Related papers: Hypercube emulation of interconnection networks to…
A Fibonacci string is a length n binary string containing no two consecutive 1s. Fibonacci cubes (FC), Extended Fibonacci cubes (ELC) and Lucas cubes (LC) are subgraphs of hypercube defined in terms of Fibonacci strings. All these cubes…
This tutorial covers a few recent papers in the field of network embedding. Network embedding is a collective term for techniques for mapping graph nodes to vectors of real numbers in a multidimensional space. To be useful, a good embedding…
We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…
In the parallel processing field, graph embedding is motivated by simulation interconnection networks to another. The quadtree is an important technique used to present spatial data and is used in many application domains, especially…
We describe an infinite family of edge-decompositions of complete graphs into two graphs, each of which triangulate the same orientable surface. Previously, such decompositions had only been known for only a few complete graphs. These…
The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
Networks found in the real-world are numerous and varied. A common type of network is the heterogeneous network, where the nodes (and edges) can be of different types. Accordingly, there have been efforts at learning representations of…
We explore in depth how categorical data can be processed with embeddings in the context of claim severity modeling. We develop several models that range in complexity from simple neural networks to state-of-the-art attention based…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…
We introduce $(k,l)$-regular maps, which generalize two previously studied classes of maps: affinely $k$-regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be…
The embeddings of complex plane projective curves in the plane are a cornerstone of the topological study of algebraic varieties. In this work, we deal with the local and global aspects of these embeddings, with a special attention to its…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical…
In this paper we discuss two different existing algorithms for computing topological entropy and we perform one of them in order to compute the isentropes for cubic polynomials.