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Sample records for graph transformation expert

  1. Fundamentals of algebraic graph transformation

    CERN Document Server

    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...

  2. Graph transformation tool contest 2008

    NARCIS (Netherlands)

    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

  3. Expert interpretation of bar and line graphs: The role of graphicacy in reducing the effect of graph format.

    Directory of Open Access Journals (Sweden)

    David ePeebles

    2015-10-01

    Full Text Available The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987 has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 x 2 'interaction' bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices - and contrary to the assumptions of several graph comprehension models - experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension.

  4. Graph Transformation Semantics for a QVT Language

    NARCIS (Netherlands)

    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

  5. 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...

  6. Graph Transforming Java Data

    NARCIS (Netherlands)

    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

  7. Expert and Novice Approaches to Using Graphs: Evidence from Eye-Track Experiments

    Science.gov (United States)

    Wirth, K. R.; Lindgren, J. M.

    2015-12-01

    Professionals and students in geology use an array of graphs to study the earth, but relatively little detail is known about how users interact with these graphs. Comprehension of graphical information in the earth sciences is further complicated by the common use of non-traditional formats (e.g., inverted axes, logarithmic scales, normalized plots, ternary diagrams). Many educators consider graph-reading skills an important outcome of general education science curricula, so it is critical that we understand both the development of graph-reading skills and the instructional practices that are most efficacious. Eye-tracking instruments provide quantitative information about eye movements and offer important insights into the development of expertise in graph use. We measured the graph reading skills and eye movements of novices (students with a variety of majors and educational attainment) and experts (faculty and staff from a variety of disciplines) while observing traditional and non-traditional graph formats. Individuals in the expert group consistently demonstrated significantly greater accuracy in responding to questions (e.g., retrieval, interpretation, prediction) about graphs. Among novices, only the number of college math and science courses correlated with response accuracy. Interestingly, novices and experts exhibited similar eye-tracks when they first encountered a new graph; they typically scanned through the title, x and y-axes, and data regions in the first 5-15 seconds. However, experts are readily distinguished from novices by a greater number of eye movements (20-35%) between the data and other graph elements (e.g., title, x-axis, y-axis) both during and after the initial orientation phase. We attribute the greater eye movements between the different graph elements an outcome of the generally better-developed self-regulation skills (goal-setting, monitoring, self-evaluation) that likely characterize individuals in our expert group.

  8. Improved Conflict Detection for Graph Transformation with Attributes

    Directory of Open Access Journals (Sweden)

    Géza Kulcsár

    2015-04-01

    Full Text Available In graph transformation, a conflict describes a situation where two alternative transformations cannot be arbitrarily serialized. When enriching graphs with attributes, existing conflict detection techniques typically report a conflict whenever at least one of two transformations manipulates a shared attribute. In this paper, we propose an improved, less conservative condition for static conflict detection of graph transformation with attributes by explicitly taking the semantics of the attribute operations into account. The proposed technique is based on symbolic graphs, which extend the traditional notion of graphs by logic formulas used for attribute handling. The approach is proven complete, i.e., any potential conflict is guaranteed to be detected.

  9. 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.

  10. Transformation of UML models to CSP : a case study for graph transformation tools

    NARCIS (Netherlands)

    Varró, D.; Asztalos, M.; Bisztray, D.; Boronat, A.; Dang, D.; Geiß, R.; Greenyer, J.; Van Gorp, P.M.E.; Kniemeyer, O.; Narayanan, A.; Rencis, E.; Weinell, E.; Schürr, A.; Nagl, M.; Zündorf, A.

    2008-01-01

    Graph transformation provides an intuitive mechanism for capturing model transformations. In the current paper, we investigate and compare various graph transformation tools using a compact practical model transformation case study carried out as part of the AGTIVE 2007 Tool Contest [22]. The aim of

  11. Graph Transformation for Consolidation of Creativity Sessions Results

    DEFF Research Database (Denmark)

    Dolog, Peter

    2010-01-01

    Graph transformation approach for consolidation of creativity sessions results is part of the FP7 EU/IST project idSpace: Tooling of and training for collaborative, distributed product innovation. The goal of graph transformation approach is to provide a tool for merging results of various sessions...... (such as brainstorming sessions), which are represented as graphs, when the session participants- are physically distributed....

  12. Engineering Object-Oriented Semantics Using Graph Transformations

    NARCIS (Netherlands)

    Kastenberg, H.; Kleppe, A.G.; Rensink, Arend

    In this paper we describe the application of the theory of graph transformations to the practise of language design. We have defined the semantics of a small but realistic object-oriented language (called TAAL) by mapping the language constructs to graphs and their operational semantics to graph

  13. Proving termination of graph transformation systems using weighted type graphs over semirings

    NARCIS (Netherlands)

    Bruggink, H.J.S.; König, B.; Nolte, D.; Zantema, H.; Parisi-Presicce, F.; Westfechtel, B.

    2015-01-01

    We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a

  14. Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations

    OpenAIRE

    Delzanno, Giorgio; Stückrath, Jan

    2014-01-01

    We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presenta...

  15. Strategy and pattern recognition in expert\\ud comprehension of 2 × 2 interaction graphs

    OpenAIRE

    Peebles, David

    2013-01-01

    I present a model of expert comprehension performance for 2 × 2 "interaction" graphs typically used to present data from two-way factorial research designs. Developed using the ACT-R cognitive architecture, the model simulates the cognitive and perceptual operations involved in interpreting interaction graphs and provides a detailed characterisation of the information\\ud extracted from the diagram, the prior knowledge required to interpret interaction graphs, and the knowledge generated durin...

  16. Comparing relational model transformation technologies: implementing Query/View/Transformation with Triple Graph Grammars

    DEFF Research Database (Denmark)

    Greenyer, Joel; Kindler, Ekkart

    2010-01-01

    and for model-based software engineering approaches in general. QVT (Query/View/Transformation) is the transformation technology recently proposed for this purpose by the OMG. TGGs (Triple Graph Grammars) are another transformation technology proposed in the mid-nineties, used for example in the FUJABA CASE...

  17. Transformation Strategies between Block-Oriented and Graph-Oriented Process Modelling Languages

    DEFF Research Database (Denmark)

    Mendling, Jan; Lassen, Kristian Bisgaard; Zdun, Uwe

    2006-01-01

    Much recent research work discusses the transformation between different process modelling languages. This work, however, is mainly focussed on specific process modelling languages, and thus the general reusability of the applied transformation concepts is rather limited. In this paper, we aim...... to abstract from concrete transformation strategies by distinguishing two major paradigms for representing control flow in process modelling languages: block-oriented languages (such as BPEL and BPML) and graph-oriented languages (such as EPCs and YAWL). The contribution of this paper are generic strategies...... for transforming from block-oriented process languages to graph-oriented languages, and vice versa....

  18. ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation

    Directory of Open Access Journals (Sweden)

    Sarunya Kanjanawattana

    2017-07-01

    Full Text Available Image classification plays a vital role in many areas of study, such as data mining and image processing; however, serious problems collectively referred to as the course of dimensionality have been encountered in previous studies as factors that reduce system performance. Furthermore, we also confront the problem of different graph characteristics even if graphs belong to same types. In this study, we propose a novel method of graph-type classification. Using our approach, we open up a new solution of high-dimensional images and address problems of different characteristics by converting graph images to one dimension with a discrete Fourier transformation and creating numeric datasets using wavelet and Hough transformations. Moreover, we introduce a new classifier, which is a combination between artificial neuron networks (ANNs and support vector machines (SVMs, which we call ANNSVM, to enhance accuracy. The objectives of our study are to propose an effective graph-type classification method that includes finding a new data representative used for classification instead of two-dimensional images and to investigate what features make our data separable. To evaluate the method of our study, we conducted five experiments with different methods and datasets. The input dataset we focused on was a numeric dataset containing wavelet coefficients and outputs of a Hough transformation. From our experimental results, we observed that the highest accuracy was provided using our method with Coiflet 1, which achieved a 0.91 accuracy.

  19. Graph and model transformation tools for model migration : empirical results from the transformation tool contest

    NARCIS (Netherlands)

    Rose, L.M.; Herrmannsdoerfer, M.; Mazanek, S.; Van Gorp, P.M.E.; Buchwald, S.; Horn, T.; Kalnina, E.; Koch, A.; Lano, K.; Schätz, B.; Wimmer, M.

    2014-01-01

    We describe the results of the Transformation Tool Contest 2010 workshop, in which nine graph and model transformation tools were compared for specifying model migration. The model migration problem—migration of UML activity diagrams from version 1.4 to version 2.2—is non-trivial and practically

  20. Transformation Strategies between Block-Oriented and Graph-Oriented Process Modelling Languages

    DEFF Research Database (Denmark)

    Mendling, Jan; Lassen, Kristian Bisgaard; Zdun, Uwe

    to abstract from concrete transformationstrategies by distinguishing two major paradigms for process modelling languages:block-oriented languages (such as BPEL and BPML) and graph-oriented languages(such as EPCs and YAWL). The contribution of this paper are generic strategiesfor transforming from block......Much recent research work discusses the transformation between differentprocess modelling languages. This work, however, is mainly focussed on specific processmodelling languages, and thus the general reusability of the applied transformationconcepts is rather limited. In this paper, we aim......-oriented process languages to graph-oriented languages,and vice versa. We also present two case studies of applying our strategies....

  1. Handbook of graph grammars and computing by graph transformation

    CERN Document Server

    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

  2. Exploring the brains of Baduk (Go experts: gray matter morphometry, resting-state functional connectivity, and graph theoretical analysis

    Directory of Open Access Journals (Sweden)

    Wi Hoon eJung

    2013-10-01

    Full Text Available One major characteristic of experts is intuitive judgment, which is an automatic process whereby patterns stored in memory through long-term training are recognized. Indeed, long-term training may influence brain structure and function. A recent study revealed that chess experts at rest showed differences in structure and functional connectivity (FC in the head of caudate, which is associated with rapid best next-move generation. However, less is known about the structure and function of the brains of Baduk experts compared with those of experts in other strategy games. Therefore, we performed voxel-based morphometry and FC analyses in Baduk experts to investigate structural brain differences and to clarify the influence of these differences on functional interactions. We also conducted graph theoretical analysis to explore the topological organization of whole-brain functional networks. Compared to novices, Baduk experts exhibited decreased and increased gray matter volume in the amygdala and nucleus accumbens, respectively. We also found increased FC between the amygdala and medial orbitofrontal cortex and decreased FC between the nucleus accumbens and medial prefrontal cortex. Further graph theoretical analysis revealed differences in measures of the integration of the network and in the regional nodal characteristics of various brain regions activated during Baduk. This study provides evidence for structural and functional differences as well as altered topological organization of the whole-brain functional networks in Baduk experts. Our findings also offer novel suggestions about the cognitive mechanisms behind Baduk expertise, which involves intuitive decision-making mediated by somatic marker circuitry and visuospatial processing.

  3. Clone Detection for Graph-Based Model Transformation Languages

    DEFF Research Database (Denmark)

    Strüber, Daniel; Plöger, Jennifer; Acretoaie, Vlad

    2016-01-01

    and analytical quality assurance. From these use cases, we derive a set of key requirements. We describe our customization of existing model clone detection techniques allowing us to address these requirements. Finally, we provide an experimental evaluation, indicating that our customization of ConQAT, one......Cloning is a convenient mechanism to enable reuse across and within software artifacts. On the downside, it is also a practice related to significant long-term maintainability impediments, thus generating a need to identify clones in affected artifacts. A large variety of clone detection techniques...... has been proposed for programming and modeling languages; yet no specific ones have emerged for model transformation languages. In this paper, we explore clone detection for graph-based model transformation languages. We introduce potential use cases for such techniques in the context of constructive...

  4. A Modal-Logic Based Graph Abstraction

    NARCIS (Netherlands)

    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

  5. Modelling and analysis of distributed simulation protocols with distributed graph transformation

    OpenAIRE

    Lara, Juan de; Taentzer, Gabriele

    2005-01-01

    Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. J. de Lara, and G. Taentzer, "Modelling and analysis of distributed simulation protocols with distributed graph transformation...

  6. A seminar on graph theory

    CERN Document Server

    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

  7. Formal Analysis of Functional Behaviour for Model Transformations Based on Triple Graph Grammars - Extended Version

    OpenAIRE

    Hermann, Frank; Ehrig, Hartmut; Orejas, Fernando; Ulrike, Golas

    2010-01-01

    Triple Graph Grammars (TGGs) are a well-established concept for the specification of model transformations. In previous work we have formalized and analyzed already crucial properties of model transformations like termination, correctness and completeness, but functional behaviour - especially local confluence - is missing up to now. In order to close this gap we generate forward translation rules, which extend standard forward rules by translation attributes keeping track of the elements whi...

  8. Multi-rate equivalents of cyclo-static synchronous dataflow graphs

    NARCIS (Netherlands)

    de Groote, Robert; Holzenspies, P.K.F.; Kuper, Jan; Smit, Gerardus Johannes Maria

    In this paper, we present a transformation that takes a cyclo-static dataflow (CSDF) graph and produces an equivalent multi-rate synchronous dataflow (MRSDF) graph. This fills a gap in existing analysis techniques for synchronous dataflow graphs; transformations into equivalent homogeneous

  9. An Expert System toward Buiding An Earth Science Knowledge Graph

    Science.gov (United States)

    Zhang, J.; Duan, X.; Ramachandran, R.; Lee, T. J.; Bao, Q.; Gatlin, P. N.; Maskey, M.

    2017-12-01

    In this ongoing work, we aim to build foundations of Cognitive Computing for Earth Science research. The goal of our project is to develop an end-to-end automated methodology for incrementally constructing Knowledge Graphs for Earth Science (KG4ES). These knowledge graphs can then serve as the foundational components for building cognitive systems in Earth science, enabling researchers to uncover new patterns and hypotheses that are virtually impossible to identify today. In addition, this research focuses on developing mining algorithms needed to exploit these constructed knowledge graphs. As such, these graphs will free knowledge from publications that are generated in a very linear, deterministic manner, and structure knowledge in a way that users can both interact and connect with relevant pieces of information. Our major contributions are two-fold. First, we have developed an end-to-end methodology for constructing Knowledge Graphs for Earth Science (KG4ES) using existing corpus of journal papers and reports. One of the key challenges in any machine learning, especially deep learning applications, is the need for robust and large training datasets. We have developed techniques capable of automatically retraining models and incrementally building and updating KG4ES, based on ever evolving training data. We also adopt the evaluation instrument based on common research methodologies used in Earth science research, especially in Atmospheric Science. Second, we have developed an algorithm to infer new knowledge that can exploit the constructed KG4ES. In more detail, we have developed a network prediction algorithm aiming to explore and predict possible new connections in the KG4ES and aid in new knowledge discovery.

  10. Graphing trillions of triangles.

    Science.gov (United States)

    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.

  11. A first course in graph theory

    CERN Document Server

    Chartrand, Gary

    2012-01-01

    This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications.Optional sections designated as ""excursion"" and ""exploration"" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three app

  12. The Harary index of a graph

    CERN Document Server

    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...

  13. A cognitive architecture-based model of graph comprehension

    OpenAIRE

    Peebles, David

    2012-01-01

    I present a model of expert comprehension performance for 2 × 2 "interaction" graphs typically used to present data from two-way factorial research designs. Developed using the ACT-R cognitive architecture, the model simulates the cognitive and perceptual operations involved in interpreting interaction graphs and provides a detailed characterisation of the information extracted from the diagram, the prior knowledge required to interpret interaction graphs, and the knowledge generated during t...

  14. System dynamics and control with bond graph modeling

    CERN Document Server

    Kypuros, Javier

    2013-01-01

    Part I Dynamic System ModelingIntroduction to System DynamicsIntroductionSystem Decomposition and Model ComplexityMathematical Modeling of Dynamic SystemsAnalysis and Design of Dynamic SystemsControl of Dynamic SystemsDiagrams of Dynamic SystemsA Graph-Centered Approach to ModelingSummaryPracticeExercisesBasic Bond Graph ElementsIntroductionPower and Energy VariablesBasic 1-Port ElementsBasic 2-Ports ElementsJunction ElementsSimple Bond Graph ExamplesSummaryPracticeExercisesBond Graph Synthesis and Equation DerivationIntroductionGeneral GuidelinesMechanical TranslationMechanical RotationElectrical CircuitsHydraulic CircuitsMixed SystemsState Equation DerivationState-Space RepresentationsAlgebraic Loops and Derivative CausalitySummaryPracticeExercisesImpedance Bond GraphsIntroductionLaplace Transform of the State-Space EquationBasic 1-Port ImpedancesImpedance Bond Graph SynthesisJunctions, Transformers, and GyratorsEffort and Flow DividersSign ChangesTransfer Function DerivationAlternative Derivation of Transf...

  15. PSG-EXPERT. An expert system for the diagnosis of sleep disorders.

    Science.gov (United States)

    Fred, A; Filipe, J; Partinen, M; Paiva, T

    2000-01-01

    This paper describes PSG-EXPERT, an expert system in the domain of sleep disorders exploring polysomnographic data. The developed software tool is addressed from two points of view: (1)--as an integrated environment for the development of diagnosis-oriented expert systems; (2)--as an auxiliary diagnosis tool in the particular domain of sleep disorders. Developed over a Windows platform, this software tool extends one of the most popular shells--CLIPS (C Language Integrated Production System) with the following features: backward chaining engine; graph-based explanation facilities; knowledge editor including a fuzzy fact editor and a rules editor, with facts-rules integrity checking; belief revision mechanism; built-in case generator and validation module. It therefore provides graphical support for knowledge acquisition, edition, explanation and validation. From an application domain point of view, PSG-Expert is an auxiliary diagnosis system for sleep disorders based on polysomnographic data, that aims at assisting the medical expert in his diagnosis task by providing automatic analysis of polysomnographic data, summarising the results of this analysis in terms of a report of major findings and possible diagnosis consistent with the polysomnographic data. Sleep disorders classification follows the International Classification of Sleep Disorders. Major features of the system include: browsing on patients data records; structured navigation on Sleep Disorders descriptions according to ASDA definitions; internet links to related pages; diagnosis consistent with polysomnographic data; graphical user-interface including graph-based explanatory facilities; uncertainty modelling and belief revision; production of reports; connection to remote databases.

  16. TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

    Science.gov (United States)

    Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue

    2016-01-01

    We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.

  17. Expert system validation in prolog

    Science.gov (United States)

    Stock, Todd; Stachowitz, Rolf; Chang, Chin-Liang; Combs, Jacqueline

    1988-01-01

    An overview of the Expert System Validation Assistant (EVA) is being implemented in Prolog at the Lockheed AI Center. Prolog was chosen to facilitate rapid prototyping of the structure and logic checkers and since February 1987, we have implemented code to check for irrelevance, subsumption, duplication, deadends, unreachability, and cycles. The architecture chosen is extremely flexible and expansible, yet concise and complementary with the normal interactive style of Prolog. The foundation of the system is in the connection graph representation. Rules and facts are modeled as nodes in the graph and arcs indicate common patterns between rules. The basic activity of the validation system is then a traversal of the connection graph, searching for various patterns the system recognizes as erroneous. To aid in specifying these patterns, a metalanguage is developed, providing the user with the basic facilities required to reason about the expert system. Using the metalanguage, the user can, for example, give the Prolog inference engine the goal of finding inconsistent conclusions among the rules, and Prolog will search the graph intantiations which can match the definition of inconsistency. Examples of code for some of the checkers are provided and the algorithms explained. Technical highlights include automatic construction of a connection graph, demonstration of the use of metalanguage, the A* algorithm modified to detect all unique cycles, general-purpose stacks in Prolog, and a general-purpose database browser with pattern completion.

  18. Graph based communication analysis for hardware/software codesign

    DEFF Research Database (Denmark)

    Knudsen, Peter Voigt; Madsen, Jan

    1999-01-01

    In this paper we present a coarse grain CDFG (Control/Data Flow Graph) model suitable for hardware/software partitioning of single processes and demonstrate how it is necessary to perform various transformations on the graph structure before partitioning in order to achieve a structure that allows...... for accurate estimation of communication overhead between nodes mapped to different processors. In particular, we demonstrate how various transformations of control structures can lead to a more accurate communication analysis and more efficient implementations. The purpose of the transformations is to obtain...

  19. Classical dynamics on graphs

    International Nuclear Information System (INIS)

    Barra, F.; Gaspard, P.

    2001-01-01

    We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes

  20. EIT Imaging Regularization Based on Spectral Graph Wavelets.

    Science.gov (United States)

    Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut

    2017-09-01

    The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.

  1. Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework

    Directory of Open Access Journals (Sweden)

    Maribel Fernández

    2014-07-01

    Full Text Available We present strategic portgraph rewriting as a basis for the implementation of visual modelling and analysis tools. The goal is to facilitate the specification, analysis and simulation of complex systems, using port graphs. A system is represented by an initial graph and a collection of graph rewriting rules, together with a user-defined strategy to control the application of rules. The strategy language includes constructs to deal with graph traversal and management of rewriting positions in the graph. We give a small-step operational semantics for the language, and describe its implementation in the graph transformation and visualisation tool PORGY.

  2. Efficient Extraction of High Centrality Vertices in Distributed Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Kumbhare, Alok [Univ. of Southern California, Los Angeles, CA (United States); Frincu, Marc [Univ. of Southern California, Los Angeles, CA (United States); Raghavendra, Cauligi S. [Univ. of Southern California, Los Angeles, CA (United States); Prasanna, Viktor K. [Univ. of Southern California, Los Angeles, CA (United States)

    2014-09-09

    Betweenness centrality (BC) is an important measure for identifying high value or critical vertices in graphs, in variety of domains such as communication networks, road networks, and social graphs. However, calculating betweenness values is prohibitively expensive and, more often, domain experts are interested only in the vertices with the highest centrality values. In this paper, we first propose a partition-centric algorithm (MS-BC) to calculate BC for a large distributed graph that optimizes resource utilization and improves overall performance. Further, we extend the notion of approximate BC by pruning the graph and removing a subset of edges and vertices that contribute the least to the betweenness values of other vertices (MSL-BC), which further improves the runtime performance. We evaluate the proposed algorithms using a mix of real-world and synthetic graphs on an HPC cluster and analyze its strengths and weaknesses. The experimental results show an improvement in performance of upto 12x for large sparse graphs as compared to the state-of-the-art, and at the same time highlights the need for better partitioning methods to enable a balanced workload across partitions for unbalanced graphs such as small-world or power-law graphs.

  3. Expert knowledge maps for knowledge management: a case study in Traditional Chinese Medicine research.

    Science.gov (United States)

    Cui, Meng; Yang, Shuo; Yu, Tong; Yang, Ce; Gao, Yonghong; Zhu, Haiyan

    2013-10-01

    To design a model to capture information on the state and trends of knowledge creation, at both an individual and an organizational level, in order to enhance knowledge management. We designed a graph-theoretic knowledge model, the expert knowledge map (EKM), based on literature-based annotation. A case study in the domain of Traditional Chinese Medicine research was used to illustrate the usefulness of the model. The EKM successfully captured various aspects of knowledge and enhanced knowledge management within the case-study organization through the provision of knowledge graphs, expert graphs, and expert-knowledge biography. Our model could help to reveal the hot topics, trends, and products of the research done by an organization. It can potentially be used to facilitate knowledge learning, sharing and decision-making among researchers, academicians, students, and administrators of organizations.

  4. 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....

  5. Expert System Approach For Generating And Evaluating Engine Design Alternatives

    Science.gov (United States)

    Shen, Stewart N. T.; Chew, Meng-Sang; Issa, Ghassan F.

    1989-03-01

    Artificial intelligence is becoming an increasingly important subject of study for computer scientists, engineering designers, as well as professionals in other fields. Even though AI technology is a relatively new discipline, many of its concepts have already found practical applications. Expert systems, in particular, have made significant contributions to technologies in such fields as business, medicine, engineering design, chemistry, and particle physics. This paper describes an expert system developed to aid the mechanical designer with the preliminary design of variable-stroke internal-combustion engines. The expert system accomplished its task by generating and evaluating a large number of design alternatives represented in the form of graphs. Through the application of structural and design rules directly to the graphs, optimal and near optimal preliminary design configurations of engines are deduced.

  6. Breaking new ground in the mind: an initial study of mental brittle transformation and mental rigid rotation in science experts.

    Science.gov (United States)

    Resnick, Ilyse; Shipley, Thomas F

    2013-05-01

    The current study examines the spatial skills employed in different spatial reasoning tasks, by asking how science experts who are practiced in different types of visualizations perform on different spatial tasks. Specifically, the current study examines the varieties of mental transformations. We hypothesize that there may be two broad classes of mental transformations: rigid body mental transformations and non-rigid mental transformations. We focus on the disciplines of geology and organic chemistry because different types of transformations are central to the two disciplines: While geologists and organic chemists may both confront rotation in the practice of their profession, only geologists confront brittle transformations. A new instrument was developed to measure mental brittle transformation (visualizing breaking). Geologists and organic chemists performed similarly on a measure of mental rotation, while geologists outperformed organic chemists on the mental brittle transformation test. The differential pattern of skill on the two tests for the two groups of experts suggests that mental brittle transformation and mental rotation are different spatial skills. The roles of domain general cognitive resources (attentional control, spatial working memory, and perceptual filling in) and strategy in completing mental brittle transformation are discussed. The current study illustrates how ecological and interdisciplinary approaches complement traditional cognitive science to offer a comprehensive approach to understanding the nature of spatial thinking.

  7. On construction method of shipborne and airborne radar intelligence and related equipment knowledge graph

    Science.gov (United States)

    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.

  8. Transformation reborn: A new generation expert system for planning HST operations

    Science.gov (United States)

    Gerb, Andrew

    1991-01-01

    The Transformation expert system (TRANS) converts proposals for astronomical observations with the Hubble Space Telescope (HST) into detailed observing plans. It encodes expert knowledge to solve problems faced in planning and commanding HST observations to enable their processing by the Science Operations Ground System (SOGS). Among these problems are determining an acceptable order of executing observations, grouping of observations to enhance efficiency and schedulability, inserting extra observations when necessary, and providing parameters for commanding HST instruments. TRANS is currently an operational system and plays a critical role in the HST ground system. It was originally designed using forward-chaining provided by the OPS5 expert system language, but has been reimplemented using a procedural knowledge base. This reimplementation was forced by the explosion in the amount of OPS5 code required to specify the increasingly complicated situations requiring expert-level intervention by the TRANS knowledge base. This problem was compounded by the difficulty of avoiding unintended interaction between rules. To support the TRANS knowledge base, XCL, a small but powerful extension to Commom Lisp was implemented. XCL allows a compact syntax for specifying assignments and references to object attributes. XCL also allows the capability to iterate over objects and perform keyed lookup. The reimplementation of TRANS has greatly diminished the effort needed to maintain and enhance it. As a result of this, its functions have been expanded to include warnings about observations that are difficult or impossible to schedule or command, providing data to aid SPIKE, an intelligent planning system used for HST long-term scheduling, and providing information to the Guide Star Selection System (GSSS) to aid in determination of the long range availability of guide stars.

  9. A survey and comparison of transformation tools based on the transformation tool contest

    NARCIS (Netherlands)

    Jakumeit, E.; Van Gorp, P.; Buchwald, S.; Rose, L.; Wagelaar, D.; Dan, L.; Hegedüs, Á; Hermannsdörfer, M.; Horn, T.; Kalnina, E.; Krause, C.; Lano, K.; Lepper, M.; Rensink, Arend; Rose, L.M.; Wätzoldt, S.; Mazanek, S.

    Model transformation is one of the key tasks in model-driven engineering and relies on the efficient matching and modification of graph-based data structures; its sibling graph rewriting has been used to successfully model problems in a variety of domains. Over the last years, a wide range of graph

  10. Simplifying Scalable Graph Processing with a Domain-Specific Language

    KAUST Repository

    Hong, Sungpack; Salihoglu, Semih; Widom, Jennifer; Olukotun, Kunle

    2014-01-01

    Large-scale graph processing, with its massive data sets, requires distributed processing. However, conventional frameworks for distributed graph processing, such as Pregel, use non-traditional programming models that are well-suited for parallelism and scalability but inconvenient for implementing non-trivial graph algorithms. In this paper, we use Green-Marl, a Domain-Specific Language for graph analysis, to intuitively describe graph algorithms and extend its compiler to generate equivalent Pregel implementations. Using the semantic information captured by Green-Marl, the compiler applies a set of transformation rules that convert imperative graph algorithms into Pregel's programming model. Our experiments show that the Pregel programs generated by the Green-Marl compiler perform similarly to manually coded Pregel implementations of the same algorithms. The compiler is even able to generate a Pregel implementation of a complicated graph algorithm for which a manual Pregel implementation is very challenging.

  11. Simplifying Scalable Graph Processing with a Domain-Specific Language

    KAUST Repository

    Hong, Sungpack

    2014-01-01

    Large-scale graph processing, with its massive data sets, requires distributed processing. However, conventional frameworks for distributed graph processing, such as Pregel, use non-traditional programming models that are well-suited for parallelism and scalability but inconvenient for implementing non-trivial graph algorithms. In this paper, we use Green-Marl, a Domain-Specific Language for graph analysis, to intuitively describe graph algorithms and extend its compiler to generate equivalent Pregel implementations. Using the semantic information captured by Green-Marl, the compiler applies a set of transformation rules that convert imperative graph algorithms into Pregel\\'s programming model. Our experiments show that the Pregel programs generated by the Green-Marl compiler perform similarly to manually coded Pregel implementations of the same algorithms. The compiler is even able to generate a Pregel implementation of a complicated graph algorithm for which a manual Pregel implementation is very challenging.

  12. A Qualitative Approach to Sketch the Graph of a Function.

    Science.gov (United States)

    Alson, Pedro

    1992-01-01

    Presents a qualitative and global method of graphing functions that involves transformations of the graph of a known function in the cartesian coordinate system referred to as graphic operators. Explains how the method has been taught to students and some comments about the results obtained. (MDH)

  13. Belief propagation and loop series on planar graphs

    International Nuclear Information System (INIS)

    Chertkov, Michael; Teodorescu, Razvan; Chernyak, Vladimir Y

    2008-01-01

    We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R) [cond-mat/0601487]; 2006 J. Stat. Mech. P06009 [cond-mat/0603189]) is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation (Fisher 1961 Phys. Rev. 124 1664), to evaluating the partition function of the dimer-matching model on an auxiliary planar graph. Thus, the truncated series can be easily re-summed, using the Pfaffian formula of Kasteleyn (1961 Physics 27 1209). This allows us to identify a big class of computationally tractable planar models reducible to a dimer model via the Belief Propagation (gauge) transformation. The Pfaffian representation can also be extended to the full Loop Series, in which case the expansion becomes a sum of Pfaffian contributions, each associated with dimer matchings on an extension to a subgraph of the original graph. Algorithmic consequences of the Pfaffian representation, as well as relations to quantum and non-planar models, are discussed

  14. Learning a Health Knowledge Graph from Electronic Medical Records.

    Science.gov (United States)

    Rotmensch, Maya; Halpern, Yoni; Tlimat, Abdulhakim; Horng, Steven; Sontag, David

    2017-07-20

    Demand for clinical decision support systems in medicine and self-diagnostic symptom checkers has substantially increased in recent years. Existing platforms rely on knowledge bases manually compiled through a labor-intensive process or automatically derived using simple pairwise statistics. This study explored an automated process to learn high quality knowledge bases linking diseases and symptoms directly from electronic medical records. Medical concepts were extracted from 273,174 de-identified patient records and maximum likelihood estimation of three probabilistic models was used to automatically construct knowledge graphs: logistic regression, naive Bayes classifier and a Bayesian network using noisy OR gates. A graph of disease-symptom relationships was elicited from the learned parameters and the constructed knowledge graphs were evaluated and validated, with permission, against Google's manually-constructed knowledge graph and against expert physician opinions. Our study shows that direct and automated construction of high quality health knowledge graphs from medical records using rudimentary concept extraction is feasible. The noisy OR model produces a high quality knowledge graph reaching precision of 0.85 for a recall of 0.6 in the clinical evaluation. Noisy OR significantly outperforms all tested models across evaluation frameworks (p < 0.01).

  15. A real-time expert system for self-repairing flight control

    Science.gov (United States)

    Gaither, S. A.; Agarwal, A. K.; Shah, S. C.; Duke, E. L.

    1989-01-01

    An integrated environment for specifying, prototyping, and implementing a self-repairing flight-control (SRFC) strategy is described. At an interactive workstation, the user can select paradigms such as rule-based expert systems, state-transition diagrams, and signal-flow graphs and hierarchically nest them, assign timing and priority attributes, establish blackboard-type communication, and specify concurrent execution on single or multiple processors. High-fidelity nonlinear simulations of aircraft and SRFC systems can be performed off-line, with the possibility of changing SRFC rules, inference strategies, and other heuristics to correct for control deficiencies. Finally, the off-line-generated SRFC can be transformed into highly optimized application-specific real-time C-language code. An application of this environment to the design of aircraft fault detection, isolation, and accommodation algorithms is presented in detail.

  16. Mapping Between Semantic Graphs and Sentences in Grammar Induction System

    Directory of Open Access Journals (Sweden)

    Laszlo Kovacs

    2010-06-01

    Full Text Available The proposed transformation module performs mapping be-
    tween two di®erent knowledge representation forms used in grammar induction systems. The kernel knowledge representation form is a special predicate centered conceptual graph called ECG. The ECG provides a semantic-based, language independent description of the environment. The other base representation form is some kind of language. The sentences of the language should meet the corresponding grammatical rules. The pilot project demonstrates the functionality of a translator module using this transformation engine between the ECG graph and the Hungarian language.

  17. Many-core graph analytics using accelerated sparse linear algebra routines

    Science.gov (United States)

    Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

    2016-05-01

    Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

  18. PERSEUS-HUB: Interactive and Collective Exploration of Large-Scale Graphs

    Directory of Open Access Journals (Sweden)

    Di Jin

    2017-07-01

    Full Text Available Graphs emerge naturally in many domains, such as social science, neuroscience, transportation engineering, and more. In many cases, such graphs have millions or billions of nodes and edges, and their sizes increase daily at a fast pace. How can researchers from various domains explore large graphs interactively and efficiently to find out what is ‘important’? How can multiple researchers explore a new graph dataset collectively and “help” each other with their findings? In this article, we present Perseus-Hub, a large-scale graph mining tool that computes a set of graph properties in a distributed manner, performs ensemble, multi-view anomaly detection to highlight regions that are worth investigating, and provides users with uncluttered visualization and easy interaction with complex graph statistics. Perseus-Hub uses a Spark cluster to calculate various statistics of large-scale graphs efficiently, and aggregates the results in a summary on the master node to support interactive user exploration. In Perseus-Hub, the visualized distributions of graph statistics provide preliminary analysis to understand a graph. To perform a deeper analysis, users with little prior knowledge can leverage patterns (e.g., spikes in the power-law degree distribution marked by other users or experts. Moreover, Perseus-Hub guides users to regions of interest by highlighting anomalous nodes and helps users establish a more comprehensive understanding about the graph at hand. We demonstrate our system through the case study on real, large-scale networks.

  19. A robust approach towards unknown transformation, regional adjacency graphs, multigraph matching, segmentation video frames from unnamed aerial vehicles (UAV)

    Science.gov (United States)

    Gohatre, Umakant Bhaskar; Patil, Venkat P.

    2018-04-01

    In computer vision application, the multiple object detection and tracking, in real-time operation is one of the important research field, that have gained a lot of attentions, in last few years for finding non stationary entities in the field of image sequence. The detection of object is advance towards following the moving object in video and then representation of object is step to track. The multiple object recognition proof is one of the testing assignment from detection multiple objects from video sequence. The picture enrollment has been for quite some time utilized as a reason for the location the detection of moving multiple objects. The technique of registration to discover correspondence between back to back casing sets in view of picture appearance under inflexible and relative change. The picture enrollment is not appropriate to deal with event occasion that can be result in potential missed objects. In this paper, for address such problems, designs propose novel approach. The divided video outlines utilizing area adjancy diagram of visual appearance and geometric properties. Then it performed between graph sequences by using multi graph matching, then getting matching region labeling by a proposed graph coloring algorithms which assign foreground label to respective region. The plan design is robust to unknown transformation with significant improvement in overall existing work which is related to moving multiple objects detection in real time parameters.

  20. Inferring ontology graph structures using OWL reasoning

    KAUST Repository

    Rodriguez-Garcia, Miguel Angel; Hoehndorf, Robert

    2018-01-01

    ' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies

  1. Transformation language integration based on profiles and higher order transformations

    NARCIS (Netherlands)

    Van Gorp, P.M.E.; Keller, A.; Janssens, D.; Gaševic, D.; Lämmel, R.; Van Wyk, Eric

    2009-01-01

    For about two decades, researchers have been constructing tools for applying graph transformations on large model transformation case studies. Instead of incrementally extending a common core, these competitive tool builders have repeatedly reconstructed mechanisms that were already supported by

  2. Transforming the Way We Teach Function Transformations

    Science.gov (United States)

    Faulkenberry, Eileen Durand; Faulkenberry, Thomas J.

    2010-01-01

    In this article, the authors discuss "function," a well-defined rule that relates inputs to outputs. They have found that by using the input-output definition of "function," they can examine transformations of functions simply by looking at changes to input or output and the respective changes to the graph. Applying transformations to the input…

  3. Inferring ontology graph structures using OWL reasoning

    KAUST Repository

    Rodriguez-Garcia, Miguel Angel

    2018-01-05

    Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

  4. Inferring ontology graph structures using OWL reasoning.

    Science.gov (United States)

    Rodríguez-García, Miguel Ángel; Hoehndorf, Robert

    2018-01-05

    Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

  5. Groups, graphs and random walks

    CERN Document Server

    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...

  6. A living PSA based on use of expert systems

    International Nuclear Information System (INIS)

    Ancelin, C.; Bouissou, M.; Le, P.; De Saint-Quentin, S.; Villatte, N.

    1989-01-01

    This paper presents the expert systems that are developed by EDF in the framework of the French PSA. Aimed at automatically generating reliability models (fault trees, state graphs....), these expert systems are used for the reliability studies of safety systems in the Paluel nuclear power plant. Beyond the description of the implemented method, this paper insists on the new approach proposed to the reliability engineer, when using artificial intelligence techniques

  7. Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models

    Directory of Open Access Journals (Sweden)

    Tomasz Kajdanowicz

    2016-09-01

    Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.

  8. Generalising tree traversals and tree transformations to DAGs

    DEFF Research Database (Denmark)

    Bahr, Patrick; Axelsson, Emil

    2017-01-01

    We present a recursion scheme based on attribute grammars that can be transparently applied to trees and acyclic graphs. Our recursion scheme allows the programmer to implement a tree traversal or a tree transformation and then apply it to compact graph representations of trees instead. The resul......We present a recursion scheme based on attribute grammars that can be transparently applied to trees and acyclic graphs. Our recursion scheme allows the programmer to implement a tree traversal or a tree transformation and then apply it to compact graph representations of trees instead...... as the complementing theory with a number of examples....

  9. Resistance Distances in Vertex-Face Graphs

    Science.gov (United States)

    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.

  10. Formation of Robust Multi-Agent Networks through Self-Organizing Random Regular Graphs

    KAUST Repository

    Yasin Yazicioǧlu, A.; Egerstedt, Magnus; Shamma, Jeff S.

    2015-01-01

    Multi-Agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-Agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m ϵ [k+k ] 2. Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges. © 2015 IEEE.

  11. Formation of Robust Multi-Agent Networks through Self-Organizing Random Regular Graphs

    KAUST Repository

    Yasin Yazicioǧlu, A.

    2015-11-25

    Multi-Agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-Agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m ϵ [k+k ] 2. Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges. © 2015 IEEE.

  12. Expert system for the real-time management of alarms in an electric grid. Un systeme expert pour la gestion en temps reel des alarmes dans un reseau electrique

    Energy Technology Data Exchange (ETDEWEB)

    Girouard, P.

    1987-01-01

    A model-base expert system is presented for the processing of alarm messages in power networks' control centers. This alarm processor, called GESTAL, generates concise diagnoses identifying the causes(s) of network disturbances and describing the operation of the protection and alarm systems which operate to isolate faulty components. Essentially, the alarm processor is an agenda driven expert system which is composed of a model of the power network's alarm and protection systems as well as several sets of rules. Based on the nextwork model, graph structures are constructed which represent relationships between alarms as they are received. These graph structures are then analysed in order to diagnose the disturbances(s). The alarm processor has been developed using the ART 3.0 programming language in a Symbolics Lisp-machine environment. Background material on expert systems, electric power networks, and alarm processing software is included, as well as a description of GESTAL'S functional characteristics and design. 51 refs., 28 figs.

  13. A graph rewriting programming language for graph drawing

    OpenAIRE

    Rodgers, Peter

    1998-01-01

    This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...

  14. Visualizing Dataflow Graphs of Deep Learning Models in TensorFlow.

    Science.gov (United States)

    Wongsuphasawat, Kanit; Smilkov, Daniel; Wexler, James; Wilson, Jimbo; Mane, Dandelion; Fritz, Doug; Krishnan, Dilip; Viegas, Fernanda B; Wattenberg, Martin

    2018-01-01

    We present a design study of the TensorFlow Graph Visualizer, part of the TensorFlow machine intelligence platform. This tool helps users understand complex machine learning architectures by visualizing their underlying dataflow graphs. The tool works by applying a series of graph transformations that enable standard layout techniques to produce a legible interactive diagram. To declutter the graph, we decouple non-critical nodes from the layout. To provide an overview, we build a clustered graph using the hierarchical structure annotated in the source code. To support exploration of nested structure on demand, we perform edge bundling to enable stable and responsive cluster expansion. Finally, we detect and highlight repeated structures to emphasize a model's modular composition. To demonstrate the utility of the visualizer, we describe example usage scenarios and report user feedback. Overall, users find the visualizer useful for understanding, debugging, and sharing the structures of their models.

  15. Bond graphs for modelling, control and fault diagnosis of engineering systems

    CERN Document Server

    2017-01-01

    This book presents theory and latest application work in Bond Graph methodology with a focus on: • Hybrid dynamical system models, • Model-based fault diagnosis, model-based fault tolerant control, fault prognosis • and also addresses • Open thermodynamic systems with compressible fluid flow, • Distributed parameter models of mechanical subsystems. In addition, the book covers various applications of current interest ranging from motorised wheelchairs, in-vivo surgery robots, walking machines to wind-turbines.The up-to-date presentation has been made possible by experts who are active members of the worldwide bond graph modelling community. This book is the completely revised 2nd edition of the 2011 Springer compilation text titled Bond Graph Modelling of Engineering Systems – Theory, Applications and Software Support. It extends the presentation of theory and applications of graph methodology by new developments and latest research results. Like the first edition, this book addresses readers in a...

  16. Applied and computational harmonic analysis on graphs and networks

    Science.gov (United States)

    Irion, Jeff; Saito, Naoki

    2015-09-01

    In recent years, the advent of new sensor technologies and social network infrastructure has provided huge opportunities and challenges for analyzing data recorded on such networks. In the case of data on regular lattices, computational harmonic analysis tools such as the Fourier and wavelet transforms have well-developed theories and proven track records of success. It is therefore quite important to extend such tools from the classical setting of regular lattices to the more general setting of graphs and networks. In this article, we first review basics of graph Laplacian matrices, whose eigenpairs are often interpreted as the frequencies and the Fourier basis vectors on a given graph. We point out, however, that such an interpretation is misleading unless the underlying graph is either an unweighted path or cycle. We then discuss our recent effort of constructing multiscale basis dictionaries on a graph, including the Hierarchical Graph Laplacian Eigenbasis Dictionary and the Generalized Haar-Walsh Wavelet Packet Dictionary, which are viewed as generalizations of the classical hierarchical block DCTs and the Haar-Walsh wavelet packets, respectively, to the graph setting. Finally, we demonstrate the usefulness of our dictionaries by using them to simultaneously segment and denoise 1-D noisy signals sampled on regular lattices, a problem where classical tools have difficulty.

  17. Optimization of a dynamic uncertain causality graph for fault diagnosis in nuclear power plant

    Institute of Scientific and Technical Information of China (English)

    Yue Zhao; Francesco Di Maio; Enrico Zio; Qin Zhang; Chun-Ling Dong; Jin-Ying Zhang

    2017-01-01

    Fault diagnostics is important for safe operation of nuclear power plants (NPPs).In recent years,data-driven approaches have been proposed and implemented to tackle the problem,e.g.,neural networks,fuzzy and neurofuzzy approaches,support vector machine,K-nearest neighbor classifiers and inference methodologies.Among these methods,dynamic uncertain causality graph (DUCG)has been proved effective in many practical cases.However,the causal graph construction behind the DUCG is complicate and,in many cases,results redundant on the symptoms needed to correctly classify the fault.In this paper,we propose a method to simplify causal graph construction in an automatic way.The method consists in transforming the expert knowledge-based DCUG into a fuzzy decision tree (FDT) by extracting from the DUCG a fuzzy rule base that resumes the used symptoms at the basis of the FDT.Genetic algorithm (GA) is,then,used for the optimization of the FDT,by performing a wrapper search around the FDT:the set of symptoms selected during the iterative search are taken as the best set of symptoms for the diagnosis of the faults that can occur in the system.The effectiveness of the approach is shown with respect to a DUCG model initially built to diagnose 23 faults originally using 262 symptoms of Unit-1 in the Ningde NPP of the China Guangdong Nuclear Power Corporation.The results show that the FDT,with GA-optimized symptoms and diagnosis strategy,can drive the construction of DUCG and lower the computational burden without loss of accuracy in diagnosis.

  18. Optimization of a dynamic uncertain causality graph for fault diagnosis in nuclear power plant

    Institute of Scientific and Technical Information of China (English)

    Yue Zhao; Francesco Di Maio; Enrico Zio; Qin Zhang; Chun-Ling Dong; Jin-Ying Zhang

    2017-01-01

    Fault diagnostics is important for safe operation of nuclear power plants (NPPs).In recent years,data-driven approaches have been proposed and implemented to tackle the problem,e.g.,neural networks,fuzzy and neurofuzzy approaches,support vector machine,K-nearest neighbor classifiers and inference methodologies.Among these methods,dynamic uncertain causality graph (DUCG) has been proved effective in many practical cases.However,the causal graph construction behind the DUCG is complicate and,in many cases,results redundant on the symptoms needed to correctly classify the fault.In this paper,we propose a method to simplify causal graph construction in an automatic way.The method consists in transforming the expert knowledge-based DCUG into a fuzzy decision tree (FDT) by extracting from the DUCG a fuzzy rule base that resumes the used symptoms at the basis of the FDT.Genetic algorithm (GA) is,then,used for the optimization of the FDT,by performing a wrapper search around the FDT:the set of symptoms selected during the iterative search are taken as the best set of symptoms for the diagnosis of the faults that can occur in the system.The effectiveness of the approach is shown with respect to a DUCG model initially built to diagnose 23 faults originally using 262 symptoms of Unit-1 in the Ningde NPP of the China Guangdong Nuclear Power Corporation.The results show that the FDT,with GA-optimized symptoms and diagnosis strategy,can drive the construction of DUCG and lower the computational burden without loss of accuracy in diagnosis.

  19. Overlapping community detection based on link graph using distance dynamics

    Science.gov (United States)

    Chen, Lei; Zhang, Jing; Cai, Li-Jun

    2018-01-01

    The distance dynamics model was recently proposed to detect the disjoint community of a complex network. To identify the overlapping structure of a network using the distance dynamics model, an overlapping community detection algorithm, called L-Attractor, is proposed in this paper. The process of L-Attractor mainly consists of three phases. In the first phase, L-Attractor transforms the original graph to a link graph (a new edge graph) to assure that one node has multiple distances. In the second phase, using the improved distance dynamics model, a dynamic interaction process is introduced to simulate the distance dynamics (shrink or stretch). Through the dynamic interaction process, all distances converge, and the disjoint community structure of the link graph naturally manifests itself. In the third phase, a recovery method is designed to convert the disjoint community structure of the link graph to the overlapping community structure of the original graph. Extensive experiments are conducted on the LFR benchmark networks as well as real-world networks. Based on the results, our algorithm demonstrates higher accuracy and quality than other state-of-the-art algorithms.

  20. Graph Aggregation

    NARCIS (Netherlands)

    Endriss, U.; Grandi, U.

    Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference

  1. Generating a Tolerogenic Cell Therapy Knowledge Graph from Literature

    Directory of Open Access Journals (Sweden)

    Andre Lamurias

    2017-11-01

    Full Text Available Tolerogenic cell therapies provide an alternative to conventional immunosuppressive treatments of autoimmune disease and address, among other goals, the rejection of organ or stem cell transplants. Since various methodologies can be followed to develop tolerogenic therapies, it is important to be aware and up to date on all available studies that may be relevant to their improvement. Recently, knowledge graphs have been proposed to link various sources of information, using text mining techniques. Knowledge graphs facilitate the automatic retrieval of information about the topics represented in the graph. The objective of this work was to automatically generate a knowledge graph for tolerogenic cell therapy from biomedical literature. We developed a system, ICRel, based on machine learning to extract relations between cells and cytokines from abstracts. Our system retrieves related documents from PubMed, annotates each abstract with cell and cytokine named entities, generates the possible combinations of cell–cytokine pairs cooccurring in the same sentence, and identifies meaningful relations between cells and cytokines. The extracted relations were used to generate a knowledge graph, where each edge was supported by one or more documents. We obtained a graph containing 647 cell–cytokine relations, based on 3,264 abstracts. The modules of ICRel were evaluated with cross-validation and manual evaluation of the relations extracted. The relation extraction module obtained an F-measure of 0.789 in a reference database, while the manual evaluation obtained an accuracy of 0.615. Even though the knowledge graph is based on information that was already published in other articles about immunology, the system we present is more efficient than the laborious task of manually reading all the literature to find indirect or implicit relations. The ICRel graph will help experts identify implicit relations that may not be evident in published studies.

  2. Proxy Graph: Visual Quality Metrics of Big Graph Sampling.

    Science.gov (United States)

    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.

  3. Image based Monument Recognition using Graph based Visual Saliency

    DEFF Research Database (Denmark)

    Kalliatakis, Grigorios; Triantafyllidis, Georgios

    2013-01-01

    This article presents an image-based application aiming at simple image classification of well-known monuments in the area of Heraklion, Crete, Greece. This classification takes place by utilizing Graph Based Visual Saliency (GBVS) and employing Scale Invariant Feature Transform (SIFT) or Speeded......, the images have been previously processed according to the Graph Based Visual Saliency model in order to keep either SIFT or SURF features corresponding to the actual monuments while the background “noise” is minimized. The application is then able to classify these images, helping the user to better...

  4. The graph representation approach to topological field theory in 2 + 1 dimensions

    International Nuclear Information System (INIS)

    Martin, S.P.

    1991-02-01

    An alternative definition of topological quantum field theory in 2+1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but non-local observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wavefunctions in this ''graph representation'' approach are functionals on an appropriate set of graphs. This is in contrast to the usual ''connection representation'' approach in which the theory is defined in terms of a gauge field and the wavefunctions are functionals on the space of flat spatial connections modulo gauge transformations

  5. Gems of combinatorial optimization and graph algorithms

    CERN Document Server

    Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea

    2015-01-01

    Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory?  Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar?  Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science?   Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas.  Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks.   This ...

  6. Chromatic graph theory

    CERN Document Server

    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...

  7. Construction and application research of knowledge graph in aviation risk field

    Directory of Open Access Journals (Sweden)

    Zhao Qian

    2018-01-01

    Full Text Available Since the causes of aviation accidents and risks are complicated, concealed, unpredictable and difficult to be investigated, in order to achieve the efficient organization and knowledge sharing of the historical cases of aviation risk events, this paper put forward the method of constructing vertical knowledge graph for aviation risk field. Firstly, the data-driven incremental construction technology is used to build aviation risk event ontology model. Secondly, the pattern-based knowledge mapping mechanism, which transform structured data into RDF (Resource Description Framework data for storage, is proposed. And then the application, update and maintenance of the knowledge graph are described. Finally, knowledge graph construction system in aviation risk field is developed; and the data from American Aviation Safety Reporting System (ASRS is used as an example to verify the rationality and validity of the knowledge graph construction method. Practice has proved that the construction of knowledge graph has a guiding significance for the case information organization and sharing on the field of aviation risk.

  8. Reconfiguring Independent Sets in Claw-Free Graphs

    NARCIS (Netherlands)

    Bonsma, P.S.; Kamiński, Marcin; Wrochna, Marcin; Ravi, R.; Gørtz, Inge Li

    We present a polynomial-time algorithm that, given two independent sets in a claw-free graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w (not in

  9. Application of machine learning and expert systems to Statistical Process Control (SPC) chart interpretation

    Science.gov (United States)

    Shewhart, Mark

    1991-01-01

    Statistical Process Control (SPC) charts are one of several tools used in quality control. Other tools include flow charts, histograms, cause and effect diagrams, check sheets, Pareto diagrams, graphs, and scatter diagrams. A control chart is simply a graph which indicates process variation over time. The purpose of drawing a control chart is to detect any changes in the process signalled by abnormal points or patterns on the graph. The Artificial Intelligence Support Center (AISC) of the Acquisition Logistics Division has developed a hybrid machine learning expert system prototype which automates the process of constructing and interpreting control charts.

  10. Encoding and analyzing aerial imagery using geospatial semantic graphs

    Energy Technology Data Exchange (ETDEWEB)

    Watson, Jean-Paul; Strip, David R.; McLendon, William Clarence,; Parekh, Ojas D.; Diegert, Carl F.; Martin, Shawn Bryan; Rintoul, Mark Daniel

    2014-02-01

    While collection capabilities have yielded an ever-increasing volume of aerial imagery, analytic techniques for identifying patterns in and extracting relevant information from this data have seriously lagged. The vast majority of imagery is never examined, due to a combination of the limited bandwidth of human analysts and limitations of existing analysis tools. In this report, we describe an alternative, novel approach to both encoding and analyzing aerial imagery, using the concept of a geospatial semantic graph. The advantages of our approach are twofold. First, intuitive templates can be easily specified in terms of the domain language in which an analyst converses. These templates can be used to automatically and efficiently search large graph databases, for specific patterns of interest. Second, unsupervised machine learning techniques can be applied to automatically identify patterns in the graph databases, exposing recurring motifs in imagery. We illustrate our approach using real-world data for Anne Arundel County, Maryland, and compare the performance of our approach to that of an expert human analyst.

  11. Transforming stand-alone expert system into a community of cooperating agents

    CERN Document Server

    Jennings, N R; Aarnts, R P; Fuchs, J; Skarek, Paul

    1993-01-01

    Distributed Artificial Intelligence (DAI) systems in which multiple problem solving agents cooperate to achieve a common objective is a rapidly emerging and promising technology. However, as yet, there have been relatively few reported cases of such systems being employed to tackle real-world problems in realistic domains. One of the reasons for this is that DAI researchers have given virtually no consideration to the process of incorporating pre-existing systems into a community of cooperating agents. Yet reuse is a primary consideration for any organisation with a large software base. To redress the balance, this paper reports on an experiment undertaken at the CERN laboratories, in which two pre-existing and standalone expert systems for diagnosing faults in a particle accelerator were transformed into a community of cooperating agents. The experiences and insights gained during this process provide a valuable first step towards satisfying the needs of potential users of DAI technology - identifying the ty...

  12. Using graph approach for managing connectivity in integrative landscape modelling

    Science.gov (United States)

    Rabotin, Michael; Fabre, Jean-Christophe; Libres, Aline; Lagacherie, Philippe; Crevoisier, David; Moussa, Roger

    2013-04-01

    FLUID-landr library has been developed in order i) to be used with no GIS expert skills needed (common gis formats can be read and simplified spatial management is provided), ii) to easily develop adapted rules of landscape discretization and graph creation to follow spatialized model requirements and iii) to allow model developers to manage dynamic and complex spatial topology. Graph management in OpenFLUID are shown with i) examples of hydrological modelizations on complex farmed landscapes and ii) the new implementation of Geo-MHYDAS tool based on the OpenFLUID-landr library, which allows to discretize a landscape and create graph structure for the MHYDAS model requirements.

  13. Graph sampling

    OpenAIRE

    Zhang, L.-C.; Patone, M.

    2017-01-01

    We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.

  14. The Shrinkage Model And Expert System Of Plastic Lens Formation

    Science.gov (United States)

    Chang, Rong-Seng

    1988-06-01

    Shrinkage causes both the appearance & dimension defects of the injected plastic lens. We have built up a model of state equations with the help of finite element analysis program to estimate the volume change (shrinkage and swelling) under the combinations of injection variables such as pressure and temperature etc., then the personal computer expert system has been build up to make that knowledge conveniently available to the user in the model design, process planning, process operation and some other work. The domain knowledge is represented by a R-graph (Relationship-graph) model which states the relationships of variables & equations. This model could be compare with other models in the expert system. If the user has better model to solve the shrinkage problem, the program will evaluate it automatically and a learning file will be trigger by the expert system to teach the user to update their knowledge base and modify the old model by this better model. The Rubin's model and Gilmore's model have been input to the expert system. The conflict has been solved both from the user and the deeper knowledge base. A cube prism and the convex lens examples have been shown in this paper. This program is written by MULISP language in IBM PC-AT. The natural language provides English Explaination of know why and know how and the automatic English translation for the equation rules and the production rules.

  15. Algorithms for Planar Graphs and Graphs in Metric Spaces

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...

  16. Regularization of EIT reconstruction based on multi-scales wavelet transforms

    Directory of Open Access Journals (Sweden)

    Gong Bo

    2016-09-01

    Full Text Available Electrical Impedance Tomography (EIT intends to obtain the conductivity distribution of a domain from the electrical boundary conditions. This is an ill-posed inverse problem usually solved on finite element meshes. Wavelet transforms are widely used for medical image reconstruction. However, because of the irregular form of the finite element meshes, the canonical wavelet transforms is impossible to perform on meshes. In this article, we present a framework that combines multi-scales wavelet transforms and finite element meshes by viewing meshes as undirected graphs and applying spectral graph wavelet transform on the meshes.

  17. Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph

    Directory of Open Access Journals (Sweden)

    P. Anusha Devi

    2015-10-01

    Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$  The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.

  18. Introduction to graph theory

    CERN Document Server

    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

  19. 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.

  20. On an edge partition and root graphs of some classes of line graphs

    Directory of Open Access Journals (Sweden)

    K Pravas

    2017-04-01

    Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.

  1. Graphs and matrices

    CERN Document Server

    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...

  2. 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 $Hcong overline{F_n}$.

  3. A Solution to the Flowgraphs Case Study using Triple Graph Grammars and eMoflon

    Directory of Open Access Journals (Sweden)

    Anthony Anjorin

    2013-11-01

    Full Text Available After 20 years of Triple Graph Grammars (TGGs and numerous actively maintained implementations, there is now a need for challenging examples and success stories to show that TGGs can be used for real-world bidirectional model transformations. Our primary goal in recent years has been to increase the expressiveness of TGGs by providing a set of pragmatic features that allow a controlled fallback to programmed graph transformations and Java. Based on the Flowgraphs case study of the Transformation Tool Contest (TTC 2013, we present (i attribute constraints used to express complex bidirectional attribute manipulation, (ii binding expressions for specifying arbitrary context relationships, and (iii post-processing methods as a black box extension for TGG rules. In each case, we discuss the enabled trade-off between guaranteed formal properties and expressiveness. Our solution, implemented with our metamodelling and model transformation tool eMoflon (www.emoflon.org, is available as a virtual machine hosted on Share.

  4. Expert and novice categorization of introductory physics problems

    Science.gov (United States)

    Wolf, Steven Frederick

    Since it was first published 30 years ago, Chi et al.'s seminal paper on expert and novice categorization of introductory problems led to a plethora of follow-up studies within and outside of the area of physics [Chi et al. Cognitive Science 5, 121 -- 152 (1981)]. These studies frequently encompass "card-sorting" exercises whereby the participants group problems. The study firmly established the paradigm that novices categorize physics problems by "surface features" (e.g. "incline," "pendulum," "projectile motion,"... ), while experts use "deep structure" (e.g. "energy conservation," "Newton 2,"... ). While this technique certainly allows insights into problem solving approaches, simple descriptive statistics more often than not fail to find significant differences between experts and novices. In most experiments, the clean-cut outcome of the original study cannot be reproduced. Given the widespread implications of the original study, the frequent failure to reproduce its findings warrants a closer look. We developed a less subjective statistical analysis method for the card sorting outcome and studied how the "successful" outcome of the experiment depends on the choice of the original card set. Thus, in a first step, we are moving beyond descriptive statistics, and develop a novel microscopic approach that takes into account the individual identity of the cards and uses graph theory and models to visualize, analyze, and interpret problem categorization experiments. These graphs are compared macroscopically, using standard graph theoretic statistics, and microscopically, using a distance metric that we have developed. This macroscopic sorting behavior is described using our Cognitive Categorization Model. The microscopic comparison allows us to visualize our sorters using Principal Components Analysis and compare the expert sorters to the novice sorters as a group. In the second step, we ask the question: Which properties of problems are most important in problem

  5. Graph embedding with rich information through heterogeneous graph

    KAUST Repository

    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.

  6. Topics in graph theory graphs and their Cartesian product

    CERN Document Server

    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.

  7. Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph

    Science.gov (United States)

    Nagarathinam, R.; Parvathi, N.

    2018-04-01

    Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat

  8. Classification of user interfaces for graph-based online analytical processing

    Science.gov (United States)

    Michaelis, James R.

    2016-05-01

    In the domain of business intelligence, user-oriented software for conducting multidimensional analysis via Online- Analytical Processing (OLAP) is now commonplace. In this setting, datasets commonly have well-defined sets of dimensions and measures around which analysis tasks can be conducted. However, many forms of data used in intelligence operations - deriving from social networks, online communications, and text corpora - will consist of graphs with varying forms of potential dimensional structure. Hence, enabling OLAP over such data collections requires explicit definition and extraction of supporting dimensions and measures. Further, as Graph OLAP remains an emerging technique, limited research has been done on its user interface requirements. Namely, on effective pairing of interface designs to different types of graph-derived dimensions and measures. This paper presents a novel technique for pairing of user interface designs to Graph OLAP datasets, rooted in Analytic Hierarchy Process (AHP) driven comparisons. Attributes of the classification strategy are encoded through an AHP ontology, developed in our alternate work and extended to support pairwise comparison of interfaces. Specifically, according to their ability, as perceived by Subject Matter Experts, to support dimensions and measures corresponding to Graph OLAP dataset attributes. To frame this discussion, a survey is provided both on existing variations of Graph OLAP, as well as existing interface designs previously applied in multidimensional analysis settings. Following this, a review of our AHP ontology is provided, along with a listing of corresponding dataset and interface attributes applicable toward SME recommendation structuring. A walkthrough of AHP-based recommendation encoding via the ontology-based approach is then provided. The paper concludes with a short summary of proposed future directions seen as essential for this research area.

  9. Novel Ontologies-based Optical Character Recognition-error Correction Cooperating with Graph Component Extraction

    Directory of Open Access Journals (Sweden)

    Sarunya Kanjanawattana

    2017-01-01

    Full Text Available literature. Extracting graph information clearly contributes to readers, who are interested in graph information interpretation, because we can obtain significant information presenting in the graph. A typical tool used to transform image-based characters to computer editable characters is optical character recognition (OCR. Unfortunately, OCR cannot guarantee perfect results, because it is sensitive to noise and input quality. This becomes a serious problem because misrecognition provides misunderstanding information to readers and causes misleading communication. In this study, we present a novel method for OCR-error correction based on bar graphs using semantics, such as ontologies and dependency parsing. Moreover, we used a graph component extraction proposed in our previous study to omit irrelevant parts from graph components. It was applied to clean and prepare input data for this OCR-error correction. The main objectives of this paper are to extract significant information from the graph using OCR and to correct OCR errors using semantics. As a result, our method provided remarkable performance with the highest accuracies and F-measures. Moreover, we examined that our input data contained less of noise because of an efficiency of our graph component extraction. Based on the evidence, we conclude that our solution to the OCR problem achieves the objectives.

  10. Occupation times distribution for Brownian motion on graphs

    CERN Document Server

    Desbois, J

    2002-01-01

    Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)

  11. Assessment of tautomer distribution using the condensed reaction graph approach

    Science.gov (United States)

    Gimadiev, T. R.; Madzhidov, T. I.; Nugmanov, R. I.; Baskin, I. I.; Antipin, I. S.; Varnek, A.

    2018-03-01

    We report the first direct QSPR modeling of equilibrium constants of tautomeric transformations (logK T ) in different solvents and at different temperatures, which do not require intermediate assessment of acidity (basicity) constants for all tautomeric forms. The key step of the modeling consisted in the merging of two tautomers in one sole molecular graph ("condensed reaction graph") which enables to compute molecular descriptors characterizing entire equilibrium. The support vector regression method was used to build the models. The training set consisted of 785 transformations belonging to 11 types of tautomeric reactions with equilibrium constants measured in different solvents and at different temperatures. The models obtained perform well both in cross-validation (Q2 = 0.81 RMSE = 0.7 logK T units) and on two external test sets. Benchmarking studies demonstrate that our models outperform results obtained with DFT B3LYP/6-311 ++ G(d,p) and ChemAxon Tautomerizer applicable only in water at room temperature.

  12. Integrated color face graphs for plant accident display

    International Nuclear Information System (INIS)

    Hara, Fumio

    1987-01-01

    This paper presents an integrated man-machine interface that uses cartoon-like colored graphs in the form of faces, that, through different facial expressions, display a plant condition. This is done by drawing the face on a CRT by nonlinearly transforming 31 variables and coloring the face. This integrated color graphics technique is applied to display the progess of events in the Three Mile Island nuclear power plant accident. Human visual perceptive characteristics are investigated in relation to the perception of the plant accident process, the naturality in face color change, and the consistency between facial expressions and colors. This paper concludes that colors used in an integrated color face graphs must be completely consistent with emotional feelings perceived from the colors. (author)

  13. Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

    Directory of Open Access Journals (Sweden)

    Katona Gyula Y.

    2014-11-01

    Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

  14. Graphs and Homomorphisms

    CERN Document Server

    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

  15. Adiabatic graph-state quantum computation

    International Nuclear Information System (INIS)

    Antonio, B; Anders, J; Markham, D

    2014-01-01

    Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any MBQC on a graph state with generalized flow (gflow) can be converted into an adiabatically driven holonomic computation, which we call adiabatic graph-state quantum computation (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of H-dot as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated. (paper)

  16. Graph-Based Specification and Simulation of Featherweight Java with Around Advice

    NARCIS (Netherlands)

    Staijen, T.; Rensink, Arend

    In this paper we specify an operational run-time semantics of Assignment Featherweight Java -- a minimal subset of Java with assignments -- with around advice, using graph transformations. We introduce a notion of correctness of our specification with respect to an existing semantics and claim a

  17. 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 co...

  18. Non-heuristic reduction of the graph in graph-cut optimization

    International Nuclear Information System (INIS)

    Malgouyres, François; Lermé, Nicolas

    2012-01-01

    During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut.

  19. Graph embedding with rich information through heterogeneous graph

    KAUST Repository

    Sun, Guolei

    2017-01-01

    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

  20. Graph Transformation and Designing Parallel Sparse Matrix Algorithms beyond Data Dependence Analysis

    Directory of Open Access Journals (Sweden)

    H.X. Lin

    2004-01-01

    Full Text Available Algorithms are often parallelized based on data dependence analysis manually or by means of parallel compilers. Some vector/matrix computations such as the matrix-vector products with simple data dependence structures (data parallelism can be easily parallelized. For problems with more complicated data dependence structures, parallelization is less straightforward. The data dependence graph is a powerful means for designing and analyzing parallel algorithms. However, for sparse matrix computations, parallelization based on solely exploiting the existing parallelism in an algorithm does not always give satisfactory results. For example, the conventional Gaussian elimination algorithm for the solution of a tri-diagonal system is inherently sequential, so algorithms specially for parallel computation has to be designed. After briefly reviewing different parallelization approaches, a powerful graph formalism for designing parallel algorithms is introduced. This formalism will be discussed using a tri-diagonal system as an example. Its application to general matrix computations is also discussed. Its power in designing parallel algorithms beyond the ability of data dependence analysis is shown by means of a new algorithm called ACER (Alternating Cyclic Elimination and Reduction algorithm.

  1. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

    Science.gov (United States)

    Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

    2016-01-01

    There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

  2. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

    Science.gov (United States)

    Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

    2016-08-25

    There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

  3. Adaptive Graph Convolutional Neural Networks

    OpenAIRE

    Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou

    2018-01-01

    Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...

  4. Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?

    Directory of Open Access Journals (Sweden)

    Mehmet Fatih Öçal

    2017-01-01

    Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.

  5. High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs

    Science.gov (United States)

    Kempton, Mark

    This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.

  6. X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

    Science.gov (United States)

    2017-09-01

    are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph

  7. On the sizes of expander graphs and minimum distances of graph codes

    DEFF Research Database (Denmark)

    Høholdt, Tom; Justesen, Jørn

    2014-01-01

    We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....

  8. Similarity Measure of Graphs

    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.

  9. Expert systems for automated maintenance of a Mars oxygen production system

    Science.gov (United States)

    Huang, Jen-Kuang; Ho, Ming-Tsang; Ash, Robert L.

    1992-08-01

    Application of expert system concepts to a breadboard Mars oxygen processor unit have been studied and tested. The research was directed toward developing the methodology required to enable autonomous operation and control of these simple chemical processors at Mars. Failure detection and isolation was the key area of concern, and schemes using forward chaining, backward chaining, knowledge-based expert systems, and rule-based expert systems were examined. Tests and simulations were conducted that investigated self-health checkout, emergency shutdown, and fault detection, in addition to normal control activities. A dynamic system model was developed using the Bond-Graph technique. The dynamic model agreed well with tests involving sudden reductions in throughput. However, nonlinear effects were observed during tests that incorporated step function increases in flow variables. Computer simulations and experiments have demonstrated the feasibility of expert systems utilizing rule-based diagnosis and decision-making algorithms.

  10. Spectra of Graphs

    NARCIS (Netherlands)

    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

  11. Pattern graph rewrite systems

    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.

  12. On middle cube graphs

    Directory of Open Access Journals (Sweden)

    C. Dalfo

    2015-10-01

    Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.

  13. Graph visualization (Invited talk)

    NARCIS (Netherlands)

    Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.

    2012-01-01

    Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.

  14. Adventures in graph theory

    CERN Document Server

    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...

  15. AGM: A DSL for mobile cloud computing based on directed graph

    Science.gov (United States)

    Tanković, Nikola; Grbac, Tihana Galinac

    2016-06-01

    This paper summarizes a novel approach for consuming a domain specific language (DSL) by transforming it to a directed graph representation persisted by a graph database. Using such specialized database enables advanced navigation trough the stored model exposing only relevant subsets of meta-data to different involved services and components. We applied this approach in a mobile cloud computing system and used it to model several mobile applications in retail, supply chain management and merchandising domain. These application are distributed in a Software-as-a-Service (SaaS) fashion and used by thousands of customers in Croatia. We report on lessons learned and propose further research on this topic.

  16. Distance-regular graphs

    NARCIS (Netherlands)

    van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime

    2016-01-01

    This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,

  17. On the strong metric dimension of generalized butterfly graph, starbarbell graph, and {C}_{m}\\odot {P}_{n} graph

    Science.gov (United States)

    Yunia Mayasari, Ratih; Atmojo Kusmayadi, Tri

    2018-04-01

    Let G be a connected graph with vertex set V(G) and edge set E(G). For every pair of vertices u,v\\in V(G), the interval I[u, v] between u and v to be the collection of all vertices that belong to some shortest u ‑ v path. A vertex s\\in V(G) strongly resolves two vertices u and v if u belongs to a shortest v ‑ s path or v belongs to a shortest u ‑ s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this paper we determine the strong metric dimension of a generalized butterfly graph, starbarbell graph, and {C}mȯ {P}n graph. We obtain the strong metric dimension of generalized butterfly graph is sdim(BFn ) = 2n ‑ 2. The strong metric dimension of starbarbell graph is sdim(S{B}{m1,{m}2,\\ldots,{m}n})={\\sum }i=1n({m}i-1)-1. The strong metric dimension of {C}mȯ {P}n graph are sdim({C}mȯ {P}n)=2m-1 for m > 3 and n = 2, and sdim({C}mȯ {P}n)=2m-2 for m > 3 and n > 2.

  18. GeoSciGraph: An Ontological Framework for EarthCube Semantic Infrastructure

    Science.gov (United States)

    Gupta, A.; Schachne, A.; Condit, C.; Valentine, D.; Richard, S.; Zaslavsky, I.

    2015-12-01

    The CINERGI (Community Inventory of EarthCube Resources for Geosciences Interoperability) project compiles an inventory of a wide variety of earth science resources including documents, catalogs, vocabularies, data models, data services, process models, information repositories, domain-specific ontologies etc. developed by research groups and data practitioners. We have developed a multidisciplinary semantic framework called GeoSciGraph semantic ingration of earth science resources. An integrated ontology is constructed with Basic Formal Ontology (BFO) as its upper ontology and currently ingests multiple component ontologies including the SWEET ontology, GeoSciML's lithology ontology, Tematres controlled vocabulary server, GeoNames, GCMD vocabularies on equipment, platforms and institutions, software ontology, CUAHSI hydrology vocabulary, the environmental ontology (ENVO) and several more. These ontologies are connected through bridging axioms; GeoSciGraph identifies lexically close terms and creates equivalence class or subclass relationships between them after human verification. GeoSciGraph allows a community to create community-specific customizations of the integrated ontology. GeoSciGraph uses the Neo4J,a graph database that can hold several billion concepts and relationships. GeoSciGraph provides a number of REST services that can be called by other software modules like the CINERGI information augmentation pipeline. 1) Vocabulary services are used to find exact and approximate terms, term categories (community-provided clusters of terms e.g., measurement-related terms or environmental material related terms), synonyms, term definitions and annotations. 2) Lexical services are used for text parsing to find entities, which can then be included into the ontology by a domain expert. 3) Graph services provide the ability to perform traversal centric operations e.g., finding paths and neighborhoods which can be used to perform ontological operations like

  19. Subgraph detection using graph signals

    KAUST Repository

    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.

  20. Subgraph detection using graph signals

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2017-01-01

    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.

  1. Graph spectrum

    NARCIS (Netherlands)

    Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.

    2012-01-01

    This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.

  2. TGGs for Transforming UML to CSP

    DEFF Research Database (Denmark)

    Greenyer, Joel; Kindler, Ekkart; Rieke, Jan

    Contest. The second transformation problem, a transformation from UML activity diagrams to CSP processes, i.e. a transformation between two models, is a typical application for Triple Graph Grammars (TGGs). We present our contributed solution, presenting the TGG rules and the implementation of our TGG...... interpreter. Moreover, we point out the advantages of our soulution as well as some restrictions of the current implementation. This paper will only briefly state the transformation problem and focus on our TGG approach and the discussion of the rules....

  3. Pragmatic Graph Rewriting Modifications

    OpenAIRE

    Rodgers, Peter; Vidal, Natalia

    1999-01-01

    We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...

  4. Simplicial complexes of graphs

    CERN Document Server

    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.

  5. The STAPL Parallel Graph Library

    KAUST Repository

    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.

  6. Topic Model for Graph Mining.

    Science.gov (United States)

    Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng

    2015-12-01

    Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.

  7. Modern graph theory

    CERN Document Server

    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 ...

  8. A graph edit dictionary for correcting errors in roof topology graphs reconstructed from point clouds

    Science.gov (United States)

    Xiong, B.; Oude Elberink, S.; Vosselman, G.

    2014-07-01

    In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.

  9. GRAPH-BASED POST INCIDENT INTERNAL AUDIT METHOD OF COMPUTER EQUIPMENT

    Directory of Open Access Journals (Sweden)

    I. S. Pantiukhin

    2016-05-01

    Full Text Available Graph-based post incident internal audit method of computer equipment is proposed. The essence of the proposed solution consists in the establishing of relationships among hard disk damps (image, RAM and network. This method is intended for description of information security incident properties during the internal post incident audit of computer equipment. Hard disk damps receiving and formation process takes place at the first step. It is followed by separation of these damps into the set of components. The set of components includes a large set of attributes that forms the basis for the formation of the graph. Separated data is recorded into the non-relational database management system (NoSQL that is adapted for graph storage, fast access and processing. Damps linking application method is applied at the final step. The presented method gives the possibility to human expert in information security or computer forensics for more precise, informative internal audit of computer equipment. The proposed method allows reducing the time spent on internal audit of computer equipment, increasing accuracy and informativeness of such audit. The method has a development potential and can be applied along with the other components in the tasks of users’ identification and computer forensics.

  10. Introduction to quantum graphs

    CERN Document Server

    Berkolaiko, Gregory

    2012-01-01

    A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...

  11. SemaTyP: a knowledge graph based literature mining method for drug discovery.

    Science.gov (United States)

    Sang, Shengtian; Yang, Zhihao; Wang, Lei; Liu, Xiaoxia; Lin, Hongfei; Wang, Jian

    2018-05-30

    Drug discovery is the process through which potential new medicines are identified. High-throughput screening and computer-aided drug discovery/design are the two main drug discovery methods for now, which have successfully discovered a series of drugs. However, development of new drugs is still an extremely time-consuming and expensive process. Biomedical literature contains important clues for the identification of potential treatments. It could support experts in biomedicine on their way towards new discoveries. Here, we propose a biomedical knowledge graph-based drug discovery method called SemaTyP, which discovers candidate drugs for diseases by mining published biomedical literature. We first construct a biomedical knowledge graph with the relations extracted from biomedical abstracts, then a logistic regression model is trained by learning the semantic types of paths of known drug therapies' existing in the biomedical knowledge graph, finally the learned model is used to discover drug therapies for new diseases. The experimental results show that our method could not only effectively discover new drug therapies for new diseases, but also could provide the potential mechanism of action of the candidate drugs. In this paper we propose a novel knowledge graph based literature mining method for drug discovery. It could be a supplementary method for current drug discovery methods.

  12. Graph Generator Survey

    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.

  13. Functions and graphs

    CERN Document Server

    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

  14. Loose Graph Simulations

    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...

  15. Autoregressive Moving Average Graph Filtering

    OpenAIRE

    Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert

    2016-01-01

    One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...

  16. 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.

  17. Quantum walks on quotient graphs

    International Nuclear Information System (INIS)

    Krovi, Hari; Brun, Todd A.

    2007-01-01

    A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup

  18. HAIM OMLET: An Expert System For Research In Orthomodular Lattices And Related Structures

    Science.gov (United States)

    Dankel, D. D.; Rodriguez, R. V.; Anger, F. D.

    1986-03-01

    This paper describes research towards the construction of an expert system combining the brute force power of algorithmic computation and the inductive reasoning power of a rule-based inference engine in the mathematical area of discrete structures. Little research has been conducted on extending existing expert systems' technology to computationally complex areas. This research addresses the extension of expert systems into areas such as these, where the process of inference by itself will not produce the proper results. Additionally, the research will demonstrate the benefits of combining inference engines and mathematical algorithms to attack computationally complex problems. The specific aim is to produce an expert system which embodies expert level knowledge of orthomodular lattices, graphs, structure spaces, boolean algebras, incidence relations, and projective configurations. The resulting system, implemented on a micro-computer, will provide researchers a powerful and accessible tool for exploring these discrete structures. The system's "shell" will provide a structure for developing other expert systems with similar capabilities in such related areas as coding theory, categories, monoids, automata theory, and non-standard logics.

  19. Graph-based modelling in engineering

    CERN Document Server

    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. .

  20. BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

    Science.gov (United States)

    Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

    2013-02-01

    Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

  1. Expert systems to assist plant operation

    International Nuclear Information System (INIS)

    Matsumoto, Yoshihiro; Mori, Nobuyuki; Wada, Norio

    1985-01-01

    Large-scale real-time process control systems, such as those for electric power dispatching, large thermal and nuclear power stations, steel mill plants and manufacturing automation systems, need expert systems to assist operator's decision. The expert systems newly developed to fulfill the requirement are founded on OKBS (object oriented knowledge based system). OKBS provides various object types: fuzzy logic type, production rule type, frame type, state transition type, abstract data type and input/output transformation type. (author)

  2. Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

    Science.gov (United States)

    Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

    2017-01-01

    An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

  3. Equipackable graphs

    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 gr...

  4. Khovanov homology of graph-links

    Energy Technology Data Exchange (ETDEWEB)

    Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

    2012-08-31

    Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.

  5. Generalized connectivity of graphs

    CERN Document Server

    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.

  6. On two energy-like invariants of line graphs and related graph operations

    Directory of Open Access Journals (Sweden)

    Xiaodan Chen

    2016-02-01

    Full Text Available Abstract For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\\mu_{1}\\geq\\mu_{2}\\geq\\cdots\\geq\\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\\geq q_{2}\\geq\\cdots\\geq q_{n}\\geq0$ be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, LEL ( G = ∑ i = 1 n − 1 μ i and IE ( G = ∑ i = 1 n q i . $$\\mathit{LEL}(G=\\sum_{i=1}^{n-1}\\sqrt{ \\mu_{i}} \\quad\\mbox{and}\\quad \\mathit {IE}(G=\\sum_{i=1}^{n} \\sqrt{q_{i}}. $$ In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results. The main tools we use here are the Cauchy-Schwarz inequality and the Ozeki inequality.

  7. Local unitary versus local Clifford equivalence of stabilizer and graph states

    International Nuclear Information System (INIS)

    Zeng, Bei; Chung, Hyeyoun; Cross, Andrew W.; Chuang, Isaac L.

    2007-01-01

    The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU-equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [Phys. Rev. A 71, 062323 (2005)]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence (LU LC) to include all stabilizer states represented by graphs with cycles of length neither 3 nor 4. To compare our result with Van den Nest et al.'s, we show that any stabilizer state of distance δ=2 is beyond their criterion. We then further prove that LU LC holds for a more general class of stabilizer states of δ=2. We also explicitly construct graphs representing δ>2 stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with 2 m -1 (m≥4) vertices using quantum error-correcting codes which have non-Clifford transversal gates

  8. Price Competition on Graphs

    OpenAIRE

    Adriaan R. Soetevent

    2010-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...

  9. Price Competition on Graphs

    OpenAIRE

    Pim Heijnen; Adriaan Soetevent

    2014-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...

  10. Skew-adjacency matrices of graphs

    NARCIS (Netherlands)

    Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

    2012-01-01

    The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

  11. Graph theory

    CERN Document Server

    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...

  12. 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...

  13. Graph Sampling for Covariance Estimation

    KAUST Repository

    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.

  14. Price competition on graphs

    NARCIS (Netherlands)

    Soetevent, A.R.

    2010-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial

  15. Graphing the order of the sexes: constructing, recalling, interpreting, and putting the self in gender difference graphs.

    Science.gov (United States)

    Hegarty, Peter; Lemieux, Anthony F; McQueen, Grant

    2010-03-01

    Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit sexism at work. Yet, in 6 studies (N = 741), women and men constructed (Study 1) and recalled (Study 2) gender difference graphs with men's data first, and graphed powerful groups (Study 3) and individuals (Study 4) ahead of weaker ones. Participants who interpreted graph order as evidence of author "bias" inferred that the author graphed his or her own gender group first (Study 5). Women's, but not men's, preferences to graph men first were mitigated when participants graphed a difference between themselves and an opposite-sex friend prior to graphing gender differences (Study 6). Graph production and comprehension are affected by beliefs and suppositions about the groups represented in graphs to a greater degree than cognitive models of graph comprehension or realist models of scientific thinking have yet acknowledged.

  16. Collective Rationality in Graph Aggregation

    NARCIS (Netherlands)

    Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.

    2014-01-01

    Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the

  17. GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

    Energy Technology Data Exchange (ETDEWEB)

    Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor

    2014-08-25

    Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.

  18. Graph Theory. 1. Fragmentation of Structural Graphs

    Directory of Open Access Journals (Sweden)

    Lorentz JÄNTSCHI

    2002-12-01

    Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.

  19. Integrating atlas and graph cut methods for right ventricle blood-pool segmentation from cardiac cine MRI

    Science.gov (United States)

    Dangi, Shusil; Linte, Cristian A.

    2017-03-01

    Segmentation of right ventricle from cardiac MRI images can be used to build pre-operative anatomical heart models to precisely identify regions of interest during minimally invasive therapy. Furthermore, many functional parameters of right heart such as right ventricular volume, ejection fraction, myocardial mass and thickness can also be assessed from the segmented images. To obtain an accurate and computationally efficient segmentation of right ventricle from cardiac cine MRI, we propose a segmentation algorithm formulated as an energy minimization problem in a graph. Shape prior obtained by propagating label from an average atlas using affine registration is incorporated into the graph framework to overcome problems in ill-defined image regions. The optimal segmentation corresponding to the labeling with minimum energy configuration of the graph is obtained via graph-cuts and is iteratively refined to produce the final right ventricle blood pool segmentation. We quantitatively compare the segmentation results obtained from our algorithm to the provided gold-standard expert manual segmentation for 16 cine-MRI datasets available through the MICCAI 2012 Cardiac MR Right Ventricle Segmentation Challenge according to several similarity metrics, including Dice coefficient, Jaccard coefficient, Hausdorff distance, and Mean absolute distance error.

  20. Introductory graph theory

    CERN Document Server

    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

  1. Creating more effective graphs

    CERN Document Server

    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

  2. Graph Compression by BFS

    Directory of Open Access Journals (Sweden)

    Alberto Apostolico

    2009-08-01

    Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.

  3. Graphing Inequalities, Connecting Meaning

    Science.gov (United States)

    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…

  4. Fuzzy Graph Language Recognizability

    OpenAIRE

    Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros

    2012-01-01

    Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

  5. 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)

  6. Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs

    NARCIS (Netherlands)

    I.Z. Emiris; E.P. Tsigaridas; A. Varvitsiotis (Antonios); A. Mucherino (Antonio); C. Lavor; L. Liberti; N. Maculan

    2013-01-01

    htmlabstractA graph G is called generically minimally rigid in Rd if, for any choice of sufficiently generic edge lengths, it can be embedded in Rd in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining tight bounds on the number of such

  7. Quantitative graph theory mathematical foundations and applications

    CERN Document Server

    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

  8. 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....

  9. Spectral fluctuations of quantum graphs

    International Nuclear Information System (INIS)

    Pluhař, Z.; Weidenmüller, H. A.

    2014-01-01

    We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry

  10. Multiple graph regularized protein domain ranking.

    Science.gov (United States)

    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.

  11. 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...

  12. SIMULATION OF DRIVER’S LOCOMOTIVE-HANDLING ACTIVITY USING THE THEORY OF FUZZY GRAPHS

    Directory of Open Access Journals (Sweden)

    T. V. Butko

    2015-03-01

    Full Text Available Purpose. The efficiency and safety of locomotive control improving is important and relevant scientific and practical problem. Every driver during the trains-handling bases on his experience and knowledge, that is why the compilation and detection the most efficient ways to control the locomotive-handling is one of the stages of measures development to reduce transportation costs. The purpose of this paper is a formalization process description of locomotive-handling and quality parameters determination of this process. Methodology. In order to achieve this goal the theory of fuzzy probabilistic graphs was used. Vertices of the graph correspond to the events start and end operations at train-handling. The graph arcs describe operations on train-handling. Graph consists of thirteen peaks corresponding to the main control actions of the engine-driver. The weighting factors of transitions between vertices are assigned by fuzzy numbers. Their values were obtained by expert estimates. Fuzzy probabilities and transition time are presented as numbers with trapezoidal membership function. Findings. Using successive merging of parallel arcs, loops and vertices elimination, the equivalent fuzzy graph of train-handling and the corresponding L-matrix were obtained. Equivalent graph takes into account separately activity of the driver during normal operation and during emergency situations. Originality. The theoretical foundations of describing process formalization in driver’s locomotive-handling activity were developed using the fuzzy probabilistic graph. The parameters characterizing the decision-making process of engineer were obtained. Practical value. With the resulting model it is possible to estimate the available reserves for the quality improvement of locomotive-handling. Reduction in the time for decision-making will lead to the approximation the current mode of control to the rational one and decrease costs of hauling operations. And reduction

  13. ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS

    OpenAIRE

    Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache

    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.

  14. Practical graph mining with R

    CERN Document Server

    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...

  15. 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.

  16. Extremal graph theory

    CERN Document Server

    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

  17. Multiple graph regularized protein domain ranking

    KAUST Repository

    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.

  18. Multiple graph regularized protein domain ranking

    KAUST Repository

    Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

    2012-01-01

    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.

  19. 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.

  20. 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.

  1. Fast Discrete Fourier Transform Computations Using the Reduced Adder Graph Technique

    Directory of Open Access Journals (Sweden)

    Andrew G. Dempster

    2007-01-01

    Full Text Available It has recently been shown that the n-dimensional reduced adder graph (RAG-n technique is beneficial for many DSP applications such as for FIR and IIR filters, where multipliers can be grouped in multiplier blocks. This paper highlights the importance of DFT and FFT as DSP objects and also explores how the RAG-n technique can be applied to these algorithms. This RAG-n DFT will be shown to be of low complexity and possess an attractively regular VLSI data flow when implemented with the Rader DFT algorithm or the Bluestein chirp-z algorithm. ASIC synthesis data are provided and demonstrate the low complexity and high speed of the design when compared to other alternatives.

  2. Fast Discrete Fourier Transform Computations Using the Reduced Adder Graph Technique

    Directory of Open Access Journals (Sweden)

    Dempster Andrew G

    2007-01-01

    Full Text Available It has recently been shown that the -dimensional reduced adder graph (RAG- technique is beneficial for many DSP applications such as for FIR and IIR filters, where multipliers can be grouped in multiplier blocks. This paper highlights the importance of DFT and FFT as DSP objects and also explores how the RAG- technique can be applied to these algorithms. This RAG- DFT will be shown to be of low complexity and possess an attractively regular VLSI data flow when implemented with the Rader DFT algorithm or the Bluestein chirp- algorithm. ASIC synthesis data are provided and demonstrate the low complexity and high speed of the design when compared to other alternatives.

  3. idSpace D2.2 – Semantic meta-model, integration and transformations v1

    DEFF Research Database (Denmark)

    Dolog, Peter; Lin, Yujian; Dols, Roger

    2009-01-01

    This report introduces a topic maps based meta-model for creativity techniques, creativity process, and idea maps as results from creativity process. It proposes a graph based and hierarchical graph based transformation of idea maps for combination and integration of results of different creativi...

  4. 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.

  5. Graph Colouring Algorithms

    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...

  6. The fascinating world of graph theory

    CERN Document Server

    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

  7. Groupies in multitype random graphs

    OpenAIRE

    Shang, Yilun

    2016-01-01

    A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

  8. Canonic FFT flow graphs for real-valued even/odd symmetric inputs

    Science.gov (United States)

    Lao, Yingjie; Parhi, Keshab K.

    2017-12-01

    Canonic real-valued fast Fourier transform (RFFT) has been proposed to reduce the arithmetic complexity by eliminating redundancies. In a canonic N-point RFFT, the number of signal values at each stage is canonic with respect to the number of signal values, i.e., N. The major advantage of the canonic RFFTs is that these require the least number of butterfly operations and only real datapaths when mapped to architectures. In this paper, we consider the FFT computation whose inputs are not only real but also even/odd symmetric, which indeed lead to the well-known discrete cosine and sine transforms (DCTs and DSTs). Novel algorithms for generating the flow graphs of canonic RFFTs with even/odd symmetric inputs are proposed. It is shown that the proposed algorithms lead to canonic structures with N/2 +1 signal values at each stage for an N-point real even symmetric FFT (REFFT) or N/2 -1 signal values at each stage for an N-point RFFT real odd symmetric FFT (ROFFT). In order to remove butterfly operations, several twiddle factor transformations are proposed in this paper. We also discuss the design of canonic REFFT for any composite length. Performances of the canonic REFFT/ROFFT are also discussed. It is shown that the flow graph of canonic REFFT/ROFFT has less number of interconnections, less butterfly operations, and less twiddle factor operations, compared to prior works.

  9. 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.)

  10. 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.

  11. 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.

  12. Network reconstruction via graph blending

    Science.gov (United States)

    Estrada, Rolando

    2016-05-01

    Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.

  13. Interaction graphs

    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...

  14. Groupies in multitype random graphs.

    Science.gov (United States)

    Shang, Yilun

    2016-01-01

    A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

  15. AN EXPERIMENT WITH THE USE OF PREDICATE TRANSFORMERS IN UNITY

    NARCIS (Netherlands)

    DIJKSTRA, RM

    1995-01-01

    Recent work on UNITY is directed towards replacing the relations from UNITY logic by predicated transformers. In one of his Notes on UNITY. Jayadev Misra uses UNITY logic to prove a theorem about dynamic graphs. In this paper we use predicate transformers to prove the same theorem. We consider the

  16. An Efficient Downlink Scheduling Strategy Using Normal Graphs for Multiuser MIMO Wireless Systems

    Science.gov (United States)

    Chen, Jung-Chieh; Wu, Cheng-Hsuan; Lee, Yao-Nan; Wen, Chao-Kai

    Inspired by the success of the low-density parity-check (LDPC) codes in the field of error-control coding, in this paper we propose transforming the downlink multiuser multiple-input multiple-output scheduling problem into an LDPC-like problem using the normal graph. Based on the normal graph framework, soft information, which indicates the probability that each user will be scheduled to transmit packets at the access point through a specified angle-frequency sub-channel, is exchanged among the local processors to iteratively optimize the multiuser transmission schedule. Computer simulations show that the proposed algorithm can efficiently schedule simultaneous multiuser transmission which then increases the overall channel utilization and reduces the average packet delay.

  17. Graph mining for next generation sequencing: leveraging the assembly graph for biological insights.

    Science.gov (United States)

    Warnke-Sommer, Julia; Ali, Hesham

    2016-05-06

    The assembly of Next Generation Sequencing (NGS) reads remains a challenging task. This is especially true for the assembly of metagenomics data that originate from environmental samples potentially containing hundreds to thousands of unique species. The principle objective of current assembly tools is to assemble NGS reads into contiguous stretches of sequence called contigs while maximizing for both accuracy and contig length. The end goal of this process is to produce longer contigs with the major focus being on assembly only. Sequence read assembly is an aggregative process, during which read overlap relationship information is lost as reads are merged into longer sequences or contigs. The assembly graph is information rich and capable of capturing the genomic architecture of an input read data set. We have developed a novel hybrid graph in which nodes represent sequence regions at different levels of granularity. This model, utilized in the assembly and analysis pipeline Focus, presents a concise yet feature rich view of a given input data set, allowing for the extraction of biologically relevant graph structures for graph mining purposes. Focus was used to create hybrid graphs to model metagenomics data sets obtained from the gut microbiomes of five individuals with Crohn's disease and eight healthy individuals. Repetitive and mobile genetic elements are found to be associated with hybrid graph structure. Using graph mining techniques, a comparative study of the Crohn's disease and healthy data sets was conducted with focus on antibiotics resistance genes associated with transposase genes. Results demonstrated significant differences in the phylogenetic distribution of categories of antibiotics resistance genes in the healthy and diseased patients. Focus was also evaluated as a pure assembly tool and produced excellent results when compared against the Meta-velvet, Omega, and UD-IDBA assemblers. Mining the hybrid graph can reveal biological phenomena captured

  18. Distance-transitive graphs

    NARCIS (Netherlands)

    Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.

    2004-01-01

    In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite

  19. 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.

  20. The complexity of the matching-cut problem for planar graphs and other graph classes

    NARCIS (Netherlands)

    Bonsma, P.S.

    2009-01-01

    The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it

  1. 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.

  2. Integer Flows and Circuit Covers of Graphs and Signed Graphs

    Science.gov (United States)

    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

  3. Port-Hamiltonian Systems on Open Graphs

    NARCIS (Netherlands)

    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

  4. Towards a theory of geometric graphs

    CERN Document Server

    Pach, Janos

    2004-01-01

    The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

  5. Quantum walk on a chimera graph

    Science.gov (United States)

    Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.

    2018-05-01

    We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

  6. 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.

  7. What Would a Graph Look Like in this Layout? A Machine Learning Approach to Large Graph Visualization.

    Science.gov (United States)

    Kwon, Oh-Hyun; Crnovrsanin, Tarik; Ma, Kwan-Liu

    2018-01-01

    Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to selecting a good layout is to use aesthetic criteria and visual inspection. However, fully calculating various layouts and their associated aesthetic metrics is computationally expensive. In this paper, we present a machine learning approach to large graph visualization based on computing the topological similarity of graphs using graph kernels. For a given graph, our approach can show what the graph would look like in different layouts and estimate their corresponding aesthetic metrics. An important contribution of our work is the development of a new framework to design graph kernels. Our experimental study shows that our estimation calculation is considerably faster than computing the actual layouts and their aesthetic metrics. Also, our graph kernels outperform the state-of-the-art ones in both time and accuracy. In addition, we conducted a user study to demonstrate that the topological similarity computed with our graph kernel matches perceptual similarity assessed by human users.

  8. Text-Filled Stacked Area Graphs

    DEFF Research Database (Denmark)

    Kraus, Martin

    2011-01-01

    -filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....

  9. 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 t......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...

  10. On dominator colorings in graphs

    Indian Academy of Sciences (India)

    colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.

  11. Graphs with branchwidth at most three

    NARCIS (Netherlands)

    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

  12. Planar graphs theory and algorithms

    CERN Document Server

    Nishizeki, T

    1988-01-01

    Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

  13. 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.

  14. CORECLUSTER: A Degeneracy Based Graph Clustering Framework

    OpenAIRE

    Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis

    2014-01-01

    International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...

  15. Coloring sums of extensions of certain graphs

    Directory of Open Access Journals (Sweden)

    Johan Kok

    2017-12-01

    Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.

  16. On a conjecture concerning helly circle graphs

    Directory of Open Access Journals (Sweden)

    Durán Guillermo

    2003-01-01

    Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.

  17. How patent experts create patent breadth

    DEFF Research Database (Denmark)

    Beukel, Karin

    2014-01-01

    Science as an input to patented inventions is a fundamental of economic growth. However, our understanding of how science is transformed into patents is limited. In the present paper I seek to fill this gap by examining the micro-foundations of science-patent transformations. Using an inductive......, grounded theory approach to study the transformation of 12 scientific discoveries into patents I recast the relationship between science and patents: I show it as a particular process that affects patent breadth. Exploiting surplus patent breadth depends on the processes of abstraction and cognitive...... variety, which can be mobilized by patenting experts. The theory is tested using a recently published algebraic interpretive method for examining causal relationships in small-N studies....

  18. How patent experts create patent breadth

    DEFF Research Database (Denmark)

    Beukel, Karin

    2018-01-01

    Science as an input to patented inventions is a fundamental of economic growth. However, our understanding of how science is transformed into patents is limited. In the present paper I seek to fill this gap by examining the micro-foundations of science-patent transformations. Using an inductive......, grounded theory approach to study the transformation of 12 scientific discoveries into patents I recast the relationship between science and patents: I show it as a particular process that affects patent breadth. Exploiting surplus patent breadth depends on the processes of abstraction and cognitive...... variety, which can be mobilized by patenting experts. The theory is tested using a recently published algebraic interpretive method for examining causal relationships in small-N studies....

  19. Optimization Problems on Threshold Graphs

    Directory of Open Access Journals (Sweden)

    Elena Nechita

    2010-06-01

    Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.

  20. 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.

  1. Hierarchy of modular graph identities

    International Nuclear Information System (INIS)

    D’Hoker, Eric; Kaidi, Justin

    2016-01-01

    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.

  2. 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 perf...

  3. 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.

  4. REXS : A financial risk diagnostic expert system

    Directory of Open Access Journals (Sweden)

    W. Richter

    2012-01-01

    Full Text Available

    ENGLISH ABSTRACT: Artificial intelligence techniques are rapidly emerging as important contributors to more effective management. One of the greatest growth areas probably lies in the use of Expert System methodology for supporting managerial decision processes.
    Existing Decision Support Systems often attempt to apply analytical techniques in combination with traditional data access and retrieval functions. One of the problems usually encountered while developing such decision support systems is the need to transform an unstructured problem environment into a structured analytical model. Using an expert system approach to strategic decision making in such unstructured problem environments may provide significant advantages.
    The financial Risk diagnostic EXpert System (REXS concentrates on Financial Risk Analysis. Based on a Forecasting Model the system will, with the support of several expert system knowledge bases, attempt to evaluate the financial risk of a business and provide guidelines for improvement.

    AFRIKAANSE OPSOMMING: Tegnieke gebaseer op Kunsmatige Intelligensie toon tans die belofte om belangrike bydraes te maak tot meerBestaande Besluitsteunstelsels poog dikwels om analitiese tegnieke en lradisionele datatoegang- en onttrekkingsfunksies te kombineer. Een van die probleme wat gewoonlik ondervind word gedurende die ontwikkeling van '0 besluitsteunstelsel bestaan uit die behoefte om 'n ongestruktueerde probleemomgewing te transformeer na 'n gestruktueerde analitiese model. 'n Ekspertstelselbenadering lot strategiese besluitneming in 'n ongeSlruktureerde probleemomgewing mag betekenisvolle voordele inhou.
    Die "financial Risk diagnostic EXpert System (REXS" konsentreer op fmansiele risiko-analise. Uitgaande vanaf 'n Vooruitskattingsmode~ en deur gebruik te maak van verskeie ekspertstelselkennisbasisse, poog die stelsel om die fmansiele risiko van 'n onderneming te evalueer en riglyne vir moontlike verbetering

  5. Rapid Separation of Disconnected Triangle Meshes Based on Graph Traversal

    International Nuclear Information System (INIS)

    Ji, S J; Wang, Y

    2006-01-01

    In recent year, The STL file become a de facto standard on the file presentation in CAD/CAM, computer graph and reverse engineering. When point cloud which is obtained by scanning object body using optical instrument is used to reconstruct an original model, the points cloud is presented by the STL file. Usually, datum of several separated and relative objects are stored in a single STL file, when such a file is operated by a computer, the datum in the file is firstly separated and then each element of every triangle pitch on the triangle mesh is traversed and visited and is calculated. The problem is analyzed and studied by many experts, but there is still a lack of a simple and quick algorithm. An algorithm which uses graph traversal to traverse each element of the triangle meshes and separate several disconnected triangle meshes is presented by the paper, the searching and calculating speed of the data on the triangle meshes is enhanced, memory size of the computer is reduced, complexity of the data structure is simplified and powerful guarantee is made for the next process by using this algorithm

  6. 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.

  7. On 4-critical t-perfect graphs

    OpenAIRE

    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...

  8. Local adjacency metric dimension of sun graph and stacked book graph

    Science.gov (United States)

    Yulisda Badri, Alifiah; Darmaji

    2018-03-01

    A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.

  9. Mechatronic modeling and simulation using bond graphs

    CERN Document Server

    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 ...

  10. Path Index Based Keywords to SPARQL Query Transformation for Semantic Data Federations

    Directory of Open Access Journals (Sweden)

    Thilini Cooray

    2016-06-01

    Full Text Available Semantic web is a highly emerging research domain. Enhancing the ability of keyword query processing on Semantic Web data provides a huge support for familiarizing the usefulness of Semantic Web to the general public. Most of the existing approaches focus on just user keyword matching to RDF graphs and output the connecting elements as results. Semantic Web consists of SPARQL query language which can process queries more accurately and efficiently than general keyword matching. There are only about a couple of approaches available for transforming keyword queries to SPARQL. They basically rely on real time graph traversals? for identifying subgraphs which can connect user keywords. Those approaches are either limited to query processing on a single data store or a set of interlinked data sets. They have not focused on query processing on a federation of independent data sets which belongs to the same domain. This research proposes a Path Index based approach eliminating real time graph traversal for transforming keyword queries to SPARQL. We have introduced an ontology alignment based approach for keyword query transforming on a federation of RDF data stored using multiple heterogeneous vocabularies. Evaluation shows that the proposed approach have the ability to generate SPARQL queries which can provide highly relevant results for user keyword queries. The Path Index based query transformation approach has also achieved high efficiency compared to the existing approach.

  11. DIMENSI METRIK GRAPH LOBSTER Ln (q;r

    Directory of Open Access Journals (Sweden)

    PANDE GDE DONY GUMILAR

    2013-05-01

    Full Text Available The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph Ln (q;r. Lobster graph Ln (q;r is a regular lobster graph with vertices backbone on the main path, every backbone vertex is connected to q hand vertices and every hand vertex is connected to r finger vertices, with n, q, r element of N. We obtain the metric dimension of lobster graph L2 (1;1 is 1, the metric dimension of lobster graph L2 (1;1 for n > 2 is 2.

  12. Summary: beyond fault trees to fault graphs

    International Nuclear Information System (INIS)

    Alesso, H.P.; Prassinos, P.; Smith, C.F.

    1984-09-01

    Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability

  13. FPFH-based graph matching for 3D point cloud registration

    Science.gov (United States)

    Zhao, Jiapeng; Li, Chen; Tian, Lihua; Zhu, Jihua

    2018-04-01

    Correspondence detection is a vital step in point cloud registration and it can help getting a reliable initial alignment. In this paper, we put forward an advanced point feature-based graph matching algorithm to solve the initial alignment problem of rigid 3D point cloud registration with partial overlap. Specifically, Fast Point Feature Histograms are used to determine the initial possible correspondences firstly. Next, a new objective function is provided to make the graph matching more suitable for partially overlapping point cloud. The objective function is optimized by the simulated annealing algorithm for final group of correct correspondences. Finally, we present a novel set partitioning method which can transform the NP-hard optimization problem into a O(n3)-solvable one. Experiments on the Stanford and UWA public data sets indicates that our method can obtain better result in terms of both accuracy and time cost compared with other point cloud registration methods.

  14. 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.

  15. Eulerian Graphs and Related Topics

    CERN Document Server

    Fleischner, Herbert

    1990-01-01

    The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a

  16. Dependency Parsing with Transformed Feature

    Directory of Open Access Journals (Sweden)

    Fuxiang Wu

    2017-01-01

    Full Text Available Dependency parsing is an important subtask of natural language processing. In this paper, we propose an embedding feature transforming method for graph-based parsing, transform-based parsing, which directly utilizes the inner similarity of the features to extract information from all feature strings including the un-indexed strings and alleviate the feature sparse problem. The model transforms the extracted features to transformed features via applying a feature weight matrix, which consists of similarities between the feature strings. Since the matrix is usually rank-deficient because of similar feature strings, it would influence the strength of constraints. However, it is proven that the duplicate transformed features do not degrade the optimization algorithm: the margin infused relaxed algorithm. Moreover, this problem can be alleviated by reducing the number of the nearest transformed features of a feature. In addition, to further improve the parsing accuracy, a fusion parser is introduced to integrate transformed and original features. Our experiments verify that both transform-based and fusion parser improve the parsing accuracy compared to the corresponding feature-based parser.

  17. The One Universal Graph — a free and open graph database

    Science.gov (United States)

    Ng, Liang S.; Champion, Corbin

    2016-02-01

    Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks.

  18. Degree-based graph construction

    International Nuclear Information System (INIS)

    Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A

    2009-01-01

    Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)

  19. Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the Gyroid wire network

    Energy Technology Data Exchange (ETDEWEB)

    Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit

    2012-08-15

    Motivated by Harper Hamiltonians on skeletal graphs and their C{sup *}-geometry, we study a certain class of graph Hamiltonians. These Hamiltonians can be thought of as a finite groupoid representation in separable Hilbert spaces. Here the groupoid is the path groupoid of a finite graph. Given such a setup, we consider the possible matrix versions of the Hamiltonian, which are indexed by the choice of a rooted spanning tree and an order of the vertices. The first result is that all the matrix representations are linked to each other via the conjugation action of a re-gauging groupoid. We furthermore show that the symmetries of the underlying graph give rise to an action on the Hamiltonians of a group of extended symmetries. The new concept for the extension is to allow phase transformations on the vertices. In the commutative case, we prove that the extended symmetries act via a projective representation giving rise to isotypical decompositions and super-selection rules. We then apply these results to the PDG and honeycomb graphs using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the Gyroid and the honeycomb.

  20. Downhill Domination in Graphs

    Directory of Open Access Journals (Sweden)

    Haynes Teresa W.

    2014-08-01

    Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds

  1. Subsampling for graph power spectrum estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2016-01-01

    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.

  2. Proving relations between modular graph functions

    International Nuclear Information System (INIS)

    Basu, Anirban

    2016-01-01

    We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links. (paper)

  3. Subsampling for graph power spectrum estimation

    KAUST Repository

    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.

  4. Semantic graphs and associative memories

    Science.gov (United States)

    Pomi, Andrés; Mizraji, Eduardo

    2004-12-01

    Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

  5. RNA graph partitioning for the discovery of RNA modularity: a novel application of graph partition algorithm to biology.

    Directory of Open Access Journals (Sweden)

    Namhee Kim

    Full Text Available Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2 corresponding to the second eigenvalues (λ2 associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides. While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs

  6. A generalization of total graphs

    Indian Academy of Sciences (India)

    M Afkhami

    2018-04-12

    Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.

  7. 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....

  8. Commuting graphs of matrix algebras

    International Nuclear Information System (INIS)

    Akbari, S.; Bidkhori, H.; Mohammadian, A.

    2006-08-01

    The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)

  9. Data transformations in custom digital workflows : Property graphs as a data model for user-defined mappings

    NARCIS (Netherlands)

    Janssen, P.; Stouffs, R.M.F.; Chaszar, A.T.; Boeykens, S.; Toth, B.

    2012-01-01

    This paper describes the use of property graphs for mapping data between AEC software tools, which are not linked by common data formats and/or other interoperability measures. The intention of introducing this in practice, education and research is to facilitate the use of diverse, non-integrated

  10. Graph-theoretical concepts and physicochemical data

    Directory of Open Access Journals (Sweden)

    Lionello Pogliani

    2003-02-01

    Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.

  11. Graphs whose complement and square are isomorphic

    DEFF Research Database (Denmark)

    Pedersen, Anders Sune

    2014-01-01

    We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...

  12. Graphs & digraphs

    CERN Document Server

    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...

  13. 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

  14. Continuous-time quantum walks on star graphs

    International Nuclear Information System (INIS)

    Salimi, S.

    2009-01-01

    In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K 2 graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

  15. 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.

  16. Telecontrol - Expert systems. Real-time monitoring and remote diagnostic

    Energy Technology Data Exchange (ETDEWEB)

    Lam, A.

    1996-09-01

    The role of expert systems in programming simple and complex tasks in utilities companies was discussed with examples from B.C. Hydro, where expert systems have been used in such diverse applications as an in-house programmable logic controller (PLC) training course, and a machine audit on a 150 MW steam turbine generating unit at their Burrard Thermal Generating Plant. The PLC tutoring program uses expert system technology for the air blast circuit breakers` air drier system, for individualized on-site training. The steam turbine audits (an eight-month long project) were performed remotely by dialing an on-site computer configured with customized expert software. Details of these, and other potential applications, such as transformer monitoring and diagnostics, circuit breaker performance analysis, and information management, were described.

  17. The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs

    Directory of Open Access Journals (Sweden)

    Unil Yun

    2016-05-01

    Full Text Available Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.

  18. Relating zeta functions of discrete and quantum graphs

    Science.gov (United States)

    Harrison, Jonathan; Weyand, Tracy

    2018-02-01

    We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

  19. A comparison between fault tree analysis and reliability graph with general gates

    International Nuclear Information System (INIS)

    Kim, Man Cheol; Seong, Poong Hyun; Jung, Woo Sik

    2004-01-01

    Currently, level-1 probabilistic safety assessment (PSA) is performed on the basis of event tree analysis and fault tree analysis. Kim and Seong developed a new method for system reliability analysis named reliability graph with general gates (RGGG). The RGGG is an extension of conventional reliability graph, and it utilizes the transformation of system structures to equivalent Bayesian networks for quantitative calculation. The RGGG is considered to be intuitive and easy-to-use while as powerful as fault tree analysis. As an example, Kim and Seong already showed that the Bayesian network model for digital plant protection system (DPPS), which is transformed from the RGGG model for DPPS, can be shown in 1 page, while the fault tree model for DPPS consists of 64 pages of fault trees. Kim and Seong also insisted that Bayesian network model for DPPS is more intuitive because the one-to-one matching between each node in the Bayesian network model and an actual component of DPPS is possible. In this paper, we are going to give a comparison between fault tree analysis and the RGGG method with two example systems. The two example systems are the recirculation of in Korean standard nuclear power plants (KSNP) and the fault tree model developed by Rauzy

  20. The One Universal Graph — a free and open graph database

    International Nuclear Information System (INIS)

    Ng, Liang S.; Champion, Corbin

    2016-01-01

    Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks. (paper)

  1. Recognition of fractal graphs

    NARCIS (Netherlands)

    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

  2. Interactive Graph Layout of a Million Nodes

    OpenAIRE

    Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North

    2016-01-01

    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 to...

  3. RATGRAPH: Computer Graphing of Rational Functions.

    Science.gov (United States)

    Minch, Bradley A.

    1987-01-01

    Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

  4. 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.

  5. 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.

  6. Deep Learning with Dynamic Computation Graphs

    OpenAIRE

    Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter

    2017-01-01

    Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...

  7. Constructs for Programming with Graph Rewrites

    OpenAIRE

    Rodgers, Peter

    2000-01-01

    Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...

  8. Quantum chaos on discrete graphs

    International Nuclear Information System (INIS)

    Smilansky, Uzy

    2007-01-01

    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 ζ 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 ζ 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)

  9. RJSplot: Interactive Graphs with R.

    Science.gov (United States)

    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.

  10. Bipartite separability and nonlocal quantum operations on graphs

    Science.gov (United States)

    Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.

    2016-07-01

    In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

  11. Algorithms and Data Structures for Graphs

    DEFF Research Database (Denmark)

    Rotenberg, Eva

    are planar graphs, which are those that can be drawn on a piece of paper without any pair of edges crossing. For planar graphs where each edge can only be traversed in one direction, a fundamental question is whether there is a route from vertex A to vertex B in the graph. We show how such a graph can...... of the form: "Is there an edge such that all paths between A and B go via that edge?" and which can quickly be updated when edges are inserted or deleted. We further show how to represent a planar graph such that we can quickly update our representation when an edge is deleted, and such that questions...

  12. On the nullity number of graphs

    Directory of Open Access Journals (Sweden)

    Mustapha Aouchiche

    2017-10-01

    Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.

  13. Graph processing platforms at scale: practices and experiences

    Energy Technology Data Exchange (ETDEWEB)

    Lim, Seung-Hwan [ORNL; Lee, Sangkeun (Matt) [ORNL; Brown, Tyler C [ORNL; Sukumar, Sreenivas R [ORNL; Ganesh, Gautam [ORNL

    2015-01-01

    Graph analysis unveils hidden associations of data in many phenomena and artifacts, such as road network, social networks, genomic information, and scientific collaboration. Unfortunately, a wide diversity in the characteristics of graphs and graph operations make it challenging to find a right combination of tools and implementation of algorithms to discover desired knowledge from the target data set. This study presents an extensive empirical study of three representative graph processing platforms: Pegasus, GraphX, and Urika. Each system represents a combination of options in data model, processing paradigm, and infrastructure. We benchmarked each platform using three popular graph operations, degree distribution, connected components, and PageRank over a variety of real-world graphs. Our experiments show that each graph processing platform shows different strength, depending the type of graph operations. While Urika performs the best in non-iterative operations like degree distribution, GraphX outputforms iterative operations like connected components and PageRank. In addition, we discuss challenges to optimize the performance of each platform over large scale real world graphs.

  14. Generalized hypercube graph $\\Q_n(S$, graph products and self-orthogonal codes

    Directory of Open Access Journals (Sweden)

    Pani Seneviratne

    2016-01-01

    Full Text Available A generalized hypercube graph $\\Q_n(S$ has $\\F_{2}^{n}=\\{0,1\\}^n$ as the vertex set and two vertices being adjacent whenever their mutual Hamming distance belongs to $S$, where $n \\ge 1$ and $S\\subseteq \\{1,2,\\ldots, n\\}$. The graph $\\Q_n(\\{1\\}$ is the $n$-cube, usually denoted by $\\Q_n$.We study graph boolean products $G_1 = \\Q_n(S\\times \\Q_1, G_2 = \\Q_{n}(S\\wedge \\Q_1$, $G_3 = \\Q_{n}(S[\\Q_1]$ and show that binary codes from neighborhood designs of $G_1, G_2$ and $G_3$ are self-orthogonal for all choices of $n$ and $S$. More over, we show that the class of codes $C_1$ are self-dual. Further we find subgroups of the automorphism group of these graphs and use these subgroups to obtain PD-sets for permutation decoding. As an example we find a full error-correcting PD set for the binary $[32, 16, 8]$ extremal self-dual code.

  15. 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.

  16. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    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…

  17. 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.

  18. On some labelings of triangular snake and central graph of triangular snake graph

    Science.gov (United States)

    Agasthi, P.; Parvathi, N.

    2018-04-01

    A Triangular snake Tn is obtained from a path u 1 u 2 … u n by joining ui and u i+1 to a new vertex wi for 1≤i≤n‑1. A Central graph of Triangular snake C(T n ) is obtained by subdividing each edge of Tn exactly once and joining all the non adjacent vertices of Tn . In this paper the ways to construct square sum, square difference, Root Mean square, strongly Multiplicative, Even Mean and Odd Mean labeling for Triangular Snake and Central graph of Triangular Snake graphs are reported.

  19. A signal-flow-graph approach to on-line gradient calculation.

    Science.gov (United States)

    Campolucci, P; Uncini, A; Piazza, F

    2000-08-01

    A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple one-input, one-output transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both on-line and batch-backward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and time-variant, dynamic system represented by an SFG, in particular any feedforward, time-delay, or recurrent neural network. In this work, we use discrete-time notation, but the same theory holds for the continuous-time case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both off-line and on-line. On-line learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion.

  20. Orientations of infinite graphs with prescribed edge-connectivity

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2016-01-01

    We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex...... set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989....

  1. Genus Ranges of 4-Regular Rigid Vertex Graphs.

    Science.gov (United States)

    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.

  2. A new cluster algorithm for graphs

    NARCIS (Netherlands)

    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

  3. Large-Scale Graph Processing Using Apache Giraph

    KAUST Repository

    Sakr, Sherif

    2017-01-07

    This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

  4. Large-Scale Graph Processing Using Apache Giraph

    KAUST Repository

    Sakr, Sherif; Orakzai, Faisal Moeen; Abdelaziz, Ibrahim; Khayyat, Zuhair

    2017-01-01

    This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

  5. Graph Algorithm Animation with Grrr

    OpenAIRE

    Rodgers, Peter; Vidal, Natalia

    2000-01-01

    We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...

  6. My Bar Graph Tells a Story

    Science.gov (United States)

    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…

  7. 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....

  8. Trajectories entropy in dynamical graphs with memory

    Directory of Open Access Journals (Sweden)

    Francesco eCaravelli

    2016-04-01

    Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

  9. On revealing graph cycles via boundary measurements

    International Nuclear Information System (INIS)

    Belishev, M I; Wada, N

    2009-01-01

    This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)

  10. 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).

  11. Pixels to Graphs by Associative Embedding

    KAUST Repository

    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.

  12. A faithful functor among algebras and graphs

    OpenAIRE

    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.

  13. Application of analytic hierarchy process to extract the user's purpose of expert systems

    International Nuclear Information System (INIS)

    Gofuku, Akio; Wakabayashi, Jiro; Morimoto, Takashi.

    1992-01-01

    This paper deals with an application of analytic hierarchy process (AHP) to extract the user's purpose which must be input to expert systems. In the AHP, the process to obtain the weights for criteria by pairwise comparisons is interpreted as the extraction of the decision marker's idea about the importance of each criterion. With this interpretation, the analytic hierarchy process is applied to extract the analyst's idea of the weights of several factors to select constitutive equations suitable for a target analysis in a model selection support expert system under development for numerical simulation of nuclear thermal-hydraulics; the constitutive equations are ordinary introduced in a liquid-vapor two-phase flow analysis. Furthermore, an algorithm by applying the graph theory is shown to evaluate covering condition to obtain the weights from incomplete pairwise comparisons. (author)

  14. Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

    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.

  15. The color space of a graph

    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....

  16. Box graphs and resolutions I

    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.

  17. A Novel Strategy Using Factor Graphs and the Sum-Product Algorithm for Satellite Broadcast Scheduling Problems

    Science.gov (United States)

    Chen, Jung-Chieh

    This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.

  18. Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

    Directory of Open Access Journals (Sweden)

    Borowiecka-Olszewska Marta

    2017-05-01

    Full Text Available A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.

  19. 47 CFR 80.761 - Conversion graphs.

    Science.gov (United States)

    2010-10-01

    ... 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... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761...

  20. Building Scalable Knowledge Graphs for Earth Science

    Science.gov (United States)

    Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian

    2017-01-01

    Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.

  1. On the diameter of dot-critical graphs

    Directory of Open Access Journals (Sweden)

    Doost Ali Mojdeh

    2009-01-01

    Full Text Available A graph G is \\(k\\-dot-critical (totaly \\(k\\-dot-critical if \\(G\\ is dot-critical (totaly dot-critical and the domination number is \\(k\\. In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306 (2006, 11-18] the following question is posed: What are the best bounds for the diameter of a \\(k\\-dot-critical graph and a totally \\(k\\-dot-critical graph \\(G\\ with no critical vertices for \\(k \\geq 4\\? We find the best bound for the diameter of a \\(k\\-dot-critical graph, where \\(k \\in\\{4,5,6\\}\\ and we give a family of \\(k\\-dot-critical graphs (with no critical vertices with sharp diameter \\(2k-3\\ for even \\(k \\geq 4\\.

  2. graphkernels: R and Python packages for graph comparison.

    Science.gov (United States)

    Sugiyama, Mahito; Ghisu, M Elisabetta; Llinares-López, Felipe; Borgwardt, Karsten

    2018-02-01

    Measuring the similarity of graphs is a fundamental step in the analysis of graph-structured data, which is omnipresent in computational biology. Graph kernels have been proposed as a powerful and efficient approach to this problem of graph comparison. Here we provide graphkernels, the first R and Python graph kernel libraries including baseline kernels such as label histogram based kernels, classic graph kernels such as random walk based kernels, and the state-of-the-art Weisfeiler-Lehman graph kernel. The core of all graph kernels is implemented in C ++ for efficiency. Using the kernel matrices computed by the package, we can easily perform tasks such as classification, regression and clustering on graph-structured samples. The R and Python packages including source code are available at https://CRAN.R-project.org/package=graphkernels and https://pypi.python.org/pypi/graphkernels. mahito@nii.ac.jp or elisabetta.ghisu@bsse.ethz.ch. Supplementary data are available online at Bioinformatics. © The Author(s) 2017. Published by Oxford University Press.

  3. 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.

  4. Processing Expert Judgements in Accident Consequence Modelling (invited paper)

    International Nuclear Information System (INIS)

    Kraan, B.C.P.; Cooke, R.M.

    2000-01-01

    In performing uncertainty analysis a distribution on the code input parameters is required. The construction of the distribution on the code input parameters for the joint CEC/USNRC Accident Consequence Code Uncertainty Analysis using Expert Judgement is discussed. An example from the food chain module is used to illustrate the construction. Different mathematical techniques have been developed to transform the expert judgements into the required format. Finally, the effect of taking account of correlations in performing uncertainty analysis is investigated. (author)

  5. Graphs, groups and surfaces

    CERN Document Server

    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''''.

  6. Subdominant pseudoultrametric on graphs

    Energy Technology Data Exchange (ETDEWEB)

    Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

    2013-08-31

    Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.

  7. Equitable Colorings Of Corona Multiproducts Of Graphs

    Directory of Open Access Journals (Sweden)

    Furmánczyk Hanna

    2017-11-01

    Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].

  8. Sphere and dot product representations of graphs

    NARCIS (Netherlands)

    R.J. Kang (Ross); T. Müller (Tobias)

    2012-01-01

    textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such

  9. Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures

    Science.gov (United States)

    Xie, Wen-Jie; Han, Rui-Qi; Jiang, Zhi-Qiang; Wei, Lijian; Zhou, Wei-Xing

    2017-08-01

    Complex network is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. The algorithm of horizontal visibility graph (HVG) maps time series into graphs, whose degree distributions are numerically and analytically investigated for certain time series. We derive the degree distributions of HVGs through an iterative construction process of HVGs. The degree distributions of the HVG and the directed HVG for random series are derived to be exponential, which confirms the analytical results from other methods. We also obtained the analytical expressions of degree distributions of HVGs and in-degree and out-degree distributions of directed HVGs transformed from multifractal binomial measures, which agree excellently with numerical simulations.

  10. Graph Query Portal

    OpenAIRE

    Dayal, Amit; Brock, David

    2018-01-01

    Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...

  11. An Association-Oriented Partitioning Approach for Streaming Graph Query

    Directory of Open Access Journals (Sweden)

    Yun Hao

    2017-01-01

    Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.

  12. Multiresolution analysis over graphs for a motor imagery based online BCI game.

    Science.gov (United States)

    Asensio-Cubero, Javier; Gan, John Q; Palaniappan, Ramaswamy

    2016-01-01

    Multiresolution analysis (MRA) over graph representation of EEG data has proved to be a promising method for offline brain-computer interfacing (BCI) data analysis. For the first time we aim to prove the feasibility of the graph lifting transform in an online BCI system. Instead of developing a pointer device or a wheel-chair controller as test bed for human-machine interaction, we have designed and developed an engaging game which can be controlled by means of imaginary limb movements. Some modifications to the existing MRA analysis over graphs for BCI have also been proposed, such as the use of common spatial patterns for feature extraction at the different levels of decomposition, and sequential floating forward search as a best basis selection technique. In the online game experiment we obtained for three classes an average classification rate of 63.0% for fourteen naive subjects. The application of a best basis selection method helps significantly decrease the computing resources needed. The present study allows us to further understand and assess the benefits of the use of tailored wavelet analysis for processing motor imagery data and contributes to the further development of BCI for gaming purposes. Copyright © 2015 Elsevier Ltd. All rights reserved.

  13. A comparative study of applying Mason’s Rule in the case of flow-graphs and bond-graphs

    Directory of Open Access Journals (Sweden)

    Adriana Grava

    2009-05-01

    Full Text Available The paper presents two methods to analyzethe electric circuits using the flow-graphs and thebond-graphs studying the differences between thesemethods.As it can be noticed, the two methods are totallydifferent; their common point being Mason’s rule thatis applied in both cases but it is applied differently foreach type of graphs.

  14. An algebraic approach to graph codes

    DEFF Research Database (Denmark)

    Pinero, Fernando

    This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... 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...

  15. Replica methods for loopy sparse random graphs

    International Nuclear Information System (INIS)

    Coolen, ACC

    2016-01-01

    I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)

  16. The STAPL Parallel Graph Library

    KAUST Repository

    Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence

    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

  17. Coloring and The Lonely Graph

    OpenAIRE

    Rabern, Landon

    2007-01-01

    We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...

  18. 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.

  19. A model of language inflection graphs

    Science.gov (United States)

    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.

  20. Poor textural image tie point matching via graph theory

    Science.gov (United States)

    Yuan, Xiuxiao; Chen, Shiyu; Yuan, Wei; Cai, Yang

    2017-07-01

    Feature matching aims to find corresponding points to serve as tie points between images. Robust matching is still a challenging task when input images are characterized by low contrast or contain repetitive patterns, occlusions, or homogeneous textures. In this paper, a novel feature matching algorithm based on graph theory is proposed. This algorithm integrates both geometric and radiometric constraints into an edge-weighted (EW) affinity tensor. Tie points are then obtained by high-order graph matching. Four pairs of poor textural images covering forests, deserts, bare lands, and urban areas are tested. For comparison, three state-of-the-art matching techniques, namely, scale-invariant feature transform (SIFT), speeded up robust features (SURF), and features from accelerated segment test (FAST), are also used. The experimental results show that the matching recall obtained by SIFT, SURF, and FAST varies from 0 to 35% in different types of poor textures. However, through the integration of both geometry and radiometry and the EW strategy, the recall obtained by the proposed algorithm is better than 50% in all four image pairs. The better matching recall improves the number of correct matches, dispersion, and positional accuracy.

  1. Incremental Frequent Subgraph Mining on Large Evolving Graphs

    KAUST Repository

    Abdelhamid, Ehab

    2017-08-22

    Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.

  2. Smooth Bundling of Large Streaming and Sequence Graphs

    NARCIS (Netherlands)

    Hurter, C.; Ersoy, O.; Telea, A.

    2013-01-01

    Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent image-based graph bundling

  3. The groupies of random multipartite graphs

    OpenAIRE

    Portmann, Marius; Wang, Hongyun

    2012-01-01

    If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.

  4. 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.

  5. Properly colored connectivity of graphs

    CERN Document Server

    Li, Xueliang; Qin, Zhongmei

    2018-01-01

    A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.

  6. Optical generation of matter qubit graph states

    International Nuclear Information System (INIS)

    Benjamin, S C; Eisert, J; Stace, T M

    2005-01-01

    We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple three-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph-state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph-state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus

  7. XML Graphs in Program Analysis

    DEFF Research Database (Denmark)

    Møller, Anders; Schwartzbach, Michael I.

    2011-01-01

    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......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...

  8. Graphs with Eulerian unit spheres

    OpenAIRE

    Knill, Oliver

    2015-01-01

    d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...

  9. Augmenting Conceptual Design Trajectory Tradespace Exploration with Graph Theory

    Science.gov (United States)

    Dees, Patrick D.; Zwack, Mathew R.; Steffens, Michael; Edwards, Stephen

    2016-01-01

    Within conceptual design changes occur rapidly due to a combination of uncertainty and shifting requirements. To stay relevant in this fluid time, trade studies must also be performed rapidly. In order to drive down analysis time while improving the information gained by these studies, surrogate models can be created to represent the complex output of a tool or tools within a specified tradespace. In order to create this model however, a large amount of data must be collected in a short amount of time. By this method, the historical approach of relying on subject matter experts to generate the data required is schedule infeasible. However, by implementing automation and distributed analysis the required data can be generated in a fraction of the time. Previous work focused on setting up a tool called multiPOST capable of orchestrating many simultaneous runs of an analysis tool assessing these automated analyses utilizing heuristics gleaned from the best practices of current subject matter experts. In this update to the previous work, elements of graph theory are included to further drive down analysis time by leveraging data previously gathered. It is shown to outperform the previous method in both time required, and the quantity and quality of data produced.

  10. The Container Problem in Bubble-Sort Graphs

    Science.gov (United States)

    Suzuki, Yasuto; Kaneko, Keiichi

    Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

  11. The many faces of graph dynamics

    Science.gov (United States)

    Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles

    2017-06-01

    The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

  12. Low-algorithmic-complexity entropy-deceiving graphs

    KAUST Repository

    Zenil, Hector

    2017-07-08

    In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure\\'s range of applications and demonstrating the weaknesses of computable measures of complexity.

  13. Multiple graph regularized nonnegative matrix factorization

    KAUST Repository

    Wang, Jim Jing-Yan

    2013-10-01

    Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.

  14. Low-algorithmic-complexity entropy-deceiving graphs

    KAUST Repository

    Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

    2017-01-01

    In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.

  15. idSpace D2.3 – Semantic meta-model integration and transformations v2

    DEFF Research Database (Denmark)

    Dolog, Peter; Grube, Pascal; Schmid, Klaus

    2009-01-01

    This deliverable discusses an extended set of requirements for transformations and metamodel for creativity techniques. Based on the requirements, the deliverable provides refined meta-model. The metamodel allows for more advanced transforma-tion concepts besides the previously delivered graph tr...... oriented implemen-tation with portlets and widgets in the Liferay portal....

  16. Graph Sampling for Covariance Estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2017-01-01

    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

  17. G-Bean: an ontology-graph based web tool for biomedical literature retrieval.

    Science.gov (United States)

    Wang, James Z; Zhang, Yuanyuan; Dong, Liang; Li, Lin; Srimani, Pradip K; Yu, Philip S

    2014-01-01

    Currently, most people use NCBI's PubMed to search the MEDLINE database, an important bibliographical information source for life science and biomedical information. However, PubMed has some drawbacks that make it difficult to find relevant publications pertaining to users' individual intentions, especially for non-expert users. To ameliorate the disadvantages of PubMed, we developed G-Bean, a graph based biomedical search engine, to search biomedical articles in MEDLINE database more efficiently. G-Bean addresses PubMed's limitations with three innovations: (1) Parallel document index creation: a multithreaded index creation strategy is employed to generate the document index for G-Bean in parallel; (2) Ontology-graph based query expansion: an ontology graph is constructed by merging four major UMLS (Version 2013AA) vocabularies, MeSH, SNOMEDCT, CSP and AOD, to cover all concepts in National Library of Medicine (NLM) database; a Personalized PageRank algorithm is used to compute concept relevance in this ontology graph and the Term Frequency - Inverse Document Frequency (TF-IDF) weighting scheme is used to re-rank the concepts. The top 500 ranked concepts are selected for expanding the initial query to retrieve more accurate and relevant information; (3) Retrieval and re-ranking of documents based on user's search intention: after the user selects any article from the existing search results, G-Bean analyzes user's selections to determine his/her true search intention and then uses more relevant and more specific terms to retrieve additional related articles. The new articles are presented to the user in the order of their relevance to the already selected articles. Performance evaluation with 106 OHSUMED benchmark queries shows that G-Bean returns more relevant results than PubMed does when using these queries to search the MEDLINE database. PubMed could not even return any search result for some OHSUMED queries because it failed to form the appropriate Boolean

  18. The game of cops and robbers on graphs

    CERN Document Server

    Bonato, Anthony

    2011-01-01

    This book is the first and only one of its kind on the topic of Cops and Robbers games, and more generally, on the field of vertex pursuit games on graphs. The book is written in a lively and highly readable fashion, which should appeal to both senior undergraduates and experts in the field (and everyone in between). One of the main goals of the book is to bring together the key results in the field; as such, it presents structural, probabilistic, and algorithmic results on Cops and Robbers games. Several recent and new results are discussed, along with a comprehensive set of references. The book is suitable for self-study or as a textbook, owing in part to the over 200 exercises. The reader will gain insight into all the main directions of research in the field and will be exposed to a number of open problems.

  19. Particle transport in breathing quantum graph

    International Nuclear Information System (INIS)

    Matrasulov, D.U.; Yusupov, J.R.; Sabirov, K.K.; Sobirov, Z.A.

    2012-01-01

    Full text: Particle transport in nanoscale networks and discrete structures is of fundamental and practical importance. Usually such systems are modeled by so-called quantum graphs, the systems attracting much attention in physics and mathematics during past two decades [1-5]. During last two decades quantum graphs found numerous applications in modeling different discrete structures and networks in nanoscale and mesoscopic physics (e.g., see reviews [1-3]). Despite considerable progress made in the study of particle dynamics most of the problems deal with unperturbed case and the case of time-dependent perturbation has not yet be explored. In this work we treat particle dynamics for quantum star graph with time-dependent bonds. In particular, we consider harmonically breathing quantum star graphs, the cases of monotonically contracting and expanding graphs. The latter can be solved exactly analytically. Edge boundaries are considered to be time-dependent, while branching point is assumed to be fixed. Quantum dynamics of a particle in such graphs is studied by solving Schrodinger equation with time-dependent boundary conditions given on a star graph. Time-dependence of the average kinetic energy is analyzed. Space-time evolution of the Gaussian wave packet is treated for harmonically breathing star graph. It is found that for certain frequencies energy is a periodic function of time, while for others it can be non-monotonically growing function of time. Such a feature can be caused by possible synchronization of the particles motion and the motions of the moving edges of graph bonds. (authors) References: [1] Tsampikos Kottos and Uzy Smilansky, Ann. Phys., 76, 274 (1999). [2] Sven Gnutzmann and Uzy Smilansky, Adv. Phys. 55, 527 (2006). [3] S. GnutzmannJ.P. Keating, F. Piotet, Ann. Phys., 325, 2595 (2010). [4] P.Exner, P.Seba, P.Stovicek, J. Phys. A: Math. Gen. 21, 4009 (1988). [5] J. Boman, P. Kurasov, Adv. Appl. Math., 35, 58 (2005)

  20. Interacting particle systems on graphs

    Science.gov (United States)

    Sood, Vishal

    In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations

  1. Transduction on Directed Graphs via Absorbing Random Walks.

    Science.gov (United States)

    De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li

    2017-08-11

    In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.

  2. Managing the water chemistry of a CANDU reactor with an expert system

    International Nuclear Information System (INIS)

    Lamirande, S.; Roberge, P.R.

    1990-01-01

    The aim of this project was to capture the expertise of Ontario Hydro in the water chemistry of the heat transport system (HTS) of the CANDU nuclear reactor and transform it into an Expert System prototype. The end product is an Expert System which can realistically diagnose situations and recommend proper courses of action based on the user's water chemistry analysis

  3. High-performance analysis of filtered semantic graphs

    OpenAIRE

    Buluç, A; Fox, A; Gilbert, JR; Kamil, S; Lugowski, A; Oliker, L; Williams, S

    2012-01-01

    High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry \\attributes" of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must either view the graph through a filter that passes only those individual vertices and edges of interest, or else must first materialize a subgraph or subgraphs consisting of only the vertices ...

  4. Bond graph modeling of centrifugal compression systems

    OpenAIRE

    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...

  5. On the local edge antimagicness of m-splitting graphs

    Science.gov (United States)

    Albirri, E. R.; Dafik; Slamin; Agustin, I. H.; Alfarisi, R.

    2018-04-01

    Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v‧ in every vertex v‧ such that v‧ adjacent to v in graph G. An m-splitting graph is a graph which has m v‧-vertices, denoted by mSpl(G). A local edge antimagic coloring in G = (V, E) graph is a bijection f:V (G)\\to \\{1,2,3,\\ldots,|V(G)|\\} in which for any two adjacent edges e 1 and e 2 satisfies w({e}1)\

  6. Augmented marked graphs

    CERN Document Server

    Cheung, King Sing

    2014-01-01

    Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume

  7. Co-Roman domination in graphs

    Indian Academy of Sciences (India)

    1National Centre for Advanced Research in Discrete Mathematics ... 3Department of Computer Science, Ball State University, Muncie, IN, USA .... The corona of two disjoint graphs G1 and G2 is defined to be the graph G = G1 ◦ G2,.

  8. 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...

  9. A cluster algorithm for graphs

    NARCIS (Netherlands)

    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)

  10. Generating random networks and graphs

    CERN Document Server

    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...

  11. On the Recognition of Fuzzy Circular Interval Graphs

    OpenAIRE

    Oriolo, Gianpaolo; Pietropaoli, Ugo; Stauffer, Gautier

    2011-01-01

    Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.

  12. Expert Systems: What Is an Expert System?

    Science.gov (United States)

    Duval, Beverly K.; Main, Linda

    1994-01-01

    Describes expert systems and discusses their use in libraries. Highlights include parts of an expert system; expert system shells; an example of how to build an expert system; a bibliography of 34 sources of information on expert systems in libraries; and a list of 10 expert system shells used in libraries. (Contains five references.) (LRW)

  13. The Thickness of Amalgamations and Cartesian Product of Graphs

    Directory of Open Access Journals (Sweden)

    Yang Yan

    2017-08-01

    Full Text Available The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.

  14. Generating Realistic Labelled, Weighted Random Graphs

    Directory of Open Access Journals (Sweden)

    Michael Charles Davis

    2015-12-01

    Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

  15. 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].

  16. Disease management research using event graphs.

    Science.gov (United States)

    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.

  17. Measuring Two-Event Structural Correlations on Graphs

    Science.gov (United States)

    2012-08-01

    2012 to 00-00-2012 4. TITLE AND SUBTITLE Measuring Two-Event Structural Correlations on Graphs 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ...by event simulation on the DBLP graph. Then we examine the efficiency and scala - bility of the framework with a Twitter network. The third part of...correlation pattern mining for large graphs. In Proc. of the 8th Workshop on Mining and Learning with Graphs, pages 119–126, 2010. [23] T. Smith. A

  18. Reconstructing Nearly Simple Polytopes from their Graph

    OpenAIRE

    Doolittle, Joseph

    2017-01-01

    We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$-nearly simple and prove that 1-nearly simple and 2-nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3-nearly simple polytope which is not reconstructible from its graph. Fu...

  19. 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

  20. Modeling Software Evolution using Algebraic Graph Rewriting

    NARCIS (Netherlands)

    Ciraci, Selim; van den Broek, Pim

    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

  1. Cycles in weighted graphs and related topics

    NARCIS (Netherlands)

    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

  2. Probabilistic Graph Layout for Uncertain Network Visualization.

    Science.gov (United States)

    Schulz, Christoph; Nocaj, Arlind; Goertler, Jochen; Deussen, Oliver; Brandes, Ulrik; Weiskopf, Daniel

    2017-01-01

    We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

  3. Optimizing graph algorithms on pregel-like systems

    KAUST Repository

    Salihoglu, Semih

    2014-03-01

    We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel\\'s vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.

  4. Politics or law: what is more in the approaches of public expert monopoly?

    Directory of Open Access Journals (Sweden)

    Оксана Михайлівна Калужна

    2018-03-01

    It is concluded that the model of judicial expert support of legal proceedings in Ukraine, that is established by «judicial reform» (Law No. 2147-VIII in the wording that will come into force on March 18, 2018 is a milestone in its historical development, which certainly should be modified depending on its effectiveness and the demand of the society, public, professional and state institutions. So public forensic expert monopoly is not an ideal model of forensic expert support of justice because of corporate and political interests, corruption component, abuse of forensic experts etc. Therefore, it will undergo a review and transformation.

  5. Electrical transformer handbook

    Energy Technology Data Exchange (ETDEWEB)

    Hurst, R.W.; Horne, D. (eds.)

    2005-07-01

    This handbook is a valuable user guide intended for electrical engineering and maintenance personnel, electrical contractors and electrical engineering students. It provides current information on techniques and technologies that can help extend the life of transformers. It discusses transformer testing, monitoring, design, commissioning, retrofitting and other elements involved in keeping electrical transformers in safe and efficient operation. It demonstrates how a power transformer can be put to use and common problems faced by owners. In addition to covering control techniques, testing and maintenance procedures, this handbook covers the power transformer; control electrical power transformer; electrical power transformer; electrical theory transformer; used electrical transformer; down electrical step transformer; electrical manufacturer transformer; electrical picture transformer; electrical transformer work; electrical surplus transformer; current transformer; step down transformer; voltage transformer; step up transformer; isolation transformer; low voltage transformer; toroidal transformer; high voltage transformer; and control power transformer. The handbook includes articles from leading experts on overcurrent protection of transformers; ventilated dry-type transformers; metered load factors for low-voltage, and dry-type transformers in buildings. The maintenance of both dry-type or oil-filled transformers was discussed with reference to sealing, gaskets, oils, moisture and testing. The adoption of dynamic load practices was also discussed along with the reclamation or recycling of used lube oil, transformer dielectric fluids and aged solid insulation. A buyer's guide and directory of transformer manufacturers and suppliers was also included. refs., tabs., figs.

  6. Automorphism group of the modified bubble-sort graph

    OpenAIRE

    Ganesan, Ashwin

    2014-01-01

    The modified bubble-sort graph of dimension $n$ is the Cayley graph of $S_n$ generated by $n$ cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension $n$ is $S_n \\times D_{2n}$, for all $n \\ge 5$. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct product decomposition is seen to hold for arbitrary normal Cayley graphs generate...

  7. Total dominator chromatic number of a graph

    Directory of Open Access Journals (Sweden)

    Adel P. Kazemi

    2015-06-01

    Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.

  8. Khovanov-Rozansky Graph Homology and Composition Product

    DEFF Research Database (Denmark)

    Wagner, Emmanuel

    2008-01-01

    In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology.......In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology....

  9. Graph-based clustering and data visualization algorithms

    CERN Document Server

    Vathy-Fogarassy, Ágnes

    2013-01-01

    This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on

  10. 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.

  11. Holographic Transformation, Belief Propagation and Loop Calculus for Generalized Probabilistic Theories

    OpenAIRE

    Mori, Ryuhei

    2015-01-01

    The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is represented by an inner product of two high-dimensional vectors both of which can be decomposed to tensor products of low-dimensional vectors. On the representation, the holographic transformation is clearly understood by using adjoint linear maps. Furthermore, on th...

  12. On a Fuzzy Algebra for Querying Graph Databases

    OpenAIRE

    Pivert , Olivier; Thion , Virginie; Jaudoin , Hélène; Smits , Grégory

    2014-01-01

    International audience; This paper proposes a notion of fuzzy graph database and describes a fuzzy query algebra that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. The algebra, based on fuzzy set theory and the concept of a fuzzy graph, is composed of a set of operators that can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. In a s...

  13. Graphs of groups on surfaces interactions and models

    CERN Document Server

    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

  14. A Type Graph Model for Java Programs

    NARCIS (Netherlands)

    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

  15. Mutual proximity graphs for improved reachability in music recommendation.

    Science.gov (United States)

    Flexer, Arthur; Stevens, Jeff

    2018-01-01

    This paper is concerned with the impact of hubness, a general problem of machine learning in high-dimensional spaces, on a real-world music recommendation system based on visualisation of a k-nearest neighbour (knn) graph. Due to a problem of measuring distances in high dimensions, hub objects are recommended over and over again while anti-hubs are nonexistent in recommendation lists, resulting in poor reachability of the music catalogue. We present mutual proximity graphs, which are an alternative to knn and mutual knn graphs, and are able to avoid hub vertices having abnormally high connectivity. We show that mutual proximity graphs yield much better graph connectivity resulting in improved reachability compared to knn graphs, mutual knn graphs and mutual knn graphs enhanced with minimum spanning trees, while simultaneously reducing the negative effects of hubness.

  16. Efficient dynamic graph construction for inductive semi-supervised learning.

    Science.gov (United States)

    Dornaika, F; Dahbi, R; Bosaghzadeh, A; Ruichek, Y

    2017-10-01

    Most of graph construction techniques assume a transductive setting in which the whole data collection is available at construction time. Addressing graph construction for inductive setting, in which data are coming sequentially, has received much less attention. For inductive settings, constructing the graph from scratch can be very time consuming. This paper introduces a generic framework that is able to make any graph construction method incremental. This framework yields an efficient and dynamic graph construction method that adds new samples (labeled or unlabeled) to a previously constructed graph. As a case study, we use the recently proposed Two Phase Weighted Regularized Least Square (TPWRLS) graph construction method. The paper has two main contributions. First, we use the TPWRLS coding scheme to represent new sample(s) with respect to an existing database. The representative coefficients are then used to update the graph affinity matrix. The proposed method not only appends the new samples to the graph but also updates the whole graph structure by discovering which nodes are affected by the introduction of new samples and by updating their edge weights. The second contribution of the article is the application of the proposed framework to the problem of graph-based label propagation using multiple observations for vision-based recognition tasks. Experiments on several image databases show that, without any significant loss in the accuracy of the final classification, the proposed dynamic graph construction is more efficient than the batch graph construction. Copyright © 2017 Elsevier Ltd. All rights reserved.

  17. Coloring geographical threshold graphs

    Energy Technology Data Exchange (ETDEWEB)

    Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH

    2008-01-01

    We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.

  18. 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

  19. Quantum Graphs And Their Resonance Properties

    International Nuclear Information System (INIS)

    Lipovsky, J.

    2016-01-01

    In the current review, we study the model of quantum graphs. We focus mainly on the resonance properties of quantum graphs. We define resolvent and scattering resonances and show their equivalence. We present various results on the asymptotics of the number of resolvent resonances in both non-magnetic and magnetic quantum graphs and find bounds on the coefficient by the leading term of the asymptotics. We explain methods how to find the spectral and resonance condition. Most of the notions and theorems are illustrated in examples. We show how to find resonances numerically and, in a simple example, we find trajectories of resonances in the complex plane. We discuss Fermi’s golden rule for quantum graphs and distribution of the mean intensity for the topological resonances. (author)

  20. Determining X-chains in graph states

    International Nuclear Information System (INIS)

    Wu, Jun-Yi; Kampermann, Hermann; Bruß, Dagmar

    2016-01-01

    The representation of graph states in the X-basis as well as the calculation of graph state overlaps can efficiently be performed by using the concept of X-chains (Wu et al 2015 Phys. Rev. A 92 012322). We present a necessary and sufficient criterion for X-chains and show that they can efficiently be determined by the Bareiss algorithm. An analytical approach for searching X-chain groups of a graph state is proposed. Furthermore we generalize the concept of X-chains to so-called Euler chains, whose induced subgraphs are Eulerian. This approach helps to determine if a given vertex set is an X-chain and we show how Euler chains can be used in the construction of multipartite Bell inequalities for graph states. (paper)

  1. Fixation probability on clique-based graphs

    Science.gov (United States)

    Choi, Jeong-Ok; Yu, Unjong

    2018-02-01

    The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.

  2. Development of an expert system for analysis of Shuttle atmospheric revitalization and pressure control subsystem anomalies

    Science.gov (United States)

    Lafuse, Sharon A.

    1991-01-01

    The paper describes the Shuttle Leak Management Expert System (SLMES), a preprototype expert system developed to enable the ECLSS subsystem manager to analyze subsystem anomalies and to formulate flight procedures based on flight data. The SLMES combines the rule-based expert system technology with the traditional FORTRAN-based software into an integrated system. SLMES analyzes the data using rules, and, when it detects a problem that requires simulation, it sets up the input for the FORTRAN-based simulation program ARPCS2AT2, which predicts the cabin total pressure and composition as a function of time. The program simulates the pressure control system, the crew oxygen masks, the airlock repress/depress valves, and the leakage. When the simulation has completed, other SLMES rules are triggered to examine the results of simulation contrary to flight data and to suggest methods for correcting the problem. Results are then presented in form of graphs and tables.

  3. Steiner Distance in Graphs--A Survey

    OpenAIRE

    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 ...

  4. Girth 5 graphs from relative difference sets

    DEFF Research Database (Denmark)

    Jørgensen, Leif Kjær

    2005-01-01

    We consider the problem of construction of graphs with given degree $k$ 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 ...

  5. A Type Graph Model for Java Programs

    NARCIS (Netherlands)

    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

  6. Analyzing locomotion synthesis with feature-based motion graphs.

    Science.gov (United States)

    Mahmudi, Mentar; Kallmann, Marcelo

    2013-05-01

    We propose feature-based motion graphs for realistic locomotion synthesis among obstacles. Among several advantages, feature-based motion graphs achieve improved results in search queries, eliminate the need of postprocessing for foot skating removal, and reduce the computational requirements in comparison to traditional motion graphs. Our contributions are threefold. First, we show that choosing transitions based on relevant features significantly reduces graph construction time and leads to improved search performances. Second, we employ a fast channel search method that confines the motion graph search to a free channel with guaranteed clearance among obstacles, achieving faster and improved results that avoid expensive collision checking. Lastly, we present a motion deformation model based on Inverse Kinematics applied over the transitions of a solution branch. Each transition is assigned a continuous deformation range that does not exceed the original transition cost threshold specified by the user for the graph construction. The obtained deformation improves the reachability of the feature-based motion graph and in turn also reduces the time spent during search. The results obtained by the proposed methods are evaluated and quantified, and they demonstrate significant improvements in comparison to traditional motion graph techniques.

  7. Supporting Fourth Graders' Ability to Interpret Graphs through Real-Time Graphing Technology: A Preliminary Study

    Science.gov (United States)

    Deniz, Hasan; Dulger, Mehmet F.

    2012-01-01

    This study examined to what extent inquiry-based instruction supported with real-time graphing technology improves fourth grader's ability to interpret graphs as representations of physical science concepts such as motion and temperature. This study also examined whether there is any difference between inquiry-based instruction supported with…

  8. Torsional rigidity, isospectrality and quantum graphs

    International Nuclear Information System (INIS)

    Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon

    2017-01-01

    We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)

  9. Joint Graph Layouts for Visualizing Collections of Segmented Meshes

    KAUST Repository

    Ren, Jing

    2017-09-12

    We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.

  10. Joint Graph Layouts for Visualizing Collections of Segmented Meshes

    KAUST Repository

    Ren, Jing; Schneider, Jens; Ovsjanikov, Maks; Wonka, Peter

    2017-01-01

    We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.

  11. Learning a Nonnegative Sparse Graph for Linear Regression.

    Science.gov (United States)

    Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung

    2015-09-01

    Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.

  12. GRAMI: Generalized Frequent Subgraph Mining in Large Graphs

    KAUST Repository

    El Saeedy, Mohammed El Sayed

    2011-07-24

    Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper we propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. We developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. We also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. Our experiments on real data demonstrate that our framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.

  13. 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...

  14. A Characterization of 2-Tree Probe Interval Graphs

    Directory of Open Access Journals (Sweden)

    Brown David E.

    2014-08-01

    Full Text Available A graph is a probe interval graph if its vertices correspond to some set of intervals of the real line and can be partitioned into sets P and N so that vertices are adjacent if and only if their corresponding intervals intersect and at least one belongs to P. We characterize the 2-trees which are probe interval graphs and extend a list of forbidden induced subgraphs for such graphs created by Pržulj and Corneil in [2-tree probe interval graphs have a large obstruction set, Discrete Appl. Math. 150 (2005 216-231

  15. A distributed query execution engine of big attributed graphs.

    Science.gov (United States)

    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.

  16. Interval Routing and Minor-Monotone Graph Parameters

    NARCIS (Netherlands)

    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

  17. 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 polyn...

  18. A new characterization of trivially perfect graphs

    Directory of Open Access Journals (Sweden)

    Christian Rubio Montiel

    2015-03-01

    Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.

  19. Improper colouring of (random) unit disk graphs

    NARCIS (Netherlands)

    Kang, R.J.; Müller, T.; Sereni, J.S.

    2008-01-01

    For any graph G, the k-improper chromatic number ¿k(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate ¿k for unit disk graphs and random unit disk graphs to generalise results of McDiarmid and Reed

  20. Transforming process models : executable rewrite rules versus a formalized Java program

    NARCIS (Netherlands)

    Van Gorp, P.M.E.; Eshuis, H.

    2010-01-01

    In the business process management community, transformations for process models are usually programmed using imperative languages. The underlying mapping rules tend to be documented using informal visual rules whereas they tend to be formalized using mathematical set constructs. In the Graph and

  1. Modification of Duval Triangle for Diagnostic Transformer Fault through a Procedure of Dissolved Gases Analysis

    Directory of Open Access Journals (Sweden)

    Sobhy Serry Dessouky

    2016-08-01

        The evaluation is carried out on DGA data obtained from three different groups of transformers. A Matlab program was developed to automate the evaluation of  Duval Triangle graph to numerical modification, Also the fault gases can be generated due to oil decomposing effected by transformer over excitation which increasing thetransformer exciting current lead to rising the temperature inside transformer core beside the other causes.

  2. Three Syntactic Theories for Combinatory Graph Reduction

    DEFF Research Database (Denmark)

    Danvy, Olivier; Zerny, Ian

    2011-01-01

    in a third syntactic theory. The structure of the store-based abstract machine corresponding to this third syntactic theory oincides with that of Turner's original reduction machine. The three syntactic theories presented here The three syntactic heories presented here therefore have the following......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...

  3. Three Syntactic Theories for Combinatory Graph Reduction

    DEFF Research Database (Denmark)

    Danvy, Olivier; Zerny, Ian

    2013-01-01

    , as a store-based reduction semantics of combinatory term graphs. We then refocus this store-based reduction semantics into a store-based abstract machine. The architecture of this store-based abstract machine coincides with that of Turner's original reduction machine. The three syntactic theories presented......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 rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...

  4. Approximate Computing Techniques for Iterative Graph Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

    2017-12-18

    Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

  5. A Clustering Graph Generator

    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.

  6. Carbon Nanotubes’ Effect on Mitochondrial Oxygen Flux Dynamics: Polarography Experimental Study and Machine Learning Models using Star Graph Trace Invariants of Raman Spectra

    Directory of Open Access Journals (Sweden)

    Michael González-Durruthy

    2017-11-01

    Full Text Available This study presents the impact of carbon nanotubes (CNTs on mitochondrial oxygen mass flux (Jm under three experimental conditions. New experimental results and a new methodology are reported for the first time and they are based on CNT Raman spectra star graph transform (spectral moments and perturbation theory. The experimental measures of Jm showed that no tested CNT family can inhibit the oxygen consumption profiles of mitochondria. The best model for the prediction of Jm for other CNTs was provided by random forest using eight features, obtaining test R-squared (R2 of 0.863 and test root-mean-square error (RMSE of 0.0461. The results demonstrate the capability of encoding CNT information into spectral moments of the Raman star graphs (SG transform with a potential applicability as predictive tools in nanotechnology and material risk assessments.

  7. Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs

    KAUST Repository

    Jamour, Fuad Tarek

    2017-10-17

    Betweenness centrality quantifies the importance of nodes in a graph in many applications, including network analysis, community detection and identification of influential users. Typically, graphs in such applications evolve over time. Thus, the computation of betweenness centrality should be performed incrementally. This is challenging because updating even a single edge may trigger the computation of all-pairs shortest paths in the entire graph. Existing approaches cannot scale to large graphs: they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving graphs. We decompose the graph into biconnected components and prove that processing can be localized within the affected components. iCentral is the first algorithm to support incremental betweeness centrality computation within a graph component. This is done efficiently, in linear space; consequently, iCentral scales to large graphs. We demonstrate with real datasets that the serial implementation of iCentral is up to 3.7 times faster than existing serial methods. Our parallel implementation that scales to large graphs, is an order of magnitude faster than the state-of-the-art parallel algorithm, while using an order of magnitude less computational resources.

  8. Mathematical Minute: Rotating a Function Graph

    Science.gov (United States)

    Bravo, Daniel; Fera, Joseph

    2013-01-01

    Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

  9. Mizan: Optimizing Graph Mining in Large Parallel Systems

    KAUST Repository

    Kalnis, Panos

    2012-03-01

    Extracting information from graphs, from nding shortest paths to complex graph mining, is essential for many ap- plications. Due to the shear size of modern graphs (e.g., social networks), processing must be done on large paral- lel computing infrastructures (e.g., the cloud). Earlier ap- proaches relied on the MapReduce framework, which was proved inadequate for graph algorithms. More recently, the message passing model (e.g., Pregel) has emerged. Although the Pregel model has many advantages, it is agnostic to the graph properties and the architecture of the underlying com- puting infrastructure, leading to suboptimal performance. In this paper, we propose Mizan, a layer between the users\\' code and the computing infrastructure. Mizan considers the structure of the input graph and the architecture of the in- frastructure in order to: (i) decide whether it is bene cial to generate a near-optimal partitioning of the graph in a pre- processing step, and (ii) choose between typical point-to- point message passing and a novel approach that puts com- puting nodes in a virtual overlay ring. We deployed Mizan on a small local Linux cluster, on the cloud (256 virtual machines in Amazon EC2), and on an IBM Blue Gene/P supercomputer (1024 CPUs). We show that Mizan executes common algorithms on very large graphs 1-2 orders of mag- nitude faster than MapReduce-based implementations and up to one order of magnitude faster than implementations relying on Pregel-like hash-based graph partitioning.

  10. Stability notions in synthetic graph generation: a preliminary study

    NARCIS (Netherlands)

    van Leeuwen, W.; Fletcher, G.H.L.; Yakovets, N.; Bonifati, A.; Markl, Volker; Orlando, Salvatore; Mitschang, Bernhard

    2017-01-01

    With the rise in adoption of massive graph data, it be- comes increasingly important to design graph processing algorithms which have predictable behavior as the graph scales. This work presents an initial study of stability in the context of a schema-driven synthetic graph generation. Specifically,

  11. Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces

    NARCIS (Netherlands)

    F. Vallentin (Frank)

    2008-01-01

    htmlabstractIn this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite

  12. Application of Bipolar Fuzzy Sets in Graph Structures

    Directory of Open Access Journals (Sweden)

    Muhammad Akram

    2016-01-01

    Full Text Available A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS, strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study ϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.

  13. Low-Rank Matrix Factorization With Adaptive Graph Regularizer.

    Science.gov (United States)

    Lu, Gui-Fu; Wang, Yong; Zou, Jian

    2016-05-01

    In this paper, we present a novel low-rank matrix factorization algorithm with adaptive graph regularizer (LMFAGR). We extend the recently proposed low-rank matrix with manifold regularization (MMF) method with an adaptive regularizer. Different from MMF, which constructs an affinity graph in advance, LMFAGR can simultaneously seek graph weight matrix and low-dimensional representations of data. That is, graph construction and low-rank matrix factorization are incorporated into a unified framework, which results in an automatically updated graph rather than a predefined one. The experimental results on some data sets demonstrate that the proposed algorithm outperforms the state-of-the-art low-rank matrix factorization methods.

  14. Groupies in random bipartite graphs

    OpenAIRE

    Yilun Shang

    2010-01-01

    A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.

  15. The planar cubic Cayley graphs

    CERN Document Server

    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.

  16. Genus of total graphs from rings: A survey

    Directory of Open Access Journals (Sweden)

    T. Tamizh Chelvam

    2018-04-01

    Full Text Available Let R be a commutative ring. The total graph T Γ ( R of R is the undirected graph with vertex set R and two distinct vertices x and y are adjacent if x + y is a zero divisor in R . In this paper, we present a survey of results on the genus of T Γ ( R and three of its generalizations. Keywords: Commutative ring, Total graph, Cayley graph, Genus, Planar

  17. Quick Mining of Isomorphic Exact Large Patterns from Large Graphs

    KAUST Repository

    Almasri, Islam

    2014-12-01

    The applications of the sub graph isomorphism search are growing with the growing number of areas that model their systems using graphs or networks. Specifically, many biological systems, such as protein interaction networks, molecular structures and protein contact maps, are modeled as graphs. The sub graph isomorphism search is concerned with finding all sub graphs that are isomorphic to a relevant query graph, the existence of such sub graphs can reflect on the characteristics of the modeled system. The most computationally expensive step in the search for isomorphic sub graphs is the backtracking algorithm that traverses the nodes of the target graph. In this paper, we propose a pruning approach that is inspired by the minimum remaining value heuristic that achieves greater scalability over large query and target graphs. Our testing on various biological networks shows that performance enhancement of our approach over existing state-of-the-art approaches varies between 6x and 53x. © 2014 IEEE.

  18. Quick Mining of Isomorphic Exact Large Patterns from Large Graphs

    KAUST Repository

    Almasri, Islam; Gao, Xin; Fedoroff, Nina V.

    2014-01-01

    The applications of the sub graph isomorphism search are growing with the growing number of areas that model their systems using graphs or networks. Specifically, many biological systems, such as protein interaction networks, molecular structures and protein contact maps, are modeled as graphs. The sub graph isomorphism search is concerned with finding all sub graphs that are isomorphic to a relevant query graph, the existence of such sub graphs can reflect on the characteristics of the modeled system. The most computationally expensive step in the search for isomorphic sub graphs is the backtracking algorithm that traverses the nodes of the target graph. In this paper, we propose a pruning approach that is inspired by the minimum remaining value heuristic that achieves greater scalability over large query and target graphs. Our testing on various biological networks shows that performance enhancement of our approach over existing state-of-the-art approaches varies between 6x and 53x. © 2014 IEEE.

  19. Eigenfunction statistics on quantum graphs

    International Nuclear Information System (INIS)

    Gnutzmann, S.; Keating, J.P.; Piotet, F.

    2010-01-01

    We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

  20. Regular graph construction for semi-supervised learning

    International Nuclear Information System (INIS)

    Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang

    2014-01-01

    Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN

  1. Combining Lead Exposure Measurements and Experts' Judgment Through a Bayesian Framework.

    Science.gov (United States)

    Koh, Dong-Hee; Park, Ju-Hyun; Lee, Sang-Gil; Kim, Hwan-Cheol; Choi, Sangjun; Jung, Hyejung; Park, Dong-Uk

    2017-11-10

    CARcinogen EXposure (CAREX) is a carcinogen-surveillance system employed in many countries. To develop Korean CAREX, the intensity of exposure to lead, as an example, was estimated across industries. Airborne-lead measurement records were extracted from the work-environment measurement database (WEMD), which is a nationwide workplace-monitoring database. Lead measurements were log-transformed; then, the log-transformed geometric means (LGMs) and log-transformed geometric standard deviations (LGSDs) were calculated for each industry. However, the data of many industries was limited. To address this shortcoming, experts' judgments of the lead exposure levels across industries were elicited. Experts provided their estimates of lead exposure levels as the boundary of the 5th and 95th percentiles, and it is assumed that these estimates are based on the log-normal distributions of exposure levels. Estimates of LGM and LGSD were extracted from each expert's response and then combined to quantify the experts' prior distribution. Then, the experts' prior distributions for each industry were updated with the corresponding LGMs and LGSDs calculated from the WEMD data through a Bayesian framework, yielding posterior distributions of the LGM and LGSD. The WEMD contains 83035 airborne-lead measurements that were collected between 2002 and 2007. A total of 17 occupational-hygiene professionals with >20 years of experience provided lead exposure estimates. In industries where measurement data were abundant, the measurement data dominated the posterior exposure estimates. For example, for one industry, 'Manufacture of Accumulator, Primary Cells, and Primary Batteries,' 1152 lead measurements [with a geometric mean (GM) of 14.42 µg m-3 and a geometric standard deviation (GSD) of 3.31] were available and 15 experts' responses (with a GM of 7.06 µg m-3 and a GSD of 4.15) were collected, resulting in a posterior exposure estimate of 14.41µg m-3 as the GM with a GSD of 3.31. For

  2. Automatic Transformation of MPI Programs to Asynchronous, Graph-Driven Form

    Energy Technology Data Exchange (ETDEWEB)

    Baden, Scott B [University of California, San Diego; Weare, John H [University of California, San Diego; Bylaska, Eric J [Pacific Northwest National Laboratory

    2013-04-30

    The goals of this project are to develop new, scalable, high-fidelity algorithms for atomic-level simulations and program transformations that automatically restructure existing applications, enabling them to scale forward to Petascale systems and beyond. The techniques enable legacy MPI application code to exploit greater parallelism though increased latency hiding and improved workload assignment. The techniques were successfully demonstrated on high-end scalable systems located at DOE laboratories. Besides the automatic MPI program transformations efforts, the project also developed several new scalable algorithms for ab-initio molecular dynamics, including new massively parallel algorithms for hybrid DFT and new parallel in time algorithms for molecular dynamics and ab-initio molecular dynamics. These algorithms were shown to scale to very large number of cores, and they were designed to work in the latency hiding framework developed in this project. The effectiveness of the developments was enhanced by the direct application to real grand challenge simulation problems covering a wide range of technologically important applications, time scales and accuracies. These included the simulation of the electronic structure of mineral/fluid interfaces, the very accurate simulation of chemical reactions in microsolvated environments, and the simulation of chemical behavior in very large enzyme reactions.

  3. Pristine transfinite graphs and permissive electrical networks

    CERN Document Server

    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...

  4. Embodied mental rotation: A special link between egocentric transformation and the bodily self

    Directory of Open Access Journals (Sweden)

    Sandra eKaltner

    2014-06-01

    Full Text Available This experiment investigated the influence of motor expertise on object-based versus egocentric transformations in a chronometric mental rotation task using images of either the own or another person’s body as stimulus material. According to the embodied cognition viewpoint, we hypothesized motor-experts to outperform non-motor experts specifically in the egocentric condition because of higher kinesthetic representation and motor simulations compared to object-based transformations. In line with this, we expected that images of the own body are solved faster than another person’s body stimuli. Results showed a benefit of motor expertise and representations of another person’s body, but only for the object-based transformation task. That is, this other-advantage diminishes in egocentric transformations. Since motor experts didn’t show any specific expertise in rotational movements, we concluded that using human bodies as stimulus material elicits embodied spatial transformations, which facilitates performance exclusively for egocentric transformations. Regarding stimulus material, the other-advantage ascribed to increased self-awareness-consciousness distracting attention-demanding resources, disappeared in the egocentric condition. This result may be due to the stronger link between the bodily self and motor representations compared to that emerging in object-based transformations.

  5. Graph Processing on GPUs: A Survey

    DEFF Research Database (Denmark)

    Shi, Xuanhua; Zheng, Zhigao; Zhou, Yongluan

    2018-01-01

    hundreds of billions, has attracted much attention in both industry and academia. It still remains a great challenge to process such large-scale graphs. Researchers have been seeking for new possible solutions. Because of the massive degree of parallelism and the high memory access bandwidth in GPU......, 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...

  6. A heterogeneous graph-based recommendation simulator

    Energy Technology Data Exchange (ETDEWEB)

    Yeonchan, Ahn [Seoul National University; Sungchan, Park [Seoul National University; Lee, Matt Sangkeun [ORNL; Sang-goo, Lee [Seoul National University

    2013-01-01

    Heterogeneous graph-based recommendation frameworks have flexibility in that they can incorporate various recommendation algorithms and various kinds of information to produce better results. In this demonstration, we present a heterogeneous graph-based recommendation simulator which enables participants to experience the flexibility of a heterogeneous graph-based recommendation method. With our system, participants can simulate various recommendation semantics by expressing the semantics via meaningful paths like User Movie User Movie. The simulator then returns the recommendation results on the fly based on the user-customized semantics using a fast Monte Carlo algorithm.

  7. Giant Components in Biased Graph Processes

    OpenAIRE

    Amir, Gideon; Gurel-Gurevich, Ori; Lubetzky, Eyal; Singer, Amit

    2005-01-01

    A random graph process, $\\Gorg[1](n)$, is a sequence of graphs on $n$ vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution on the missing edges. It is well known that in such a process a giant component (of linear size) typically emerges after $(1+o(1))\\frac{n}{2}$ edges (a phenomenon known as ``the double jump''), i.e., at time $t=1$ when using a timescale of $n/2$ edges in each step. We consider a generalization of ...

  8. Graph Theory to Pure Mathematics: Some Illustrative Examples

    Indian Academy of Sciences (India)

    Graph Theory to Pure Mathematics: Some. Illustrative Examples v Yegnanarayanan is a. Professor of Mathematics at MNM Jain Engineering. College, Chennai. His research interests include graph theory and its applications to both pure maths and theoretical computer science. Keywords. Graph theory, matching theory,.

  9. 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.

  10. Attack Graph Construction for Security Events Analysis

    Directory of Open Access Journals (Sweden)

    Andrey Alexeevich Chechulin

    2014-09-01

    Full Text Available The paper is devoted to investigation of the attack graphs construction and analysis task for a network security evaluation and real-time security event processing. Main object of this research is the attack modeling process. The paper contains the description of attack graphs building, modifying and analysis technique as well as overview of implemented prototype for network security analysis based on attack graph approach.

  11. Profinite graphs and groups

    CERN Document Server

    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...

  12. A New Graph Drawing Scheme for Social Network

    Directory of Open Access Journals (Sweden)

    Eric Ke Wang

    2014-01-01

    visualization is employed to extract the potential information from the large scale of social network data and present the information briefly as visualized graphs. In the process of information visualization, graph drawing is a crucial part. In this paper, we study the graph layout algorithms and propose a new graph drawing scheme combining multilevel and single-level drawing approaches, including the graph division method based on communities and refining approach based on partitioning strategy. Besides, we compare the effectiveness of our scheme and FM3 in experiments. The experiment results show that our scheme can achieve a clearer diagram and effectively extract the community structure of the social network to be applied to drawing schemes.

  13. Two-colorable graph states with maximal Schmidt measure

    International Nuclear Information System (INIS)

    Severini, Simone

    2006-01-01

    The Schmidt measure was introduced by Eisert and Briegel for quantifying the degree of entanglement of multipartite quantum systems [J. Eisert, H.-J. Briegel, Phys. Rev. A 64 (2001) 22306]. For two-colorable graph states, the Schmidt measure is related to the spectrum of the associated graph. We observe that almost all two-colorable graph states have maximal Schmidt measure and we construct specific examples. By making appeal to a result of Ehrenfeucht et al. [A. Ehrenfeucht, T. Harju, G. Rozenberg, Discrete Math. 278 (2004) 45], we point out that the graph operations called local complementation and switching form a transitive group acting on the set of all graph states of a given dimension

  14. Using graph theory for automated electric circuit solving

    International Nuclear Information System (INIS)

    Toscano, L; Stella, S; Milotti, E

    2015-01-01

    Graph theory plays many important roles in modern physics and in many different contexts, spanning diverse topics such as the description of scale-free networks and the structure of the universe as a complex directed graph in causal set theory. Graph theory is also ideally suited to describe many concepts in computer science. Therefore it is increasingly important for physics students to master the basic concepts of graph theory. Here we describe a student project where we develop a computational approach to electric circuit solving which is based on graph theoretic concepts. This highly multidisciplinary approach combines abstract mathematics, linear algebra, the physics of circuits, and computer programming to reach the ambitious goal of implementing automated circuit solving. (paper)

  15. Solved and unsolved problems of chemical graph theory

    International Nuclear Information System (INIS)

    Trinajstic, N.; Klein, D.J.; Randic, M.

    1986-01-01

    The development of several novel graph theoretical concepts and their applications in different branches of chemistry are reviewed. After a few introductory remarks they follow with an outline of selected important graph theoretical invariants, introducing some new results and indicating some open problems. They continue with discussing the problem of graph characterization and construction of graphs of chemical interest, with a particular emphasis on large systems. Finally they consider various problems and difficulties associated with special subgraphs, including subgraphs representing Kekule valence structures. The paper ends with a brief review of structure-property and structure-activity correlations, the topic which is one of prime motivations for application of graph theory to chemistry

  16. Graph theory and the Virasoro master equation

    International Nuclear Information System (INIS)

    Obers, N.A.J.

    1991-01-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n) diag , which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {g metric }, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g metric is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n) diag in the Cartesian basis of SO(n), and the ansatz SU(n) metric in the Pauli-like basis of SU(n). Finally, he defines the 'sine-area graphs' of SU(n), which label the conformal field theories of SU(n) metric , and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g metric

  17. Water Sensation During Passive Propulsion for Expert and Nonexpert Swimmers.

    Science.gov (United States)

    Kusanagi, Kenta; Sato, Daisuke; Hashimoto, Yasuhiro; Yamada, Norimasa

    2017-06-01

    This study determined whether expert swimmers, compared with nonexperts, have superior movement perception and physical sensations of propulsion in water. Expert (national level competitors, n = 10) and nonexpert (able to swim 50 m in > 3 styles, n = 10) swimmers estimated distance traveled in water with their eyes closed. Both groups indicated their subjective physical sensations in the water. For each of two trials, two-dimensional coordinates were obtained from video recordings using the two-dimensional direct linear transformation method for calculating changes in speed. The mean absolute error of the difference between the actual and estimated distance traveled in the water was significantly lower for expert swimmers (0.90 ± 0.71 meters) compared with nonexpert swimmers (3.85 ± 0.84 m). Expert swimmers described the sensation of propulsion in water in cutaneous terms as the "sense of flow" and sensation of "skin resistance." Therefore, expert swimmers appear to have a superior sense of distance during their movement in the water compared with that of nonexpert swimmers. In addition, expert swimmers may have a better perception of movement in water. We propose that expert swimmers integrate sensations and proprioceptive senses, enabling them to better perceive and estimate distance moved through water.

  18. Comparison between state graphs and fault trees for sequential and repairable systems

    International Nuclear Information System (INIS)

    Soussan, D.; Saignes, P.

    1996-01-01

    In French PSA (Probabilistic Safety Assessment) 1300 for the 1300 Mwe PWR plants carried out by EDF, sequential and reparable systems are modeled with state graphs. This method is particularly convenient for modeling dynamic systems with long-term missions but induces a bad traceability and understandability of models. In the objective of providing elements for rewriting PSA 1300 with only boolean models, EDF has asked CEA to participate to a methodological study. The aim is to carry out a feasibility study of transposition of state graphs models into fault trees on Component Cooling System and Essential Service Water System (CCS/ESWS) and to draw a methodological guide for transposition. The study realized on CCS/ESWS involves two main axes: quantification of cold source loss (as an accident sequence initiating event, called H1); quantification of the CCS/ESWS missions in accident sequences. The subject of this article is to show that this transformation is applicable with minimum distortions of the results and to determine the hypotheses, the conditions and the limits of application of this conversion. (authors). 2 refs

  19. Bipartite Diametrical Graphs of Diameter 4 and Extreme Orders

    Directory of Open Access Journals (Sweden)

    Salah Al-Addasi

    2008-01-01

    in which this upper bound is attained, this graph can be viewed as a generalization of the Rhombic Dodecahedron. Then we show that for any ≥2, the graph (2,2 is the unique (up to isomorphism bipartite diametrical graph of diameter 4 and partite sets of cardinalities 2 and 2, and hence in particular, for =3, the graph (6,8 which is just the Rhombic Dodecahedron is the unique (up to isomorphism bipartite diametrical graph of such a diameter and cardinalities of partite sets. Thus we complete a characterization of -graphs of diameter 4 and cardinality of the smaller partite set not exceeding 6. We prove that the neighborhoods of vertices of the larger partite set of (2,2 form a matroid whose basis graph is the hypercube . We prove that any -graph of diameter 4 is bipartite self complementary, thus in particular (2,2. Finally, we study some additional properties of (2,2 concerning the order of its automorphism group, girth, domination number, and when being Eulerian.

  20. Compression-based inference on graph data

    NARCIS (Netherlands)

    Bloem, P.; van den Bosch, A.; Heskes, T.; van Leeuwen, D.

    2013-01-01

    We investigate the use of compression-based learning on graph data. General purpose compressors operate on bitstrings or other sequential representations. A single graph can be represented sequentially in many ways, which may in uence the performance of sequential compressors. Using Normalized

  1. Generating hierarchial scale-free graphs from fractals

    Energy Technology Data Exchange (ETDEWEB)

    Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)

    2011-08-15

    Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.

  2. Percolator: Scalable Pattern Discovery in Dynamic Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Choudhury, Sutanay; Purohit, Sumit; Lin, Peng; Wu, Yinghui; Holder, Lawrence B.; Agarwal, Khushbu

    2018-02-06

    We demonstrate Percolator, a distributed system for graph pattern discovery in dynamic graphs. In contrast to conventional mining systems, Percolator advocates efficient pattern mining schemes that (1) support pattern detection with keywords; (2) integrate incremental and parallel pattern mining; and (3) support analytical queries such as trend analysis. The core idea of Percolator is to dynamically decide and verify a small fraction of patterns and their in- stances that must be inspected in response to buffered updates in dynamic graphs, with a total mining cost independent of graph size. We demonstrate a) the feasibility of incremental pattern mining by walking through each component of Percolator, b) the efficiency and scalability of Percolator over the sheer size of real-world dynamic graphs, and c) how the user-friendly GUI of Percolator inter- acts with users to support keyword-based queries that detect, browse and inspect trending patterns. We also demonstrate two user cases of Percolator, in social media trend analysis and academic collaboration analysis, respectively.

  3. Embedded graph invariants in Chern-Simons theory

    International Nuclear Information System (INIS)

    Major, Seth A.

    1999-01-01

    Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices

  4. Spectral Results on Some Hamiltonian Properties of Graphs

    Directory of Open Access Journals (Sweden)

    Rao Li

    2014-10-01

    Full Text Available Using Lotker’s interlacing theorem on the Laplacian eigenvalues of a graph in [5] and Wang and Belardo’s interlacing theorem on the signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian properties of graphs

  5. Graph Processing in Main-Memory Column Stores

    OpenAIRE

    Paradies, Marcus

    2017-01-01

    Evermore, novel and traditional business applications leverage the advantages of a graph data model, such as the offered schema flexibility and an explicit representation of relationships between entities. As a consequence, companies are confronted with the challenge of storing, manipulating, and querying terabytes of graph data for enterprise-critical applications. Although these business applications operate on graph-structured data, they still require direct access to the relational data a...

  6. Density conditions for triangles in multipartite graphs

    DEFF Research Database (Denmark)

    Bondy, Adrian; Shen, Jin; Thomassé, Stephan

    2006-01-01

    subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has...... a triangle, provided that the edge density between any two parts is greater than 1/2....

  7. PERANCANGAN SISTEM PENJADWALAN PEMBELAJARAN MENGGUNAKAN GRAPH COLORING

    Directory of Open Access Journals (Sweden)

    Taufik Hidayatulloh

    2016-03-01

    Full Text Available Abstract - In learning scheduling problem often faced by schools in the new academic year. Sometimes collisions on the schedule was not found when the learning process has begun, so it is necessary to re-schedule on the schedule. And this resulted in the teaching and learning first weeks less to run well. Researchers previously have used various methods to solve the scheduling as Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (coloring of a graph is the simplest method and the experimental results indicate that the development of methods of scheduling Graph Coloring deliver results that meet an average of 93% across the specified constraints. At the time of split schedules that require extra energy at the start of learning did not experience a collision. With this system is expected to facilitate the allocation of space, teachers, lessons to avoid a collision. Keywords: Information Systems, Scheduling, graph coloring Abstraksi - Dalam masalah penjadwalan pembelajaran sering dihadapi sekolah pada tahun ajaran baru. Terkadang tabrakan pada jadwal itu baru ditemukan ketika proses belajar mengajar telah dimulai, sehingga perlu dilakukan penjadwalan ulang pada jadwal tersebut. Dan hal ini mengakibatkan kegiatan belajar mengajar pada minggu-minggu pertama kurang dapat berjalan dengan baik. Para peneliti sebelumnya telah menggunakan berbagai metode untuk memecahkan penjadwalan seperti Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (pewarnaan graf merupakan metode yang paling sederhana dan hasil percobaan menunjukkan bahwa pengembangan metode Graph Coloring memberikan hasil penjadwalan yang memenuhi rata-rata 93% seluruh constraints yang ditentukan. Pada saat membagi jadwal memerlukan energi ekstra agar pada saat di mulai pembelajaran tidak mengalami tabrakan. Dengan sistem ini diharapkan dapat mempermudah dalam mengalokasikan ruangan, guru, pelajaran agar tidak mengalami tabrakan. Kata

  8. Further results on super graceful labeling of graphs

    Directory of Open Access Journals (Sweden)

    Gee-Choon Lau

    2016-08-01

    Full Text Available Let G=(V(G,E(G be a simple, finite and undirected graph of order p and size q. A bijection f:V(G∪E(G→{k,k+1,k+2,…,k+p+q−1} such that f(uv=|f(u−f(v| for every edge uv∈E(G is said to be a k-super graceful labeling of G. We say G is k-super graceful if it admits a k-super graceful labeling. For k=1, the function f is called a super graceful labeling and a graph is super graceful if it admits a super graceful labeling. In this paper, we study the super gracefulness of complete graph, the disjoint union of certain star graphs, the complete tripartite graphs K(1,1,n, and certain families of trees. We also present four methods of constructing new super graceful graphs. In particular, all trees of order at most 7 are super graceful. We conjecture that all trees are super graceful.

  9. Some results on square-free colorings of graphs

    DEFF Research Database (Denmark)

    Barat, Janos

    2004-01-01

    on the vertices or edges of a path. Conversely one can form sequences from a vertex or edge coloring of a graph in different ways. Thus there are several possibilities to generalize the square-free concept to graphs. Following Alon, Grytczuk, Haluszczak, Riordan and Bresar, Klavzar we study several so called...... square-free graph parameters, and answer some questions they posed. The main result is that the class of k-trees has bounded square-free vertex coloring parameter. Thus we can color the vertices of a k-tree using O(c^k) colors if c>6 such that the color sequence on any path is square......-free. It is conjectured that a similar phenomenon holds for planar graphs, so a finite number of colors are enough. We support this conjecture by showing that this number is at most 12 for outerplanar graphs. On the other hand we prove that some outerplanar graphs require at least 7 colors. Using this latter we construct...

  10. Declarative Event-Based Workflow as Distributed Dynamic Condition Response Graphs

    DEFF Research Database (Denmark)

    Hildebrandt, Thomas; Mukkamala, Raghava Rao

    2010-01-01

    We present Dynamic Condition Response Graphs (DCR Graphs) as a declarative, event-based process model inspired by the workflow language employed by our industrial partner and conservatively generalizing prime event structures. A dynamic condition response graph is a directed graph with nodes repr...... exemplify the use of distributed DCR Graphs on a simple workflow taken from a field study at a Danish hospital, pointing out their flexibility compared to imperative workflow models. Finally we provide a mapping from DCR Graphs to Buchi-automata....

  11. 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...... to include k=9 but we show that in every graph with circumference nine we can destroy all 9-cycles by removing 1/5 of the vertices. We consider the analogous problem for digraphs and show that for digraphs with circumference k=2,3, it suffices to remove 1/k of the vertices. However this does not hold for k≥4....

  12. External memory K-bisimulation reduction of big graphs

    NARCIS (Netherlands)

    Luo, Y.; Fletcher, G.H.L.; Hidders, A.J.H.; Wu, Y.; De Bra, P.M.E.

    2013-01-01

    In this paper, we present, to our knowledge, the first known I/O efficient solutions for computing the k-bisimulation partition of a massive directed graph, and performing maintenance of such a partition upon updates to the underlying graph. Ubiquitous in the theory and application of graph data,

  13. 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...

  14. Greenberger-Horne-Zeilinger paradoxes from qudit graph states.

    Science.gov (United States)

    Tang, Weidong; Yu, Sixia; Oh, C H

    2013-03-08

    One fascinating way of revealing quantum nonlocality is the all-versus-nothing test due to Greenberger, Horne, and Zeilinger (GHZ) known as the GHZ paradox. So far genuine multipartite and multilevel GHZ paradoxes are known to exist only in systems containing an odd number of particles. Here we shall construct GHZ paradoxes for an arbitrary number (greater than 3) of particles with the help of qudit graph states on a special kind of graphs, called GHZ graphs. Furthermore, based on the GHZ paradox arising from a GHZ graph, we derive a Bell inequality with two d-outcome observables for each observer, whose maximal violation attained by the corresponding graph state, and a Kochen-Specker inequality testing the quantum contextuality in a state-independent fashion.

  15. A Note on the PageRank of Undirected Graphs

    OpenAIRE

    Grolmusz, Vince

    2012-01-01

    The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the literature it is widely noted that the PageRank for undirected graphs are proportional to the degrees of the vertices of the graph. We prove that statement for a particular personalization vector in the definition of the PageRank, and we also show that in gene...

  16. 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...... of nodes. We introduce and study the betweenness oracle, where bet(a, m, z) is true iff m lies on a shortest path between a and z. This oracle is strictly weaker than a distance oracle, in the sense that a betweenness query can be simulated by a constant number of distance queries, but not vice versa...

  17. Graph theory and its applications

    CERN Document Server

    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.

  18. On the size of edge chromatic 5-critical graphs

    Directory of Open Access Journals (Sweden)

    K. Kayathri

    2017-04-01

    Full Text Available In this paper, we study the size of edge chromatic 5-critical graphs in several classes of 5-critical graphs. In most of the classes of 5-critical graphs in this paper, we have obtained their exact size and in the other classes of 5-critical graphs, we give new bounds on their number of major vertices and size.

  19. RetroTransformDB: A Dataset of Generic Transforms for Retrosynthetic Analysis

    Directory of Open Access Journals (Sweden)

    Svetlana Avramova

    2018-04-01

    Full Text Available Presently, software tools for retrosynthetic analysis are widely used by organic, medicinal, and computational chemists. Rule-based systems extensively use collections of retro-reactions (transforms. While there are many public datasets with reactions in synthetic direction (usually non-generic reactions, there are no publicly-available databases with generic reactions in computer-readable format which can be used for the purposes of retrosynthetic analysis. Here we present RetroTransformDB—a dataset of transforms, compiled and coded in SMIRKS line notation by us. The collection is comprised of more than 100 records, with each one including the reaction name, SMIRKS linear notation, the functional group to be obtained, and the transform type classification. All SMIRKS transforms were tested syntactically, semantically, and from a chemical point of view in different software platforms. The overall dataset design and the retrosynthetic fitness were analyzed and curated by organic chemistry experts. The RetroTransformDB dataset may be used by open-source and commercial software packages, as well as chemoinformatics tools.

  20. Efficient Algorithmic Frameworks via Structural Graph Theory

    Science.gov (United States)

    2016-10-28

    constant. For example, they measured that, on large samples of the entire network, the Amazon graph has average degree 17.7, the Facebook graph has average...department heads’ opinions of departments, and generally lack transparency and well-defined measures . On the other hand, the National Research Council (the...Efficient and practical resource block allocation for LTE -based D2D network via graph coloring. Wireless Networks 20(4): 611-624 (2014) 50. Hossein

  1. Spectral radius of graphs

    CERN Document Server

    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

  2. Do Graphs Promote Learning in Principles of Economics?

    Science.gov (United States)

    Cohn, Elchanan; Cohn, Sharon; Balch, Donald C.; Bradley, James, Jr.

    2001-01-01

    Tests the effects on student performance when using graphs as part of a University of South Carolina (Columbia) principles of economics lecture. Finds in 1995 that students in the lecture with graphs had significantly lower gain scores than those in the no-graphs lecture. Finds no significant difference in 1997. (RLH)

  3. How Symmetric Are Real-World Graphs? A Large-Scale Study

    Directory of Open Access Journals (Sweden)

    Fabian Ball

    2018-01-01

    Full Text Available The analysis of symmetry is a main principle in natural sciences, especially physics. For network sciences, for example, in social sciences, computer science and data science, only a few small-scale studies of the symmetry of complex real-world graphs exist. Graph symmetry is a topic rooted in mathematics and is not yet well-received and applied in practice. This article underlines the importance of analyzing symmetry by showing the existence of symmetry in real-world graphs. An analysis of over 1500 graph datasets from the meta-repository networkrepository.com is carried out and a normalized version of the “network redundancy” measure is presented. It quantifies graph symmetry in terms of the number of orbits of the symmetry group from zero (no symmetries to one (completely symmetric, and improves the recognition of asymmetric graphs. Over 70% of the analyzed graphs contain symmetries (i.e., graph automorphisms, independent of size and modularity. Therefore, we conclude that real-world graphs are likely to contain symmetries. This contribution is the first larger-scale study of symmetry in graphs and it shows the necessity of handling symmetry in data analysis: The existence of symmetries in graphs is the cause of two problems in graph clustering we are aware of, namely, the existence of multiple equivalent solutions with the same value of the clustering criterion and, secondly, the inability of all standard partition-comparison measures of cluster analysis to identify automorphic partitions as equivalent.

  4. 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.

  5. Quantum snake walk on graphs

    International Nuclear Information System (INIS)

    Rosmanis, Ansis

    2011-01-01

    I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.

  6. 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...

  7. A formal definition of data flow graph models

    Science.gov (United States)

    Kavi, Krishna M.; Buckles, Bill P.; Bhat, U. Narayan

    1986-01-01

    In this paper, a new model for parallel computations and parallel computer systems that is based on data flow principles is presented. Uninterpreted data flow graphs can be used to model computer systems including data driven and parallel processors. A data flow graph is defined to be a bipartite graph with actors and links as the two vertex classes. Actors can be considered similar to transitions in Petri nets, and links similar to places. The nondeterministic nature of uninterpreted data flow graphs necessitates the derivation of liveness conditions.

  8. On the partition dimension of two-component graphs

    Indian Academy of Sciences (India)

    D O Haryeni

    2017-11-17

    Nov 17, 2017 ... Partition dimension; disconnected graph; component. 2010 Mathematics Subject Classification. 05C12, 05C15. 1. Introduction. The study of the partition dimension for graphs was initiated by Chartrand et al. [2] aimed at finding a new way to solve the problem in metric dimensions of graphs. Many results.

  9. Distance matrices and quadratic embedding of graphs

    Directory of Open Access Journals (Sweden)

    Nobuaki Obata

    2018-04-01

    Full Text Available A connected graph is said to be of QE class if it admits  a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.

  10. Using Pathfinder networks to discover alignment between expert and consumer conceptual knowledge from online vaccine content.

    Science.gov (United States)

    Amith, Muhammad; Cunningham, Rachel; Savas, Lara S; Boom, Julie; Schvaneveldt, Roger; Tao, Cui; Cohen, Trevor

    2017-10-01

    This study demonstrates the use of distributed vector representations and Pathfinder Network Scaling (PFNETS) to represent online vaccine content created by health experts and by laypeople. By analyzing a target audience's conceptualization of a topic, domain experts can develop targeted interventions to improve the basic health knowledge of consumers. The underlying assumption is that the content created by different groups reflects the mental organization of their knowledge. Applying automated text analysis to this content may elucidate differences between the knowledge structures of laypeople (heath consumers) and professionals (health experts). This paper utilizes vaccine information generated by laypeople and health experts to investigate the utility of this approach. We used an established technique from cognitive psychology, Pathfinder Network Scaling to infer the structure of the associational networks between concepts learned from online content using methods of distributional semantics. In doing so, we extend the original application of PFNETS to infer knowledge structures from individual participants, to infer the prevailing knowledge structures within communities of content authors. The resulting graphs reveal opportunities for public health and vaccination education experts to improve communication and intervention efforts directed towards health consumers. Our efforts demonstrate the feasibility of using an automated procedure to examine the manifestation of conceptual models within large bodies of free text, revealing evidence of conflicting understanding of vaccine concepts among health consumers as compared with health experts. Additionally, this study provides insight into the differences between consumer and expert abstraction of domain knowledge, revealing vaccine-related knowledge gaps that suggest opportunities to improve provider-patient communication. Copyright © 2017 Elsevier Inc. All rights reserved.

  11. 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

  12. Supplantation of Mental Operations on Graphs

    Science.gov (United States)

    Vogel, Markus; Girwidz, Raimund; Engel, Joachim

    2007-01-01

    Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

  13. 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 ...

  14. Pixels to Graphs by Associative Embedding

    KAUST Repository

    Newell, Alejandro; Deng, Jia

    2017-01-01

    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

  15. On Longest Cycles in Essentially 4-Connected Planar Graphs

    Directory of Open Access Journals (Sweden)

    Fabrici Igor

    2016-08-01

    Full Text Available A planar 3-connected graph G is essentially 4-connected if, for any 3-separator S of G, one component of the graph obtained from G by removing S is a single vertex. Jackson and Wormald proved that an essentially 4-connected planar graph on n vertices contains a cycle C such that . For a cubic essentially 4-connected planar graph G, Grünbaum with Malkevitch, and Zhang showed that G has a cycle on at least ¾ n vertices. In the present paper the result of Jackson and Wormald is improved. Moreover, new lower bounds on the length of a longest cycle of G are presented if G is an essentially 4-connected planar graph of maximum degree 4 or G is an essentially 4-connected maximal planar graph.

  16. A graph model for opportunistic network coding

    KAUST Repository

    Sorour, Sameh

    2015-08-12

    © 2015 IEEE. Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase in complexity. In this paper, we design a simple IDNC-like graph model for a specific subclass of ONC, by introducing a more generalized definition of its vertices and the notion of vertex aggregation in order to represent the storage of non-instantly-decodable packets in ONC. Based on this representation, we determine the set of pairwise vertex adjacency conditions that can populate this graph with edges so as to guarantee decodability or aggregation for the vertices of each clique in this graph. We then develop the algorithmic procedures that can be applied on the designed graph model to optimize any performance metric for this ONC subclass. A case study on reducing the completion time shows that the proposed framework improves on the performance of IDNC and gets very close to the optimal performance.

  17. INTRA graphical package - INTRA-Graph 1.0

    International Nuclear Information System (INIS)

    Hofman, D.; Edlund, O.

    2001-04-01

    INTRA-Graph 1.0 has been developed at Studsvik Eco and Safety AB in the frame of the European Fusion Technology Programme for application in the safety analysis using the INTRA code. INTRA-Graph 1.0 is a graphical package producing 2-dimensional plots of results generated by the INTRA code. INTRA-Graph 1.0 has been developed by extending the Grace package source code, distributed under the terms of GNU General Public License. The changes in the Grace source files are limited to provide easy updates of the INTRA-Graph when a new version of Grace will be released. The INTRA-related functionality has been implemented in new source files. The present report describes and gives complete listing of these files. The changes in the Grace source files are also described and the listing of the changed parts of the files is presented. The report gives detailed explanations and examples of files required for installation and configuration of INTRA-Graph on the different types of Unix workstations

  18. Dynamic planar embeddings of dynamic graphs

    DEFF Research Database (Denmark)

    Holm, Jacob; Rotenberg, Eva

    2017-01-01

    query, one-flip- linkable(u,v) providing a suggestion for a flip that will make them linkable if one exists. We support all updates and queries in O(log 2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler......, 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...

  19. Quantum complexity of graph and algebraic problems

    International Nuclear Information System (INIS)

    Doern, Sebastian

    2008-01-01

    This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)

  20. Quantum complexity of graph and algebraic problems

    Energy Technology Data Exchange (ETDEWEB)

    Doern, Sebastian

    2008-02-04

    This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)