Related papers: Medial/skeletal linking structures for multi-regio…
The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal…
Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's equations, on the…
We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…
Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…
We introduce techniques for analysing the structure of quantum states of many-body localized (MBL) spin chains by identifying correlation clusters from pairwise correlations. These techniques proceed by interpreting pairwise correlations in…
Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement.…
Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization. Specifically, accounting for knowledge of anatomical pathways connecting brain regions should lead to desirable outcomes such…
We revisit the concept of minimal rigidity as applied to soft repulsive, frictionless sphere packings in two-dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's…
We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…
Food webs, networks of feeding relationships among organisms, provide fundamental insights into mechanisms that determine ecosystem stability and persistence. Despite long-standing interest in the compartmental structure of food webs, past…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Table structure recognition is a challenging task due to the various structures and complicated cell spanning relations. Previous methods handled the problem starting from elements in different granularities (rows/columns, text regions),…
The work proposes an image segmentation algorithm that isolates slender regions in three-dimensional microstructures. Characterizing slender regions in material microstructures is an extremely important aspect in material science because…
Skeletal polyhedra are discrete connected structures consisting of finite (planar or skew) or infinite (linear, planar, or spatial) polygons as faces, with two faces on each edge and a circular vertex figure at each vertex. The present…
Networks often exhibit structure at disparate scales. We propose a method for identifying community structure at different scales based on multiresolution modularity and consensus clustering. Our contribution consists of two parts. First,…
The choice of structural resolution is a fundamental aspect of protein modelling, determining the balance between descriptive power and interpretability. Although atomistic simulations provide maximal detail, much of this information is…
We study the cohomology of spaces of string links and braids in $\mathbb{R}^n$ for $n\geq 3$ using configuration space integrals. For $n>3$, these integrals give a chain map from certain diagram complexes to the deRham algebra of…
Shape had been intuitively recognized to play a dominant role in determining the global motion patterns of bio-molecular assemblies. However, it is not clear exactly how shape determines the motion patterns. What about the local…
A multiple group rack is a rack which is a disjoint union of groups equipped with a binary operation satisfying some conditions. It is used to define invariants of spatial surfaces, i.e., oriented compact surfaces with boundaries embedded…