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
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Khovanov homology of graph-links
Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-08-31
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Homology groups for particles on one-connected graphs
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.
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
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.
Computing Homology Group Generators of Images Using Irregular Graph Pyramids
Peltier , Samuel; Ion , Adrian; Haxhimusa , Yll; Kropatsch , Walter; Damiand , Guillaume
2007-01-01
International audience; We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built, by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on...
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
Khovanov-Rozansky Graph Homology and Composition Product
Wagner, Emmanuel
2008-01-01
In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology.......In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology....
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Planar graphs theory and algorithms
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.
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
Graph Theory. 1. Fragmentation of Structural Graphs
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.
Towards a theory of geometric graphs
Pach, Janos
2004-01-01
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...
Three Syntactic Theories for Combinatory Graph Reduction
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...
Three Syntactic Theories for Combinatory Graph Reduction
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...
A first course in graph theory
Chartrand, Gary
2012-01-01
This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications.Optional sections designated as ""excursion"" and ""exploration"" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three app
Homological methods, representation theory, and cluster algebras
Trepode, Sonia
2018-01-01
This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, wh...
A homology theory for smale spaces
Putnam, Ian F
2014-01-01
The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.
Graph theory and the Virasoro master equation
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
Graph Theory to Pure Mathematics: Some Illustrative Examples
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,.
Algebraic Graph Theory Morphisms, Monoids and Matrices
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
Homological Perturbation Theory for Nonperturbative Integrals
Johnson-Freyd, Theo
2015-11-01
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler-Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.
Graphs on Surfaces and the Partition Function of String Theory
Garcia-Islas, J. Manuel
2007-01-01
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the relation between graph theory and the mathematical physics of discrete string theory. In this description we present problems of the combinatorial world of real importance for graph theorists. The mathematical details of the paper are as follows: There is a com...
Graph Theory. 2. Vertex Descriptors and Graph Coloring
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.
A local homology theory for linearly compact modules
Nguyen Tu Cuong; Tran Tuan Nam
2004-11-01
We introduce a local homology theory for linearly modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties of local homology modules are shown such as: the vanishing and non-vanishing, the noetherianness of local homology modules. By using duality, we extend some well-known results in theory of local cohomology of A. Grothendieck. (author)
Some Results on the Graph Theory for Complex Neutrosophic Sets
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.
Graph Theory Approach for Studying Food Webs
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.
Molecular orbital calculations using chemical graph theory
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...
On some interconnections between combinatorial optimization and extremal graph theory
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.
Graph theory for alternating hydrocarbons with attached ports
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 Theory in Paris : Conference in Memory of Claude Berge
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.
The $K$-theory of real graph $C*$-algebras
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...
A first course in graph theory and combinatorics
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.
Efficient Algorithmic Frameworks via Structural Graph Theory
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
Using graph theory for automated electric circuit solving
Toscano, L; Stella, S; Milotti, E
2015-01-01
Graph theory plays many important roles in modern physics and in many different contexts, spanning diverse topics such as the description of scale-free networks and the structure of the universe as a complex directed graph in causal set theory. Graph theory is also ideally suited to describe many concepts in computer science. Therefore it is increasingly important for physics students to master the basic concepts of graph theory. Here we describe a student project where we develop a computational approach to electric circuit solving which is based on graph theoretic concepts. This highly multidisciplinary approach combines abstract mathematics, linear algebra, the physics of circuits, and computer programming to reach the ambitious goal of implementing automated circuit solving. (paper)
High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs
Kempton, Mark
This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.
Graph-based linear scaling electronic structure theory
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.
Fractional graph theory a rational approach to the theory of graphs
Scheinerman, Edward R
2013-01-01
A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. The final chapter examines additional topics such as fractional domination, fractional intersection numbers
Applying Graph Theory to Problems in Air Traffic Management
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.
Anderson, Jonas T., E-mail: jonastyleranderson@gmail.com
2013-03-15
In this paper we define homological stabilizer codes on qubits which encompass codes such as Kitaev's toric code and the topological color codes. These codes are defined solely by the graphs they reside on. This feature allows us to use properties of topological graph theory to determine the graphs which are suitable as homological stabilizer codes. We then show that all toric codes are equivalent to homological stabilizer codes on 4-valent graphs. We show that the topological color codes and toric codes correspond to two distinct classes of graphs. We define the notion of label set equivalencies and show that under a small set of constraints the only homological stabilizer codes without local logical operators are equivalent to Kitaev's toric code or to the topological color codes. - Highlights: Black-Right-Pointing-Pointer We show that Kitaev's toric codes are equivalent to homological stabilizer codes on 4-valent graphs. Black-Right-Pointing-Pointer We show that toric codes and color codes correspond to homological stabilizer codes on distinct graphs. Black-Right-Pointing-Pointer We find and classify all 2D homological stabilizer codes. Black-Right-Pointing-Pointer We find optimal codes among the homological stabilizer codes.
Solved and unsolved problems of chemical graph theory
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
Quantifying Riverscape Connectivity with Graph Theory
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
Equity trees and graphs via information theory
Harré, M.; Bossomaier, T.
2010-01-01
We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the "genus 0" condition recently introduced in order to study the networks of equities.
Embedded graph invariants in Chern-Simons theory
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
BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.
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
Modeling of tethered satellite formations using graph theory
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...
On discrete symmetries and torsion homology in F-theory
Mayrhofer, Christoph [Arnold-Sommerfeld-Center, Ludwig-Maximilians-Universität München,München (Germany); Palti, Eran; Till, Oskar; Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg,Heidelberg (Germany)
2015-06-04
We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a ℤ{sub 2} symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a ℤ{sub 2} gauge symmetry. We show that the resulting five-dimensional theories do not have a ℤ{sub 2} symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a ℤ{sub 2} symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.
Vertex maps on graphs -- Perron-Frobenius Theory
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.
Intersection spaces, spatial homology truncation, and string theory
Banagl, Markus
2010-01-01
Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest to homotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.
Simulating activation propagation in social networks using the graph theory
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.
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions
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.
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
Utilization of graph theory in security analysis of power grid
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.
Graph theory and binary alloys passivated by nickel
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
Graph Theory Roots of Spatial Operators for Kinematics and Dynamics
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
Dilogarithm identities in conformal field theory and group homology
Dupont, J.L.
1994-01-01
Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin (equivalent to an identity found earlier by Lewin) can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all 2x2 real matrices viewed as a discrete group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic K-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all 2x2 real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with a summary of a number of open conjectures on the mathematical side. (orig.)
Graph theory favorite conjectures and open problems 1
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...
GCPSO in cooperation with graph theory to distribution network reconfiguration for energy saving
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.
Poor textural image tie point matching via graph theory
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.
Application of graph theory to the morphological analysis of settlements
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 THEORY APPROACH TO QUANTIFY UNCERTAINTY OF PERFORMANCE MEASURES
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.
Political Discourse Analysis Through Solving Problems of Graph Theory
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].
Valued Graphs and the Representation Theory of Lie Algebras
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.
The graph representation approach to topological field theory in 2 + 1 dimensions
Martin, S.P.
1991-02-01
An alternative definition of topological quantum field theory in 2+1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but non-local observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wavefunctions in this ''graph representation'' approach are functionals on an appropriate set of graphs. This is in contrast to the usual ''connection representation'' approach in which the theory is defined in terms of a gauge field and the wavefunctions are functionals on the space of flat spatial connections modulo gauge transformations
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
Generating loop graphs via Hopf algebra in quantum field theory
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
Augmenting Conceptual Design Trajectory Tradespace Exploration with Graph Theory
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.
Application of graph theory to the morphological analysis of settlements
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.
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.
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…
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 ...
Fisch, J.M.L.
1990-01-01
The algebraic structure of the antifield-antibracket formalism for both reducible and irreducible gauge theories is clarified. This is done by using the methods of Homological Perturbation Theory (HPT). A crucial ingredient of the construction is the Koszul-Tate complex associated with the stationary surface of the classical extremals. The Koszul-Tate differential acts on the antifields and is graded by the antighost number. It provides a resolution of the algebra A of functions defined on the stationary surface, namely, it is acyclic except at degree zero where its homology group reduces to A. Acyclicity only holds because of the introduction of the ghosts of ghosts and provides an alternative criterion for what is meant by a proper solution of the master equation. The existence of the BRST symmetry follows from the techniques of HPT. The classical Lagrangian BRST cohomology is completely worked out and shown to be isomorphic with the cohomology of the exterior derivative along the gauge orbits on the stationary surface. The algebraic structure of the formalism is identical with the structure of the Hamiltonian BRST construction. The role played there by the constraint surface is played here by the stationary surface. Only elementary quantum questions (general properties of the measure) are addressed. (orig.)
Quantum entanglement in non-local games, graph parameters and zero-error information theory
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
Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
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.
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...
POOR TEXTURAL IMAGE MATCHING BASED ON GRAPH THEORY
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.
MACCIA, ELIZABETH S.; AND OTHERS
AN ANNOTATED BIBLIOGRAPHY OF 20 ITEMS AND A DISCUSSION OF ITS SIGNIFICANCE WAS PRESENTED TO DESCRIBE CURRENT UTILIZATION OF SUBJECT THEORIES IN THE CONSTRUCTION OF AN EDUCATIONAL THEORY. ALSO, A THEORY MODEL WAS USED TO DEMONSTRATE CONSTRUCTION OF A SCIENTIFIC EDUCATIONAL THEORY. THE THEORY MODEL INCORPORATED SET THEORY (S), INFORMATION THEORY…
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.
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.
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.
Mechanical system reliability analysis using a combination of graph theory and Boolean function
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
Factors and factorizations of graphs proof techniques in factor theory
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.
An Application of Graph Theory in Markov Chains Reliability Analysis
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.
Modal Analysis of In-Wheel Motor-Driven Electric Vehicle Based on Bond Graph Theory
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.
Comparing brain networks of different size and connectivity density using graph theory.
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.
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.
Сlassification of methods of production of computer forensic by usage approach of graph theory
Anna Ravilyevna Smolina
2016-06-01
Full Text Available Сlassification of methods of production of computer forensic by usage approach of graph theory is proposed. If use this classification, it is possible to accelerate and simplify the search of methods of production of computer forensic and this process to automatize.
Сlassification of methods of production of computer forensic by usage approach of graph theory
Anna Ravilyevna Smolina; Alexander Alexandrovich Shelupanov
2016-01-01
Сlassification of methods of production of computer forensic by usage approach of graph theory is proposed. If use this classification, it is possible to accelerate and simplify the search of methods of production of computer forensic and this process to automatize.
A Qualitative Analysis Framework Using Natural Language Processing and Graph Theory
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…
Semantic Mining based on graph theory and ontologies. Case Study: Cell Signaling Pathways
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.
PROBLEMS IN TOPOLOGICAL GRAPH THEORY : QUESTIONS I CAN'T ANSWER
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.
Feynman graphs and gauge theories for experimental physicists. 2. rev. ed.
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)
Routing Planning As An Application Of Graph Theory with Fuzzy Logic
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.
SIMULATION OF DRIVER’S LOCOMOTIVE-HANDLING ACTIVITY USING THE THEORY OF FUZZY GRAPHS
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
Graph theory applied to noise and vibration control in statistical energy analysis models.
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.
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.
Connections between the Sznajd model with general confidence rules and graph theory
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).
Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory
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
Identifying patients with Alzheimer's disease using resting-state fMRI and graph theory.
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.
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.
Hadronic equation of state in the statistical bootstrap model and linear graph theory
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
Using Zipf-Mandelbrot law and graph theory to evaluate animal welfare
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
Energy Minimization of Discrete Protein Titration State Models Using Graph Theory
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.
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.
Summing Feynman graphs by Monte Carlo: Planar φ3-theory and dynamically triangulated random surfaces
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.)
A graph-theory framework for evaluating landscape connectivity and conservation planning.
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.
An unprecedented multi attribute decision making using graph theory matrix approach
N.K. Geetha
2018-02-01
Full Text Available A frame work for investigating the best combination of functioning parameters on a variable compression ratio diesel engine is proposed in the present study using a multi attribute optimization methodology, Graph Theory Matrix Approach. The functioning parameters, attributes, sub attributes and functioning variables of sub attributes are chosen based on expert’s opinion and literature review. The directed graphs are developed for attributes and sub attributes. The ‘Parameter Index’ was calculated for all trials to choose the best trial. The experimental results are verified with the theoretical data. Functioning parameters with combination of compression ratio of 17, fuel injection pressure of 20 N/mm2 and fuel injection pressure of 21°bTDC was found to be best. The proposed method allows the decision maker to systematically and logically find the best combination of functioning parameters.
Classification of mini-dimmings associated with extreme ultraviolet eruptions by using graph theory
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.
The Stability Analysis Method of the Cohesive Granular Slope on the Basis of Graph Theory.
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.
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.
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.
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.
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.
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
The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI.
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
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
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
Analysis of the enzyme network involved in cattle milk production using graph theory.
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.
An application of the graph theory which examines the metro networks
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.
Differences in graph theory functional connectivity in left and right temporal lobe epilepsy.
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.
The obstruction to excision in K-theory and in cyclic homology
Cortinas, Guillermo
2001-11-01
Let f:A→B be a ring homomorphism of not necessarily unital rings and I∇A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K * (A:I)→K * (B:f(I)) to be an isomorphism; it is measured by the birelative groups K * (A,B:I). We show that these are rationally isomorphic to the corresponding birelative groups for cyclic homology up to a dimension shift. In the particular case when A and B are Q-algebras we obtain an integral isomorphism. (author)
PDB2Graph: A toolbox for identifying critical amino acids map in proteins based on graph theory.
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.
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.
Quantification of three-dimensional cell-mediated collagen remodeling using graph theory.
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.
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.
The Epstein-Glaser approach to perturbative quantum field theory: graphs and Hopf algebras
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
Development of a new loss allocation method for a hybrid electricity market using graph theory
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)
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
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.
Topological quantum field theories in terms of coloured graphs associated to quantum groups
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.)
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...
P. B. Lanjewar
2016-06-01
Full Text Available The evaluation and selection of energy technologies involve a large number of attributes whose selection and weighting is decided in accordance with the social, environmental, technical and economic framework. In the present work an integrated multiple attribute decision making methodology is developed by combining graph theory and analytic hierarchy process methods to deal with the evaluation and selection of energy technologies. The energy technology selection attributes digraph enables a quick visual appraisal of the energy technology selection attributes and their interrelationships. The preference index provides a total objective score for comparison of energy technologies alternatives. Application of matrix permanent offers a better appreciation of the considered attributes and helps to analyze the different alternatives from combinatorial viewpoint. The AHP is used to assign relative weights to the attributes. Four examples of evaluation and selection of energy technologies are considered in order to demonstrate and validate the proposed method.
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...
Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms
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...
K-theory and periodic cyclic homology of some noncompact quantum algebras
Do Ngoc Diep; Kuku, Aderemi O.
2003-07-01
We prove in this paper that the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of connected and simply connected Lie group, are isomorphic to the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of compact maximal subgroups, without localization. Some noncompact quantum groups and algebras were constructed and their irreducible representations were classified in recent works of Do Ngoc Diep and Nguyen Viet Hai [DH1]-[DH2] and Do Due Hanh [DD] by using deformation quantization. In this paper we compute their K-groups, periodic cyclic homology groups and their Chern characters. (author)
Huang, Yun-An; Jastorff, Jan; Van den Stock, Jan; Van de Vliet, Laura; Dupont, Patrick; Vandenbulcke, Mathieu
2018-05-15
Psychological construction models of emotion state that emotions are variable concepts constructed by fundamental psychological processes, whereas according to basic emotion theory, emotions cannot be divided into more fundamental units and each basic emotion is represented by a unique and innate neural circuitry. In a previous study, we found evidence for the psychological construction account by showing that several brain regions were commonly activated when perceiving different emotions (i.e. a general emotion network). Moreover, this set of brain regions included areas associated with core affect, conceptualization and executive control, as predicted by psychological construction models. Here we investigate directed functional brain connectivity in the same dataset to address two questions: 1) is there a common pathway within the general emotion network for the perception of different emotions and 2) if so, does this common pathway contain information to distinguish between different emotions? We used generalized psychophysiological interactions and information flow indices to examine the connectivity within the general emotion network. The results revealed a general emotion pathway that connects neural nodes involved in core affect, conceptualization, language and executive control. Perception of different emotions could not be accurately classified based on the connectivity patterns from the nodes of the general emotion pathway. Successful classification was achieved when connections outside the general emotion pathway were included. We propose that the general emotion pathway functions as a common pathway within the general emotion network and is involved in shared basic psychological processes across emotions. However, additional connections within the general emotion network are required to classify different emotions, consistent with a constructionist account. Copyright © 2018 Elsevier Inc. All rights reserved.
Keown, Christopher L; Datko, Michael C; Chen, Colleen P; Maximo, José Omar; Jahedi, Afrooz; Müller, Ralph-Axel
2017-01-01
Despite abundant evidence of brain network anomalies in autism spectrum disorder (ASD), findings have varied from broad functional underconnectivity to broad overconnectivity. Rather than pursuing overly simplifying general hypotheses ('under' vs. 'over'), we tested the hypothesis of atypical network distribution in ASD (i.e., participation of unusual loci in distributed functional networks). We used a selective high-quality data subset from the ABIDE datashare (including 111 ASD and 174 typically developing [TD] participants) and several graph theory metrics. Resting state functional MRI data were preprocessed and analyzed for detection of low-frequency intrinsic signal correlations. Groups were tightly matched for available demographics and head motion. As hypothesized, the Rand Index (reflecting how similar network organization was to a normative set of networks) was significantly lower in ASD than TD participants. This was accounted for by globally reduced cohesion and density, but increased dispersion of networks. While differences in hub architecture did not survive correction, rich club connectivity (among the hubs) was increased in the ASD group. Our findings support the model of reduced network integration (connectivity with networks) and differentiation (or segregation; based on connectivity outside network boundaries) in ASD. While the findings applied at the global level, they were not equally robust across all networks and in one case (greater cohesion within ventral attention network in ASD) even reversed.
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
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.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
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.
Cytoscape.js: a graph theory library for visualisation and analysis.
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.
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.
Fuzzy Graph Language Recognizability
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.
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.
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.
Bond graph modelling of engineering systems: theory, applications and software support
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 ...
Anticipation-related brain connectivity in bipolar and unipolar depression: a graph theory approach.
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
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
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.
Introduction to quantum graphs
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...
Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs
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
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
Ruffino, Fabio Ferrari
2013-01-01
Given a cohomology theory, there is a well-known abstract way to define the dual homology theory using the theory of spectra. In [4] the author provides a more geometric construction of the homology theory, using a generalization of the bordism groups. Such a generalization involves in its definition the vector bundle modification, which is a particular case of the Gysin map. In this paper we provide a more natural variant of that construction, which replaces the vector bundle modification wi...
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'
Gabriel Kocevar
2016-10-01
Full Text Available Purpose: In this work, we introduce a method to classify Multiple Sclerosis (MS patients into four clinical profiles using structural connectivity information. For the first time, we try to solve this question in a fully automated way using a computer-based method. The main goal is to show how the combination of graph-derived metrics with machine learning techniques constitutes a powerful tool for a better characterization and classification of MS clinical profiles.Materials and methods: Sixty-four MS patients (12 Clinical Isolated Syndrome (CIS, 24 Relapsing Remitting (RR, 24 Secondary Progressive (SP, and 17 Primary Progressive (PP along with 26 healthy controls (HC underwent MR examination. T1 and diffusion tensor imaging (DTI were used to obtain structural connectivity matrices for each subject. Global graph metrics, such as density and modularity, were estimated and compared between subjects’ groups. These metrics were further used to classify patients using tuned Support Vector Machine (SVM combined with Radial Basic Function (RBF kernel.Results: When comparing MS patients to HC subjects, a greater assortativity, transitivity and characteristic path length as well as a lower global efficiency were found. Using all graph metrics, the best F-Measures (91.8%, 91.8%, 75.6% and 70.6% were obtained for binary (HC-CIS, CIS-RR, RR-PP and multi-class (CIS-RR-SP classification tasks, respectively. When using only one graph metric, the best F-Measures (83.6%, 88.9% and 70.7% were achieved for modularity with previous binary classification tasks.Conclusion: Based on a simple DTI acquisition associated with structural brain connectivity analysis, this automatic method allowed an accurate classification of different MS patients’ clinical profiles.
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...
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
A new paradigm for particle tracking velocimetry, based on graph-theory and pulsed neural network
Derou, D.; Herault, L.
1994-01-01
The Particle Tracking Velocimetry (PTV) technique works by recording, at different instances in time, positions of small tracers particles following a flow and illuminated by a sheet, or pseudo sheet, of light. It aims to recognize each particle trajectory, constituted of n different spots and determine thus each particle velocity vector. In this paper, we devise a new method, taking into account a global consistency of the trajectories to be extracted, in terms of visual perception and physical properties. It is based on a graph-theoretic formulation of the particle tracking problem and the use of an original neural network, called pulsed neural network. (authors). 4 figs
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
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.
Automatic Assignment of Methyl-NMR Spectra of Supramolecular Machines Using Graph Theory.
Pritišanac, Iva; Degiacomi, Matteo T; Alderson, T Reid; Carneiro, Marta G; Ab, Eiso; Siegal, Gregg; Baldwin, Andrew J
2017-07-19
Methyl groups are powerful probes for the analysis of structure, dynamics and function of supramolecular assemblies, using both solution- and solid-state NMR. Widespread application of the methodology has been limited due to the challenges associated with assigning spectral resonances to specific locations within a biomolecule. Here, we present Methyl Assignment by Graph Matching (MAGMA), for the automatic assignment of methyl resonances. A graph matching protocol examines all possibilities for each resonance in order to determine an exact assignment that includes a complete description of any ambiguity. MAGMA gives 100% accuracy in confident assignments when tested against both synthetic data, and 9 cross-validated examples using both solution- and solid-state NMR data. We show that this remarkable accuracy enables a user to distinguish between alternative protein structures. In a drug discovery application on HSP90, we show the method can rapidly and efficiently distinguish between possible ligand binding modes. By providing an exact and robust solution to methyl resonance assignment, MAGMA can facilitate significantly accelerated studies of supramolecular machines using methyl-based NMR spectroscopy.
Foodsheds in Virtual Water Flow Networks: A Spectral Graph Theory Approach
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.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
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.
Rao, R Venkata
2013-01-01
Decision Making in Manufacturing Environment Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods presents the concepts and details of applications of MADM methods. A range of methods are covered including Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VIšekriterijumsko KOmpromisno Rangiranje (VIKOR), Data Envelopment Analysis (DEA), Preference Ranking METHod for Enrichment Evaluations (PROMETHEE), ELimination Et Choix Traduisant la Realité (ELECTRE), COmplex PRoportional ASsessment (COPRAS), Grey Relational Analysis (GRA), UTility Additive (UTA), and Ordered Weighted Averaging (OWA). The existing MADM methods are improved upon and three novel multiple attribute decision making methods for solving the decision making problems of the manufacturing environment are proposed. The concept of integrated weights is introduced in the proposed subjective and objective integrated weights (SOIW) method and the weighted Euclidean distance ba...
A Study towards Building An Optimal Graph Theory Based Model For The Design of Tourism Website
Panigrahi, Goutam; Das, Anirban; Basu, Kajla
2010-10-01
Effective tourism website is a key to attract tourists from different parts of the world. Here we identify the factors of improving the effectiveness of website by considering it as a graph, where web pages including homepage are the nodes and hyperlinks are the edges between the nodes. In this model, the design constraints for building a tourism website are taken into consideration. Our objectives are to build a framework of an effective tourism website providing adequate level of information, service and also to enable the users to reach to the desired page by spending minimal loading time. In this paper an information hierarchy specifying the upper limit of outgoing link of a page has also been proposed. Following the hierarchy, the web developer can prepare an effective tourism website. Here loading time depends on page size and network traffic. We have assumed network traffic as uniform and the loading time is directly proportional with page size. This approach is done by quantifying the link structure of a tourism website. In this approach we also propose a page size distribution pattern of a tourism website.
An Analysis of the Influence of Graph Theory When Preparing for Programming Contests
Cristina Jordán
2017-01-01
Full Text Available The subject known as Programming Contests in the Bachelor’s Degree in Computer Engineering course focuses on solving programming problems frequently met within contests such as the Southwest Europe Regional Contest (SWERC. In order to solve these problems one first needs to model the problem correctly, find the ideal solution, and then be able to program it without making any mistakes in a very short period of time. Leading multinationals such as Google, Apple, IBM, Facebook and Microsoft place a very high value on these abilities when selecting candidates for posts in their companies. In this communication we present some preliminary results of an analysis of the interaction between two optional subjects in the Computer Science Degree course: Programming Contests (PC and Graphs, Models and Applications (GMA. The results of this analysis enabled us to make changes to some of the contents in GMA in order to better prepare the students to deal with the challenges they have to face in programming contests.
A systematic composite service design modeling method using graph-based theory.
Elhag, Arafat Abdulgader Mohammed; Mohamad, Radziah; Aziz, Muhammad Waqar; Zeshan, Furkh
2015-01-01
The composite service design modeling is an essential process of the service-oriented software development life cycle, where the candidate services, composite services, operations and their dependencies are required to be identified and specified before their design. However, a systematic service-oriented design modeling method for composite services is still in its infancy as most of the existing approaches provide the modeling of atomic services only. For these reasons, a new method (ComSDM) is proposed in this work for modeling the concept of service-oriented design to increase the reusability and decrease the complexity of system while keeping the service composition considerations in mind. Furthermore, the ComSDM method provides the mathematical representation of the components of service-oriented design using the graph-based theoryto facilitate the design quality measurement. To demonstrate that the ComSDM method is also suitable for composite service design modeling of distributed embedded real-time systems along with enterprise software development, it is implemented in the case study of a smart home. The results of the case study not only check the applicability of ComSDM, but can also be used to validate the complexity and reusability of ComSDM. This also guides the future research towards the design quality measurement such as using the ComSDM method to measure the quality of composite service design in service-oriented software system.
Abnormal brain white matter network in young smokers: a graph theory analysis study.
Zhang, Yajuan; Li, Min; Wang, Ruonan; Bi, Yanzhi; Li, Yangding; Yi, Zhang; Liu, Jixin; Yu, Dahua; Yuan, Kai
2018-04-01
Previous diffusion tensor imaging (DTI) studies had investigated the white matter (WM) integrity abnormalities in some specific fiber bundles in smokers. However, little is known about the changes in topological organization of WM structural network in young smokers. In current study, we acquired DTI datasets from 58 male young smokers and 51 matched nonsmokers and constructed the WM networks by the deterministic fiber tracking approach. Graph theoretical analysis was used to compare the topological parameters of WM network (global and nodal) and the inter-regional fractional anisotropy (FA) weighted WM connections between groups. The results demonstrated that both young smokers and nonsmokers had small-world topology in WM network. Further analysis revealed that the young smokers exhibited the abnormal topological organization, i.e., increased network strength, global efficiency, and decreased shortest path length. In addition, the increased nodal efficiency predominately was located in frontal cortex, striatum and anterior cingulate gyrus (ACG) in smokers. Moreover, based on network-based statistic (NBS) approach, the significant increased FA-weighted WM connections were mainly found in the PFC, ACG and supplementary motor area (SMA) regions. Meanwhile, the network parameters were correlated with the nicotine dependence severity (FTND) scores, and the nodal efficiency of orbitofrontal cortex was positive correlation with the cigarette per day (CPD) in young smokers. We revealed the abnormal topological organization of WM network in young smokers, which may improve our understanding of the neural mechanism of young smokers form WM topological organization level.
Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory
T. K. Das
2014-01-01
Full Text Available With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model or global dynamics (e.g., the Ising model have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions.
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.)
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Zhou, Chaoyang; Hu, Xiaofei; Hu, Jun; Liang, Minglong; Yin, Xuntao; Chen, Lin; Zhang, Jiuquan; Wang, Jian
2016-01-01
Amyotrophic lateral sclerosis (ALS) is a rare degenerative disorder characterized by loss of upper and lower motor neurons. Neuroimaging has provided noticeable evidence that ALS is a complex disease, and shown that anatomical and functional lesions extend beyond precentral cortices and corticospinal tracts, to include the corpus callosum; frontal, sensory, and premotor cortices; thalamus; and midbrain. The aim of this study is to investigate graph theory-based functional network abnormalities at voxel-wise level in ALS patients on a whole brain scale. Forty-three ALS patients and 44 age- and sex-matched healthy volunteers were enrolled. The voxel-wise network degree centrality (DC), a commonly employed graph-based measure of network organization, was used to characterize the alteration of whole brain functional network. Compared with the controls, the ALS patients showed significant increase of DC in the left cerebellum posterior lobes, bilateral cerebellum crus, bilateral occipital poles, right orbital frontal lobe, and bilateral prefrontal lobes; significant decrease of DC in the bilateral primary motor cortex, bilateral sensory motor region, right prefrontal lobe, left bilateral precuneus, bilateral lateral temporal lobes, left cingulate cortex, and bilateral visual processing cortex. The DC's z-scores of right inferior occipital gyrus were significant negative correlated with the ALSFRS-r scores. Our findings confirm that the regions with abnormal network DC in ALS patients were located in multiple brain regions including primary motor, somatosensory and extra-motor areas, supporting the concept that ALS is a multisystem disorder. Specifically, our study found that DC in the visual areas was altered and ALS patients with higher DC in right inferior occipital gyrus have more severity of disease. The result demonstrated that the altered DC value in this region can probably be used to assess severity of ALS.
Chaoyang eZhou
2016-05-01
Full Text Available Amyotrophic lateral sclerosis (ALS is a rare degenerative disorder characterized by loss of upper and lower motor neurons. Neuroimaging has provided noticeable evidence that ALS is a complex disease, and shown that anatomical and functional lesions extend beyond precentral cortices and corticospinal tracts, to include the corpus callosum; frontal, sensory, and premotor cortices; thalamus; and midbrain. The aim of this study is to investigate graph theory-based functional network abnormalities at voxel-wise level in ALS patients on a whole brain scale. Forty-three ALS patients and 44 age- and sex- matched healthy volunteers were enrolled. The voxel-wise network degree centrality (DC, a commonly employed graph-based measure of network organization, was used to characterize the alteration of whole brain functional network. Compared with the controls, the ALS patients showed significant increase of DC in the left cerebellum posterior lobes, bilateral cerebellum crus, bilateral occipital poles, right orbital frontal lobe and bilateral prefrontal lobes; significant decrease of DC in the bilateral primary motor cortex, bilateral sensory motor region, right prefrontal lobe, left bilateral precuneus, bilateral lateral temporal lobes, left cingulate cortex, and bilateral visual processing cortex. The DC’s z-scores of right inferior occipital gyrus were significant negative correlated with the ALSFRS-r scores. Our findings confirm that the regions with abnormal network DC in ALS patients were located in multiple brain regions including primary motor, somatosensory and extra-motor areas, supporting the concept that ALS is a multisystem disorder. Specifically, our study found that DC in the visual areas was altered and ALS patients with higher DC in right inferior occipital gyrus have more severity of disease. The result demonstrated that the altered DC value in this region can probably be used to assess severity of ALS.
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.
Eulerian Graphs and Related Topics
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
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.
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)
Spectral fluctuations of quantum graphs
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
Amedeo Ganciu
2018-02-01
Full Text Available The distribution of services across a territory generates daily commuting flows, which have a significant influence on the development of the territory and often causes congestion in large areas. This negatively affects the environmental, economic and social components of the metropolitan landscape. Using the graph theory, we constructed and analyzed various (in typologies of transportation and moving time flow networks in the two main Italian metropolitan areas: Rome (MCR and Milan (MCM. The analysis of these networks provided us with strategic information on the dynamics of the two urban macro-systems. In particular, the aim of our study was to: (i identify the characteristics, distribution and direction of the main attractive forces within the regional systems under study; (ii identify the main differences in size and structure of commuter networks between the two metropolitan areas and between the two regional systems that include the two mother cities; and, (iii identify the main differences in the size and structure of the two commuting networks by transport modes (private, public, non-motorized mobility and the travel time. The results highlighted significant differences between the two case studies regarding volume flows, complexity and structure networks, and the spatial extension of the territories that are governed by the two metropolitan areas. MCR is a strongly monocentric urban system with a regional influence centred on the mother city of Rome, while MCM is a diffused polycentric regional metropolitan system centred on multiple mother cities. The findings many have a role in urban planning choices and in the evaluation of policies aimed to favor sustainable mobility.
Marie-Christine eOttet
2013-09-01
Full Text Available Schizophrenia is postulated to be the prototypical dysconnection disorder, in which hallucinations are the core symptom. Due to high heterogeneity in methodology across studies and the clinical phenotype, it remains unclear whether the structural brain dysconnection is global or focal and if clinical symptoms result from this dysconnection. In the present work, we attempt to clarify this issue by studying a population considered as a homogeneous genetic sub-type of schizophrenia, namely the 22q11.2 deletion syndrome (22q11.2DS. Cerebral MRIs were acquired for 46 patients and 48 age and gender matched controls (aged 6 to 26, respectively mean age = 15.20 ± 4.53 and 15.28 ± 4.35 years old. Using the Connectome mapper pipeline (connectomics.org that combines structural and diffusion MRI, we created a whole brain network for each individual. The graph theory was used to quantify the global and local properties in the brain network organization for each participant. A global degree loss of 6% was found in patients’ network along with an increased Characteristic Path Length. After identifying and comparing hubs, a significant loss of degree in patients’ hubs was found in 58% of them. Based on Allen’s brain network model for hallucinations, we explored the association between local efficiency and symptom severity. Negative correlations were found in the Broca’s area (p<0.004, the Wernicke area (p<0.023 and a positive correlation was found in the dorsolateral prefrontal cortex (DLPFC (p<0.014. In line with the dysconnection findings in schizophrenia, our results provide preliminary evidence for a targeted alteration in the brain network hubs’organisation in individuals with a genetic risk for schizophrenia. The study of specific disorganization in language, speech and thought regulation networks sharing similar network properties may help to understand their role in the hallucination mechanism.
Butler, William E; Atai, Nadia; Carter, Bob; Hochberg, Fred
2014-01-01
The Richard Floor Biorepository supports collaborative studies of extracellular vesicles (EVs) found in human fluids and tissue specimens. The current emphasis is on biomarkers for central nervous system neoplasms but its structure may serve as a template for collaborative EV translational studies in other fields. The informatic system provides specimen inventory tracking with bar codes assigned to specimens and containers and projects, is hosted on globalized cloud computing resources, and embeds a suite of shared documents, calendars, and video-conferencing features. Clinical data are recorded in relation to molecular EV attributes and may be tagged with terms drawn from a network of externally maintained ontologies thus offering expansion of the system as the field matures. We fashioned the graphical user interface (GUI) around a web-based data visualization package. This system is now in an early stage of deployment, mainly focused on specimen tracking and clinical, laboratory, and imaging data capture in support of studies to optimize detection and analysis of brain tumour-specific mutations. It currently includes 4,392 specimens drawn from 611 subjects, the majority with brain tumours. As EV science evolves, we plan biorepository changes which may reflect multi-institutional collaborations, proteomic interfaces, additional biofluids, changes in operating procedures and kits for specimen handling, novel procedures for detection of tumour-specific EVs, and for RNA extraction and changes in the taxonomy of EVs. We have used an ontology-driven data model and web-based architecture with a graph theory-driven GUI to accommodate and stimulate the semantic web of EV science.
Combinatorics and graph theory
Vasudev, C
2007-01-01
About the Book: This text has been carefully designed for flexible use for First Semester M.C.A. course of Uttar Pradesh Technical University (U.P.T.U.), and it contains the following features: Precise mathematical language is used without excessive formalism and abstraction. Over 900 exercises (problem sets) in the text with many different types of questions posed. Care has been taken to balance the mix of notation and words in mathematical statements. Problem sets (exercises) are stated clearly and unambiguously and all are carefully graded for various levels of difficulty. Contents:
Graph theory with applications
Vasudev, C
2006-01-01
Salient Features Over 1500 problems are used to illustrate concepts, related to different topics, and introduce applications. Over 1000 exercises in the text with many different types of questions posed. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements. Problem sets are stated clearly and unambiguously, and all are carefully graded for various levels of difficulty. This text has been carefully designed for flexible use.
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Yu, C. W.; Hodges, B. R.; Liu, F.
2017-12-01
Development of continental-scale river network models creates challenges where the massive amount of boundary condition data encounters the sensitivity of a dynamic nu- merical model. The topographic data sets used to define the river channel characteristics may include either corrupt data or complex configurations that cause instabilities in a numerical solution of the Saint-Venant equations. For local-scale river models (e.g. HEC- RAS), modelers typically rely on past experience to make ad hoc boundary condition adjustments that ensure a stable solution - the proof of the adjustment is merely the sta- bility of the solution. To date, there do not exist any formal methodologies or automated procedures for a priori detecting/fixing boundary conditions that cause instabilities in a dynamic model. Formal methodologies for data screening and adjustment are a critical need for simulations with a large number of river reaches that draw their boundary con- dition data from a wide variety of sources. At the continental scale, we simply cannot assume that we will have access to river-channel cross-section data that has been ade- quately analyzed and processed. Herein, we argue that problematic boundary condition data for unsteady dynamic modeling can be identified through numerical modeling with the steady-state Saint-Venant equations. The fragility of numerical stability increases with the complexity of branching in river network system and instabilities (even in an unsteady solution) are typically triggered by the nonlinear advection term in Saint-Venant equations. It follows that the behavior of the simpler steady-state equations (which retain the nonlin- ear term) can be used to screen the boundary condition data for problematic regions. In this research, we propose a graph-theory based method to isolate the location of corrupted boundary condition data in a continental-scale river network and demonstrate its utility with a network of O(10^4) elements. Acknowledgement
Optimization Problems on Threshold Graphs
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.
Glassman, Robert B
2003-04-15
Cognitive experimentation suggests that at any single instant only three or four items ("chunks") are simultaneously prominent as a working memory (WM) trace, if we disregard the rehearsal component of WM. The reason for small WM capacity may concern combinatorial manageability. How might the neural representations of these few coactive chunks occupy a spatially distributed set of areas of the sheet-like cortex, while providing both order and flexibility to associate items in WM? Each attribute of each simultaneously active WM item must have broad access to the representational facilities of the cortical sheet, comprising tens of thousands of modular "cortical columns." The two hypothesized neural levels of WM during any moment of cognition comprise (a) "binding" together of many distributed attribute representations within each respective WM chunk, and (b) combinatorial play among three or four WM chunk-representations. Anatomical and functional evidence of cortical unity through its depth suggests that cortex may be viewed as essentially planar in its distribution of activations. Thus, a moment's WM is hypothesized here to reside in myriad activated cortical planar "patches," each subdivided into up to four amoeboid "subpatches." Two different lines of topological reasoning suggest orderly associations of such representations. (1) The four-color principle of map topology, and the related K(4) is planar theorem of graph theory, imply that if a small cortical area is dynamically subdivided into no more than four, discretely bounded planar subareas, then each such segment has ample free access to each of the others. (2) A hypothetical alternative to such associative adjacency of simultaneously active cortical representations of chunk-attributes is associative overlap, whereby, in dense cortical neuropil, activated subpatches behave like Venn diagrams of intersecting sets. As the number of Venn-like coactive subpatches within a patch increases, maintaining ad hoc
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
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.
Computing decay rates for new physics theories with FeynRules and MadGraph 5 _aMC@NLO
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.
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''''.
An algebraic approach to graph codes
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...
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...
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
Rational Homological Stability for Automorphisms of Manifolds
Grey, Matthias
In this thesis we prove rational homological stability for the classifying spaces of the homotopy automorphisms and block di↵eomorphisms of iterated connected sums of products of spheres of a certain connectivity.The results in particular apply to the manifolds Npg,q = (#g(Sp x Sq)) - int...... with coefficients in the homology of the universal covering, which is studied using rational homology theory. The result for the block di↵eomorphisms is deduced from the homological stability for the homotopy automorphisms upon using Surgery theory. Themain theorems of this thesis extend the homological stability...
Vanicek, Thomas; Hahn, Andreas; Traub-Weidinger, Tatjana; Hilger, Eva; Spies, Marie; Wadsak, Wolfgang; Lanzenberger, Rupert; Pataraia, Ekaterina; Asenbaum-Nan, Susanne
2016-06-28
The human brain exhibits marked hemispheric differences, though it is not fully understood to what extent lateralization of the epileptic focus is relevant. Preoperative [(18)F]FDG-PET depicts lateralization of seizure focus in patients with temporal lobe epilepsy and reveals dysfunctional metabolic brain connectivity. The aim of the present study was to compare metabolic connectivity, inferred from inter-regional [(18)F]FDG PET uptake correlations, in right-sided (RTLE; n = 30) and left-sided TLE (LTLE; n = 32) with healthy controls (HC; n = 31) using graph theory based network analysis. Comparing LTLE and RTLE and patient groups separately to HC, we observed higher lobar connectivity weights in RTLE compared to LTLE for connections of the temporal and the parietal lobe of the contralateral hemisphere (CH). Moreover, especially in RTLE compared to LTLE higher local efficiency were found in the temporal cortices and other brain regions of the CH. The results of this investigation implicate altered metabolic networks in patients with TLE specific to the lateralization of seizure focus, and describe compensatory mechanisms especially in the CH of patients with RTLE. We propose that graph theoretical analysis of metabolic connectivity using [(18)F]FDG-PET offers an important additional modality to explore brain networks.
Polanía, Rafael; Paulus, Walter; Antal, Andrea; Nitsche, Michael A
2011-02-01
Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique that alters cortical excitability and activity in a polarity-dependent way. Stimulation for a few minutes has been shown to induce plastic alterations of cortical excitability and to improve cognitive performance. These effects might be related to stimulation-induced alterations of functional cortical network connectivity. We aimed to investigate the impact of tDCS on cortical network function by functional connectivity and graph theoretical analysis of the BOLD fMRI spontaneous activity. fMRI resting-state datasets were acquired immediately before and after 10-min bipolar tDCS during rest, with the anode placed over the left primary motor cortex (M1) and the cathode over the contralateral frontopolar cortex. For each dataset, grey matter voxel-based synchronization matrices were calculated and thresholded to construct undirected graphs. Nodal connectivity degree and minimum path length maps were calculated and compared before and after tDCS. Nodal minimum path lengths significantly increased in the left somatomotor (SM1) cortex after anodal tDCS, which means that the number of direct functional connections from the left SM1 to topologically distant grey matter voxels significantly decreased. In contrast, functional coupling between premotor and superior parietal areas with the left SM1 significantly increased. Additionally, the nodal connectivity degree in the left posterior cingulate cortex (PCC) area as well as in the right dorsolateral prefrontal cortex (right DLPFC) significantly increased. In summary, we provide initial support that tDCS-induced neuroplastic alterations might be related to functional connectivity changes in the human brain. Additionally, we propose our approach as a powerful method to track for neuroplastic changes in the human brain. Copyright © 2010 Elsevier Inc. All rights reserved.
Bell inequalities for graph states
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)
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Graphs with Eulerian unit spheres
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...
Proving relations between modular graph functions
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)
Vecchio, Fabrizio; Miraglia, Francesca; Curcio, Giuseppe; Altavilla, Riccardo; Scrascia, Federica; Giambattistelli, Federica; Quattrocchi, Carlo Cosimo; Bramanti, Placido; Vernieri, Fabrizio; Rossini, Paolo Maria
2015-01-01
A relatively new approach to brain function in neuroscience is the "functional connectivity", namely the synchrony in time of activity in anatomically-distinct but functionally-collaborating brain regions. On the other hand, diffusion tensor imaging (DTI) is a recently developed magnetic resonance imaging (MRI)-based technique with the capability to detect brain structural connection with fractional anisotropy (FA) identification. FA decrease has been observed in the corpus callosum of subjects with Alzheimer's disease (AD) and mild cognitive impairment (MCI, an AD prodromal stage). Corpus callosum splenium DTI abnormalities are thought to be associated with functional disconnections among cortical areas. This study aimed to investigate possible correlations between structural damage, measured by MRI-DTI, and functional abnormalities of brain integration, measured by characteristic path length detected in resting state EEG source activity (40 participants: 9 healthy controls, 10 MCI, 10 mild AD, 11 moderate AD). For each subject, undirected and weighted brain network was built to evaluate graph core measures. eLORETA lagged linear connectivity values were used as weight of the edges of the network. Results showed that callosal FA reduction is associated to a loss of brain interhemispheric functional connectivity characterized by increased delta and decreased alpha path length. These findings suggest that "global" (average network shortest path length representing an index of how efficient is the information transfer between two parts of the network) functional measure can reflect the reduction of fiber connecting the two hemispheres as revealed by DTI analysis and also anticipate in time this structural loss.
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Mod two homology and cohomology
Hausmann, Jean-Claude
2014-01-01
Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: It leads more quickly to the essentials of the subject, An absence of signs and orientation considerations simplifies the theory, Computations and advanced applications can be presented at an earlier stage, Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ula...
Topological fixed point theory of multivalued mappings
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...
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...
Fredholm Modules over Graph C^{∗}-Algebras
Crisp, Tyrone
2015-01-01
We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C∗-algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank commutators, and we exhibit generating Fredholm modules...
Quantum information processing with graph states
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.)
Replica methods for loopy sparse random graphs
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)
The n-th Power Signed Graphs-II
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.
On path hypercompositions in graphs and automata
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.
Bouillé F.
2006-11-01
Full Text Available La saisie des informations d'une carte géologique par les méthodes classiques (grilles ou relevés aléatoires de courbes ne constitue pas une base de données opérationnelle. Par contre, l'assimilation des limites géologiques à un graphe orienté répond aux critères d'optimalité (encombrement très réduit, temps minimal, fiabilité, et permet une digitalisation rationnelle de la carte, une bonne structuration du fichier, et la réalisation d'applications intéressantes : restitutions graphiques sélectives à toutes échelles, calculs de pendages, surfaces, volumes, études de corrélation. Nous avons donc établi une chaîne de traitement de la carte géologique dont chaque maillon (saisie des informations; contrôle, mise à jour, consultation, application opère sur un ou plusieurs graphes. Obtaining data from geological maps by conventional methods (grids or random curve plotting is not an operational data base. However, the comparison of geological boundaries with a directional graph meets criteria of optimalness (very small bulk, minimum time, reliability and makes it possible to digitize the map rationally, to structure the file properly and to achieve significant applications such as selective graph plotting on all scales, calculating dips, areas and volumes, and making correlotion analyses. Therefore, we worked out a geological map processing sequence in which each element (data acquisition, checking, updating, consulting, applications operates on one or several graphs.
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.
Lectures on homology with internal symmetries
Solovyov, Yu.
1993-09-01
Homology with internal symmetries is a natural generalization of cyclic homology introduced, independently, by Connes and Tsygan, which has turned out to be a very useful tool in a number of problems of algebra, geometry topology, analysis and mathematical physics. It suffices to say cycling homology and cohomology are successfully applied in the index theory of elliptic operators on foliations, in the description of the homotopy type of pseudoisotopy spaces, in the theory of characteristic classes in algebraic K-theory. They are also applied in noncommutative differential geometry and in the cohomology of Lie algebras, the branches of mathematics which brought them to life in the first place. Essentially, we consider dihedral homology, which was successfully applied for the description of the homology type of groups of homeomorphisms and diffeomorphisms of simply connected manifolds. (author). 27 refs
Chromatic polynomials of random graphs
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.
Graphs of groups on surfaces interactions and models
White, AT
2001-01-01
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English
Relative K-homology and normal operators
Manuilov, Vladimir; Thomsen, Klaus
2009-01-01
-term exact sequence which generalizes the excision six-term exact sequence in the first variable of KK-theory. Subsequently we investigate the relative K-homology which arises from the group of relative extensions by specializing to abelian $C^*$-algebras. It turns out that this relative K-homology carries...
Eigenfunction statistics on quantum graphs
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.
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Engineering Object-Oriented Semantics Using Graph Transformations
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
External memory K-bisimulation reduction of big graphs
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,
Expander graphs in pure and applied mathematics
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.
Adaptive Graph Convolutional Neural Networks
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...
K-homology and K-cohomology constructions of relations
Abd El-Sattar, A. Dabbour; Bayoumy, F.M.
1990-08-01
One of the important homology (cohomology) theories, based on systems of covering of the space, is the homology (cohomology) theory of relations. In the present work, by using the idea of K-homology and K-cohomology groups different varieties of the Dowker's theory are introduced and studied. These constructions are defined on the category of pairs of topological spaces and over a pair of coefficient groups. (author). 14 refs
Pure homology of algebraic varieties
Weber, Andrzej
2003-01-01
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce "image homology" for noncomplete varieties.
Pristine transfinite graphs and permissive electrical networks
Zemanian, Armen H
2001-01-01
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...
Disease management research using event graphs.
Allore, H G; Schruben, L W
2000-08-01
Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.
Soetevent, A.R.
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
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.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Touzé, Antoine
2015-01-01
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is o...
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Spectral clustering and biclustering learning large graphs and contingency tables
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
Interacting particle systems on graphs
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
On a Fuzzy Algebra for Querying Graph Databases
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...
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Szabó, György; Fáth, Gábor
2007-07-01
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Adriaan R. Soetevent
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...
Pim Heijnen; Adriaan Soetevent
2014-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Quantum complexity of graph and algebraic problems
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
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.)
The signed permutation group on Feynman graphs
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.
A graph rewriting programming language for graph drawing
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...
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
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Packing Degenerate Graphs Greedily
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
A librarian's guide to graphs, data and the semantic web
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...
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.
Resistance Distances in Vertex-Face Graphs
Shangguan, Yingmin; Chen, Haiyan
2018-01-01
The computation of two-point resistances in networks is a classical problem in electric circuit theory and graph theory. Let G be a triangulation graph with n vertices embedded on an orientable surface. Define K(G) to be the graph obtained from G by inserting a new vertex vϕ to each face ϕ of G and adding three new edges (u, vϕ), (v, vϕ) and (w, vϕ), where u, v and w are three vertices on the boundary of ϕ. In this paper, using star-triangle transformation and resistance local-sum rules, explicit relations between resistance distances in K(G) and those in G are obtained. These relations enable us to compute resistance distance between any two points of Kk(G) recursively. As explanation examples, some resistances in several networks are computed, including the modified Apollonian network and networks constructed from tetrahedron, octahedron and icosahedron, respectively.
Counting the number of Feynman graphs in QCD
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.
A Median-Type Condition for Graph Tiling
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
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
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Tailored Random Graph Ensembles
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Hyperbolicity in median graphs
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,.
Uniform Single Valued Neutrosophic Graphs
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.
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Wen, Hongwei; Liu, Yue; Wang, Shengpei; Zhang, Jishui; Peng, Yun; He, Huiguang
2017-03-01
Tourette syndrome (TS) is a childhood-onset neurobehavioral disorder. At present, the topological disruptions of the whole brain white matter (WM) structural networks remain poorly understood in TS children. Considering the unique position of the topologically central role of densely interconnected brain hubs, namely the rich club regions, therefore, we aimed to investigate whether the rich club regions and their related connections would be particularly vulnerable in early TS children. In our study, we used diffusion tractography and graph theoretical analyses to explore the rich club structures in 44 TS children and 48 healthy children. The structural networks of TS children exhibited significantly increased normalized rich club coefficient, suggesting that TS is characterized by increased structural integrity of this centrally embedded rich club backbone, potentially resulting in increased global communication capacity. In addition, TS children showed a reorganization of rich club regions, as well as significantly increased density and decreased number in feeder connections. Furthermore, the increased rich club coefficients and feeder connections density of TS children were significantly positively correlated to tic severity, indicating that TS may be characterized by a selective alteration of the structural connectivity of the rich club regions, tending to have higher bridging with non-rich club regions, which may increase the integration among tic-related brain circuits with more excitability but less inhibition for information exchanges between highly centered brain regions and peripheral areas. In all, our results suggest the disrupted rich club organization in early TS children and provide structural insights into the brain networks.
Colored Kauffman homology and super-A-polynomials
Nawata, Satoshi; Ramadevi, P.; Zodinmawia
2014-01-01
We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for the trefoil and the figure-eight are determined. In addition, making use of relations from representation theory, we also obtain the HOMFLY homologies colored by rectangular Young tableaux with two rows for these knots. Furthermore, the notion of super-A-polynomials is extended in order to encompass two-parameter deformations of PSL(2,ℂ) character varieties
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.
chromatic number of a complete balanced multipartite graph
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.
Representation and integration of sociological knowledge using knowledge graphs
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
Evolutionary Graphs with Frequency Dependent Fitness
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.
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
On some covering graphs of a graph
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
Herdable Systems Over Signed, Directed Graphs
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.
Learning molecular energies using localized graph kernels
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.
Herdable Systems Over Signed, Directed Graphs
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.
The investigation of social networks based on multi-component random graphs
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.
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Exclusivity structures and graph representatives of local complementation orbits
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.
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Graph embedding with rich information through heterogeneous graph
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
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
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.
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Probability on graphs random processes on graphs and lattices
Grimmett, Geoffrey
2018-01-01
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Coloring geographical threshold graphs
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
The STAPL Parallel Graph Library
Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Groupies in multitype random graphs
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Groupies in multitype random graphs.
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Temporal Representation in Semantic Graphs
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Quantum walks on quotient graphs
Krovi, Hari; Brun, Todd A.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
Query optimization for graph analytics on linked data using SPARQL
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.
Isotropic covariance functions on graphs and their edges
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....
A generalization of total graphs
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
On dominator colorings in graphs
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng
2015-12-01
Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.
Algorithms for Planar Graphs and Graphs in Metric Spaces
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...
Dynamic Representations of Sparse Graphs
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Domination criticality in product graphs
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Graph Creation, Visualisation and Transformation
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
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
Thermal operator representation of finite temperature graphs
Brandt, F.T.; Frenkel, J.; Das, Ashok; Espinosa, Olivier; Perez, Silvana
2005-01-01
Using the mixed space representation (t,p→) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed
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...
Canonical Labelling of Site Graphs
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Understanding Charts and Graphs.
1987-07-28
Farenheit degrees, which have no Onaturalo zero ); finally, ratio scales have numbers that are ordered so that the magnitudes of differences are important and...system. They have to do with the very nature of how marks serve as meaningful symbols. In the ideal case, a chart or graph will be absolutely unambiguous...and these laws comprise this principle (see Stevens, 1974). Absolute discriminability: A minimal magnitude of a mark is necessary for it to be detected
On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics
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
Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph
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.
Community detection by graph Voronoi diagrams
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.
On the reachability and observability of path and cycle graphs
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...
Coloring triangle-free graphs with fixed size
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...
The K-homology of nets of C∗-algebras
Ruzzi, Giuseppe; Vasselli, Ezio
2014-12-01
Let X be a space, intended as a possibly curved space-time, and A a precosheaf of C∗-algebras on X. Motivated by algebraic quantum field theory, we study the Kasparov and Θ-summable K-homology of A interpreting them in terms of the holonomy equivariant K-homology of the associated C∗-dynamical system. This yields a characteristic class for K-homology cycles of A with values in the odd cohomology of X, that we interpret as a generalized statistical dimension.
Graphs cospectral with a friendship graph or its complement
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 $Hcong overline{F_n}$.
Homological mirror symmetry and tropical geometry
Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia
2014-01-01
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...
Discrete Morse functions for graph configuration spaces
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)
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
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...
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph
Chemical shift homology in proteins
Potts, Barbara C.M.; Chazin, Walter J.
1998-01-01
The degree of chemical shift similarity for homologous proteins has been determined from a chemical shift database of over 50 proteins representing a variety of families and folds, and spanning a wide range of sequence homologies. After sequence alignment, the similarity of the secondary chemical shifts of C α protons was examined as a function of amino acid sequence identity for 37 pairs of structurally homologous proteins. A correlation between sequence identity and secondary chemical shift rmsd was observed. Important insights are provided by examining the sequence identity of homologous proteins versus percentage of secondary chemical shifts that fall within 0.1 and 0.3 ppm thresholds. These results begin to establish practical guidelines for the extent of chemical shift similarity to expect among structurally homologous proteins
Using graph approach for managing connectivity in integrative landscape modelling
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
GraphAlignment: Bayesian pairwise alignment of biological networks
Kolář Michal
2012-11-01
Full Text Available Abstract Background With increased experimental availability and accuracy of bio-molecular networks, tools for their comparative and evolutionary analysis are needed. A key component for such studies is the alignment of networks. Results We introduce the Bioconductor package GraphAlignment for pairwise alignment of bio-molecular networks. The alignment incorporates information both from network vertices and network edges and is based on an explicit evolutionary model, allowing inference of all scoring parameters directly from empirical data. We compare the performance of our algorithm to an alternative algorithm, Græmlin 2.0. On simulated data, GraphAlignment outperforms Græmlin 2.0 in several benchmarks except for computational complexity. When there is little or no noise in the data, GraphAlignment is slower than Græmlin 2.0. It is faster than Græmlin 2.0 when processing noisy data containing spurious vertex associations. Its typical case complexity grows approximately as O(N2.6. On empirical bacterial protein-protein interaction networks (PIN and gene co-expression networks, GraphAlignment outperforms Græmlin 2.0 with respect to coverage and specificity, albeit by a small margin. On large eukaryotic PIN, Græmlin 2.0 outperforms GraphAlignment. Conclusions The GraphAlignment algorithm is robust to spurious vertex associations, correctly resolves paralogs, and shows very good performance in identification of homologous vertices defined by high vertex and/or interaction similarity. The simplicity and generality of GraphAlignment edge scoring makes the algorithm an appropriate choice for global alignment of networks.
Endomorphisms of graph algebras
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Graph Algorithm Animation with Grrr
Rodgers, Peter; Vidal, Natalia
2000-01-01
We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...
Applied and computational harmonic analysis on graphs and networks
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.
Gems of combinatorial optimization and graph algorithms
Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea
2015-01-01
Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory? Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar? Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science? Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas. Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks. This ...
Graph-theoretic approach to quantum correlations.
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.
Graph theoretic aspects of music theory
Althuis, T.A.; Göbel, F.
2001-01-01
The cycle on twelve points is a well-known representation of the twelve pitch classes of the traditional scale. We treat a more general situation where the number of pitch classes can be different from twelve and where, moreover, other measures of closeness are taken into account. We determine all
Pearls in graph theory a comprehensive introduction
Hartsfield, Nora
2003-01-01
""Innovative introductory text . . . clear exposition of unusual and more advanced topics . . . Develops material to substantial level.""--American Mathematical Monthly""Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples.""--American Mathematical Monthly"" . . . An excellent textbook for an undergraduate course.""--Australian Computer JournalA stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written
Khovanov homology for virtual knots with arbitrary coefficients
Manturov, Vassily O
2007-01-01
The Khovanov homology theory over an arbitrary coefficient ring is extended to the case of virtual knots. We introduce a complex which is well-defined in the virtual case and is homotopy equivalent to the original Khovanov complex in the classical case. Unlike Khovanov's original construction, our definition of the complex does not use any additional prescription of signs to the edges of a cube. Moreover, our method enables us to construct a Khovanov homology theory for 'twisted virtual knots' in the sense of Bourgoin and Viro (including knots in three-dimensional projective space). We generalize a number of results of Khovanov homology theory (the Wehrli complex, minimality problems, Frobenius extensions) to virtual knots with non-orientable atoms
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Clustering evolving proteins into homologous families.
Chan, Cheong Xin; Mahbob, Maisarah; Ragan, Mark A
2013-04-08
Clustering sequences into groups of putative homologs (families) is a critical first step in many areas of comparative biology and bioinformatics. The performance of clustering approaches in delineating biologically meaningful families depends strongly on characteristics of the data, including content bias and degree of divergence. New, highly scalable methods have recently been introduced to cluster the very large datasets being generated by next-generation sequencing technologies. However, there has been little systematic investigation of how characteristics of the data impact the performance of these approaches. Using clusters from a manually curated dataset as reference, we examined the performance of a widely used graph-based Markov clustering algorithm (MCL) and a greedy heuristic approach (UCLUST) in delineating protein families coded by three sets of bacterial genomes of different G+C content. Both MCL and UCLUST generated clusters that are comparable to the reference sets at specific parameter settings, although UCLUST tends to under-cluster compositionally biased sequences (G+C content 33% and 66%). Using simulated data, we sought to assess the individual effects of sequence divergence, rate heterogeneity, and underlying G+C content. Performance decreased with increasing sequence divergence, decreasing among-site rate variation, and increasing G+C bias. Two MCL-based methods recovered the simulated families more accurately than did UCLUST. MCL using local alignment distances is more robust across the investigated range of sequence features than are greedy heuristics using distances based on global alignment. Our results demonstrate that sequence divergence, rate heterogeneity and content bias can individually and in combination affect the accuracy with which MCL and UCLUST can recover homologous protein families. For application to data that are more divergent, and exhibit higher among-site rate variation and/or content bias, MCL may often be the better
Compositional Homology and Creative Thinking
Salvatore Tedesco
2015-05-01
Full Text Available The concept of homology is the most solid theoretical basis elaborated by the morphological thinking during its history. The enucleation of some general criteria for the interpretation of homology is today a fundamental tool for life sciences, and for restoring their own opening to the question of qualitative innovation that arose so powerfully in the original Darwinian project. The aim of this paper is to verify the possible uses of the concept of compositional homology in order to provide of an adequate understanding of the dynamics of creative thinking.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
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.
Multiresolution persistent homology for excessively large biomolecular datasets
Xia, Kelin; Zhao, Zhixiong [Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 (United States); Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan 48824 (United States)
2015-10-07
Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibility-rigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs.
Bounds for percolation thresholds on directed and undirected graphs
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.
Local adjacency metric dimension of sun graph and stacked book graph
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.
On an edge partition and root graphs of some classes of line graphs
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.
Quandle and Biquandle Homology Calculation in R
Roger Fenn
2018-01-01
Full Text Available In knot theory several knot invariants have been found over the last decades. This paper concerns itself with invariants of several of those invariants, namely the Homology of racks, quandles, biracks and biquandles. The software described in this paper calculates the rack, quandle and degenerate homology groups of racks and biracks. It works for any rack/quandle with finite elements where there are homology coefficients in 'Z'k. The up and down actions can be given either as a function of the elements of 'Z'k or provided as a matrix. When calculating a rack, the down action should coincide with the identity map. We have provided actions for both the general dihedral quandle and the group quandle over 'S'3. We also provide a second function to test if a set with a given action (or with both actions gives rise to a quandle or biquandle. The program is provided as an R package and can be found at https://github.com/ansgarwenzel/quhomology. AMS subject classification: 57M27; 57M25
Graph theoretical model of a sensorimotor connectome in zebrafish.
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.
Graph theoretical model of a sensorimotor connectome in zebrafish.
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.
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Groupies in random bipartite graphs
Yilun Shang
2010-01-01
A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.
Nested Dynamic Condition Response Graphs
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
Quantum chaos on discrete graphs
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
On characterizing terrain visibility graphs
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
CORECLUSTER: A Degeneracy Based Graph Clustering Framework
Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis
2014-01-01
International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...
The forwarding indices of graphs - a survey
Jun-Ming Xu
2013-01-01
Full Text Available A routing \\(R\\ of a connected graph \\(G\\ of order \\(n\\ is a collection of \\(n(n-1\\ simple paths connecting every ordered pair of vertices of \\(G\\. The vertex-forwarding index \\(\\xi(G,R\\ of \\(G\\ with respect to a routing \\(R\\ is defined as the maximum number of paths in \\(R\\ passing through any vertex of \\(G\\. The vertex-forwarding index \\(\\xi(G\\ of \\(G\\ is defined as the minimum \\(\\xi(G,R\\ over all routings \\(R\\ of \\(G\\. Similarly, the edge-forwarding index \\(\\pi(G,R\\ of \\(G\\ with respect to a routing \\(R\\ is the maximum number of paths in \\(R\\ passing through any edge of \\(G\\. The edge-forwarding index \\(\\pi(G\\ of \\(G\\ is the minimum \\(\\pi(G,R\\ over all routings \\(R\\ of \\(G\\. The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory.
Resistance and relatedness on an evolutionary graph
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
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Semantic graphs and associative memories
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Homological mirror symmetry. New developments and perspectives
Kapustin, Anton; Kreuzer, Maximilian; Schlesinger, Karl-Georg
2009-01-01
Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory. (orig.)
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
Rabern, Landon
2007-01-01
We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...
On the Cogosvili functor generated by a homology
Abd El-Satter, A. Dabbour; Mahmoud, S.
1991-09-01
In the present work we discuss the Cogosvili functor generated by a homology, and study the construction of the corresponding groups and their induced homomorphisms. Moreover, we investigate the properties of this functor and prove that the set of such functors are isomorphic to the Bauer homotopy theory. (author). 19 refs
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.
Persistent homology of complex networks
Horak, Danijela; Maletić, Slobodan; Rajković, Milan
2009-01-01
Long-lived topological features are distinguished from short-lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and presented as a parameterized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent topological attributes, shown to be related to the robust quality of networks, also reflect the deficiency in certain connectivity properties of networks. Random networks, networks with exponential connectivity distribution and scale-free networks were considered for homological persistency analysis
Properly colored connectivity of graphs
Li, Xueliang; Qin, Zhongmei
2018-01-01
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Graph anomalies in cyber communications
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Open Graphs and Computational Reasoning
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Woeginger, G.J.
1998-01-01
In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).
Component efficient solutions in line-graph games with applications
van den Brink, J.R.; van der Laan, G.; Vasil'ev, V.
2007-01-01
Recently, applications of cooperative game theory to economic allocation problems have gained popularity. We investigate a class of cooperative games that generalizes some economic applications with a similar structure. These are the so-called line-graph games being cooperative TU-games in which the
Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model
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
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Graphs whose complement and square are isomorphic
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Acyclicity in edge-colored graphs
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian
2017-01-01
Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
Commuting graphs of matrix algebras
Akbari, S.; Bidkhori, H.; Mohammadian, A.
2006-08-01
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)
Graph Quasicontinuous Functions and Densely Continuous Forms
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
More on homological supersymmetric quantum mechanics
Behtash, Alireza
2018-03-01
In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantum mechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for nonzero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N =4 quantum mechanics with background R -symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The R -anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos parameters appear in the intersection coefficients for the relative homology of the quiver quantum mechanics resulting from dimensional reduction of 2 d N =(2 ,2 ) gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in N =4 C Pk -1 model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantum mechanics is indicated.
Homological stability of diffeomorphism groups
Berglund, Alexander; Madsen, Ib Henning
2013-01-01
In this paper we prove a stability theorem for block diffeomorphisms of 2d -dimensional manifolds that are connected sums of S d ×S d . Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet’s lemma of disjunction, we determine the homology of the classifying space ...
Interactive Graph Layout of a Million Nodes
Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North
2016-01-01
Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...
Spectral analysis of growing graphs a quantum probability point of view
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...
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
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.
Bond graphs : an integrating tool for design of mechatronic systems
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.
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Degree-based graph construction
Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A
2009-01-01
Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)
Hierarchical organisation of causal graphs
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Böhm Reduction in Infinitary Term Graph Rewriting Systems
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....
Random Walks and Diffusions on Graphs and Databases An Introduction
Blanchard, Philippe
2011-01-01
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
On a connection of number theory with graph theory
Somer, L.; Křížek, Michal
2004-01-01
Roč. 54, č. 2 (2004), s. 465-485 ISSN 0011-4642 R&D Projects: GA ČR GA201/02/1058 Institutional research plan: CEZ:AV0Z1019905 Keywords : Fermat numbers * Chinese remainder theorem * primality Subject RIV: BA - General Mathematics Impact factor: 0.131, year: 2004
Homological algebra in -abelian categories
Deren Luo
2017-08-16
Aug 16, 2017 ... Homological algebra in n-abelian categories. 627. We recall the Comparison lemma, together with its dual, plays a central role in the sequel. Lemma 2.1 [13, Comparison lemma 2.1]. Let C be an additive category and X ∈ Ch. ≥0(C) a complex such that for all k ≥ 0the morphism dk+1. X is a weak cokernel ...
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomá s; Motwani, Rajeev
2009-01-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Rosmanis, Ansis
2011-01-01
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games
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
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
Krueger, Benedikt
2016-01-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
Krueger, Benedikt
2016-07-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
On Graph Rewriting, Reduction and Evaluation
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Graph topologies on closed multifunctions
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Cyclic graphs and Apery's theorem
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
GLASSgo – Automated and Reliable Detection of sRNA Homologs From a Single Input Sequence
Steffen C. Lott
2018-04-01
Full Text Available Bacterial small RNAs (sRNAs are important post-transcriptional regulators of gene expression. The functional and evolutionary characterization of sRNAs requires the identification of homologs, which is frequently challenging due to their heterogeneity, short length and partly, little sequence conservation. We developed the GLobal Automatic Small RNA Search go (GLASSgo algorithm to identify sRNA homologs in complex genomic databases starting from a single sequence. GLASSgo combines an iterative BLAST strategy with pairwise identity filtering and a graph-based clustering method that utilizes RNA secondary structure information. We tested the specificity, sensitivity and runtime of GLASSgo, BLAST and the combination RNAlien/cmsearch in a typical use case scenario on 40 bacterial sRNA families. The sensitivity of the tested methods was similar, while the specificity of GLASSgo and RNAlien/cmsearch was significantly higher than that of BLAST. GLASSgo was on average ∼87 times faster than RNAlien/cmsearch, and only ∼7.5 times slower than BLAST, which shows that GLASSgo optimizes the trade-off between speed and accuracy in the task of finding sRNA homologs. GLASSgo is fully automated, whereas BLAST often recovers only parts of homologs and RNAlien/cmsearch requires extensive additional bioinformatic work to get a comprehensive set of homologs. GLASSgo is available as an easy-to-use web server to find homologous sRNAs in large databases.
Bond graphs for modelling, control and fault diagnosis of engineering systems
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...
Evolutionary stability of mixed strategies on graphs
Li, Yan; Liu, Xinsheng; Claussen, Jens Christian
2016-01-01
Up to the present time, the study of evolutionary dynamics mostly focused on pure strategy games in finite discrete strategy space, either in well-mixed or structured populations. In this paper, we study mixed strategy games in continuous strategy space on graphs of degree k . Each player is arranged on a vertex of the graph. The edges denote the interaction between two individuals. In the limit of weak selection, we first derive the payoff functions of two mixed strategies under three different updating rules, named birth–death, death–birth and imitation. Then we obtain the conditions for a strategy being a continuously stable strategy (CSS), and we also confirm that the equilibrium distribution corresponding to the CSS is neighborhood attracting and strongly uninvadable. Finally, we apply our theory to the prisoner’s dilemma and the snowdrift game to obtain possible CSS. Simulations are performed for the two special games and the results are well consistent with the conclusions we made. (paper)
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-01-01
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-11-19
Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Multiple graph regularized protein domain ranking
Wang Jim
2012-11-01
Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Direct computation of scattering matrices for general quantum graphs
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.
Combinatorial and geometric aspects of Feynman graphs and Feynman integrals
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
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
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Partitioning graphs into connected parts
Hof, van 't P.; Paulusma, D.; Woeginger, G.J.; Frid, A.; Morozov, A.S.; Rybalchenko, A.; Wagner, K.W.
2009-01-01
The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest
Isoperimetric inequalities for minimal graphs
Pacelli Bessa, G.; Montenegro, J.F.
2007-09-01
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N x R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. (author)
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Contracting a planar graph efficiently
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar...
Graph Model Based Indoor Tracking
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...
A graph with fractional revival
Bernard, Pierre-Antoine; Chan, Ada; Loranger, Érika; Tamon, Christino; Vinet, Luc
2018-02-01
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each face are connected and, the coherent transport of single excitations in the extension of the Krawtchouk spin chain with next-to-nearest neighbour interactions.
Coloring sums of extensions of certain graphs
Johan Kok
2017-12-01
Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.
Mathematical Minute: Rotating a Function Graph
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
Bounds on Gromov hyperbolicity constant in graphs
Infinite graphs; Cartesian product graphs; independence number; domin- ation number; geodesics ... the secure transmission of information through the internet (see [15, 16]). In particular, ..... In particular, δ(G) is an integer multiple of 1/4.
Summary: beyond fault trees to fault graphs
Alesso, H.P.; Prassinos, P.; Smith, C.F.
1984-09-01
Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability
Torsional rigidity, isospectrality and quantum graphs
Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon
2017-01-01
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)
Bond graph modeling of centrifugal compression systems
Uddin, Nur; Gravdahl, Jan Tommy
2015-01-01
A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...
A Graph Calculus for Predicate Logic
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Sphere and dot product representations of graphs
R.J. Kang (Ross); T. Müller (Tobias)
2012-01-01
textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such
Deep Learning with Dynamic Computation Graphs
Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter
2017-01-01
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...
Constructs for Programming with Graph Rewrites
Rodgers, Peter
2000-01-01
Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...
Kuranishi homology and Kuranishi cohomology
Joyce, Dominic
2007-01-01
A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. Let Y be an orbifold and R a commutative ring or Q-algebra. We define two kinds of Kuranishi homology KH_*(Y;R). The chain complex KC_*(Y;R) defining KH_*(Y;R) is spanned over R by [X,f,G], for X a compact oriented Kuranishi space with corners, f : X --> Y smooth, and G "gauge-fixing data" which ma...
Feynman graph derivation of Einstein quadrupole formula
Dass, N.D.H.; Soni, V.
1980-11-01
The one graviton transition operator, and consequently, the classical energy loss formula for gravitational radiation are derived from the Feynman graphs of helicity +- 2 theories of gravitation. The calculations are done both for the case of electromagnetic and gravitational scattering. The departure of the in and out states from plane waves owing to the long range nature of gravitation is taken into account to improve the Born approximation calculations. This also includes a long range modification of the graviton wave function which is shown to be equivalent to the classical problem of the true light cones deviating logarithmically at large distances from the flat space light cones. The transition from the S-matrix elements calculated graphically to the graviton transition operator is done by using complimentarity of space-time and momentum descriptions. The energy loss formula derived originally by Einstein is shown to be correct. (Auth.)
Proceedings 3rd Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014)
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...
Geometric structure of chemistry-relevant graphs zigzags and central circuits
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.
Homology and isomorphism: Bourdieu in conversation with New Institutionalism.
Wang, Yingyao
2016-06-01
Bourdieusian Field Theory (BFT) provided decisive inspiration for the early conceptual formulation of New Institutionalism (NI). This paper attempts to reinvigorate the stalled intellectual dialogue between NI and BFT by comparing NI's concept of isomorphism with BFT's notion of homology. I argue that Bourdieu's understanding of domination-oriented social action, transposable habitus, and a non-linear causality, embodied in his neglected concept of homology, provides an alternative theorization of field-level convergence to New Institutionalism's central idea of institutional isomorphism. To showcase how BFT can be useful for organizational research, I postulate a habitus-informed and field-conditioned theory of transference to enrich NI's spin-off thesis of 'diffusion'. I propose that while NI can benefit from BFT's potential of bringing social structure back into organizational research, BFT can enrich its social analysis by borrowing from NI's elaboration of the symbolic system of organizations. © London School of Economics and Political Science 2016.
On the sizes of expander graphs and minimum distances of graph codes
Høholdt, Tom; Justesen, Jørn
2014-01-01
We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
The groupies of random multipartite graphs
Portmann, Marius; Wang, Hongyun
2012-01-01
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; van den Broek, Pim
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
An intersection graph of straight lines
Thomassen, Carsten
2002-01-01
G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....
Girth 5 graphs from relative difference sets
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...
Cycles in weighted graphs and related topics
Zhang, Shenggui
2002-01-01
This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain
Graph Transformation Semantics for a QVT Language
Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel
It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to
Girth 5 graphs from relative difference sets
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
Improper colouring of (random) unit disk graphs
Kang, R.J.; Müller, T.; Sereni, J.S.
2008-01-01
For any graph G, the k-improper chromatic number ¿k(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate ¿k for unit disk graphs and random unit disk graphs to generalise results of McDiarmid and Reed
Alliances and Bisection Width for Planar Graphs
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances in polyn...
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
RATGRAPH: Computer Graphing of Rational Functions.
Minch, Bradley A.
1987-01-01
Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)
A new cluster algorithm for graphs
S. van Dongen
1998-01-01
textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a
Well-covered graphs and factors
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...
A new characterization of trivially perfect graphs
Christian Rubio Montiel
2015-03-01
Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
47 CFR 80.761 - Conversion graphs.
2010-10-01
... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units is... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761...
Torus actions, combinatorial topology, and homological algebra
Bukhshtaber, V M; Panov, T E
2000-01-01
This paper is a survey of new results and open problems connected with fundamental combinatorial concepts, including polytopes, simplicial complexes, cubical complexes, and arrangements of subspaces. Attention is concentrated on simplicial and cubical subdivisions of manifolds, and especially on spheres. Important constructions are described that enable one to study these combinatorial objects by using commutative and homological algebra. The proposed approach to combinatorial problems is based on the theory of moment-angle complexes recently developed by the authors. The crucial construction assigns to each simplicial complex K with m vertices a T m -space Z K with special bigraded cellular decomposition. In the framework of this theory, well-known non-singular toric varieties arise as orbit spaces of maximally free actions of subtori on moment-angle complexes corresponding to simplicial spheres. It is shown that diverse invariants of simplicial complexes and related combinatorial-geometric objects can be expressed in terms of bigraded cohomology rings of the corresponding moment-angle complexes. Finally, it is shown that the new relationships between combinatorics, geometry, and topology lead to solutions of some well-known topological problems
Total Domination Versus Paired-Domination in Regular Graphs
Cyman Joanna
2018-05-01
Full Text Available A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G, is the minimum cardinality of a dominating set of G, while the minimum cardinalities of a total dominating set and paired-dominating set are the total domination number, γt(G, and the paired-domination number, γpr(G, respectively. For k ≥ 2, let G be a connected k-regular graph. It is known [Schaudt, Total domination versus paired domination, Discuss. Math. Graph Theory 32 (2012 435–447] that γpr(G/γt(G ≤ (2k/(k+1. In the special case when k = 2, we observe that γpr(G/γt(G ≤ 4/3, with equality if and only if G ≅ C5. When k = 3, we show that γpr(G/γt(G ≤ 3/2, with equality if and only if G is the Petersen graph. More generally for k ≥ 2, if G has girth at least 5 and satisfies γpr(G/γt(G = (2k/(k + 1, then we show that G is a diameter-2 Moore graph. As a consequence of this result, we prove that for k ≥ 2 and k ≠ 57, if G has girth at least 5, then γpr(G/γt(G ≤ (2k/(k +1, with equality if and only if k = 2 and G ≅ C5 or k = 3 and G is the Petersen graph.
Function spaces with uniform, fine and graph topologies
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.
On a conjecture concerning helly circle graphs
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.
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
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.
Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems
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.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2016-01-01
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
On 4-critical t-perfect graphs
Benchetrit, Yohann
2016-01-01
It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
On a conjecture about inverse domination in graphs
Frendrup, Allan; Henning, Michael A.; Randerath, Bert
Let G = (V,E) be a graph with no isolated vertex. A classical observation in domination theory is that if D is a minimum dominating set of G, then V \\D is also a dominating set of G. A set D′ is an inverse dominating set of G if D′ is a dominating set of G and D′ ⊆ V \\D for some minimum dominatin...
Xiong, B.; Oude Elberink, S.; Vosselman, G.
2014-07-01
In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.
Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings.
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).
Significance evaluation in factor graphs
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
Flux networks in metabolic graphs
Warren, P B; Queiros, S M Duarte; Jones, J L
2009-01-01
A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms
3-biplacement of bipartite graphs
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
On the centrality of some graphs
Vecdi Aytac
2017-10-01
Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
Quantum walk on a chimera graph
Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.
2018-05-01
We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.
Fibonacci number of the tadpole graph
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Software for Graph Analysis and Visualization
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.
Parallel External Memory Graph Algorithms
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Submanifolds weakly associated with graphs
A CARRIAZO, L M FERN ´ANDEZ and A RODRÍGUEZ-HIDALGO. Department of Geometry and Topology, ..... by means of trees (connected graphs without cycles) and forests (disjoint unions of trees, see [6]) given in [3], by extending it to weak ... CR-submanifold. In this case, every tree is a K2. Finally, Theorem 3.8 of [3] can ...