Related papers: Locked and Unlocked Polygonal Chains in 3D

Shape change enables new capabilities for robots. One class of robots capable of dramatic shape change is soft growing "vine" robots. These robots usually feature global actuation methods for bending that limit them to simple,…

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…

To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a…

Given any two convex polyhedra P and Q, we prove as one of our main results that the surface of P can be reshaped to a homothet of Q by a finite sequence of "tailoring" steps. Each tailoring excises a digon surrounding a single vertex and…

A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…

The shape of a polymer plays an important role in determining its interactions with other molecules and with the environment, and is in turn affected by both of them. As a consequence, in the literature the shape properties of a chain in…

This article demonstrates that convolutional operation can be converted to matrix multiplication, which has the same calculation way with fully connected layer. The article is helpful for the beginners of the neural network to understand…

Given a plane graph $G$ (i.e., a planar graph with a fixed planar embedding) and a simple cycle $C$ in $G$ whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar…

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized…

Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model,…

Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…

We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q "lives on a cone" to both sides; it includes simple,…

We present an algorithm that enumerates and classifies all edge-to-edge gluings of unit squares that correspond to convex polyhedra. We show that the number of such gluings of $n$ squares is polynomial in $n$, and the algorithm runs in time…

Visibility graph reconstruction, which asks us to construct a polygon that has a given visibility graph, is a fundamental problem with unknown complexity (although visibility graph recognition is known to be in PSPACE). We show that two…

We discuss the problem of embedding univalent functions into Loewner chains in higher dimension. In particular, we prove that a normalized univalent map of the ball in $\C^n$ whose image is a smooth strongly pseudoconvex domain is…

To push a vertex $v$ of a directed graph $\overrightarrow{G}$ is to change the orientations of all the arcs incident with $v$. An oriented graph is a directed graph without any cycle of length at most 2. An oriented clique is an oriented…

We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…

This paper investigated the problem of embedding a simple Hamiltonian Cycle with n vertices on n points inside a simple polygon. This problem seeks to embed a straight-line cycle (without bends), which does not intersect either itself or…

Curvilinear structures are present in various fields in image processing such as blood vessels in medical imaging or roads in remote sensing. Their detection is crucial for many applications. In this article, we propose an unsupervised…

We consider the escape of a flexible, self-avoiding polymer chain out of a confined geometry. By means of simulations, we demonstrate that the translocation time can be described by a simple scaling law that exhibits a nonlinear dependence…