We investigate the problem ol embedding graphs in boob. A book is some number or halfplanes (the page• or the book), which share a common line as boundary (the qine or the book). A book embedding or a graph embeds the vertices on the spine in some order and embeds each edge in some page so that in each page no two edges intersect. The pagenumber ol a graph is the number or pages in a minimum-pa...

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a cycle in the graph. The strong embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected graph without V8 (the M obius 4-ladder) as a minor has a closed 2-cell embedding in some surface. As a c...

Purpose Experiments are the backbone of development process data-driven predictive models for scientific applications. The quality experiments directly impacts model performance. Uncertainty inherently affects experiment measurements and is often missing in available data sets due to its estimation cost. For similar reasons, very few compared other sources. Discarding based on uncertainty value...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 December 2020Accepted: 23 February 2021Published online: 04 November 2021Keywordsdeep neural networks, high-dimensionality, latent space, similarity, uncertainty quantification, intrinsic dimension, graph embedding at scaleAMS Subject Headings68T07, 05C62, 94A15, 68T37...

Despite the importance and abundance of temporal knowledge graphs, most current research has been focused on reasoning static graphs. In this paper, we study challenging problem inference over particular, task link prediction. general, is a difficult due to data non-stationarity, heterogeneity, its complex dependencies. We propose Chronological Rotation embedding (ChronoR), novel model for lear...

In this work, we propose a novel Knowledge Graph Embedding (KGE) strategy, called M\"{o}biusE, in which the entities and relations are embedded to surface of M\"{o}bius ring. The proposition such strategy is inspired by classic TorusE, addition two arbitrary elements subject modulus operation. sense, TorusE naturally guarantees critical boundedness embedding vectors KGE. However, nonlinear prop...

In a closed 2-cell embedding of a graph each face is homeomorphic to an open disk and is bounded by a cycle in the graph. The Orientable Strong Embedding Conjecture says that every 2-connected graph has a closed 2-cell embedding in some orientable surface. This implies both the Cycle Double Cover Conjecture and the Strong Embedding Conjecture. In this paper we prove that every 2-connected proje...