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...

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,.

Graph Theory Approach for Studying Food Webs

Science.gov (United States)

Longjas, A.; Tejedor, A.; Foufoula-Georgiou, E.

2017-12-01

Food webs are complex networks of feeding interactions among species in ecological communities. Metrics describing food web structure have been proposed to compare and classify food webs ranging from food chain length, connectance, degree distribution, centrality measures, to the presence of motifs (distinct compartments), among others. However, formal methodologies for studying both food web topology and the dynamic processes operating on them are still lacking. Here, we utilize a quantitative framework using graph theory within which a food web is represented by a directed graph, i.e., a collection of vertices (species or trophic species defined as sets of species sharing the same predators and prey) and directed edges (predation links). This framework allows us to identify apex (environmental "source" node) to outlet (top predators) subnetworks and compute the steady-state flux (e.g., carbon, nutrients, energy etc.) in the food web. We use this framework to (1) construct vulnerability maps that quantify the relative change of flux delivery to the top predators in response to perturbations in prey species (2) identify keystone species, whose loss would precipitate further species extinction, and (3) introduce a suite of graph-theoretic metrics to quantify the topologic (imposed by food web connectivity) and dynamic (dictated by the flux partitioning and distribution) components of a food web's complexity. By projecting food webs into a 2D Topodynamic Complexity Space whose coordinates are given by Number of alternative paths (topologic) and Leakage Index (dynamic), we show that this space provides a basis for food web comparison and provide physical insights into their dynamic behavior.

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

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...

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...

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

Semantic Mining based on graph theory and ontologies. Case Study: Cell Signaling Pathways

Directory of Open Access Journals (Sweden)

Carlos R. Rangel

2016-08-01

Full Text Available In this paper we use concepts from graph theory and cellular biology represented as ontologies, to carry out semantic mining tasks on signaling pathway networks. Specifically, the paper describes the semantic enrichment of signaling pathway networks. A cell signaling network describes the basic cellular activities and their interactions. The main contribution of this paper is in the signaling pathway research area, it proposes a new technique to analyze and understand how changes in these networks may affect the transmission and flow of information, which produce diseases such as cancer and diabetes. Our approach is based on three concepts from graph theory (modularity, clustering and centrality frequently used on social networks analysis. Our approach consists into two phases: the first uses the graph theory concepts to determine the cellular groups in the network, which we will call them communities; the second uses ontologies for the semantic enrichment of the cellular communities. The measures used from the graph theory allow us to determine the set of cells that are close (for example, in a disease, and the main cells in each community. We analyze our approach in two cases: TGF-ß and the Alzheimer Disease.

Graph theory

CERN Document Server

Gould, Ronald

2012-01-01

This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S

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

The $K$-theory of real graph $C*$-algebras

OpenAIRE

Boersema, Jeffrey L.

2014-01-01

In this paper, we will introduce real graph algebras and develop the theory to the point of being able to calculate the $K$-theory of such algebras. The $K$-theory situation is significantly more complicated than in the case for complex graph algebras. To develop the long exact sequence to compute the $K$-theory of a real graph algebra, we need to develop a generalized theory of crossed products for real C*-algebras for groups with involution. We also need to deal with the additional algebrai...

Mechanical system reliability analysis using a combination of graph theory and Boolean function

International Nuclear Information System (INIS)

Tang, J.

2001-01-01

A new method based on graph theory and Boolean function for assessing reliability of mechanical systems is proposed. The procedure for this approach consists of two parts. By using the graph theory, the formula for the reliability of a mechanical system that considers the interrelations of subsystems or components is generated. Use of the Boolean function to examine the failure interactions of two particular elements of the system, followed with demonstrations of how to incorporate such failure dependencies into the analysis of larger systems, a constructive algorithm for quantifying the genuine interconnections between the subsystems or components is provided. The combination of graph theory and Boolean function provides an effective way to evaluate the reliability of a large, complex mechanical system. A numerical example demonstrates that this method an effective approaches in system reliability analysis

The Epstein-Glaser approach to perturbative quantum field theory: graphs and Hopf algebras

International Nuclear Information System (INIS)

Lange, Alexander

2005-01-01

The paper aims at investigating perturbative quantum field theory in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudounitarity, causal regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on operator-valued distributions equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the corresponding physical framework, covering the two EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occurring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the context of EG is modeled via a HA and interpreted as the EG analog of Kreimer's HA

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.

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.

Graph theory for alternating hydrocarbons with attached ports

NARCIS (Netherlands)

Hesselink, Wim H.

Properties of molecules of certain hydrocarbons give rise to difficult questions in graph theory. This paper is primarily devoted to the graph theory, but the physico-chemical motivation, which is somewhat speculative, is also presented. Molecules of unsaturated hydrocarbons exhibit alternating

Graph-based linear scaling electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.; Swart, Pieter J.; Germann, Timothy C.; Bock, Nicolas [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mniszewski, Susan M.; Mohd-Yusof, Jamal; Wall, Michael E.; Djidjev, Hristo [Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Rubensson, Emanuel H. [Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala (Sweden)

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Graphs on Surfaces and the Partition Function of String Theory

OpenAIRE

Garcia-Islas, J. Manuel

2007-01-01

Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the relation between graph theory and the mathematical physics of discrete string theory. In this description we present problems of the combinatorial world of real importance for graph theorists. The mathematical details of the paper are as follows: There is a com...

Introduction to graph theory

CERN Document Server

Wilson, Robin J

1985-01-01

Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.

On some interconnections between combinatorial optimization and extremal graph theory

Directory of Open Access Journals (Sweden)

Cvetković Dragoš M.

2004-01-01

Full Text Available The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.

A first course in graph theory and combinatorics

CERN Document Server

Cioabă, Sebastian M

2009-01-01

The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.

A Graph Theory Approach for Geovisualization of Anthropogenic Land Use Change: An application to Lisbon

Directory of Open Access Journals (Sweden)

Eric Vaz

2013-12-01

Full Text Available Urban sprawl and growth has experienced increased concern in geographic and environmental literature. Preceding the existence of robust frameworks found in regional and urban planning, as well as urban geography and economics, the spatial properties of allocation of urban land use are still far from being completely understood. This is largely due to the underlying complexity of the change found at the spatial level of urban land use, merging social, economic and natural drivers. The spatial patterns formed, and the connectivity established among the different subsets of land-use types, becomes a complex network of interactions over time, helping to shape the structure of the city. The possibility to merge the configuration of land-use with complex networks may be assessed elegantly through graph theory. Nodes and edges can become abstract representations of typologies of space and are represented into a topological space of different land use types which traditionally share common spatial boundaries. Within a regional framework, the links between adjacent and neighboring urban land use types become better understood, by means of a KamadaKawai algorithm. This study uses land use in Lisbon over three years, 1990, 2000 and 2006, to develop a Kamada-Kawai graph interpretation of land-use as a result of neighboring power. The rapid change witnessed in Lisbon since the nineties, as well as the availability of CORINE Land Cover data in these three time stamps, permits a reflection on anthropogenic land-use change in urban and semi-urban areas in Portugal’s capital. This paper responds to (1 the structure and connectivity of urban land use over time, demonstrating that most of the agricultural land is stressed to transform to urban, gaining a central role in future. (2 Offer a systemic approach to land-use transitions generating what we call spatial memory, where land use change is often unpredictable over space, but becomes evident in a graph theory

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.

GRAPH THEORY APPROACH TO QUANTIFY UNCERTAINTY OF PERFORMANCE MEASURES

Directory of Open Access Journals (Sweden)

Sérgio D. Sousa

2015-03-01

Full Text Available In this work, the performance measurement process is studied to quantify the uncertainty induced in the resulting performance measure (PM. To that end, the causes of uncertainty are identified, analysing the activities undertaken in the three following stages of the performance measurement process: design and implementation, data collection and record, and determination and analysis. A quantitative methodology based on graph theory and on the sources of uncertainty of the performance measurement process is used to calculate an uncertainty index to evaluate the level of uncertainty of a given PM or (key performance indicator. An application example is presented. The quantification of PM uncertainty could contribute to better represent the risk associated with a given decision and also to improve the PM to increase its precision and reliability.

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

Applying Graph Theory to Problems in Air Traffic Management

Science.gov (United States)

Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

A Qualitative Analysis Framework Using Natural Language Processing and Graph Theory

Science.gov (United States)

Tierney, Patrick J.

2012-01-01

This paper introduces a method of extending natural language-based processing of qualitative data analysis with the use of a very quantitative tool--graph theory. It is not an attempt to convert qualitative research to a positivist approach with a mathematical black box, nor is it a "graphical solution". Rather, it is a method to help qualitative…

GCPSO in cooperation with graph theory to distribution network reconfiguration for energy saving

International Nuclear Information System (INIS)

Assadian, Mehdi; Farsangi, Malihe M.; Nezamabadi-pour, Hossein

2010-01-01

Network reconfiguration for loss reduction in distribution system is an important way to save energy. This paper investigates the ability of guaranteed convergence particle swarm optimization (GCPSO) and particle swarm optimization (PSO) in cooperation with graph theory for network reconfiguration to reduce the power loss and enhancement of voltage profile of distribution systems. Numerical results of three distribution systems are presented which illustrate the feasibility of the proposed method by GCPSO and PSO using the graph theory. To validate the obtained results, genetic algorithm (GA) using graph theory is also applied and is compared with the proposed GCPSO and PSO using graph theory.

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

Graph Theory in Paris : Conference in Memory of Claude Berge

CERN Document Server

Fonlupt, Jean; Fouquet, Jean-Luc; Fournier, Jean-Claude; Alfonsín, Jorge

2007-01-01

In July 2004, a conference on graph theory was held in Paris in memory of Claude Berge, one of the pioneers of the field. The event brought together many prominent specialists on topics, such as perfect graphs and matching theory, upon which Claude Berge's work has had a major impact. This volume includes contributions to these and other topics from many of the participants.

Some Results on the Graph Theory for Complex Neutrosophic Sets

Directory of Open Access Journals (Sweden)

Shio Gai Quek

2018-05-01

Full Text Available Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1. We then present a matrix representation for it and study some properties of this new concept. The concept of CNG1 is an extension of the generalized fuzzy graphs of type 1 (GFG1 and generalized single-valued neutrosophic graphs of type 1 (GSVNG1. The utility of the CNG1 introduced here are applied to a multi-attribute decision making problem related to Internet server selection.

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.

Algebraic Graph Theory Morphisms, Monoids and Matrices

CERN Document Server

Knauer, Ulrich

2011-01-01

This is a highly self-contained book about algebraic graph theory which iswritten with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures -like roads, computers, telephones -instances of abstract data structures -likelists, stacks, trees -and functional or object orient

Multiscale connectivity and graph theory highlight critical areas for conservation under climate change.

Science.gov (United States)

Dilt, Thomas E; Weisberg, Peter J; Leitner, Philip; Matocq, Marjorie D; Inman, Richard D; Nussear, Kenneth E; Esque, Todd C

2016-06-01

Conservation planning and biodiversity management require information on landscape connectivity across a range of spatial scales from individual home ranges to large regions. Reduction in landscape connectivity due changes in land use or development is expected to act synergistically with alterations to habitat mosaic configuration arising from climate change. We illustrate a multiscale connectivity framework to aid habitat conservation prioritization in the context of changing land use and climate. Our approach, which builds upon the strengths of multiple landscape connectivity methods, including graph theory, circuit theory, and least-cost path analysis, is here applied to the conservation planning requirements of the Mohave ground squirrel. The distribution of this threatened Californian species, as for numerous other desert species, overlaps with the proposed placement of several utility-scale renewable energy developments in the American southwest. Our approach uses information derived at three spatial scales to forecast potential changes in habitat connectivity under various scenarios of energy development and climate change. By disentangling the potential effects of habitat loss and fragmentation across multiple scales, we identify priority conservation areas for both core habitat and critical corridor or stepping stone habitats. This approach is a first step toward applying graph theory to analyze habitat connectivity for species with continuously distributed habitat and should be applicable across a broad range of taxa.

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...

A graph-theory framework for evaluating landscape connectivity and conservation planning.

Science.gov (United States)

Minor, Emily S; Urban, Dean L

2008-04-01

Connectivity of habitat patches is thought to be important for movement of genes, individuals, populations, and species over multiple temporal and spatial scales. We used graph theory to characterize multiple aspects of landscape connectivity in a habitat network in the North Carolina Piedmont (U.S.A). We compared this landscape with simulated networks with known topology, resistance to disturbance, and rate of movement. We introduced graph measures such as compartmentalization and clustering, which can be used to identify locations on the landscape that may be especially resilient to human development or areas that may be most suitable for conservation. Our analyses indicated that for songbirds the Piedmont habitat network was well connected. Furthermore, the habitat network had commonalities with planar networks, which exhibit slow movement, and scale-free networks, which are resistant to random disturbances. These results suggest that connectivity in the habitat network was high enough to prevent the negative consequences of isolation but not so high as to allow rapid spread of disease. Our graph-theory framework provided insight into regional and emergent global network properties in an intuitive and visual way and allowed us to make inferences about rates and paths of species movements and vulnerability to disturbance. This approach can be applied easily to assessing habitat connectivity in any fragmented or patchy landscape.

Using Zipf-Mandelbrot law and graph theory to evaluate animal welfare

Science.gov (United States)

de Oliveira, Caprice G. L.; Miranda, José G. V.; Japyassú, Hilton F.; El-Hani, Charbel N.

2018-02-01

This work deals with the construction and testing of metrics of welfare based on behavioral complexity, using assumptions derived from Zipf-Mandelbrot law and graph theory. To test these metrics we compared yellow-breasted capuchins (Sapajus xanthosternos) (Wied-Neuwied, 1826) (PRIMATES CEBIDAE) found in two institutions, subjected to different captive conditions: a Zoobotanical Garden (hereafter, ZOO; n = 14), in good welfare condition, and a Wildlife Rescue Center (hereafter, WRC; n = 8), in poor welfare condition. In the Zipf-Mandelbrot-based analysis, the power law exponent was calculated using behavior frequency values versus behavior rank value. These values allow us to evaluate variations in individual behavioral complexity. For each individual we also constructed a graph using the sequence of behavioral units displayed in each recording (average recording time per individual: 4 h 26 min in the ZOO, 4 h 30 min in the WRC). Then, we calculated the values of the main graph attributes, which allowed us to analyze the complexity of the connectivity of the behaviors displayed in the individuals' behavioral sequences. We found significant differences between the two groups for the slope values in the Zipf-Mandelbrot analysis. The slope values for the ZOO individuals approached -1, with graphs representing a power law, while the values for the WRC individuals diverged from -1, differing from a power law pattern. Likewise, we found significant differences for the graph attributes average degree, weighted average degree, and clustering coefficient when comparing the ZOO and WRC individual graphs. However, no significant difference was found for the attributes modularity and average path length. Both analyses were effective in detecting differences between the patterns of behavioral complexity in the two groups. The slope values for the ZOO individuals indicated a higher behavioral complexity when compared to the WRC individuals. Similarly, graph construction and the

Vertex maps on graphs -- Perron-Frobenius Theory

OpenAIRE

Bernhardt, Chris

2015-01-01

The goal of this paper is to describe the connections between Perron-Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron-Frobenius theory gives results about the sets of integers that can arise as periods of periodic orbits, about the concepts of transitivity and topological mixing, and about horseshoes and topological entropy. This is a preprint. The final version will appear in the Journal of Difference Equations and Applications.

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.

Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions

Science.gov (United States)

Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

2018-04-01

In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute

Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions.

Science.gov (United States)

Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

2018-04-20

In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute

Support vector machine classification of major depressive disorder using diffusion-weighted neuroimaging and graph theory.

Science.gov (United States)

Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H

2015-01-01

Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on "support vector machines" to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.

Comparing brain networks of different size and connectivity density using graph theory.

Directory of Open Access Journals (Sweden)

Bernadette C M van Wijk

Full Text Available Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N and the average degree (k of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring non-significant (significant connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

Multi-scale connectivity and graph theory highlight critical areas for conservation under climate change

Science.gov (United States)

Dilts, Thomas E.; Weisberg, Peter J.; Leitner, Phillip; Matocq, Marjorie D.; Inman, Richard D.; Nussear, Ken E.; Esque, Todd C.

2016-01-01

Conservation planning and biodiversity management require information on landscape connectivity across a range of spatial scales from individual home ranges to large regions. Reduction in landscape connectivity due changes in land-use or development is expected to act synergistically with alterations to habitat mosaic configuration arising from climate change. We illustrate a multi-scale connectivity framework to aid habitat conservation prioritization in the context of changing land use and climate. Our approach, which builds upon the strengths of multiple landscape connectivity methods including graph theory, circuit theory and least-cost path analysis, is here applied to the conservation planning requirements of the Mohave ground squirrel. The distribution of this California threatened species, as for numerous other desert species, overlaps with the proposed placement of several utility-scale renewable energy developments in the American Southwest. Our approach uses information derived at three spatial scales to forecast potential changes in habitat connectivity under various scenarios of energy development and climate change. By disentangling the potential effects of habitat loss and fragmentation across multiple scales, we identify priority conservation areas for both core habitat and critical corridor or stepping stone habitats. This approach is a first step toward applying graph theory to analyze habitat connectivity for species with continuously-distributed habitat, and should be applicable across a broad range of taxa.

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.

Identifying patients with Alzheimer's disease using resting-state fMRI and graph theory.

Science.gov (United States)

Khazaee, Ali; Ebrahimzadeh, Ata; Babajani-Feremi, Abbas

2015-11-01

Study of brain network on the basis of resting-state functional magnetic resonance imaging (fMRI) has provided promising results to investigate changes in connectivity among different brain regions because of diseases. Graph theory can efficiently characterize different aspects of the brain network by calculating measures of integration and segregation. In this study, we combine graph theoretical approaches with advanced machine learning methods to study functional brain network alteration in patients with Alzheimer's disease (AD). Support vector machine (SVM) was used to explore the ability of graph measures in diagnosis of AD. We applied our method on the resting-state fMRI data of twenty patients with AD and twenty age and gender matched healthy subjects. The data were preprocessed and each subject's graph was constructed by parcellation of the whole brain into 90 distinct regions using the automated anatomical labeling (AAL) atlas. The graph measures were then calculated and used as the discriminating features. Extracted network-based features were fed to different feature selection algorithms to choose most significant features. In addition to the machine learning approach, statistical analysis was performed on connectivity matrices to find altered connectivity patterns in patients with AD. Using the selected features, we were able to accurately classify patients with AD from healthy subjects with accuracy of 100%. Results of this study show that pattern recognition and graph of brain network, on the basis of the resting state fMRI data, can efficiently assist in the diagnosis of AD. Classification based on the resting-state fMRI can be used as a non-invasive and automatic tool to diagnosis of Alzheimer's disease. Copyright © 2015 International Federation of Clinical Neurophysiology. All rights reserved.

Hadronic equation of state in the statistical bootstrap model and linear graph theory

International Nuclear Information System (INIS)

Fre, P.; Page, R.

1976-01-01

Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed

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.

Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

Science.gov (United States)

Bradlyn, Barry; Elcoro, L.; Vergniory, M. G.; Cano, Jennifer; Wang, Zhijun; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei

2018-01-01

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k .p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

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

In cultivated landscapes, a lot of landscape elements such as field boundaries, ditches or banks strongly impact water flows, mass and energy fluxes. At the watershed scale, these impacts are strongly conditionned by the connectivity of these landscape elements. An accurate representation of these elements and of their complex spatial arrangements is therefore of great importance for modelling and predicting these impacts.We developped in the framework of the OpenFLUID platform (Software Environment for Modelling Fluxes in Landscapes) a digital landscape representation that takes into account the spatial variabilities and connectivities of diverse landscape elements through the application of the graph theory concepts. The proposed landscape representation consider spatial units connected together to represent the flux exchanges or any other information exchanges. Each spatial unit of the landscape is represented as a node of a graph and relations between units as graph connections. The connections are of two types - parent-child connection and up/downstream connection - which allows OpenFLUID to handle hierarchical graphs. Connections can also carry informations and graph evolution during simulation is possible (connections or elements modifications). This graph approach allows a better genericity on landscape representation, a management of complex connections and facilitate development of new landscape representation algorithms. Graph management is fully operational in OpenFLUID for developers or modelers ; and several graph tools are available such as graph traversal algorithms or graph displays. Graph representation can be managed i) manually by the user (for example in simple catchments) through XML-based files in easily editable and readable format or ii) by using methods of the OpenFLUID-landr library which is an OpenFLUID library relying on common open-source spatial libraries (ogr vector, geos topologic vector and gdal raster libraries). Open

A Multi-Level Middle-Out Cross-Zooming Approach for Large Graph Analytics

Energy Technology Data Exchange (ETDEWEB)

Wong, Pak C.; Mackey, Patrick S.; Cook, Kristin A.; Rohrer, Randall M.; Foote, Harlan P.; Whiting, Mark A.

2009-10-11

This paper presents a working graph analytics model that embraces the strengths of the traditional top-down and bottom-up approaches with a resilient crossover concept to exploit the vast middle-ground information overlooked by the two extreme analytical approaches. Our graph analytics model is developed in collaboration with researchers and users, who carefully studied the functional requirements that reflect the critical thinking and interaction pattern of a real-life intelligence analyst. To evaluate the model, we implement a system prototype, known as GreenHornet, which allows our analysts to test the theory in practice, identify the technological and usage-related gaps in the model, and then adapt the new technology in their work space. The paper describes the implementation of GreenHornet and compares its strengths and weaknesses against the other prevailing models and tools.

Support vector machine classification of Major Depressive Disorder using diffusion-weighted neuroimaging and graph theory

Directory of Open Access Journals (Sweden)

Matthew D Sacchet

2015-02-01

Full Text Available Recently there has been considerable interest in understanding brain networks in Major Depressive Disorder (MDD. Neural pathways can be tracked in the living brain using diffusion weighted imaging (DWI; graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on ‘support vector machines’ to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and co-morbidities.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

Science.gov (United States)

Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing

2015-07-01

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Graph theory favorite conjectures and open problems 1

CERN Document Server

Hedetniemi, Stephen; Larson, Craig

2016-01-01

This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In...

Modeling of tethered satellite formations using graph theory

DEFF Research Database (Denmark)

Larsen, Martin Birkelund; Smith, Roy S; Blanke, Mogens

2011-01-01

satellite formation and proposes a method to deduce the equations of motion for the attitude dynamics of the formation in a compact form. The use of graph theory and Lagrange mechanics together allows a broad class of formations to be described using the same framework. A method is stated for finding...

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

Graph-theoretic approach to quantum correlations.

Science.gov (United States)

Cabello, Adán; Severini, Simone; Winter, Andreas

2014-01-31

Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.

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...

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...

A Hybrid Approach to Processing Big Data Graphs on Memory-Restricted Systems

KAUST Repository

Harshvardhan,

2015-05-01

With the advent of big-data, processing large graphs quickly has become increasingly important. Most existing approaches either utilize in-memory processing techniques that can only process graphs that fit completely in RAM, or disk-based techniques that sacrifice performance. In this work, we propose a novel RAM-Disk hybrid approach to graph processing that can scale well from a single shared-memory node to large distributed-memory systems. It works by partitioning the graph into sub graphs that fit in RAM and uses a paging-like technique to load sub graphs. We show that without modifying the algorithms, this approach can scale from small memory-constrained systems (such as tablets) to large-scale distributed machines with 16, 000+ cores.

Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory

Directory of Open Access Journals (Sweden)

Karolina Taczanowska

2017-12-01

Full Text Available Mountain protected areas (PAs aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an approach to evaluate the structure and use of designated skiing zones in PAs combining Global Positioning System (GPS tracking and analytical methods based on graph theory. The study is based on empirical data (n = 609 GPS tracks of backcountry skiers collected in Tatra National Park (TNP, Poland. The physical structure of the entire skiing zones system has been simplified into a graph structure (structural network; undirected graph. In a second step, the actual use of the area by skiers (functional network; directed graph was analyzed using a graph-theoretic approach. Network coherence (connectivity indices: β, γ, α, movement directions at path segments, and relative importance of network nodes (node centrality measures: degree, betweenness, closeness, and proximity prestige were calculated. The system of designated backcountry skiing zones was not evenly used by the visitors. Therefore, the calculated parameters differ significantly between the structural and the functional network. In particular, measures related to the actually used trails are of high importance from the management point of view. Information about the most important node locations can be used for planning sign-posts, on-site maps, interpretative boards, or other tourist infrastructure.

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.

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.

Graph theory and binary alloys passivated by nickel

International Nuclear Information System (INIS)

McCafferty, E.

2005-01-01

The passivity of a nickel binary alloy is considered in terms of a network of -Ni-O-Ni- bridges in the oxide film, where Ni is the component of the binary alloy which produces passivity. The structure of the oxide is represented by a mathematical graph, and graph theory is used to calculate the connectivity of the oxide, given by the product of the number of edges in the graph and the Randic index. A stochastic calculation is employed to insert ions of the second metal into the oxide film so as to disrupt the connectivity of the -Ni-O-Ni- network. This disruption occurs at a critical ionic concentration of the oxide film. Mathematical relationships are developed for the introduction of a general ion B +n into the oxide film, and critical ionic compositions are calculated for oxide films on the nickel binary alloys. The notation B refers to any metal B which produces B +n ions in the oxide film, where +n is the oxidation number of the ion. The results of this analysis for Fe-Ni and Cu-Ni binary alloys are in good agreement with experimental results

Simulating activation propagation in social networks using the graph theory

Directory of Open Access Journals (Sweden)

František Dařena

2010-01-01

Full Text Available The social-network formation and analysis is nowadays one of objects that are in a focus of intensive research. The objective of the paper is to suggest the perspective of representing social networks as graphs, with the application of the graph theory to problems connected with studying the network-like structures and to study spreading activation algorithm for reasons of analyzing these structures. The paper presents the process of modeling multidimensional networks by means of directed graphs with several characteristics. The paper also demonstrates using Spreading Activation algorithm as a good method for analyzing multidimensional network with the main focus on recommender systems. The experiments showed that the choice of parameters of the algorithm is crucial, that some kind of constraint should be included and that the algorithm is able to provide a stable environment for simulations with networks.

Quantum entanglement in non-local games, graph parameters and zero-error information theory

NARCIS (Netherlands)

Scarpa, G.

2013-01-01

We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory. In Chapter 2 we address the question of how much quantum correlations generated by entanglement can

Identification Of The Epileptogenic Zone From Stereo-EEG Signals: A Connectivity-Graph Theory Approach

Directory of Open Access Journals (Sweden)

Ferruccio ePanzica

2013-11-01

Full Text Available In the context of focal drug-resistant epilepsies, the surgical resection of the epileptogenic zone (EZ, the cortical region responsible for the onset, early seizures organization and propagation, may be the only therapeutic option for reducing or suppressing seizures. The rather high rate of failure in epilepsy surgery of extra-temporal epilepsies highlights that the precise identification of the EZ, mandatory objective to achieve seizure freedom, is still an unsolved problem that requires more sophisticated methods of investigation.Despite the wide range of non-invasive investigations, intracranial stereo-EEG (SEEG recordings still represent, in many patients, the gold standard for the EZ identification. In this contest, the EZ localization is still based on visual analysis of SEEG, inevitably affected by the drawback of subjectivity and strongly time-consuming. Over the last years, considerable efforts have been made to develop advanced signal analysis techniques able to improve the identification of the EZ. Particular attention has been paid to those methods aimed at quantifying and characterising the interactions and causal relationships between neuronal populations, since is nowadays well assumed that epileptic phenomena are associated with abnormal changes in brain synchronisation mechanisms, and initial evidence has shown the suitability of this approach for the EZ localisation. The aim of this review is to provide an overview of the different EEG signal processing methods applied to study connectivity between distinct brain cortical regions, namely in focal epilepsies. In addition, with the aim of localizing the EZ, the approach based on graph theory will be described, since the study of the topological properties of the networks has strongly improved the study of brain connectivity mechanisms.

A Graph-Based Approach for 3D Building Model Reconstruction from Airborne LiDAR Point Clouds

Directory of Open Access Journals (Sweden)

Bin Wu

2017-01-01

Full Text Available 3D building model reconstruction is of great importance for environmental and urban applications. Airborne light detection and ranging (LiDAR is a very useful data source for acquiring detailed geometric and topological information of building objects. In this study, we employed a graph-based method based on hierarchical structure analysis of building contours derived from LiDAR data to reconstruct urban building models. The proposed approach first uses a graph theory-based localized contour tree method to represent the topological structure of buildings, then separates the buildings into different parts by analyzing their topological relationships, and finally reconstructs the building model by integrating all the individual models established through the bipartite graph matching process. Our approach provides a more complete topological and geometrical description of building contours than existing approaches. We evaluated the proposed method by applying it to the Lujiazui region in Shanghai, China, a complex and large urban scene with various types of buildings. The results revealed that complex buildings could be reconstructed successfully with a mean modeling error of 0.32 m. Our proposed method offers a promising solution for 3D building model reconstruction from airborne LiDAR point clouds.

A hierarchical approach to reducing communication in parallel graph algorithms

KAUST Repository

Harshvardhan,

2015-01-01

Large-scale graph computing has become critical due to the ever-increasing size of data. However, distributed graph computations are limited in their scalability and performance due to the heavy communication inherent in such computations. This is exacerbated in scale-free networks, such as social and web graphs, which contain hub vertices that have large degrees and therefore send a large number of messages over the network. Furthermore, many graph algorithms and computations send the same data to each of the neighbors of a vertex. Our proposed approach recognizes this, and reduces communication performed by the algorithm without change to user-code, through a hierarchical machine model imposed upon the input graph. The hierarchical model takes advantage of locale information of the neighboring vertices to reduce communication, both in message volume and total number of bytes sent. It is also able to better exploit the machine hierarchy to further reduce the communication costs, by aggregating traffic between different levels of the machine hierarchy. Results of an implementation in the STAPL GL shows improved scalability and performance over the traditional level-synchronous approach, with 2.5 × - 8× improvement for a variety of graph algorithms at 12, 000+ cores.

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.

Geographic information modeling of Econet of Northwestern Federal District territory on graph theory basis

Science.gov (United States)

Kopylova, N. S.; Bykova, A. A.; Beregovoy, D. N.

2018-05-01

Based on the landscape-geographical approach, a structural and logical scheme for the Northwestern Federal District Econet has been developed, which can be integrated into the federal and world ecological network in order to improve the environmental infrastructure of the region. The method of Northwestern Federal District Econet organization on the basis of graph theory by means of the Quantum GIS geographic information system is proposed as an effective mean of preserving and recreating the unique biodiversity of landscapes, regulation of the sphere of environmental protection.

PROBLEMS IN TOPOLOGICAL GRAPH THEORY : QUESTIONS I CAN'T ANSWER

OpenAIRE

Archdeacon, Dan

1999-01-01

This paper describes my Problems in Topological Graph Theory, which can be accessed through the world-wide-web at http: //www.emba .uvm.edu/~arcceack/problems/problems.html This list of problems is constantly being revised; the interested reader is encouraged to submit additions and updates.

Utilization of graph theory in security analysis of power grid

Directory of Open Access Journals (Sweden)

Dalibor Válek

2014-12-01

Full Text Available This paper describes way how to use graph theory in security analysis. As an environment is used network of power lines and devices which are included here. Power grid is considered as a system of nodes which make together graph (network. On the simple example is applied Fiedler´s theory which is able to select the most important power lines of whole network. Components related to these lines are logicly ordered and considered by author´s modified analysis. This method has been improved and optimalized for risks related with illegal acts. Each power grid component has been connected with possible kind of attack and every of this device was gradually evaluated by five coefficients which takes values from 1 to 10. On the coefficient basis was assessed the level of risk. In the last phase the most risky power grid components have been selected. On the selected devices have been proposed security measures.

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...

Detectable states, cycle fluxes, and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis

Science.gov (United States)

Ren, Jie

2017-12-01

The process by which a kinesin motor couples its ATPase activity with concerted mechanical hand-over-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.

Modal Analysis of In-Wheel Motor-Driven Electric Vehicle Based on Bond Graph Theory

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Di Tan

2017-01-01

Full Text Available A half-car vibration model of an electric vehicle driven by rear in-wheel motors was developed using bond graph theory and the modular modeling method. Based on the bond graph model, modal analysis was carried out to study the vibration characteristics of the electric vehicle. To verify the effectiveness of the established model, the results were compared to ones computed on the ground of modal analysis and Newton equations. The comparison shows that the vibration model of the electric vehicle based on bond graph theory not only is able to better compute the natural frequency but also can easily determine the deformation mode, momentum mode, and other isomorphism modes and describe the dynamic characteristics of an electric vehicle driven by in-wheel motors more comprehensively than other modal analysis methods.

A Brief Historical Introduction to Euler's Formula for Polyhedra, Topology, Graph Theory and Networks

Science.gov (United States)

Debnath, Lokenath

2010-01-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…

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.)

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.

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.

Coupling graph perturbation theory with scalable parallel algorithms for large-scale enumeration of maximal cliques in biological graphs

International Nuclear Information System (INIS)

Samatova, N F; Schmidt, M C; Hendrix, W; Breimyer, P; Thomas, K; Park, B-H

2008-01-01

Data-driven construction of predictive models for biological systems faces challenges from data intensity, uncertainty, and computational complexity. Data-driven model inference is often considered a combinatorial graph problem where an enumeration of all feasible models is sought. The data-intensive and the NP-hard nature of such problems, however, challenges existing methods to meet the required scale of data size and uncertainty, even on modern supercomputers. Maximal clique enumeration (MCE) in a graph derived from such biological data is often a rate-limiting step in detecting protein complexes in protein interaction data, finding clusters of co-expressed genes in microarray data, or identifying clusters of orthologous genes in protein sequence data. We report two key advances that address this challenge. We designed and implemented the first (to the best of our knowledge) parallel MCE algorithm that scales linearly on thousands of processors running MCE on real-world biological networks with thousands and hundreds of thousands of vertices. In addition, we proposed and developed the Graph Perturbation Theory (GPT) that establishes a foundation for efficiently solving the MCE problem in perturbed graphs, which model the uncertainty in the data. GPT formulates necessary and sufficient conditions for detecting the differences between the sets of maximal cliques in the original and perturbed graphs and reduces the enumeration time by more than 80% compared to complete recomputation

ARTICLE Robust Diagnosis of Mechatronics System by Bond Graph Approach

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Abderrahmene Sellami

2018-03-01

Full Text Available This article presents design of a robust diagnostic system based on bond graph model for a mechatronic system. Mechatronics is the synergistic and systemic combination of mechanics, electronics and computer science. The design of a mechatronic system modeled by the bond graph model becomes easier and more generous. The bond graph tool is a unified graphical language for all areas of engineering sciences and confirmed as a structured approach to modeling and simulation of multidisciplinary systems.

A Hybrid Approach to Processing Big Data Graphs on Memory-Restricted Systems

KAUST Repository

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

2015-01-01

that sacrifice performance. In this work, we propose a novel RAM-Disk hybrid approach to graph processing that can scale well from a single shared-memory node to large distributed-memory systems. It works by partitioning the graph into sub graphs that fit in RAM

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

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.

Discrete Mathematics - Special Issue: Graph Theory - dedicated to Carsten Thomassen on his 60th birthday

DEFF Research Database (Denmark)

2011-01-01

Carsten Thomassen belongs to the worlds's absolute top graph theorists, and to the world's top mathematicians in general. The special issue is a rather somewhat random collection of good papers in graph theory, by many different authors, dedicated to Carsten Thomassen on his 60th birthday. Guest ...

Feynman graphs and gauge theories for experimental physicists. 2. rev. ed.

International Nuclear Information System (INIS)

Schmueser, P.

1995-01-01

This book is an introduction to the foundations of quantum field theory with special regards to gauge theory. After a general introduction to relativistic wave equations the concept of Feynman graphs is introduced. Then after an introduction to the phenomenology of weak interactions and the principle of gauge invariance the standard model of the electroweak interaction is presented. Finally quantum chromodynamics is described. Every chapter contains exercise problems. (HSI)

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. .

Routing Planning As An Application Of Graph Theory with Fuzzy Logic

Directory of Open Access Journals (Sweden)

Tomasz Neumann

2016-12-01

Full Text Available The routing planning one of the classic problems in graph theory. Its application have various practical uses ranging from the transportation, civil engineering and other applications. The resolution of this paper is to find a solution for route planning in a transport networks, where the description of tracks, factor of safety and travel time are ambiguous. In the study the ranking system based on the theory of possibility is proposed.

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...

Connections between the Sznajd model with general confidence rules and graph theory

Science.gov (United States)

Timpanaro, André M.; Prado, Carmen P. C.

2012-10-01

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Engineering system dynamics a unified graph-centered approach

CERN Document Server

Brown, Forbes T

2006-01-01

For today's students, learning to model the dynamics of complex systems is increasingly important across nearly all engineering disciplines. First published in 2001, Forbes T. Brown's Engineering System Dynamics: A Unified Graph-Centered Approach introduced students to a unique and highly successful approach to modeling system dynamics using bond graphs. Updated with nearly one-third new material, this second edition expands this approach to an even broader range of topics. What's New in the Second Edition? In addition to new material, this edition was restructured to build students' competence in traditional linear mathematical methods before they have gone too far into the modeling that still plays a pivotal role. New topics include magnetic circuits and motors including simulation with magnetic hysteresis; extensive new material on the modeling, analysis, and simulation of distributed-parameter systems; kinetic energy in thermodynamic systems; and Lagrangian and Hamiltonian methods. MATLAB(R) figures promi...

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.

MetricForensics: A Multi-Level Approach for Mining Volatile Graphs

Energy Technology Data Exchange (ETDEWEB)

Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eliassi-Rad, Tina [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Faloutsos, Christos [Carnegie Mellon Univ., Pittsburgh, PA (United States); Akoglu, Leman [Carnegie Mellon Univ., Pittsburgh, PA (United States); Li, Lei [Carnegie Mellon Univ., Pittsburgh, PA (United States); Maruhashi, Koji [Fujitsu Laboratories Ltd., Kanagawa (Japan); Prakash, B. Aditya [Carnegie Mellon Univ., Pittsburgh, PA (United States); Tong, H [Carnegie Mellon Univ., Pittsburgh, PA (United States)

2010-02-08

Advances in data collection and storage capacity have made it increasingly possible to collect highly volatile graph data for analysis. Existing graph analysis techniques are not appropriate for such data, especially in cases where streaming or near-real-time results are required. An example that has drawn significant research interest is the cyber-security domain, where internet communication traces are collected and real-time discovery of events, behaviors, patterns and anomalies is desired. We propose MetricForensics, a scalable framework for analysis of volatile graphs. MetricForensics combines a multi-level “drill down" approach, a collection of user-selected graph metrics and a collection of analysis techniques. At each successive level, more sophisticated metrics are computed and the graph is viewed at a finer temporal resolution. In this way, MetricForensics scales to highly volatile graphs by only allocating resources for computationally expensive analysis when an interesting event is discovered at a coarser resolution first. We test MetricForensics on three real-world graphs: an enterprise IP trace, a trace of legitimate and malicious network traffic from a research institution, and the MIT Reality Mining proximity sensor data. Our largest graph has »3M vertices and »32M edges, spanning 4:5 days. The results demonstrate the scalability and capability of MetricForensics in analyzing volatile graphs; and highlight four novel phenomena in such graphs: elbows, broken correlations, prolonged spikes, and strange stars.

Visibility graphs for fMRI data: Multiplex temporal graphs and their modulations across resting-state networks

Directory of Open Access Journals (Sweden)

Speranza Sannino

2017-10-01

Full Text Available Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach. Here we present the first application of multivariate visibility graphs to fMRI data. Visibility graphs are a way to represent a time series as a temporal network, evidencing specific aspects of its dynamics, such as extreme events. Multivariate time series, as those encountered in neuroscience, and in fMRI in particular, can be seen as a multiplex network, in which each layer represents a time series (a region of interest in the brain in our case. Here we report the method, we describe some relevant aspects of its application to BOLD time series, and we discuss the analogies and differences with existing methods. Finally, we present an application to a high-quality, publicly available dataset, containing healthy subjects and psychotic patients, and we discuss our findings. All the code to reproduce the analyses and the

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

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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.

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

Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

Science.gov (United States)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government

A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.

Science.gov (United States)

Wei, Wei; Gao, Bin; Liu, Tie-Yan; Wang, Taifeng; Li, Guohui; Li, Hang

2016-04-01

Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.

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.

Dynamical graph theory networks techniques for the analysis of sparse connectivity networks in dementia

Science.gov (United States)

Tahmassebi, Amirhessam; Pinker-Domenig, Katja; Wengert, Georg; Lobbes, Marc; Stadlbauer, Andreas; Romero, Francisco J.; Morales, Diego P.; Castillo, Encarnacion; Garcia, Antonio; Botella, Guillermo; Meyer-Bäse, Anke

2017-05-01

Graph network models in dementia have become an important computational technique in neuroscience to study fundamental organizational principles of brain structure and function of neurodegenerative diseases such as dementia. The graph connectivity is reflected in the connectome, the complete set of structural and functional connections of the graph network, which is mostly based on simple Pearson correlation links. In contrast to simple Pearson correlation networks, the partial correlations (PC) only identify direct correlations while indirect associations are eliminated. In addition to this, the state-of-the-art techniques in brain research are based on static graph theory, which is unable to capture the dynamic behavior of the brain connectivity, as it alters with disease evolution. We propose a new research avenue in neuroimaging connectomics based on combining dynamic graph network theory and modeling strategies at different time scales. We present the theoretical framework for area aggregation and time-scale modeling in brain networks as they pertain to disease evolution in dementia. This novel paradigm is extremely powerful, since we can derive both static parameters pertaining to node and area parameters, as well as dynamic parameters, such as system's eigenvalues. By implementing and analyzing dynamically both disease driven PC-networks and regular concentration networks, we reveal differences in the structure of these network that play an important role in the temporal evolution of this disease. The described research is key to advance biomedical research on novel disease prediction trajectories and dementia therapies.

Foodsheds in Virtual Water Flow Networks: A Spectral Graph Theory Approach

Directory of Open Access Journals (Sweden)

Nina Kshetry

2017-06-01

Full Text Available A foodshed is a geographic area from which a population derives its food supply, but a method to determine boundaries of foodsheds has not been formalized. Drawing on the food–water–energy nexus, we propose a formal network science definition of foodsheds by using data from virtual water flows, i.e., water that is virtually embedded in food. In particular, we use spectral graph partitioning for directed graphs. If foodsheds turn out to be geographically compact, it suggests the food system is local and therefore reduces energy and externality costs of food transport. Using our proposed method we compute foodshed boundaries at the global-scale, and at the national-scale in the case of two of the largest agricultural countries: India and the United States. Based on our determination of foodshed boundaries, we are able to better understand commodity flows and whether foodsheds are contiguous and compact, and other factors that impact environmental sustainability. The formal method we propose may be used more broadly to study commodity flows and their impact on environmental sustainability.

An approach to multiscale modelling with graph grammars.

Science.gov (United States)

Ong, Yongzhi; Streit, Katarína; Henke, Michael; Kurth, Winfried

2014-09-01

Functional-structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs. A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL. Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas. The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.

Bounds for percolation thresholds on directed and undirected graphs

Science.gov (United States)

Hamilton, Kathleen; Pryadko, Leonid

2015-03-01

Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.

Graph theory applied to noise and vibration control in statistical energy analysis models.

Science.gov (United States)

Guasch, Oriol; Cortés, Lluís

2009-06-01

A fundamental aspect of noise and vibration control in statistical energy analysis (SEA) models consists in first identifying and then reducing the energy flow paths between subsystems. In this work, it is proposed to make use of some results from graph theory to address both issues. On the one hand, linear and path algebras applied to adjacency matrices of SEA graphs are used to determine the existence of any order paths between subsystems, counting and labeling them, finding extremal paths, or determining the power flow contributions from groups of paths. On the other hand, a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one, modifying as few internal and coupling loss factors as possible.

Domain configurations in dislocations embedded hexagonal manganite systems: From the view of graph theory

Science.gov (United States)

Cheng, Shaobo; Zhang, Dong; Deng, Shiqing; Li, Xing; Li, Jun; Tan, Guotai; Zhu, Yimei; Zhu, Jing

2018-04-01

Topological defects and their interactions often arouse multiple types of emerging phenomena from edge states in Skyrmions to disclination pairs in liquid crystals. In hexagonal manganites, partial edge dislocations, a prototype topological defect, are ubiquitous and they significantly alter the topologically protected domains and their behaviors. Herein, combining electron microscopy experiment and graph theory analysis, we report a systematic study of the connections and configurations of domains in this dislocation embedded system. Rules for domain arrangement are established. The dividing line between domains, which can be attributed by the strain field of dislocations, is accurately described by a genus model from a higher dimension in the graph theory. Our results open a door for the understanding of domain patterns in topologically protected multiferroic systems.

Information fusion-based approach for studying influence on Twitter using belief theory.

Science.gov (United States)

Azaza, Lobna; Kirgizov, Sergey; Savonnet, Marinette; Leclercq, Éric; Gastineau, Nicolas; Faiz, Rim

2016-01-01

Influence in Twitter has become recently a hot research topic, since this micro-blogging service is widely used to share and disseminate information. Some users are more able than others to influence and persuade peers. Thus, studying most influential users leads to reach a large-scale information diffusion area, something very useful in marketing or political campaigns. In this study, we propose a new approach for multi-level influence assessment on multi-relational networks, such as Twitter . We define a social graph to model the relationships between users as a multiplex graph where users are represented by nodes, and links model the different relations between them (e.g., retweets , mentions , and replies ). We explore how relations between nodes in this graph could reveal about the influence degree and propose a generic computational model to assess influence degree of a certain node. This is based on the conjunctive combination rule from the belief functions theory to combine different types of relations. We experiment the proposed method on a large amount of data gathered from Twitter during the European Elections 2014 and deduce top influential candidates. The results show that our model is flexible enough to to consider multiple interactions combination according to social scientists needs or requirements and that the numerical results of the belief theory are accurate. We also evaluate the approach over the CLEF RepLab 2014 data set and show that our approach leads to quite interesting results.

Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

International Nuclear Information System (INIS)

Rosicka, M; Ramanathan, R; Gnaciński, P; Horodecki, M; Horodecki, K; Horodecki, P; Severini, S

2016-01-01

We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions. (paper)

Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

Science.gov (United States)

Rosicka, M.; Ramanathan, R.; Gnaciński, P.; Horodecki, K.; Horodecki, M.; Horodecki, P.; Severini, S.

2016-04-01

We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions.

iBGP: A Bipartite Graph Propagation Approach for Mobile Advertising Fraud Detection

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Jinlong Hu

2017-01-01

Full Text Available Online mobile advertising plays a vital financial role in supporting free mobile apps, but detecting malicious apps publishers who generate fraudulent actions on the advertisements hosted on their apps is difficult, since fraudulent traffic often mimics behaviors of legitimate users and evolves rapidly. In this paper, we propose a novel bipartite graph-based propagation approach, iBGP, for mobile apps advertising fraud detection in large advertising system. We exploit the characteristics of mobile advertising user’s behavior and identify two persistent patterns: power law distribution and pertinence and propose an automatic initial score learning algorithm to formulate both concepts to learn the initial scores of non-seed nodes. We propose a weighted graph propagation algorithm to propagate the scores of all nodes in the user-app bipartite graphs until convergence. To extend our approach for large-scale settings, we decompose the objective function of the initial score learning model into separate one-dimensional problems and parallelize the whole approach on an Apache Spark cluster. iBGP was applied on a large synthetic dataset and a large real-world mobile advertising dataset; experiment results demonstrate that iBGP significantly outperforms other popular graph-based propagation methods.

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.

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

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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

Anticipation-related brain connectivity in bipolar and unipolar depression: a graph theory approach.

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Manelis, Anna; Almeida, Jorge R C; Stiffler, Richelle; Lockovich, Jeanette C; Aslam, Haris A; Phillips, Mary L

2016-09-01

Bipolar disorder is often misdiagnosed as major depressive disorder, which leads to inadequate treatment. Depressed individuals versus healthy control subjects, show increased expectation of negative outcomes. Due to increased impulsivity and risk for mania, however, depressed individuals with bipolar disorder may differ from those with major depressive disorder in neural mechanisms underlying anticipation processes. Graph theory methods for neuroimaging data analysis allow the identification of connectivity between multiple brain regions without prior model specification, and may help to identify neurobiological markers differentiating these disorders, thereby facilitating development of better therapeutic interventions. This study aimed to compare brain connectivity among regions involved in win/loss anticipation in depressed individuals with bipolar disorder (BDD) versus depressed individuals with major depressive disorder (MDD) versus healthy control subjects using graph theory methods. The study was conducted at the University of Pittsburgh Medical Center and included 31 BDD, 39 MDD, and 36 healthy control subjects. Participants were scanned while performing a number guessing reward task that included the periods of win and loss anticipation. We first identified the anticipatory network across all 106 participants by contrasting brain activation during all anticipation periods (win anticipation + loss anticipation) versus baseline, and win anticipation versus loss anticipation. Brain connectivity within the identified network was determined using the Independent Multiple sample Greedy Equivalence Search (IMaGES) and Linear non-Gaussian Orientation, Fixed Structure (LOFS) algorithms. Density of connections (the number of connections in the network), path length, and the global connectivity direction ('top-down' versus 'bottom-up') were compared across groups (BDD/MDD/healthy control subjects) and conditions (win/loss anticipation). These analyses showed that

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Science.gov (United States)

Jain, Abhinandan

2011-01-01

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component

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

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

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.

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.

On middle cube graphs

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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.

Neural networks for link prediction in realistic biomedical graphs: a multi-dimensional evaluation of graph embedding-based approaches.

Science.gov (United States)

Crichton, Gamal; Guo, Yufan; Pyysalo, Sampo; Korhonen, Anna

2018-05-21

Link prediction in biomedical graphs has several important applications including predicting Drug-Target Interactions (DTI), Protein-Protein Interaction (PPI) prediction and Literature-Based Discovery (LBD). It can be done using a classifier to output the probability of link formation between nodes. Recently several works have used neural networks to create node representations which allow rich inputs to neural classifiers. Preliminary works were done on this and report promising results. However they did not use realistic settings like time-slicing, evaluate performances with comprehensive metrics or explain when or why neural network methods outperform. We investigated how inputs from four node representation algorithms affect performance of a neural link predictor on random- and time-sliced biomedical graphs of real-world sizes (∼ 6 million edges) containing information relevant to DTI, PPI and LBD. We compared the performance of the neural link predictor to those of established baselines and report performance across five metrics. In random- and time-sliced experiments when the neural network methods were able to learn good node representations and there was a negligible amount of disconnected nodes, those approaches outperformed the baselines. In the smallest graph (∼ 15,000 edges) and in larger graphs with approximately 14% disconnected nodes, baselines such as Common Neighbours proved a justifiable choice for link prediction. At low recall levels (∼ 0.3) the approaches were mostly equal, but at higher recall levels across all nodes and average performance at individual nodes, neural network approaches were superior. Analysis showed that neural network methods performed well on links between nodes with no previous common neighbours; potentially the most interesting links. Additionally, while neural network methods benefit from large amounts of data, they require considerable amounts of computational resources to utilise them. Our results indicate

Learning molecular energies using localized graph kernels

Science.gov (United States)

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-01

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Homology groups for particles on one-connected graphs

Science.gov (United States)

MaciÄ Żek, Tomasz; Sawicki, Adam

2017-06-01

We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our approach is based on some fundamental combinatorial properties of the configuration spaces, Mayer-Vietoris sequences for different parts of configuration spaces, and some limited use of discrete Morse theory. As one of the results, we derive the closed-form formulae for ranks of the homology groups for indistinguishable particles on tree graphs. We also give a detailed discussion of the second homology group of the configuration space of both distinguishable and indistinguishable particles. Our motivation is the search for new kinds of quantum statistics.

Artistic image analysis using graph-based learning approaches.

Science.gov (United States)

Carneiro, Gustavo

2013-08-01

We introduce a new methodology for the problem of artistic image analysis, which among other tasks, involves the automatic identification of visual classes present in an art work. In this paper, we advocate the idea that artistic image analysis must explore a graph that captures the network of artistic influences by computing the similarities in terms of appearance and manual annotation. One of the novelties of our methodology is the proposed formulation that is a principled way of combining these two similarities in a single graph. Using this graph, we show that an efficient random walk algorithm based on an inverted label propagation formulation produces more accurate annotation and retrieval results compared with the following baseline algorithms: bag of visual words, label propagation, matrix completion, and structural learning. We also show that the proposed approach leads to a more efficient inference and training procedures. This experiment is run on a database containing 988 artistic images (with 49 visual classification problems divided into a multiclass problem with 27 classes and 48 binary problems), where we show the inference and training running times, and quantitative comparisons with respect to several retrieval and annotation performance measures.

An application of the graph theory which examines the metro networks

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Svetla STOILOVA

2015-06-01

Full Text Available The graph theory gives a mathematical representation of transport networks and allows us to study their characteristics effectively. A research of the structure of metro system has been conducted in the study by using the graph theory. The study includes subway systems of 22 European capitals. New indicators have been defined in the research such as a degree of routing, a connectivity of the route, average length per link (which takes into account the number of routes, intensity of the route, density of the route. The new and the existing indicators have been used to analyze and classify the metro networks. The statistical method cluster analysis has been applied to classify the networks. Ten indicators have been used to carry out an analysis. The metro systems in European capitals have been classified in three clusters. The first cluster includes large metro systems, the second one includes small metro networks whereas the third cluster includes metro networks with only one line. The combination of both two methods has been used for the first time in this research. The methodology could be used to evaluate other existing metro networks as well as for preliminary analysis in the design of subway systems.

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.

A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains

Science.gov (United States)

Gan, Tingyue; Cameron, Maria

2017-06-01

Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical timescales at which the qualitative behavior of a given Markov chain changes, and give an effective description of the dynamics on each of them. This approach is valid for both time-reversible and time-irreversible Markov processes, with or without symmetry. Central to this approach are two graph algorithms, Algorithm 1 and Algorithm 2, for obtaining the sequences of the critical timescales and the hierarchies of Typical Transition Graphs or T-graphs indicating the most likely transitions in the system without and with symmetry, respectively. The sequence of critical timescales includes the subsequence of the reciprocals of the real parts of eigenvalues. Under a certain assumption, we prove sharp asymptotic estimates for eigenvalues (including pre-factors) and show how one can extract them from the output of Algorithm 1. We discuss the relationship between Algorithms 1 and 2 and explain how one needs to interpret the output of Algorithm 1 if it is applied in the case with symmetry instead of Algorithm 2. Finally, we analyze an example motivated by R. D. Astumian's model of the dynamics of kinesin, a molecular motor, by means of Algorithm 2.

Predicting conversion from MCI to AD using resting-state fMRI, graph theoretical approach and SVM.

Science.gov (United States)

Hojjati, Seyed Hani; Ebrahimzadeh, Ata; Khazaee, Ali; Babajani-Feremi, Abbas

2017-04-15

We investigated identifying patients with mild cognitive impairment (MCI) who progress to Alzheimer's disease (AD), MCI converter (MCI-C), from those with MCI who do not progress to AD, MCI non-converter (MCI-NC), based on resting-state fMRI (rs-fMRI). Graph theory and machine learning approach were utilized to predict progress of patients with MCI to AD using rs-fMRI. Eighteen MCI converts (average age 73.6 years; 11 male) and 62 age-matched MCI non-converters (average age 73.0 years, 28 male) were included in this study. We trained and tested a support vector machine (SVM) to classify MCI-C from MCI-NC using features constructed based on the local and global graph measures. A novel feature selection algorithm was developed and utilized to select an optimal subset of features. Using subset of optimal features in SVM, we classified MCI-C from MCI-NC with an accuracy, sensitivity, specificity, and the area under the receiver operating characteristic (ROC) curve of 91.4%, 83.24%, 90.1%, and 0.95, respectively. Furthermore, results of our statistical analyses were used to identify the affected brain regions in AD. To the best of our knowledge, this is the first study that combines the graph measures (constructed based on rs-fMRI) with machine learning approach and accurately classify MCI-C from MCI-NC. Results of this study demonstrate potential of the proposed approach for early AD diagnosis and demonstrate capability of rs-fMRI to predict conversion from MCI to AD by identifying affected brain regions underlying this conversion. Copyright © 2017 Elsevier B.V. All rights reserved.

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

Science.gov (United States)

Peña, Jorge; Rochat, Yannick

2012-01-01

By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures. PMID:22970237

Information Retrieval and Graph Analysis Approaches for Book Recommendation

Directory of Open Access Journals (Sweden)

Chahinez Benkoussas

2015-01-01

Full Text Available A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

Information Retrieval and Graph Analysis Approaches for Book Recommendation.

Science.gov (United States)

Benkoussas, Chahinez; Bellot, Patrice

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

A combinatorial approach to diffeomorphism invariant quantum gauge theories

International Nuclear Information System (INIS)

Zapata, J.A.

1997-01-01

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in separable Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory. copyright 1997 American Institute of Physics

Community detection by graph Voronoi diagrams

Science.gov (United States)

Deritei, Dávid; Lázár, Zsolt I.; Papp, István; Járai-Szabó, Ferenc; Sumi, Róbert; Varga, Levente; Ravasz Regan, Erzsébet; Ercsey-Ravasz, Mária

2014-06-01

Accurate and efficient community detection in networks is a key challenge for complex network theory and its applications. The problem is analogous to cluster analysis in data mining, a field rich in metric space-based methods. Common to these methods is a geometric, distance-based definition of clusters or communities. Here we propose a new geometric approach to graph community detection based on graph Voronoi diagrams. Our method serves as proof of principle that the definition of appropriate distance metrics on graphs can bring a rich set of metric space-based clustering methods to network science. We employ a simple edge metric that reflects the intra- or inter-community character of edges, and a graph density-based rule to identify seed nodes of Voronoi cells. Our algorithm outperforms most network community detection methods applicable to large networks on benchmark as well as real-world networks. In addition to offering a computationally efficient alternative for community detection, our method opens new avenues for adapting a wide range of data mining algorithms to complex networks from the class of centroid- and density-based clustering methods.

Political Discourse Analysis Through Solving Problems of Graph Theory

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Monica Patrut

2010-03-01

Full Text Available In this article, we show how, using graph theory, we can make a content analysis of political discourse. Assumptions of this analysis are:
- we have a corpus of speech of each party or candidate;
- we consider that speech conveys economic, political, socio-cultural values, these taking the form of words or word families;
- we consider that there are interdependences between the values of a political discourse; they are given by the co-occurrence of two values, as words in the text, within a well defined fragment, or they are determined by the internal logic of political discourse;
- established links between values in a political speech have associated positive numbers indicating the "power" of those links; these "powers" are defined according to both the number of co-occurrences of values, and the internal logic of the discourse where they occur.
In this context we intend to highlight the following:
a which is the dominant value in a political speech;
b which groups of values have ties between them and have no connection with the rest;
c which is the order in which political values should be set in order to obtain an equivalent but more synthetic speech compared to the already given one;
d which are the links between values that form the "core" political speech.
To solve these problems, we shall use the Political Analyst program. After that, we shall present the concepts necessary to the understanding of the introductory graph theory, useful in understanding the analysis of the software and then the operation of the program. This paper extends the previous paper [6].

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.

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.

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

Renormalization in quantum field theory and the Riemann-Hilbert problem. I. Hopf algebra structure of graphs and the main theorem

International Nuclear Information System (INIS)

Connes, A.; Kreimer, D.

2000-01-01

This paper gives a complete selfcontained proof of our result (1999) showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra H which is commutative asan algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra G whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of H. We show then that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop γ(z) element of G, z element of C, where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ + of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. (orig.)

Discrete Morse functions for graph configuration spaces

International Nuclear Information System (INIS)

Sawicki, A

2012-01-01

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear. (paper)

Matching theory

CERN Document Server

Plummer, MD

1986-01-01

This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.

Classification of mini-dimmings associated with extreme ultraviolet eruptions by using graph theory

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S Bazargan

2016-09-01

Full Text Available Coronal dimmings in both micro and macro scales, can be observed by extreme ultraviolet images, recorded from Solar Dynamics Observatory or Atmospheric Imaging Assembly (SDO/AIA. Mini-dimmings are sometimes associated with wave-like brightening, called coronal mass ejections. Here, the sun full disk images with 171 Å wavelenght, cadence of 2.5, and  0.6 arcsec cell size, were taken on 3 March 2012, then the obtained data were analyzed. Using Zernike Moment and Support Vector Machine (SVM, mini dimmings are detected. 538 active region events, 680 coronal hole events and 723 quiet sun events have been recognized using algorithm. The position, time duration and spatial expansion of these events were computed .The eruptive dimmings have a more spatial development than thermal dimmings after eruptions. This is evident in their graph characteristics length. Then, using graph theory, eruptive and thermal mini-dimmings were classified, with 13% error, for 200 dimmings. 68 dimmings were classified as thermal, and 132 as eruptive. To do this, evolution of graph characteristic length were used.

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

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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

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)

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...

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...

Molecular orbital calculations using chemical graph theory

CERN Document Server

Dias, Jerry Ray

1993-01-01

Professor John D. Roberts published a highly readable book on Molecular Orbital Calculations directed toward chemists in 1962. That timely book is the model for this book. The audience this book is directed toward are senior undergraduate and beginning graduate students as well as practicing bench chemists who have a desire to develop conceptual tools for understanding chemical phenomena. Although, ab initio and more advanced semi-empirical MO methods are regarded as being more reliable than HMO in an absolute sense, there is good evidence that HMO provides reliable relative answers particularly when comparing related molecular species. Thus, HMO can be used to rationalize electronic structure in 1t-systems, aromaticity, and the shape use HMO to gain insight of simple molecular orbitals. Experimentalists still into subtle electronic interactions for interpretation of UV and photoelectron spectra. Herein, it will be shown that one can use graph theory to streamline their HMO computational efforts and to arrive...

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.

PDB2Graph: A toolbox for identifying critical amino acids map in proteins based on graph theory.

Science.gov (United States)

Niknam, Niloofar; Khakzad, Hamed; Arab, Seyed Shahriar; Naderi-Manesh, Hossein

2016-05-01

The integrative and cooperative nature of protein structure involves the assessment of topological and global features of constituent parts. Network concept takes complete advantage of both of these properties in the analysis concomitantly. High compatibility to structural concepts or physicochemical properties in addition to exploiting a remarkable simplification in the system has made network an ideal tool to explore biological systems. There are numerous examples in which different protein structural and functional characteristics have been clarified by the network approach. Here, we present an interactive and user-friendly Matlab-based toolbox, PDB2Graph, devoted to protein structure network construction, visualization, and analysis. Moreover, PDB2Graph is an appropriate tool for identifying critical nodes involved in protein structural robustness and function based on centrality indices. It maps critical amino acids in protein networks and can greatly aid structural biologists in selecting proper amino acid candidates for manipulating protein structures in a more reasonable and rational manner. To introduce the capability and efficiency of PDB2Graph in detail, the structural modification of Calmodulin through allosteric binding of Ca(2+) is considered. In addition, a mutational analysis for three well-identified model proteins including Phage T4 lysozyme, Barnase and Ribonuclease HI, was performed to inspect the influence of mutating important central residues on protein activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

Query optimization for graph analytics on linked data using SPARQL

Energy Technology Data Exchange (ETDEWEB)

Hong, Seokyong [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lim, Seung -Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sukumar, Sreenivas R. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Vatsavai, Ranga Raju [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2015-07-01

Triplestores that support query languages such as SPARQL are emerging as the preferred and scalable solution to represent data and meta-data as massive heterogeneous graphs using Semantic Web standards. With increasing adoption, the desire to conduct graph-theoretic mining and exploratory analysis has also increased. Addressing that desire, this paper presents a solution that is the marriage of Graph Theory and the Semantic Web. We present software that can analyze Linked Data using graph operations such as counting triangles, finding eccentricity, testing connectedness, and computing PageRank directly on triple stores via the SPARQL interface. We describe the process of optimizing performance of the SPARQL-based implementation of such popular graph algorithms by reducing the space-overhead, simplifying iterative complexity and removing redundant computations by understanding query plans. Our optimized approach shows significant performance gains on triplestores hosted on stand-alone workstations as well as hardware-optimized scalable supercomputers such as the Cray XMT.

Optimization Problems on Threshold Graphs

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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.

Similarity Measure of Graphs

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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.

Coexistence of graph-oriented and relational data file organisations in a data bank system

International Nuclear Information System (INIS)

Engel, K.D.

1980-01-01

It is shown that a coexistence of hierarchical and relational data bank structures in computer networks in a common data bank system is possible. This coexistence model, first established by NIJSSEN, regards the graph theory CODASYL approach and CODD's relational model as graph-oriented, or rather table-oriented, data file organisation as presented to the user of a common logical structure of the data bank. (WB) [de

INTEGRATED APPROACH TO GENERATION OF PRECEDENCE RELATIONS AND PRECEDENCE GRAPHS FOR ASSEMBLY SEQUENCE PLANNING

Institute of Scientific and Technical Information of China (English)

无

2002-01-01

An integrated approach to generation of precedence relations and precedence graphs for assembly sequence planning is presented, which contains more assembly flexibility. The approach involves two stages. Based on the assembly model, the components in the assembly can be divided into partially constrained components and completely constrained components in the first stage, and then geometric precedence relation for every component is generated automatically. According to the result of the first stage, the second stage determines and constructs all precedence graphs. The algorithms of these two stages proposed are verified by two assembly examples.

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

Application of graph theory to the morphological analysis of settlements

OpenAIRE

Szmytkie Robert

2017-01-01

In the following paper, the analyses of morphology of settlements were conducted using graph methods. The intention of the author was to create a quantifiable and simple measure, which, in a quantitative way, would express the degree of development of a graph (the spatial pattern of settlement). When analysing examples of graphs assigned to a set of small towns and large villages, it was noticed that the graph development index should depend on: a relative number of edges in relation to the n...

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

Application of graph theory to the morphological analysis of settlements

Directory of Open Access Journals (Sweden)

Szmytkie Robert

2017-12-01

Full Text Available In the following paper, the analyses of morphology of settlements were conducted using graph methods. The intention of the author was to create a quantifiable and simple measure, which, in a quantitative way, would express the degree of development of a graph (the spatial pattern of settlement. When analysing examples of graphs assigned to a set of small towns and large villages, it was noticed that the graph development index should depend on: a relative number of edges in relation to the number of nodes (β index, the number of cycles (urban blocks, which evidences the complexity of the spatial pattern of settlement, and the average rank of nodes of a graph, which expresses the degree of complexity of a street network.

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.

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)

Development of a new loss allocation method for a hybrid electricity market using graph theory

International Nuclear Information System (INIS)

Lim, Valerie S.C.; McDonald, John D.F.; Saha, Tapan K.

2009-01-01

This paper introduces a new method for allocating losses in a power system using a loop-based representation of system behaviour. Using the new method, network behaviour is formulated as a series of presumed power transfers directly between market participants. In contrast to many existing loss allocation methods, this makes it easier to justify the resulting loss distribution. In addition to circumventing the problems of non-unique loss allocations, a formalised process of loop identification, using graph theory concepts, is introduced. The proposed method is applied to both the IEEE 14-bus system and a modified CIGRE Nordic 32-bus system. The results provide a demonstration of the capability of the proposed method to allocate losses in the hybrid market, and demonstrate the approach's capacity to link the technical performance of the network to market instruments. (author)

Graph theory analysis of complex brain networks: new concepts in brain mapping applied to neurosurgery.

Science.gov (United States)

Hart, Michael G; Ypma, Rolf J F; Romero-Garcia, Rafael; Price, Stephen J; Suckling, John

2016-06-01

Neuroanatomy has entered a new era, culminating in the search for the connectome, otherwise known as the brain's wiring diagram. While this approach has led to landmark discoveries in neuroscience, potential neurosurgical applications and collaborations have been lagging. In this article, the authors describe the ideas and concepts behind the connectome and its analysis with graph theory. Following this they then describe how to form a connectome using resting state functional MRI data as an example. Next they highlight selected insights into healthy brain function that have been derived from connectome analysis and illustrate how studies into normal development, cognitive function, and the effects of synthetic lesioning can be relevant to neurosurgery. Finally, they provide a précis of early applications of the connectome and related techniques to traumatic brain injury, functional neurosurgery, and neurooncology.

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

Counting the number of Feynman graphs in QCD

Science.gov (United States)

Kaneko, T.

2018-05-01

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a computer algebra system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.

Valued Graphs and the Representation Theory of Lie Algebras

Directory of Open Access Journals (Sweden)

Joel Lemay

2012-07-01

Full Text Available Quivers (directed graphs, species (a generalization of quivers and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this paper, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field. Namely, we show that the category of K -species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K -species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

A Community-Aware Approach to Minimizing Dissemination in Graphs

KAUST Repository

Zhang, Chuxu

2017-08-02

Given a graph, can we minimize the spread of an entity (such as a meme or a virus) while maintaining the graph’s community structure (defined as groups of nodes with denser intra-connectivity than inter-connectivity)? At first glance, these two objectives seem at odds with each other. To minimize dissemination, nodes or links are often deleted to reduce the graph’s connectivity. These deletions can (and often do) destroy the graph’s community structure, which is an important construct in real-world settings (e.g., communities promote trust among their members). We utilize rewiring of links to achieve both objectives. Examples of rewiring in real life are prevalent, such as purchasing products from a new farm since the local farm has signs of mad cow disease; getting information from a new source after a disaster since your usual source is no longer available, etc. Our community-aware approach, called constrCRlink (short for Constraint Community Relink), preserves (on average) 98.6% of the efficacy of the best community-agnostic link-deletion approach (namely, NetMelt+), but changes the original community structure of the graph by only 4.5%. In contrast, NetMelt+ changes 13.6% of the original community structure.

Graph approach to the gradient expansion of density functionals

International Nuclear Information System (INIS)

Kozlowski, P.M.; Nalewajski, R.F.

1986-01-01

A graph representation of terms in the gradient expansion of the kinetic energy density functional is presented. They briefly discuss the implications of the virial theorem for the graph structure and relations between possible graphs at a given order of expansion

Summing Feynman graphs by Monte Carlo: Planar φ3-theory and dynamically triangulated random surfaces

International Nuclear Information System (INIS)

Boulatov, D.V.

1988-01-01

New combinatorial identities are suggested relating the ratio of (n-1)th and nth orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the nth order. These identities are used for Monte Carlo calculation of critical exponents γ str (string susceptibility) in planar φ 3 -theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D=1 the exact critical properties of the theory are reproduced numerically. (orig.)

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)

Information Retrieval and Graph Analysis Approaches for Book Recommendation

OpenAIRE

Chahinez Benkoussas; Patrice Bellot

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval ...

Expander graphs in pure and applied mathematics

OpenAIRE

Lubotzky, Alexander

2012-01-01

Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing role also in pure mathematics: number theory, group theory, geometry and more. This expository article describes their constructions and various applications in pure and applied mathematics.

Does Guiding Toward Task-Relevant Information Help Improve Graph Processing and Graph Comprehension of Individuals with Low or High Numeracy? An Eye-Tracker Experiment.

Science.gov (United States)

Keller, Carmen; Junghans, Alex

2017-11-01

Individuals with low numeracy have difficulties with understanding complex graphs. Combining the information-processing approach to numeracy with graph comprehension and information-reduction theories, we examined whether high numerates' better comprehension might be explained by their closer attention to task-relevant graphical elements, from which they would expect numerical information to understand the graph. Furthermore, we investigated whether participants could be trained in improving their attention to task-relevant information and graph comprehension. In an eye-tracker experiment ( N = 110) involving a sample from the general population, we presented participants with 2 hypothetical scenarios (stomach cancer, leukemia) showing survival curves for 2 treatments. In the training condition, participants received written instructions on how to read the graph. In the control condition, participants received another text. We tracked participants' eye movements while they answered 9 knowledge questions. The sum constituted graph comprehension. We analyzed visual attention to task-relevant graphical elements by using relative fixation durations and relative fixation counts. The mediation analysis revealed a significant ( P attention to task-relevant information, which did not differ between the 2 conditions. Training had a significant main effect on visual attention ( P attention to task-relevant graphical elements than individuals with low numeracy. With appropriate instructions, both groups can be trained to improve their graph-processing efficiency. Future research should examine (e.g., motivational) mediators between visual attention and graph comprehension to develop appropriate instructions that also result in higher graph comprehension.

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

The investigation of social networks based on multi-component random graphs

Science.gov (United States)

Zadorozhnyi, V. N.; Yudin, E. B.

2018-01-01

The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed by the theory of random graphs with the nonlinear preferential attachment rule and the theory of Erdôs-Rényi random graphs. In fact, well-calibrated network graph models and computer experiments with these models would help developers (owners) of the networks to predict their development correctly and to choose effective strategies for controlling network projects.

Analysis of the enzyme network involved in cattle milk production using graph theory.

Science.gov (United States)

Ghorbani, Sholeh; Tahmoorespur, Mojtaba; Masoudi Nejad, Ali; Nasiri, Mohammad; Asgari, Yazdan

2015-06-01

Understanding cattle metabolism and its relationship with milk products is important in bovine breeding. A systemic view could lead to consequences that will result in a better understanding of existing concepts. Topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. In the present work, the enzyme network involved in cattle milk production was reconstructed and analyzed based on available bovine genome information using several public datasets (NCBI, Uniprot, KEGG, and Brenda). The reconstructed network consisted of 3605 reactions named by KEGG compound numbers and 646 enzymes that catalyzed the corresponding reactions. The characteristics of the directed and undirected network were analyzed using Graph Theory. The mean path length was calculated to be4.39 and 5.41 for directed and undirected networks, respectively. The top 11 hub enzymes whose abnormality could harm bovine health and reduce milk production were determined. Therefore, the aim of constructing the enzyme centric network was twofold; first to find out whether such network followed the same properties of other biological networks, and second, to find the key enzymes. The results of the present study can improve our understanding of milk production in cattle. Also, analysis of the enzyme network can help improve the modeling and simulation of biological systems and help design desired phenotypes to increase milk production quality or quantity.

Differences in graph theory functional connectivity in left and right temporal lobe epilepsy.

Science.gov (United States)

Chiang, Sharon; Stern, John M; Engel, Jerome; Levin, Harvey S; Haneef, Zulfi

2014-12-01

To investigate lateralized differences in limbic system functional connectivity between left and right temporal lobe epilepsy (TLE) using graph theory. Interictal resting state fMRI was performed in 14 left TLE patients, 11 right TLE patients, and 12 controls. Graph theory analysis of 10 bilateral limbic regions of interest was conducted. Changes in edgewise functional connectivity, network topology, and regional topology were quantified, and then left and right TLE were compared. Limbic edgewise functional connectivity was predominantly reduced in both left and right TLE. More regional connections were reduced in right TLE, most prominently involving reduced interhemispheric connectivity between the bilateral insula and bilateral hippocampi. A smaller number of limbic connections were increased in TLE, more so in left than in right TLE. Topologically, the most pronounced change was a reduction in average network betweenness centrality and concurrent increase in left hippocampal betweenness centrality in right TLE. In contrast, left TLE exhibited a weak trend toward increased right hippocampal betweenness centrality, with no change in average network betweenness centrality. Limbic functional connectivity is predominantly reduced in both left and right TLE, with more pronounced reductions in right TLE. In contrast, left TLE exhibits both edgewise and topological changes that suggest a tendency toward reorganization. Network changes in TLE and lateralized differences thereof may have important diagnostic and prognostic implications. Published by Elsevier B.V.

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,

ESIP's Earth Science Knowledge Graph (ESKG) Testbed Project: An Automatic Approach to Building Interdisciplinary Earth Science Knowledge Graphs to Improve Data Discovery

Science.gov (United States)

McGibbney, L. J.; Jiang, Y.; Burgess, A. B.

2017-12-01

Big Earth observation data have been produced, archived and made available online, but discovering the right data in a manner that precisely and efficiently satisfies user needs presents a significant challenge to the Earth Science (ES) community. An emerging trend in information retrieval community is to utilize knowledge graphs to assist users in quickly finding desired information from across knowledge sources. This is particularly prevalent within the fields of social media and complex multimodal information processing to name but a few, however building a domain-specific knowledge graph is labour-intensive and hard to keep up-to-date. In this work, we update our progress on the Earth Science Knowledge Graph (ESKG) project; an ESIP-funded testbed project which provides an automatic approach to building a dynamic knowledge graph for ES to improve interdisciplinary data discovery by leveraging implicit, latent existing knowledge present within across several U.S Federal Agencies e.g. NASA, NOAA and USGS. ESKG strengthens ties between observations and user communities by: 1) developing a knowledge graph derived from various sources e.g. Web pages, Web Services, etc. via natural language processing and knowledge extraction techniques; 2) allowing users to traverse, explore, query, reason and navigate ES data via knowledge graph interaction. ESKG has the potential to revolutionize the way in which ES communities interact with ES data in the open world through the entity, spatial and temporal linkages and characteristics that make it up. This project enables the advancement of ESIP collaboration areas including both Discovery and Semantic Technologies by putting graph information right at our fingertips in an interactive, modern manner and reducing the efforts to constructing ontology. To demonstrate the ESKG concept, we will demonstrate use of our framework across NASA JPL's PO.DAAC, NOAA's Earth Observation Requirements Evaluation System (EORES) and various USGS

Visibility graph approach to exchange rate series

Science.gov (United States)

Yang, Yue; Wang, Jianbo; Yang, Huijie; Mang, Jingshi

2009-10-01

By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.

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.

Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Bergbauer, Christoph

2009-06-11

The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

International Nuclear Information System (INIS)

Bergbauer, Christoph

2009-01-01

The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI.

Science.gov (United States)

Gargouri, Fatma; Kallel, Fathi; Delphine, Sebastien; Ben Hamida, Ahmed; Lehéricy, Stéphane; Valabregue, Romain

2018-01-01

Resting state functional MRI (rs-fMRI) is an imaging technique that allows the spontaneous activity of the brain to be measured. Measures of functional connectivity highly depend on the quality of the BOLD signal data processing. In this study, our aim was to study the influence of preprocessing steps and their order of application on small-world topology and their efficiency in resting state fMRI data analysis using graph theory. We applied the most standard preprocessing steps: slice-timing, realign, smoothing, filtering, and the tCompCor method. In particular, we were interested in how preprocessing can retain the small-world economic properties and how to maximize the local and global efficiency of a network while minimizing the cost. Tests that we conducted in 54 healthy subjects showed that the choice and ordering of preprocessing steps impacted the graph measures. We found that the csr (where we applied realignment, smoothing, and tCompCor as a final step) and the scr (where we applied realignment, tCompCor and smoothing as a final step) strategies had the highest mean values of global efficiency (eg) . Furthermore, we found that the fscr strategy (where we applied realignment, tCompCor, smoothing, and filtering as a final step), had the highest mean local efficiency (el) values. These results confirm that the graph theory measures of functional connectivity depend on the ordering of the processing steps, with the best results being obtained using smoothing and tCompCor as the final steps for global efficiency with additional filtering for local efficiency.

The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI

Directory of Open Access Journals (Sweden)

Fatma Gargouri

2018-02-01

Full Text Available Resting state functional MRI (rs-fMRI is an imaging technique that allows the spontaneous activity of the brain to be measured. Measures of functional connectivity highly depend on the quality of the BOLD signal data processing. In this study, our aim was to study the influence of preprocessing steps and their order of application on small-world topology and their efficiency in resting state fMRI data analysis using graph theory. We applied the most standard preprocessing steps: slice-timing, realign, smoothing, filtering, and the tCompCor method. In particular, we were interested in how preprocessing can retain the small-world economic properties and how to maximize the local and global efficiency of a network while minimizing the cost. Tests that we conducted in 54 healthy subjects showed that the choice and ordering of preprocessing steps impacted the graph measures. We found that the csr (where we applied realignment, smoothing, and tCompCor as a final step and the scr (where we applied realignment, tCompCor and smoothing as a final step strategies had the highest mean values of global efficiency (eg. Furthermore, we found that the fscr strategy (where we applied realignment, tCompCor, smoothing, and filtering as a final step, had the highest mean local efficiency (el values. These results confirm that the graph theory measures of functional connectivity depend on the ordering of the processing steps, with the best results being obtained using smoothing and tCompCor as the final steps for global efficiency with additional filtering for local efficiency.

The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI

Science.gov (United States)

Gargouri, Fatma; Kallel, Fathi; Delphine, Sebastien; Ben Hamida, Ahmed; Lehéricy, Stéphane; Valabregue, Romain

2018-01-01

Resting state functional MRI (rs-fMRI) is an imaging technique that allows the spontaneous activity of the brain to be measured. Measures of functional connectivity highly depend on the quality of the BOLD signal data processing. In this study, our aim was to study the influence of preprocessing steps and their order of application on small-world topology and their efficiency in resting state fMRI data analysis using graph theory. We applied the most standard preprocessing steps: slice-timing, realign, smoothing, filtering, and the tCompCor method. In particular, we were interested in how preprocessing can retain the small-world economic properties and how to maximize the local and global efficiency of a network while minimizing the cost. Tests that we conducted in 54 healthy subjects showed that the choice and ordering of preprocessing steps impacted the graph measures. We found that the csr (where we applied realignment, smoothing, and tCompCor as a final step) and the scr (where we applied realignment, tCompCor and smoothing as a final step) strategies had the highest mean values of global efficiency (eg). Furthermore, we found that the fscr strategy (where we applied realignment, tCompCor, smoothing, and filtering as a final step), had the highest mean local efficiency (el) values. These results confirm that the graph theory measures of functional connectivity depend on the ordering of the processing steps, with the best results being obtained using smoothing and tCompCor as the final steps for global efficiency with additional filtering for local efficiency. PMID:29497372

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.

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...

A Structure-graph Approach to Diagnosis and Control Reconfiguration Design - exemplified by Station-keeping Control

DEFF Research Database (Denmark)

Blanke, Mogens

2005-01-01

This paper addresses the design process of diagnosis and fault-tolerant control when a system should operate despite multiple failures in sensors or actuators. Graph-theory based analysis of system's structure is demonstrated to be a unique design methodology that can cope with the diagnosis desi...

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.

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.

The n-th Power Signed Graphs-II

OpenAIRE

Reddyy, P. Siva Kota; Vijay, S.; Lokeshaz, V.

2010-01-01

For standard terminology and notion in graph theory we refer the reader to Harary [6]; the non-standard will be given in this paper as and when required. We treat only finite simple graphs without self loops and isolates.

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

A Parallel Approach for Frequent Subgraph Mining in a Single Large Graph Using Spark

Directory of Open Access Journals (Sweden)

Fengcai Qiao

2018-02-01

Full Text Available Frequent subgraph mining (FSM plays an important role in graph mining, attracting a great deal of attention in many areas, such as bioinformatics, web data mining and social networks. In this paper, we propose SSiGraM (Spark based Single Graph Mining, a Spark based parallel frequent subgraph mining algorithm in a single large graph. Aiming to approach the two computational challenges of FSM, we conduct the subgraph extension and support evaluation parallel across all the distributed cluster worker nodes. In addition, we also employ a heuristic search strategy and three novel optimizations: load balancing, pre-search pruning and top-down pruning in the support evaluation process, which significantly improve the performance. Extensive experiments with four different real-world datasets demonstrate that the proposed algorithm outperforms the existing GraMi (Graph Mining algorithm by an order of magnitude for all datasets and can work with a lower support threshold.

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.

Graph theory enables drug repurposing--how a mathematical model can drive the discovery of hidden mechanisms of action.

Science.gov (United States)

Gramatica, Ruggero; Di Matteo, T; Giorgetti, Stefano; Barbiani, Massimo; Bevec, Dorian; Aste, Tomaso

2014-01-01

We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automatically analysed to discover hidden relations between any drug and any disease: these relations are specific paths among the biomedical entities of the graph, representing possible Modes of Action for any given pharmacological compound. We propose a measure for the likeliness of these paths based on a stochastic process on the graph. This measure depends on the abundance of indirect paths between a peptide and a disease, rather than solely on the strength of the shortest path connecting them. We provide real-world examples, showing how the method successfully retrieves known pathophysiological Mode of Action and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. Applications of this methodology are presented, and prove the efficacy of the method for selecting drugs as treatment options for rare diseases.

Graph theory enables drug repurposing--how a mathematical model can drive the discovery of hidden mechanisms of action.

Directory of Open Access Journals (Sweden)

Ruggero Gramatica

Full Text Available We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automatically analysed to discover hidden relations between any drug and any disease: these relations are specific paths among the biomedical entities of the graph, representing possible Modes of Action for any given pharmacological compound. We propose a measure for the likeliness of these paths based on a stochastic process on the graph. This measure depends on the abundance of indirect paths between a peptide and a disease, rather than solely on the strength of the shortest path connecting them. We provide real-world examples, showing how the method successfully retrieves known pathophysiological Mode of Action and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. Applications of this methodology are presented, and prove the efficacy of the method for selecting drugs as treatment options for rare diseases.

State space model extraction of thermohydraulic systems – Part I: A linear graph approach

International Nuclear Information System (INIS)

Uren, K.R.; Schoor, G. van

2013-01-01

Thermohydraulic simulation codes are increasingly making use of graphical design interfaces. The user can quickly and easily design a thermohydraulic system by placing symbols on the screen resembling system components. These components can then be connected to form a system representation. Such system models may then be used to obtain detailed simulations of the physical system. Usually this kind of simulation models are too complex and not ideal for control system design. Therefore, a need exists for automated techniques to extract lumped parameter models useful for control system design. The goal of this first paper, in a two part series, is to propose a method that utilises a graphical representation of a thermohydraulic system, and a lumped parameter modelling approach, to extract state space models. In this methodology each physical domain of the thermohydraulic system is represented by a linear graph. These linear graphs capture the interaction between all components within and across energy domains – hydraulic, thermal and mechanical. These linear graphs are analysed using a graph-theoretic approach to derive reduced order state space models. These models capture the dominant dynamics of the thermohydraulic system and are ideal for control system design purposes. The proposed state space model extraction method is demonstrated by considering a U-tube system. A non-linear state space model is extracted representing both the hydraulic and thermal domain dynamics of the system. The simulated state space model is compared with a Flownex ® model of the U-tube. Flownex ® is a validated systems thermal-fluid simulation software package. - Highlights: • A state space model extraction methodology based on graph-theoretic concepts. • An energy-based approach to consider multi-domain systems in a common framework. • Allow extraction of transparent (white-box) state space models automatically. • Reduced order models containing only independent state

A graph-based approach to detect spatiotemporal dynamics in satellite image time series

Science.gov (United States)

Guttler, Fabio; Ienco, Dino; Nin, Jordi; Teisseire, Maguelonne; Poncelet, Pascal

2017-08-01

Enhancing the frequency of satellite acquisitions represents a key issue for Earth Observation community nowadays. Repeated observations are crucial for monitoring purposes, particularly when intra-annual process should be taken into account. Time series of images constitute a valuable source of information in these cases. The goal of this paper is to propose a new methodological framework to automatically detect and extract spatiotemporal information from satellite image time series (SITS). Existing methods dealing with such kind of data are usually classification-oriented and cannot provide information about evolutions and temporal behaviors. In this paper we propose a graph-based strategy that combines object-based image analysis (OBIA) with data mining techniques. Image objects computed at each individual timestamp are connected across the time series and generates a set of evolution graphs. Each evolution graph is associated to a particular area within the study site and stores information about its temporal evolution. Such information can be deeply explored at the evolution graph scale or used to compare the graphs and supply a general picture at the study site scale. We validated our framework on two study sites located in the South of France and involving different types of natural, semi-natural and agricultural areas. The results obtained from a Landsat SITS support the quality of the methodological approach and illustrate how the framework can be employed to extract and characterize spatiotemporal dynamics.

Graph theoretical model of a sensorimotor connectome in zebrafish.

Science.gov (United States)

Stobb, Michael; Peterson, Joshua M; Mazzag, Borbala; Gahtan, Ethan

2012-01-01

Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

A librarian's guide to graphs, data and the semantic web

CERN Document Server

Powell, James

2015-01-01

Graphs are about connections, and are an important part of our connected and data-driven world. A Librarian's Guide to Graphs, Data and the Semantic Web is geared toward library and information science professionals, including librarians, software developers and information systems architects who want to understand the fundamentals of graph theory, how it is used to represent and explore data, and how it relates to the semantic web. This title provides a firm grounding in the field at a level suitable for a broad audience, with an emphasis on open source solutions and what problems these tools solve at a conceptual level, with minimal emphasis on algorithms or mathematics. The text will also be of special interest to data science librarians and data professionals, since it introduces many graph theory concepts by exploring data-driven networks from various scientific disciplines. The first two chapters consider graphs in theory and the science of networks, before the following chapters cover networks in vario...

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''''.

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...

Key Concept Identification: A Comprehensive Analysis of Frequency and Topical Graph-Based Approaches

Directory of Open Access Journals (Sweden)

Muhammad Aman

2018-05-01

Full Text Available Automatic key concept extraction from text is the main challenging task in information extraction, information retrieval and digital libraries, ontology learning, and text analysis. The statistical frequency and topical graph-based ranking are the two kinds of potentially powerful and leading unsupervised approaches in this area, devised to address the problem. To utilize the potential of these approaches and improve key concept identification, a comprehensive performance analysis of these approaches on datasets from different domains is needed. The objective of the study presented in this paper is to perform a comprehensive empirical analysis of selected frequency and topical graph-based algorithms for key concept extraction on three different datasets, to identify the major sources of error in these approaches. For experimental analysis, we have selected TF-IDF, KP-Miner and TopicRank. Three major sources of error, i.e., frequency errors, syntactical errors and semantical errors, and the factors that contribute to these errors are identified. Analysis of the results reveals that performance of the selected approaches is significantly degraded by these errors. These findings can help us develop an intelligent solution for key concept extraction in the future.

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...

Cytoscape.js: a graph theory library for visualisation and analysis.

Science.gov (United States)

Franz, Max; Lopes, Christian T; Huck, Gerardo; Dong, Yue; Sumer, Onur; Bader, Gary D

2016-01-15

Cytoscape.js is an open-source JavaScript-based graph library. Its most common use case is as a visualization software component, so it can be used to render interactive graphs in a web browser. It also can be used in a headless manner, useful for graph operations on a server, such as Node.js. Cytoscape.js is implemented in JavaScript. Documentation, downloads and source code are available at http://js.cytoscape.org. gary.bader@utoronto.ca. © The Author 2015. Published by Oxford University Press.

Multiscale Analysis of Time Irreversibility Based on Phase-Space Reconstruction and Horizontal Visibility Graph Approach

Science.gov (United States)

Zhang, Yongping; Shang, Pengjian; Xiong, Hui; Xia, Jianan

Time irreversibility is an important property of nonequilibrium dynamic systems. A visibility graph approach was recently proposed, and this approach is generally effective to measure time irreversibility of time series. However, its result may be unreliable when dealing with high-dimensional systems. In this work, we consider the joint concept of time irreversibility and adopt the phase-space reconstruction technique to improve this visibility graph approach. Compared with the previous approach, the improved approach gives a more accurate estimate for the irreversibility of time series, and is more effective to distinguish irreversible and reversible stochastic processes. We also use this approach to extract the multiscale irreversibility to account for the multiple inherent dynamics of time series. Finally, we apply the approach to detect the multiscale irreversibility of financial time series, and succeed to distinguish the time of financial crisis and the plateau. In addition, Asian stock indexes away from other indexes are clearly visible in higher time scales. Simulations and real data support the effectiveness of the improved approach when detecting time irreversibility.

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.

Mining chemical reactions using neighborhood behavior and condensed graphs of reactions approaches.

Science.gov (United States)

de Luca, Aurélie; Horvath, Dragos; Marcou, Gilles; Solov'ev, Vitaly; Varnek, Alexandre

2012-09-24

This work addresses the problem of similarity search and classification of chemical reactions using Neighborhood Behavior (NB) and Condensed Graphs of Reaction (CGR) approaches. The CGR formalism represents chemical reactions as a classical molecular graph with dynamic bonds, enabling descriptor calculations on this graph. Different types of the ISIDA fragment descriptors generated for CGRs in combination with two metrics--Tanimoto and Euclidean--were considered as chemical spaces, to serve for reaction dissimilarity scoring. The NB method has been used to select an optimal combination of descriptors which distinguish different types of chemical reactions in a database containing 8544 reactions of 9 classes. Relevance of NB analysis has been validated in generic (multiclass) similarity search and in clustering with Self-Organizing Maps (SOM). NB-compliant sets of descriptors were shown to display enhanced mapping propensities, allowing the construction of better Self-Organizing Maps and similarity searches (NB and classical similarity search criteria--AUC ROC--correlate at a level of 0.7). The analysis of the SOM clusters proved chemically meaningful CGR substructures representing specific reaction signatures.

Monitoring Effective Connectivity in the Preterm Brain: A Graph Approach to Study Maturation

Directory of Open Access Journals (Sweden)

M. Lavanga

2017-01-01

Full Text Available In recent years, functional connectivity in the developmental science received increasing attention. Although it has been reported that the anatomical connectivity in the preterm brain develops dramatically during the last months of pregnancy, little is known about how functional and effective connectivity change with maturation. The present study investigated how effective connectivity in premature infants evolves. To assess it, we use EEG measurements and graph-theory methodologies. We recorded data from 25 preterm babies, who underwent long-EEG monitoring at least twice during their stay in the NICU. The recordings took place from 27 weeks postmenstrual age (PMA until 42 weeks PMA. Results showed that the EEG-connectivity, assessed using graph-theory indices, moved from a small-world network to a random one, since the clustering coefficient increases and the path length decreases. This shift can be due to the development of the thalamocortical connections and long-range cortical connections. Based on the network indices, we developed different age-prediction models. The best result showed that it is possible to predict the age of the infant with a root mean-squared error (MSE equal to 2.11 weeks. These results are similar to the ones reported in the literature for age prediction in preterm babies.

Quantifying Riverscape Connectivity with Graph Theory

Science.gov (United States)

Carbonneau, P.; Milledge, D.; Sinha, R.; Tandon, S. K.

2013-12-01

Fluvial catchments convey fluxes of water, sediment, nutrients and aquatic biota. At continental scales, crustal topography defines the overall path of channels whilst at local scales depositional and/or erosional features generally determine the exact path of a channel. Furthermore, constructions such as dams, for either water abstraction or hydropower, often have a significant impact on channel networks.The concept of ';connectivity' is commonly invoked when conceptualising the structure of a river network.This concept is easy to grasp but there have been uneven efforts across the environmental sciences to actually quantify connectivity. Currently there have only been a few studies reporting quantitative indices of connectivity in river sciences, notably, in the study of avulsion processes. However, the majority of current work describing some form of environmental connectivity in a quantitative manner is in the field of landscape ecology. Driven by the need to quantify habitat fragmentation, landscape ecologists have returned to graph theory. Within this formal setting, landscape ecologists have successfully developed a range of indices which can model connectivity loss. Such formal connectivity metrics are currently needed for a range of applications in fluvial sciences. One of the most urgent needs relates to dam construction. In the developed world, hydropower development has generally slowed and in many countries, dams are actually being removed. However, this is not the case in the developing world where hydropower is seen as a key element to low-emissions power-security. For example, several dam projects are envisaged in Himalayan catchments in the next 2 decades. This region is already under severe pressure from climate change and urbanisation, and a better understanding of the network fragmentation which can be expected in this system is urgently needed. In this paper, we apply and adapt connectivity metrics from landscape ecology. We then examine the

Spectral clustering and biclustering learning large graphs and contingency tables

CERN Document Server

Bolla, Marianna

2013-01-01

Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, mult

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.

Quantification of three-dimensional cell-mediated collagen remodeling using graph theory.

Science.gov (United States)

Bilgin, Cemal Cagatay; Lund, Amanda W; Can, Ali; Plopper, George E; Yener, Bülent

2010-09-30

Cell cooperation is a critical event during tissue development. We present the first precise metrics to quantify the interaction between mesenchymal stem cells (MSCs) and extra cellular matrix (ECM). In particular, we describe cooperative collagen alignment process with respect to the spatio-temporal organization and function of mesenchymal stem cells in three dimensions. We defined two precise metrics: Collagen Alignment Index and Cell Dissatisfaction Level, for quantitatively tracking type I collagen and fibrillogenesis remodeling by mesenchymal stem cells over time. Computation of these metrics was based on graph theory and vector calculus. The cells and their three dimensional type I collagen microenvironment were modeled by three dimensional cell-graphs and collagen fiber organization was calculated from gradient vectors. With the enhancement of mesenchymal stem cell differentiation, acceleration through different phases was quantitatively demonstrated. The phases were clustered in a statistically significant manner based on collagen organization, with late phases of remodeling by untreated cells clustering strongly with early phases of remodeling by differentiating cells. The experiments were repeated three times to conclude that the metrics could successfully identify critical phases of collagen remodeling that were dependent upon cooperativity within the cell population. Definition of early metrics that are able to predict long-term functionality by linking engineered tissue structure to function is an important step toward optimizing biomaterials for the purposes of regenerative medicine.

Quantification of three-dimensional cell-mediated collagen remodeling using graph theory.

Directory of Open Access Journals (Sweden)

Cemal Cagatay Bilgin

2010-09-01

Full Text Available Cell cooperation is a critical event during tissue development. We present the first precise metrics to quantify the interaction between mesenchymal stem cells (MSCs and extra cellular matrix (ECM. In particular, we describe cooperative collagen alignment process with respect to the spatio-temporal organization and function of mesenchymal stem cells in three dimensions.We defined two precise metrics: Collagen Alignment Index and Cell Dissatisfaction Level, for quantitatively tracking type I collagen and fibrillogenesis remodeling by mesenchymal stem cells over time. Computation of these metrics was based on graph theory and vector calculus. The cells and their three dimensional type I collagen microenvironment were modeled by three dimensional cell-graphs and collagen fiber organization was calculated from gradient vectors. With the enhancement of mesenchymal stem cell differentiation, acceleration through different phases was quantitatively demonstrated. The phases were clustered in a statistically significant manner based on collagen organization, with late phases of remodeling by untreated cells clustering strongly with early phases of remodeling by differentiating cells. The experiments were repeated three times to conclude that the metrics could successfully identify critical phases of collagen remodeling that were dependent upon cooperativity within the cell population.Definition of early metrics that are able to predict long-term functionality by linking engineered tissue structure to function is an important step toward optimizing biomaterials for the purposes of regenerative medicine.

Graph theoretical model of a sensorimotor connectome in zebrafish.

Directory of Open Access Journals (Sweden)

Michael Stobb

Full Text Available Mapping the detailed connectivity patterns (connectomes of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

Exclusivity structures and graph representatives of local complementation orbits

Science.gov (United States)

Cabello, Adán; Parker, Matthew G.; Scarpa, Giannicola; Severini, Simone

2013-07-01

We describe a construction that maps any connected graph G on three or more vertices into a larger graph, H(G), whose independence number is strictly smaller than its Lovász number which is equal to its fractional packing number. The vertices of H(G) represent all possible events consistent with the stabilizer group of the graph state associated with G, and exclusive events are adjacent. Mathematically, the graph H(G) corresponds to the orbit of G under local complementation. Physically, the construction translates into graph-theoretic terms the connection between a graph state and a Bell inequality maximally violated by quantum mechanics. In the context of zero-error information theory, the construction suggests a protocol achieving the maximum rate of entanglement-assisted capacity, a quantum mechanical analogue of the Shannon capacity, for each H(G). The violation of the Bell inequality is expressed by the one-shot version of this capacity being strictly larger than the independence number. Finally, given the correspondence between graphs and exclusivity structures, we are able to compute the independence number for certain infinite families of graphs with the use of quantum non-locality, therefore highlighting an application of quantum theory in the proof of a purely combinatorial statement.

Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms

OpenAIRE

Chen, Pin-Yu; Hero, Alfred O.

2017-01-01

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a multilayer spectral graph clustering (SGC) framework that performs convex layer aggregation. Under a multilayer signal plus noise model, we provide a phase transition analys...

Resistance and relatedness on an evolutionary graph

Science.gov (United States)

Maciejewski, Wes

2012-01-01

When investigating evolution in structured populations, it is often convenient to consider the population as an evolutionary graph—individuals as nodes, and whom they may act with as edges. There has, in recent years, been a surge of interest in evolutionary graphs, especially in the study of the evolution of social behaviours. An inclusive fitness framework is best suited for this type of study. A central requirement for an inclusive fitness analysis is an expression for the genetic similarity between individuals residing on the graph. This has been a major hindrance for work in this area as highly technical mathematics are often required. Here, I derive a result that links genetic relatedness between haploid individuals on an evolutionary graph to the resistance between vertices on a corresponding electrical network. An example that demonstrates the potential computational advantage of this result over contemporary approaches is provided. This result offers more, however, to the study of population genetics than strictly computationally efficient methods. By establishing a link between gene transfer and electric circuit theory, conceptualizations of the latter can enhance understanding of the former. PMID:21849384

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...

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.

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.)

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.)

A Median-Type Condition for Graph Tiling

Czech Academy of Sciences Publication Activity Database

Piguet, Diana; Saumell, Maria

2017-01-01

Roč. 61, August (2017), s. 979-985 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Grant - others:GA MŠk(CZ) LO1506 Institutional support: RVO:67985807 Keywords : extremal graph theory * graph tiling * regularity lemma * LP-duality Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

Genetic Algorithm and Graph Theory Based Matrix Factorization Method for Online Friend Recommendation

Directory of Open Access Journals (Sweden)

Qu Li

2014-01-01

Full Text Available Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.

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.

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.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

International Nuclear Information System (INIS)

Lacasa, Lucas

2014-01-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein–Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments. (paper)

Generating loop graphs via Hopf algebra in quantum field theory

International Nuclear Information System (INIS)

Mestre, Angela; Oeckl, Robert

2006-01-01

We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

Energy Technology Data Exchange (ETDEWEB)

Shi, Xuanhua; Luo, Xuan; Liang, Junling; Zhao, Peng; Di, Sheng; He, Bingsheng; Jin, Hai

2018-01-01

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weight asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and

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...

Guidelines for a graph-theoretic implementation of structural equation modeling

Science.gov (United States)

Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William

2012-01-01

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for

Using the graphs models for evaluating in-core monitoring systems reliability by the method of imiting simulaton

International Nuclear Information System (INIS)

Golovanov, M.N.; Zyuzin, N.N.; Levin, G.L.; Chesnokov, A.N.

1987-01-01

An approach for estimation of reliability factors of complex reserved systems at early stages of development using the method of imitating simulation is considered. Different types of models, their merits and lacks are given. Features of in-core monitoring systems and advosability of graph model and graph theory element application for estimating reliability of such systems are shown. The results of investigation of the reliability factors of the reactor monitoring, control and core local protection subsystem are shown

Brain Graph Topology Changes Associated with Anti-Epileptic Drug Use

Science.gov (United States)

Levin, Harvey S.; Chiang, Sharon

2015-01-01

Abstract Neuroimaging studies of functional connectivity using graph theory have furthered our understanding of the network structure in temporal lobe epilepsy (TLE). Brain network effects of anti-epileptic drugs could influence such studies, but have not been systematically studied. Resting-state functional MRI was analyzed in 25 patients with TLE using graph theory analysis. Patients were divided into two groups based on anti-epileptic medication use: those taking carbamazepine/oxcarbazepine (CBZ/OXC) (n=9) and those not taking CBZ/OXC (n=16) as a part of their medication regimen. The following graph topology metrics were analyzed: global efficiency, betweenness centrality (BC), clustering coefficient, and small-world index. Multiple linear regression was used to examine the association of CBZ/OXC with graph topology. The two groups did not differ from each other based on epilepsy characteristics. Use of CBZ/OXC was associated with a lower BC. Longer epilepsy duration was also associated with a lower BC. These findings can inform graph theory-based studies in patients with TLE. The changes observed are discussed in relation to the anti-epileptic mechanism of action and adverse effects of CBZ/OXC. PMID:25492633

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)

Row—column visibility graph approach to two-dimensional landscapes

International Nuclear Information System (INIS)

Xiao Qin; Pan Xue; Li Xin-Li; Stephen Mutua; Yang Hui-Jie; Jiang Yan; Wang Jian-Yong; Zhang Qing-Jun

2014-01-01

A new concept, called the row—column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough (e.g., H > 0.5), the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H < 0.5 is destroyed completely. Hence, the row—column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes. (interdisciplinary physics and related areas of science and technology)

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

Science.gov (United States)

Vanchurin, Vitaly

2018-05-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Study of a class of photovoltaic systems using a bond graph approach. Modeling, analysis and control; Etude d'une classe de systemes photovoltaiques par une approche bond graph. Modelisation, analyse et commande

Energy Technology Data Exchange (ETDEWEB)

Andoulsi, R.

2001-12-01

We present in this thesis a study of a class of photovoltaic system by a bond graph approach. This study concerns the modelling, the analysis and the control of some configurations including PV generator, DC/DC converters and DC motor-pumps. The modelling of the different elements of a photovoltaic system is an indispensable stage that must precede all application of sizing, identification or simulation. However, theses PV systems are of hybrid type and their modelling is complex. It is why we use a unified modelling approach based on the bond graph technique. This methodology is completely systematic and has a sufficient flexibility for allowing the introduction of different components in the system. In the first chapter, we recall the principle of functioning of a photovoltaic generator and we treat mainly the MPPT (Maximum Power Point Tracking) working. In the second chapter, we elaborate bond graph models of various photovoltaic system configurations. For the PV source, we elaborate, in a first stage, a complete model taking into account the various physical phenomena influencing the quality of the PV source. In a second stage, we deduce a reduced bond graph model more easy to use for analysis and control purposes. For the DC/DC converters, we recall the bond graph modelling of switching elements and the average bond graph of the DC/DC converters developed in the literature. Thus, we deduce the bond graphs models of the various DC/DC converters to be used. The third chapter presents a dynamic study of some configurations stability in linear procedure. In the fourth chapter, we study the feasibility of non linear controllers by input/output linearization for some configurations of PV systems. In this study, we use the concept of inverse bond graph to determine, by a bond graph approach, the expression of the control input and the nature of the stability of the internal dynamics (dynamics of zeros). The fifth chapter is dedicated for the presentation of some

Fixation Time for Evolutionary Graphs

Science.gov (United States)

Nie, Pu-Yan; Zhang, Pei-Ai

Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.

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....

The Stability Analysis Method of the Cohesive Granular Slope on the Basis of Graph Theory.

Science.gov (United States)

Guan, Yanpeng; Liu, Xiaoli; Wang, Enzhi; Wang, Sijing

2017-02-27

This paper attempted to provide a method to calculate progressive failure of the cohesivefrictional granular geomaterial and the spatial distribution of the stability of the cohesive granular slope. The methodology can be divided into two parts: the characterization method of macro-contact and the analysis of the slope stability. Based on the graph theory, the vertexes, the edges and the edge sequences are abstracted out to characterize the voids, the particle contact and the macro-contact, respectively, bridging the gap between the mesoscopic and macro scales of granular materials. This paper adopts this characterization method to extract a graph from a granular slope and characterize the macro sliding surface, then the weighted graph is analyzed to calculate the slope safety factor. Each edge has three weights representing the sliding moment, the anti-sliding moment and the braking index of contact-bond, respectively, . The safety factor of the slope is calculated by presupposing a certain number of sliding routes and reducing Weight repeatedly and counting the mesoscopic failure of the edge. It is a kind of slope analysis method from mesoscopic perspective so it can present more detail of the mesoscopic property of the granular slope. In the respect of macro scale, the spatial distribution of the stability of the granular slope is in agreement with the theoretical solution.

POOR TEXTURAL IMAGE MATCHING BASED ON GRAPH THEORY

Directory of Open Access Journals (Sweden)

S. Chen

2016-06-01

Full Text Available Image matching lies at the heart of photogrammetry and computer vision. For poor textural images, the matching result is affected by low contrast, repetitive patterns, discontinuity or occlusion, few or homogeneous textures. Recently, graph matching became popular for its integration of geometric and radiometric information. Focused on poor textural image matching problem, it is proposed an edge-weight strategy to improve graph matching algorithm. A series of experiments have been conducted including 4 typical landscapes: Forest, desert, farmland, and urban areas. And it is experimentally found that our new algorithm achieves better performance. Compared to SIFT, doubled corresponding points were acquired, and the overall recall rate reached up to 68%, which verifies the feasibility and effectiveness of the algorithm.

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...

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.

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

Analysis of the 2005-2016 Earthquake Sequence in Northern Iran Using the Visibility Graph Method

Science.gov (United States)

Khoshnevis, Naeem; Taborda, Ricardo; Azizzadeh-Roodpish, Shima; Telesca, Luciano

2017-11-01

We present an analysis of the seismicity of northern Iran in the period between 2005 and 2016 using a recently introduced method based on concepts of graph theory. The method relies on the inter-event visibility defined in terms of a connectivity degree parameter, k, which is correlated with the earthquake magnitude, M. Previous studies show that the slope m of the line fitting the k- M plot by the least squares method also observes a relationship with the b value from the Gutenberg-Richter law, thus rendering the graph analysis useful to examine the seismicity of a region. These correlations seem to hold for the analysis of relatively small sequences of earthquakes, offering the possibility of studying seismicity parameters in time. We apply this approach to the case of the seismicity of northern Iran, using an earthquake catalog for the tectonic seismic regions of Azerbaijan, Alborz, and Kopeh Dagh. We use results drawn for this region with the visibility graph approach in combination with results from other similar studies to further improve the universal relationship between m and b, and show that the visibility graph approach can be considered as a valid alternative for analyzing regional seismicity properties and earthquake sequences.

Factors and factorizations of graphs proof techniques in factor theory

CERN Document Server

Akiyama, Jin

2011-01-01

This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings.

Science.gov (United States)

Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

2017-12-15

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory-such as Hall's marriage problem-are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

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.

An advanced method for classifying atmospheric circulation types based on prototypes connectivity graph

Science.gov (United States)

Zagouras, Athanassios; Argiriou, Athanassios A.; Flocas, Helena A.; Economou, George; Fotopoulos, Spiros

2012-11-01

Classification of weather maps at various isobaric levels as a methodological tool is used in several problems related to meteorology, climatology, atmospheric pollution and to other fields for many years. Initially the classification was performed manually. The criteria used by the person performing the classification are features of isobars or isopleths of geopotential height, depending on the type of maps to be classified. Although manual classifications integrate the perceptual experience and other unquantifiable qualities of the meteorology specialists involved, these are typically subjective and time consuming. Furthermore, during the last years different approaches of automated methods for atmospheric circulation classification have been proposed, which present automated and so-called objective classifications. In this paper a new method of atmospheric circulation classification of isobaric maps is presented. The method is based on graph theory. It starts with an intelligent prototype selection using an over-partitioning mode of fuzzy c-means (FCM) algorithm, proceeds to a graph formulation for the entire dataset and produces the clusters based on the contemporary dominant sets clustering method. Graph theory is a novel mathematical approach, allowing a more efficient representation of spatially correlated data, compared to the classical Euclidian space representation approaches, used in conventional classification methods. The method has been applied to the classification of 850 hPa atmospheric circulation over the Eastern Mediterranean. The evaluation of the automated methods is performed by statistical indexes; results indicate that the classification is adequately comparable with other state-of-the-art automated map classification methods, for a variable number of clusters.

Presurgery resting-state local graph-theory measures predict neurocognitive outcomes after brain surgery in temporal lobe epilepsy.

Science.gov (United States)

Doucet, Gaelle E; Rider, Robert; Taylor, Nathan; Skidmore, Christopher; Sharan, Ashwini; Sperling, Michael; Tracy, Joseph I

2015-04-01

This study determined the ability of resting-state functional connectivity (rsFC) graph-theory measures to predict neurocognitive status postsurgery in patients with temporal lobe epilepsy (TLE) who underwent anterior temporal lobectomy (ATL). A presurgical resting-state functional magnetic resonance imaging (fMRI) condition was collected in 16 left and 16 right TLE patients who underwent ATL. In addition, patients received neuropsychological testing pre- and postsurgery in verbal and nonverbal episodic memory, language, working memory, and attention domains. Regarding the functional data, we investigated three graph-theory properties (local efficiency, distance, and participation), measuring segregation, integration and centrality, respectively. These measures were only computed in regions of functional relevance to the ictal pathology, or the cognitive domain. Linear regression analyses were computed to predict the change in each neurocognitive domain. Our analyses revealed that cognitive outcome was successfully predicted with at least 68% of the variance explained in each model, for both TLE groups. The only model not significantly predictive involved nonverbal episodic memory outcome in right TLE. Measures involving the healthy hippocampus were the most common among the predictors, suggesting that enhanced integration of this structure with the rest of the brain may improve cognitive outcomes. Regardless of TLE group, left inferior frontal regions were the best predictors of language outcome. Working memory outcome was predicted mostly by right-sided regions, in both groups. Overall, the results indicated our integration measure was the most predictive of neurocognitive outcome. In contrast, our segregation measure was the least predictive. This study provides evidence that presurgery rsFC measures may help determine neurocognitive outcomes following ATL. The results have implications for refining our understanding of compensatory reorganization and predicting

Coloring triangle-free graphs with fixed size

DEFF Research Database (Denmark)

Thomassen, Carsten; Gimbel, John

2000-01-01

Combining recent results on colorings and Ramsey theory, we show that if G is a triangle-free graph with e edges then the chromatic number of G is at most cel(1/3)(log e)(-2/3) for some constant c. In a previous paper, we found an upper bound on the chromatic number of a triangle-free graph of ge...

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.

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.

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.

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.

Bond graphs : an integrating tool for design of mechatronic systems

International Nuclear Information System (INIS)

Ould Bouamama, B.

2011-01-01

Bond graph is a powerful tool well known for dynamic modelling of multi physical systems: This is the only modelling technique to generate automatically state space or non-linear models using dedicated software tools (CAMP-G, 20-Sim, Symbols, Dymola...). Recently several fundamental theories have been developed for using a bond graph model not only for modeling but also as a real integrated tool from conceptual ideas to optimal practical realization of mechatronic system. This keynote presents a synthesis of those new theories which exploit some particular properties (such as causal, structural and behavioral) of this graphical methodology. Based on a pedagogical example, it will be shown how from a physical system (not a transfer function or state equation) and using only one representation (Bond graph), the following results can be performed: modeling (formal state equations generation), Control analysis (observability, controllability, Structural I/O decouplability, dynamic decoupling,...) diagnosis analysis (automatic generation of robust fault indicators, sensor placement, structural diagnosability) and finally sizing of actuators. The presentation will be illustrated by real industrial applications. Limits and perspectives of bond graph theory conclude the keynote.

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...

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.

Spectral analysis of growing graphs a quantum probability point of view

CERN Document Server

Obata, Nobuaki

2017-01-01

This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectr...

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...

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.

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.

An original approach to the mathematical concept of graph from braid crafts

Directory of Open Access Journals (Sweden)

Albanese Veronica

2016-01-01

Full Text Available In previous researches we found that a community of Argentinean artisans models its own practices of braiding using graphs. Inspired by these findings, we designed an educational activity to introduce the concept of graphs. The study of graphs helps students to develop combinatorial and systematic thinking as well as skills to model reality and abstract and generalize patterns from particular situations. The tasks proposed aim to construct the concept of graphs, then identify characteristics that allow some graphs to be models of braids and finally use them to invent more graphs for new braids. The activity performed in a secondary school teachers’ educational course, had quite satisfactory results due to the number of braids invented and the small amount of mistakes made by the participants.

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...

Data structures theory and practice

CERN Document Server

Berztiss, A T

1971-01-01

Computer Science and Applied Mathematics: Data Structures: Theory and Practice focuses on the processes, methodologies, principles, and approaches involved in data structures, including algorithms, decision trees, Boolean functions, lattices, and matrices. The book first offers information on set theory, functions, and relations, and graph theory. Discussions focus on linear formulas of digraphs, isomorphism of digraphs, basic definitions in the theory of digraphs, Boolean functions and forms, lattices, indexed sets, algebra of sets, and order pair and related concepts. The text then examines

Towards Scalable Graph Computation on Mobile Devices.

Science.gov (United States)

Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng

2014-10-01

Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach.

Towards Scalable Graph Computation on Mobile Devices

Science.gov (United States)

Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng

2015-01-01

Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach. PMID:25859564

A hierarchical approach to reducing communication in parallel graph algorithms

KAUST Repository

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

2015-01-01

. This is exacerbated in scale-free networks, such as social and web graphs, which contain hub vertices that have large degrees and therefore send a large number of messages over the network. Furthermore, many graph algorithms and computations send the same data to each

A Bond Graph Approach for the Modeling and Simulation of a Buck Converter

Directory of Open Access Journals (Sweden)

Rached Zrafi

2018-01-01

Full Text Available This paper deals with the modeling of bond graph buck converter systems. The bond graph formalism, which represents a heterogeneous formalism for physical modeling, is used to design a sub-model of a power MOSFET and PiN diode switchers. These bond graph models are based on the device’s electrical elements. The application of these models to a bond graph buck converter permit us to obtain an invariant causal structure when the switch devices change state. This paper shows the usefulness of the bond graph device’s modeling to simulate an implicit bond graph buck converter.

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)

iBGP: A Bipartite Graph Propagation Approach for Mobile Advertising Fraud Detection

OpenAIRE

Hu, Jinlong; Liang, Junjie; Dong, Shoubin

2017-01-01

Online mobile advertising plays a vital financial role in supporting free mobile apps, but detecting malicious apps publishers who generate fraudulent actions on the advertisements hosted on their apps is difficult, since fraudulent traffic often mimics behaviors of legitimate users and evolves rapidly. In this paper, we propose a novel bipartite graph-based propagation approach, iBGP, for mobile apps advertising fraud detection in large advertising system. We exploit the characteristics of m...

Screw-vector bond graphs for kinetic-static modelling and analysis of mechanisms

International Nuclear Information System (INIS)

Bidard, Catherine

1994-01-01

This dissertation deals with the kinetic-static modelling and analysis of spatial mechanisms used in robotics systems. A framework is proposed, which embodies a geometrical and a network approach for kinetic-static modelling. For this purpose we use screw theory and bond graphs. A new form of bond graphs is introduced: the screw-vector bond graph, whose power variables are defined to be wrenches and twists expressed as intrinsic screw-vectors. The mechanism is then identified as a network, whose components are kinematic pairs and whose topology is described by a directed graph. A screw-vector Simple Junction Structure represents the topological constraints. Kinematic pairs are represented by one-port elements, defined by two reciprocal screw-vector spaces. Using dual bases of screw-vectors, a generic decomposition of kinematic pair elements is given. The reduction of kinetic-static models of series and parallel kinematic chains is used in order to derive kinetic-static functional models in geometric form. Thereupon, the computational causality assignment is adapted for the graphical analysis of the mobility and the functioning of spatial mechanisms, based on completely or incompletely specified models. (author) [fr

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.

Direct computation of scattering matrices for general quantum graphs

International Nuclear Information System (INIS)

Caudrelier, V.; Ragoucy, E.

2010-01-01

We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired by the formalism of Reflection-Transmission algebras and quantum field theory on graphs though the results hold independently of this formalism. It yields a simple and direct algebraic derivation of the formula for the total scattering and has a number of advantages compared to existing recursive methods. The case of loops (or tadpoles) is easily incorporated in our method. This provides an extension of recent similar results obtained in a completely different way in the context of abstract graph theory. It also allows us to discuss briefly the inverse scattering problem in the presence of loops using an explicit example to show that the solution is not unique in general. On top of being conceptually very easy, the computational advantage of the method is illustrated on two examples of 'three-dimensional' graphs (tetrahedron and cube) for which other methods are rather heavy or even impractical.

Multithreaded Asynchronous Graph Traversal for In-Memory and Semi-External Memory

KAUST Repository

Pearce, Roger

2010-11-01

Processing large graphs is becoming increasingly important for many domains such as social networks, bioinformatics, etc. Unfortunately, many algorithms and implementations do not scale with increasing graph sizes. As a result, researchers have attempted to meet the growing data demands using parallel and external memory techniques. We present a novel asynchronous approach to compute Breadth-First-Search (BFS), Single-Source-Shortest-Paths, and Connected Components for large graphs in shared memory. Our highly parallel asynchronous approach hides data latency due to both poor locality and delays in the underlying graph data storage. We present an experimental study applying our technique to both In-Memory and Semi-External Memory graphs utilizing multi-core processors and solid-state memory devices. Our experiments using synthetic and real-world datasets show that our asynchronous approach is able to overcome data latencies and provide significant speedup over alternative approaches. For example, on billion vertex graphs our asynchronous BFS scales up to 14x on 16-cores. © 2010 IEEE.

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.

An approach for brain-controlled prostheses based on Scene Graph Steady-State Visual Evoked Potentials.

Science.gov (United States)

Li, Rui; Zhang, Xiaodong; Li, Hanzhe; Zhang, Liming; Lu, Zhufeng; Chen, Jiangcheng

2018-08-01

Brain control technology can restore communication between the brain and a prosthesis, and choosing a Brain-Computer Interface (BCI) paradigm to evoke electroencephalogram (EEG) signals is an essential step for developing this technology. In this paper, the Scene Graph paradigm used for controlling prostheses was proposed; this paradigm is based on Steady-State Visual Evoked Potentials (SSVEPs) regarding the Scene Graph of a subject's intention. A mathematic model was built to predict SSVEPs evoked by the proposed paradigm and a sinusoidal stimulation method was used to present the Scene Graph stimulus to elicit SSVEPs from subjects. Then, a 2-degree of freedom (2-DOF) brain-controlled prosthesis system was constructed to validate the performance of the Scene Graph-SSVEP (SG-SSVEP)-based BCI. The classification of SG-SSVEPs was detected via the Canonical Correlation Analysis (CCA) approach. To assess the efficiency of proposed BCI system, the performances of traditional SSVEP-BCI system were compared. Experimental results from six subjects suggested that the proposed system effectively enhanced the SSVEP responses, decreased the degradation of SSVEP strength and reduced the visual fatigue in comparison with the traditional SSVEP-BCI system. The average signal to noise ratio (SNR) of SG-SSVEP was 6.31 ± 2.64 dB, versus 3.38 ± 0.78 dB of traditional-SSVEP. In addition, the proposed system achieved good performances in prosthesis control. The average accuracy was 94.58% ± 7.05%, and the corresponding high information transfer rate (IRT) was 19.55 ± 3.07 bit/min. The experimental results revealed that the SG-SSVEP based BCI system achieves the good performance and improved the stability relative to the conventional approach. Copyright © 2018 Elsevier B.V. All rights reserved.

Development of a new nuclide generation and depletion code using a topological solver based on graph theory

Energy Technology Data Exchange (ETDEWEB)

Kasselmann, S., E-mail: s.kasselmann@fz-juelich.de [Forschungszentrum Jülich, 52425 Jülich (Germany); Schitthelm, O. [Forschungszentrum Jülich, 52425 Jülich (Germany); Tantillo, F. [Forschungszentrum Jülich, 52425 Jülich (Germany); Institute for Reactor Safety and Reactor Technology, RWTH-Aachen, 52064 Aachen (Germany); Scholthaus, S.; Rössel, C. [Forschungszentrum Jülich, 52425 Jülich (Germany); Allelein, H.-J. [Forschungszentrum Jülich, 52425 Jülich (Germany); Institute for Reactor Safety and Reactor Technology, RWTH-Aachen, 52064 Aachen (Germany)

2016-09-15

The problem of calculating the amounts of a coupled nuclide system varying with time especially when exposed to a neutron flux is a well-known problem and has been addressed by a number of computer codes. These codes cover a broad spectrum of applications, are based on comprehensive validation work and are therefore justifiably renowned among their users. However, due to their long development history, they are lacking a modern interface, which impedes a fast and robust internal coupling to other codes applied in the field of nuclear reactor physics. Therefore a project has been initiated to develop a new object-oriented nuclide transmutation code. It comprises an innovative solver based on graph theory, which exploits the topology of nuclide chains and therefore speeds up the calculation scheme. Highest priority has been given to the existence of a generic software interface well as an easy handling by making use of XML files for the user input. In this paper we report on the status of the code development and present first benchmark results, which prove the applicability of the selected approach.

Isotropic covariance functions on graphs and their edges

DEFF Research Database (Denmark)

Anderes, E.; Møller, Jesper; Rasmussen, Jakob Gulddahl

We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points...... on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory...... functions in the spatial statistics literature (the power exponential, Matérn, generalized Cauchy, and Dagum classes) are shown to be valid with respect to the resistance metric for any graph with Euclidean edges, whilst they are only valid with respect to the geodesic metric in more special cases....

Modeling flow and transport in fracture networks using graphs

Science.gov (United States)

Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.

2018-03-01

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O (104) times lower times than

Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

KAUST Repository

Xu, Zhiqiang

2017-02-16

Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

KAUST Repository

Xu, Zhiqiang; Cheng, James; Xiao, Xiaokui; Fujimaki, Ryohei; Muraoka, Yusuke

2017-01-01

Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

The cavity approach to parallel dynamics of Ising spins on a graph

International Nuclear Information System (INIS)

Neri, I; Bollé, D

2009-01-01

We use the cavity method to study the parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single-site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively directed edges we find an exact expression for the stationary distribution. We present the phase diagrams for an Ising model on an asymmetric Bethe lattice and for a neural network with Hebbian interactions on an asymmetric scale-free graph. For graphs with a nonzero fraction of symmetric edges the equations can be solved for a finite number of time steps. Theoretical predictions are confirmed by simulations. Using a heuristic method the cavity equations are extended to a set of equations that determine the marginals of the stationary distribution of Ising models on graphs with a nonzero fraction of symmetric edges. The results from this method are discussed and compared with simulations

Evolutionary Graphs with Frequency Dependent Fitness

Science.gov (United States)

Nie, Pu-Yan; Zhang, Pei-Ai

Evolutionary graph theory was recently proposed by Lieberman et al. in 2005. In the previous papers about evolutionary graphs (EGs), the fitness of the residents in the EGs is in general assumed to be unity, and the fitness of a mutant is assumed to be a constant r. We aim to extend EG to general cases in this paper, namely, the fitness of a mutant is heavily dependent upon frequency. The corresponding properties for these new EGs are analyzed, and the fixation probability is obtained for large population.

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.

Herdable Systems Over Signed, Directed Graphs

KAUST Repository

Ruf, Sebastian F.; Egerstedt, Magnus; Shamma, Jeff S.

2018-01-01

This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.

Herdable Systems Over Signed, Directed Graphs

KAUST Repository

Ruf, Sebastian F.

2018-04-11

This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.

Comparison of a traditional with a new approach based on Graph Theory to vulnerability assessment to natural hazards: a study case on a socio-economic complex system

Science.gov (United States)

Arosio, Marcello; Martina, Mario L. V.

2017-04-01

The emergent behaviour of the contemporary complex, socio-technical and interconnected society makes the collective risk greater than the sum of the parts and this requires a holistic, systematic and integrated approach. Although there have been major improvements in recent years, there are still some limitation in term of a holistic approach that is able to include the emergent value hidden in the connections between exposed elements and the interactions between the different spheres of the multi-hazards, vulnerability, exposure and resilience. To deal with these challenges it is necessary to consider the connections between the exposed elements (e.g. populations, schools, hospital, etc.) and to quantify the relative importance of the elements and their interconnections (e.g. the need of injured people to go to hospital or children to school). In a system (e.g. road, hospital and ecological network, etc.), or in a System of System (e.g. socio-technical urban service), there are critical elements that, beyond the intrinsic vulnerability, can be characterized by greater or lower vulnerability because of their physical, geographical, cyber or logical connections. To this aim, we propose in this study a comparative analysis between traditional reductionist approach and a new holistic approach to vulnerability assessment to natural hazards. The analysis considers a study case of a socio-economic complex system through an innovative approach based on the properties of graph G=(N,L). A graph consists of two sets N (nodes) and L (links): the nodes represent the single exposed elements (physical, social, environmental, etc.) to a hazard, while the links (or connections) represent the interaction between the elements. The final goal is to illustrate an application of this innovative approach of integrated collective vulnerability assessment.

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...

An Application of Graph Theory in Markov Chains Reliability Analysis

Directory of Open Access Journals (Sweden)

Pavel Skalny

2014-01-01

Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.

Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph

Directory of Open Access Journals (Sweden)

Ch. Ramprasad

2017-01-01

Full Text Available Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an m-polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and μ-complement of an m-polar fuzzy graph are defined and some properties are studied. An application of an m-polar fuzzy graph is also presented in this article.

On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics

NARCIS (Netherlands)

Rao, Shodhan; Jayawardhana, Bayu; Schaft, Arjan van der

2012-01-01

Motivated by the recent progresses on the interplay between the graph theory and systems theory, we revisit the analysis of reversible chemical reaction networks described by mass action kinetics by reformulating it using the graph knowledge of the underlying networks. Based on this formulation, we

On characterizing terrain visibility graphs

Directory of Open Access Journals (Sweden)

William Evans

2015-06-01

Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.

Graph theoretical analysis and application of fMRI-based brain network in Alzheimer's disease

Directory of Open Access Journals (Sweden)

LIU Xue-na

2012-08-01

Full Text Available Alzheimer's disease (AD, a progressive neurodegenerative disease, is clinically characterized by impaired memory and many other cognitive functions. However, the pathophysiological mechanisms underlying the disease are not thoroughly understood. In recent years, using functional magnetic resonance imaging (fMRI as well as advanced graph theory based network analysis approach, several studies of patients with AD suggested abnormal topological organization in both global and regional properties of functional brain networks, specifically, as demonstrated by a loss of small-world network characteristics. These studies provide novel insights into the pathophysiological mechanisms of AD and could be helpful in developing imaging biomarkers for disease diagnosis. In this paper we introduce the essential concepts of complex brain networks theory, and review recent advances of the study on human functional brain networks in AD, especially focusing on the graph theoretical analysis of small-world network based on fMRI. We also propound the existent problems and research orientation.

Analysis of the Usage of Magnetic Force-directed Approach and Visual Techniques for Interactive Context-based Drawing of Multi-attributed Graphs

Directory of Open Access Journals (Sweden)

Zabiniako Vitaly

2014-12-01

Full Text Available In this article, the authors perform an analysis in order to assess adaptation of magnetic force-directed algorithms for context-based information extraction from multi-attributed graphs during visualization sessions. Theoretic standings behind magnetic force-directed approach are stated together with review on how particular features of respective algorithms in combination with appropriate visual techniques are especially suitable for improved processing and presenting of knowledge that is captured in form of graphs. The complexity of retrieving multi-attributed information within the proposed approach is handled with dedicated tools, such as selective attraction of nodes to MFE (Magnetic Force Emitter based on search criteria, localization of POI (Point of Interest regions, graph node anchoring, etc. Implicit compatibility of aforementioned tools with interactive nature of data exploration is distinguished. Description of case study, based on bibliometric network analysis is given, which is followed by the review of existing related works in this field. Conclusions are made and further studies in the field of visualization of multi-attributed graphs are defined.

Bond graph modelling of engineering systems: theory, applications and software support

National Research Council Canada - National Science Library

Borutzky, Wolfgang; Margolis, Donald L

2011-01-01

... way such that analytical or computer response predictions can be straightforwardly carried out. Bond graphs are a concise pictorial representation of all types of interacting energetic systems. In my experience working with engineers on the development of complex systems it is obvious that these systems suffer from thermal problems, structural problems, vibration and noise problems, and control and stability issues that do not fit into a single discipline. Bond graphs provide the link by which all these different ...

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.

On The Determinant of q-Distance Matrix of a Graph

Directory of Open Access Journals (Sweden)

Li Hong-Hai

2014-02-01

Full Text Available In this note, we show how the determinant of the q-distance matrix Dq(T of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph G by adding the weighted branches to G, and so generalize in part the results obtained by Bapat et al. [R.B. Bapat, S. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005 193- 209]. In particular, as a consequence, determinantal formulae of q-distance matrices for unicyclic graphs and one class of bicyclic graphs are presented.

Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application.

Science.gov (United States)

Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco

2012-11-01

In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating

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.

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

Scalable force directed graph layout algorithms using fast multipole methods

KAUST Repository

Yunis, Enas Abdulrahman; Yokota, Rio; Ahmadia, Aron

2012-01-01

We present an extension to ExaFMM, a Fast Multipole Method library, as a generalized approach for fast and scalable execution of the Force-Directed Graph Layout algorithm. The Force-Directed Graph Layout algorithm is a physics-based approach

The signed permutation group on Feynman graphs

Energy Technology Data Exchange (ETDEWEB)

Purkart, Julian, E-mail: purkart@physik.hu-berlin.de [Institute of Physics, Humboldt University, D-12489 Berlin (Germany)

2016-08-15

The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.

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.

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.

A study of brain networks associated with swallowing using graph-theoretical approaches.

Directory of Open Access Journals (Sweden)

Bo Luan

Full Text Available Functional connectivity between brain regions during swallowing tasks is still not well understood. Understanding these complex interactions is of great interest from both a scientific and a clinical perspective. In this study, functional magnetic resonance imaging (fMRI was utilized to study brain functional networks during voluntary saliva swallowing in twenty-two adult healthy subjects (all females, [Formula: see text] years of age. To construct these functional connections, we computed mean partial correlation matrices over ninety brain regions for each participant. Two regions were determined to be functionally connected if their correlation was above a certain threshold. These correlation matrices were then analyzed using graph-theoretical approaches. In particular, we considered several network measures for the whole brain and for swallowing-related brain regions. The results have shown that significant pairwise functional connections were, mostly, either local and intra-hemispheric or symmetrically inter-hemispheric. Furthermore, we showed that all human brain functional network, although varying in some degree, had typical small-world properties as compared to regular networks and random networks. These properties allow information transfer within the network at a relatively high efficiency. Swallowing-related brain regions also had higher values for some of the network measures in comparison to when these measures were calculated for the whole brain. The current results warrant further investigation of graph-theoretical approaches as a potential tool for understanding the neural basis of dysphagia.

A cluster expansion approach to exponential random graph models

International Nuclear Information System (INIS)

Yin, Mei

2012-01-01

The exponential family of random graphs are among the most widely studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated using cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region

A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs

Energy Technology Data Exchange (ETDEWEB)

Choudhury, Sutanay; Holder, Larry; Chin, George; Agarwal, Khushbu; Feo, John T.

2015-05-27

Cyber security is one of the most significant technical challenges in current times. Detecting adversarial activities, prevention of theft of intellectual properties and customer data is a high priority for corporations and government agencies around the world. Cyber defenders need to analyze massive-scale, high-resolution network flows to identify, categorize, and mitigate attacks involving networks spanning institutional and national boundaries. Many of the cyber attacks can be described as subgraph patterns, with prominent examples being insider infiltrations (path queries), denial of service (parallel paths) and malicious spreads (tree queries). This motivates us to explore subgraph matching on streaming graphs in a continuous setting. The novelty of our work lies in using the subgraph distributional statistics collected from the streaming graph to determine the query processing strategy. We introduce a ``Lazy Search" algorithm where the search strategy is decided on a vertex-to-vertex basis depending on the likelihood of a match in the vertex neighborhood. We also propose a metric named ``Relative Selectivity" that is used to select between different query processing strategies. Our experiments performed on real online news, network traffic stream and a synthetic social network benchmark demonstrate 10-100x speedups over non-incremental, selectivity agnostic approaches.

Field theory approach to gravitation

International Nuclear Information System (INIS)

Yilmaz, H.

1978-01-01

A number of authors considered the possibility of formulating a field-theory approach to gravitation with the claim that such an approach would uniquely lead to Einstein's theory of general relativity. In this article it is shown that the field theory approach is more generally applicable and uniqueness cannot be claimed. Theoretical and experimental reasons are given showing that the Einsteinian limit appears to be unviable

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.

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.

Towards a classification of fusion rule algebras in rational conformal field theories

International Nuclear Information System (INIS)

Ravanini, F.

1991-01-01

We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields (≤4). We then turn our attention to FRA's generated polynomially by one (real) fundamental field, for which a classification is known. Attempting to generalize this result, we describe some connections between FRA's and Graph Theory. The possibility to get new results on the subject following this ''graph'' approach is briefly discussed. (author)

Incremental Frequent Subgraph Mining on Large Evolving Graphs

KAUST Repository

Abdelhamid, Ehab; Canim, Mustafa; Sadoghi, Mohammad; Bhatta, Bishwaranjan; Chang, Yuan-Chi; Kalnis, Panos

2017-01-01

, 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

Topological quantum field theories in terms of coloured graphs associated to quantum groups

International Nuclear Information System (INIS)

Karowski, M.

1993-01-01

Apart from obvious mathematical applications the investigation is motivated by the problem of braid group statistics in physics. Statistics is one of the central concepts in many body quantum systems. Consider a system of two identical particles located at x 1 and x 2 in R d with Schroedinger wave function ψ(x 1 , x 2 ). Under the exchange of particles with these coordinates one usually has Bose or Fermi statistics in case ψ(x 2 , x 1 )=±ψ(x-1,x T 2). For a quick access to the problem consider the following classical geometric space-time description of the exchange of position for two identical particles, reflecting itself in two quantum mechanical transformation laws. We briefly review the set-up of topological quantum field theory and present our new formulation in terms of coloured graphs. (orig.)

Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory

Directory of Open Access Journals (Sweden)

van der Flier Wiesje M

2009-08-01

Full Text Available Abstract Background Although a large body of knowledge about both brain structure and function has been gathered over the last decades, we still have a poor understanding of their exact relationship. Graph theory provides a method to study the relation between network structure and function, and its application to neuroscientific data is an emerging research field. We investigated topological changes in large-scale functional brain networks in patients with Alzheimer's disease (AD and frontotemporal lobar degeneration (FTLD by means of graph theoretical analysis of resting-state EEG recordings. EEGs of 20 patients with mild to moderate AD, 15 FTLD patients, and 23 non-demented individuals were recorded in an eyes-closed resting-state. The synchronization likelihood (SL, a measure of functional connectivity, was calculated for each sensor pair in 0.5–4 Hz, 4–8 Hz, 8–10 Hz, 10–13 Hz, 13–30 Hz and 30–45 Hz frequency bands. The resulting connectivity matrices were converted to unweighted graphs, whose structure was characterized with several measures: mean clustering coefficient (local connectivity, characteristic path length (global connectivity and degree correlation (network 'assortativity'. All results were normalized for network size and compared with random control networks. Results In AD, the clustering coefficient decreased in the lower alpha and beta bands (p Conclusion With decreasing local and global connectivity parameters, the large-scale functional brain network organization in AD deviates from the optimal 'small-world' network structure towards a more 'random' type. This is associated with less efficient information exchange between brain areas, supporting the disconnection hypothesis of AD. Surprisingly, FTLD patients show changes in the opposite direction, towards a (perhaps excessively more 'ordered' network structure, possibly reflecting a different underlying pathophysiological process.

Partition function expansion on region graphs and message-passing equations

International Nuclear Information System (INIS)

Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong

2011-01-01

Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)

A Graph Cut Approach to Artery/Vein Classification in Ultra-Widefield Scanning Laser Ophthalmoscopy.

Science.gov (United States)

Pellegrini, Enrico; Robertson, Gavin; MacGillivray, Tom; van Hemert, Jano; Houston, Graeme; Trucco, Emanuele

2018-02-01

The classification of blood vessels into arterioles and venules is a fundamental step in the automatic investigation of retinal biomarkers for systemic diseases. In this paper, we present a novel technique for vessel classification on ultra-wide-field-of-view images of the retinal fundus acquired with a scanning laser ophthalmoscope. To the best of our knowledge, this is the first time that a fully automated artery/vein classification technique for this type of retinal imaging with no manual intervention has been presented. The proposed method exploits hand-crafted features based on local vessel intensity and vascular morphology to formulate a graph representation from which a globally optimal separation between the arterial and venular networks is computed by graph cut approach. The technique was tested on three different data sets (one publicly available and two local) and achieved an average classification accuracy of 0.883 in the largest data set.

A graph signal filtering-based approach for detection of different edge types on airborne lidar data

Science.gov (United States)

Bayram, Eda; Vural, Elif; Alatan, Aydin

2017-10-01

Airborne Laser Scanning is a well-known remote sensing technology, which provides a dense and highly accurate, yet unorganized point cloud of earth surface. During the last decade, extracting information from the data generated by airborne LiDAR systems has been addressed by many studies in geo-spatial analysis and urban monitoring applications. However, the processing of LiDAR point clouds is challenging due to their irregular structure and 3D geometry. In this study, we propose a novel framework for the detection of the boundaries of an object or scene captured by LiDAR. Our approach is motivated by edge detection techniques in vision research and it is established on graph signal filtering which is an exciting and promising field of signal processing for irregular data types. Due to the convenient applicability of graph signal processing tools on unstructured point clouds, we achieve the detection of the edge points directly on 3D data by using a graph representation that is constructed exclusively to answer the requirements of the application. Moreover, considering the elevation data as the (graph) signal, we leverage aerial characteristic of the airborne LiDAR data. The proposed method can be employed both for discovering the jump edges on a segmentation problem and for exploring the crease edges on a LiDAR object on a reconstruction/modeling problem, by only adjusting the filter characteristics.

chromatic number of a complete balanced multipartite graph

African Journals Online (AJOL)

2006-12-29

Dec 29, 2006 ... †Applied Mathematics Division, Department of Mathematical Sciences, University of ..... classes originally comprising discrete entities (graph vertices) are replaced by collections of ...... Journal of Combinatorial Theory, 6, pp.

Development of a new nuclide generation and depletion code using a topological solver based on graph theory

International Nuclear Information System (INIS)

Kasselmann, S.; Scholthaus, S.; Rössel, C.; Allelein, H.-J.

2014-01-01

The problem of calculating the amounts of a coupled nuclide system varying with time especially when exposed to a neutron flux is a well-known problem and has been addressed by a number of computer codes. These codes cover a broad spectrum of applications, are based on comprehensive validation work and are therefore justifiably renowned among their users. However, due to their long development history, they are lacking a modern interface, which impedes a fast and robust internal coupling to other codes applied in the field of nuclear reactor physics. Therefore a project has been initiated to develop a new object-oriented nuclide transmutation code. It comprises an innovative solver based on graph theory, which exploits the topology of nuclide chains. This allows to always deal with the smallest nuclide system for the problem of interest. Highest priority has been given to the existence of a generic software interfaces well as an easy handling by making use of XML files for input and output. In this paper we report on the status of the code development and present first benchmark results, which prove the applicability of the selected approach. (author)

Automatic segmentation of closed-contour features in ophthalmic images using graph theory and dynamic programming

Science.gov (United States)

Chiu, Stephanie J.; Toth, Cynthia A.; Bowes Rickman, Catherine; Izatt, Joseph A.; Farsiu, Sina

2012-01-01

This paper presents a generalized framework for segmenting closed-contour anatomical and pathological features using graph theory and dynamic programming (GTDP). More specifically, the GTDP method previously developed for quantifying retinal and corneal layer thicknesses is extended to segment objects such as cells and cysts. The presented technique relies on a transform that maps closed-contour features in the Cartesian domain into lines in the quasi-polar domain. The features of interest are then segmented as layers via GTDP. Application of this method to segment closed-contour features in several ophthalmic image types is shown. Quantitative validation experiments for retinal pigmented epithelium cell segmentation in confocal fluorescence microscopy images attests to the accuracy of the presented technique. PMID:22567602

Probabilistic graphs as a conceptual and computational tool in hydrology and water management

Science.gov (United States)

Schoups, Gerrit

2014-05-01

Originally developed in the fields of machine learning and artificial intelligence, probabilistic graphs constitute a general framework for modeling complex systems in the presence of uncertainty. The framework consists of three components: 1. Representation of the model as a graph (or network), with nodes depicting random variables in the model (e.g. parameters, states, etc), which are joined together by factors. Factors are local probabilistic or deterministic relations between subsets of variables, which, when multiplied together, yield the joint distribution over all variables. 2. Consistent use of probability theory for quantifying uncertainty, relying on basic rules of probability for assimilating data into the model and expressing unknown variables as a function of observations (via the posterior distribution). 3. Efficient, distributed approximation of the posterior distribution using general-purpose algorithms that exploit model structure encoded in the graph. These attributes make probabilistic graphs potentially useful as a conceptual and computational tool in hydrology and water management (and beyond). Conceptually, they can provide a common framework for existing and new probabilistic modeling approaches (e.g. by drawing inspiration from other fields of application), while computationally they can make probabilistic inference feasible in larger hydrological models. The presentation explores, via examples, some of these benefits.

Geometric structure of chemistry-relevant graphs zigzags and central circuits

CERN Document Server

Deza, Michel-Marie; Shtogrin, Mikhail Ivanovitch

2015-01-01

The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.

Impaired cerebral blood flow networks in temporal lobe epilepsy with hippocampal sclerosis: A graph theoretical approach.

Science.gov (United States)

Sone, Daichi; Matsuda, Hiroshi; Ota, Miho; Maikusa, Norihide; Kimura, Yukio; Sumida, Kaoru; Yokoyama, Kota; Imabayashi, Etsuko; Watanabe, Masako; Watanabe, Yutaka; Okazaki, Mitsutoshi; Sato, Noriko

2016-09-01

Graph theory is an emerging method to investigate brain networks. Altered cerebral blood flow (CBF) has frequently been reported in temporal lobe epilepsy (TLE), but graph theoretical findings of CBF are poorly understood. Here, we explored graph theoretical networks of CBF in TLE using arterial spin labeling imaging. We recruited patients with TLE and unilateral hippocampal sclerosis (HS) (19 patients with left TLE, and 21 with right TLE) and 20 gender- and age-matched healthy control subjects. We obtained all participants' CBF maps using pseudo-continuous arterial spin labeling and analyzed them using the Graph Analysis Toolbox (GAT) software program. As a result, compared to the controls, the patients with left TLE showed a significantly low clustering coefficient (p=0.024), local efficiency (p=0.001), global efficiency (p=0.010), and high transitivity (p=0.015), whereas the patients with right TLE showed significantly high assortativity (p=0.046) and transitivity (p=0.011). The group with right TLE also had high characteristic path length values (p=0.085), low global efficiency (p=0.078), and low resilience to targeted attack (p=0.101) at a trend level. Lower normalized clustering coefficient (p=0.081) in the left TLE and higher normalized characteristic path length (p=0.089) in the right TLE were found also at a trend level. Both the patients with left and right TLE showed significantly decreased clustering in similar areas, i.e., the cingulate gyri, precuneus, and occipital lobe. Our findings revealed differing left-right network metrics in which an inefficient CBF network in left TLE and vulnerability to irritation in right TLE are suggested. The left-right common finding of regional decreased clustering might reflect impaired default-mode networks in TLE. Copyright © 2016 Elsevier Inc. All rights reserved.

A Practical Approach to Constructing a Knowledge Graph for Cybersecurity

Directory of Open Access Journals (Sweden)

Yan Jia

2018-02-01

Full Text Available Cyberattack forms are complex and varied, and the detection and prediction of dynamic types of attack are always challenging tasks. Research on knowledge graphs is becoming increasingly mature in many fields. At present, it is very significant that certain scholars have combined the concept of the knowledge graph with cybersecurity in order to construct a cybersecurity knowledge base. This paper presents a cybersecurity knowledge base and deduction rules based on a quintuple model. Using machine learning, we extract entities and build ontology to obtain a cybersecurity knowledge base. New rules are then deduced by calculating formulas and using the path-ranking algorithm. The Stanford named entity recognizer (NER is also used to train an extractor to extract useful information. Experimental results show that the Stanford NER provides many features and the useGazettes parameter may be used to train a recognizer in the cybersecurity domain in preparation for future work. Keywords: Cybersecurity, Knowledge graph, Knowledge deduction

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...

GRAMI: Frequent subgraph and pattern mining in a single large graph

KAUST Repository

Elseidy, M.

2014-01-01

Mining frequent subgraphs is an important operation on graphs; it is defined as finding all subgraphs that appear frequently in a database according to a given frequency threshold. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs, or proteinprotein interactions in bioinformatics, are modeled as a single large graph. In this paper we present GRAMI, a novel framework for frequent subgraph mining in a single large graph. GRAMI undertakes a novel approach that only finds the minimal set of instances to satisfy the frequency threshold and avoids the costly enumeration of all instances required by previous approaches. We accompany our approach with a heuristic and optimizations that significantly improve performance. Additionally, we present an extension of GRAMI that mines frequent patterns. Compared to subgraphs, patterns offer a more powerful version of matching that captures transitive interactions between graph nodes (like friend of a friend) which are very common in modern applications. Finally, we present CGRAMI, a version supporting structural and semantic constraints, and AGRAMI, an approximate version producing results with no false positives. Our experiments on real data demonstrate that our framework is up to 2 orders of magnitude faster and discovers more interesting patterns than existing approaches. 2014 VLDB Endowment.

Hyperbolicity in median graphs

Indian Academy of Sciences (India)

mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.

The Partial Mapping of the Web Graph

Directory of Open Access Journals (Sweden)

Kristina Machova

2009-06-01

Full Text Available The paper presents an approach to partial mapping of a web sub-graph. This sub-graph contains the nearest surroundings of an actual web page. Our work deals with acquiring relevant Hyperlinks of a base web site, generation of adjacency matrix, the nearest distance matrix and matrix of converted distances of Hyperlinks, detection of compactness of web representation, and visualization of its graphical representation. The paper introduces an LWP algorithm – a technique for Hyperlink filtration.  This work attempts to help users with the orientation within the web graph.

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

An internet graph model based on trade-off optimization

Science.gov (United States)

Alvarez-Hamelin, J. I.; Schabanel, N.

2004-03-01

This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in[CITE] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.

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.

Product shipping information using graceful labeling on undirected tree graph approach

Science.gov (United States)

Kuan, Yoong Kooi; Ghani, Ahmad Termimi Ab

2017-08-01

Product shipping information is the related information of an ordered product that ready to be shipped to the foreign customer's company, where the information represents as an irrefutable proof in black and white to the local manufacturer by E-mails. This messy and unordered list of information is stored in E-mail folders by the people incharge, which do not function in collating the information properly. So, in this paper, an algorithm is proposed on how to rearrange the messy information from the sequence of a path graph structure into a concise version of a caterpillar graph with achieving the concept of graceful labeling. The final graceful caterpillar graph consists of the full listed information together with the numbering, which able to assist people get the information fleetly for shipping arrangement procedure.

Scalable force directed graph layout algorithms using fast multipole methods

KAUST Repository

Yunis, Enas Abdulrahman

2012-06-01

We present an extension to ExaFMM, a Fast Multipole Method library, as a generalized approach for fast and scalable execution of the Force-Directed Graph Layout algorithm. The Force-Directed Graph Layout algorithm is a physics-based approach to graph layout that treats the vertices V as repelling charged particles with the edges E connecting them acting as springs. Traditionally, the amount of work required in applying the Force-Directed Graph Layout algorithm is O(|V|2 + |E|) using direct calculations and O(|V| log |V| + |E|) using truncation, filtering, and/or multi-level techniques. Correct application of the Fast Multipole Method allows us to maintain a lower complexity of O(|V| + |E|) while regaining most of the precision lost in other techniques. Solving layout problems for truly large graphs with millions of vertices still requires a scalable algorithm and implementation. We have been able to leverage the scalability and architectural adaptability of the ExaFMM library to create a Force-Directed Graph Layout implementation that runs efficiently on distributed multicore and multi-GPU architectures. © 2012 IEEE.

Graphing and Percentage Applications Using the Personal Computer.

Science.gov (United States)

Innes, Jay

1985-01-01

The paper describes how "IBM Graphing Assistant" and "Apple Softgraph" can foster a multifaceted approach to application of mathematical concepts and how a survey can be undertaken using the computer as word processor, data bank, and source of visual displays. Mathematical skills reinforced include estimating, rounding, graphing, and solving…

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...

Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula

Directory of Open Access Journals (Sweden)

Marlowe Thomas J.

1998-01-01

Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants. We illustrate this approach using threshhold graphs, and show that any computation of reliability using Gilbert's formula will be polynomial-time if and only if the number of invariants considered is polynomial; we then show families of graphs with polynomial-time, and non-polynomial reliability computation, and show that these encompass most previously known results. We then codify our approach to indicate how it can be used for other classes of graphs, and suggest several classes to which the technique can be applied.

Nonschematic drawing recognition: a new approach based on attributed graph grammar with flexible embedding

Science.gov (United States)

Lee, Kyu J.; Kunii, T. L.; Noma, T.

1993-01-01

In this paper, we propose a syntactic pattern recognition method for non-schematic drawings, based on a new attributed graph grammar with flexible embedding. In our graph grammar, the embedding rule permits the nodes of a guest graph to be arbitrarily connected with the nodes of a host graph. The ambiguity caused by this flexible embedding is controlled with the evaluation of synthesized attributes and the check of context sensitivity. To integrate parsing with the synthesized attribute evaluation and the context sensitivity check, we also develop a bottom up parsing algorithm.

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

Science.gov (United States)

Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

2017-12-01

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory—such as Hall's marriage problem—are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

A Novel Efficient Graph Model for the Multiple Longest Common Subsequences (MLCS Problem

Directory of Open Access Journals (Sweden)

Zhan Peng

2017-08-01

Full Text Available Searching for the Multiple Longest Common Subsequences (MLCS of multiple sequences is a classical NP-hard problem, which has been used in many applications. One of the most effective exact approaches for the MLCS problem is based on dominant point graph, which is a kind of directed acyclic graph (DAG. However, the time and space efficiency of the leading dominant point graph based approaches is still unsatisfactory: constructing the dominated point graph used by these approaches requires a huge amount of time and space, which hinders the applications of these approaches to large-scale and long sequences. To address this issue, in this paper, we propose a new time and space efficient graph model called the Leveled-DAG for the MLCS problem. The Leveled-DAG can timely eliminate all the nodes in the graph that cannot contribute to the construction of MLCS during constructing. At any moment, only the current level and some previously generated nodes in the graph need to be kept in memory, which can greatly reduce the memory consumption. Also, the final graph contains only one node in which all of the wanted MLCS are saved, thus, no additional operations for searching the MLCS are needed. The experiments are conducted on real biological sequences with different numbers and lengths respectively, and the proposed algorithm is compared with three state-of-the-art algorithms. The experimental results show that the time and space needed for the Leveled-DAG approach are smaller than those for the compared algorithms especially on large-scale and long sequences.

International Space Station Centrifuge Rotor Models A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

Science.gov (United States)

Nguyen, Louis H.; Ramakrishnan, Jayant; Granda, Jose J.

2006-01-01

The assembly and operation of the International Space Station (ISS) require extensive testing and engineering analysis to verify that the Space Station system of systems would work together without any adverse interactions. Since the dynamic behavior of an entire Space Station cannot be tested on earth, math models of the Space Station structures and mechanical systems have to be built and integrated in computer simulations and analysis tools to analyze and predict what will happen in space. The ISS Centrifuge Rotor (CR) is one of many mechanical systems that need to be modeled and analyzed to verify the ISS integrated system performance on-orbit. This study investigates using Bond Graph modeling techniques as quick and simplified ways to generate models of the ISS Centrifuge Rotor. This paper outlines the steps used to generate simple and more complex models of the CR using Bond Graph Computer Aided Modeling Program with Graphical Input (CAMP-G). Comparisons of the Bond Graph CR models with those derived from Euler-Lagrange equations in MATLAB and those developed using multibody dynamic simulation at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) are presented to demonstrate the usefulness of the Bond Graph modeling approach for aeronautics and space applications.

Independence theory in combinatorics an introductory account with applications to graphs and transversals

CERN Document Server

Bryant, Victor

1980-01-01

Combinatorics may very loosely be described as that branch of mathematics which is concerned with the problems of arranging objects in accordance with various imposed constraints. It covers a wide range of ideas and because of its fundamental nature it has applications throughout mathematics. Among the well-established areas of combinatorics may now be included the studies of graphs and networks, block designs, games, transversals, and enumeration problem s concerning permutations and combinations, from which the subject earned its title, as weil as the theory of independence spaces (or matroids). Along this broad front,various central themes link together the very diverse ideas. The theme which we introduce in this book is that of the abstract concept of independence. Here the reason for the abstraction is to unify; and, as we sh all see, this unification pays off handsomely with applications and illuminating sidelights in a wide variety of combinatorial situations. The study of combinatorics in general, and...

Conceptual graph grammar--a simple formalism for sublanguage.

Science.gov (United States)

Johnson, S B

1998-11-01

There are a wide variety of computer applications that deal with various aspects of medical language: concept representation, controlled vocabulary, natural language processing, and information retrieval. While technical and theoretical methods appear to differ, all approaches investigate different aspects of the same phenomenon: medical sublanguage. This paper surveys the properties of medical sublanguage from a formal perspective, based on detailed analyses cited in the literature. A review of several computer systems based on sublanguage approaches shows some of the difficulties in addressing the interaction between the syntactic and semantic aspects of sublanguage. A formalism called Conceptual Graph Grammar is presented that attempts to combine both syntax and semantics into a single notation by extending standard Conceptual Graph notation. Examples from the domain of pathology diagnoses are provided to illustrate the use of this formalism in medical language analysis. The strengths and weaknesses of the approach are then considered. Conceptual Graph Grammar is an attempt to synthesize the common properties of different approaches to sublanguage into a single formalism, and to begin to define a common foundation for language-related research in medical informatics.

Left-ventricle segmentation in real-time 3D echocardiography using a hybrid active shape model and optimal graph search approach

Science.gov (United States)

Zhang, Honghai; Abiose, Ademola K.; Campbell, Dwayne N.; Sonka, Milan; Martins, James B.; Wahle, Andreas

2010-03-01

Quantitative analysis of the left ventricular shape and motion patterns associated with left ventricular mechanical dyssynchrony (LVMD) is essential for diagnosis and treatment planning in congestive heart failure. Real-time 3D echocardiography (RT3DE) used for LVMD analysis is frequently limited by heavy speckle noise or partially incomplete data, thus a segmentation method utilizing learned global shape knowledge is beneficial. In this study, the endocardial surface of the left ventricle (LV) is segmented using a hybrid approach combining active shape model (ASM) with optimal graph search. The latter is used to achieve landmark refinement in the ASM framework. Optimal graph search translates the 3D segmentation into the detection of a minimum-cost closed set in a graph and can produce a globally optimal result. Various information-gradient, intensity distributions, and regional-property terms-are used to define the costs for the graph search. The developed method was tested on 44 RT3DE datasets acquired from 26 LVMD patients. The segmentation accuracy was assessed by surface positioning error and volume overlap measured for the whole LV as well as 16 standard LV regions. The segmentation produced very good results that were not achievable using ASM or graph search alone.

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.

Calculating Graph Algorithms for Dominance and Shortest Path

DEFF Research Database (Denmark)

Sergey, Ilya; Midtgaard, Jan; Clarke, Dave

2012-01-01

We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point...... expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length. The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school...... of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation...

Graph-based network analysis of resting-state functional MRI

Directory of Open Access Journals (Sweden)

Jinhui Wang

2010-06-01

Full Text Available In the past decade, resting-state functional MRI (R-fMRI measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain’s spontaneous or intrinsic (i.e., task-free activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain’s intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.

Graph-based network analysis of resting-state functional MRI.

Science.gov (United States)

Wang, Jinhui; Zuo, Xinian; He, Yong

2010-01-01

In the past decade, resting-state functional MRI (R-fMRI) measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain's spontaneous or intrinsic (i.e., task-free) activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain's intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging, and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.

On the reachability and observability of path and cycle graphs

OpenAIRE

Parlangeli, Gianfranco; Notarstefano, Giuseppe

2011-01-01

In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: (i) a path graph...

Equity trees and graphs via information theory

Science.gov (United States)

Harré, M.; Bossomaier, T.

2010-01-01

We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the "genus 0" condition recently introduced in order to study the networks of equities.

Computing decay rates for new physics theories with FeynRules  and MadGraph 5 _aMC@NLO

CERN Document Server

Alwall, Johan; Fuks, Benjamin; Mattelaer, Olivier; Öztürk, Deniz Gizem; Shen, Chia-Hsien

2015-01-01

We present new features of the FeynRules and MadGraph5/aMC@NLO programs for the automatic computation of decay widths that consistently include channels of arbitrary final-state multiplicity. The implementations are generic enough so that they can be used in the framework of any quantum field theory, possibly including higher-dimensional operators. We extend at the same time the conventions of the Universal FeynRules Output (or UFO) format to include decay tables and information on the total widths. We finally provide a set of representative examples of the usage of the new functions of the different codes in the framework of the Standard Model, the Higgs Effective Field Theory, the Strongly Interacting Light Higgs model and the Minimal Supersymmetric Standard Model and compare the results to available literature and programs for validation purposes.

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.

Boundary conditions in rational conformal field theories

International Nuclear Information System (INIS)

Behrend, Roger E.; Pearce, Paul A.; Petkova, Valentina B.; Zuber, Jean-Bernard

2000-01-01

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalisation of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints

The Quantified Characterization Method of the Micro-Macro Contacts of Three-Dimensional Granular Materials on the Basis of Graph Theory.

Science.gov (United States)

Guan, Yanpeng; Wang, Enzhi; Liu, Xiaoli; Wang, Sijing; Luan, Hebing

2017-08-03

We have attempted a multiscale and quantified characterization method of the contact in three-dimensional granular material made of spherical particles, particularly in cemented granular material. Particle contact is defined as a type of surface contact with voids in its surroundings, rather than a point contact. Macro contact is a particle contact set satisfying the restrictive condition of a two-dimensional manifold with a boundary. On the basis of graph theory, two dual geometrical systems are abstracted from the granular pack. The face and the face set, which satisfies the two-dimensional manifold with a boundary in the solid cell system, are extracted to characterize the particle contact and the macro contact, respectively. This characterization method is utilized to improve the post-processing in DEM (Discrete Element Method) from a micro perspective to describe the macro effect of the cemented granular material made of spherical particles. Since the crack has the same shape as its corresponding contact, this method is adopted to characterize the crack and realize its visualization. The integral failure route of the sample can be determined by a graph theory algorithm. The contact force is assigned to the weight value of the face characterizing the particle contact. Since the force vectors can be added, the macro contact force can be solved by adding the weight of its corresponding faces.

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 $Hcong overline{F_n}$.

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.

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.

Algorithmic approach to diagram techniques

International Nuclear Information System (INIS)

Ponticopoulos, L.

1980-10-01

An algorithmic approach to diagram techniques of elementary particles is proposed. The definition and axiomatics of the theory of algorithms are presented, followed by the list of instructions of an algorithm formalizing the construction of graphs and the assignment of mathematical objects to them. (T.A.)

Models construction for acetone-butanol-ethanol fermentations with acetate/butyrate consecutively feeding by graph theory.

Science.gov (United States)

Li, Zhigang; Shi, Zhongping; Li, Xin

2014-05-01

Several fermentations with consecutively feeding of acetate/butyrate were conducted in a 7 L fermentor and the results indicated that exogenous acetate/butyrate enhanced solvents productivities by 47.1% and 39.2% respectively, and changed butyrate/acetate ratios greatly. Then extracellular butyrate/acetate ratios were utilized for calculation of acids rates and the results revealed that acetate and butyrate formation pathways were almost blocked by corresponding acids feeding. In addition, models for acetate/butyrate feeding fermentations were constructed by graph theory based on calculation results and relevant reports. Solvents concentrations and butanol/acetone ratios of these fermentations were also calculated and the results of models calculation matched fermentation data accurately which demonstrated that models were constructed in a reasonable way. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analysis of a planetary gear modelled with a contour graph considering the decision making complexity of game-tree structures

Directory of Open Access Journals (Sweden)

Deptuła Adam

2017-01-01

Full Text Available Analysis and synthesis of mechanisms is one of the fundamental tasks of engineering. Mechanisms can suffer from errors due to versatile reasons. Graph-based methods of analysis and synthesis of planetary gears constitute an alternative method for checking their correctness. Previous applications of the graph theory concerned modelling gears for dynamic analysis, kinematic analysis, synthesis, structural analysis, gearshift optimization and automatic design based on so-called graph grammars. Some tasks may be performed only with the methods resulting from the graph theory, e.g. enumeration of structural solutions. The contour plot method consists in distinguishing a series of consecutive rigid units of the analysed mechanism, forming a closed loop (so-called contour. At a later stage, it is possible to analyze the obtained contour graph as a directed graph of dependence. This work presents an example of the application of game-tree structures in describing the contour graph of a planetary gear. In addition, complex parametric tree structures are included.

Image-Based Edge Bundles : Simplified Visualization of Large Graphs

NARCIS (Netherlands)

Telea, A.; Ersoy, O.

2010-01-01

We present a new approach aimed at understanding the structure of connections in edge-bundling layouts. We combine the advantages of edge bundles with a bundle-centric simplified visual representation of a graph's structure. For this, we first compute a hierarchical edge clustering of a given graph

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.

Topological fixed point theory of multivalued mappings

CERN Document Server

Górniewicz, Lech

1999-01-01

This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal

Science.gov (United States)

Zamudio, Gabriel S.; José, Marco V.

2018-03-01

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

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.

Scaling up graph-based semisupervised learning via prototype vector machines.

Science.gov (United States)

Zhang, Kai; Lan, Liang; Kwok, James T; Vucetic, Slobodan; Parvin, Bahram

2015-03-01

When the amount of labeled data are limited, semisupervised learning can improve the learner's performance by also using the often easily available unlabeled data. In particular, a popular approach requires the learned function to be smooth on the underlying data manifold. By approximating this manifold as a weighted graph, such graph-based techniques can often achieve state-of-the-art performance. However, their high time and space complexities make them less attractive on large data sets. In this paper, we propose to scale up graph-based semisupervised learning using a set of sparse prototypes derived from the data. These prototypes serve as a small set of data representatives, which can be used to approximate the graph-based regularizer and to control model complexity. Consequently, both training and testing become much more efficient. Moreover, when the Gaussian kernel is used to define the graph affinity, a simple and principled method to select the prototypes can be obtained. Experiments on a number of real-world data sets demonstrate encouraging performance and scaling properties of the proposed approach. It also compares favorably with models learned via l1 -regularization at the same level of model sparsity. These results demonstrate the efficacy of the proposed approach in producing highly parsimonious and accurate models for semisupervised learning.

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

The R{sup ∗}-operation for Feynman graphs with generic numerators

Energy Technology Data Exchange (ETDEWEB)

Herzog, Franz [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Ruijl, Ben [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Leiden University,Niels Bohrweg 1, 2333 CA Leiden (Netherlands)

2017-05-08

The R{sup ∗}-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R{sup ∗}-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ{sup 3} theory.

Function spaces with uniform, fine and graph topologies

CERN Document Server

McCoy, Robert A; Jindal, Varun

2018-01-01

This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.

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

Information-optimal genome assembly via sparse read-overlap graphs.

Science.gov (United States)

Shomorony, Ilan; Kim, Samuel H; Courtade, Thomas A; Tse, David N C

2016-09-01

In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence? Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph. Unlike most other assembly algorithms, Not-So-Greedy comes with a performance guarantee: whenever information feasibility conditions are satisfied, the algorithm reduces the assembly problem to an Eulerian path problem on the resulting graph, and can thus be solved in linear time. In practice, this theoretical guarantee translates into assemblies of higher quality. Evaluations on both simulated reads from real genomes and a PacBio Escherichia coli K12 dataset demonstrate that Not-So-Greedy compares favorably with standard string graph approaches in terms of accuracy of the resulting read-overlap graph and contig N50. Available at github.com/samhykim/nsg courtade@eecs.berkeley.edu or dntse@stanford.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Proceedings 3rd Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014)

DEFF Research Database (Denmark)

2014-01-01

is to foster the convergence on research interests from several communities dealing with graph analysis in all its forms in computer science, with a particular attention to software development and analysis. Graphs are used to represent data and processes in many application areas, and they are subjected......These are the proceedings of the Third Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014), which took place on April 5, 2014 in Grenoble, France, as a satellite event of the 17th European Joint Conferences on Theory and Practice of Software (ETAPS 2014). The aim of GRAPHITE...... to various computational algorithms in order to analyze them. Just restricting the attention to the analysis of software, graph analysis algorithms are used, for instance, to verify properties using model checking techniques that explore the system's state space graph or static analysis techniques based...

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems.

Science.gov (United States)

Elmeligy Abdelhamid, Sherif H; Kuhlman, Chris J; Marathe, Madhav V; Mortveit, Henning S; Ravi, S S

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.

Identifying Threats Using Graph-based Anomaly Detection

Science.gov (United States)

Eberle, William; Holder, Lawrence; Cook, Diane

Much of the data collected during the monitoring of cyber and other infrastructures is structural in nature, consisting of various types of entities and relationships between them. The detection of threatening anomalies in such data is crucial to protecting these infrastructures. We present an approach to detecting anomalies in a graph-based representation of such data that explicitly represents these entities and relationships. The approach consists of first finding normative patterns in the data using graph-based data mining and then searching for small, unexpected deviations to these normative patterns, assuming illicit behavior tries to mimic legitimate, normative behavior. The approach is evaluated using several synthetic and real-world datasets. Results show that the approach has high truepositive rates, low false-positive rates, and is capable of detecting complex structural anomalies in real-world domains including email communications, cellphone calls and network traffic.

Networks as a Privileged Way to Develop Mesoscopic Level Approaches in Systems Biology

OpenAIRE

Alessandro Giuliani

2014-01-01

The methodologies advocated in computational biology are in many cases proper system-level approaches. These methodologies are variously connected to the notion of “mesosystem” and thus on the focus on relational structures that are at the basis of biological regulation. Here, I describe how the formalization of biological systems by means of graph theory constitutes an extremely fruitful approach to biology. I suggest the epistemological relevance of the notion of graph resides in its multil...

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.

Refining intra-protein contact prediction by graph analysis

Directory of Open Access Journals (Sweden)

Eyal Eran

2007-05-01

Full Text Available Abstract Background Accurate prediction of intra-protein residue contacts from sequence information will allow the prediction of protein structures. Basic predictions of such specific contacts can be further refined by jointly analyzing predicted contacts, and by adding information on the relative positions of contacts in the protein primary sequence. Results We introduce a method for graph analysis refinement of intra-protein contacts, termed GARP. Our previously presented intra-contact prediction method by means of pair-to-pair substitution matrix (P2PConPred was used to test the GARP method. In our approach, the top contact predictions obtained by a basic prediction method were used as edges to create a weighted graph. The edges were scored by a mutual clustering coefficient that identifies highly connected graph regions, and by the density of edges between the sequence regions of the edge nodes. A test set of 57 proteins with known structures was used to determine contacts. GARP improves the accuracy of the P2PConPred basic prediction method in whole proteins from 12% to 18%. Conclusion Using a simple approach we increased the contact prediction accuracy of a basic method by 1.5 times. Our graph approach is simple to implement, can be used with various basic prediction methods, and can provide input for further downstream analyses.

A closed graph theorem for order bounded operators | Harm van der ...

African Journals Online (AJOL)

... theory to prove a version of the closed graph theorem for order bounded operators on Archimedean vector lattices. This illustrates the usefulness of convergence spaces in dealing with problems in vector lattice theory, problems that may fail to be amenable to the usual Hausdorff-Kuratowski-Bourbaki concept of topology.

Böhm Reduction in Infinitary Term Graph Rewriting Systems

DEFF Research Database (Denmark)

Bahr, Patrick

2017-01-01

a corresponding theory of Böhm reduction for term graphs. Our main result is that partial order convergence in a term graph rewriting system can be truthfully and faithfully simulated by metric convergence in the Böhm extension of the system. To prove this result we generalise the notion of residuals...... that `meaningless terms' can be contracted to a fresh constant ⊥. In previous work, we have established that Böhm reduction can be instead characterised by a different mode of convergences of transfinite reductions that is based on a partial order structure instead of a metric space. In this paper, we develop...... and projections to the setting of infinitary term graph rewriting. As ancillary results we prove the infinitary strip lemma and the compression property, both for partial order and metric convergence....

Representation and integration of sociological knowledge using knowledge graphs

NARCIS (Netherlands)

Popping, R; Strijker, [No Value

1997-01-01

The representation and integration of sociological knowledge using knowledge graphs, a specific kind of semantic network, is discussed. Knowledge it systematically searched this reveals. inconsistencies, reducing superfluous research and knowledge, and showing gaps in a theory. This representation

Intraplate seismicity in Canada: a graph theoretic approach to data analysis and interpretation

Directory of Open Access Journals (Sweden)

K. Vasudevan

2010-10-01

Full Text Available Intraplate seismicity occurs in central and northern Canada, but the underlying origin and dynamics remain poorly understood. Here, we apply a graph theoretic approach to characterize the statistical structure of spatiotemporal clustering exhibited by intraplate seismicity, a direct consequence of the underlying nonlinear dynamics. Using a recently proposed definition of "recurrences" based on record breaking processes (Davidsen et al., 2006, 2008, we have constructed directed graphs using catalogue data for three selected regions (Region 1: 45°−48° N/74°−80° W; Region 2: 51°−55° N/77°−83° W; and Region 3: 56°−70° N/65°−95° W, with attributes drawn from the location, origin time and the magnitude of the events. Based on comparisons with a null model derived from Poisson distribution or Monte Carlo shuffling of the catalogue data, our results provide strong evidence in support of spatiotemporal correlations of seismicity in all three regions considered. Similar evidence for spatiotemporal clustering has been documented using seismicity catalogues for southern California, suggesting possible similarities in underlying earthquake dynamics of both regions despite huge differences in the variability of seismic activity.

Query Optimizations over Decentralized RDF Graphs

KAUST Repository

Abdelaziz, Ibrahim; Mansour, Essam; Ouzzani, Mourad; Aboulnaga, Ashraf; Kalnis, Panos

2017-01-01

Applications in life sciences, decentralized social networks, Internet of Things, and statistical linked dataspaces integrate data from multiple decentralized RDF graphs via SPARQL queries. Several approaches have been proposed to optimize query

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.

Worst-case Throughput Analysis for Parametric Rate and Parametric Actor Execution Time Scenario-Aware Dataflow Graphs

Directory of Open Access Journals (Sweden)

Mladen Skelin

2014-03-01

Full Text Available Scenario-aware dataflow (SADF is a prominent tool for modeling and analysis of dynamic embedded dataflow applications. In SADF the application is represented as a finite collection of synchronous dataflow (SDF graphs, each of which represents one possible application behaviour or scenario. A finite state machine (FSM specifies the possible orders of scenario occurrences. The SADF model renders the tightest possible performance guarantees, but is limited by its finiteness. This means that from a practical point of view, it can only handle dynamic dataflow applications that are characterized by a reasonably sized set of possible behaviours or scenarios. In this paper we remove this limitation for a class of SADF graphs by means of SADF model parametrization in terms of graph port rates and actor execution times. First, we formally define the semantics of the model relevant for throughput analysis based on (max,+ linear system theory and (max,+ automata. Second, by generalizing some of the existing results, we give the algorithms for worst-case throughput analysis of parametric rate and parametric actor execution time acyclic SADF graphs with a fully connected, possibly infinite state transition system. Third, we demonstrate our approach on a few realistic applications from digital signal processing (DSP domain mapped onto an embedded multi-processor architecture.

On the discrete spectrum of the Dirac operator on bent chain quantum graph

Directory of Open Access Journals (Sweden)

Belov Michail

2017-01-01

Full Text Available We study Dirac operators on an infinite quantum graph of a bent chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter α ∈ ℝ. We are interested in the discrete spectrum of the corresponding Hamiltonian. It can be non-empty due to a local (geometrical perturbation of the corresponding infinite chain of rings. The quantum graph of analogous geometry with the Schrodinger operator on the edges was considered by Duclos, Exner and Turek in 2008. They showed that the absence of δ-couplings at vertices (i.e. the Kirchhoff condition at the vertices lead to the absence of eigenvalues. We consider the relativistic particle (the Dirac operator instead of the Schrodinger one but the result is analogous. Quantum graphs of such type are suitable for description of grapheme-based nanostructures. It is established that the negativity of α is the necessary and sufficient condition for the existence of eigenvalues of the Dirac operator (i.e. the discrete spectrum of the Hamiltonian in this case is not empty. The continuous spectrum of the Hamiltonian for bent chain graph coincides with that for the corresponding straight infinite chain. Conditions for appearance of more than one eigenvalue are obtained. It is related to the bending angle. The investigation is based on the transfer-matrix approach. It allows one to reduce the problem to an algebraic task. δ-couplings was introduced by the operator extensions theory method.

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.

The use of graph theory in the sensitivity analysis of the model output: a second order screening method

International Nuclear Information System (INIS)

Campolongo, Francesca; Braddock, Roger

1999-01-01

Sensitivity analysis screening methods aim to isolate the most important factors in experiments involving a large number of significant factors and interactions. This paper extends the one-factor-at-a-time screening method proposed by Morris. The new method, in addition to the 'overall' sensitivity measures already provided by the traditional Morris method, offers estimates of the two-factor interaction effects. The number of model evaluations required is O(k 2 ), where k is the number of model input factors. The efficient sampling strategy in the parameter space is based on concepts of graph theory and on the solution of the 'handcuffed prisoner problem'

Bond Graph Modeling and Simulation of Mechatronic Systems

DEFF Research Database (Denmark)

Habib, Tufail; Nielsen, Kjeld; Jørgensen, Kaj Asbjørn

2012-01-01

One of the demanding steps in the design and development of Mechatronic systems is to develop the initial model to visualize the response of a system. The Bond Graph (BG) method is a graphical approach for the design of multidomain systems. That is ideal for visualizing the essential characterist......One of the demanding steps in the design and development of Mechatronic systems is to develop the initial model to visualize the response of a system. The Bond Graph (BG) method is a graphical approach for the design of multidomain systems. That is ideal for visualizing the essential...

Maximum-entropy networks pattern detection, network reconstruction and graph combinatorics

CERN Document Server

Squartini, Tiziano

2017-01-01

This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties.  After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem o...

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...

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.

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

Total colourings of graphs

CERN Document Server

Yap, Hian-Poh

1996-01-01

This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.

Noise reduction in protein-protein interaction graphs by the implementation of a novel weighting scheme

Directory of Open Access Journals (Sweden)

Moschopoulos Charalampos

2011-06-01

Full Text Available Abstract Background Recent technological advances applied to biology such as yeast-two-hybrid, phage display and mass spectrometry have enabled us to create a detailed map of protein interaction networks. These interaction networks represent a rich, yet noisy, source of data that could be used to extract meaningful information, such as protein complexes. Several interaction network weighting schemes have been proposed so far in the literature in order to eliminate the noise inherent in interactome data. In this paper, we propose a novel weighting scheme and apply it to the S. cerevisiae interactome. Complex prediction rates are improved by up to 39%, depending on the clustering algorithm applied. Results We adopt a two step procedure. During the first step, by applying both novel and well established protein-protein interaction (PPI weighting methods, weights are introduced to the original interactome graph based on the confidence level that a given interaction is a true-positive one. The second step applies clustering using established algorithms in the field of graph theory, as well as two variations of Spectral clustering. The clustered interactome networks are also cross-validated against the confirmed protein complexes present in the MIPS database. Conclusions The results of our experimental work demonstrate that interactome graph weighting methods clearly improve the clustering results of several clustering algorithms. Moreover, our proposed weighting scheme outperforms other approaches of PPI graph weighting.

Quantum vacuum energy in graphs and billiards

International Nuclear Information System (INIS)

Kaplan, L.

2010-01-01

The vacuum (Casimir) energy in quantum field theory is a problem relevant both to new nanotechnology devices and to dark energy in cosmology. The crucial question is the dependence of the energy on the system geometry. Despite much progress since the first prediction of the Casimir effect in 1948 and its subsequent experimental verification in simple geometries, even the sign of the force in nontrivial situations is still a matter of controversy. Mathematically, vacuum energy fits squarely into the spectral theory of second-order self-adjoint elliptic linear differential operators. Specifically one promising approach is based on the small-t asymptotics of the cylinder kernel e -t√(H) , where H is the self-adjoint operator under study. In contrast with the well-studied heat kernel e -tH , the cylinder kernel depends in a non-local way on the geometry of the problem. We discuss some results by the Louisiana-Oklahoma-Texas collaboration on vacuum energy in model systems, including quantum graphs and two-dimensional cavities. The results may shed light on general questions, including the relationship between vacuum energy and periodic or closed classical orbits, and the contribution to vacuum energy of boundaries, edges, and corners.

Multithreaded Asynchronous Graph Traversal for In-Memory and Semi-External Memory

KAUST Repository

Pearce, Roger; Gokhale, Maya; Amato, Nancy M.

2010-01-01

. Our highly parallel asynchronous approach hides data latency due to both poor locality and delays in the underlying graph data storage. We present an experimental study applying our technique to both In-Memory and Semi-External Memory graphs utilizing

Parallel Algorithms for Graph Optimization using Tree Decompositions

Energy Technology Data Exchange (ETDEWEB)

Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL; Groer, Christopher S [ORNL

2012-06-01

Although many $\\cal{NP}$-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the necessary dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree decomposition-based approach to solve the maximum weighted independent set problem. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.

Using graph theory to analyze the vulnerability of process plants in the context of cascading effects

International Nuclear Information System (INIS)

Khakzad, Nima; Reniers, Genserik

2015-01-01

Dealing with large quantities of flammable and explosive materials, usually at high-pressure high-temperature conditions, makes process plants very vulnerable to cascading effects compared with other infrastructures. The combination of the extremely low frequency of cascading effects and the high complexity and interdependencies of process plants makes risk assessment and vulnerability analysis of process plants very challenging in the context of such events. In the present study, cascading effects were represented as a directed graph; accordingly, the efficacy of a set of graph metrics and measurements was examined in both unit and plant-wide vulnerability analysis of process plants. We demonstrated that vertex-level closeness and betweenness can be used in the unit vulnerability analysis of process plants for the identification of critical units within a process plant. Furthermore, the graph-level closeness metric can be used in the plant-wide vulnerability analysis for the identification of the most vulnerable plant layout with respect to the escalation of cascading effects. Furthermore, the results from the application of the graph metrics have been verified using a Bayesian network methodology. - Highlights: • Graph metrics can effectively be employed to identify vulnerable units and layouts in process plants. • Units with larger vertex-level closeness result in more probable and severe cascading effects. • Units with larger vertex-level betweenness contribute more to the escalation of cascading effects. • Layouts with larger graph-level closeness are more vulnerable to the escalation of cascading effects

Causal inference, probability theory, and graphical insights.

Science.gov (United States)

Baker, Stuart G

2013-11-10

Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design. Published 2013. This article is a US Government work and is in the public domain in the USA.

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...

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.

Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs

Science.gov (United States)

2013-06-28

3380. [DEL12a] Xavier Desquesnes, Abderrahim Elmoataz, and Olivier Lézoray, Eikonal equation adapta- tion on weighted graphs: Fast geometric diffusion...Abderrahim Elmoataz, Olivier Lézoray, and Vinh-Thong Ta, Efficient algorithms for image and high dimensional data processing using eikonal equation on

Application-Specific Graph Sampling for Frequent Subgraph Mining and Community Detection

Energy Technology Data Exchange (ETDEWEB)

Purohit, Sumit; Choudhury, Sutanay; Holder, Lawrence B.

2017-12-11

Graph mining is an important data analysis methodology, but struggles as the input graph size increases. The scalability and usability challenges posed by such large graphs make it imperative to sample the input graph and reduce its size. The critical challenge in sampling is to identify the appropriate algorithm to insure the resulting analysis does not suffer heavily from the data reduction. Predicting the expected performance degradation for a given graph and sampling algorithm is also useful. In this paper, we present different sampling approaches for graph mining applications such as Frequent Subgrpah Mining (FSM), and Community Detection (CD). We explore graph metrics such as PageRank, Triangles, and Diversity to sample a graph and conclude that for heterogeneous graphs Triangles and Diversity perform better than degree based metrics. We also present two new sampling variations for targeted graph mining applications. We present empirical results to show that knowledge of the target application, along with input graph properties can be used to select the best sampling algorithm. We also conclude that performance degradation is an abrupt, rather than gradual phenomena, as the sample size decreases. We present the empirical results to show that the performance degradation follows a logistic function.