Related papers: Minimal distance transformations between links and…
We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…
Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…
We study expansion/contraction properties of some common classes of mappings of the Euclidean space ${\mathbb R}^n, n\ge 2\,,$ with respect to the distance ratio metric. The first main case is the behavior of M\"obius transformations of the…
The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the…
The conformational complexity of linear polymers far exceeds that of point-like atoms and molecules. Polymers can bend, twist, even become knotted. Thus they may also display a much richer phase structure than point particles. But it is not…
An important application of distance geometry to biochemistry studies the embeddings of the vertices of a weighted graph in the three-dimensional Euclidean space such that the edge weights are equal to the Euclidean distances between…
A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…
The paper introduces a special case of the Euclidean distance matrix completion problem (edmcp) of interest in statistical data analysis where only the minimal spanning tree distances are given and the matrix completion must preserve the…
Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of…
Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most phenomenological models of the unfolding process are two-state and/or one dimensional, with the details of the…
The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
Two ring polymers close to each other in space may be either in a segregated phase if there is a strong repulsion between monomers in the polymers, or intermingle in a mixed phase if there is a strong attractive force between the monomers.…
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…
We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a…