Related papers: Graphical composition of mapping spaces between mo…
This paper studies the configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that,…
We define and study exact, efficient representations of realization spaces of a natural class of underconstrained 2D Euclidean Distance Constraint Systems(EDCS) or Frameworks based on 1-dof Henneberg-I graphs. Each representation…
The classifying space of the embedded cobordism category has been identified in by Galatius, Tillmann, Madsen, and Weiss as the infinite loop space of a certain Thom spectrum. This identifies the set of path components with the classical…
A framework and method are proposed for the study of constituent composition in fMRI. The method produces estimates of neural patterns encoding complex linguistic structures, under the assumption that the contributions of individual…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift of the usual functor of $R$-chains and the…
We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes. We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V |--> emb(V,N) from the poset O of open subsets of M…
The functor that takes a manifold to its configuration category exhibits a type of full faithfulness in some cases.
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph…
The paper gives an explicit description of the Weiss embedding tower in terms of spaces of maps of truncated modules over the framed Fulton-MacPherson operad.
Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…
We give a complete combinatorial description of the bifurcation structure in the space of exponential maps $z\mapsto\exp(z)+\kappa$. This combinatorial structure is the basis for a number of important results about exponential parameter…
Mapping spaces of supermanifolds are usually thought as exclusively in functorial terms (i.e. trough the Grothendieck functor of points). In this work we provide a geometric description of such mapping spaces in terms of…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
We compare two combinatorial models for the moduli space of two-dimensional cobordisms: B\"odigheimer's radial slit configurations and Godin's admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map.…