Rectangular diagrams of links are link diagrams in the plane ${\mathbb R}^2$ such that they are composed of vertical line segments and horizontal line segments and vertical segments go over horizontal segments at all crossings. P. R.…

Bipartite networks are a well known strategy to study a variety of phenomena. The commonly used method to deal with this type of network is to project the bipartite data into a unipartite weighted graph and then using a backboning technique…

It is well-known that all 2-knots are slice. Are all 2-links slice? This is an outstanding open question. In this paper we prove the following: For any 2-component 2-link (J,K)in the 4-sphere which bounds the 5-ball B^5, there is an…

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…

A system of particles with motility variable in terms of a vision-type of perception is here investigated by a combination of Langevin dynamics simulations in two-dimensional systems and an analytical approach based on conservation law…

Alignments are a well-known process mining technique for reconciling system logs and normative process models. Evidence of certain behaviors in a real system may only be present in one representation - either a log or a model - but not in…

It is well known that the edge vector space of an oriented graph can be decomposed in terms of cycles and cocycles (alias cuts, or bonds), and that a basis for the cycle and the cocycle spaces can be generated by adding and removing edges…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a…

A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…