Article
Mathematics, Applied
Gabriele Di Stefano
Summary: This paper studies mutual visibility in undirected graphs and introduces the Mutual-Visibility problem. It is shown that the Mutual-Visibility problem is NP-complete, but checking whether a given set of points is a mutual-visibility set is solvable in polynomial time. Special classes of graphs, like block graphs, trees, grids, tori, complete bipartite graphs, and cographs, are studied in terms of mutual-visibility sets and numbers.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Weiting Cao, Douglas B. West, Yan Yang
Summary: The T-bar visibility representation assigns each vertex of a graph up to t horizontal bars in the plane, with two vertices being adjacent if one bar can see another bar through an unobstructed vertical channel. The bar visibility number of G, denoted by b(G), is the least t such that G has a t-bar visibility representation. The equality of the lower bound for the complete bipartite graph K-m,K-n from Euler's formula is proven to hold.
SIAM JOURNAL ON DISCRETE MATHEMATICS
(2021)
Article
Computer Science, Artificial Intelligence
Yusheng Huang, Xiaoyan Mao, Yong Deng
Summary: The degree sequence of the NVG transformation provides useful motif information for practical usage, as shown in a study on stock trend prediction. The proposed natural visibility encoding and moving window strategy have been proven effective and robust in classifying time series. Further investigation into the degree sequence of the NVG transformation is encouraged based on the success of the proposed framework.
KNOWLEDGE-BASED SYSTEMS
(2021)
Article
Physics, Fluids & Plasmas
H. Masoomy, V. Adami, M. N. Najafi
Summary: Centrality measures play a fundamental role in classifying complex networks, and the maximal b-k exponent for scale-free networks is found to be 2. However, this conjecture is proven to be invalid for some correlated time series, such as the BTW model and FBM. The failure of the conjecture is attributed to large fluctuations in the scaling b-k relation, resulting in emergent anomalous behavior.
Article
Computer Science, Information Systems
Musrrat Ali, Sanoj Kumar, Rahul Pal, Manoj K. Singh, Deepika Saini
Summary: Texture analysis is an important task in image processing and computer vision. This paper proposes a method for texture classification using graphs, specifically the natural and horizontal visibility graphs. The suggested method outperforms traditional techniques and even approaches the performance of convolutional neural networks. The results show the potential of graph methods for texture classification.
Article
Mathematics, Interdisciplinary Applications
Weikai Ren, Zhijun Jin
Summary: In this study, a topological approach is introduced to quantify the dynamical complexity of time series. A novel complex network of visibility graph family is proposed based on defining visibility algorithm in phase space. The statistical properties of the constructed network show powerful potentiality for distinguishing stochastic and chaotic systems. For some remarkable chaotic systems, it allows for quantitative correspondence with Lyapunov exponents. The potential practical application of this approach is demonstrated on the multiphase flow system and bearing fault identification.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Sadegh Sulaimany, Aso Mafakheri
Summary: This research proposes a method to convert web server log files into horizontal visibility graphs, and demonstrates its application on popular datasets. It also introduces a web prefetching algorithm based on the extracted visibility graph and evaluates its performance. Furthermore, several choices for extending the research are proposed.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Psychology, Multidisciplinary
Fang Zhao, Robert Gaschler
Summary: The study showed that graph schemas are based on a common invariant structure rather than a specific schema for each graph. Tally charts were found to be more efficient for group comparison compared to bar graphs, and processing time increased with greater differences in the positions of compared groups.
FRONTIERS IN PSYCHOLOGY
(2021)
Review
Neurosciences
Sadegh Sulaimany, Zhino Safahi
Summary: In the past two decades, network-based analysis has gained significant attention for analyzing time series data in various fields. The visibility graph (VG) approach, widely used in transforming time series data into graphs or networks, has extensive applications in comprehending, identifying, and predicting specific characteristics of time series data. This research presents a scoping review of scholarly articles focusing on VG-based analysis methods related to brain disorders, aiming to provide a foundation for future research and exploration. The study conducted a systematic search and analysis of 51 selected articles, covering publication years, types of VG used, rationale for utilization, machine learning algorithms employed, frequently occurring keywords, top authors and universities, evaluation metrics, applied network properties, and brain disorders examined. Recommendations for future advancements were also provided, including the utilization of cutting-edge techniques like graph machine learning and deep learning, as well as exploring understudied medical conditions such as attention deficit hyperactivity disorder and Parkinson's disease.
FRONTIERS IN NEUROSCIENCE
(2023)
Article
Engineering, Biomedical
Chen Kan, Zehao Ye, Houliang Zhou, Sreekanth R. Cheruku
Summary: Representation learning of electrocardiogram (ECG) has been an active research field for the automated detection of cardiac disease. Many deep learning models are deployed as blackboxes without fully exploring disease-pertinent information hidden in the signal. To address this problem, we develop a new multi-stream deep graph learning of ECG (DG-ECG) framework, which integrates multi-stream graph neural networks to uncover disease-altered ECG patterns from multifold perspectives. Experimental results have demonstrated that the developed DG-ECG is better capable of gleaning disease-pertinent information from multi-channel ECG signals compared to benchmark models.
BIOMEDICAL SIGNAL PROCESSING AND CONTROL
(2023)
Article
Environmental Sciences
Qunzhao Li, Fei Xie, Jing Zhao, Bing Xu, Jiquan Yang, Xixiang Liu, Hongbo Suo
Summary: This paper proposes a path planner based on the visibility graph (v-graph) for mobile robots, which uses sparse methods to speed up and simplify the construction of the v-graph. The proposed method improves the efficiency and accuracy in complex environments.
Article
Computer Science, Interdisciplinary Applications
Zhiyong Zhou, Robert Weibel, Kai-Florian Richter, Haosheng Huang
Summary: This article proposes a hierarchical indoor visibility-based graph (HiVG) and its generation algorithm for navigation guidance in multi-storey buildings, demonstrating its potential and applicability through experiments and case studies.
COMPUTERS ENVIRONMENT AND URBAN SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Ali Olamat, Pinar Ozel, Aydin Akan
Summary: This study introduces a new method based on graph analysis and statistical rescale range analysis to assess and interpret the changes in EEG recordings from different brain regions in epilepsy disorders. The analysis reveals an increase in motif persistence during the seizure phase, indicating increased synchronization. The findings suggest that the new method is in good agreement with existing approaches and is more efficient. The most significant contribution of this research is the introduction of a novel nonlinear analysis technique called generalized synchronization.
INTERNATIONAL JOURNAL OF NEURAL SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Haci Ismail Aslan, Chang Choi
Summary: Biometric information, such as an individual's electrocardiogram (ECG), is extensively used in the field of cybersecurity for authentication schemes. The VisGIN model, which utilizes Graph Neural Networks (GNN) and Visibility Graphs (VG), shows promising results in ECG authentication, achieving an average classification accuracy of 99.76%. This study provides a valuable advancement in enhancing the security and reliability of authentication systems.
EXPERT SYSTEMS WITH APPLICATIONS
(2024)
Article
Mathematics
Omer Akguller, Mehmet Ali Balci, Larissa M. Batrancea, Lucian Gaban
Summary: Using networks to analyze time series has become popular, where individual time series are mapped to visibility graphs. The Borsa Istanbul 100 (BIST 100) companies' market visibility graphs were collected for analysis. A novel kernel function of the visibility graphs was constructed to account for local extreme values. Sector-level and sector-to-sector analyses were conducted using this metric, including the COVID-19 crisis period in the study's dataset. The findings indicate the development of an effective strategy for analyzing financial time series.
Article
Mathematics
John Caughman, John Krussel, James Mahoney
GRAPHS AND COMBINATORICS
(2017)
Article
Mathematics
Louis Anthony Agong, Carmen Amarra, John S. Caughman, Ari J. Herman, Taiyo S. Terada
DISCRETE MATHEMATICS
(2018)
Article
Mathematics
John S. Caughman, Elizabeth J. Hart, Jianmin Ma
DISCRETE MATHEMATICS
(2008)
Article
Mathematics
John S. Caughman, Clifford R. Haithcock, J. J. P. Veerman
DISCRETE MATHEMATICS
(2008)
Article
Mathematics
John S. Caughman, Charles Lundon, Nancy Ann Neudauer, Colin L. Starr
DISCRETE MATHEMATICS
(2011)
Article
Mathematics, Applied
Peter Banda, John Caughman, Martin Cenek, Christof Teuscher
Article
Multidisciplinary Sciences
Ari Herman, John Caughman
Summary: The paper demonstrates that Zermelo-Fraenkel set theory with Choice conflicts with basic intuitions about randomness, showing contradiction between a weak form of Choice and common sense assumptions about probability based on symmetry and independence.
Article
Education & Educational Research
Elise Lockwood, John S. Caughman, Keith Weber
EDUCATIONAL STUDIES IN MATHEMATICS
(2020)
Proceedings Paper
Automation & Control Systems
Rahul Dhal, Gerardo Lafferriere, John Caughman
2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2016)
Proceedings Paper
Computer Science, Software Engineering
Linh Tran, Addison Gronquist, Marek Perkowski, John Caughman
2016 IEEE 46TH INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC (ISMVL 2016)
(2016)
Article
Mathematics, Applied
Nichole L. Schimanski, John S. Caughman
ELECTRONIC JOURNAL OF COMBINATORICS
(2016)
Article
Computer Science, Theory & Methods
Peter Banda, John Caughman, Jiri Pospichal
JOURNAL OF CELLULAR AUTOMATA
(2015)
Proceedings Paper
Computer Science, Theory & Methods
John S. Caughman, Charles L. Dunn, Joshua D. Laison, Nancy Ann Neudauer, Colin L. Starr
GRAPH DRAWING (GD 2014)
(2014)
Article
Education & Educational Research
Estrella Johnson, John Caughman, Julie Fredericks, Lee Gibson
JOURNAL OF MATHEMATICAL BEHAVIOR
(2013)