相关论文: Juggling braids and links

When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…

The aim of the paper is to clarify the nature of combinatorial structures associated with maps on closed compact surfaces. We prove that maps give rise to Lagrangian matroids representable in a setting provided by cohomology of the surface…

We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly $(d+1)$-colored) triangulation of a combinatorial $d$-manifold into another balanced triangulation. These moves form a natural analog of bistellar…

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating)…

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…

We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding…

We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By…

Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…

This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a…

Let $\Gamma$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\Gamma$ on the circle is either trivial or semi-conjugate to a unique minimal action on the so-called simple circle.

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…

We show that if two tensor algebras of topological graphs are algebraically isomorphic, then the graphs are locally conjugate. Conversely, if the base space is at most one dimensional and the edge space is compact, then locally conjugate…

The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph and a matching. We show that this conjecture holds for the class of connected plane cubic graphs.

It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.

A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…

We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some…

The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…

In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.