Related papers: Singularities of Hinge Structures
Lattice-model simulations and experiments of some small proteins suggest that folding is essentially controlled by a few conserved contacts. Residues of these conserved contacts form the minimum set of native contacts needed to ensure…
The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…
This paper investigates the hanging chain problem in the simply isotropic plane as well as its 2-dimensional analog in the simply isotropic space. The simply isotropic plane and space are two- and three-dimensional geometries equipped with…
Two planar embedded circle patterns with the same combinatorics and the same intersection angles can be considered to define a discrete conformal map. We show that two locally finite circle patterns covering the unit disc are related by a…
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously…
We show that relativistic strings of open and closed types in Minkowski space-time of dimension 3 and 4 have topologically stable singular points. This paper describes the structure of singularities, derives their normal forms, and…
We review properties of affine special Kaehler structures focusing on singularities of such structures in the simplest case of real dimension two. We describe all possible isolated singularities and compute the monodromy of the flat…
Although buckling is a prime route to achieve functionalization and synthesis of single colloids, buckling of colloidal structures---made up of multiple colloids---remains poorly studied. Here, we investigate the buckling of the simplest…
Protein structure is generally conceptualized as the global arrangement or of smaller, local motifs of helices, sheets, and loops. These regular, recurring secondary structural elements have well-understood and standardized definitions in…
We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint,…
We investigate point-line geometries whose singular subspaces correspond to binary equidistant codes. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial…
This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to…
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…
In this work the dynamics of a freely jointed random chain with small masses attached to the joints is studied from a microscopic point of view. The chain is treated using a stringy approach, in which a statistical sum is performed over all…
We develop a correspondence between the structure of Turing machines and the structure of singularities of real analytic functions, based on connecting the Ehrhard-Regnier derivative from linear logic with the role of geometry in Watanabe's…
A small fraction of all protein structures characterized so far are entangled. The challenge of understanding the properties of these knotted proteins, and the why and the how of their natural folding process, has been taken up in the past…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and "tennis racket" shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important…
In simple models side chains are often represented implicitly (e.g., by spin-states) or simplified as one atom. We study side chain effects using square lattice and tetrahedral lattice models, with explicitly side chains of two atoms. We…