Molecular configurations can be modeled as sets of spheres in 3D. By imposing geometric constraints on the spheres based on molecular biology one can apply efficient techniques [3], for example, to analyze the complexity of molecular surface [1]. Guibas et al. [2] introduced a model called necklace that finds applications in computer graphics, computer vision, robotics, geographic information s...

Abstract We introduce a new technique to prove connectivity of subsets covering spaces (so called inductive connectivity), and apply it Galois theory problems enumerative geometry. As model example, consider the problem permuting roots complex polynomial $$f(x) = c_0 + c_1 x^{d_1} \cdots c_k x^{d_k}$$ f <mml:m...

In many advanced segmentation problems objects have inhomogeneous boundaries, hindering segmentation under uniform boundary assumption. We present a multifeature image segmentation method, called necklaces, that exploits local inhomogeneities to reduce the complexity of the segmentation problem. Multiple continuous boundary features, deduced from a set of training objects, are statistically ana...

A connected graph G is caterpillar-pure if each spanning tree of G is a caterpillar. The caterpillar-pure graphs are fully characterized. Loosely speaking they are strings or necklaces of so-called pearls, except for a number of small exceptional cases. An upper bound for the number of edges in terms of the order is given for caterpillar-pure graphs, and those which attain the upper bound are c...

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from [L] about the rigidification...