Embedding oriented graphs in books

A book consists of a line L in [special characters omitted]3, called the spine, and a collection of half planes, called pages, whose common boundary is L. A k-book is book with k pages. A k-page book embedding is a continuous one-to-one mapping of a graph G into a book such that the vertices are mapped into L and the edges are each mapped to either the spine or a particular page, such that no two edges cross in any page. Each page contains a planar subgraph of G. The book thickness, denoted bt(G), is the minimum number of pages for a graph to have a k-page book embedding. We focus on oriented graphs, and propose a new way to embed oriented graphs into books, called an oriented book embedding, and define oriented book thickness . We investigate oriented graphs having oriented book thickness k using k-page critical oriented graphs, oriented graphs with oriented book thickness equal to k, but, for each arc, the deletion of that arc yields an oriented graph with oriented book thickness equal to k –1. We discuss several classes of two-page critical oriented graphs, and use them to characterize oriented graphs with oriented book thickness equal to one that are strictly uni-dicyclic graphs, oriented graphs having exactly one cycle, which is a directed cycle. We give a similar result for strictly bi-dicyclic graphs, oriented graphs having exactly two cycles, which are directed cycles

Modelling knowledge in Electronic Study Books

Knowledge graphs are a new form of knowledge representation. They are closely related to semantic networks and can be looked upon as in line with Schank's conceptual dependency theory and Sowa's conceptual graphs. The special feature of knowledge graphs is the use of a very restricted set of types of relations, that is considered to be the basic set of primitive relations. The theory of knowledge graphs is outlined in the first part of the paper. In the second part the possibilities of knowledge graphs for solving problems posed by Electronic (Study) Books will be discussed

Ripple Knowledge Graph Convolutional Networks For Recommendation Systems

Using knowledge graphs to assist deep learning models in making recommendation decisions has recently been proven to effectively improve the model's interpretability and accuracy. This paper introduces an end-to-end deep learning model, named RKGCN, which dynamically analyses each user's preferences and makes a recommendation of suitable items. It combines knowledge graphs on both the item side and user side to enrich their representations to maximize the utilization of the abundant information in knowledge graphs. RKGCN is able to offer more personalized and relevant recommendations in three different scenarios. The experimental results show the superior effectiveness of our model over 5 baseline models on three real-world datasets including movies, books, and music

Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages

An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum number of pages over all its book embeddings. For planar graphs, a fundamental result is due to Yannakakis, who proposed an algorithm to compute embeddings of planar graphs in books with four pages. Our main contribution is a technique that generalizes this result to a much wider family of nonplanar graphs, which is characterized by a biconnected skeleton of crossing-free edges whose faces have bounded degree. Notably, this family includes all 1-planar and all optimal 2-planar graphs as subgraphs. We prove that this family of graphs has bounded book thickness, and as a corollary, we obtain the first constant upper bound for the book thickness of optimal 2-planar graphs

Academia/Industry DynAmics (AIDA): A knowledge Graph within the scholarly domain and its applications

Scholarly knowledge graphs are a form of knowledge representation that aims to capture and organize the information and knowledge contained in scholarly publications, such as research papers, books, patents, and datasets. Scholarly knowledge graphs can provide a comprehensive and structured view of the scholarly domain, covering various aspects such as authors, affiliations, research topics, methods, results, citations, and impact. Scholarly knowledge graphs can enable various applications and services that can facilitate and enhance scholarly communication, such as information retrieval, data analysis, recommendation systems, semantic search, and knowledge discovery. However, constructing and maintaining scholarly knowledge graphs is a challenging task that requires dealing with large-scale, heterogeneous, and dynamic data sources. Moreover, extracting and integrating the relevant information and knowledge from unstructured or semi-structured text is not trivial, as it involves natural language processing, machine learning, ontology engineering, and semantic web technologies. Furthermore, ensuring the quality and validity of the scholarly knowledge graphs is essential for their usability and reliability

Recommendations for Your Data Visualization Bookshelf

Over the years that I’ve been involved in data visualization, I have collected a number of books on the topic. Not every book in my library is great, but a few stand out as particularly useful for businesspeople who wish to become experts in using visualizations to analyze and communicate quantitative data. I have intentionally not included most of the books that focus on the visualization needs of scientists and statisticians. A few books that venture in this direction have been included, however, because they provide a great deal of general content that is extremely worthwhile, such as those by Edward Tufte and William Cleveland. Fundamentals of Graph Design I will begin the list with those books that cover the fundamentals of graph design for the communication of quantitative business information. Even though it will appear self-promoting, I unapologetically recommend my own book, Show Me the Numbers: Designing Tables and Graphs to Enlighten, as the best available resource on the design of graphs (and tables) for communicating quantitative business information. As someone who has been involved in the business intelligence industry for many years, I am intimately aware of the needs of businesspeople who must make sense of quantitativ

Kids Count Alaska 2009-2010

For information on children across America, visit the Kids Count Data Center (www.datacenter.kidscount.org). Developed by the national KIDS COUNT program, the site provides data on children and teenagers for every state and hundreds of cities and counties. For Alaska, you can select indicators for each of the state’s seven regions and create your own maps, trend lines, and charts. There are also maps and graphs you can put on your website or blog. You can go directly to that national site or link from our website (kidscount.alaska.edu). This book and all previous data books are available on our website, with each book divided into sections for faster downloading. Also on our site is a link to the most recent national KIDS COUNT data book, as well as other publications and reports.Annie E. Casey FoundationIntroduction / Infancy / Economic Well-Being / Education / Children in Danger / Juvenile Justic

Diagnostics in Colorectal Surgery

The rapid development in radiological examinations has opened a new chapter in colorectal surgery. Unlike classical books, in this section we preferred to use more modern and everyday practical methods such as endoscopy or magnetic resonance imaging or endorectal ultrasonography, rather than sparing less used examinations such as X-rays and barium graphs