White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Graphs on Surfaces and the Partition Function of String Theory
Garcia-Islas, J. Manuel
2007-01-01
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the relation between graph theory and the mathematical physics of discrete string theory. In this description we present problems of the combinatorial world of real importance for graph theorists. The mathematical details of the paper are as follows: There is a com...
Visual exploratory search of relationship graphs on smartphones.
Directory of Open Access Journals (Sweden)
Jianquan Ouyang
Full Text Available This paper presents a novel framework for Visual Exploratory Search of Relationship Graphs on Smartphones (VESRGS that is composed of three major components: inference and representation of semantic relationship graphs on the Web via meta-search, visual exploratory search of relationship graphs through both querying and browsing strategies, and human-computer interactions via the multi-touch interface and mobile Internet on smartphones. In comparison with traditional lookup search methodologies, the proposed VESRGS system is characterized with the following perceived advantages. 1 It infers rich semantic relationships between the querying keywords and other related concepts from large-scale meta-search results from Google, Yahoo! and Bing search engines, and represents semantic relationships via graphs; 2 the exploratory search approach empowers users to naturally and effectively explore, adventure and discover knowledge in a rich information world of interlinked relationship graphs in a personalized fashion; 3 it effectively takes the advantages of smartphones' user-friendly interfaces and ubiquitous Internet connection and portability. Our extensive experimental results have demonstrated that the VESRGS framework can significantly improve the users' capability of seeking the most relevant relationship information to their own specific needs. We envision that the VESRGS framework can be a starting point for future exploration of novel, effective search strategies in the mobile Internet era.
Visual exploratory search of relationship graphs on smartphones.
Ouyang, Jianquan; Zheng, Hao; Kong, Fanbin; Liu, Tianming
2013-01-01
This paper presents a novel framework for Visual Exploratory Search of Relationship Graphs on Smartphones (VESRGS) that is composed of three major components: inference and representation of semantic relationship graphs on the Web via meta-search, visual exploratory search of relationship graphs through both querying and browsing strategies, and human-computer interactions via the multi-touch interface and mobile Internet on smartphones. In comparison with traditional lookup search methodologies, the proposed VESRGS system is characterized with the following perceived advantages. 1) It infers rich semantic relationships between the querying keywords and other related concepts from large-scale meta-search results from Google, Yahoo! and Bing search engines, and represents semantic relationships via graphs; 2) the exploratory search approach empowers users to naturally and effectively explore, adventure and discover knowledge in a rich information world of interlinked relationship graphs in a personalized fashion; 3) it effectively takes the advantages of smartphones' user-friendly interfaces and ubiquitous Internet connection and portability. Our extensive experimental results have demonstrated that the VESRGS framework can significantly improve the users' capability of seeking the most relevant relationship information to their own specific needs. We envision that the VESRGS framework can be a starting point for future exploration of novel, effective search strategies in the mobile Internet era.
Analyzing Social Media Relationships in Context with Discussion Graphs
DEFF Research Database (Denmark)
Kiciman, Emre; Choudhury, Munmun De; Counts, Scott
2013-01-01
We present discussion graphs, a hyper-graph-based representation of social media discussions that captures both the structural features of the relationships among entities as well as the context of the discussions from which they were derived. Building on previous analyses of social media networks....... First, we extend standard hyper-graph representations of networks to include the distribution of contexts surrounding discussions in social media networks. Second, we demonstrate how this context is useful for understanding the results of common graph measures and analyses, such as network centrality...... and pseudo-cliques, when applied to the analysis of textual social media content. We apply our framework across several domains captured in Twitter, including the mining of peoples' statements about their locations and activities and discussions of the U.S. 2012 elections....
Dimers on surface graphs and spin structures. II
DEFF Research Database (Denmark)
Cimasoni, David; Reshetikhin, Nicolai
2009-01-01
In a previous paper [3], we showed how certain orientations of the edges of a graph Γ embedded in a closed oriented surface Σ can be understood as discrete spin structures on Σ. We then used this correspondence to give a geometric proof of the Pfaffian formula for the partition function of the di......In a previous paper [3], we showed how certain orientations of the edges of a graph Γ embedded in a closed oriented surface Σ can be understood as discrete spin structures on Σ. We then used this correspondence to give a geometric proof of the Pfaffian formula for the partition function...... model as a quantum field theory on surface graphs....
Harris, David; Gomez Zwiep, Susan
2013-01-01
Graphs represent complex information. They show relationships and help students see patterns and compare data. Students often do not appreciate the illuminating power of graphs, interpreting them literally rather than as symbolic representations (Leinhardt, Zaslavsky, and Stein 1990). Students often read graphs point by point instead of seeing…
Graph Complexes and the Moduli Space of Riemann Surfaces
DEFF Research Database (Denmark)
Egas Santander, Daniela
In this thesis we compare several combinatorial models for the moduli space of open-closed cobordisms and their compactifications. More precisely, we study Godin's category of admissible fat graphs, Costello's chain complex of black and white graphs, and Bödigheimer's space of radial slit......, that the complex of black and white graphs is a homological model of this mapping class group. Beyond giving new proofs of these results, the methods used give a new interpretation of Costello's model in terms of admissible fat graphs, which is a more classical model of moduli space. This connection could...... potentially allow to transfer constructions in fat graphs to the black and white model. Moreover, we compare Bödigheimer's radial slit configurations and the space of metric admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map. This critical graph map descends...
Graphs of groups on surfaces interactions and models
White, AT
2001-01-01
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English
Graph Complexes and the Moduli Space of Riemann Surfaces
DEFF Research Database (Denmark)
Egas Santander, Daniela
potentially allow to transfer constructions in fat graphs to the black and white model. Moreover, we compare Bödigheimer's radial slit configurations and the space of metric admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map. This critical graph map descends...... to a homeomorphism between the Unimodular Harmonic compactification and the space of Sullivan diagrams, which are natural compactifications of the space of radial slit configurations and the space of metric admissible fat graphs, respectively. Finally, we use experimental methods to compute the homology of the chain......In this thesis we compare several combinatorial models for the moduli space of open-closed cobordisms and their compactifications. More precisely, we study Godin's category of admissible fat graphs, Costello's chain complex of black and white graphs, and Bödigheimer's space of radial slit...
The chromatic number of a graph of girth 5 on a fixed surface
DEFF Research Database (Denmark)
Thomassen, Carsten
2003-01-01
We prove a color extension result implying that, for every fixed surface S, there are only finitely many 4-color-critical graphs of girth 5 on S. The result is best possible in the sense that there are infinitely many 4-color-critical graphs of girth 4 on S, except when S is the sphere, As a cons......, As a consequence, the chromatic number of graphs of girth 5 on S can be found in polynomial time....
Analyzing Intersectorial Water Relationships by means of Graph Theory
Esther Velazquez Alonso
2003-01-01
The aim of this work is to demonstrate the relationships between an economy’s productive sectors and the water consumption generated during productive processes. We shall study the andalusian reality, a region of southern Spain characterized by water scarcity, and we will examine whether excessive dependence on water resources which, may occur in some productive sectors, might affect not only the conservation and quality of this resource, but also have negative effects upon the solidity of th...
DEFF Research Database (Denmark)
Kraft, Peter; Sørensen, Jens Otto
with a unified graphic model is more efficient and less error-prone than working with more complex ER models and models based on lexical description. Key terms: Entity-relationship model, path expressions, entity-relationship language, derived interface view, view updates, graphical models.......Interface Abstract: The paper describes an Entity Relationship (ER) model with a diagrammed schema and extensions modeled into a graph. The semantics of schema symbols are fundamentally simple implying a unified model where given conceptualizations of environments are diagrammed uniquely...
Berg, Craig A.; Phillips, Darrell G.
This study investigates the relationship between logical thinking structures and the ability to construct and interpret line graphs. Seventy-two subjects in 7th, 9th, and 11th grades were administered individual Piagetian tasks to assess five specific mental structures: (Euclidean spatial structures) (a) Placement and Displacement of Objects (maintaining horizontal and vertical reference frames) and (b) One-One Multiplication of Placement and Displacement Relations (coordinate systems); (c) Multiplicative Measurement; (d) Multiplicative Seriation; and (e) Proportional Reasoning. Graphing abilities were assessed by having the subjects construct and interpret numerous graphs of varying content and difficulty. To minimize the researcher's guesses about interpretation, each subject's answers and reasons were subsequently explored during a clinical interview. The results indicate significant relationships of logical thinking to graphing ability. Multiplicative seriation, multiplicative measurement, and Euclidean spatial structures positively influenced graphing abilities. Subjects who showed evidence of proportional reasoning did significantly better on many graphing situations including choosing the part of the graph with the greatest rate of change. Locating points on a graph without a grid was significantly related to horizontal/vertical frames of reference. Students who did not possess the logical thinking structures were more likely to be dependent upon, and influenced by, perceptual cues and less able to interpret or construct graphs correctly.Received: 16 March 1993; Revised: 18 October 1993;
Dimers on Surface Graphs and Spin Structures. I
DEFF Research Database (Denmark)
Cimasoni, David; Reshetikhin, Nicolai
2007-01-01
Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures....
Global spectral graph wavelet signature for surface analysis of carpal bones
Masoumi, Majid; Rezaei, Mahsa; Ben Hamza, A.
2018-02-01
Quantitative shape comparison is a fundamental problem in computer vision, geometry processing and medical imaging. In this paper, we present a spectral graph wavelet approach for shape analysis of carpal bones of the human wrist. We employ spectral graph wavelets to represent the cortical surface of a carpal bone via the spectral geometric analysis of the Laplace-Beltrami operator in the discrete domain. We propose global spectral graph wavelet (GSGW) descriptor that is isometric invariant, efficient to compute, and combines the advantages of both low-pass and band-pass filters. We perform experiments on shapes of the carpal bones of ten women and ten men from a publicly-available database of wrist bones. Using one-way multivariate analysis of variance (MANOVA) and permutation testing, we show through extensive experiments that the proposed GSGW framework gives a much better performance compared to the global point signature embedding approach for comparing shapes of the carpal bones across populations.
Gupta-Ostermann, Disha; Hu, Ye; Bajorath, Jürgen
2012-06-14
A graphical method is introduced for compound data mining and structure-activity relationship (SAR) data analysis that is based upon a canonical structural organization scheme and captures a compound-scaffold-skeleton hierarchy. The graph representation has a constant layout, integrates compound activity data, and provides direct access to SAR information. Characteristic SAR patterns that emerge from the graph are easily identified. The molecular hierarchy enables "forward-backward" analysis of compound data and reveals both global and local SAR patterns. For example, in heterogeneous data sets, compound series are immediately identified that convey interpretable SAR information in isolation or in the structural context of related series, which often define SAR pathways through data sets.
The number of k-colorings of a graph on a fixed surface
DEFF Research Database (Denmark)
Thomassen, Carsten
2006-01-01
with n vertices on S that has precisely c center dot 2(n) distinct 5-colorings. For the sphere the constant c is 15/2, and for each other surface, it is a finite problem to determine c. There is an analogous result for k-colorings for each natural number k > 5. (c) 2006 Elsevier B.V. All rights reserved.......We prove that, for every fixed surface S, there exists a largest positive constant c such that every 5-colorable graph with n vertices on S has at least c center dot 2(n) distinct 5-colorings. This is best possible in the sense that, for each sufficiently large natural number n, there is a graph...
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
Crisp, John; Wiest, Bert
2003-01-01
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) nev...
Generalised power graph compression reveals dominant relationship patterns in complex networks.
Ahnert, Sebastian E
2014-03-25
We introduce a framework for the discovery of dominant relationship patterns in complex networks, by compressing the networks into power graphs with overlapping power nodes. When paired with enrichment analysis of node classification terms, the most compressible sets of edges provide a highly informative sketch of the dominant relationship patterns that define the network. In addition, this procedure also gives rise to a novel, link-based definition of overlapping node communities in which nodes are defined by their relationships with sets of other nodes, rather than through connections within the community. We show that this completely general approach can be applied to undirected, directed, and bipartite networks, yielding valuable insights into the large-scale structure of real-world networks, including social networks and food webs. Our approach therefore provides a novel way in which network architecture can be studied, defined and classified.
International Nuclear Information System (INIS)
Grines, V Z; Pochinka, O V; Kapkaeva, S Kh
2014-01-01
In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces. Bibliography: 25 titles
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Arias Lorza, Andres M; van Engelen, Arna; Petersen, Jens; van der Lugt, Aad; de Bruijne, Marleen
2018-03-01
We present a segmentation method that maximizes regional probabilities enclosed by coupled surfaces using an Optimal Surface Graph (OSG) cut approach. This OSG cut determines the globally optimal solution given a graph constructed around an initial surface. While most methods for vessel wall segmentation only use edge information, we show that maximizing regional probabilities using an OSG improves the segmentation results. We applied this to automatically segment the vessel wall of the carotid artery in magnetic resonance images. First, voxel-wise regional probability maps were obtained using a Support Vector Machine classifier trained on local image features. Then, the OSG segments the regions which maximizes the regional probabilities considering smoothness and topological constraints. The method was evaluated on 49 carotid arteries from 30 subjects. The proposed method shows good accuracy with a Dice wall overlap of 74.1 ± 4.3%, and significantly outperforms a published method based on an OSG using only surface information, the obtained segmentations using voxel-wise classification alone, and another published artery wall segmentation method based on a deformable surface model. Intraclass correlations (ICC) with manually measured lumen and wall volumes were similar to those obtained between observers. Finally, we show a good reproducibility of the method with ICC = 0.86 between the volumes measured in scans repeated within a short time interval. In this work, a new segmentation method that uses both an OSG and regional probabilities is presented. The method shows good segmentations of the carotid artery in MRI and outperformed another segmentation method that uses OSG and edge information and the voxel-wise segmentation using the probability maps. © 2018 American Association of Physicists in Medicine.
Seiller, Thomas
2014-01-01
In two previous papers, we exposed a combinatorial approach to the program of Geometry of Interaction, a program initiated by Jean-Yves Girard. The strength of our approach lies in the fact that we interpret proofs by simpler structures - graphs - than Girard's constructions, while generalizing the latter since they can be recovered as special cases of our setting. This third paper extends this approach by considering a generalization of graphs named graphings, which is in some way a geometri...
Bektasli, Behzat
Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking
Jones, Jonathan-Lee; Essa, Ehab; Xie, Xianghua
2015-01-01
We present a novel method to segment the lymph vessel wall in confocal microscopy images using Optimal Surface Segmentation (OSS) and hidden Markov Models (HMM). OSS is used to preform a pre-segmentation on the images, to act as the initial state for the HMM. We utilize a steerable filter to determine edge based filters for both of these segmentations, and use these features to build Gaussian probability distributions for both the vessel walls and the background. From this we infer the emission probability for the HMM, and the transmission probability is learned using a Baum-Welch algorithm. We transform the segmentation problem into one of cost minimization, with each node in the graph corresponding to one state, and the weight for each node being defined using its emission probability. We define the inter-relations between neighboring nodes using the transmission probability. Having constructed the problem, it is solved using the Viterbi algorithm, allowing the vessel to be reconstructed. The optimal solution can be found in polynomial time. We present qualitative and quantitative analysis to show the performance of the proposed method.
Noble, S D; Welsh, D J A
2000-01-01
We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycle spaces is an effective numerical invariant of these classes.
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
De Jong, Marvin L.
1993-01-01
Describes the powerful graphing ability of computer algebra systems (CAS) to create three-dimensional graphs or surface graphics of electric potentials. Provides equations along with examples of the printouts. Lists the programs Mathematica, Maple, Derive, Theorist, MathCad, and MATLAB as promising CAS systems. (MVL)
Mining and Indexing Graph Databases
Yuan, Dayu
2013-01-01
Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…
DEFF Research Database (Denmark)
Hartnell, B.L.; Vestergaard, Preben Dahl
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done......, the graph that remains can still be decomposed (such graphs are called or ). In this paper we consider the follwing variation. Given a fixed graph H, determine which graphs (call them ) have the property that every edge disjoint packing with H is maximum. In the case that the graph H is isomorphic...... to the path on 3 nodes, we characterize the equipackable graphs of girth 5 or more. randomly packable randomly decomposable equipackable maximal...
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done......, the graph that remains can still be decomposed (such graphs are called randomly packable or randomly decomposable). In this paper we consider the following variation. Given a fixed graph H, determine which graphs (call them equipackable) have the property that every maximal edge disjoint packing with H...... is maximum. In the case that the graph H is isomorphic to the path on 3 nodes, we characterize the equipackable graphs of girth 5 or more....
Comparison and Enumeration of Chemical Graphs
Akutsu, Tatsuya; Nagamochi, Hiroshi
2013-01-01
Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds. PMID:24688697
Graph passing in graph transformation
Ghamarian, A.H.; Rensink, Arend; Fish, Andrew; Lambers, Leen
Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which
Graph Passing in Graph Transformation
Ghamarian, A.H.; Rensink, Arend
2012-01-01
Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which
DEFF Research Database (Denmark)
Merker, Martin
The topic of this PhD thesis is graph decompositions. While there exist various kinds of decompositions, this thesis focuses on three problems concerning edgedecompositions. Given a family of graphs H we ask the following question: When can the edge-set of a graph be partitioned so that each part...... k(T)-edge-connected graph whose size is divisible by the size of T admits a T-decomposition. This proves a conjecture by Barát and Thomassen from 2006. Moreover, we introduce a new arboricity notion where we restrict the diameter of the trees in a decomposition into forests. We conjecture......-connected planar graph contains two edge-disjoint 18/19 -thin spanning trees. Finally, we make progress on a conjecture by Baudon, Bensmail, Przybyło, and Wozniak stating that if a graph can be decomposed into locally irregular graphs, then there exists such a decomposition with at most 3 parts. We show...
Jiao, Can; Wang, Ting; Liu, Jianxin; Wu, Huanjie; Cui, Fang; Peng, Xiaozhe
2017-01-01
The influences of peer relationships on adolescent subjective well-being were investigated within the framework of social network analysis, using exponential random graph models as a methodological tool. The participants in the study were 1,279 students (678 boys and 601 girls) from nine junior middle schools in Shenzhen, China. The initial stage of the research used a peer nomination questionnaire and a subjective well-being scale (used in previous studies) to collect data on the peer relationship networks and the subjective well-being of the students. Exponential random graph models were then used to explore the relationships between students with the aim of clarifying the character of the peer relationship networks and the influence of peer relationships on subjective well being. The results showed that all the adolescent peer relationship networks in our investigation had positive reciprocal effects, positive transitivity effects and negative expansiveness effects. However, none of the relationship networks had obvious receiver effects or leaders. The adolescents in partial peer relationship networks presented similar levels of subjective well-being on three dimensions (satisfaction with life, positive affects and negative affects) though not all network friends presented these similarities. The study shows that peer networks can affect an individual's subjective well-being. However, whether similarities among adolescents are the result of social influences or social choices needs further exploration, including longitudinal studies that investigate the potential processes of subjective well-being similarities among adolescents.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Witman, Matthew; Ling, Sanliang; Boyd, Peter; Barthel, Senja; Haranczyk, Maciej; Slater, Ben; Smit, Berend
2018-02-28
Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal-organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.
Shao, Zheng; Hirayama, Yuya; Yamanishi, Yoshihiro; Saigo, Hiroto
2015-12-28
Graph data are becoming increasingly common in machine learning and data mining, and its application field pervades to bioinformatics and cheminformatics. Accordingly, as a method to extract patterns from graph data, graph mining recently has been studied and developed rapidly. Since the number of patterns in graph data is huge, a central issue is how to efficiently collect informative patterns suitable for subsequent tasks such as classification or regression. In this paper, we consider mining discriminative subgraphs from graph data with multiple labels. The resulting task has important applications in cheminformatics, such as finding common functional groups that trigger multiple drug side effects, or identifying ligand functional groups that hit multiple targets. In computational experiments, we first verify the effectiveness of the proposed approach in synthetic data, then we apply it to drug adverse effect prediction problem. In the latter dataset, we compared the proposed method with L1-norm logistic regression in combination with the PubChem/Open Babel fingerprint, in that the proposed method showed superior performance with a much smaller number of subgraph patterns. Software is available from https://github.com/axot/GLP.
2005-06-01
relationship, trust, etc.) between people. • User Psychology : Clickstream graphs are bipartite graphs connecting Internet users to the websites they visit...document groups (say, science fiction novels and thrillers ), based on the word groups that occur most frequently in them. A user who prefers one
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
DEFF Research Database (Denmark)
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Directory of Open Access Journals (Sweden)
Luciano Telesca
Full Text Available By using the method of the visibility graph (VG the synthetic seismicity generated by a simple stick-slip system with asperities is analysed. The stick-slip system mimics the interaction between tectonic plates, whose asperities are given by sandpapers of different granularity degrees. The VG properties of the seismic sequences have been put in relationship with the typical seismological parameter, the b-value of the Gutenberg-Richter law. Between the b-value of the synthetic seismicity and the slope of the least square line fitting the k-M plot (relationship between the magnitude M of each synthetic event and its connectivity degree k a close linear relationship is found, also verified by real seismicity.
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Variability of soil moisture and its relationship with surface albedo ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 119; Issue 4. Variability of soil moisture and its relationship with surface albedo and soil thermal ... The diurnal variation of surface albedo appears as a U-shaped curve on sunny days. Surface albedo decreases with the increase of solar elevation angle, and it tends ...
Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs
R.C. Laskar (R.C.); H.M. Mulder (Martyn); B. Novick (Beth)
2011-01-01
textabstractMaximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices, two of these being adjacent
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
CHARACTERISATION OF REGULAR GRAPHS AS LOOP GRAPHS ...
African Journals Online (AJOL)
There have been various generalisations of Cayley graphs, prototypes of transitive graphs. The most generalised is the description of graphs on general groupoids. What has clearly emerged in this exercise is that the philosophy of constructing graphs on groupoids offers a fruitful avenue from which we may understand ...
De Bruijn graphs and DNA graphs
Pendavingh, Rudi; Schuurman, Petra; Woeginger, Gerhard; Brandstädt, Andreas; Le, Van Bang
2001-01-01
In this paper we prove the NP-hardness of various recognition problems for subgraphs of De Bruijn graphs. In particular, the recognition of DNA graphs is shown to be NP-hard; DNA graphs are the vertex induced subgraphs of De Bruijn graphs over a four letter alphabet. As a consequence, two open
Directory of Open Access Journals (Sweden)
Falcon Seth
2007-09-01
Full Text Available Abstract Graph theoretical concepts are useful for the description and analysis of interactions and relationships in biological systems. We give a brief introduction into some of the concepts and their areas of application in molecular biology. We discuss software that is available through the Bioconductor project and present a simple example application to the integration of a protein-protein interaction and a co-expression network.
Students' and Teachers' Application of Surface Area to Volume Relationships
Taylor, Amy R.; Jones, M. Gail
2013-02-01
The National Science Education Standards emphasize teaching unifying concepts and processes such as basic functions of living organisms, the living environment, and scale (NRC 2011). Scale includes understanding that different characteristics, properties, or relationships within a system might change as its dimensions are increased or decreased (NRC 2011). One such relationship involves surface area to volume which is a pervasive concept that can be found throughout different sciences. This concept is important for students to not only understand the association of the two, but to also be able to apply this relationship in science contexts. The purpose of this study is to investigate the factors that influence the understanding surface area to volume relationships. This study examined middle school students', high school students', and science teachers' logical thinking skills (including proportional reasoning), visual-spatial skills, and understandings of surface area to volume relationships. Regression results indicated that participants' reasoning abilities and components of visual-spatial skills could be possible predictors for one's ability to understand surface area to volume relationships. Implications for teaching scale concepts such as surface area to volume relationships in the science classroom are discussed.
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail.The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
Graphs, Ideal Flow, and the Transportation Network
Teknomo, Kardi
2016-01-01
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of agents in using the network graph. I show the similarity and relationship between the structural pattern of the network and network utilization.
Knowledge graph analysis of particles in Japanese
Hoede, C.
2005-01-01
The theory of knowledge graphs is a structuralistic theory of language. Its ontology consists of eight types of binary relationships and four types of so-called frames. The relationships connect so-called tokens, that represent semantic units. In this way a graph structure arises. Japanese particles
Graph limits and hereditary properties
Janson, Svante
2011-01-01
We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs, chordal graphs, cographs, interval graphs, unit interval graphs, threshold graphs, and line graphs.
First Reformulated Zagreb Indices of Some Classes of Graphs
Directory of Open Access Journals (Sweden)
V. Kaladevi
2017-12-01
Full Text Available A topological index of a graph is a parameter related to the graph; it does not depend on labeling or pictorial representation of the graph. Graph operations plays a vital role to analyze the structure and properties of a large graph which is derived from the smaller graphs. The Zagreb indices are the important topological indices found to have the applications in Quantitative Structure Property Relationship(QSPR and Quantitative Structure Activity Relationship(QSAR studies as well. There are various study of different versions of Zagreb indices. One of the most important Zagreb indices is the reformulated Zagreb index which is used in QSPR study.In this paper, we obtain the first reformulated Zagreb indices of some derived graphs such as double graph, extended double graph, thorn graph, subdivision vertex corona graph, subdivision graph and triangle parallel graph. In addition, we compute the first reformulated Zagreb indices of two important transformation graphs such as the generalized transformation graph and generalized Mycielskian graph.
Relations between the set-complexity and the structure of graphs and their sub-graphs.
Ignac, Tomasz M; Sakhanenko, Nikita A; Galas, David J
2012-09-21
: We describe some new conceptual tools for the rigorous, mathematical description of the "set-complexity" of graphs. This set-complexity has been shown previously to be a useful measure for analyzing some biological networks, and in discussing biological information in a quantitative fashion. The advances described here allow us to define some significant relationships between the set-complexity measure and the structure of graphs, and of their component sub-graphs. We show here that modular graph structures tend to maximize the set-complexity of graphs. We point out the relationship between modularity and redundancy, and discuss the significance of set-complexity in this regard. We specifically discuss the relationship between complexity and entropy in the case of complete-bipartite graphs, and present a new method for constructing highly complex, binary graphs. These results can be extended to the case of ternary graphs, and to other multi-edge graphs, which are fundamentally more relevant to biological structures and systems. Finally, our results lead us to an approach for extracting high complexity modular graphs from large, noisy graphs with low information content. We illustrate this approach with two examples.
Tejedor, Alejandro; Longjas, Anthony; Zaliapin, Ilya; Foufoula-Georgiou, Efi
2015-06-01
River deltas are intricate landscapes with complex channel networks that self-organize to deliver water, sediment, and nutrients from the apex to the delta top and eventually to the coastal zone. The natural balance of material and energy fluxes, which maintains a stable hydrologic, geomorphologic, and ecological state of a river delta, is often disrupted by external perturbations causing topological and dynamical changes in the delta structure and function. A formal quantitative framework for studying delta channel network connectivity and transport dynamics and their response to change is lacking. Here we present such a framework based on spectral graph theory and demonstrate its value in computing delta's steady state fluxes and identifying upstream (contributing) and downstream (nourishment) areas and fluxes from any point in the network. We use this framework to construct vulnerability maps that quantify the relative change of sediment and water delivery to the shoreline outlets in response to possible perturbations in hundreds of upstream links. The framework is applied to the Wax Lake delta in the Louisiana coast of the U.S. and the Niger delta in West Africa. In a companion paper, we present a comprehensive suite of metrics that quantify topologic and dynamic complexity of delta channel networks and, via application to seven deltas in diverse environments, demonstrate their potential to reveal delta morphodynamics and relate to notions of vulnerability and robustness.
Variability of soil moisture and its relationship with surface albedo ...
Indian Academy of Sciences (India)
30 N latitude) are used to study the diurnal, monthly and seasonal soil moisture variations. The effect of rainfall on diurnal and seasonal soil moisture is discussed. We have investigated relationships of soil moisture with sur- face albedo and soil thermal diffusivity. The diurnal variation of surface albedo appears as a.
Genus Ranges of 4-Regular Rigid Vertex Graphs.
Buck, Dorothy; Dolzhenko, Egor; Jonoska, Nataša; Saito, Masahico; Valencia, Karin
2015-01-01
A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a graph is embedded cellularly, and the embeddings of rigid vertex graphs are required to preserve the prescribed cyclic order of incident edges at every vertex. The genus ranges of 4-regular rigid vertex graphs are sets of consecutive integers, and we address two questions: which intervals of integers appear as genus ranges of such graphs, and what types of graphs realize a given genus range. For graphs with 2 n vertices ( n > 1), we prove that all intervals [ a, b ] for all a genus ranges. For graphs with 2 n - 1 vertices ( n ≥ 1), we prove that all intervals [ a, b ] for all a genus ranges. We also provide constructions of graphs that realize these ranges.
Erdeniz, Burak; Serin, Emin; İbadi, Yelda; Taş, Cumhur
2017-12-30
Schizophrenia is a complex disorder in which abnormalities in brain connectivity and social functioning play a central role. The aim of this study is to explore small-world network properties, and understand their relationship with social functioning and social cognition in the context of schizophrenia, by testing functional connectivity differences in network properties and its relation to clinical behavioral measures. Resting-state fMRI time series data were acquired from 23 patients diagnosed with schizophrenia and 23 healthy volunteers. The results revealed that patients with schizophrenia show significantly decreased connectivity between a range of brain regions, particularly involving connections among the right orbitofrontal cortex, bilateral putamen and left amygdala. Furthermore, topological properties of functional brain networks in patients with schizophrenia were characterized by reduced path length compared to healthy controls; however, no significant difference was found for clustering coefficient, local efficiency or global efficiency. Additionally, we found that nodal efficiency of the amygdala and the putamen were significantly correlated with the independence-performance subscale of social functioning scale (SFC), and Reading the Mind in the Eyes test; however, the correlations do not survive correction for multiple comparison. The current results help to clarify the relationship between social functioning deficits and topological brain measures in schizophrenia. Copyright © 2017 Elsevier B.V. All rights reserved.
Toughness Condition for a Graph to Be a Fractional (g,f,n-Critical Deleted Graph
Directory of Open Access Journals (Sweden)
Wei Gao
2014-01-01
Full Text Available A graph G is called a fractional (g,f-deleted graph if G-{e} admits a fractional (g,f-factor for any e∈E(G. A graph G is called a fractional (g,f,n-critical deleted graph if, after deleting any n vertices from G, the resulting graph is still a fractional (g,f-deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received significant attention in computer science. In this paper, we present the relationship between toughness and fractional (g,f,n-critical deleted graphs. It is determined that G is fractional (g,f,n-critical deleted if t(G≥((b2-1+bn/a.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Survey of Approaches to Generate Realistic Synthetic Graphs
Energy Technology Data Exchange (ETDEWEB)
Lim, Seung-Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Imam, Neena [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-10-01
A graph is a flexible data structure that can represent relationships between entities. As with other data analysis tasks, the use of realistic graphs is critical to obtaining valid research results. Unfortunately, using the actual ("real-world") graphs for research and new algorithm development is difficult due to the presence of sensitive information in the data or due to the scale of data. This results in practitioners developing algorithms and systems that employ synthetic graphs instead of real-world graphs. Generating realistic synthetic graphs that provide reliable statistical confidence to algorithmic analysis and system evaluation involves addressing technical hurdles in a broad set of areas. This report surveys the state of the art in approaches to generate realistic graphs that are derived from fitted graph models on real-world graphs.
Interval Routing and Minor-Monotone Graph Parameters
Bakker, E.M.; Bodlaender, H.L.; Tan, R.B.; Leeuwen, J. van
2006-01-01
We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdi`ere’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the
DEFF Research Database (Denmark)
Kiciman, Emre; Counts, Scott; Gamon, Michael
2014-01-01
a simple framework for specifying and implementing common social media analyses that makes it trivial to inspect and condition on contextual information. Our data model—discussion graphs—captures both the structural features of relationships inferred from social media as well as the context......, time and other confounding factors, few of the studies that attempt to extract information from social media actually condition on such factors due to the difficulty in extracting these factors from naturalistic data and the added complexity of including them in analyses. In this paper, we present...... of the discussions from which they are derived, such as who is participating in the discussions, when and where the discussions are occurring, and what else is being discussed in conjunction. We implement our framework in a tool called DGT , and present case studies on its use. In particular, we show how analyses...
Study the Relationship between Pavement Surface Distress and Roughness Data
Directory of Open Access Journals (Sweden)
Mubaraki Muhammad
2016-01-01
Full Text Available In this paper, pavement sections from the highway connected Jeddah to Jazan were selected and analyzed to investigate the relationship between International Roughness Index (IRI and pavement damage including; cracking, rutting, and raveling. The Ministry of Transport (MOT of Saudi Arabia has been collecting pavement condition data using the Road Surface Tester (RST vehicle. The MOT measures Roughness, Rutting (RUT, Cracking (CRA, raveling (RAV. Roughness measurements are calculated in terms of the International Roughness Index (IRI. The IRI is calculated over equally spaced intervals along the road profile. Roughness measurements are performed at speed between at 80 kilometers per hour. Thus RST vehicle has been used to evaluate highways across the country. The paper shows three relationships including; cracking (CRA verses roughness (IRI, rutting (RUT verses IRI, and raveling (RAV verses IRI. Also, the paper developed two models namely; model relates IRI to the three distress under study, and model relates IRI to ride quality. The results of the analysis claim at 95% confidence that a significant relationship exist between IRI and cracking, and raveling. It’s also shown that rutting did not show significant relationship to IRI values. That’s leads to conclude that the distresses types: cracking and raveling may possibly be described as ride quality distresses at different level of significant. Rutting distress described as non-ride quality type’s distresses.
Integral trees and integral graphs
Wang, Ligong
2005-01-01
This monograph deals with integral graphs, Laplacian integral regular graphs, cospectral graphs and cospectral integral graphs. The organization of this work, which consists of eight chapters, is as follows.
Directory of Open Access Journals (Sweden)
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
Loukas, A.
2015-01-01
We have recently seen a surge of research focusing on the processing of graph data. The emerging field of signal processing on graphs focuses on the extension of classical discrete signal processing techniques to the graph setting. Arguably, the greatest breakthrough of the field has been the
Indian Academy of Sciences (India)
IAS Admin
graph. We also note before closing this general discus- sion that among the family of regular and connected graphs, the graphs in the family of SRGs are character- ized by having exactly three distinct eigenvalues of the adjacency matrix. The friendship theorem asserts that if friendship in a community is a symmetric relation ...
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Pluhař, Z; Weidenmüller, H A
2014-04-11
For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.
Sotirov, Renata
2017-01-01
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e., ( X ) = inf { ≥ 0 : X is − hyperbolic } . In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its ...
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
A model of language inflection graphs
Fukś, Henryk; Farzad, Babak; Cao, Yi
2014-01-01
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.
Disease management research using event graphs.
Allore, H G; Schruben, L W
2000-08-01
Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.
Yoshida, Kenichiro; Miyaki, Masahiro; Ojima, Nobutoshi; Iwata, Kayoko
2012-06-01
The behavior of reflected light in skin affects skin appearance and provides clues as to the internal condition of the skin. Surface topography is one of the central physical factors contributing to surface reflection. We tried to clarify the relationship between microstructure of the skin surface and surface reflection based on geometric optics. Microstructures and surface reflections in the left cheeks of adult females were evaluated. Skin topography was acquired measuring replicas using confocal laser microscopy. Surface topography was used to calculate arithmetical mean deviation of the surface (S(a)), and geometric index from gradient of the surface (S(grad)), which is expected to correlate with the directionality of surface reflection (DoSR) based on geometric optics. A surface reflection image was acquired from differently polarized pictures of a face, and the index of surface reflection (I(obs)) was calculated as the average pixel value of the area of shine. Correlations between indices were then evaluated. S(grad) and S(a) showed significant correlation (preflection from the reflection model than S(a). In addition, S(grad) can explain differences in DoSR for some panelists even in the case of an identical S(a). The topographic element involved in DoSR was extracted from height mapping. S(grad) reflects the ratio of flat area, offering a more effective indicator than S(a) for distinguishing topographic characteristics with respect to surface reflection. Copyright © 2012 Japanese Society for Investigative Dermatology. Published by Elsevier Ireland Ltd. All rights reserved.
Gross, Jonathan L
2003-01-01
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as ""pure"" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to fi
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.
2008-12-23
Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
NOUS: A Knowledge Graph Management System
Energy Technology Data Exchange (ETDEWEB)
2017-06-26
Knowledge graphs represent information as entities and relationships between them. For tasks such as natural language question answering or automated analysis of text, a knowledge graph provides valuable context to establish the specific type of entities being discussed. It allow us to derive better context about newly arriving information and leads to intelligent reasoning capabilities. We address two primary needs: A) Automated construction of knowledge graphs is a technically challenging, expensive process; and B) The ability to synthesize new information by monitoring newly emerging knowledge is a transformational capability that does not exist in state of the art systems.
Integer sequence discovery from small graphs.
Hoppe, Travis; Petrone, Anna
2016-03-11
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work.
Integer sequence discovery from small graphs
Hoppe, Travis; Petrone, Anna
2015-01-01
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work. PMID:27034526
Lateral posterior fossa venous sinus relationships to surface landmarks.
Avci, Emel; Kocaogullar, Yalcin; Fossett, Damirez; Caputy, Anthony
2003-05-01
Knowing the location of the venous sinuses in the combined lateral posterior fossa and lateral cranial base approach is important to prevent their inadvertent injury. The identification of surface landmarks related to these structures is useful in planning such surgical approaches. Twelve injected adult cadaver specimens and 10 dried skulls were used to study the relationship of the venous sinuses to various surface anatomic structures. The asterion was not clearly seen in 60% of the studied cadaver sides. The asterion was always clearly seen in the dry skull preparations. The upper margin of the superior nuchal line was found to range from 1.5 mm to 14 mm inferior to the lower margin of the lateral transverse sinus. In 85% of our specimens, the mastoid groove was found to completely overlie the sigmoid sinus. The asterion was found to be variable in its anatomic relations to other identifiable structures. This variability in relation to other posterior fossa bony landmarks limits its overall usefulness as a consistently stable marker for intracranial structures. The first and most superolateral burr hole for lateral posterior fossa procedures can be safely placed 1 cm below the superior nuchal line and 1 cm medial to the top of the mastoid groove. A burr hole in this location will avoid the transverse and sigmoid sinuses, as well as the transverse-sigmoid junction, yet will be high enough and lateral enough to provide easy exposure of these venous sinuses for all lateral posterior fossa procedures.
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Uncertain Graph Sparsification
Parchas, Panos; Papailiou, Nikolaos; Papadias, Dimitris; Bonchi, Francesco
2016-01-01
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce...
Incremental View Maintenance for Deductive Graph Databases Using Generalized Discrimination Networks
Directory of Open Access Journals (Sweden)
Thomas Beyhl
2016-12-01
Full Text Available Nowadays, graph databases are employed when relationships between entities are in the scope of database queries to avoid performance-critical join operations of relational databases. Graph queries are used to query and modify graphs stored in graph databases. Graph queries employ graph pattern matching that is NP-complete for subgraph isomorphism. Graph database views can be employed that keep ready answers in terms of precalculated graph pattern matches for often stated and complex graph queries to increase query performance. However, such graph database views must be kept consistent with the graphs stored in the graph database. In this paper, we describe how to use incremental graph pattern matching as technique for maintaining graph database views. We present an incremental maintenance algorithm for graph database views, which works for imperatively and declaratively specified graph queries. The evaluation shows that our maintenance algorithm scales when the number of nodes and edges stored in the graph database increases. Furthermore, our evaluation shows that our approach can outperform existing approaches for the incremental maintenance of graph query results.
Directory of Open Access Journals (Sweden)
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
DEFF Research Database (Denmark)
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.......We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k....
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Energy Technology Data Exchange (ETDEWEB)
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
Characterisations of Intersection Graphs by Vertex Orderings
Wood, David R.
2004-01-01
Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs, co-comparability graphs, AT-free graphs, and split graphs have bandwidth bounded by their maximum degree.
Bounds on Gromov hyperbolicity constant in graphs
Indian Academy of Sciences (India)
is a topic of recent and increasing interest in graph theory; see, for instance [3–5, 8–10,. 15–17, 18–20, 22, 23, 25–27]. The theory ..... the Laplace matrix μ∗, we have δ(G) ≤ n(μ∗ − d0) μ∗ . Proof. ..... [27] Tourís E, Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces,. J. Math. Anal. Appl. 380 (2011) ...
Querying 3D Data by Adjacency Graphs
Bore, Nils; Jensfelt, Patric; Folkesson, John
2015-01-01
The need for robots to search the 3D data they have saved is becoming more apparent. We present an approach for finding structures in 3D models such as those built by robots of their environment. The method extracts geometric primitives from point cloud data. An attributed graph over these primitives forms our representation of the surface structures. Recurring substructures are found with frequent graph mining techniques. We investigate if a model invariant to changes in size and reflection ...
Quantitative comparison and analysis of sulcal patterns using sulcal graph matching: a twin study.
Im, Kiho; Pienaar, Rudolph; Lee, Jong-Min; Seong, Joon-Kyung; Choi, Yu Yong; Lee, Kun Ho; Grant, P Ellen
2011-08-01
The global pattern of cortical sulci provides important information on brain development and functional compartmentalization. Sulcal patterns are routinely used to determine fetal brain health and detect cerebral malformations. We present a quantitative method for automatically comparing and analyzing the sulcal pattern between individuals using a graph matching approach. White matter surfaces were reconstructed from volumetric T1 MRI data and sulcal pits, the deepest points in local sulci, were identified on this surface. The sulcal pattern was then represented as a graph structure with sulcal pits as nodes. The similarity between graphs was computed with a spectral-based matching algorithm by using the geometric features of nodes (3D position, depth and area) and their relationship. In particular, we exploited the feature of graph topology (the number of edges and the paths between nodes) to highlight the interrelated arrangement and patterning of sulcal folds. We applied this methodology to 48 monozygotic twins and showed that the similarity of the sulcal graphs in twin pairs was significantly higher than in unrelated pairs for all hemispheres and lobar regions, consistent with a genetic influence on sulcal patterning. This novel approach has the potential to provide a quantitative and reliable means to compare sulcal patterns. Copyright © 2011 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
A. Assari
2016-01-01
Full Text Available In this paper, a graph is assigned to any probability measure on the σ-algebra of Borel sets of a topological space. Using this construction, it is proved that given any number n (finite or infinite there exists a nonregular graph such that its clique, chromatic, and dominating number equals n.
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Packing Degenerate Graphs Greedily
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
DEFF Research Database (Denmark)
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
Directory of Open Access Journals (Sweden)
Behnaz Tolue
2018-07-01
Full Text Available In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1\\cap H_2\
Scaling relationship for surface water transport in stream networks and sub-surface flow interaction
Worman, A.
2005-12-01
Ground surface topography is known to control the circulation pattern of groundwater and also reflects the surface hydrological pathways through the landscape. This means that similar geometrical distributions typical to the landscape can be related physically-mathematically to the overall circulation of water and solute elements on land. Such understanding is needed in the management of water resources, especially on the watershed scale or larger. This paper outlines a theory by which we represent landscape topography in terms of its Fourier spectrum of a typical wave-function, formally relate this spectrum to the sub-surface flow of water and solute elements. Further, the stream network characteristics is analysed both in terms of the fractal distribution of individual stream lengths and the distribution of total transport distances in the watershed. Empirical relationships between the three types of distributions are established for two example watersheds in the middle and southern Sweden. Because the flow of water and solute elements in the stream network can also be described by convoluting unit solutions over the stream network, this paper describes an approach that relate lanscape topography to hydrological and geochemical circulation. The study shows that surface topography, stream network characteristics and thickness of quaternary deposits controls the circulation pattern of the deep groundwater. The water exchange is controlled by topography on both the continental scale as well as regional scale. The residence of deep groundwater in the stream network - before entering the coastal zone - is, therefore also controlled by the landscape topography.
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Product of Locally Primitive Graphs
Directory of Open Access Journals (Sweden)
Amir Assari
2014-01-01
Full Text Available Many large graphs can be constructed from existing smaller graphs by using graph operations, such as the product of two graphs. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this paper we consider the product of two locally primitive graphs and prove that only tensor product of them will also be locally primitive.
Graph Abstraction and Abstract Graph Transformation
Boneva, I.B.; Rensink, Arend; Kurban, M.E.; Bauer, J.
2007-01-01
Many important systems like concurrent heap-manipulating programs, communication networks, or distributed algorithms are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation of states of these systems, where transitions can be conveniently described
Mi, S. J.; Li, Y. T.; Wang, F.; Li, L.; Ge, Y.; Luo, L.; Zhang, C. L.; Chen, J. B.
2017-09-01
different in arid areas and wet areas. During the research time, frost heaving firstly accounted for a large proportion both in the arid and wet areas with the decrease of downward radiation from July to December; after December, thaw settlement came into prominence with the increase downward radiation in the arid areas, while in the wet areas, surface put into diverse situations because of water transformation leading to severe deformation. In summary, soil moisture is an important factor that influences the surface deformation. This relationship between deformation process and soil moisture will be researched more in our further work.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
DEFF Research Database (Denmark)
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently...... conjectured by Baudon et al. that every undirected graph admits a decomposition into at most three locally irregular graphs, except for a well-characterized set of indecomposable graphs. We herein consider an oriented version of this conjecture. Namely, can every oriented graph be decomposed into at most...... three locally irregular oriented graphs, i.e. whose adjacent vertices have distinct outdegrees? We start by supporting this conjecture by verifying it for several classes of oriented graphs. We then prove a weaker version of this conjecture. Namely, we prove that every oriented graph can be decomposed...
The relationship of post-fire white ash cover to surface fuel consumption
Andrew T. Hudak; Roger D. Ottmar; Robert E. Vihnanek; Nolan W. Brewer; Alistair M. S. Smith; Penelope Morgan
2013-01-01
White ash results from the complete combustion of surface fuels, making it a logically simple retrospective indicator of surface fuel consumption. However, the strength of this relationship has been neither tested nor adequately demonstrated with field measurements. We measured surface fuel loads and cover fractions of white ash and four other surface materials (green...
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Tailored Random Graph Ensembles
International Nuclear Information System (INIS)
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Learning Probabilistic Decision Graphs
DEFF Research Database (Denmark)
Jaeger, Manfred; Dalgaard, Jens; Silander, Tomi
2004-01-01
Probabilistic decision graphs (PDGs) are a representation language for probability distributions based on binary decision diagrams. PDGs can encode (context-specific) independence relations that cannot be captured in a Bayesian network structure, and can sometimes provide computationally more...
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Efficiently Controllable Graphs.
Gokler, Can; Lloyd, Seth; Shor, Peter; Thompson, Kevin
2017-06-30
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that, when a controllable quantum network is described by such a graph and the gaps in eigenfrequencies and in transition frequencies are bounded exponentially in the number of vertices, the network is efficiently controllable, in the sense that universal quantum computation can be performed using a control sequence polynomial in the size of the network while controlling a vanishingly small fraction of subsystems. We show that networks corresponding to finite-dimensional lattices are efficiently controllable and explore generalizations to percolation clusters and random graphs. We show that the classical computational complexity of estimating the ground state of Hamiltonians described by controllable graphs is polynomial in the number of subsystems or qubits.
Interaction Graphs: Exponentials
Seiller, Thomas
2013-01-01
This paper is the fourth of a series exposing a systematic combinatorial approach to Girard's Geometry of Interaction program. This program aims at obtaining particular realizability models for linear logic that accounts for the dynamics of cut-elimination. This fourth paper tackles the complex issue of defining exponential connectives in this framework. In order to succeed in this, we use the notion of graphings, a generalization of graphs which was defined in earlier work. We explain how we...
DEFF Research Database (Denmark)
Bakhshesh, Davood; Barba, Luis; Bose, Prosenjit
2018-01-01
In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points S⊂R2 and an angle 0Yao graph cY(θ) with vertex set S and angle θ as follows. For each p,q∈S, we add an edge from p to q in cY(θ) if there exists a cone with apex p...
Uniform Single Valued Neutrosophic Graphs
Directory of Open Access Journals (Sweden)
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Local Interaction on Random Graphs
Directory of Open Access Journals (Sweden)
Hans Haller
2010-08-01
Full Text Available We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph cannot change over time.
Rashmanlou, Hossein; Samanta, Sovan; Pal, Madhumangal; Borzooei, R A
2016-01-01
The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined.
Categorical constructions in graph theory
Directory of Open Access Journals (Sweden)
Richard T. Bumby
1986-01-01
Full Text Available This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
Commuting projections on graphs
Energy Technology Data Exchange (ETDEWEB)
Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2013-02-19
For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ_{2}-projection Q_{H} onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π _{H} from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π _{H} and Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Searches over graphs representing geospatial-temporal remote sensing data
Energy Technology Data Exchange (ETDEWEB)
Brost, Randolph; Perkins, David Nikolaus
2018-03-06
Various technologies pertaining to identifying objects of interest in remote sensing images by searching over geospatial-temporal graph representations are described herein. Graphs are constructed by representing objects in remote sensing images as nodes, and connecting nodes with undirected edges representing either distance or adjacency relationships between objects and directed edges representing changes in time. Geospatial-temporal graph searches are made computationally efficient by taking advantage of characteristics of geospatial-temporal data in remote sensing images through the application of various graph search techniques.
Ringo: Interactive Graph Analytics on Big-Memory Machines
Perez, Yonathan; Sosič, Rok; Banerjee, Arijit; Puttagunta, Rohan; Raison, Martin; Shah, Pararth; Leskovec, Jure
2016-01-01
We present Ringo, a system for analysis of large graphs. Graphs provide a way to represent and analyze systems of interacting objects (people, proteins, webpages) with edges between the objects denoting interactions (friendships, physical interactions, links). Mining graphs provides valuable insights about individual objects as well as the relationships among them. In building Ringo, we take advantage of the fact that machines with large memory and many cores are widely available and also relatively affordable. This allows us to build an easy-to-use interactive high-performance graph analytics system. Graphs also need to be built from input data, which often resides in the form of relational tables. Thus, Ringo provides rich functionality for manipulating raw input data tables into various kinds of graphs. Furthermore, Ringo also provides over 200 graph analytics functions that can then be applied to constructed graphs. We show that a single big-memory machine provides a very attractive platform for performing analytics on all but the largest graphs as it offers excellent performance and ease of use as compared to alternative approaches. With Ringo, we also demonstrate how to integrate graph analytics with an iterative process of trial-and-error data exploration and rapid experimentation, common in data mining workloads. PMID:27081215
Hierarchy of graph matchbox manifolds
Lukina, Olga
2011-01-01
We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call its level. We develop the fusion construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is simple, it gives us a powerful tool to study graph foliated spaces. Using fusi...
Linear representation of a graph
Directory of Open Access Journals (Sweden)
Eduardo Montenegro
2019-10-01
Full Text Available In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\\mathbb{R}$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area
Relationships between cell surface insulin binding and endocytosis in adipocytes
International Nuclear Information System (INIS)
Jochen, A.L.
1988-01-01
Chymotrypsin substrate analogues, such as N-acetyl-Tyr ethyl ester, have recently been demonstrated to inhibit the endocytic uptake of insulin in isolated rat adipocytes. In this study, the effect of N-acetyl-Tyr ethyl ester on cell surface insulin binding and dissociation were examined. Surface-bound 125 I-insulin was distinguished from intracellular 125 I-insulin by the sensitivity of the former to rapid dissociation with an acidic buffer. Plateau levels of surface-bound insulin at 37 degree C were increased 70% by inhibiting the internalization pathway. This increase was temperature and insulin concentration dependent. Thus differences in surface binding were small at 12 degree C and also at high insulin concentrations. Inhibition of internalization with N-acetyl-Tyr ethyl ester markedly slowed the loss of surface-bound insulin observed during dissociation the loss of surface-bound insulin observed during dissociation studies. After 20-30 min of dissociation, the remaining levels of surface-bound insulin were three- to fourfold higher in treated adipocytes compared with control adipocytes. Added unlabeled insulin retained its ability to accelerate the dissociation of insulin in N-acetyl-Tyr ethyl ester-treated cells. These observations indicate that the internalization pathway is a quantitatively important factor in determining levels of surface binding at 37 degree C and in determining the rat of deactivation of insulin binding
Kajian Implementasi Graph Database pada Rute Bus Rapid Transit
Directory of Open Access Journals (Sweden)
Panji Wisnu Wirawan
2017-12-01
Full Text Available Bus Rapid Transit (BRT merupakan salah satu sarana transportasi publik yang memiliki rute perjalanan tertentu atau disebut sebagai koridor. Satu koridor BRT dengan koridor yang lain bukanlah koridor yang terpisah, melainkan saling terhubung. Dalam melakukan perjalanan, penumpang BRT boleh jadi melakukan perpindahan koridor melalui shelter. Informasi tersebut perlu didapatkan seorang calon penumpang sebelum melakukan perjalanan supaya tidak terjadi perpindahan koridor yang salah. Teknologi informasi memungkinkan representasi informasi pencarian koridor yang tepat ketika penumpang akan melakukan sebuah perjalanan, terlebih dengan hadirnya graph database. Graph Database memungkinkan representasi BRT yang baik karena sifat graph yang secara standar telah menunjukkan node dan relationship. Artikel ini mengkaji penerapan graph database untuk data pada BRT. Selain itu, artikel ini mendesain sebuah algoritma pencarian koridor BRT. Harapannya, algoritma tersebut dapat digunakan untuk membangun aplikasi yang memanfaatkan data pada graph database. Hasil kajian menunjukkan bahwa graph database dapat diterapkan untuk data BRT dan algoritma yang dibangun dapat digunakan untuk menyajikan informasi rute sekaligus menyampaikan informasi perpindahan koridor.
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
Agreement dynamics on directed random graphs
Lipowski, Adam; Lipowska, Dorota; Ferreira, António Luis
2017-06-01
We examine some agreement-dynamics models that are placed on directed random graphs. In such systems, a fraction of sites \\exp(-z) , where z is the average degree, become permanently fixed or flickering. In the voter model, which has no surface tension, such zealots or flickers freely spread their opinions and that makes the system disordered. For models with a surface tension, like the Ising model or the Naming Game model, their role is limited, and such systems are ordered at large z. However, when z decreases, the density of zealots or flickers increases, and below a certain threshold (z∼ 1.9-2.0 ) the system becomes disordered. On undirected random graphs, agreement dynamics is very different and ordering appears as soon the graph is above the percolation threshold at z = 1.
A distributed query execution engine of big attributed graphs.
Batarfi, Omar; Elshawi, Radwa; Fayoumi, Ayman; Barnawi, Ahmed; Sakr, Sherif
2016-01-01
A graph is a popular data model that has become pervasively used for modeling structural relationships between objects. In practice, in many real-world graphs, the graph vertices and edges need to be associated with descriptive attributes. Such type of graphs are referred to as attributed graphs. G-SPARQL has been proposed as an expressive language, with a centralized execution engine, for querying attributed graphs. G-SPARQL supports various types of graph querying operations including reachability, pattern matching and shortest path where any G-SPARQL query may include value-based predicates on the descriptive information (attributes) of the graph edges/vertices in addition to the structural predicates. In general, a main limitation of centralized systems is that their vertical scalability is always restricted by the physical limits of computer systems. This article describes the design, implementation in addition to the performance evaluation of DG-SPARQL, a distributed, hybrid and adaptive parallel execution engine of G-SPARQL queries. In this engine, the topology of the graph is distributed over the main memory of the underlying nodes while the graph data are maintained in a relational store which is replicated on the disk of each of the underlying nodes. DG-SPARQL evaluates parts of the query plan via SQL queries which are pushed to the underlying relational stores while other parts of the query plan, as necessary, are evaluated via indexless memory-based graph traversal algorithms. Our experimental evaluation shows the efficiency and the scalability of DG-SPARQL on querying massive attributed graph datasets in addition to its ability to outperform the performance of Apache Giraph, a popular distributed graph processing system, by orders of magnitudes.
Colour Mathematics: With Graphs and Numbers
LoPresto, Michael C.
2009-01-01
The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…
Directory of Open Access Journals (Sweden)
Marc-Thorsten Hütt
2012-06-01
Full Text Available Cellular automata (CA are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
Towards information inequalities for generalized graph entropies.
Directory of Open Access Journals (Sweden)
Lavanya Sivakumar
Full Text Available In this article, we discuss the problem of establishing relations between information measures for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the Rényi entropy have been considered for this study. Our main results involve establishing formal relationships, by means of inequalities, between these two kinds of measures. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and partition-independent entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Relationship between ultrasonic Rayleigh waves and surface residual stress
International Nuclear Information System (INIS)
Adler, L.; Cook, K.V.; Dewey, B.R.; King, R.T.
1977-01-01
Local variations of Rayleigh (surface) circumferential ultrasonic wave velocity near a pipe-girth weld in large-diameter thin-wall type 316H stainless steel pipe were measured. The weldment was similar to those anticipated for the Liquid Metal Fast Breeder Reactor (LMFBR) piping systems. The residual stress distribution was estimated independently from shell theory for an elastic, infinite, thin shell with circumferential line loading. An upper bound on the magnitude of the residual stresses was estimated assuming the deformation of the shell was entirely elastic. The pattern of surface wave velocity variations matches the theoretical residual stress pattern closely. It is suggested that the monitoring of surface wave velocity variations might be used for characterizing residual stress patterns near critical welds in piping, aiding in design calculations, and for in-service monitoring of the state of stress of weldments
Surface Wave Velocity-Stress Relationship in Uniaxially Loaded Concrete
DEFF Research Database (Denmark)
Shokouhi, Parisa; Zoëga, Andreas; Wiggenhauser, Herbert
2012-01-01
loading cycles revealed that the velocities show a stress-memory effect in good agreement with the Kaiser effect. Comparing the velocities measured during loading and unloading, the effects of stress and damage on the measured velocities could be differentiated. Moreover, the stress dependency of surface......The sonic surface wave (or Rayleigh wave) velocity measured on prismatic concrete specimens under uniaxial compression was found to be highly stress-dependent. At low stress levels, the acoustoelastic effect and the closure of existing microcracks results in a gradual increase in surface wave...... velocities. At higher stress levels, concrete suffers irrecoverable damage: the existing microcracks widen and coalesce and new microcracks form. This progressive damage process leads first to the flattening and eventually the drop in the velocity-stress curves. Measurements on specimens undergoing several...
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Feature Tracking Using Reeb Graphs
Energy Technology Data Exchange (ETDEWEB)
Weber, Gunther H.; Bremer, Peer-Timo; Day, Marcus S.; Bell, John B.; Pascucci, Valerio
2010-08-02
Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a temperature isosurface. Tracking such regions as they merge and split over time can provide important insights into the impact of turbulence on the combustion process. However, the convoluted nature of the temperature isosurface and its rapid movement make this analysis particularly challenging. Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field. It then obtains isosurfaces for the original simulation time steps and labels individual connected 'burning' regions based on the local fuel consumption value. Based on this information, a boundary surface between burning and non-burning regions is constructed. The Reeb graph of this boundary surface is the tracking graph for burning regions.
Graph theory and interconnection networks
Hsu, Lih-Hsing
2008-01-01
The advancement of large scale integrated circuit technology has enabled the construction of complex interconnection networks. Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to graph terminology, the book presents well-known interconnection networks as examples of graphs, followed by in-depth coverage of Hamiltonian graphs. Different types of problems illustrate the wide range of available methods for solving such problems. The text also explores recent progress on the diagnosability of graphs under various models.
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...
Relationships between surface solar radiation and wheat yield in Spain
Hernandez-Barrera, Sara; Rodriguez-Puebla, Concepción
2017-04-01
Here we examine the role of solar radiation to describe wheat-yield variability in Spain. We used Partial Least Square regression to capture the modes of surface solar radiation that drive wheat-yield variability. We will show that surface solar radiation introduces the effects of teleconnection patterns on wheat yield and also it is associated with drought and diurnal temperature range. We highlight the importance of surface solar radiation to obtain models for wheat-yield projections because it could reduce uncertainty with respect to the projections based on temperatures and precipitation variables. In addition, the significance of the model based on surface solar radiation is greater than the previous one based on drought and diurnal temperature range (Hernandez-Barrera et al., 2016). According to our results, the increase of solar radiation over Spain for 21st century could force a wheat-yield decrease (Hernandez-Barrera et al., 2017). Hernandez-Barrera S., Rodríguez-Puebla C. and Challinor A.J. 2016 Effects of diurnal temperature range and drought on wheat yield in Spain. Theoretical and Applied Climatology. DOI: 10.1007/s00704-016-1779-9 Hernandez-Barrera S., Rodríguez-Puebla C. 2017 Wheat yield in Spain and associated solar radiation patterns. International Journal of Climatology. DOI: 10.1002/joc.4975
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D......_E of C*(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Chen, Chun; Ye, Sudan; Hu, Huajun; Xue, Chengmei; Yu, Xiaoping
2018-01-01
A real-time qPCR method was developed, validated, and used to quantity the fungal pathogen, P. neoaphidis, within aphids at different times during infection; colonization rate fitted the Gompertz model well (R 2 = 0.9356). Feeding behaviour of P. neoaphidis-infected and uninfected M. persicae were investigated, for the first time, using DC-electrical penetration graphs (DC-EPG) that characterized the waveforms made during different aphid stylet probing periods corresponding to epidermis penetration, salivation and ingestion. In the 6 h following the 12-h incubation period (to achieve infection), there were significant differences in the number of events of Np (non-probing) and C (stylet pathway) between infected and uninfected aphids. However, the difference between total duration of Np and C were not significantly different between infected and uninfected aphids. There were no significant differences in the number of events or total duration of E1 (phloem salivation) or E2 (phloem ingestion) between infected and uninfected aphids. There were significant differences in mean number of events and total duration of the pd waveform (intracellular punctures) in infected and uninfected aphids. In the 16 h prior to death, the same differences in behaviour were observed but they were even more obvious. Furthermore, the total duration time of E2 was significantly greater in uninfected aphids than infected aphids, a change that had not been observed in the first 6 h observation period. In conclusion, qPCR quantification demonstrated 'molecular' colonization levels throughout infection, and EPG data analysis during the two periods (during early infection and then during late infection just prior to death) demonstrated the actual physical effects of fungal infection on feeding behaviour of M. persicae; this has the potential to decrease the aphid's capacity of transmission and dispersal. These studies increase our understanding of the interaction between P
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Hierarchical graphs for rule-based modeling of biochemical systems
Directory of Open Access Journals (Sweden)
Hu Bin
2011-02-01
Full Text Available Abstract Background In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal of an edge represents a class of association (dissociation reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Results For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Conclusions Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for
Hierarchical graphs for rule-based modeling of biochemical systems.
Lemons, Nathan W; Hu, Bin; Hlavacek, William S
2011-02-02
In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language
Using Graph Transformations and Graph Abstractions for Software Verification
Zambon, Eduardo; Rensink, Arend
In this paper we describe our intended approach for the verification of software written in imperative programming languages. We base our approach on model checking of graph transition systems, where each state is a graph and the transitions are specified by graph transformation rules. We believe
Robustness of random graphs based on graph spectra.
Wu, Jun; Barahona, Mauricio; Tan, Yue-Jin; Deng, Hong-Zhong
2012-12-01
It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.
Codes related to line graphs of triangular graphs and permutation ...
African Journals Online (AJOL)
For any prime p, we consider p-ary linear codes obtained from the row span of incidence matrices of line graphs of triangular graphs and adjacency matrices of their line graphs. We determine parameters of the codes, their automorphism groups and exhibit permutation decoding sets (PD-sets) for partial permutation ...
Resistance Distances in Vertex-Face Graphs
Shangguan, Yingmin; Chen, Haiyan
2018-01-01
The computation of two-point resistances in networks is a classical problem in electric circuit theory and graph theory. Let G be a triangulation graph with n vertices embedded on an orientable surface. Define K(G) to be the graph obtained from G by inserting a new vertex vϕ to each face ϕ of G and adding three new edges (u, vϕ), (v, vϕ) and (w, vϕ), where u, v and w are three vertices on the boundary of ϕ. In this paper, using star-triangle transformation and resistance local-sum rules, explicit relations between resistance distances in K(G) and those in G are obtained. These relations enable us to compute resistance distance between any two points of Kk(G) recursively. As explanation examples, some resistances in several networks are computed, including the modified Apollonian network and networks constructed from tetrahedron, octahedron and icosahedron, respectively.
GOGrapher: A Python library for GO graph representation and analysis.
Muller, Brian; Richards, Adam J; Jin, Bo; Lu, Xinghua
2009-07-07
The Gene Ontology is the most commonly used controlled vocabulary for annotating proteins. The concepts in the ontology are organized as a directed acyclic graph, in which a node corresponds to a biological concept and a directed edge denotes the parent-child semantic relationship between a pair of terms. A large number of protein annotations further create links between proteins and their functional annotations, reflecting the contemporary knowledge about proteins and their functional relationships. This leads to a complex graph consisting of interleaved biological concepts and their associated proteins. What is needed is a simple, open source library that provides tools to not only create and view the Gene Ontology graph, but to analyze and manipulate it as well. Here we describe the development and use of GOGrapher, a Python library that can be used for the creation, analysis, manipulation, and visualization of Gene Ontology related graphs. An object-oriented approach was adopted to organize the hierarchy of the graphs types and associated classes. An Application Programming Interface is provided through which different types of graphs can be pragmatically created, manipulated, and visualized. GOGrapher has been successfully utilized in multiple research projects, e.g., a graph-based multi-label text classifier for protein annotation. The GOGrapher project provides a reusable programming library designed for the manipulation and analysis of Gene Ontology graphs. The library is freely available for the scientific community to use and improve.
GOGrapher: A Python library for GO graph representation and analysis
Directory of Open Access Journals (Sweden)
Lu Xinghua
2009-07-01
Full Text Available Abstract Background The Gene Ontology is the most commonly used controlled vocabulary for annotating proteins. The concepts in the ontology are organized as a directed acyclic graph, in which a node corresponds to a biological concept and a directed edge denotes the parent-child semantic relationship between a pair of terms. A large number of protein annotations further create links between proteins and their functional annotations, reflecting the contemporary knowledge about proteins and their functional relationships. This leads to a complex graph consisting of interleaved biological concepts and their associated proteins. What is needed is a simple, open source library that provides tools to not only create and view the Gene Ontology graph, but to analyze and manipulate it as well. Here we describe the development and use of GOGrapher, a Python library that can be used for the creation, analysis, manipulation, and visualization of Gene Ontology related graphs. Findings An object-oriented approach was adopted to organize the hierarchy of the graphs types and associated classes. An Application Programming Interface is provided through which different types of graphs can be pragmatically created, manipulated, and visualized. GOGrapher has been successfully utilized in multiple research projects, e.g., a graph-based multi-label text classifier for protein annotation. Conclusion The GOGrapher project provides a reusable programming library designed for the manipulation and analysis of Gene Ontology graphs. The library is freely available for the scientific community to use and improve.
Visualizing automorphisms of graph algebras
DEFF Research Database (Denmark)
Avery, James Emil; Johansen, Rune; Szymanski, Wojciech
2018-01-01
Graph C*-algebras have been celebrated as C*-algebras that can be seen, because many important properties may be determined by looking at the underlying graph. This paper introduces the permutation graph for a permutative endomorphism of a graph C*-algebra as a labeled directed multigraph...... that gives a visual representation of the endomorphism and facilitates computations. Combinatorial criteria have previously been developed for deciding when such an endomorphism is an automorphism, but here the question is reformulated in terms of the permutation graph and new proofs are given. Furthermore......, it is shown how to use permutation graphs to efficiently generate exhaustive collections of permutative automorphisms. Permutation graphs provide a natural link to the textile systems representing induced endomorphisms on the edge shift of the given graph, and this allows the powerful tools of the theory...
Rensink, Arend; Schmidt, David
2004-01-01
Graphs are an intuitive model for states of a (software) system that include pointer structures | for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary in order
Rensink, Arend; Schmidt, D.A.
2004-01-01
Abstract. Graphs are an intuitive model for states of a (software) system that include pointer structures — for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary
Dujmović, Vida; Sidiropoulos, Anastasios; Wood, David R.
2015-01-01
Bourgain and Yehudayoff recently constructed $O(1)$-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.
S.M. Heditniemi (Sandra); R.C. Laskar (R.C.); H.M. Mulder (Martyn)
2012-01-01
textabstractLet $G = (V,E)$ be a graph. A partition $\\pi = \\{V_1, V_2, \\ldots, V_k \\}$ of the vertices $V$ of $G$ into $k$ {\\it color classes} $V_i$, with $1 \\leq i \\leq k$, is called a {\\it quorum coloring} if for every vertex $v \\in V$, at least half of the vertices in the closed neighborhood
Cooper, Carol
1975-01-01
Teachers of an integrated elementary classroom used cookie-sharing time as a learning experience for students. Responsible for dividing varying amounts of cookies daily, the students learned to translate their experiences to graphs of differing sophistication and analyses. Further interpretation and application were done by individual students…
Grabmayer, C.A.; van Oostrom, V.
2014-01-01
We report on work in progress on `nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 9. Decoding Codes on Graphs - Low Density Parity Check Codes. A S Madhu Aditya Nori. General Article Volume 8 Issue 9 September 2003 pp 49-59. Fulltext. Click here to view fulltext PDF. Permanent link:
Energy Technology Data Exchange (ETDEWEB)
Simmons, G.J.
1985-01-01
Given a graph G and an ordering phi of the vertices, V(G), we define a parsimonious proper coloring (PPC) of V(G) under phi to be a proper coloring of V(G) in the order phi, where a new color is introduced only when a vertex cannot be properly colored in its order with any of the colors already used.
Spectral reflectance of surface soils: Relationships with some soil properties
Kiesewetter, C. H.
1983-01-01
Using a published atlas of reflectance curves and physicochemical properties of soils, a statistical analysis was carried out. Reflectance bands which correspond to five of the wavebands used by NASA's Thematic Mapper were examined for relationships to specific soil properties. The properties considered in this study include: Sand Content, Silt Content, Clay Content, Organic Matter Content, Cation Exchange Capacity, Iron Oxide Content and Moisture Content. Regression of these seven properties on the mean values of five TM bands produced results that indicate that the predictability of the properties can be increased by stratifying the data. The data was stratified by parent material, taxonomic order, temperature zone, moisture zone and climate (combined temperature and moisture). The best results were obtained when the sample was examined by climatic classes. The middle Infra-red bands, 5 and 7, as well as the visible bands, 2 and 3, are significant in the model. The near Infra-red band, band 4, is almost as useful and should be included in any studies. General linear modeling procedures examined relationships of the seven properties with certain wavebands in the stratified samples.
The surface heat island of Rotterdam and its relationship with urban surface characteristics
Klok, L.; Zwart, S.; Verhagen, H.; Mauri, E.
2012-01-01
Thermal infrared high resolution satellite images from Landsat sensors were used to spatially quantify the surface heat island (SHI) of Rotterdam in the Netherlands. Based on surface temperature maps retrieved on 15 summer days since 1984, the average surface temperature of each district and
On dominator colorings in graphs
Indian Academy of Sciences (India)
Graph coloring and domination are two major areas in graph theory that have been ... independent set if no two vertices in S are adjacent. ... independent set. The corona G1 ◦ G2 of two graphs G1 and G2 is defined to be the graph. G obtained by taking one copy of G1 and |V(G1)| copies of G2, and then joining the i-th.
Hamiltonian paths on Platonic graphs
Directory of Open Access Journals (Sweden)
Brian Hopkins
2004-07-01
Full Text Available We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topologically uniquely Hamiltonian.
Energy Technology Data Exchange (ETDEWEB)
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Nullspace embeddings for outerplanar graphs
L. Lovász (László); A. Schrijver (Alexander)
2017-01-01
textabstractWe study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G=(V,E), we define a "good" G-matrix as a V×V matrix with negative entries corresponding to adjacent nodes, zero
Nullspace embeddings for outerplanar graphs
L. Lovász (László); A. Schrijver (Alexander); M. Loebl (Martin); J. Nešetřil (Jaroslav); R. Thomas (Robin)
2017-01-01
htmlabstractWe study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a "good” G-matrix as a V × V matrix with negative
Nullspace embeddings for outerplanar graphs
Lovász, L.; Schrijver, A.; Loebl, M.; Nešetřil, J.; Thomas, R.
2017-01-01
We study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a “good” G-matrix as a V × V matrix with negative entries corresponding to adjacent nodes, zero entries
Pattern-Based Graph Abstraction
Rensink, Arend; Zambon, Eduardo; Ehrig, H; Engels, G.; Kreowski, H.J.; Rozenberg, G.
We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered
Generalised compositionality in graph transformation
Ghamarian, A.H.; Rensink, Arend; Ehrig, H; Engels, G.; Kreowski, H.J.; Rozenberg, G.
We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph
Hopkins, Brian
2004-01-01
The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low ...
Asteroidal Quadruples in non Rooted Path Graphs
Directory of Open Access Journals (Sweden)
Gutierrez Marisa
2015-11-01
Full Text Available A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.
Fish Mercury and Surface Water Sulfate Relationships in the Everglades Protection Area
Few published studies present data on relationships between fish mercury and surface or pore water sulfate concentrations, particularly on an ecosystem-wide basis. Resource managers can use these relationships to identify the sulfate conditions that contain fish with health-conce...
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Domination criticality in product graphs
Directory of Open Access Journals (Sweden)
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Dynamic Representations of Sparse Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Graph Creation, Visualisation and Transformation
Directory of Open Access Journals (Sweden)
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Kang, J. H.; Song, H. J.; Han, H. J.; Ha, J. H.
2016-12-01
The observation processing system, KPOP (KIAPS - Korea Institute of Atmospheric Prediction Systems - Package for Observation Processing) have developed to provide optimal observations to the data assimilation system for the KIAPS Integrated Model (KIM). Currently, the KPOP has capable of processing almost all of observations for the KMA (Korea Meteorological Administration) operational global data assimilation system. The height adjustment of SURFACE observations are essential for the quality control due to the difference in height between observation station and model topography. For the SURFACE observation, it is usual to adjust the height using lapse rate or hypsometric equation, which decides values mainly depending on the difference of height. We have a question of whether the height can be properly adjusted following to the linear or exponential relationship solely with regard to the difference of height, with disregard the atmospheric conditions. In this study, firstly we analyse the change of surface variables such as temperature (T2m), pressure (Psfc), humidity (RH2m and Q2m), and wind components (U and V) according to the height difference. Additionally, we look further into the relationships among surface variables . The difference of pressure shows a strong linear relationship with difference of height. But the difference of temperature according to the height shows a significant correlation with difference of relative humidity than with the height difference. A development of reliable model for the height-adjustment of surface temperature is being undertaken based on the preliminary results.
Changes in Thickness and Surface Area of the Human Cortex and Their Relationship with Intelligence
Schnack, Hugo G.; Van Haren, Neeltje E M; Brouwer, Rachel M.; Evans, Alan; Durston, Sarah; Boomsma, Dorret I.; Kahn, René S.; Hulshoff Pol, Hilleke E.
2015-01-01
Changes in cortical thickness over time have been related to intelligence, but whether changes in cortical surface area are related to general cognitive functioning is unknown. We therefore examined the relationship between intelligence quotient (IQ) and changes in cortical thickness and surface
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Canonical Labelling of Site Graphs
Directory of Open Access Journals (Sweden)
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Directory of Open Access Journals (Sweden)
Burhan Selçuk
2017-06-01
Full Text Available Hypercube is a popular interconnection network. Due to the popularity of hypercube, more researchers pay a great effort to develop the different variants of hypercube. In this paper, we have proposed a variant of hypercube which is called as “Connected Cubic Network Graphs”, and have investigated the Hamilton-like properties of Connected Cubic Network Graphs (CCNG. Firstly, we defined CCNG and showed the characteristic analyses of CCNG. Then, we showed that the CCNG has the properties of Hamilton graph, and can be labeled using a Gray coding based recursive algorithm. Finally, we gave the comparison results, a routing algorithm and a bitonic sort algorithm for CCNG. In case of sparsity and cost, CCNG is better than Hypercube.
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
Graphs cospectral with a friendship graph or its complement
Directory of Open Access Journals (Sweden)
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
parallel implementations for many key graph algorithms, conversions between tables and graphs and Python language bindings. SNAP is widely deployed...1. We have used Delite to develop a suite of DSLs for data analysis (query processing, machine learning , and graph processing). Approved for Public...range of users, interested in network analysis: support for Python - a major programming language for data scientists, documentation, tutorials, and
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, R.; Maskey, M.; Gatlin, P. N.; Zhang, J.; Duan, X.; Bugbee, K.; Christopher, S. A.; Miller, J. J.
2017-12-01
Estimates indicate that the world's information will grow by 800% in the next five years. In any given field, a single researcher or a team of researchers cannot keep up with this rate of knowledge expansion without the help of cognitive systems. Cognitive computing, defined as the use of information technology to augment human cognition, can help tackle large systemic problems. Knowledge graphs, one of the foundational components of cognitive systems, link key entities in a specific domain with other entities via relationships. Researchers could mine these graphs to make probabilistic recommendations and to infer new knowledge. At this point, however, there is a dearth of tools to generate scalable Knowledge graphs using existing corpus of scientific literature for Earth science research. Our project is currently developing an end-to-end automated methodology for incrementally constructing Knowledge graphs for Earth Science. Semantic Entity Recognition (SER) is one of the key steps in this methodology. SER for Earth Science uses external resources (including metadata catalogs and controlled vocabulary) as references to guide entity extraction and recognition (i.e., labeling) from unstructured text, in order to build a large training set to seed the subsequent auto-learning component in our algorithm. Results from several SER experiments will be presented as well as lessons learned.
Enhancing SAMOS Data Access in DOMS via a Neo4j Property Graph Database.
Stallard, A. P.; Smith, S. R.; Elya, J. L.
2016-12-01
The Shipboard Automated Meteorological and Oceanographic System (SAMOS) initiative provides routine access to high-quality marine meteorological and near-surface oceanographic observations from research vessels. The Distributed Oceanographic Match-Up Service (DOMS) under development is a centralized service that allows researchers to easily match in situ and satellite oceanographic data from distributed sources to facilitate satellite calibration, validation, and retrieval algorithm development. The service currently uses Apache Solr as a backend search engine on each node in the distributed network. While Solr is a high-performance solution that facilitates creation and maintenance of indexed data, it is limited in the sense that its schema is fixed. The property graph model escapes this limitation by creating relationships between data objects. The authors will present the development of the SAMOS Neo4j property graph database including new search possibilities that take advantage of the property graph model, performance comparisons with Apache Solr, and a vision for graph databases as a storage tool for oceanographic data. The integration of the SAMOS Neo4j graph into DOMS will also be described. Currently, Neo4j contains spatial and temporal records from SAMOS which are modeled into a time tree and r-tree using Graph Aware and Spatial plugin tools for Neo4j. These extensions provide callable Java procedures within CYPHER (Neo4j's query language) that generate in-graph structures. Once generated, these structures can be queried using procedures from these libraries, or directly via CYPHER statements. Neo4j excels at performing relationship and path-based queries, which challenge relational-SQL databases because they require memory intensive joins due to the limitation of their design. Consider a user who wants to find records over several years, but only for specific months. If a traditional database only stores timestamps, this type of query would be complex
Burleigh, Scott C.
2011-01-01
Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic
Graphs Theory and Applications
Fournier, Jean-Claude
2008-01-01
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the
Nested Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...... Exformatics, a danish provider of case and workflow management systems. We formalize the semantics by giving first a map from Nested to (flat) DCR Graphs with milestones, and then extending the previously given mapping from DCR Graphs to Buchi-automata to include the milestone relation....
Spectral partitioning in equitable graphs.
Barucca, Paolo
2017-06-01
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.
Energy Technology Data Exchange (ETDEWEB)
Berryman, J.G.
1987-01-01
A result of Debye, Anderson, and Brumberger (P. Debye, H. R. Anderson, Jr., and H. Brumberger, J. Appl. Phys. 28, 679 (1957)) for isotropic porous media states that the derivative of the two-point spatial correlation at the origin is equal to minus one-quarter of the specific surface area. This result is generalized for nonisotropic media by noting that the angular average of the anisotropic two-point spatial correlation function has the same relationship to the specific surface area.
ILIGRA : An Efficient Inverse Line Graph Algorithm
Liu, D.; Trajanovski, S.; Van Mieghem, P.
2014-01-01
This paper presents a new and efficient algorithm, ILIGRA, for inverse line graph construction. Given a line graph H, ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H. If ILIGRA does not know whether the given graph H is a line graph, it firstly
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter......-derive a third style of graph reduction: a graph evaluator....
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Broumi, Said; Talea, Mohamed; Bakali, Assia; Smarandache, Florentin
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Using Graph Transformations and Graph Abstractions for Software Verification
Zambon, Eduardo; Ehrig, Hartmut; Rensink, Arend; Rozenberg, Grzegorz; Schurr, Andy
In this abstract we present an overview of our intended approach for the verification of software written in imperative programming languages. This approach is based on model checking of graph transition systems (GTS), where each program state is modeled as a graph and the exploration engine is
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
We define the -repetition of to be the graph obtained by joining y i to x j for each i ∈ V ( T ) and each child of . In this paper, we compute the Kirchhoff index of the -repetition of in terms of parameters of and . Also we study how K f ( G ) behaves under some graph operations such as joining vertices or ...
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Directory of Open Access Journals (Sweden)
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
Chordal Graphs and Semidefinite Optimization
DEFF Research Database (Denmark)
Vandenberghe, Lieven; Andersen, Martin Skovgaard
2015-01-01
Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite optimization problems and in related con-vex optimization problems involving sparse positive semidefinite matrices. Chordal graph properties are also fundamental to several classical results in combinat...
DYNAMICALLY MAINTAINING THE VISIBILITY GRAPH
VEGTER, G
1991-01-01
An algorithm is presented to maintain the visibility graph of a set of N line segments in the plane in O(log2 N + K log N) time, where K is the total number of arcs of the visibility graph that are destroyed or created upon insertion or deletion of a line segment. The line segments should be
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
The planar cubic cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Hoede, C.; Liu, X
1998-01-01
In continuation of the paper of Hoede and Li on word graphs for a set of prepositions, word graphs are given for adjectives, adverbs and Chinese classifier words. It is argued that these three classes of words belong to a general class of words that may be called adwords. These words express the
Bell inequalities for graph states
International Nuclear Information System (INIS)
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some special families. Keywords. Almost Hermitian ...
Subgraph Enumeration in Massive Graphs
DEFF Research Database (Denmark)
Silvestri, Francesco
We consider the problem of enumerating all instances of a given sample graph in a large data graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges in the data graph, $k=\\BO{1}$ be the number of vertexes in the sample graph, $B......$ be the block length, and $M$ be the main memory size. The main result of the paper is a randomized algorithm that enumerates all instances of the sample graph in $\\BO{E^{k/2}/\\left(BM^{k/2-1}\\right)}$ expected I/Os if the maximum vertex degree of the data graph is $\\sqrt{EM}$. Under some assumptions, the same...... bound also applies with high probability. Our algorithm is I/O optimal, in the worst-case, when the sample graph belongs to the Alon class, which includes cliques, cycles and every graph with a perfect matching: indeed, we show that any algorithm enumerating $T$ instances must always use $\\BOM...
Pan, Chen; Zhu, Xi-yang; Jia, Wen-xiao; Yang, Fang; Liu, Ming; Xiang, Wei-ning
2015-07-01
Land use change and fossil fuel combustion due to urbanization have a significant effect on global carbon cycle and climate change. It's important to have an explicit understanding of the spatial distribution of CO2 to recognize and control GHG emission, which is helpful to reduce human-induced contribution to global climate change. The study area of this project was set in the city of Shanghai with intensive human activity and rapid urbanization. The monitoring of near surface CO2 concentration along 3 transects was conducted across an urban-rural gradient by means of near infrared gas analyzer Li-840A in spring, 2014. Remote sensing data were also used to derive underlying surface information. Further quantitative analysis of the mechanism of CO2 concentration's response to the characteristics of underlying surface was presented in this paper. The results showed that the average near surface CO2 concentration was (443.4±22.0) µmol . mol-1. CO2 concentration in city center was in average 12.5% (52.5 µLmol . mol-1) higher than that in the suburban area. Also, CO2 concentration showed a significant spatial differentiation, with the highest CO2 concentration in the northwest, the second highest in the southwest, and the lowest in the southeast, which was in accordance with the urbanization level of the underlying surface. The results revealed that the vegetation coverage rate (CVeg) was an important indicator to describe near surface CO2 concentration with a negative correlation, and the impervious surface area coverage rate (CISA) had lower explanatory power with a positive correlation. The study also found that the determination coefficient (R2) between CO2 concentration (CCO2) and CISA or CVeg achieved its highest value when the buffer distance was 5 km, and their quantitative relationships be described by a stepwise regression equation: CCO2=0.32CISA-0.89CVeg+445.13 (R2 =0.66, P<0.01).
Changes in thickness and surface area of the human cortex and their relationship with intelligence.
Schnack, Hugo G; van Haren, Neeltje E M; Brouwer, Rachel M; Evans, Alan; Durston, Sarah; Boomsma, Dorret I; Kahn, René S; Hulshoff Pol, Hilleke E
2015-06-01
Changes in cortical thickness over time have been related to intelligence, but whether changes in cortical surface area are related to general cognitive functioning is unknown. We therefore examined the relationship between intelligence quotient (IQ) and changes in cortical thickness and surface over time in 504 healthy subjects. At 10 years of age, more intelligent children have a slightly thinner cortex than children with a lower IQ. This relationship becomes more pronounced with increasing age: with higher IQ, a faster thinning of the cortex is found over time. In the more intelligent young adults, this relationship reverses so that by the age of 42 a thicker cortex is associated with higher intelligence. In contrast, cortical surface is larger in more intelligent children at the age of 10. The cortical surface is still expanding, reaching its maximum area during adolescence. With higher IQ, cortical expansion is completed at a younger age; and once completed, surface area decreases at a higher rate. These findings suggest that intelligence may be more related to the magnitude and timing of changes in brain structure during development than to brain structure per se, and that the cortex is never completed but shows continuing intelligence-dependent development. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Milatz, Anne; Lüftenegger, Marko; Schober, Barbara
2015-01-01
Teachers’ relationship quality with students has been argued to be an important source of teacher wellbeing. Thus, the current study aimed to investigate to what extent teachers’ relationship closeness toward students, combined with attachment security is a resource protecting against teacher burnout. Eighty-three elementary school teachers reported on their most and least attached student’s relationship closeness, their attachment security and levels of burnout, as measured by emotional exhaustion, depersonalization and personal accomplishment. Response surface analysis (RSA), enabling researchers to investigate the effect of congruence/incongruence of two predictors on an outcome, revealed that teachers’ depersonalization and emotional exhaustion were lowest when they developed homogenous close relationships toward the students within their classroom and when teachers in general made congruent relationship experiences. No RSA model could be specified for personal accomplishment, even though a correlational analysis revealed that increasing closeness with students fostered teachers’ personal accomplishment. Teachers’ secure attachment experiences were not directly related to burnout, but enhanced their capability to establish close relationships toward their students. Findings suggest that teachers’ relationships toward students are a resource for the teacher’s wellbeing, which highlights once again the importance of student–teacher relationships in education. PMID:26779045
Koster, Randal D.; Mahanama, Sarith P.
2012-01-01
The inherent soil moisture-evaporation relationships used in today 's land surface models (LSMs) arguably reflect a lot of guesswork given the lack of contemporaneous evaporation and soil moisture observations at the spatial scales represented by regional and global models. The inherent soil moisture-runoff relationships used in the LSMs are also of uncertain accuracy. Evaluating these relationships is difficult but crucial given that they have a major impact on how the land component contributes to hydrological and meteorological variability within the climate system. The relationships, it turns out, can be examined efficiently and effectively with a simple water balance model framework. The simple water balance model, driven with multi-decadal observations covering the conterminous United States, shows how different prescribed relationships lead to different manifestations of hydrological variability, some of which can be compared directly to observations. Through the testing of a wide suite of relationships, the simple model provides estimates for the underlying relationships that operate in nature and that should be operating in LSMs. We examine the relationships currently used in a number of different LSMs in the context of the simple water balance model results and make recommendations for potential first-order improvements to these LSMs.
A Collection of Features for Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Eliassi-Rad, T; Fodor, I K; Gallagher, B
2007-05-02
Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.
Directory of Open Access Journals (Sweden)
Marco Raberto
Full Text Available In this paper, we outline a model of graph (or network dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Quantum chaos on discrete graphs
Energy Technology Data Exchange (ETDEWEB)
Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel); Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH (United Kingdom)
2007-07-06
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral {zeta} functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of {zeta} functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
Directory of Open Access Journals (Sweden)
I. Sahul Hamid
2016-07-01
Full Text Available A set D of vertices of a graph G is called a dominating set of G if every vertex in V(G−D is adjacent to a vertex in D. A dominating set S such that the subgraph 〈S〉 induced by S has at least one isolated vertex is called an isolate dominating set. An isolate dominating set none of whose proper subset is an isolate dominating set is a minimal isolate dominating set. The minimum and maximum cardinality of a minimal isolate dominating set are called the isolate domination number γ0 and the upper isolate domination number Γ0 respectively. In this paper we initiate a study on these parameters.
Environmental evolutionary graph theory.
Maciejewski, Wes; Puleo, Gregory J
2014-11-07
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have received relatively less attention. Here we present a structured population model where different individuals are best suited to different regions of their environment. The underlying structure is a graph: individuals occupy vertices, which are connected by edges. If an individual is suited for their vertex, they receive an increase in fecundity. This framework allows attention to be restricted to the spatial arrangement of suitable habitat. We prove some basic properties of this model and find some counter-intuitive results. Notably, (1) the arrangement of suitable sites is as important as their proportion, and (2) decreasing the proportion of suitable sites may result in a decrease in the fixation time of an allele. Copyright © 2014 Elsevier Ltd. All rights reserved.
Local graph cut criterion for supervised dimensionality reduction
Zhang, Xiangrong; Zhou, Sisi; Jiao, Licheng
2009-10-01
Graph cut criterion has been proven to be robust and applicable in clustering problems. In this paper the graph cut criterion is applied to construct a supervised dimensionality reduction. A new graph cut, scaling cut, is proposed based on the classical normalized cut. Scaling cut depicts the relationship between samples, which makes it can handle the heteroscedastic and multimodel data in which LDA fails. Meanwhile, the solution to scaling cut is global optimal for it is a generalized eigenvalue problem. To obtain a more reasonable projection matrix and reduce the computational complexity as well, the localized k-nearest neighbor graph is introduced in, which leads to equivalent or better results compared with scaling cut.
Narrative Collage of Image Collections by Scene Graph Recombination.
Fang, Fei; Yi, Miao; Feng, Hui; Hu, Shenghong; Xiao, Chunxia
2017-10-04
Narrative collage is an interesting image editing art to summarize the main theme or storyline behind an image collection. We present a novel method to generate narrative images with plausible semantic scene structures. To achieve this goal, we introduce a layer graph and a scene graph to represent relative depth order and semantic relationship between image objects, respectively. We firstly cluster the input image collection to select representative images, and then extract a group of semantic salient objects from each representative image. Both Layer graphs and scene graphs are constructed and combined according to our specific rules for reorganizing the extracted objects in every image. We design an energy model to appropriately locate every object on the final canvas. Experiment results show that our method can produce competitive narrative collage result and works well on a wide range of image collections.
Hyperspectral image classification through bilayer graph-based learning.
Gao, Yue; Ji, Rongrong; Cui, Peng; Dai, Qionghai; Hua, Gang
2014-07-01
Hyperspectral image classification with limited number of labeled pixels is a challenging task. In this paper, we propose a bilayer graph-based learning framework to address this problem. For graph-based classification, how to establish the neighboring relationship among the pixels from the high dimensional features is the key toward a successful classification. Our graph learning algorithm contains two layers. The first-layer constructs a simple graph, where each vertex denotes one pixel and the edge weight encodes the similarity between two pixels. Unsupervised learning is then conducted to estimate the grouping relations among different pixels. These relations are subsequently fed into the second layer to form a hypergraph structure, on top of which, semisupervised transductive learning is conducted to obtain the final classification results. Our experiments on three data sets demonstrate the merits of our proposed approach, which compares favorably with state of the art.
On characterizing terrain visibility graphs
Directory of Open Access Journals (Sweden)
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
Optimal graph based segmentation using flow lines with application to airway wall segmentation
DEFF Research Database (Denmark)
Petersen, Jens; Nielsen, Mads; Lo, Pechin Chien Pau
2011-01-01
This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited for ...
Optimal graph based segmentation using flow lines with application to airway wall segmentation
DEFF Research Database (Denmark)
Petersen, Jens; Nielsen, Mads; Lo, Pechin
2011-01-01
This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited...
Directory of Open Access Journals (Sweden)
Jean Stawiaski
2011-05-01
Full Text Available In this paper, we discuss the use of graph-cuts to merge the regions of the watershed transform optimally. Watershed is a simple, intuitive and efficient way of segmenting an image. Unfortunately it presents a few limitations such as over-segmentation and poor detection of low boundaries. Our segmentation process merges regions of the watershed over-segmentation by minimizing a specific criterion using graph-cuts optimization. Two methods will be introduced in this paper. The first is based on regions histogram and dissimilarity measures between adjacent regions. The second method deals with efficient approximation of minimal surfaces and geodesics. Experimental results show that these techniques can efficiently be used for large images segmentation when a pre-computed low level segmentation is available. We will present these methods in the context of interactive medical image segmentation.
National Oceanic and Atmospheric Administration, Department of Commerce — Surface Total Alkalinity fields were estimated from five regional TA relationships presented in Lee et al. 2006, using monthly mean sea surface temperature and...
On some properties of doughnut graphs
Directory of Open Access Journals (Sweden)
Md. Rezaul Karim
2016-08-01
Full Text Available The class of doughnut graphs is a subclass of 5-connected planar graphs. It is known that a doughnut graph admits a straight-line grid drawing with linear area, the outerplanarity of a doughnut graph is 3, and a doughnut graph is k-partitionable. In this paper we show that a doughnut graph exhibits a recursive structure. We also give an efficient algorithm for finding a shortest path between any pair of vertices in a doughnut graph. We also propose a nice application of a doughnut graph based on its properties.
Completeness and regularity of generalized fuzzy graphs.
Samanta, Sovan; Sarkar, Biswajit; Shin, Dongmin; Pal, Madhumangal
2016-01-01
Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.
External Memory Graph Algorithms and Range Searching Data Structures
DEFF Research Database (Denmark)
Walderveen, Freek van
Every day larger amounts of data are generated that describe our world in terms of networks or graphs. Think for example about maps of roads or rivers, social networks, or the internet (either as a network of computers or as a network of hyperlinks). Besides this, also surface models, such as hei......Every day larger amounts of data are generated that describe our world in terms of networks or graphs. Think for example about maps of roads or rivers, social networks, or the internet (either as a network of computers or as a network of hyperlinks). Besides this, also surface models......, such as height models of the Earth, are often represented using graph structures. Traditionally, graphs were easily processed by computers using algorithms taught to any computer science undergraduate. Nowadays, however, graphs are so big that the assumptions underlying traditional algorithms no longer hold......: what used to be a simple graph traversal taking no time worth mentioning, suddenly takes years to complete. This increase is not merely a direct result of the bigger amount of data being processed, but mostly a result of the fact that this amount of data does not t in the computer's main memory anymore...
A graph-graph approach to the analysis of the set of associative rules
Belim, S. V.; Smirnova, T. B.; Mironenko, A. N.
2018-01-01
The article proposes a method for processing a set of associative rules, which makes it possible to identify additional relationships between the set of objects under study. The proposed approach consists of three stages. At the first stage, associative rules are revealed from the statistical data. At the second stage, constructed weighted oriented graph of relationships between the objects of the system. The third stage analyses the graph and identifies the community (community), which allows you to determine the groups of the most related objects. As an example, is given an analysis of the activities of public organizations. The result of the work is a method that allows to identify patterns from the analysis of a set of associative rules, and not just from a separate associative rule.
Colored graphs and matrix integrals
International Nuclear Information System (INIS)
Artamkin, I.V.
2007-12-01
In this article we discuss two different asymptotic expansions of matrix integrals. The original approach using the so-called Feynman diagram techniques leads to sums over isomorphism classes of ribbon graphs. Asymptotic expansions of more general Gaussian integrals are sums over isomorphism classes of colored graphs without ribbon structure. Here we derive the former expansion from the latter one. This provides an independent proof for the expansion used by Kontsevich. It might be very interesting to compare the algebra arising in these two approaches. The asymptotic expansion using ribbon graphs leads to the tau function of the KDV hierarchy while the sums over colored graphs satisfy simple partial differential equations which generalize the Burgers equation. We describe the general approach using colored graphs in the second section. In the third section we specialize the results of the second section for the matrix integral. In this section we also derive the expansion over ribbon graphs. The proof is based on simple topological considerations which are contained in section 5. In the last section we give an explicit calculation of the first term of the expansion using colored graphs
Hierarchy of modular graph identities
Energy Technology Data Exchange (ETDEWEB)
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Identifying vertex covers in graphs
DEFF Research Database (Denmark)
Henning, Michael A.; Yeo, Anders
2012-01-01
An identifying vertex cover in a graph G is a subset T of vertices in G that has a nonempty intersection with every edge of G such that T distinguishes the edges, that is, e∩T ≠ 0 for every edge e in G and e∩T ≠ f∩T for every two distinct edges e and f in G. The identifying vertex cover number TD......(G) of G is the minimum size of an identifying vertex cover in G. We observe that TD(G)+ρ(G) = |V (G)|, where ρ(G) denotes the packing number of G. We conjecture that if G is a graph of order n and size m with maximum degree Δ, then TD(G) ≤(Δ(Δ-1)/ Δ2+1)n + (2/Δ2+1) m. If the conjecture is true......, then the bound is best possible for all Δ ≥ 1. We prove this conjecture when Δ ≥ 1 and G is a Δ-regular graph. The three known Moore graphs of diameter 2, namely the 5-cycle, the Petersen graph and the Hoffman-Singleton graph, are examples of regular graphs that achieves equality in the upper bound. We also...
Energy Technology Data Exchange (ETDEWEB)
Romanchuk, Anna Y.; Kalmykov, Stephan N. [Lomonosov Moscow State Univ., Moscow (Russian Federation). Dept. of Chemistry
2014-07-01
The sorption of actinides in different valence states - Am(III), Th(IV), Np(V) and U(VI) onto hematite have been revisited with the special emphasis on the equilibrium constants of formation of surface species. The experimental sorption data have been treated using surface complexation modeling from which the set of new values of equilibrium constants were obtained. Formation of inner sphere monodentate surface species adequately describes the pH-sorption edges for actinide ions indicative the ionic electrostatic nature of bonding with small or no covalency contribution. The linear free energy relationship representing the correlation between the hydrolysis constants and surface complexation constants has been developed for various cations including K(I), Li(I), Na(I), Ag(I), Tl(I), Sr(II), Cu(II), Co(II), La(III), Eu(III), Ga(III), Am(III), Th(IV), Np(V), U(VI). (orig.)
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar...... (transformations between XML and non-XML data), and XSLT (stylesheets for transforming XML documents)....
Large networks and graph limits
Lovász, László
2012-01-01
Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. Developing a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as "property testing" in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact for
Relationship between types of surface shear stress profiles and membrane fouling.
Chan, C C V; Bérubé, P R; Hall, E R
2011-12-01
Shear stress has been recognized as an important parameter in controlling particle back-transport from membrane surfaces. However, little is known of the relationship between transient shear conditions induced by air sparging and fouling control near membrane surfaces. In this paper, the different types of surface shear stress profiles that had beneficial effects on minimizing reversible surface fouling were examined. The relationship between different statistical shear parameters (e.g. time-averaged shear, standard deviation of shear and amplitude of shear) and fouling control that have been used by others were examined as well. It was found that the fouling rate for membranes subjected to transient shear conditions was lower than for membranes subjected to constant shear conditions. The magnitude, duration and frequency of the shear conditions were found to have an impact on the fouling rate of membranes. It was also found that although some statistical shear parameters could generally be used to relate shear and fouling, they were inadequate to relate surface shear stress to fouling, for all transient shear conditions examined. Copyright Â© 2011 Elsevier Ltd. All rights reserved.
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
Abstract. Let T be a rooted tree, G a connected graph, x,y ∈ V(G) be fixed and Gi's be |V(T )| disjoint copies of G with xi and yi denoting the corresponding copies of x and y in Gi, respectively. We define the T -repetition of G to be the graph obtained by joining yi to xj for each i ∈ V(T ) and each child j of i. In this paper, we ...
Analysis of relationships between NDVI and land surface temperature in coastal area
Ning, Jicai; Gao, Zhiqiang; Chen, Maosi
2017-09-01
Using Landsat 5 Thematic Mapper and Landsat 8 Operational Land Imager and Thermal Infrared Sensor imagery of the Yellow River Delta, this study analyzed the relationships between NDVI and LST (land surface temperature). Six Landsat images comprising two time series were used to calculate the land surface temperature and correlated vegetation indices. The Yellow River Delta area has expanded substantially because of the deposited sediment carried from upstream reaches of the river. Between 1986 and 2015, approximately 35% of the land use area of the Yellow River Delta has been transformed into salterns and aquaculture ponds. Overall, land use conversion has occurred primarily from poorly utilized land into highly utilized land. To analyze the variation of land surface temperature, a mono-window algorithm was applied to retrieve the regional land surface temperature. The results showed bilinear correlation between land surface temperature and the vegetation indices (i.e., Normalized Difference Vegetation Index, Adjusted-Normalized Vegetation Index, Soil-Adjusted Vegetation Index, and Modified Soil-Adjusted Vegetation Index). Generally, values of the vegetation indices greater than the inflection point mean the land surface temperature and the vegetation indices are correlated negatively, and vice versa. Land surface temperature in coastal areas is affected considerably by local seawater temperature and weather conditions.
Graph theory and combinatorial optimization
Marcotte, Odile; Avis, David
2006-01-01
A current treatment of cutting-edge topics in Graph Theory and Combinatorial Optimization by leading researchersIncludes heuristic advances and novel approaches to solving combinatorial optimization problems.
Open Graphs and Computational Reasoning
Directory of Open Access Journals (Sweden)
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...... infrastructure for different symbolic positioning technologies, e.g., Bluetooth and RFID. More specifically, the paper proposes a model of indoor space that comprises a base graph and mappings that represent the topology of indoor space at different levels. The resulting model can be used for one or several...... indoor positioning technologies. Focusing on RFID-based positioning, an RFID specific reader deployment graph model is built from the base graph model. This model is then used in several algorithms for constructing and refining trajectories from raw RFID readings. Empirical studies with implementations...
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
Leuven: Katholieke Universiteit Leuven). (1990). [5] Etayo F, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen 53 (1998) 217–223. [6] Harary F, Graph Theory (Reading: Addison-Wesley) (1972). [7] Papaghiuc N ...
Graph anomalies in cyber communications
Energy Technology Data Exchange (ETDEWEB)
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
A contribution to queens graphs
DEFF Research Database (Denmark)
Barat, Janos
A graph $G$ is a queens graph if the vertices of $G$ can be mapped to queens on the chessboard such that two vertices are adjacent if and only if the corresponding queens attack each other, i.e. they are in horizontal, vertical or diagonal position. We prove a conjecture of Beineke, Broere...... and Henning that the Cartesian product of an odd cycle and a path is a queens graph. We show that the same does not hold for two odd cycles. % is not representable in the same way. The representation of the Cartesian product of an odd cycle and an even cycle remains an open problem. We also prove...... constructively that any finite subgraph of the grid or the hexagonal grid is a queens graph....
Equity trees and graphs via information theory
Harré, M.; Bossomaier, T.
2010-01-01
We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the "genus 0" condition recently introduced in order to study the networks of equities.
Entropy and the Complexity of Graphs Revisited
Directory of Open Access Journals (Sweden)
Matthias Dehmer
2012-03-01
Full Text Available This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined; and intrinsic (e.g., classical measures and extrinsic (e.g., Körner entropy variants of entropy-based models are discussed in some detail.
Adaptive visualization for large-scale graph
International Nuclear Information System (INIS)
Nakamura, Hiroko; Shinano, Yuji; Ohzahata, Satoshi
2010-01-01
We propose an adoptive visualization technique for representing a large-scale hierarchical dataset within limited display space. A hierarchical dataset has nodes and links showing the parent-child relationship between the nodes. These nodes and links are described using graphics primitives. When the number of these primitives is large, it is difficult to recognize the structure of the hierarchical data because many primitives are overlapped within a limited region. To overcome this difficulty, we propose an adaptive visualization technique for hierarchical datasets. The proposed technique selects an appropriate graph style according to the nodal density in each area. (author)
SOUR graphs for efficient completion
Lynch, Christopher; Strogova, Polina
1998-01-01
International audience; We introduce a data structure called \\emphSOUR graphs and present an efficient Knuth-Bendix completion procedure based on it. \\emphSOUR graphs allow for a maximal structure sharing of terms in rewriting systems. The term representation is a dag representation, except that edges are labelled with equational constraints and variable renamings. The rewrite rules correspond to rewrite edges, the unification problems to unification edges. The Critical Pair and Simplificatio...
Rectilinear Graphs and Angular Resolution
Bodlaender, H.L.; Tel, G.
2003-01-01
In this note we show that a planar graph with angular resolution at least π/2 can be drawn with all angles an integer multiple of π/2, that is, in a rectilinear manner. Moreover, we show that for d ≠ 4, d › 2, having an angular resolution of 2π/d does not imply that the graph can be drawn with all
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
On dominator colorings in graphs
Indian Academy of Sciences (India)
A dominator coloring of a graph G is a proper coloring of G in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G and is denoted by χd(G). In this paper we present several results on graphs ...
a generalization of total graphs
Indian Academy of Sciences (India)
8
Abstract. Let R be a commutative ring with nonzero identity, Ln(R) be the set of all lower triangular n × n matrices, and U be a triangular subset of. Rn i.e. the product of any lower triangular matrix with the transpose of any element of U, belongs to U. The graph GTn. U (Rn) is a simple graph whose ver- tices consists of all ...
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Summary 2: Graph Grammar Verification through Abstraction
Baldan, P.; Koenig, B.; Rensink, A.; Rensink, Arend; König, B.; Montanari, U.; Gardner, P.
2005-01-01
Until now there have been few contributions concerning the verification of graph grammars, specifically of infinite-state graph grammars. This paper compares two existing approaches, based on abstractions of graph transformation systems. While in the unfolding approach graph grammars are
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2009-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also inter-derive a graph evaluator....
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Hard graphs for the maximum clique problem
Hoede, C.
1988-01-01
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number.
Dynamic Programming on Nominal Graphs
Directory of Open Access Journals (Sweden)
Nicklas Hoch
2015-04-01
Full Text Available Many optimization problems can be naturally represented as (hyper graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.
Chromatic polynomials of random graphs
International Nuclear Information System (INIS)
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Graph Quasicontinuous Functions and Densely Continuous Forms
Directory of Open Access Journals (Sweden)
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
On P-transitive graphs and applications
Directory of Open Access Journals (Sweden)
Giacomo Lenzi
2011-06-01
Full Text Available We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.
Phage, Itumeleng B.; Lemmer, Miriam; Hitge, Mariette
2017-01-01
Students' graph comprehension may be affected by the background of the students who are the readers or interpreters of the graph, their knowledge of the context in which the graph is set, and the inferential processes required by the graph operation. This research study investigated these aspects of graph comprehension for 152 first year…
Hao, Ruizhe; Huang, Jian
2017-08-01
Knowledge graph construction in military intelligence domain is sprouting but technically immature. This paper presents a method to construct the heterogeneous knowledge graph in the field of shipborne and airborne radar and equipment. Based on the expert knowledge and the up-to-date Internet open source information, we construct the knowledge graph of radar characteristic information and the equipment respectively, and establish relationships between two graphs, providing the pipeline and method for the intelligence organization and management in the context of the crowding battlefields big data.
Improving Students' Understanding of Waves by Plotting a Displacement-Time Graph in Class
Wei, Yajun
2012-04-01
The topic of waves is one that many high school physics students find difficult to understand. This is especially true when using some A-level textbooks1,2used in the U.K., where the concept of waves is introduced prior to the concept of simple harmonic oscillations. One of the challenges my students encounter is understanding the difference between displacement-time graphs and displacement-position graphs. Many students wonder why these two graphs have the same sinusoidal shape. Having the students use multimedia simulations allows them to see, in a hands-on fashion, the relationship between the two graphs.
Extraction of Graph Information Based on Image Contents and the Use of Ontology
Kanjanawattana, Sarunya; Kimura, Masaomi
2016-01-01
A graph is an effective form of data representation used to summarize complex information. Explicit information such as the relationship between the X- and Y-axes can be easily extracted from a graph by applying human intelligence. However, implicit knowledge such as information obtained from other related concepts in an ontology also resides in…
Y. Liu; W. Wu; M. P. Jensen; T. Toto
2011-01-01
This paper focuses on three interconnected topics: (1) quantitative relationship between surface shortwave cloud radiative forcing, cloud fraction, and cloud albedo; (2) surfaced-based approach for measuring cloud albedo; (3) multiscale (diurnal, annual and inter-annual) variations and covariations of surface shortwave cloud radiative forcing, cloud fraction, and cloud albedo. An analytical expression is first derived to quantify the relationship between cloud radiative forcing, cloud fractio...
Y. Liu; W. Wu; M. P. Jensen; T. Toto
2011-01-01
This paper focuses on three interconnected topics: (1) quantitative relationship between surface shortwave cloud radiative forcing, cloud fraction, and cloud albedo; (2) surface-based approach for measuring cloud albedo; (3) multiscale (diurnal, annual and inter-annual) variations and covariations of surface shortwave cloud radiative forcing, cloud fraction, and cloud albedo. An analytical expression is first derived to quantify the relationship between cloud radiative forcing, cloud fraction...
Geometry of Graph Edit Distance Spaces
Jain, Brijnesh J.
2015-01-01
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem. It states that a graph is a point in some geometrical space, called orbit space. Orbit spaces are well investigated and easier to explore than the original graph space. We derive a number of geometrical results from the orbit space representation, translate ...
GraphMeta: Managing HPC Rich Metadata in Graphs
Energy Technology Data Exchange (ETDEWEB)
Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert
2016-01-01
High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
Directory of Open Access Journals (Sweden)
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Directory of Open Access Journals (Sweden)
Nicholas A. Famoso
2016-07-01
Full Text Available Enamel patterns on the occlusal surfaces of equid teeth are asserted to have tribal-level differences. The most notable example compares the Equini and Hipparionini, where Equini have higher crowned teeth with less enamel-band complexity and less total occlusal enamel than Hipparionini. Whereas previous work has successfully quantified differences in enamel band shape by dividing the length of enamel band by the square root of the occlusal surface area (Occlusal Enamel Index, OEI, it was clear that OEI only partially removes the effect of body size. Because enamel band length scales allometrically, body size still has an influence on OEI, with larger individuals having relatively longer enamel bands than smaller individuals. Fractal dimensionality (D can be scaled to any level, so we have used it to quantify occlusal enamel complexity in a way that allows us to get at an accurate representation of the relationship between complexity and body size. To test the hypothesis of tribal-level complexity differences between Equini and Hipparionini, we digitally traced a sample of 98 teeth, one tooth per individual; 31 Hipparionini and 67 Equini. We restricted our sampling to the P3-M2 to reduce the effect of tooth position. After calculating the D of these teeth with the fractal box method which uses the number of boxes of various sizes to calculate the D of a line, we performed a t-test on the individual values of D for each specimen, comparing the means between the two tribes, and a phylogenetically informed generalized least squares regression (PGLS for each tribe with occlusal surface area as the independent variable and D as the dependent variable. The slopes of both PGLS analyses were compared using a t-test to determine if the same linear relationship existed between the two tribes. The t-test between tribes was significant (p < 0.0001, suggesting different D populations for each lineage. The PGLS for Hipparionini was a positive but not
Yang, Qiquan; Huang, Xin; Li, Jiayi
2017-08-24
The urban heat island (UHI) effect exerts a great influence on the Earth's environment and human health and has been the subject of considerable attention. Landscape patterns are among the most important factors relevant to surface UHIs (SUHIs); however, the relationship between SUHIs and landscape patterns is poorly understood over large areas. In this study, the surface UHI intensity (SUHII) is defined as the temperature difference between urban and suburban areas, and the landscape patterns are quantified by the urban-suburban differences in several typical landscape metrics (ΔLMs). Temperature and land-cover classification datasets based on satellite observations were applied to analyze the relationship between SUHII and ΔLMs in 332 cities/city agglomerations distributed in different climatic zones of China. The results indicate that SUHII and its correlations with ΔLMs are profoundly influenced by seasonal, diurnal, and climatic factors. The impacts of different land-cover types on SUHIs are different, and the landscape patterns of the built-up and vegetation (including forest, grassland, and cultivated land) classes have the most significant effects on SUHIs. The results of this study will help us to gain a deeper understanding of the relationship between the SUHI effect and landscape patterns.
Rudén, Jonas; Frenning, Göran; Bramer, Tobias; Thalberg, Kyrre; Alderborn, Göran
2018-04-25
The aim of this paper was to study relationships between the content of fine particles and the powder mechanics of binary adhesive mixtures and link these relationships to the blend state. Mixtures with increasing amounts of fine particles (increasing surface coverage ratios (SCR)) were prepared using Lactopress SD as carrier and micro particles of lactose as fines (2.7 µm). Indicators of unsettled bulk density, compressibility and flowability were derived and the blend state was visually examined by imaging. The powder properties studied showed relationships to the SCR characterised by stages. At low SCR, the fine particles predominantly gathered in cavities of the carriers, giving increased bulk density and unchanged or improved flow. Thereafter, increased SCR gave a deposition of particles at the enveloped carrier surface with a gradually more irregular adhesion layer leading to a reduced bulk density and a step-wise reduced flowability. The mechanics of the mixtures at a certain stage were dependent on the structure and the dynamics of the adhesion layer and transitions between the stages were controlled by the evolution of the adhesion layer. It is advisable to use techniques based on different types of flow in order to comprehensively study the mechanics of adhesive mixtures. Copyright © 2018 Elsevier B.V. All rights reserved.
Subaer, Ekaputri, Januari Jaya; Fansuri, Hamzah; Abdullah, Mustafa Al Bakri
2017-09-01
An experimental study to investigate the relationship between Vickers microhardness and compressive strength of geopolymers made from metakaolin has been conducted. Samples were prepared by using metakaolin activated with a sodium silicate solution at a different ratio of Si to Al and Na to Al and cured at 70oC for one hour. The resulting geopolymers were stored in an open air for 28 days before conducting any measurement. Bulk density and apparent porosity of the samples were measured by using Archimedes's method. Vickers microhardness measurements were performed on a polished surface of geopolymers with a load ranging from 0.3 - 1.0 kg. The topographic of indented samples were examined by using scanning electron microscopy (SEM). Compressive strength of the resulting geopolymers was measured on the cylindrical samples with a ratio of height to the diameter was 2:1. The results showed that the molar ratios of geopolymers compositions play important roles in the magnitude of bulk density, porosity, Vickers's microhardness as well as the compressive strength. The porosity reduced exponentially the magnitude of the strength of geopolymers. It was found that the relationship between Vickers microhardness and compressive strength was linear. At the request of all authors and with the approval of the proceedings editor, article 020188 titled, "The relationship between vickers microhardness and compressive strength of functional surface geopolymers," is being retracted from the public record due to the fact that it is a duplication of article 020170 published in the same volume.
Spatio-Temporal Relationship Between Surface Temperature and NDVI Using Remotely Sensed data
Ghobadi, Yasser; Pradhan, Biswajeet; Kabiri, Keivan
2016-07-01
Land surface temperature (LST) is a significant factor to analyze the global climate changes, and LULC (Land use/Land cover) changes, as well as urban thermal behavior. Land surface temperature exhibit the surface atmosphere in relation with energy flux between earth and atmosphere. This paper intended to examine the evaluation of LST and assessment of relationship between LST and normalized difference vegetation index (NDVI) with associated different LULC. Al- Hawizeh wetland located in the Iraq-Iran border was selected as a study area. Two Landsat satellite thermal infrared (TIR) images of October 26, 1998, thematic mapper (TM), and October 26, 2002 enhanced thematic mapper (ETM+) were used. Both images were corrected geometrically and atmospherically before carried out any analysis. NDVI was estimated from reflectance values of the visible band (band 3, Red) and the near infrared band (band 4, VNIR). Maximum likelihood classifier (MLC) was applied to determine the different LULC. Plank equation was utilized to extract land surface temperature over the study region. The results provide information about the spatial distribution of LST over different LULC during mentioned date. The highest mean temperature was observed over the rangeland and the lowest mean temperature was found in water bodies. The results of regression analysis exhibited that the LST and NDVI has an inverse correlation except for water bodies. The negative correlation coefficient was observed over vegetation (-0.733, R2=0.66). Keywords-component; Land Surface Temperature, Remote Sensing, Al-Havizeh wetland, Regression Analysis, NDVI, GIS
Nagura, Yuko; Tsujimoto, Akimasa; Barkmeier, Wayne W; Watanabe, Hidehiko; Johnson, William W; Takamizawa, Toshiki; Latta, Mark A; Miyazaki, Masashi
2018-04-01
The relationship between enamel bond fatigue durability and surface free-energy characteristics with universal adhesives was investigated. The initial shear bond strengths and shear fatigue strengths of five universal adhesives to enamel were determined with and without phosphoric acid pre-etching. The surface free-energy characteristics of adhesive-treated enamel with and without pre-etching were also determined. The initial shear bond strength and shear fatigue strength of universal adhesive to pre-etched enamel were higher than those to ground enamel. The initial shear bond strength and shear fatigue strength of universal adhesive to pre-etched enamel were material dependent, unlike those to ground enamel. The surface free-energy of the solid (γ S ) and the hydrogen-bonding force (γSh) of universal adhesive-treated enamel were different depending on the adhesive, regardless of the presence or absence of pre-etching. The bond fatigue durability of universal adhesives was higher to pre-etched enamel than to ground enamel. In addition, the bond fatigue durability to pre-etched enamel was material dependent, unlike that to ground enamel. The surface free-energy characteristics of universal adhesive-treated enamel were influenced by the adhesive type, regardless of the presence or absence of pre-etching. The surface free-energy characteristics of universal adhesive-treated enamel were related to the results of the bond fatigue durability. © 2018 Eur J Oral Sci.
Directory of Open Access Journals (Sweden)
Peleg Kremer
2018-02-01
Full Text Available Understanding the relationship between urban structure and ecological function—or environmental performance—is important for the planning of sustainable cities, and requires examination of how components in urban systems are organized. In this paper, we develop a Structure of Urban Landscape (STURLA classification, identifying common compositions of urban components using Berlin, Germany as a case study. We compute the surface temperature corresponding to each classification grid cell, and perform within-cell and neighborhood analysis for the most common composite classes in Berlin. We found that with-class composition and neighborhood composition as well as the interaction between them drive surface temperature. Our findings suggest that the spatial organization of urban components is important in determining the surface temperature and that specific combinations, such as low-rise buildings surrounded by neighborhood trees, or mid-rise buildings surrounded by high-rise buildings, compound to create a cooling effect. These findings are important for developing an understanding of how urban planning can harness structure-function relationships and improve urban sustainability.
Jackson, C.; Zaroff, S.; Heim, N. A.; Payne, J.
2014-12-01
In 1877 Joseph Allen proposed that endothermic terrestrial organisms would have lower surface area to volume ratios (SAVR) in colder climates and higher SAVRs in warmer climates. With a smaller surface area compared to volume, organisms can retain more heat in cold climates. We tested to see if this principle applied to ostracods, a type of ectothermic marine invertebrate. We hypothesised that Allen's rule applies to ostracods, as Allen's rule has been demonstrated in frogs (Alho 2011), which are also ectotherms . We used the linear dimensions of the three major carapace axes of ostracod holotypes to estimate the SAVR. We compared ostracod SAVRs with paleotemperatures from Royer et al. (2004). We found that there was a correlation between surface area and temperature; it is a small, but statistically significant correlation (adj. R2=0.0167). This means that as temperature increased, the SAVR also increased. We also found a negative correlation between ostracod SAVR to geologic time(adj. R2=0.0114), which shows us that as time has gone on, ostracod SAVR has decreased. We then plotted the correlation coefficient of SAVR to temperature over geologic time to explore trends in the strength of Allen's rule. For most of time there was no relationship but during the Devonian, Allen's Rule did explain the trend. In short, temperature does explain some of the correlation between the SAVR and temperature, but it is likely there were other environmental factors affecting this relationship.
Calculators, Graphs, Gestures and the Production of Meaning
Radford, Luis; Demers, Serge; Guzman, Jose; Cerulli, Michele
2003-01-01
In this paper we report an analysis of a teaching sequence in which Grade 11 students were asked to produce some graphs corresponding to the relationship between time and distance of a cylinder moving up and down an inclined plane. The students were also asked to carry out the experience using a TI 83+ graphic calculator equipped with a sensor,…
Directory of Open Access Journals (Sweden)
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Hierarchical organisation of causal graphs
International Nuclear Information System (INIS)
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
preprocessing time, an O(n log n) time algorithm for the replacement paths problem, and a min st-cut oracle with nearlinear preprocessing time. We also give improved time bounds for computing various graph invariants such as diameter and girth. In the second part, we consider stretch factor problems...... a graph with new edges while minimizing stretch factor. The third and final part of the thesis deals with the Steiner tree problem in the plane equipped with a weighted fixed orientation metric. Here, we give an improved theoretical analysis of the strength of pruning techniques applied by many Steiner...
An algebraic approach to graph codes
DEFF Research Database (Denmark)
Pinero, Fernando
theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...... are optimal or best known for their parameters. In chapter five we study some graph codes with Reed–Solomon component codes. The underlying graph is well known and widely used for its good characteristics. This helps us to compute the dimension of the graph codes. We also introduce a combinatorial concept...... related to the iterative encoding of graph codes with MDS component code. The last chapter deals with affine Grassmann codes and Grassmann codes. We begin with some previously known codes and prove that they are also Tanner codes of the incidence graph of the point–line partial geometry...
A novel line segment detection algorithm based on graph search
Zhao, Hong-dan; Liu, Guo-ying; Song, Xu
2018-02-01
To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).
Near-surface turbulence as a missing link in modeling evapotranspiration-soil moisture relationships
Haghighi, Erfan; Kirchner, James W.
2017-07-01
Despite many efforts to develop evapotranspiration (ET) models with improved parametrizations of resistance terms for water vapor transfer into the atmosphere, estimates of ET and its partitioning remain prone to bias. Much of this bias could arise from inadequate representations of physical interactions near nonuniform surfaces from which localized heat and water vapor fluxes emanate. This study aims to provide a mechanistic bridge from land-surface characteristics to vertical transport predictions, and proposes a new physically based ET model that builds on a recently developed bluff-rough bare soil evaporation model incorporating coupled soil moisture-atmospheric controls. The newly developed ET model explicitly accounts for (1) near-surface turbulent interactions affecting soil drying and (2) soil-moisture-dependent stomatal responses to atmospheric evaporative demand that influence leaf (and canopy) transpiration. Model estimates of ET and its partitioning were in good agreement with available field-scale data, and highlight hidden processes not accounted for by commonly used ET schemes. One such process, nonlinear vegetation-induced turbulence (as a function of vegetation stature and cover fraction) significantly influences ET-soil moisture relationships. Our results are particularly important for water resources and land use planning of semiarid sparsely vegetated ecosystems where soil surface interactions are known to play a critical role in land-climate interactions. This study potentially facilitates a mathematically tractable description of the strength (i.e., the slope) of the ET-soil moisture relationship, which is a core component of models that seek to predict land-atmosphere coupling and its feedback to the climate system in a changing climate.
Relationship among land surface temperature and LUCC, NDVI in typical karst area.
Deng, Yuanhong; Wang, Shijie; Bai, Xiaoyong; Tian, Yichao; Wu, Luhua; Xiao, Jianyong; Chen, Fei; Qian, Qinghuan
2018-01-12
Land surface temperature (LST) can reflect the land surface water-heat exchange process comprehensively, which is considerably significant to the study of environmental change. However, research about LST in karst mountain areas with complex topography is scarce. Therefore, we retrieved the LST in a karst mountain area from Landsat 8 data and explored its relationships with LUCC and NDVI. The results showed that LST of the study area was noticeably affected by altitude and underlying surface type. In summer, abnormal high-temperature zones were observed in the study area, perhaps due to karst rocky desertification. LSTs among different land use types significantly differed with the highest in construction land and the lowest in woodland. The spatial distributions of NDVI and LST exhibited opposite patterns. Under the spatial combination of different land use types, the LST-NDVI feature space showed an obtuse-angled triangle shape and showed a negative linear correlation after removing water body data. In summary, the LST can be retrieved well by the atmospheric correction model from Landsat 8 data. Moreover, the LST of the karst mountain area is controlled by altitude, underlying surface type and aspect. This study provides a reference for land use planning, ecological environment restoration in karst areas.
International Nuclear Information System (INIS)
Kay, S.E.; Dougherty, M.E.; Pelton, J.R.
1994-01-01
Seismic velocity has been shown in previous engineering studies to be related to the fracture characteristics and rippability of rock outcrops. However, common methods of measuring seismic velocity in outcrops do not take into account the many possible travel paths for wave propagation and the fact that velocity zones may exist within an outcrop. Presented here are the results of using raytracing inversion of first-arrival travel-time data to map P-velocity structure in basalt outcrops, and also the investigation of the relationship of the mapped velocities to observed surface fractures and hand-sample P-velocities. It is shown that basalt outcrops commonly consist of an irregular near-surface low-velocity zone underlain by higher velocity material; that velocity gradients can exist in outcrops; that hand-sample velocity measurements are typically higher than outcrop-scale measurements; and that the characteristics of surface fractures are empirically related to near-surface P-velocity. All of these findings are relevant to the estimated rippability of rock in geotechnical engineering. The data for this study are derived from eleven sites on basalt outcrops of the Troodos Ophiolite in Cyprus. The basalt types include pillow basalts, massive flows, and a pillow breccia. A commonly available raytracing inversion program (RAYINVR) was used to produce a velocity profile of each outcrop. Different velocity zones were detailed by inverting observed travel times to produce a model of outcrop velocity structure which produces rippability profiles for each outcrop. 16 refs., 9 figs
Nodal Statistics on Quantum Graphs
Alon, Lior; Band, Ram; Berkolaiko, Gregory
2018-03-01
It has been suggested that the distribution of the suitably normalized number of zeros of Laplacian eigenfunctions contains information about the geometry of the underlying domain. We study this distribution (more precisely, the distribution of the "nodal surplus") for Laplacian eigenfunctions of a metric graph. The existence of the distribution is established, along with its symmetry. One consequence of the symmetry is that the graph's first Betti number can be recovered as twice the average nodal surplus of its eigenfunctions. Furthermore, for graphs with disjoint cycles it is proven that the distribution has a universal form—it is binomial over the allowed range of values of the surplus. To prove the latter result, we introduce the notion of a local nodal surplus and study its symmetry and dependence properties, establishing that the local nodal surpluses of disjoint cycles behave like independent Bernoulli variables.
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Hoyer, J.; Madsen, K. S.; Englyst, P. N.
2017-12-01
Determining the surface and near surface air temperature from models or observations in the Polar Regions is challenging due to the extreme conditions and the lack of in situ observations. The errors in near surface temperature products are typically larger than for other regions of the world, and the potential for using Earth Observations is large. As part of the EU project, EUSTACE, we have developed empirical models for the relationship between the satellite observed skin ice temperatures and 2m air temperatures. We use the Arctic and Antarctic Sea and sea ice Surface Temperatures from thermal Infrared satellite sensors (AASTI) reanalysis to estimate daily surface air temperature over land ice and sea ice for the Arctic and the Antarctic. Large efforts have been put into collecting and quality controlling in situ observations from various data portals and research projects. The reconstruction is independent of numerical weather prediction models and thus provides an important alternative to modelled air temperature estimates. The new surface air temperature data record has been validated against more than 58.000 independent in situ measurements for the four surface types: Arctic sea ice, Greenland ice sheet, Antarctic sea ice and Antarctic ice sheet. The average correlations are 92-97% and average root mean square errors are 3.1-3.6°C for the four surface types. The root mean square error includes the uncertainty of the in-situ measurement, which ranges from 0.5 to 2°C. A comparison with ERA-Interim shows a consistently better performance of the satellite based air temperatures than the ERA-Interim for the Greenland ice sheet, when compared against observations not used in any of the two estimates. This is encouraging and demonstrates the values of these products. In addition, the procedure presented here works on satellite observations that are available in near real time and this opens up for a near real time estimation of the surface air temperature over
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
An intersection graph of straight lines
DEFF Research Database (Denmark)
Thomassen, Carsten
2002-01-01
G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is.......G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
Graph Processing on GPUs: A Survey
DEFF Research Database (Denmark)
Shi, Xuanhua; Zheng, Zhigao; Zhou, Yongluan
2018-01-01
In the big data era, much real-world data can be naturally represented as graphs. Consequently, many application domains can be modeled as graph processing. Graph processing, especially the processing of the large-scale graphs with the number of vertices and edges in the order of billions or even......, utilizing GPU to accelerate graph processing proves to be a promising solution. This article surveys the key issues of graph processing on GPUs, including data layout, memory access pattern, workload mapping, and specific GPU programming. In this article, we summarize the state-of-the-art research on GPU...
47 CFR 73.184 - Groundwave field strength graphs.
2010-10-01
... variation of the groundwave field strength with distance to be expected for transmission from a vertical... Propagation of Radio Waves Over the Surface of the Earth and in the Upper Atmosphere,” Part II, by Mr. K.A... 80f1/3 MHz kilometers (i.e., 80 kilometers at 1 MHz). Then, using a light box, place the plotted graph...
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Andersson, Mattias
2011-01-01
A star graph consists of a vertex to which a set of edges are connected. Such an object can be used to, among other things, model the electromagnetic properties of quantum wires. A scalar field theory is constructed on the star graph and its properties are investigated. It turns out that there exist Kirchoff's rules for the conserved charges in the system leading to restrictions of the possible type of boundary conditions at the vertex. Scale invariant boundary conditions are investigated in...
Completely Described Undirected Graph Structure
Directory of Open Access Journals (Sweden)
G. S. Ivanova
2016-01-01
Full Text Available The objects of research are undirected graphs. The paper considers a problem of their isomorphism. A literature analysis of its solution, has shown that there is no way to define a complete graph invariant in the form of unique structural characteristics of each its vertex, which has a computational complexity of definition better than О (n 4 .The work objective is to provide the characteristics of the graph structure, which could be used to solve the problem of their isomorphism for a time better than О (n 4 . As such characteristics, the paper proposes to use the set of codes of tree roots of all the shortest - in terms of the number of edges - paths from each vertex to the others, uniquely defining the structure of each tree. It proves the theorem that it is possible to reduce the problem of isomorphism of the undirected graphs to the isomorphism problem of their splitting into the trees of all the shortest - in terms of the number of edges - paths of each vertex to the others. An algorithm to construct the shortest paths from each vertex to all others and to compute codes of their vertices has been developed. As the latter, are used Aho-codes, which find application in recognising the isomorphism of trees. The computational complexity to obtain structural characteristics of vertices has been estimated to be about О (n 3 .The pilot studies involved the full-scale experiment using the developed complex programmes to generate raw data, i.e. analytic representation of the graph with the number of vertices equal to 1200, and a programme to provide codes of the tree roots. To have an estimate of - "the worst" in terms of time - complexity of expansion algorithm of graphs into trees of the shortest paths and define the codes of their roots has been an experimentally studied how the number of tree vertices depends on the graph density. For the worst case was obtained a dependence of the number of tree vertices on the number of graph vertices
Some Invariants of Jahangir Graphs
Directory of Open Access Journals (Sweden)
Mobeen Munir
2017-01-01
Full Text Available In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results.
Graph abstraction and abstract graph transformations (Amended version)
Boneva, I.B.; Kreiker, Jörg; Kurban, M.E.; Rensink, Arend; Zambon, Eduardo
2012-01-01
Many important systems such as concurrent heap-manipulating programs, communication networks, or distributed algorithms, are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation for the states of these systems, where transitions can be conveniently
Directory of Open Access Journals (Sweden)
S. B. Kakade
2012-01-01
Full Text Available Effective Strength Index (ESI is the relative strength of NAO and SO. ESI tendency is the algebraic difference between April-ESI and January-ESI and it represents the simultaneous evolution of NAO and SO from winter to spring. During positive (negative phase of ESI tendency, NAO restores positive (negative phase and SO restores negative (positive phase before the beginning of summer season. Thus during contrasting phases (positive and negative of ESI tendency, the evolution of NAO and SO is out of phase. In this paper we have studied the spatial and temporal variability of winter-time temperature field over Europe, Arabian Sea and Bay of Bengal during contrasting phases of ESI tendency. The study reveals that during positive (negative ESI tendency, smaller (larger region of Europe is showing significant winter-time cooling (warming at surface. The relationship between winter-time surface temperature over above regions and Indian summer monsoon rainfall (ISMR also shows spatial and temporal variability. The probable explanation for this change in the relationship is discussed in the paper. Two sets of temperature parameters for two different phases of ESI tendency are found out. Multiple regression equations are developed for the prediction of ISMR in each phase of ESI tendency. The performance of these equations is also discussed in this paper.
International Nuclear Information System (INIS)
Narayan, Padma; Hancock, Bruno C.
2003-01-01
Several common pharmaceutical excipient powders were compacted at a constant solid fraction (SF) in order to study the relationship between powder properties, compact surface roughness, and compact mechanical properties such as hardness, elasticity, and brittleness. The materials used in this study included microcrystalline cellulose (MCC), fumaric acid, mannitol, lactose monohydrate, spray dried lactose, sucrose, and dibasic calcium phosphate dihydrate. A slow consolidation process was used to make compacts at a SF of 0.85 (typical for most pharmaceutical tablets) from single excipient components. A model was proposed to describe the surface roughness of compacts based on the brittle or ductile deformation tendencies of the powder materials. The roughness profile would also be dependent upon the magnitude of the compression stress in relation to the yield stress (onset of irreversible deformation) values of the excipients. It was hypothesized that brittle materials would produce smooth compacts with high surface variability due to particle fracture, and the converse would apply for ductile materials. Compact surfaces should be smoother if the materials were compressed above their yield pressure values. Non-contact optical profilometry was used along with scanning electron microscopy to quantify and characterize the surface morphology of the excipient compacts. The roughness parameters R a (average roughness), R q (RMS roughness), R q /R a (ratio describing surface variability), and R sk (skewness) were found to correlate with the deformation properties of the excipients. Brittle materials such as lactose, sucrose, and calcium phosphate produced compacts with low values of R a and R q , high variability, and negative R sk . The opposite was found with plastic materials such as MCC, mannitol, and fumaric acid. The highly negative skewness values for brittle material compacts may indicate their propensity to be vulnerable to cracks or surface defects. These findings
GraphCom: A multidimensional measure of graphic complexity applied to 131 written languages.
Chang, Li-Yun; Chen, Yen-Chi; Perfetti, Charles A
2018-02-01
We report a new multidimensional measure of visual complexity (GraphCom) that captures variability in the complexity of graphs within and across writing systems. We applied the measure to 131 written languages, allowing comparisons of complexity and providing a basis for empirical testing of GraphCom. The measure includes four dimensions whose value in capturing the different visual properties of graphs had been demonstrated in prior reading research-(1) perimetric complexity, sensitive to the ratio of a written form to its surrounding white space (Pelli, Burns, Farell, & Moore-Page, 2006); (2) number of disconnected components, sensitive to discontinuity (Gibson, 1969); (3) number of connected points, sensitive to continuity (Lanthier, Risko, Stolz, & Besner, 2009); and (4) number of simple features, sensitive to the strokes that compose graphs (Wu, Zhou, & Shu, 1999). In our analysis of the complexity of 21,550 graphs, we (a) determined the complexity variation across writing systems along each dimension, (b) examined the relationships among complexity patterns within and across writing systems, and (c) compared the dimensions in their abilities to differentiate the graphs from different writing systems, in order to predict human perceptual judgments (n = 180) of graphs with varying complexity. The results from the computational and experimental comparisons showed that GraphCom provides a measure of graphic complexity that exceeds previous measures in its empirical validation. The measure can be universally applied across writing systems, providing a research tool for studies of reading and writing.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-11-19
Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Multiple graph regularized protein domain ranking
Directory of Open Access Journals (Sweden)
Wang Jim
2012-11-01
Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Graph reconstruction with a betweenness oracle
DEFF Research Database (Denmark)
Abrahamsen, Mikkel; Bodwin, Greg; Rotenberg, Eva
2016-01-01
Graph reconstruction algorithms seek to learn a hidden graph by repeatedly querying a blackbox oracle for information about the graph structure. Perhaps the most well studied and applied version of the problem uses a distance oracle, which can report the shortest path distance between any pair....... Despite this, we are able to develop betweenness reconstruction algorithms that match the current state of the art for distance reconstruction, and even improve it for certain types of graphs. We obtain the following algorithms: 1. Reconstruction of general graphs in O(n2) queries 2. Reconstruction...... of degree-bounded graphs in Õ(n3/2) queries 3. Reconstruction of geodetic degree-bounded graphs in Õ(n) queries In addition to being a fundamental graph theoretic problem with some natural applications, our new results shed light on some avenues for progress in the distance reconstruction problem....
Use of Spatial Transformations in Graph Comprehension
National Research Council Canada - National Science Library
Trickett, Susan B; Trafton, J. G
2004-01-01
Current theories of graph comprehension are largely silent about the processes by which inferences are made from graphs, although it is apparent that people are able to make such inferences. In Trickett & Trafton (2004...
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 12; Issue 1. A Problem in Graph Theory. K P Savithri. Think It Over Volume 12 Issue 1 January 2007 pp 81-81. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/012/01/0081-0081. Author Affiliations.
Box graphs and singular fibers
International Nuclear Information System (INIS)
Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schäfer-Nameki, Sakura
2014-01-01
We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6 , E 7 and E 8
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Contracting a planar graph efficiently
DEFF Research Database (Denmark)
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges. By applying th...
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Indian Academy of Sciences (India)
Examples: Some explicit computations. Throughout this section, we will assume that ( , μ) is a finite, connected, weighted graph. The adjacency matrix of (which, by abuse of notation, will also be denoted by ) is, as usual, the symmetric matrix with rows and columns indexed by the vertex set V of and. (v, w) = |{e ∈ E : s(e) = v, ...
Affect and Graphing Calculator Use
McCulloch, Allison W.
2011-01-01
This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…
On dominator colorings in graphs
Indian Academy of Sciences (India)
A dominator coloring of a graph is a proper coloring of in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of is called the dominator chromatic number of and is denoted by d ( G ) . In this paper we present several results on ...
Czech Academy of Sciences Publication Activity Database
Hussein, A.; Krejčiřík, David; Siegl, P.
2015-01-01
Roč. 367, č. 4 (2015), s. 2921-2957 ISSN 0002-9947 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Laplacians on metric graphs * non-self-adjoint boundary conditions * similarity transforms to self-adjoint operators * Riesz basis Subject RIV: BE - Theoretical Physics Impact factor: 1.196, year: 2015
GRAPHIE: graph based histology image explorer.
Ding, Hao; Wang, Chao; Huang, Kun; Machiraju, Raghu
2015-01-01
Histology images comprise one of the important sources of knowledge for phenotyping studies in systems biology. However, the annotation and analyses of histological data have remained a manual, subjective and relatively low-throughput process. We introduce Graph based Histology Image Explorer (GRAPHIE)-a visual analytics tool to explore, annotate and discover potential relationships in histology image collections within a biologically relevant context. The design of GRAPHIE is guided by domain experts' requirements and well-known InfoVis mantras. By representing each image with informative features and then subsequently visualizing the image collection with a graph, GRAPHIE allows users to effectively explore the image collection. The features were designed to capture localized morphological properties in the given tissue specimen. More importantly, users can perform feature selection in an interactive way to improve the visualization of the image collection and the overall annotation process. Finally, the annotation allows for a better prospective examination of datasets as demonstrated in the users study. Thus, our design of GRAPHIE allows for the users to navigate and explore large collections of histology image datasets. We demonstrated the usefulness of our visual analytics approach through two case studies. Both of the cases showed efficient annotation and analysis of histology image collection.
Application of graph database for analytical tasks
Günzl, Richard
2014-01-01
This diploma thesis is about graph databases, which belong to the category of database systems known as NoSQL databases, but graph databases are beyond NoSQL databases. Graph databases are useful in many cases thanks to native storing of interconnections between data, which brings advantageous properties in comparison with traditional relational database system, especially in querying. The main goal of the thesis is: to describe principles, properties and advantages of graph database; to desi...
Bond graph modeling of centrifugal compression systems
Uddin, Nur; Gravdahl, Jan Tommy
2015-01-01
A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...
A Graph Calculus for Predicate Logic
Directory of Open Access Journals (Sweden)
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Unsupervised Deep Haar Scattering on Graphs
Chen, Xu; Cheng, Xiuyuan; Mallat, Stéphane
2014-01-01
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep cascade of additions, subtractions and absolute values, which iteratively compute orthogonal Haar wavelet transforms. Multiscale neighborhoods of unknown graphs are estimated by minimizing an average total variation, with a pair matching algorith...
Sheng, Bo; Lv, Furong; Xiao, Zhibo; Ouyang, Yu; Lv, Fajin; Deng, Jinmu; You, Yunfeng; Liu, Nan
2012-10-01
The purpose of this study was to determine the reliability of applying conventional anatomical landmarks to locate venous sinus in posterior fossa using subtraction computed tomography angiography (CTA) technique. We retrospectively reconstructed transverse sinus (TS), sigmoid sinus (SS), and cranial imaging from 100 patients undergoing head CTA examination. Subtraction CTA data was merged with nonenhanced data and then cranium transparency was adjusted to 50% on three-dimensional volume rendering, indicating the anatomical relationship between surface landmarks of cranium and confluens sinuum, TS, and SS. CTA technique precisely displayed the anatomical relations between venous sinus in posterior fossa and cranial surface landmarks. The asterion was located directly over the transverse-sigmoid sinus junction (TSST) in 81% cases, inferior to TSST in 15%, and superior to TSST in 4%, mainly distributing on the TS side of TSST, namely the distal-end of TS. Superior nuchal line had complex relation with TS and the line drawn from the zygoma root to the inion (LZI), but failed to represent the location of TS and the trend of LZI. In proximal-end of TS, majority of LZI overlapped with TS line. However, most LZI was gradually positioned below TS line as TS moved outwards. Almost half of line drawn from the squamosal-parietomastoid suture junction to the inion and line drawn from the asterion to the inion shared the same trend with TS. Subtraction CTA merged into nonenhanced cranial bone with 50% skull transparency provides a feasible method to identify the anatomical relation between venous sinus and surface landmarks of cranium, which is significantly varied among individuals, so it is not accurate to determine venous sinus in posterior fossa merely using surface landmarks.
On m-Neighbourly Irregular Instuitionistic Fuzzy Graphs
N.R.Santhi Maheswari; C.Sekar
2016-01-01
In this paper, m-neighbourly irregular intuitionistic fuzzy graphs and m- neighbourly totally irregular intuitionistic fuzzy graphs are defined. Relation between m-neighbourly irregular intuitionistic fuzzy graph and m-neighbourly totally irregular intuitionistic fuzzy graph are discussed.
Construction of cycle double covers for certain classes of graphs
Hoede, C.; Kriesell, M.; Uttuggadewa, S.
2000-01-01
We introduce two classes of graphs, Indonesian graphs and $k$-doughnut graphs. Cycle double covers are constructed for these classes. In case of doughnut graphs this is done for the values $k=1,2,3$ and 4.
Graph Partitioning Models for Parallel Computing
Energy Technology Data Exchange (ETDEWEB)
Hendrickson, B.; Kolda, T.G.
1999-03-02
Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, S.; van den Broek, P.M.; Avgeriou, P.; Zdun, U.; Borne, I.
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
Cycles in weighted graphs and related topics
Zhang, Shenggui
2002-01-01
This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain
Collaborative Robotic Instruction: A Graph Teaching Experience
Mitnik, Ruben; Recabarren, Matias; Nussbaum, Miguel; Soto, Alvaro
2009-01-01
Graphing is a key skill in the study of Physics. Drawing and interpreting graphs play a key role in the understanding of science, while the lack of these has proved to be a handicap and a limiting factor in the learning of scientific concepts. It has been observed that despite the amount of previous graph-working experience, students of all ages…
Integral complete r-partite graphs
Wang, Ligong; Li, Xueliang; Hoede, C.
2004-01-01
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that
Verification Techniques for Graph Rewriting (Tutorial)
Rensink, Arend; Abdulla, Parosh Aziz; Gadducci, Fabio; König, Barbara; Vafeiadis, Viktor
This tutorial paints a high-level picture of the concepts involved in verification of graph transformation systems. We distinguish three fundamentally different application scenarios for graph rewriting: (1) as grammars (in which case we are interested in the language, or set, of terminal graphs for
Graph Transformation Semantics for a QVT Language
Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel
It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to
A new cluster algorithm for graphs
S. van Dongen
1998-01-01
textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
Destroying longest cycles in graphs and digraphs
DEFF Research Database (Denmark)
Van Aardt, Susan A.; Burger, Alewyn P.; Dunbar, Jean E.
2015-01-01
In 1978, C. Thomassen proved that in any graph one can destroy all the longest cycles by deleting at most one third of the vertices. We show that for graphs with circumference k≤8 it suffices to remove at most 1/k of the vertices. The Petersen graph demonstrates that this result cannot be extended...
Structure of simplicial complexes of graphs representing ...
Indian Academy of Sciences (India)
Abstract. Mapping time series onto graphs and the use of graph theory methods opens up the possibility to study the structure of the phase space manifolds underlying the fluctuations of a dynamical variable. Here, we go beyond the standard graph measures and analyze the higher-order structures such as triangles, ...
Strongly 2-connected orientations of graphs
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove that a graph admits a strongly 2-connected orientation if and only if it is 4-edge-connected, and every vertex-deleted subgraph is 2-edge-connected. In particular, every 4-connected graph has such an orientation while no cubic 3-connected graph has such an orientation....
So Many Graphs, So Little Time
Wall, Jennifer J.; Benson, Christine C.
2009-01-01
Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…
On topological indices for small RNA graphs.
Churkin, Alexander; Gabdank, Idan; Barash, Danny
2012-12-01
The secondary structure of RNAs can be represented by graphs at various resolutions. While it was shown that RNA secondary structures can be represented by coarse grain tree-graphs and meaningful topological indices can be used to distinguish between various structures, small RNAs are needed to be represented by full graphs. No meaningful topological index has yet been suggested for the analysis of such type of RNA graphs. Recalling that the second eigenvalue of the Laplacian matrix can be used to track topological changes in the case of coarse grain tree-graphs, it is plausible to assume that a topological index such as the Wiener index that represents all Laplacian eigenvalues may provide a similar guide for full graphs. However, by its original definition, the Wiener index was defined for acyclic graphs. Nevertheless, similarly to cyclic chemical graphs, small RNA graphs can be analyzed using elementary cuts, which enables the calculation of topological indices for small RNAs in an intuitive way. We show how to calculate a structural descriptor that is suitable for cyclic graphs, the Szeged index, for small RNA graphs by elementary cuts. We discuss potential uses of such a procedure that considers all eigenvalues of the associated Laplacian matrices to quantify the topology of small RNA graphs. Copyright © 2012 Elsevier Ltd. All rights reserved.
47 CFR 80.761 - Conversion graphs.
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units is...
Graphs with many valencies and few eigenvalues
van Dam, Edwin; Koolen, J.H.; Xia, Zheng-Jiang
Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily many distinct valencies. The graphs with four
Algorithms and Data Structures for Graphs
DEFF Research Database (Denmark)
Rotenberg, Eva
A graph consists of a set of vertices and a set of edges between vertices. Graphs are a popular mathematical model for road maps, communication networks, electrical circuits, social networks, disease transmission networks, job assignments, resource allocation, and more. A special class of graphs ...
On 3-Chromatic Distance-Regular Graphs
Blokhuis, A.; Brouwer, A.E.; Haemers, W.H.
2006-01-01
We give some necessary conditions for a graph to be 3-chromatic in terms of the spectrum of the adjacency matrix.For all known distance-regular graphs it is determined whether they are 3-chromatic.A start is made with the classification of 3-chromatic distance-regular graphs, and it is shown that
Surface-Based Body Shape Index and Its Relationship with All-Cause Mortality.
Directory of Open Access Journals (Sweden)
Syed Ashiqur Rahman
Full Text Available Obesity is a global public health challenge. In the US, for instance, obesity prevalence remains high at more than one-third of the adult population, while over two-thirds are obese or overweight. Obesity is associated with various health problems, such as diabetes, cardiovascular diseases (CVDs, depression, some forms of cancer, sleep apnea, osteoarthritis, among others. The body mass index (BMI is one of the best known measures of obesity. The BMI, however, has serious limitations, for instance, its inability to capture the distribution of lean mass and adipose tissue, which is a better predictor of diabetes and CVDs, and its curved ("U-shaped" relationship with mortality hazard. Other anthropometric measures and their relation to obesity have been studied, each with its advantages and limitations. In this work, we introduce a new anthropometric measure (called Surface-based Body Shape Index, SBSI that accounts for both body shape and body size, and evaluate its performance as a predictor of all-cause mortality.We analyzed data on 11,808 subjects (ages 18-85, from the National Health and Human Nutrition Examination Survey (NHANES 1999-2004, with 8-year mortality follow up. Based on the analysis, we introduce a new body shape index constructed from four important anthropometric determinants of body shape and body size: body surface area (BSA, vertical trunk circumference (VTC, height (H and waist circumference (WC. The surface-based body shape index (SBSI is defined as follows: SBSI = ((H(7/4(WC(5/6/(BSA VTC (1 SBSI has negative correlation with BMI and weight respectively, no correlation with WC, and shows a generally linear relationship with age. Results on mortality hazard prediction using both the Cox proportionality model, and Kaplan-Meier curves each show that SBSI outperforms currently popular body shape indices (e.g., BMI, WC, waist-to-height ratio (WHtR, waist-to-hip ratio (WHR, A Body Shape Index (ABSI in predicting all
Abstract graph-like space and vector-valued metric graphs
Post, Olaf
2016-01-01
In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum graphs or graph-like manifolds. We show a spectral analysis of graph-like spaces, and consider as a special case vector-valued quantum graphs. Moreover, we provide a prototype of a convergence theorem for shrinking graph-like spaces with Dirichlet boundary c...
Moving to 3D: relationships between coral planar area, surface area and volume.
House, Jenny E; Brambilla, Viviana; Bidaut, Luc M; Christie, Alec P; Pizarro, Oscar; Madin, Joshua S; Dornelas, Maria
2018-01-01
Coral reefs are a valuable and vulnerable marine ecosystem. The structure of coral reefs influences their health and ability to fulfill ecosystem functions and services. However, monitoring reef corals largely relies on 1D or 2D estimates of coral cover and abundance that overlook change in ecologically significant aspects of the reefs because they do not incorporate vertical or volumetric information. This study explores the relationship between 2D and 3D metrics of coral size. We show that surface area and volume scale consistently with planar area, albeit with morphotype specific conversion parameters. We use a photogrammetric approach using open-source software to estimate the ability of photogrammetry to provide measurement estimates of corals in 3D. Technological developments have made photogrammetry a valid and practical technique for studying coral reefs. We anticipate that these techniques for moving coral research from 2D into 3D will facilitate answering ecological questions by incorporating the 3rd dimension into monitoring.
Reappraising the surface anatomy of the pterion and its relationship to the middle meningeal artery.
Ma, Siyan; Baillie, Louisa J M; Stringer, Mark D
2012-04-01
Despite its clinical importance, the surface anatomy of the pterion is inconsistently reported. This study reappraises the surface marking of the pterion and its relationship to the middle meningeal artery (MMA). The position and morphology of the pterion were analyzed in the Frankfurt plane in 76 adult skulls and 50 adult cranial cone beam CT scans. Relationship to the anterior branch of the MMA was examined in the skulls. Measurement reproducibility was assessed in a 20% randomly selected sample. In the skulls, the majority of pteria were sphenoparietal (78%), followed by epipteric (16%) and frontotemporal (5%). The center of the pterion was a mean of 26 ± 4 mm behind and 11 ± 4 mm above the posterolateral margin of the frontozygomatic suture; measurements were reproducible and consistent between sides and genders. Distances from the frontozygomatic suture were slightly greater (29 and 16 mm, respectively) in cranial CTs. A one centimeter circle centered on the midpoint of the pterion overlapped the anterior branch of the MMA in 68% of skulls; the artery was a few millimeters posterior in the remainder. Mean skull thickness at the midpoint of the pterion was 4.4 mm compared to 1 mm at its thinnest point in the squamous temporal bone. In conclusion, in most adults, the pterion lies within a one centimeter diameter circle 2.6 cm behind and 1.3 cm above the posterolateral margin of the frontozygomatic suture (which is easily palpable in vivo). This region overlaps the anterior branch of the MMA in two-thirds of cases. Copyright © 2011 Wiley Periodicals, Inc.
Topology polymorphism graph for lung tumor segmentation in PET-CT images
Cui, Hui; Wang, Xiuying; Zhou, Jianlong; Eberl, Stefan; Yin, Yong; Feng, Dagan; Fulham, Michael
2015-06-01
Accurate lung tumor segmentation is problematic when the tumor boundary or edge, which reflects the advancing edge of the tumor, is difficult to discern on chest CT or PET. We propose a ‘topo-poly’ graph model to improve identification of the tumor extent. Our model incorporates an intensity graph and a topology graph. The intensity graph provides the joint PET-CT foreground similarity to differentiate the tumor from surrounding tissues. The topology graph is defined on the basis of contour tree to reflect the inclusion and exclusion relationship of regions. By taking into account different topology relations, the edges in our model exhibit topological polymorphism. These polymorphic edges in turn affect the energy cost when crossing different topology regions under a random walk framework, and hence contribute to appropriate tumor delineation. We validated our method on 40 patients with non-small cell lung cancer where the tumors were manually delineated by a clinical expert. The studies were separated into an ‘isolated’ group (n = 20) where the lung tumor was located in the lung parenchyma and away from associated structures / tissues in the thorax and a ‘complex’ group (n = 20) where the tumor abutted / involved a variety of adjacent structures and had heterogeneous FDG uptake. The methods were validated using Dice’s similarity coefficient (DSC) to measure the spatial volume overlap and Hausdorff distance (HD) to compare shape similarity calculated as the maximum surface distance between the segmentation results and the manual delineations. Our method achieved an average DSC of 0.881 ± 0.046 and HD of 5.311 ± 3.022 mm for the isolated cases and DSC of 0.870 ± 0.038 and HD of 9.370 ± 3.169 mm for the complex cases. Student’s t-test showed that our model outperformed the other methods (p-values <0.05).
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
Recently this concept has got a wide attention from different authors especially those interested ..... In this section, we pay attention to edge deletions and subdivisions and also joining vertices. Using Proposition 2.5 we ... Let H be the complete graph on x,y,z with ρxy(H ) = r , ρxz(H ) = a and ρyz(H ) = b. In K, {x,y} is a vertex ...
Relationship between Surface Modifications of Nanoparticle and Invasion into Suspension Cells
Energy Technology Data Exchange (ETDEWEB)
Matsui, Y; Sakai, N; Yoneda, M [Graduate School of Engineering, Kyoto University, Katsura, Kyoto 6158540 (Japan); Tsuda, A, E-mail: ymatsui@risk.env.kyoto-u.ac.jp [Department of Environmental Health, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA 02115 (United States)
2011-07-06
Nanomaterials have a variety of properties for each material. There is little information available on which kinds of material properties have effects on toxicity and kinetics. This paper presents that a relationship between material properties and hazard data by undertaking a bibliographical survey at first. With respect to cytotoxicity, it probably depends mainly on the particle volume dose and to a certain degree on particle solubility. It can be concluded from these results that there is a relationship between material properties and hazard data. Many activities involving nano risk are occurring all over the world. Secondly, we assayed actually for cellular uptake of three kinds of Quantum dots (15 nm, 5.5x10{sup 12} particles/ml) to demonstrate our result of bibliographical survey. Three different surface modification quantum dots (non-modification, -COOH, -NH3) were mixed with floating Jurkat cells in each. After thirty minute, we washed these cells three times and detected fluorescence by flow cytometer. Almost all the carboxylate particles invaded a cell, about 60% aminated them also invaded and few non-modification particles were taken up. Nanomaterials are often very broadly categorized and named based upon their basic material composition or product shape. Our results confirm that we have to examine which physical-chemical properties affect some adverse effects for each nanomaterial.
International Nuclear Information System (INIS)
Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing
2009-01-01
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.
A framework for graph-based synthesis, analysis, and visualization of HPC cluster job data.
Energy Technology Data Exchange (ETDEWEB)
Mayo, Jackson R.; Kegelmeyer, W. Philip, Jr.; Wong, Matthew H.; Pebay, Philippe Pierre; Gentile, Ann C.; Thompson, David C.; Roe, Diana C.; De Sapio, Vincent; Brandt, James M.
2010-08-01
The monitoring and system analysis of high performance computing (HPC) clusters is of increasing importance to the HPC community. Analysis of HPC job data can be used to characterize system usage and diagnose and examine failure modes and their effects. This analysis is not straightforward, however, due to the complex relationships that exist between jobs. These relationships are based on a number of factors, including shared compute nodes between jobs, proximity of jobs in time, etc. Graph-based techniques represent an approach that is particularly well suited to this problem, and provide an effective technique for discovering important relationships in job queuing and execution data. The efficacy of these techniques is rooted in the use of a semantic graph as a knowledge representation tool. In a semantic graph job data, represented in a combination of numerical and textual forms, can be flexibly processed into edges, with corresponding weights, expressing relationships between jobs, nodes, users, and other relevant entities. This graph-based representation permits formal manipulation by a number of analysis algorithms. This report presents a methodology and software implementation that leverages semantic graph-based techniques for the system-level monitoring and analysis of HPC clusters based on job queuing and execution data. Ontology development and graph synthesis is discussed with respect to the domain of HPC job data. The framework developed automates the synthesis of graphs from a database of job information. It also provides a front end, enabling visualization of the synthesized graphs. Additionally, an analysis engine is incorporated that provides performance analysis, graph-based clustering, and failure prediction capabilities for HPC systems.
Cofinite graphs and their profinite completions
Directory of Open Access Journals (Sweden)
Amrita Acharyya
2017-10-01
Full Text Available We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.The idea of constructing a cofinite graph starts with defining a uniform topological graph $\\Gamma$, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over $\\Gamma$. It is established that for any cofinite graph there exists a unique cofinite completion.
Cycle decompositions: From graphs to continua.
Georgakopoulos, Agelos
2012-01-30
We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and replace the cycle space of a graph by a new homology group for continua which is a quotient of the first singular homology group [Formula: see text]. This homology seems to be particularly apt for studying spaces with infinitely generated [Formula: see text], e.g. infinite graphs or fractals.
Modelling complex networks by random hierarchical graphs
Directory of Open Access Journals (Sweden)
M.Wróbel
2008-06-01
Full Text Available Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erdős-Rényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasket-based graphs with random "decorations". We calculate the important characteristics of these graphs - average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
On 4-critical t-perfect graphs
Benchetrit, Yohann
2016-01-01
It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...
Analyzing and synthesizing phylogenies using tree alignment graphs.
Directory of Open Access Journals (Sweden)
Stephen A Smith
Full Text Available Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG. The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees, we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
On a programming language for graph algorithms
Rheinboldt, W. C.; Basili, V. R.; Mesztenyi, C. K.
1971-01-01
An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.
Modes of Convergence for Term Graph Rewriting
DEFF Research Database (Denmark)
Bahr, Patrick
2012-01-01
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate...... counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order respectively a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term...... rewriting. We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the modes of convergence on term graphs are conservative...
Modes of Convergence for Term Graph Rewriting
DEFF Research Database (Denmark)
Bahr, Patrick
2011-01-01
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate...... counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order resp. a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting....... We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the resulting infinitary calculi of term graph rewriting exhibit...
On the centrality of some graphs
Directory of Open Access Journals (Sweden)
Vecdi Aytac
2017-10-01
Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
A kaleidoscopic view of graph colorings
Zhang, Ping
2016-01-01
This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.
Software for Graph Analysis and Visualization
Directory of Open Access Journals (Sweden)
M. I. Kolomeychenko
2014-01-01
Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.
Fibonacci number of the tadpole graph
Directory of Open Access Journals (Sweden)
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Triangle Counting in Dynamic Graph Streams
DEFF Research Database (Denmark)
Bulteau, Laurent; Froese, Vincent; Pagh, Rasmus
2015-01-01
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However......, with a few exceptions, the algorithms have considered insert-only streams. We present a new algorithm estimating the number of triangles in dynamic graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions...... for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach...
Dowding, Dawn; Merrill, Jacqueline A; Onorato, Nicole; Barrón, Yolanda; Rosati, Robert J; Russell, David
2018-02-01
To explore home care nurses' numeracy and graph literacy and their relationship to comprehension of visualized data. A multifactorial experimental design using online survey software. Nurses were recruited from 2 Medicare-certified home health agencies. Numeracy and graph literacy were measured using validated scales. Nurses were randomized to 1 of 4 experimental conditions. Each condition displayed data for 1 of 4 quality indicators, in 1 of 4 different visualized formats (bar graph, line graph, spider graph, table). A mixed linear model measured the impact of numeracy, graph literacy, and display format on data understanding. In all, 195 nurses took part in the study. They were slightly more numerate and graph literate than the general population. Overall, nurses understood information presented in bar graphs most easily (88% correct), followed by tables (81% correct), line graphs (77% correct), and spider graphs (41% correct). Individuals with low numeracy and low graph literacy had poorer comprehension of information displayed across all formats. High graph literacy appeared to enhance comprehension of data regardless of numeracy capabilities. Clinical dashboards are increasingly used to provide information to clinicians in visualized format, under the assumption that visual display reduces cognitive workload. Results of this study suggest that nurses' comprehension of visualized information is influenced by their numeracy, graph literacy, and the display format of the data. Individual differences in numeracy and graph literacy skills need to be taken into account when designing dashboard technology. © The Author 2017. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com
Graph Embedded Extreme Learning Machine.
Iosifidis, Alexandros; Tefas, Anastasios; Pitas, Ioannis
2016-01-01
In this paper, we propose a novel extension of the extreme learning machine (ELM) algorithm for single-hidden layer feedforward neural network training that is able to incorporate subspace learning (SL) criteria on the optimization process followed for the calculation of the network's output weights. The proposed graph embedded ELM (GEELM) algorithm is able to naturally exploit both intrinsic and penalty SL criteria that have been (or will be) designed under the graph embedding framework. In addition, we extend the proposed GEELM algorithm in order to be able to exploit SL criteria in arbitrary (even infinite) dimensional ELM spaces. We evaluate the proposed approach on eight standard classification problems and nine publicly available datasets designed for three problems related to human behavior analysis, i.e., the recognition of human face, facial expression, and activity. Experimental results denote the effectiveness of the proposed approach, since it outperforms other ELM-based classification schemes in all the cases.
The optimal graph partitioning problem
DEFF Research Database (Denmark)
Sørensen, Michael Malmros; Holm, Søren
1993-01-01
In this paper we consider the problem of partitioning the set of nodes in a graph in at most p classes, such that the sum of node weights in any class is not greater than the class capacity b, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal. This pr......In this paper we consider the problem of partitioning the set of nodes in a graph in at most p classes, such that the sum of node weights in any class is not greater than the class capacity b, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal...
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Significance evaluation in factor graphs
DEFF Research Database (Denmark)
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
3-biplacement of bipartite graphs
Directory of Open Access Journals (Sweden)
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
Zhang, Ping
2015-01-01
A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings...
Reachability Games on Automatic Graphs
Neider, Daniel
In this work we study two-person reachability games on finite and infinite automatic graphs. For the finite case we empirically show that automatic game encodings are competitive to well-known symbolic techniques such as BDDs, SAT and QBF formulas. For the infinite case we present a novel algorithm utilizing algorithmic learning techniques, which allows to solve huge classes of automatic reachability games.
Decomposing a graph into bistars
DEFF Research Database (Denmark)
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...
Parallel External Memory Graph Algorithms
DEFF Research Database (Denmark)
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Quantum information processing with graph states
International Nuclear Information System (INIS)
Schlingemann, Dirk-Michael
2005-04-01
Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)
Topological structure of dictionary graphs
International Nuclear Information System (INIS)
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Characterizing the relationship between land use land cover change and land surface temperature
Tran, Duy X.; Pla, Filiberto; Latorre-Carmona, Pedro; Myint, Soe W.; Caetano, Mario; Kieu, Hoan V.
2017-02-01
Exploring changes in land use land cover (LULC) to understand the urban heat island (UHI) effect is valuable for both communities and local governments in cities in developing countries, where urbanization and industrialization often take place rapidly but where coherent planning and control policies have not been applied. This work aims at determining and analyzing the relationship between LULC change and land surface temperature (LST) patterns in the context of urbanization. We first explore the relationship between LST and vegetation, man-made features, and cropland using normalized vegetation, and built-up indices within each LULC type. Afterwards, we assess the impacts of LULC change and urbanization in UHI using hot spot analysis (Getis-Ord Gi∗ statistics) and urban landscape analysis. Finally, we propose a model applying non-parametric regression to estimate future urban climate patterns using predicted land cover and land use change. Results from this work provide an effective methodology for UHI characterization, showing that (a) LST depends on a nonlinear way of LULC types; (b) hotspot analysis using Getis Ord Gi∗ statistics allows to analyze the LST pattern change through time; (c) UHI is influenced by both urban landscape and urban development type; (d) LST pattern forecast and UHI effect examination can be done by the proposed model using nonlinear regression and simulated LULC change scenarios. We chose an inner city area of Hanoi as a case-study, a small and flat plain area where LULC change is significant due to urbanization and industrialization. The methodology presented in this paper can be broadly applied in other cities which exhibit a similar dynamic growth. Our findings can represent an useful tool for policy makers and the community awareness by providing a scientific basis for sustainable urban planning and management.
Segura, S.; Estellés, V.; Utrillas, M. P.; Martínez-Lozano, J. A.
2017-10-01
Simultaneous PM2.5, PM10 and columnar (ground and satellite based) AOD measurements have been analyzed at Burjassot site in the metropolitan area of Valencia (Spain) during the period 2007-2016. The site is representative of a south European city in the Western Mediterranean coastal area, influenced by local urban pollution but also from frequent Saharan dust events. First, multiannual statistics were performed to characterize the main aerosol burden characteristics. The averages and standard deviations resulted 18 ± 9 μg m-3, 25 ± 19 μg m-3, 0.15 ± 0.11, 0.23 ± 0.17, 0.19 ± 0.15 and 1.2 ± 0.3 for PM2.5, PM10, AERONET AOD, MODIS Terra AOD, MODIS Aqua AOD, and AERONET Ångström exponent AE, respectively. The AOD is always referred to 550 nm. PM10 and AOD showed seasonal patterns with maxima in summer and minima in winter. However, PM2.5 and AE did not show such an evident seasonality. The relationship between surface and columnar measurements show a poor correlation (r down to 0.30) for daily values, although the correlation increases to r up to 0.90 for yearly averages. The relationship between PM and AOD becomes more consistent when the databases are binned in intervals of 0.05 AOD. Results for AERONET and MODIS AOD are very similar, although for daily averages is slightly worse for satellite than ground based measurements. In order to explain some seasonality effects found, the mixing layer height has been included in the analysis. Results show that the correlation is maximum when PM2.5 is used and the mixing layer height is greater than 1 000 m (r > 0.90).
Molenje, Levi
2012-01-01
This study was designed to explore secondary mathematics teachers' beliefs about graphing calculators, their practices with the graphing calculators when teaching linear and quadratic functions, and the relationship between the teachers' beliefs and their practices. The study was conducted in two phases. In the first phase, 81 teachers…
Components in time-varying graphs.
Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito
2012-06-01
Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.
Digital video, learning styles, and student understanding of kinematics graphs
Hein, Teresa Lee
1997-12-01
Student ability to analyze and interpret motion graphs following laboratory instruction that utilized interactive digital video as well as traditional instructional techniques was investigated. Research presented suggested that digital video tools serve to motivate students and may be an effective mechanism to enhance student understanding of motion concepts. Two laboratory exercises involving motion concepts were developed for this study. Students were divided into two instructional groups. The treatment group used digital video techniques and the control group used traditional techniques to perform the laboratory exercises. Student understanding of motion concepts were assessed, in part, using the Test of Understanding Graphs-Kinematics. Other assessment measures included student responses to a set of written graphical analysis questions and two post-lab activities. Possible relationships between individual learning style preferences and student understanding of motion concepts were also addressed. Learning style preferences were assessed using the Productivity Environmental Preference Survey prior to the instructional treatments. Students were asked to comment in writing about their learning styles before and after they were given the learning style assessment. Student comments revealed that the results they received from Productivity Environmental Preference Survey accurately reflected their learning styles. Results presented in this study showed that no significant relationship exists between students' learning style preferences and their ability to interpret motion graphs as measured by scores on the Test of Understanding Graphs-Kinematics. In addition, the results showed no significant difference between instructional treatment and mean scores on the Test of Understanding Graphs-Kinematics. Analysis of writing activities revealed that students in the treatment group responded more effectively than students in the control group to graphical interpretation
Perkins, David Nikolaus; Brost, Randolph; Ray, Lawrence P.
2017-08-08
Various technologies for facilitating analysis of large remote sensing and geolocation datasets to identify features of interest are described herein. A search query can be submitted to a computing system that executes searches over a geospatial temporal semantic (GTS) graph to identify features of interest. The GTS graph comprises nodes corresponding to objects described in the remote sensing and geolocation datasets, and edges that indicate geospatial or temporal relationships between pairs of nodes in the nodes. Trajectory information is encoded in the GTS graph by the inclusion of movable nodes to facilitate searches for features of interest in the datasets relative to moving objects such as vehicles.
Relationships between Indian Ocean Sea surface temperature and the rainfall of Sri Lanka
Energy Technology Data Exchange (ETDEWEB)
Suppiah, Ramasamy
1988-02-28
Spatial and temporal variations of the sea surface temperature (SST) over the Indian Ocean are examined by using empirical orthogonal function (EOF) analysis. The first EOF mode explains 20.54% of the total variance indicating positive values over the study area. The second and third EOF modes explain relatively less contribution, 5.6% and 5.1% of the total variance. A weak positive correlation coefficient is observed between the time coefficients of the first EOF mode of SST anomalies and the time coefficients of the first EOF mode of the rainfall anomalies over Sri Lanka when all months are considered. The positive relationships between SST anomalies of the Pacific and the Indian Oceans and rainfall anomalies of Sri Lanka first appear in March and April, and then gradually build up towards the significant level. In the case of the summer monsoon, Arabian Sea SST's strongly influence the rainfall of Sri Lank, particularly striking in the southwestern quadrant of the island. (8 figs, 4 tabs, 27 refs)
Content-Agnostic Malware Detection in Heterogeneous Malicious Distribution Graph
Alabdulmohsin, Ibrahim
2016-10-26
Malware detection has been widely studied by analysing either file dropping relationships or characteristics of the file distribution network. This paper, for the first time, studies a global heterogeneous malware delivery graph fusing file dropping relationship and the topology of the file distribution network. The integration offers a unique ability of structuring the end-to-end distribution relationship. However, it brings large heterogeneous graphs to analysis. In our study, an average daily generated graph has more than 4 million edges and 2.7 million nodes that differ in type, such as IPs, URLs, and files. We propose a novel Bayesian label propagation model to unify the multi-source information, including content-agnostic features of different node types and topological information of the heterogeneous network. Our approach does not need to examine the source codes nor inspect the dynamic behaviours of a binary. Instead, it estimates the maliciousness of a given file through a semi-supervised label propagation procedure, which has a linear time complexity w.r.t. the number of nodes and edges. The evaluation on 567 million real-world download events validates that our proposed approach efficiently detects malware with a high accuracy. © 2016 Copyright held by the owner/author(s).
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...... of term graphs in the sense of Barendregt et al. The corresponding storeless abstract machine and natural semantics follow mutatis mutandis. We then interpret let expressions as operations over a global store (thus shifting, in Strachey's words, from denotable entities to storable entities), resulting...
Chemical Graph Transformation with Stereo-Information
DEFF Research Database (Denmark)
Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel
2017-01-01
Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...
Double-Critical Graphs and Complete Minors
DEFF Research Database (Denmark)
Kawarabayashi, Ken-ichi; Pedersen, Anders Sune; Toft, Bjarne
2010-01-01
A connected $k$-chromatic graph $G$ is double-critical if for all edges $uv$ of $G$ the graph $G - u - v$ is $(k-2)$-colourable. The only known double-critical $k$-chromatic graph is the complete $k$-graph $K_k$. The conjecture that there are no other double-critical graphs is a special case...... of a conjecture from 1966, due to Erd\\H{o}s and Lov\\'asz. The conjecture has been verified for $k \\leq 5$. We prove for $k=6$ and $k=7$ that any non-complete double-critical $k$-chromatic graph is $6$-connected and has $K_k$ as a minor. Udgivelsesdato: 07.06....
Alliances and Bisection Width for Planar Graphs
DEFF Research Database (Denmark)
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances...... in polynomial time. We base this on a proof of an upper bound of n on the bisection width for 4-connected planar graphs with an odd number of vertices. This improves a recently published n + 1 upper bound on the bisection width of planar graphs without separating triangles and supports the folklore conjecture...... that a general upper bound of n exists for the bisection width of planar graphs....
Well-covered graphs and factors
DEFF Research Database (Denmark)
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has...... a perfect [1,2]-factor F_G, i.e. a spanning subgraph such that each component is 1-regular og 2-regular. Here, we characterize all well-covered graphs G satisfying α(G)=α(F_G) for some perfect [1,2]-factor F_G. This class contains all well-covered graphs G without isolated vertices of order n with α ≥ (n...... - 1)/2, and in particular all very well-covered graphs....
Fast Generation of Sparse Random Kernel Graphs.
Hagberg, Aric; Lemons, Nathan
2015-01-01
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most (n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity.
A Feature-Based Call Graph Distance Measure for Program Similarity Analysis
Linkola, Simo
2016-01-01
A measurement for how similar (or distant) two computer programs are has a wide range of possible applications. For example, they can be applied to malware analysis or analysis of university students' programming exercises. However, as programs may be arbitrarily structured, capturing the similarity of two non-trivial programs is a complex task. By extracting call graphs (graphs of caller-callee relationships of the program's functions, where nodes denote functions and directed edges denote f...
2-domination number of generalized Petersen graphs
Indian Academy of Sciences (India)
35
2Department of Computer Science, Yazd University, Yazd, Iran. Abstract. Let G = (V,E) be a graph. A subset S ⊆ V is a k-dominating set of. G if each vertex ... on the area of domination in graphs and its applications we refer the reader to [6, 7]. The generalized Petersen graph P(n, k)=(V,E) is defined as follows: V = {v1,v2,...
On path hypercompositions in graphs and automata
Directory of Open Access Journals (Sweden)
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Visibility graphs and landscape visibility analysis
O Sullivan, D.; Turner, A.
2001-01-01
Visibility analysis based on viewsheds is one of the most frequently used GIS analysis tools. In this paper we present an approach to visibility analysis based on the visibility graph. A visibility graph records the pattern of mutual visibility relations in a landscape, and provides a convenient way of storing and further analysing the results of multiple viewshed analyses for a particular landscape region. We describe how a visibility graph may be calculated for a landscape. We then give exa...
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
Interactive Graph Layout of a Million Nodes
Directory of Open Access Journals (Sweden)
Peng Mi
2016-12-01
Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.
Evolutionary Games of Multiplayer Cooperation on Graphs
Arranz, Jordi; Traulsen, Arne
2016-01-01
There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946
Mechatronic modeling and simulation using bond graphs
Das, Shuvra
2009-01-01
Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...
DEFF Research Database (Denmark)
Jensen, T.R.; Thomassen, Carsten
2000-01-01
If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....
Graph algorithms in the titan toolkit.
Energy Technology Data Exchange (ETDEWEB)
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
Evolutionary Games of Multiplayer Cooperation on Graphs.
Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne
2016-08-01
There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.
A Reduction of the Graph Reconstruction Conjecture
Directory of Open Access Journals (Sweden)
Monikandan S.
2014-08-01
Full Text Available A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G = 2 or diam(Ḡ = diam(G = 3 are reconstructible
Visual Adjacency Lists for Dynamic Graphs.
Hlawatsch, Marcel; Burch, Michael; Weiskopf, Daniel
2014-11-01
We present a visual representation for dynamic, weighted graphs based on the concept of adjacency lists. Two orthogonal axes are used: one for all nodes of the displayed graph, the other for the corresponding links. Colors and labels are employed to identify the nodes. The usage of color allows us to scale the visualization to single pixel level for large graphs. In contrast to other techniques, we employ an asymmetric mapping that results in an aligned and compact representation of links. Our approach is independent of the specific properties of the graph to be visualized, but certain graphs and tasks benefit from the asymmetry. As we show in our results, the strength of our technique is the visualization of dynamic graphs. In particular, sparse graphs benefit from the compact representation. Furthermore, our approach uses visual encoding by size to represent weights and therefore allows easy quantification and comparison. We evaluate our approach in a quantitative user study that confirms the suitability for dynamic and weighted graphs. Finally, we demonstrate our approach for two examples of dynamic graphs.
Dose-response relationship between periodontal inflamed surface area and HbA1c in type 2 Diabetics
Nesse, Willem; Linde, Annemiek; Abbas, Frank; Spijkervet, Frederik Karst Lucien; Dijkstra, Pieter Ubele; de Brabander, Eric Carl; Gerstenbluth, Izzy; Vissink, Arjan
Nesse W, Linde A, Abbas F, Spijkervet FKL, Dijkstra PU, de Brabander EC, Gerstenbluth I, Vissink A. Dose-response relationship between periodontal inflamed surface area and HbA1c in type 2 diabetics. J Clin Periodontol 2009; 36: 295-300. doi: 10.1111/j.1600-051X.2009.01377.x. A dose-response
Localized surface plasmon resonance induced structure-property relationships of metal nanostructures
Vilayurganapathy, Subramanian
The confluence of nanotechnology and plasmonics has led to new and interesting phenomena. The industrial need for fast, efficient and miniature devices which constantly push the boundaries on device performance tap into the happy marriage between these diverse fields. Designing devices for real life application that give superior performance when compared with existing ones are enabled by a better understanding of their structure-property relationships. Among all the design constraints, without doubt, the shape and size of the nanostructure along with the dielectric medium surrounding it has the maximum influence on the response and thereby the performance of the device. Hence a careful study of the above mentioned parameters is of utmost importance in designing efficient devices. In this dissertation, we synthesize and study the optical properties of nanostructures of different shapes and size. In particular, we estimated the plasmonic near field enhancement via surface-enhanced Raman scattering (SERS) and 2-photon Photoemission electron microscopy (2P-PEEM). We synthesized the nanostructures using four different techniques. One synthesis technique, the thermal growth method was employed to grow interesting Ag and Au nanostructures on Si. The absence of toxic chemicals during nanostructure synthesis via the thermal growth technique opens up myriad possibilities for applications in the fields of biomedical science, bioengineering, drug delivery among others along with the huge advantage of being environment friendly. The other three synthesis techniques (ion implantation, Electrodeposition and FIB lithography) were chosen with the specific goal of designing novel plasmonic metal, metal hybrid nanostructures as photocathode materials in next generation light sources. The synthesis techniques for these novel nanostructures were dictated by the requirement of high quantum efficiency, robustness under constant irradiation and coherent unidirectional electron emission
Brückner, Adrian; Heethoff, Michael; Blüthgen, Nico
2017-01-01
Long-chain cuticular hydrocarbons (CHCs) are common components of the epicuticle of terrestrial arthropods. CHC serve as a protective barrier against environmental influences but also act as semiochemicals in animal communication. Regarding the latter aspect, species- or intra-functional group specific CHCs composition and variation are relatively well studied. However, comparative knowledge about the relationship of CHC quantity and their relation to surface area-volume ratios in the context of water loss and protection is fragmentary. Hence, we aim to study the taxon-specific relationship of the CHC amount and surface-area to volume ratio related to their functional role (e.g. in water loss). We focused on flower visiting insects and analyzed the CHC amounts of three insect orders (Hymenoptera, Lepidoptera and Diptera) using gas chromatography-mass spectrometry (GC-MS). We included 113 species from two grassland plots, quantified their CHCs, and measured their body mass and surface area. We found differences in the surface area, CHCs per body mass and the CHC density (= amount of CHCs per surface area) across the three insect taxa. Especially the Hymenoptera had a higher CHC density compared to Diptera and Lepidoptera. CHC density could be explained by surface area-volume ratios in Hymenoptera but not in Diptera and Lepidoptera. Unexpectedly, CHC density decreased with increasing surface area-volume ratios.
Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs
Directory of Open Access Journals (Sweden)
Hala Kamal
2017-11-01
Full Text Available Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows for one to extract partial information and gives an alternative to classical graph approach.
Applications of Multivalued Contractions on Graphs to Graph-Directed Iterated Function Systems
Directory of Open Access Journals (Sweden)
T. Dinevari
2015-01-01
Full Text Available We apply a fixed point result for multivalued contractions on complete metric spaces endowed with a graph to graph-directed iterated function systems. More precisely, we construct a suitable metric space endowed with a graph G and a suitable G-contraction such that its fixed points permit us to obtain more information on the attractor of a graph-directed iterated function system.
Decomposing a planar graph into an independent set and a 3-degenerate graph
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We prove the conjecture made by O.V.Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and aset inducing a $3$-degenerate graph.......We prove the conjecture made by O.V.Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and aset inducing a $3$-degenerate graph....
Decomposing a planar graph into an independent set and a 3-degenerate graph
DEFF Research Database (Denmark)
Thomassen, Carsten
2001-01-01
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press.......We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....
The African upper mantle and its relationship to tectonics and surface geology
Priestley, Keith; McKenzie, Dan; Debayle, Eric; Pilidou, Sylvana
2008-12-01
This paper focuses on the upper-mantle velocity structure of the African continent and its relationship to the surface geology. The distribution of seismographs and earthquakes providing seismograms for this study results in good fundamental and higher mode path coverage by a large number of relatively short propagation paths, allowing us to image the SV-wave speed structure, with a horizontal resolution of several hundred kilometres and a vertical resolution of ~50 km, to a depth of about 400 km. The difference in mantle structure between the Archean and Pan-African terranes is apparent in our African upper-mantle shear wave model. High-velocity (4-7 per cent) roots exist beneath the cratons. Below the West African, Congo and Tanzanian Cratons, these extend to 225-250 km depth, but beneath the Kalahari Craton, the high wave speed root extends to only ~170 km. With the exception of the Damara Belt that separates the Congo and Kalahari Cratons, any high-speed upper-mantle lid below the Pan-African terranes is too thin to be resolved by our long-period surface wave technique. The Damara Belt is underlain by higher wave speeds, similar to those observed beneath the Kalahari Craton. Extremely low SV-wave speeds occur to the bottom of our model beneath the Afar region. The temperature of the African upper mantle is determined from the SV-wave speed model. Large temperature variations occur at 125 km depth with low temperatures beneath west Africa and all of southern Africa and warm mantle beneath the Pan-African terrane of northern Africa. At 175 km depth, cool upper mantle occurs below the West African, Congo, Tanzanian and Kalahari Cratons and anomalously warm mantle occurs below a zone in northcentral Africa and beneath the region surrounding the Red Sea. All of the African volcanic centres are located above regions of warm upper mantle. The temperature profiles were fit to a geotherm to determine the thickness of the African lithosphere. Thick lithosphere exists
Cyber Graph Queries for Geographically Distributed Data Centers
Energy Technology Data Exchange (ETDEWEB)
Berry, Jonathan W. [Mail Stop, Albuquerque, NM (United States); Collins, Michael [Christopher Newport Univ., VA (United States); Kearns, Aaron [Univ. of New Mexico, Albuquerque, NM (United States); Phillips, Cynthia A. [Mail Stop, Albuquerque, NM (United States); Saia, Jared [Univ. of New Mexico, Albuquerque, NM (United States)
2015-05-01
We present new algorithms for a distributed model for graph computations motivated by limited information sharing we first discussed in [20]. Two or more independent entities have collected large social graphs. They wish to compute the result of running graph algorithms on the entire set of relationships. Because the information is sensitive or economically valuable, they do not wish to simply combine the information in a single location. We consider two models for computing the solution to graph algorithms in this setting: 1) limited-sharing: the two entities can share only a polylogarithmic size subgraph; 2) low-trust: the entities must not reveal any information beyond the query answer, assuming they are all honest but curious. We believe this model captures realistic constraints on cooperating autonomous data centers. We have algorithms in both setting for s - t connectivity in both models. We also give an algorithm in the low-communication model for finding a planted clique. This is an anomaly- detection problem, finding a subgraph that is larger and denser than expected. For both the low- communication algorithms, we exploit structural properties of social networks to prove perfor- mance bounds better than what is possible for general graphs. For s - t connectivity, we use known properties. For planted clique, we propose a new property: bounded number of triangles per node. This property is based upon evidence from the social science literature. We found that classic examples of social networks do not have the bounded-triangles property. This is because many social networks contain elements that are non-human, such as accounts for a business, or other automated accounts. We describe some initial attempts to distinguish human nodes from automated nodes in social networks based only on topological properties.
Embedding graphs in Lorentzian spacetime.
Directory of Open Access Journals (Sweden)
James R Clough
Full Text Available Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG into Minkowski spacetime using Multidimensional scaling (MDS. First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
Tracking Research Data Footprints via Integration with Research Graph
Evans, B. J. K.; Wang, J.; Aryani, A.; Conlon, M.; Wyborn, L. A.; Choudhury, S. A.
2017-12-01
The researcher of today is likely to be part of a team that will use subsets of data from at least one, if not more external repositories, and that same data could be used by multiple researchers for many different purposes. At best, the repositories that host this data will know who is accessing their data, but rarely what they are using it for, resulting in funders of data collecting programs and data repositories that store the data unlikely to know: 1) which research funding contributed to the collection and preservation of a dataset, and 2) which data contributed to high impact research and publications. In days of funding shortages there is a growing need to be able to trace the footprint a data set from the originator that collected the data to the repository that stores the data and ultimately to any derived publications. The Research Data Alliance's Data Description Registry Interoperability Working Group (DDRIWG) has addressed this problem through the development of a distributed graph, called Research Graph that can map each piece of the research interaction puzzle by building aggregated graphs. It can connect datasets on the basis of co-authorship or other collaboration models such as joint funding and grants and can connect research datasets, publications, grants and researcher profiles across research repositories and infrastructures such as DataCite and ORCID. National Computational Infrastructure (NCI) in Australia is one of the early adopters of Research Graph. The graphic view and quantitative analysis helps NCI track the usage of their National reference data collections thus quantifying the role that these NCI-hosted data assets play within the funding-researcher-data-publication-cycle. The graph can unlock the complex interactions of the research projects by tracking the contribution of datasets, the various funding bodies and the downstream data users. RMap Project is a similar initiative which aims to solve complex relationships among
Computing paths and cycles in biological interaction graphs
Directory of Open Access Journals (Sweden)
von Kamp Axel
2009-06-01
Full Text Available Abstract Background Interaction graphs (signed directed graphs provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments. Results We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops. Conclusion The calculation of shortest positive
Representing vertex-transitive Vertex-transitive graphs on Groupoids
African Journals Online (AJOL)
Vertex-transitive graphs are one of the most favoured class of graphs in modelling scientific phenomena if symmetry is at issue. An understanding of these graphs should, therefore, be an obvious undertaking. Here, we present a characterisation of vertex-transitive graphs as left loop graphs and expose the measure of ...
Graph compositions and flats of cycle matroids | Mphako-Banda ...
African Journals Online (AJOL)
We give an alternative method for counting the number of graph compositions of any graph G. In particular we show that counting the number of graph compositions of a graph G is equivalent to counting the number of flats of its cycle matroid. Then we give one condition for non isomorphic graphs to have the same number ...
Distance-regular Cayley graphs with least eigenvalue -2
van Dam, Edwin; Abdollahi, Alireza; Jazaeri, Mojtaba
2017-01-01
We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible
Geometric aspects of 2-walk-regular graphs
Camara Vallejo, M.; van Dam, E.R.; Koolen, J.H.; Park, J.
2013-01-01
A t-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most t. Such graphs generalize distance-regular graphs and t-arc-transitive graphs. In this paper, we will
On cyclic orthogonal double covers of circulant graphs by special infinite graphs
Directory of Open Access Journals (Sweden)
R. El-Shanawany
2017-12-01
Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.
Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software
Zucker, Andrew; Kay, Rachel; Staudt, Carolyn
2014-01-01
Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding…
Spatial legend compatibility within versus between graphs in multiple graph comprehension.
Riechelmann, Eva; Huestegge, Lynn
2018-02-01
Previous research has shown that spatial compatibility between the data region and the legend of a graph is beneficial for comprehension. However, in multiple graphs, data-legend compatibility can come at the cost of spatial between-graph legend incompatibility. Here we aimed at determining which type of compatibility is most important for performance: global (legend-legend) compatibility between graphs, or local (data-legend) compatibility within graphs. Additionally, a baseline condition (incompatible) was included. Participants chose one out of several line graphs from a multiple panel as the answer to a data-related question. Compatibility type and the number of graphs per panel were varied. Whereas Experiment 1 involved simple graphs with only two lines/legend entries within each graph, Experiment 2 explored more complex graphs. The results indicated that compatibility speeds up comprehension, at least when a certain threshold of graph complexity is exceeded. Furthermore, we found evidence for an advantage of local over global data-legend compatibility under specific conditions. Taken together, the results further support the idea that compatibility principles strongly determine the ease of integration processes in graph comprehension and should thus be considered in multiple-panel design.
Wang, Wenli; Rinke, Annette; Moore, John C.; Ji, Duoying; Cui, Xuefeng; Peng, Shushi; Lawrence, David M.; McGuire, A. David; Burke, Eleanor J.; Chen, Xiaodong; Delire, Christine; Koven, Charles; MacDougall, Andrew; Saito, Kazuyuki; Zhang, Wenxin; Alkama, Ramdane; Bohn, Theodore J.; Ciais, Philippe; Decharme, Bertrand; Gouttevin, Isabelle; Hajima, Tomohiro; Krinner, Gerhard; Lettenmaier, Dennis P.; Miller, Paul A.; Smith, Benjamin; Sueyoshi, Tetsuo
2016-01-01
A realistic simulation of snow cover and its thermal properties are important for accurate modelling of permafrost. We analyze simulated relationships between air and near-surface (20 cm) soil temperatures in the Northern Hemisphere permafrost region during winter, with a particular focus on snow insulation effects in nine land surface models and compare them with observations from 268 Russian stations. There are large across-model differences as expressed by simulated differences between near-surface soil and air temperatures, (ΔT), of 3 to 14 K, in the gradients between soil and air temperatures (0.13 to 0.96°C/°C), and in the relationship between ΔT and snow depth. The observed relationship between ΔT and snow depth can be used as a metric to evaluate the effects of each model's representation of snow insulation, and hence guide improvements to the model’s conceptual structure and process parameterizations. Models with better performance apply multi-layer snow schemes and consider complex snow processes. Some models show poor performance in representing snow insulation due to underestimation of snow depth and/or overestimation of snow conductivity. Generally, models identified as most acceptable with respect to snow insulation simulate reasonable areas of near-surface permafrost (12–16 million km2). However, there is not a simple relationship between the quality of the snow insulation in the acceptable models and the simulated area of Northern Hemisphere near-surface permafrost, likely because several other factors such as differences in the treatment of soil organic matter, soil hydrology, surface energy calculations, and vegetation also provide important controls on simulated permafrost distribution.
Enabling Graph Appliance for Genome Assembly
Energy Technology Data Exchange (ETDEWEB)
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Probability on graphs random processes on graphs and lattices
Grimmett, Geoffrey
2018-01-01
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Got Graphs? An Assessment of Data Visualization Tools
Schaefer, C. M.; Foy, M.
2015-01-01
Graphs are powerful tools for simplifying complex data. They are useful for quickly assessing patterns and relationships among one or more variables from a dataset. As the amount of data increases, it becomes more difficult to visualize potential associations. Lifetime Surveillance of Astronaut Health (LSAH) was charged with assessing its current visualization tools along with others on the market to determine whether new tools would be useful for supporting NASA's occupational surveillance effort. It was concluded by members of LSAH that the current tools hindered their ability to provide quick results to researchers working with the department. Due to the high volume of data requests and the many iterations of visualizations requested by researchers, software with a better ability to replicate graphs and edit quickly could improve LSAH's efficiency and lead to faster research results.
International Nuclear Information System (INIS)
Lin Bing; Min Qilong; Sun Wenbo; Hu Yongxiang; Fan, Tai-Fang
2011-01-01
Increasing the knowledge in climate radiative feedbacks is critical for current climate studies. This work focuses on short-term relationships between global mean surface temperature and top-of-atmosphere (TOA) net radiation. The relationships may be used to characterize the climate feedback as suggested by some recent studies. As those recent studies, an energy balance model with ocean mixed layer and both radiative and non-radiative heat sources is used here. The significant improvement of current model is that climate system memories are considered. Based on model simulations, short-term relationship between global mean surface temperature and TOA net radiation (or the linear striation feature as suggested by previous studies) might represent climate feedbacks when the system had no memories. However, climate systems with the same short-term feedbacks but different memories would have a similar linear striation feature. This linear striation feature reflects only fast components of climate feedbacks and may not represent the total climate feedback even when the memory length of climate systems is minimal. The potential errors in the use of short-term relationships in estimations of climate sensitivity could be big. In short time scales, fast climate processes may overwhelm long-term climate feedbacks. Thus, the climate radiative feedback parameter obtained from short-term data may not provide a reliable estimate of climate sensitivity. This result also suggests that long-term observations of global surface temperature and TOA radiation are critical in the understanding of climate feedbacks and sensitivities.
Radio Channel Modelling Using Stochastic Propagation Graphs
DEFF Research Database (Denmark)
Pedersen, Troels; Fleury, Bernard Henri
2007-01-01
In this contribution the radio channel model proposed in [1] is extended to include multiple transmitters and receivers. The propagation environment is modelled using random graphs where vertices of a graph represent scatterers and edges model the wave propagation between scatterers. Furthermore...
The Minimum Distance of Graph Codes
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn
2011-01-01
We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other...
Geometric classification of simple graph algebras
DEFF Research Database (Denmark)
Sørensen, Adam Peder Wie
2013-01-01
Inspired by Franks’ classification of irreducible shifts of finite type, we provide a short list of allowed moves on graphs that preserve the stable isomorphism class of the associated C ∗ -algebras. We show that if two graphs have stably isomorphic and simple unital algebras then we can use...
From concatenated codes to graph codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2004-01-01
We consider codes based on simple bipartite expander graphs. These codes may be seen as the first step leading from product type concatenated codes to more complex graph codes. We emphasize constructions of specific codes of realistic lengths, and study the details of decoding by message passing...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
here therefore properly account for combinatory graph reduction As We Know It. These three syntactic theories scale to handling the Y combinator. This article therefore illustrates the scientic consensus of theoreticians and implementors about graph reduction: it is the same combinatory elephant....
Edge Cover Domination in Mangoldt Graph
African Journals Online (AJOL)
Bheema
Domination theory of graphs has many applications in. Engineering and Communication Networks. For these applications, the arithmetic graphs associated with certain number theoretic arithmetic functions like the Euler totient function Φ(n), the divison function d(n), the quadratic residue function and the Mangoldt function ...
Attitudes towards Graphing Calculators in Developmental Mathematics
Rajan, Shaun Thomas
2013-01-01
The purpose of this exploratory study was to examine instructor and student attitudes towards the use of the graphing calculator in the developmental mathematics classroom. A focus of the study was to see if instructors or students believed there were changes in the conceptual understanding of mathematics as a result of graphing calculator…
A Graph Library Extension of SVG
DEFF Research Database (Denmark)
Nørmark, Kurt
2007-01-01
be aggregated as a single node, and an entire graph can be embedded in a single node. In addition, a number of different graph animations are described. The starting point of the SVG extension is a library that provides an exact of mirror of SVG 1.1 in the functional programming language Scheme. Each element...
Eigenvalues and expansion of bipartite graphs
DEFF Research Database (Denmark)
Høholdt, Tom; Janwa, Heeralal
2012-01-01
We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...
Student Reasoning about Graphs in Different Contexts
Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka
2016-01-01
This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…
Acyclicity in edge-colored graphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...
Sobolev spaces on graphs | Ostrovskii | Quaestiones Mathematicae
African Journals Online (AJOL)
The present paper is devoted to discrete analogues of Sobolev spaces of smooth functions. The discrete analogues that we consider are spaces of functions on vertex sets of graphs. Such spaces have applications in Graph Theory, Metric Geometry and Convex Geometry. We present known and prove some new results on ...
Pattern Perception and the Comprehension of Graphs.
Pinker, Steven
Three experiments tested the hypothesis that graphs convey information effectively because they can display global trends as geometric patterns that visual systems encode easily. A novel type of graph was invented in which angles/lengths of line segments joined end-to-end represented variables of rainfall and temperature of a set of months. It was…
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph
Chain graph models and their causal interpretations
DEFF Research Database (Denmark)
Lauritzen, Steffen Lilholt; Richardson, Thomas S.
2002-01-01
, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from...... traditionally been used to model feed-back in econometrics....
Dynamic planar embeddings of dynamic graphs
DEFF Research Database (Denmark)
Holm, Jacob; Rotenberg, Eva
2017-01-01
, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common...
Dynamic planar embeddings of dynamic graphs
DEFF Research Database (Denmark)
Holm, Jacob; Rotenberg, Eva
2015-01-01
that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour....
An analysis of facebook's graph search
CSIR Research Space (South Africa)
Khan, ZC
2014-11-01
Full Text Available digital media. With the large number of users active on Facebook, an upgrade to Facebook’s searching capability was made through the launch of graph search. Graph search is a powerful search feature which allows users to search Facebook using queries...
Connected domination stable graphs upon edge addition ...
African Journals Online (AJOL)
A set S of vertices in a graph G is a connected dominating set of G if S dominates G and the subgraph induced by S is connected. We study the graphs for which adding any edge does not change the connected domination number. Keywords: Connected domination, connected domination stable, edge addition ...
A Ring Construction Using Finite Directed Graphs
Bardzell, Michael
2012-01-01
In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…
Toughness and Triangle-Free Graphs
Bauer, D.; van den Heuvel, J.; Schmeichel, E.
1995-01-01
In this paper, we prove that there exist triangle-free graphs with arbitrarily large toughness, thereby settling a longstanding open question. We also explore the problem of whether there exists a t-tough, n/(t + 1)-regular, triangle-free graph on n vertices for various values of t, and provide a
Declarative Process Mining for DCR Graphs
DEFF Research Database (Denmark)
Debois, Søren; Hildebrandt, Thomas T.; Laursen, Paw Høvsgaard
2017-01-01
We investigate process mining for the declarative Dynamic Condition Response (DCR) graphs process modelling language. We contribute (a) a process mining algorithm for DCR graphs, (b) a proposal for a set of metrics quantifying output model quality, and (c) a preliminary example-based comparison...
Graph Bundling by Kernel Density Estimation
Hurter, C.; Ersoy, O.; Telea, A.
We present a fast and simple method to compute bundled layouts of general graphs. For this, we first transform a given graph drawing into a density map using kernel density estimation. Next, we apply an image sharpening technique which progressively merges local height maxima by moving the convolved
Relationships between surface energy analysis and functional characteristics of dairy powders.
Kondor, Anett; Hogan, Sean A
2017-12-15
Surface energetics of demineralised whey (DMW), skimmed milk (SMP), phosphocasein (PCN) and infant milk formula (IMF) powders were determined by inverse gas chromatography (IGC). All four milk powders were amphoteric in nature with the dispersive (apolar) component of surface energy dominating the specific (polar) contribution. PCN and IMF had the highest and lowest extent of surface heterogeneity, respectively. PCN also demonstrated the poorest functional properties of the powders examined. In contrast, IMF had excellent flow and rehydration properties. Thermodynamic work of cohesion was highest in PCN and may have contributed to inadequate rehydration behaviour. Glass transition temperature of IMF powder, determined by IGC, suggested a surface dominated by lactose. Surface heterogeneity provided a better indicator of functional behaviour than total surface energy. IGC is a useful complementary technique for chemical and structural analysis of milk powders and allows improved insight into the contribution of surface and bulk factors to functionality. Copyright © 2017 Elsevier Ltd. All rights reserved.
The direct algorithm for solving of the graph isomorphism problem
Faizullin, Rashit T.; Prolubnikov, Alexander V.
2005-01-01
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
Proof-graphs for Minimal Implicational Logic
Directory of Open Access Journals (Sweden)
Marcela Quispe-Cruz
2014-03-01
Full Text Available It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study how to reduce the weight of propositional deductions. We present the formalism of proof-graphs for purely implicational logic, which are graphs of a specific shape that are intended to capture the logical structure of a deduction. The advantage of this formalism is that formulas can be shared in the reduced proof. In the present paper we give a precise definition of proof-graphs for the minimal implicational logic, together with a normalization procedure for these proof-graphs. In contrast to standard tree-like formalisms, our normalization does not increase the number of nodes, when applied to the corresponding minimal proof-graph representations.
Algorithms for Graph Rigidity and Scene Analysis
DEFF Research Database (Denmark)
Berg, Alex Rune; Jordán, Tibor
2003-01-01
We investigate algorithmic questions and structural problems concerning graph families defined by `edge-counts'. Motivated by recent developments in the unique realization problem of graphs, we give an efficient algorithm to compute the rigid, redundantly rigid, M-connected, and globally rigid...... components of a graph. Our algorithm is based on (and also extends and simplifies) the idea of Hendrickson and Jacobs, as it uses orientations as the main algorithmic tool. We also consider families of bipartite graphs which occur in parallel drawings and scene analysis. We verify a conjecture of Whiteley...... by showing that 2d-connected bipartite graphs are d-tight. We give a new algorithm for finding a maximal d-sharp subgraph. We also answer a question of Imai and show that finding a maximum size d-sharp subgraph is NP-hard....
On The Roman Domination Stable Graphs
Directory of Open Access Journals (Sweden)
Hajian Majid
2017-11-01
Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].
Pixels to Graphs by Associative Embedding
Newell, Alejandro
2017-06-22
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional neural network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them together. We benchmark on the Visual Genome dataset, and report a Recall@50 of 9.7% compared to the prior state-of-the-art at 3.4%, a nearly threefold improvement on the challenging task of scene graph generation.
Pristine transfinite graphs and permissive electrical networks
Zemanian, Armen H
2001-01-01
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...
Graph Mining Meets the Semantic Web
Energy Technology Data Exchange (ETDEWEB)
Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL
2015-01-01
The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.
OPEX: Optimized Eccentricity Computation in Graphs
Energy Technology Data Exchange (ETDEWEB)
Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2011-11-14
Real-world graphs have many properties of interest, but often these properties are expensive to compute. We focus on eccentricity, radius and diameter in this work. These properties are useful measures of the global connectivity patterns in a graph. Unfortunately, computing eccentricity for all nodes is O(n2) for a graph with n nodes. We present OPEX, a novel combination of optimizations which improves computation time of these properties by orders of magnitude in real-world experiments on graphs of many different sizes. We run OPEX on graphs with up to millions of links. OPEX gives either exact results or bounded approximations, unlike its competitors which give probabilistic approximations or sacrifice node-level information (eccentricity) to compute graphlevel information (diameter).