Supramolecular Shish Kebabs: Higher Order Dimeric Structures from Ring‐in‐Rings Complexes with Conformational Adaptivity

A general route to nanocrystal kebabs periodically assembled on stretched flexible polymer shish.

Assembling nanoparticles into one-dimensional (1D) nanostructures with precisely controlled size and shape renders the exploration of new properties and construction of 1D miniaturized devices possible. The physical properties of such nanostructures depend heavily on the size, chemical composition, and surface chemistry of nanoparticle constituents, as well as the close proximity of adjacent na...

Protein conformational space in higher order - maps

We have mapped protein conformational space from two to seven residue lengths by employing multidimensional scaling on a data matrix composed of pair-wise angular distances for multiple values collected from high-resolution protein structures. The resulting global maps show clustering of peptide conformations that reveals a dramatic reduction of conformational space as sampled by experimentally...

Dimeric Complexes of Tryptophan with M

Higher order Hessian structures on manifolds

In this paper we define nth order Hessian structures on manifolds and study them. In particular, when n = 3, we make a detailed study and establish a one-to-one correspondence between third-order Hessian structures and a certain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on th...

Ranking Users in Social Networks with Higher-Order Structures

PageRank has been widely used to measure the authority or the influence of a user in social networks. However, conventional PageRank only makes use of edge-based relations, ignoring higher-order structures captured by motifs, subgraphs consisting of a small number of nodes in complex networks. In this paper, we propose a novel framework, motif-based PageRank (MPR), to incorporate higher-order s...