Related papers: Skeletal Rigidity of Phylogenetic Trees

We characterise finite and infinitesimal rigidity for bar-joint frameworks in R^d with respect to polyhedral norms (i.e. norms with closed unit ball P a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be…

Two-dimensional (2D) origami tessellations such as the Miura-ori are often generalized to build three-dimensional (3D) architected materials with sandwich or cellular structures. However, such 3D blocks are densely packed with continuity of…

In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…

We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two…

Controlling the connectivity and rigidity of kirigami, i.e. the process of cutting paper to deploy it into an articulated system, is critical in the manifestations of kirigami in art, science and technology, as it provides the resulting…

The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials.…

This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural…

We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks…

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…

The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although…

Origami, which transforms flat sheets into three-dimensional shapes through folding patterns, has inspired the emergence of deployable systems in architecture and civil realms. Most existing origami-inspired deployable systems are based on…

Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is…

We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…

Thin sheets can be assembled into tubular origami structures that combine deployability with pronounced anisotropic stiffness, enabling applications ranging from robotics to deployable systems. However, most existing tubular origami designs…

Phylogenetic trees constitute an interesting class of objects for stochastic processes due to the non-standard nature of the space they inhabit. In particular, many statistical applications require the construction of Markov processes on…

A suffix tree is a data structure used mainly for pattern matching. It is known that the space complexity of simple suffix trees is quadratic in the length of the string. By a slight modification of the simple suffix trees one gets the…

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…

We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as…

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…