The Inhibiting Bisection Problem
Pinar, Ali; Fogel, Yonatan; Lesieutre, Bernard
2006-12-18
Given a graph where each vertex is assigned a generation orconsumption volume, we try to bisect the graph so that each part has asignificant generation/consumption mismatch, and the cutsize of thebisection is small. Our motivation comes from the vulnerability analysisof distribution systems such as the electric power system. We show thatthe constrained version of the problem, where we place either the cutsizeor the mismatch significance as a constraint and optimize the other, isNP-complete, and provide an integer programming formulation. We alsopropose an alternative relaxed formulation, which can trade-off betweenthe two objectives and show that the alternative formulation of theproblem can be solved in polynomial time by a maximum flow solver. Ourexperiments with benchmark electric power systems validate theeffectiveness of our methods.
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...
Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning
Ponce, Colin [Cornell Univ., Ithaca, NY (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-02-18
We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. We present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.
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.
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.
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 optimal graph partitioning problem
Sørensen, Michael Malmros; Holm, Søren
1993-01-01
. This problem can be formulated as a MILP, which turns out to be completely symmetrical with respect to the p classes, and the gap between the relaxed LP solution and the optimal solution is the largest one possible. These two properties make it very difficult to solve even smaller problems. In this paper...
The complexity of the matching-cut problem for planar graphs and other graph classes
Bonsma, P.S.
2009-01-01
The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it
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.
Polyhedral Computations for the Simple Graph Partitioning Problem
Sørensen, Michael Malmros
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each containing no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we present a branch-and-cut algorithm for the problem that ...
A local search for a graph clustering problem
Navrotskaya, Anna; Il'ev, Victor
2016-10-01
In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.
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
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
A bicriterion Steiner tree problem on graph
Vujošević Mirko B.
2003-01-01
Full Text Available This paper presents a formulation of bicriterion Steiner tree problem which is stated as a task of finding a Steiner tree with maximal capacity and minimal length. It is considered as a lexicographic multicriteria problem. This means that the bottleneck Steiner tree problem is solved first. After that, the next optimization problem is stated as a classical minimums Steiner tree problem under the constraint on capacity of the tree. The paper also presents some computational experiments with the multicriteria problem.
Markov bridges, bisection and variance reduction
Asmussen, Søren; Hobolth, Asger
. In this paper we firstly consider the problem of generating sample paths from a continuous-time Markov chain conditioned on the endpoints using a new algorithm based on the idea of bisection. Secondly we study the potential of the bisection algorithm for variance reduction. In particular, examples are presented......Time-continuous Markov jump processes is a popular modelling tool in disciplines ranging from computational finance and operations research to human genetics and genomics. The data is often sampled at discrete points in time, and it can be useful to simulate sample paths between the datapoints...
Local search for Steiner tree problems in graphs
Verhoeven, M.G.A.; Severens, M.E.M.; Aarts, E.H.L.; Rayward-Smith, V.J.; Reeves, C.R.; Smith, G.D.
1996-01-01
We present a local search algorithm for the Steiner tree problem in graphs, which uses a neighbourhood in which paths in a steiner tree are exchanged. The exchange function of this neigbourhood is based on multiple-source shortest path algorithm. We present computational results for a known
Searches on star graphs and equivalent oracle problems
Lee, Jaehak; Lee, Hai-Woong; Hillery, Mark
2011-01-01
We examine a search on a graph among a number of different kinds of objects (vertices), one of which we want to find. In a standard graph search, all of the vertices are the same, except for one, the marked vertex, and that is the one we wish to find. We examine the case in which the unmarked vertices can be of different types, so the background against which the search is done is not uniform. We find that the search can still be successful, but the probability of success is lower than in the uniform background case, and that probability decreases with the number of types of unmarked vertices. We also show how the graph searches can be rephrased as equivalent oracle problems.
Experimental quantum annealing: case study involving the graph isomorphism problem.
Zick, Kenneth M; Shehab, Omar; French, Matthew
2015-06-08
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.
A HYBRID ALGORITHM FOR THE ROBUST GRAPH COLORING PROBLEM
Román Anselmo Mora Gutiérrez
2016-08-01
Full Text Available A hybridalgorithm which combines mathematical programming techniques (Kruskal’s algorithm and the strategy of maintaining arc consistency to solve constraint satisfaction problem “CSP” and heuristic methods (musical composition method and DSATUR to resolve the robust graph coloring problem (RGCP is proposed in this paper. Experimental result shows that this algorithm is better than the other algorithms presented on the literature.
Distributed Graphs for Solving Co-modal Transport Problems
Karama , Jeribi; Hinda , Mejri; Hayfa , Zgaya; Slim , Hammadi
2011-01-01
International audience; The paper presents a new approach based on a special distributed graphs in order to solve co-modal transport problems. The co-modal transport system consists on combining different transport modes effectively in terms of economic, environmental, service and financial efficiency, etc. However, the problem is that these systems must deal with different distributed information sources stored in different locations and provided by different public and private companies. In...
A DNA Computing Model for the Graph Vertex Coloring Problem Based on a Probe Graph
Jin Xu
2018-02-01
Full Text Available The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows: ① The exponential explosion problem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and ② the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction (PCR technology that dramatically improves the processing speed. In this article, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonucleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thousands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to O(359. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer (5 × 1014 s−1 to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman’s research group in 2002 (with a searching capability of O(220. Keywords: DNA computing, Graph vertex coloring problem, Polymerase chain reaction
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...
The Container Problem in Bubble-Sort Graphs
Suzuki, Yasuto; Kaneko, Keiichi
Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.
The Reduction of Directed Cyclic Graph for Task Assignment Problem
Ariffin W.N.M.
2018-01-01
Full Text Available In this paper, a directed cyclic graph (DCG is proposed as the task graph. It is undesirable and impossible to complete the task according to the constraints if the cycle exists. Therefore, an effort should be done in order to eliminate the cycle to obtain a directed acyclic graph (DAG, so that the minimum amount of time required for the entire task can be found. The technique of reducing the complexity of the directed cyclic graph to a directed acyclic graph by reversing the orientation of the path is the main contribution of this study. The algorithm was coded using Java programming and consistently produced good assignment and task schedule.
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].
Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube
Mittelmann, Hans; Peng Jiming; Wu Xiaolin
2009-01-01
In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs.Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n 3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
On a directed tree problem motivated by a newly introduced graph product
Antoon H. Boode
2015-10-01
Full Text Available In this paper we introduce and study a directed tree problem motivated by a new graph product that we have recently introduced and analysed in two conference contributions in the context of periodic real-time processes. While the two conference papers were focussing more on the applications, here we mainly deal with the graph theoretical and computational complexity issues. We show that the directed tree problem is NP-complete and present and compare several heuristics for this problem.
Optimal improvement of graphs related to nuclear safeguards problems
Jacobsen, S.E.
1977-08-01
This report develops the methodology for optimally improving graphs related to nuclear safeguards issues. In particular, given a fixed number of dollars, the report provides a method for optimally allocating such dollars over the arcs of a weighted graph (the weights vary as a function of dollars spent on arcs) so as to improve the system effectiveness measure which is the shortest of all shortest paths to several targets. Arc weights can be either clock times or detection probabilities and the algorithm does not explicitly consider all paths to the targets
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.
Two-particle quantum walks applied to the graph isomorphism problem
Gamble, John King; Friesen, Mark; Zhou Dong; Joynt, Robert; Coppersmith, S. N.
2010-01-01
We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in which one wishes to determine whether two graphs are isomorphic (related to each other by a relabeling of the graph vertices), and focus on a class of graphs with particularly high symmetry called strongly regular graphs (SRGs). We study the Green's functions that characterize the dynamical evolution single-particle and two-particle quantum walks on pairs of nonisomorphic SRGs and show that interacting particles can distinguish nonisomorphic graphs that noninteracting particles cannot. We obtain the following specific results. (1) We prove that quantum walks of two noninteracting particles, fermions or bosons, cannot distinguish certain pairs of nonisomorphic SRGs. (2) We demonstrate numerically that two interacting bosons are more powerful than single particles and two noninteracting particles, in that quantum walks of interacting bosons distinguish all nonisomorphic pairs of SRGs that we examined. By utilizing high-throughput computing to perform over 500 million direct comparisons between evolution operators, we checked all tabulated pairs of nonisomorphic SRGs, including graphs with up to 64 vertices. (3) By performing a short-time expansion of the evolution operator, we derive distinguishing operators that provide analytic insight into the power of the interacting two-particle quantum walk.
Spectral Bisection with Two Eigenvectors
Rocha, Israel
2017-01-01
Roč. 61, August (2017), s. 1019-1025 ISSN 1571-0653 Institutional support: RVO:67985807 Keywords : graph partitioning * Laplacian matrix * Fiedler vector Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
Sur, Chiranjib; Shukla, Anupam
2018-03-01
Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.
Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
Cai, Leizhen; Cheng, Yongxi; Verbin, Elad
2010-01-01
The firefighter problem is the following discrete-time game on a graph. Initially, a fire starts at a vertex of the graph. In each round, a firefighter protects one vertex not yet on fire, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefig...... of Cai and Wang [SIAM J. Discrete Math., 23 (2009), pp. 1814-1826] in affirmative....
A Novel Efficient Graph Model for the Multiple Longest Common Subsequences (MLCS Problem
Zhan Peng
2017-08-01
Full Text Available Searching for the Multiple Longest Common Subsequences (MLCS of multiple sequences is a classical NP-hard problem, which has been used in many applications. One of the most effective exact approaches for the MLCS problem is based on dominant point graph, which is a kind of directed acyclic graph (DAG. However, the time and space efficiency of the leading dominant point graph based approaches is still unsatisfactory: constructing the dominated point graph used by these approaches requires a huge amount of time and space, which hinders the applications of these approaches to large-scale and long sequences. To address this issue, in this paper, we propose a new time and space efficient graph model called the Leveled-DAG for the MLCS problem. The Leveled-DAG can timely eliminate all the nodes in the graph that cannot contribute to the construction of MLCS during constructing. At any moment, only the current level and some previously generated nodes in the graph need to be kept in memory, which can greatly reduce the memory consumption. Also, the final graph contains only one node in which all of the wanted MLCS are saved, thus, no additional operations for searching the MLCS are needed. The experiments are conducted on real biological sequences with different numbers and lengths respectively, and the proposed algorithm is compared with three state-of-the-art algorithms. The experimental results show that the time and space needed for the Leveled-DAG approach are smaller than those for the compared algorithms especially on large-scale and long sequences.
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.
Solving the replacement paths problem for planar directed graphs in O(n logn) time
Wulff-Nilsen, Christian
2010-01-01
In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace...
Wøhlk, Sanne; Laporte, Gilbert
2017-01-01
The aim of this paper is to computationally compare several algorithms for the Minimum Cost Perfect Matching Problem on an undirected complete graph. Our work is motivated by the need to solve large instances of the Capacitated Arc Routing Problem (CARP) arising in the optimization of garbage...... collection in Denmark. Common heuristics for the CARP involve the optimal matching of the odd-degree nodes of a graph. The algorithms used in the comparison include the CPLEX solution of an exact formulation, the LEDA matching algorithm, a recent implementation of the Blossom algorithm, as well as six...
Solving Problem of Graph Isomorphism by Membrane-Quantum Hybrid Model
Artiom Alhazov
2015-10-01
Full Text Available This work presents the application of new parallelization methods based on membrane-quantum hybrid computing to graph isomorphism problem solving. Applied membrane-quantum hybrid computational model was developed by authors. Massive parallelism of unconventional computing is used to implement classic brute force algorithm efficiently. This approach does not suppose any restrictions of considered graphs types. The estimated performance of the model is less then quadratic that makes a very good result for the problem of \\textbf{NP} complexity.
An Adaptation of the Kernighan-Lin Heuristic to the Simple Graph Partitioning Problem
Sørensen, Michael Malmros
1999-01-01
to this problem of the Kernighan-Lin exchange heuristic, which was originally developed for the closely related 2-partition problem. The evaluation is carried out on problem instances on graphs with up to 50 nodes for which the optimal partition values are known or upper bounds are available. The computational...... results show that among all instances with known optimal values the best partition values found by a randomized version of this heuristic lie well within 1% off the optimum....
Surface wave velocity tracking by bisection method
Maeda, T.
2005-01-01
Calculation of surface wave velocity is a classic problem dating back to the well-known Haskell's transfer matrix method, which contributes to solutions of elastic wave propagation, global subsurface structure evaluation by simulating observed earthquake group velocities, and on-site evaluation of subsurface structure by simulating phase velocity dispersion curves and/or H/V spectra obtained by micro-tremor observation. Recently inversion analysis on micro-tremor observation requires efficient method of generating many model candidates and also stable, accurate, and fast computation of dispersion curves and Raleigh wave trajectory. The original Haskell's transfer matrix method has been improved in terms of its divergence tendency mainly by the generalized transmission and reflection matrix method with formulation available for surface wave velocity; however, root finding algorithm has not been fully discussed except for the one by setting threshold to the absolute value of complex characteristic functions. Since surface wave number (reciprocal to the surface wave velocity multiplied by frequency) is a root of complex valued characteristic function, it is intractable to use general root finding algorithm. We will examine characteristic function in phase plane to construct two dimensional bisection algorithm with consideration on a layer to be evaluated and algorithm for tracking roots down along frequency axis. (author)
Graphs and an exactly solvable N-body problem in one dimension
Barucchi, G [Turin Univ. (Italy). Ist. di Fisica Matematica
1980-08-21
The one-dimensional N-body classical problem with inversely quadratic pair potential is considered. A method of explicit construction, by means of graphs, of the constants of the motion is given. It is then shown how to obtain, by means of a computer, the position variables of the particles as numerical functions of time.
Scalable Parallel Distributed Coprocessor System for Graph Searching Problems with Massive Data
Wanrong Huang
2017-01-01
Full Text Available The Internet applications, such as network searching, electronic commerce, and modern medical applications, produce and process massive data. Considerable data parallelism exists in computation processes of data-intensive applications. A traversal algorithm, breadth-first search (BFS, is fundamental in many graph processing applications and metrics when a graph grows in scale. A variety of scientific programming methods have been proposed for accelerating and parallelizing BFS because of the poor temporal and spatial locality caused by inherent irregular memory access patterns. However, new parallel hardware could provide better improvement for scientific methods. To address small-world graph problems, we propose a scalable and novel field-programmable gate array-based heterogeneous multicore system for scientific programming. The core is multithread for streaming processing. And the communication network InfiniBand is adopted for scalability. We design a binary search algorithm to address mapping to unify all processor addresses. Within the limits permitted by the Graph500 test bench after 1D parallel hybrid BFS algorithm testing, our 8-core and 8-thread-per-core system achieved superior performance and efficiency compared with the prior work under the same degree of parallelism. Our system is efficient not as a special acceleration unit but as a processor platform that deals with graph searching applications.
Wahid, Juliana; Hussin, Naimah Mohd
2016-08-01
The construction of population of initial solution is a crucial task in population-based metaheuristic approach for solving curriculum-based university course timetabling problem because it can affect the convergence speed and also the quality of the final solution. This paper presents an exploration on combination of graph heuristics in construction approach in curriculum based course timetabling problem to produce a population of initial solutions. The graph heuristics were set as single and combination of two heuristics. In addition, several ways of assigning courses into room and timeslot are implemented. All settings of heuristics are then tested on the same curriculum based course timetabling problem instances and are compared with each other in terms of number of population produced. The result shows that combination of saturation degree followed by largest degree heuristic produce the highest number of population of initial solutions. The results from this study can be used in the improvement phase of algorithm that uses population of initial solutions.
Exponential-Time Algorithms and Complexity of NP-Hard Graph Problems
Taslaman, Nina Sofia
of algorithms, as well as investigations into how far such improvements can get under reasonable assumptions. The first part is concerned with detection of cycles in graphs, especially parameterized generalizations of Hamiltonian cycles. A remarkably simple Monte Carlo algorithm is presented......NP-hard problems are deemed highly unlikely to be solvable in polynomial time. Still, one can often find algorithms that are substantially faster than brute force solutions. This thesis concerns such algorithms for problems from graph theory; techniques for constructing and improving this type......, and with high probability any found solution is shortest possible. Moreover, the algorithm can be used to find a cycle of given parity through the specified elements. The second part concerns the hardness of problems encoded as evaluations of the Tutte polynomial at some fixed point in the rational plane...
Jean Chamberlain Chedjou
2015-01-01
Full Text Available This paper develops a flexible analytical concept for robust shortest path detection in dynamically reconfigurable graphs. The concept is expressed by a mathematical model representing the shortest path problem solver. The proposed mathematical model is characterized by three fundamental parameters expressing (a the graph topology (through the “incidence matrix”, (b the edge weights (with dynamic external weights’ setting capability, and (c the dynamic reconfigurability through external input(s of the source-destination nodes pair. In order to demonstrate the universality of the developed concept, a general algorithm is proposed to determine the three fundamental parameters (of the mathematical model developed for all types of graphs regardless of their topology, magnitude, and size. It is demonstrated that the main advantage of the developed concept is that arc costs, the origin-destination pair setting, and the graph topology are dynamically provided by external commands, which are inputs of the shortest path solver model. This enables high flexibility and full reconfigurability of the developed concept, without any retraining need. To validate the concept developed, benchmarking is performed leading to a comparison of its performance with the performances of two well-known concepts based on neural networks.
Space and time bisection in schizophrenia
Isidro eMartinez-Cascales
2013-11-01
Full Text Available As a test of the idea of a common brain system responsible for representing all prothetic dimensions, schizophrenic patients and healthy participants took part in a line bisection task and two visual temporal bisection tasks, one using durations from 1 to 4 seconds and another using 30 seconds long specially designed stimuli (aging faces. Against expectations, schizophrenics showed better precision (smaller variable error both in line bisection and the aging faces temporal task than healthy controls. Moreover, patients also showed less bias (smaller constant error than controls in the aging faces task. This increased precision correlated with degree of severity of schizophrenia. Although no group differences were found in the temporal task with shorter intervals, both variable and constant error measures correlated marginally with severity of schizophrenia, also in the direction of smaller error in more severe cases. Thus, overall, spatial and temporal tasks behaved similarly across groups. However, bias and precision indexes did not covary across the three tasks when correlations where computed over the whole set of participants in the present study. The results thus provide mixed support for a common system behind spatial and temporal processing and point towards the need of developing a more nuanced view of magnitude representation in the mind/brain.
Infinite graphs in systematic biology, with an application to the species problem.
Alexander, Samuel A
2013-06-01
We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T. A. Knight and C. Darwin, and sketch a decomposition result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels' question, "Can biology lead to new theorems?"
The graph-theoretic minimum energy path problem for ionic conduction
Ippei Kishida
2015-10-01
Full Text Available A new computational method was developed to analyze the ionic conduction mechanism in crystals through graph theory. The graph was organized into nodes, which represent the crystal structures modeled by ionic site occupation, and edges, which represent structure transitions via ionic jumps. We proposed a minimum energy path problem, which is similar to the shortest path problem. An effective algorithm to solve the problem was established. Since our method does not use randomized algorithm and time parameters, the computational cost to analyze conduction paths and a migration energy is very low. The power of the method was verified by applying it to α-AgI and the ionic conduction mechanism in α-AgI was revealed. The analysis using single point calculations found the minimum energy path for long-distance ionic conduction, which consists of 12 steps of ionic jumps in a unit cell. From the results, the detailed theoretical migration energy was calculated as 0.11 eV by geometry optimization and nudged elastic band method. Our method can refine candidates for possible jumps in crystals and it can be adapted to other computational methods, such as the nudged elastic band method. We expect that our method will be a powerful tool for analyzing ionic conduction mechanisms, even for large complex crystals.
A Comparison of Local Search Methods for the Multicriteria Police Districting Problem on Graph
F. Liberatore
2016-01-01
Full Text Available In the current economic climate, law enforcement agencies are facing resource shortages. The effective and efficient use of scarce resources is therefore of the utmost importance to provide a high standard public safety service. Optimization models specifically tailored to the necessity of police agencies can help to ameliorate their use. The Multicriteria Police Districting Problem (MC-PDP on a graph concerns the definition of sound patrolling sectors in a police district. The objective of this problem is to partition a graph into convex and continuous subsets, while ensuring efficiency and workload balance among the subsets. The model was originally formulated in collaboration with the Spanish National Police Corps. We propose for its solution three local search algorithms: a Simple Hill Climbing, a Steepest Descent Hill Climbing, and a Tabu Search. To improve their diversification capabilities, all the algorithms implement a multistart procedure, initialized by randomized greedy solutions. The algorithms are empirically tested on a case study on the Central District of Madrid. Our experiments show that the solutions identified by the novel Tabu Search outperform the other algorithms. Finally, research guidelines for future developments on the MC-PDP are given.
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...
Graphs as a Problem-Solving Tool in 1-D Kinematics
Desbien, Dwain M.
2008-01-01
In this age of the microcomputer-based lab (MBL), students are quite accustomed to looking at graphs of position, velocity, and acceleration versus time. A number of textbooks argue convincingly that the slope of the velocity graph gives the acceleration, the area under the velocity graph yields the displacement, and the area under the…
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...
Guariglia, Paola; Matano, Alessandro; Piccardi, Laura
2014-01-01
In the present study we analysed the bisecting behaviour of 287 chronic right brain-damaged patients by taking into account the presence and severity of extrapersonal and/or personal neglect diagnosed with the hemineglect battery. We also analysed right brain-damaged patients who had (or did not have) neglect according to their line bisection performance. Our results showed that performance of the line bisection task correlates with performance of cancellation tasks, reading and perceptual tasks, but not with the presence of personal neglect. Personal neglect seems to be unrelated to line bisection behaviour. Indeed, patients affected by extrapersonal and personal neglect do not show more severe neglect in line bisection than patients with only extrapersonal neglect. Furthermore, we observed that 20.56% of the patients were considered affected or not by neglect on the line bisection task compared with the other spatial tasks of the hemineglect battery. We conclude that using a battery with multiple tests is the only way to guarantee a reliable diagnosis and effectively plan for rehabilitative training. PMID:24937472
Magnolia Tilca
2014-10-01
Full Text Available The aim of this paper is to study the existence of the solution for the overlapping generations model, using fixed point theorems in metric spaces endowed with a graph. The overlapping generations model has been introduced and developed by Maurice Allais (1947, Paul Samuelson (1958, Peter Diamond (1965 and so on. The present paper treats the case presented by Edmond (2008 in (Edmond, 2008 for a continuous time. The theorem of existence of the solution for the prices fixed point problem derived from the overlapping generations model gives an approximation of the solution via the graph theory. The tools employed in this study are based on applications of the Jachymski fixed point theorem on metric spaces endowed with a graph (Jachymski, 2008
Chen, Jung-Chieh
This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.
Detecting Network Vulnerabilities Through Graph TheoreticalMethods
Cesarz, Patrick; Pomann, Gina-Maria; Torre, Luis de la; Villarosa, Greta; Flournoy, Tamara; Pinar, Ali; Meza Juan
2007-09-30
Identifying vulnerabilities in power networks is an important problem, as even a small number of vulnerable connections can cause billions of dollars in damage to a network. In this paper, we investigate a graph theoretical formulation for identifying vulnerabilities of a network. We first try to find the most critical components in a network by finding an optimal solution for each possible cutsize constraint for the relaxed version of the inhibiting bisection problem, which aims to find loosely coupled subgraphs with significant demand/supply mismatch. Then we investigate finding critical components by finding a flow assignment that minimizes the maximum among flow assignments on all edges. We also report experiments on IEEE 30, IEEE 118, and WSCC 179 benchmark power networks.
Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo
2012-08-01
We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.
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...
Vatutin Eduard
2017-12-01
Full Text Available The article deals with the problem of analysis of effectiveness of the heuristic methods with limited depth-first search techniques of decision obtaining in the test problem of getting the shortest path in graph. The article briefly describes the group of methods based on the limit of branches number of the combinatorial search tree and limit of analyzed subtree depth used to solve the problem. The methodology of comparing experimental data for the estimation of the quality of solutions based on the performing of computational experiments with samples of graphs with pseudo-random structure and selected vertices and arcs number using the BOINC platform is considered. It also shows description of obtained experimental results which allow to identify the areas of the preferable usage of selected subset of heuristic methods depending on the size of the problem and power of constraints. It is shown that the considered pair of methods is ineffective in the selected problem and significantly inferior to the quality of solutions that are provided by ant colony optimization method and its modification with combinatorial returns.
Vatutin, Eduard
2017-12-01
The article deals with the problem of analysis of effectiveness of the heuristic methods with limited depth-first search techniques of decision obtaining in the test problem of getting the shortest path in graph. The article briefly describes the group of methods based on the limit of branches number of the combinatorial search tree and limit of analyzed subtree depth used to solve the problem. The methodology of comparing experimental data for the estimation of the quality of solutions based on the performing of computational experiments with samples of graphs with pseudo-random structure and selected vertices and arcs number using the BOINC platform is considered. It also shows description of obtained experimental results which allow to identify the areas of the preferable usage of selected subset of heuristic methods depending on the size of the problem and power of constraints. It is shown that the considered pair of methods is ineffective in the selected problem and significantly inferior to the quality of solutions that are provided by ant colony optimization method and its modification with combinatorial returns.
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
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.
Gambler's ruin problem on Erdős-Rényi graphs
Néda, Zoltán; Davidova, Larissa; Újvári, Szeréna; Istrate, Gabriel
2017-02-01
A multiagent ruin-game is studied on Erdős-Rényi type graphs. Initially the players have the same wealth. At each time step a monopolist game is played on all active links (links that connect nodes with nonzero wealth). In such a game each player puts a unit wealth in the pot and the pot is won with equal probability by one of the players. The game ends when there are no connected players such that both of them have non-zero wealth. In order to characterize the final state for dense graphs a compact formula is given for the expected number of the remaining players with non-zero wealth and the wealth distribution among these players. Theoretical predictions are given for the expected duration of the ruin game. The dynamics of the number of active players is also investigated. Validity of the theoretical predictions is investigated by Monte Carlo experiments.
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...
Combining language and space: sentence bisection in unilateral spatial neglect.
Veronelli, Laura; Guasti, Maria T; Arduino, Lisa S; Vallar, Giuseppe
2014-10-01
In line bisection right-brain-damaged patients with left spatial neglect show a rightward deviation, with respect to the line's physical center. In word bisection ortho-phonological features of the stimulus' final (right-sided) part modulate performance of both patients and healthy participants (Veronelli, Vallar, Marinelli, Primativo, & Arduino, 2014). We investigated the role of linguistic factors in sentence bisection, in patients with and without neglect, and control participants. The effects of information in the right-sided part of the sentence (Experiment #1), and of lexical and syntactic violations (Experiment #2) were assessed. Neglect patients showed an overall rightward bias, larger than those of patients without neglect and controls. The neglect patients' bias was modulated by stimulus type, decreasing from lines, to letter strings and to all types of sentences. In sum, in visuo-manual sentence bisection a basic linguistic mechanism, such as sentence readability, brings about a more leftward appreciation of the stimulus, reducing the neglect patients' rightward bias. Copyright © 2014 Elsevier Inc. All rights reserved.
Faenza, Y.; Oriolo, G.; Stauffer, G.
2011-01-01
We propose an algorithm for solving the maximum weighted stable set problem on claw-free graphs that runs in O(n^3)-time, drastically improving the previous best known complexity bound. This algorithm is based on a novel decomposition theorem for claw-free graphs, which is also intioduced in the present paper. Despite being weaker than the well-known structure result for claw-free graphs given by Chudnovsky and Seymour, our decomposition theorem is, on the other hand, algorithmic, i.e. it is ...
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
Droit-Volet, Sylvie; Clement, Angelique; Fayol, Michel
2003-01-01
This study tested 5- and 8-year-olds and adults in a bisection task with a sequence of stimuli in which time and number co-varied. Findings indicated that the number of stimuli interfered with 5-year-olds' performance on the temporal bisection task. Number interference decreased both with age and counting strategy. In the numerical bisection task,…
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
Chen, Wenbin; Hendrix, William; Samatova, Nagiza F
2017-12-01
The problem of aligning multiple metabolic pathways is one of very challenging problems in computational biology. A metabolic pathway consists of three types of entities: reactions, compounds, and enzymes. Based on similarities between enzymes, Tohsato et al. gave an algorithm for aligning multiple metabolic pathways. However, the algorithm given by Tohsato et al. neglects the similarities among reactions, compounds, enzymes, and pathway topology. How to design algorithms for the alignment problem of multiple metabolic pathways based on the similarity of reactions, compounds, and enzymes? It is a difficult computational problem. In this article, we propose an algorithm for the problem of aligning multiple metabolic pathways based on the similarities among reactions, compounds, enzymes, and pathway topology. First, we compute a weight between each pair of like entities in different input pathways based on the entities' similarity score and topological structure using Ay et al.'s methods. We then construct a weighted k-partite graph for the reactions, compounds, and enzymes. We extract a mapping between these entities by solving the maximum-weighted k-partite matching problem by applying a novel heuristic algorithm. By analyzing the alignment results of multiple pathways in different organisms, we show that the alignments found by our algorithm correctly identify common subnetworks among multiple pathways.
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.
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...
Krange, Ingeborg; Arnseth, Hans Christian
2012-09-01
The aim of this study is to scrutinize the characteristics of conceptual meaning making when students engage with virtual worlds in combination with a spreadsheet with the aim to develop graphs. We study how these tools and the representations they contain or enable students to construct serve to influence their understanding of energy resource consumption. The data were gathered in 1st grade upper-secondary science classes and they constitute the basis for the interaction analysis of students' meaning making with representations. Our analyses demonstrate the difficulties involved in developing students' orientation toward more conceptual orientations to representations of the knowledge domain. Virtual worlds do not in themselves represent a solution to this problem.
Normative data for distal line bisection and baking tray task.
Facchin, Alessio; Beschin, Nicoletta; Pisano, Alessia; Reverberi, Cristina
2016-09-01
Line bisection is one of the tests used to diagnose unilateral spatial neglect (USN). Despite its wide application, no procedure or norms were available for the distal variant when the task was performed at distance with a laser pointer. Furthermore, the baking tray task was an ecological test aimed at diagnosing USN in a more natural context. The aim of this study was to collect normative values for these two tests in an Italian population. We recruited a sample of 191 healthy subjects with ages ranging from 20 to 89 years. They performed line bisection with a laser pointer on three different line lengths (1, 1.5, and 2 m) at a distance of 3 m. After this task, the subjects performed the baking tray task and a second repetition of line bisection to test the reliability of measurement. Multiple regression analysis revealed no significant effects of demographic variables on the performance of both tests. Normative cut-off values for the two tests were developed using non-parametric tolerance intervals. The results formed the basis for clinical use of these two tools for assessing lateralized performance of patients with brain injury and for diagnosing USN.
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.
A Comparison of Approaches for Solving Hard Graph-Theoretic Problems
2015-04-29
and Search”, in Discrete Mathematics and Its Applications, Book 7, CRC Press (1998): Boca Raton. [6] A. Lucas, “Ising Formulations of Many NP Problems...owner. 14. ABSTRACT In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many... combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a standard brute force approach on a
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.
Julien Maheut
2013-07-01
Full Text Available Purpose: The purpose of this paper is to present an algorithm that solves the supply network configuration and operations scheduling problem in a mass customization company that faces alternative operations for one specific tool machine order in a multiplant context. Design/methodology/approach: To achieve this objective, the supply chain network configuration and operations scheduling problem is presented. A model based on stroke graphs allows the design of an algorithm that enumerates all the feasible solutions. The algorithm considers the arrival of a new customized order proposal which has to be inserted into a scheduled program. A selection function is then used to choose the solutions to be simulated in a specific simulation tool implemented in a Decision Support System. Findings and Originality/value: The algorithm itself proves efficient to find all feasible solutions when alternative operations must be considered. The stroke structure is successfully used to schedule operations when considering more than one manufacturing and supply option in each step. Research limitations/implications: This paper includes only the algorithm structure for a one-by-one, sequenced introduction of new products into the list of units to be manufactured. Therefore, the lotsizing process is done on a lot-per-lot basis. Moreover, the validation analysis is done through a case study and no generalization can be done without risk. Practical implications: The result of this research would help stakeholders to determine all the feasible and practical solutions for their problem. It would also allow to assessing the total costs and delivery times of each solution. Moreover, the Decision Support System proves useful to assess alternative solutions. Originality/value: This research offers a simple algorithm that helps solve the supply network configuration problem and, simultaneously, the scheduling problem by considering alternative operations. The proposed system
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.
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.
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
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.
Zhu, Zheng; Andresen, Juan Carlos; Janzen, Katharina; Katzgraber, Helmut G.
2013-03-01
We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free graphs in a magnetic field. Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scale-free networks. When the exponent that describes the power-law decay of the connectivity of the network is strictly larger than 3, the system undergoes a spin-glass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for all temperatures. First we perform finite-temperature Monte Carlo simulations in a field to test the robustness of the spin-glass phase and show, in agreement with analytical calculations, that the system exhibits a de Almeida-Thouless line. Furthermore, we study avalanches in the system at zero temperature to see if the system displays self-organized criticality. This would suggest that damage (avalanches) can spread across the whole system with nonzero probability, i.e., that Boolean decision problems on scale-free networks with competing interactions are fragile when not in thermal equilibrium.
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
You, Dong Soo; Kim, In Soo
1986-01-01
This study was performed to compare the difference of intraoral bisecting and panoramic techniques in evaluating the relationship of antral floor and maxillary roots. The vertical distances form maxillary root apices to antral floor were measured on both orthopantomograms and bisecting projections obtained form fifth subjects. The results were as follows: 1. Tooth lengths measured on orthopantomogram were larger than on bisecting projection and the magnification ratios were 1.08-1.17. 2. The dimensions from maxillary root apices to antral floor measured on orthopantomogram were larger than on bisecting projection. 3. The above results held true regardless of age and sex.
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.
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,.
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.
The Centre Is Not in the Middle: Evidence from Line and Word Bisection
Arduino, Lisa S.; Previtali, Paola; Girelli, Luisa
2010-01-01
English and German readers have been shown to mark a position to the left of the true centre as the subjective midpoint in word bisection. This effect resembles a well-known phenomenon observed with the bisection of solid lines (pseudoneglect), although this behavioural similarity does not imply a common origin. The purpose of the present study…
Radial bisection of words and lines in right-brain-damaged patients with spatial neglect.
Veronelli, Laura; Arduino, Lisa S; Girelli, Luisa; Vallar, Giuseppe
2017-09-01
The bisection of lines positioned radially (with the two ends of the line close and far, with respect to the participant's body) has been less investigated than that of lines placed horizontally (with their two ends left and right, with respect to the body's midsagittal plane). In horizontal bisection, patients with left neglect typically show a rightward bias for both lines and words, greater with longer stimuli. As for radial bisection, available data indicate that neurologically unimpaired participants make a distal error, while results from right-brain-damaged patients with left spatial neglect are contradictory. We investigated the bisection of radially oriented words, with the prediction that, during bisection, linguistic material would be recoded to its canonical left-to-right format in reading, with the performance of neglect patients being similar to that for horizontal words. Thirteen right-brain-damaged patients (seven with left spatial neglect) and fourteen healthy controls were asked to manually bisect 40 radial and 40 horizontal words (5-10 letters), and 80 lines, 40 radial and 40 horizontal, of comparable length. Right-brain-damaged patients with spatial neglect exhibited a proximal bias in the bisection of short radial words, with the proximal part corresponding to the final right part of horizontally oriented words. This proximal error was not found in patients without neglect and healthy controls. For bisection, short radial words may be recoded to the canonical orthographic horizontal format, unveiling the impact of left neglect on radially oriented stimuli. © 2015 The British Psychological Society.
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.)
Separated-orbit bisected energy-recovered linear accelerator
Douglas, David R.
2015-09-01
A separated-orbit bisected energy-recovered linear accelerator apparatus and method. The accelerator includes a first linac, a second linac, and a plurality of arcs of differing path lengths, including a plurality of up arcs, a plurality of downgoing arcs, and a full energy arc providing a path independent of the up arcs and downgoing arcs. The up arcs have a path length that is substantially a multiple of the RF wavelength and the full energy arc includes a path length that is substantially an odd half-integer multiple of the RF wavelength. Operation of the accelerator includes accelerating the beam utilizing the linacs and up arcs until the beam is at full energy, at full energy executing a full recirculation to the second linac using a path length that is substantially an odd half-integer of the RF wavelength, and then decelerating the beam using the linacs and downgoing arcs.
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.
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
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
Waldie, Karen E.; Hausmann, Markus
2010-01-01
Visual line bisection is a reliable and valid laterality task that is typically used with patients with acquired brain damage to assess right hemisphere functioning. Neurologically normal individuals tend to bisect lines to the left of the objective midline whereas those with right parietal damage bisect lines to the right. In this study children…
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...
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...
Yoo, Illhoi; Hu, Xiaohua; Song, Il-Yeol
2007-11-27
A huge amount of biomedical textual information has been produced and collected in MEDLINE for decades. In order to easily utilize biomedical information in the free text, document clustering and text summarization together are used as a solution for text information overload problem. In this paper, we introduce a coherent graph-based semantic clustering and summarization approach for biomedical literature. Our extensive experimental results show the approach shows 45% cluster quality improvement and 72% clustering reliability improvement, in terms of misclassification index, over Bisecting K-means as a leading document clustering approach. In addition, our approach provides concise but rich text summary in key concepts and sentences. Our coherent biomedical literature clustering and summarization approach that takes advantage of ontology-enriched graphical representations significantly improves the quality of document clusters and understandability of documents through summaries.
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
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
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.
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''''.
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.
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...
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
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
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.
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
Priftis, Konstantinos; Pitteri, Marco; Meneghello, Francesca; Umiltà, Carlo; Zorzi, Marco
2012-01-01
Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) – a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus – on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG’s performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the “indifference zone” that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space. PMID:22363280
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...
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 ...
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...
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).
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...
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...
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...
Goldengorin, Boris; Vink, Marius de
1999-01-01
The Data-Correcting Algorithm (DCA) corrects the data of a hard problem instance in such a way that we obtain an instance of a well solvable special case. For a given prescribed accuracy of the solution, the DCA uses a branch and bound scheme to make sure that the solution of the corrected instance
Konstantinos ePriftis
2012-02-01
Full Text Available Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL, an analogical, visuo-spatial representation of number magnitude. The MNL is left-to-right oriented, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in processing the left side of the MNL and show a rightward deviation in the mental bisection of numerical intervals. In the present study we investigated the effects of optokinetic stimulation (OKS -a technique inducing spatial attention shifts by means of activation of the optokinetic nystagmus- on mental number interval bisection. One patient with left neglect following right hemisphere stroke (BG and four control patients with right hemisphere damage, but without neglect, performed the mental number interval bisection task in three experimental conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, but again to the right of the midpoint following rightward OKS. In contrast, the performance of controls was not significantly affected by the direction of OKS. We argue that shifts of visuospatial attention, induced by OKS, may affect the mental number interval bisection, suggesting the presence of an interaction between the processing of number magnitude and the processing of the perceptual space, in patients with neglect for the mental number space.
Adaptive gain modulation in V1 explains contextual modifications during bisection learning.
Roland Schäfer
2009-12-01
Full Text Available The neuronal processing of visual stimuli in primary visual cortex (V1 can be modified by perceptual training. Training in bisection discrimination, for instance, changes the contextual interactions in V1 elicited by parallel lines. Before training, two parallel lines inhibit their individual V1-responses. After bisection training, inhibition turns into non-symmetric excitation while performing the bisection task. Yet, the receptive field of the V1 neurons evaluated by a single line does not change during task performance. We present a model of recurrent processing in V1 where the neuronal gain can be modulated by a global attentional signal. Perceptual learning mainly consists in strengthening this attentional signal, leading to a more effective gain modulation. The model reproduces both the psychophysical results on bisection learning and the modified contextual interactions observed in V1 during task performance. It makes several predictions, for instance that imagery training should improve the performance, or that a slight stimulus wiggling can strongly affect the representation in V1 while performing the task. We conclude that strengthening a top-down induced gain increase can explain perceptual learning, and that this top-down signal can modify lateral interactions within V1, without significantly changing the classical receptive field of V1 neurons.
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
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.
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 Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.
Balázs Szalkai
Full Text Available Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections
Total dominator chromatic number of a graph
Adel P. Kazemi
2015-06-01
Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
IDA AYU EGA RAHAYUNI
2016-01-01
Full Text Available Black-Scholes model suggests that volatility is constant or fixed during the life time of the option certainly known. However, this does not fit with what happen in the real market. Therefore, the volatility has to be estimated. Implied Volatility is the etimated volatility from a market mechanism that is considered as a reasonable way to assess the volatility's value. This study was aimed to compare the Newton-Raphson, Secant, and Bisection method, in estimating the stock volatility value of PT Telkom Indonesia Tbk (TLK. It found that the three methods have the same Implied Volatilities, where Newton-Raphson method gained roots more rapidly than the two others, and it has the smallest relative error greater than Secant and Bisection methods.
Bisecting real and fake body parts: effects of prism adaptation after right brain damage
Nadia eBolognini
2012-06-01
Full Text Available The representation of body parts holds a special status in the brain, due to their prototypical shape and the contribution of multisensory (visual and somatosensory-proprioceptive information. In a previous study (Sposito et al., 2010, we showed that patients with left unilateral spatial neglect exhibit a rightward bias in setting the mid-point of their left forearm, which becomes larger when bisecting a cylindrical object comparable in size. This body part advantage, found also in control participants, suggests partly different processes for computing the extent of body parts and objects. In this study we tested 16 right-brain-damaged patients, and 10 unimpaired participants, on a manual bisection task of their own (real left forearm, or a size-matched fake forearm. We then explored the effects of adaptation to rightward displacing prism exposure, which brings about leftward aftereffects. We found that all participants showed prism adaptation and aftereffects, with right-brain-damaged patients exhibiting a reduction of the rightward bias for both real and fake forearm, with no overall differences between them. Second, correlation analyses highlighted the role of visual and proprioceptive information for the metrics of body parts. Third, single-patient analyses showed dissociations between real and fake forearm bisections, and the effects of prism adaptation, as well as a more frequent impairment with fake body parts. In sum, the rightward bias shown by right-brain-damaged patients in bisecting body parts is reduced by prism exposure, as other components of the neglect syndrome; discrete spatial representations for real and fake body parts, for which visual and proprioceptive codes play different roles, are likely to exist. Multisensory information seems to render self bodily segments more resistant to the disruption brought about by right-hemisphere injury.
Line and word bisection in right-brain-damaged patients with left spatial neglect.
Veronelli, Laura; Vallar, Giuseppe; Marinelli, Chiara V; Primativo, Silvia; Arduino, Lisa S
2014-01-01
Right-brain-damaged patients with left unilateral spatial neglect typically set the mid-point of horizontal lines to the right of the objective center. By contrast, healthy participants exhibit a reversed bias (pseudoneglect). The same effect has been described also when bisecting orthographic strings. In particular, for this latter kind of stimulus, some recent studies have shown that visuo-perceptual characteristics, like stimulus length, may contribute to both the magnitude and the direction bias of the bisection performance (Arduino et al. in Neuropsychologia 48:2140-2146, 2010). Furthermore, word stress was shown to modulate reading performances in both healthy participants, and patients with left spatial neglect and neglect dyslexia (Cubelli and Beschin in Brain Lang 95:319-326, 2005; Rusconi et al. in Neuropsychology 18:135-140, 2004). In Experiment I, 22 right-brain-damaged patients (11 with left visuo-spatial neglect) and 11 matched neurologically unimpaired control participants were asked to set the subjective mid-point of word letter strings, and of lines of comparable length. Most patients exhibited an overall disproportionate rightward bias, sensitive to stimulus length, and similar for words and lines. Importantly, in individual patients, biases differed according to stimulus type (words vs. lines), indicating that at least partly different mechanisms may be involved. In Experiment II, the putative effects on the bisection bias of ortho-phonological information (i.e., word stress endings), arising from the non-neglected right hand side of the stimulus were investigated. The orthographic cue induced a rightward shift of the perceived mid-point in both patients and controls, with short words stressed on the antepenultimate final sequence inducing a smaller rightward deviation with respect to short words stressed on the penultimate final sequence. In conclusion, partly different mechanisms, including both visuo-spatial and lexical factors, may support
Happiness takes you right: the effect of emotional stimuli on line bisection.
Cattaneo, Zaira; Lega, Carlotta; Boehringer, Jana; Gallucci, Marcello; Girelli, Luisa; Carbon, Claus-Christian
2014-01-01
Emotion recognition is mediated by a complex network of cortical and subcortical areas, with the two hemispheres likely being differently involved in processing positive and negative emotions. As results on valence-dependent hemispheric specialisation are quite inconsistent, we carried out three experiments with emotional stimuli with a task being sensitive to measure specific hemispheric processing. Participants were required to bisect visual lines that were delimited by emotional face flankers, or to haptically bisect rods while concurrently listening to emotional vocal expressions. We found that prolonged (but not transient) exposition to concurrent happy stimuli significantly shifted the bisection bias to the right compared to both sad and neutral stimuli, indexing a greater involvement of the left hemisphere in processing of positively connoted stimuli. No differences between sad and neutral stimuli were observed across the experiments. In sum, our data provide consistent evidence in favour of a greater involvement of the left hemisphere in processing positive emotions and suggest that (prolonged) exposure to stimuli expressing happiness significantly affects allocation of (spatial) attentional resources, regardless of the sensory (visual/auditory) modality in which the emotion is perceived and space is explored (visual/haptic).
What makes a word so attractive? Disclosing the urge to read while bisecting.
Girelli, Luisa; Previtali, Paola; Arduino, Lisa S
2018-04-22
Expert readers have been repeatedly reported to misperceive the centre of visual stimuli, shifting systematically to the left the bisection of any lines (pseudoneglect) while showing a cross-over effect while bisecting different types of orthographic strings (Arduino et al., 2010, Neuropsychologia, 48, 2140). This difference has been attributed to asymmetrical allocation of attention that visuo-verbal material receives when lexical access occurs (e.g., Fischer, 2004, Cognitive Brain Research, 4, 163). The aim of this study was to further examine which visual features guide recognition of potentially orthographic materials. To disentangle the role of orthography, heterogeneity, and visuo-perceptual discreteness, we presented Italian unimpaired adults with four experiments exploiting the bisection paradigm. The results showed that a cross-over effect emerges in most discrete strings, especially when their internal structure, that is being composed of heterogeneous elements, is suggestive of orthographically relevant material. Interestingly, the cross-over effect systematically characterized the processing of letter strings (Experiment 2) and words (Experiments 3 and 4), whether visually discrete or not. Overall, this pattern of results suggests that neither discreteness nor heterogeneity per se are responsible for activating visual scanning mechanisms implied in text exploration, although both contribute to increasing the chance of a visual stimulus undergoing a perceptual analysis dedicated to pre-lexical processing. © 2018 The British Psychological Society.
Visuospatial biases in preschool children: Evidence from line bisection in three-dimensional space.
Patro, Katarzyna; Nuerk, Hans-Christoph; Brugger, Peter
2018-04-09
Spatial attention in adults is characterized by systematic asymmetries across all three spatial dimensions. These asymmetries are evident when participants bisect horizontal, vertical, or radial lines and misplace their midpoints to the left, the top, or far from the body, respectively. However, bisection errors are rarely examined during early childhood. In this study, we examined the development of spatial-attentional asymmetries in three-dimensional (3D) space by asking preschool children (aged 3-6 years) to bisect horizontal, vertical, and radial lines. Children erred to the left with horizontal lines and to the top with vertical lines, consistent with the pattern reported in adults. These biases got stronger with age and were absent in the youngest preschoolers. However, by controlling for a possible failure in hitting the line, we observed an additional unpredicted pattern: Children's pointing systematically deviated away from the line to an empty space on its left side (for vertical and radial lines) or above it (for horizontal lines). Notably, this task-irrelevant deviation was pronounced in children as young as 3 or 4 years. We conclude that asymmetries in spatial-attentional functions should be measured not only in task-relevant dimensions but also in task-irrelevant dimensions because the latter may reveal biases in very young children not typically observed in task-relevant measures. Copyright © 2018 Elsevier Inc. All rights reserved.
Bipartite separability and nonlocal quantum operations on graphs
Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.
2016-07-01
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.
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
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.
Incremental Frequent Subgraph Mining on Large Evolving Graphs
Abdelhamid, Ehab; Canim, Mustafa; Sadoghi, Mohammad; Bhatta, Bishwaranjan; Chang, Yuan-Chi; Kalnis, Panos
2017-01-01
, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem
Optimizing graph algorithms on pregel-like systems
Salihoglu, Semih; Widom, Jennifer
2014-01-01
We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high
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.
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...
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.
Supplantation of Mental Operations on Graphs
Vogel, Markus; Girwidz, Raimund; Engel, Joachim
2007-01-01
Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph
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)
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...
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...
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.
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.
Ranzini, Mariagrazia; Carbè, Katia; Gevers, Wim
2017-05-01
Number interval bisection consists of estimating the mid-number within a pair (1-9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants' verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
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 i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...
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.
On the partition dimension of two-component graphs
D O Haryeni
2017-11-17
Nov 17, 2017 ... Partition dimension; disconnected graph; component. 2010 Mathematics Subject Classification. 05C12, 05C15. 1. Introduction. The study of the partition dimension for graphs was initiated by Chartrand et al. [2] aimed at finding a new way to solve the problem in metric dimensions of graphs. Many results.
Mutual proximity graphs for improved reachability in music recommendation.
Flexer, Arthur; Stevens, Jeff
2018-01-01
This paper is concerned with the impact of hubness, a general problem of machine learning in high-dimensional spaces, on a real-world music recommendation system based on visualisation of a k-nearest neighbour (knn) graph. Due to a problem of measuring distances in high dimensions, hub objects are recommended over and over again while anti-hubs are nonexistent in recommendation lists, resulting in poor reachability of the music catalogue. We present mutual proximity graphs, which are an alternative to knn and mutual knn graphs, and are able to avoid hub vertices having abnormally high connectivity. We show that mutual proximity graphs yield much better graph connectivity resulting in improved reachability compared to knn graphs, mutual knn graphs and mutual knn graphs enhanced with minimum spanning trees, while simultaneously reducing the negative effects of hubness.
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
Interactive Graph Layout of a Million Nodes
Peng Mi
2016-12-01
Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.
Equitable Colorings Of Corona Multiproducts Of Graphs
Furmánczyk Hanna
2017-11-01
Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].
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....
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…
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,
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.
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
An Association-Oriented Partitioning Approach for Streaming Graph Query
Yun Hao
2017-01-01
Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.
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%.
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...
Drago, Valeria; Finney, Glen R; Foster, Paul S; Amengual, Alejandra; Jeong, Yong; Mizuno, Tomoiuki; Crucian, Gregory P; Heilman, Kenneth M
2008-03-01
Lesion studies demonstrate that the right temporal-parietal region (RTP) is important for mediating spatial attention. The RTP is also involved in emotional experiences that can be evoked by art. Normal people vary in their ability to allocate spatial attention, thus, people who can better allocate attention might also be more influenced by the emotional messages of the paintings (evocative impact). Seventeen healthy participants bisected an unlabeled 100mm line and their performance on this task was used to create two groups, individuals who were more (mALB) and less accurate (lALB). These participants also judged 10 paintings on five qualities, Evocative Impact, Aesthetics, Novelty, Technique, and Closure by marking a 100mm line from 1 (low degree) to 10 (high degree). An ANOVA indicated differences in accuracy on the line bisection (LB) between the two groups. Additional ANOVAs, using the quality ratings as the dependent measure, revealed that the mALB group scored the Evocative Impact greater than the lALB group. These results suggest that the differences in attentional bias between the two groups, as indicated by their LB performance, might influence their evocative impact or reactions and also be a 'barometer' of other RTP functions, including emotional processing.
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
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...
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...
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
Enabling Graph Appliance for Genome Assembly
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Efficient dynamic graph construction for inductive semi-supervised learning.
Dornaika, F; Dahbi, R; Bosaghzadeh, A; Ruichek, Y
2017-10-01
Most of graph construction techniques assume a transductive setting in which the whole data collection is available at construction time. Addressing graph construction for inductive setting, in which data are coming sequentially, has received much less attention. For inductive settings, constructing the graph from scratch can be very time consuming. This paper introduces a generic framework that is able to make any graph construction method incremental. This framework yields an efficient and dynamic graph construction method that adds new samples (labeled or unlabeled) to a previously constructed graph. As a case study, we use the recently proposed Two Phase Weighted Regularized Least Square (TPWRLS) graph construction method. The paper has two main contributions. First, we use the TPWRLS coding scheme to represent new sample(s) with respect to an existing database. The representative coefficients are then used to update the graph affinity matrix. The proposed method not only appends the new samples to the graph but also updates the whole graph structure by discovering which nodes are affected by the introduction of new samples and by updating their edge weights. The second contribution of the article is the application of the proposed framework to the problem of graph-based label propagation using multiple observations for vision-based recognition tasks. Experiments on several image databases show that, without any significant loss in the accuracy of the final classification, the proposed dynamic graph construction is more efficient than the batch graph construction. Copyright © 2017 Elsevier Ltd. All rights reserved.
On revealing graph cycles via boundary measurements
Belishev, M I; Wada, N
2009-01-01
This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)
Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions
Mahayni, Malek A.
2011-01-01
developed to solve the optimal paths problem with different kinds of graphs. An algorithm that solves the problem of paths’ optimization in directed graphs relative to different cost functions is described in [1]. It follows an approach extended from
Labeled Embedding Of (n, n-2-Graphs In Their Complements
Tahraoui M.-A.
2017-11-01
Full Text Available Graph packing generally deals with unlabeled graphs. In [4], the authors have introduced a new variant of the graph packing problem, called the labeled packing of a graph. This problem has recently been studied on trees [M.A. Tahraoui, E. Duchêne and H. Kheddouci, Labeled 2-packings of trees, Discrete Math. 338 (2015 816-824] and cycles [E. Duchˆene, H. Kheddouci, R.J. Nowakowski and M.A. Tahraoui, Labeled packing of graphs, Australas. J. Combin. 57 (2013 109-126]. In this note, we present a lower bound on the labeled packing number of any (n, n − 2-graph into Kn. This result improves the bound given by Woźniak in [Embedding graphs of small size, Discrete Appl. Math. 51 (1994 233-241].
PuLP/XtraPuLP : Partitioning Tools for Extreme-Scale Graphs
2017-09-21
PuLP/XtraPulp is software for partitioning graphs from several real-world problems. Graphs occur in several places in real world from road networks, social networks and scientific simulations. For efficient parallel processing these graphs have to be partitioned (split) with respect to metrics such as computation and communication costs. Our software allows such partitioning for massive graphs.
Graph reconstruction with a betweenness oracle
Abrahamsen, Mikkel; Bodwin, Greg; Rotenberg, Eva
2016-01-01
Graph reconstruction algorithms seek to learn a hidden graph by repeatedly querying a blackbox oracle for information about the graph structure. Perhaps the most well studied and applied version of the problem uses a distance oracle, which can report the shortest path distance between any pair...... of nodes. We introduce and study the betweenness oracle, where bet(a, m, z) is true iff m lies on a shortest path between a and z. This oracle is strictly weaker than a distance oracle, in the sense that a betweenness query can be simulated by a constant number of distance queries, but not vice versa...
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
Distributed graph coloring fundamentals and recent developments
Barenboim, Leonid
2013-01-01
The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible.A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging
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...
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
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.
b-tree facets for the simple graph partitioning polytope
Sørensen, Michael Malmros
2004-01-01
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each consisting of no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we introduce a large class of facet defining inequalities...... for the simple graph partitioning polytopes P_n(b), b >= 3, associated with the complete graph on n nodes. These inequalities are induced by a graph configuration which is built upon trees of cardinality b. We provide a closed-form theorem that states all necessary and sufficient conditions for the facet...... defining property of the inequalities. Udgivelsesdato: JUN...
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
Exact two-point resistance, and the simple random walk on the complete graph minus N edges
Chair, Noureddine
2012-01-01
An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: ► We obtain exact formulas for the two-point resistance of the complete graph minus N edges. ► We obtain also the total effective resistance of this graph. ► We modified Schwatt’s formula on trigonometrical power sum to suit our computations. ► We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. ► The first passage and mean first passage times of the random walks have exact expressions.
Exact two-point resistance, and the simple random walk on the complete graph minus N edges
Chair, Noureddine, E-mail: n.chair@ju.edu.jo
2012-12-15
An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: Black-Right-Pointing-Pointer We obtain exact formulas for the two-point resistance of the complete graph minus N edges. Black-Right-Pointing-Pointer We obtain also the total effective resistance of this graph. Black-Right-Pointing-Pointer We modified Schwatt's formula on trigonometrical power sum to suit our computations. Black-Right-Pointing-Pointer We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. Black-Right-Pointing-Pointer The first passage and mean first passage times of the random walks have exact expressions.
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.
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
Borowiecka-Olszewska Marta
2017-05-01
Full Text Available A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.
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
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...
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
Vidal, Rene Victor Valqui
1994-01-01
The paper studies the problem of determining the number and dimensions of sizes of apparel so as to maximize profits. It develops a simple one-variable bisection search algorithm that gives the optimal solution. An example is solved interactively using a Macintosh LC and Math CAD, a mathematical...
Graph-theoretical concepts and physicochemical data
Lionello Pogliani
2003-02-01
Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.
A conjugate gradient method for the spectral partitioning of graphs
Kruyt, Nicolaas P.
1997-01-01
The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and
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
Distributed Large Independent Sets in One Round On Bounded-independence Graphs
Halldorsson , Magnus M.; Konrad , Christian
2015-01-01
International audience; We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor. Bounded-independence graphs capture various models of wireless networks such as the unit disc graphs model and the quasi unit disc graphs model. For instance, on unit disc graphs, our achieved approximation ratio is O((log(n)/log(log(n)))^2).A starting point of our w...
Particle transport in breathing quantum graph
Matrasulov, D.U.; Yusupov, J.R.; Sabirov, K.K.; Sobirov, Z.A.
2012-01-01
Full text: Particle transport in nanoscale networks and discrete structures is of fundamental and practical importance. Usually such systems are modeled by so-called quantum graphs, the systems attracting much attention in physics and mathematics during past two decades [1-5]. During last two decades quantum graphs found numerous applications in modeling different discrete structures and networks in nanoscale and mesoscopic physics (e.g., see reviews [1-3]). Despite considerable progress made in the study of particle dynamics most of the problems deal with unperturbed case and the case of time-dependent perturbation has not yet be explored. In this work we treat particle dynamics for quantum star graph with time-dependent bonds. In particular, we consider harmonically breathing quantum star graphs, the cases of monotonically contracting and expanding graphs. The latter can be solved exactly analytically. Edge boundaries are considered to be time-dependent, while branching point is assumed to be fixed. Quantum dynamics of a particle in such graphs is studied by solving Schrodinger equation with time-dependent boundary conditions given on a star graph. Time-dependence of the average kinetic energy is analyzed. Space-time evolution of the Gaussian wave packet is treated for harmonically breathing star graph. It is found that for certain frequencies energy is a periodic function of time, while for others it can be non-monotonically growing function of time. Such a feature can be caused by possible synchronization of the particles motion and the motions of the moving edges of graph bonds. (authors) References: [1] Tsampikos Kottos and Uzy Smilansky, Ann. Phys., 76, 274 (1999). [2] Sven Gnutzmann and Uzy Smilansky, Adv. Phys. 55, 527 (2006). [3] S. GnutzmannJ.P. Keating, F. Piotet, Ann. Phys., 325, 2595 (2010). [4] P.Exner, P.Seba, P.Stovicek, J. Phys. A: Math. Gen. 21, 4009 (1988). [5] J. Boman, P. Kurasov, Adv. Appl. Math., 35, 58 (2005)
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.
Destroying longest cycles in graphs and digraphs
Van Aardt, Susan A.; Burger, Alewyn P.; Dunbar, Jean E.
2015-01-01
In 1978, C. Thomassen proved that in any graph one can destroy all the longest cycles by deleting at most one third of the vertices. We show that for graphs with circumference k≤8 it suffices to remove at most 1/k of the vertices. The Petersen graph demonstrates that this result cannot be extended...... to include k=9 but we show that in every graph with circumference nine we can destroy all 9-cycles by removing 1/5 of the vertices. We consider the analogous problem for digraphs and show that for digraphs with circumference k=2,3, it suffices to remove 1/k of the vertices. However this does not hold for k≥4....
Non-heuristic reduction of the graph in graph-cut optimization
Malgouyres, François; Lermé, Nicolas
2012-01-01
During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut.
Biases in spatial bisection induced by viewing male and female faces.
Cattaneo, Zaira; Schiavi, Susanna; Lega, Carlotta; Renzi, Chiara; Tagliaferri, Matteo; Boehringer, Jana; Carbon, Claus-Christian; Vecchi, Tomaso
2014-01-01
Research on visual attention triggered by face gender is still relatively sparse. In the present study, three experiments are reported in which male and female participants were required to estimate the midpoint of a line (i.e., the "line bisection task"): at each end of the line a face was presented. Depending on the experimental condition, faces could be of the same gender (i.e., two males or two females) or the opposite gender. Experiments 1 and 2 converged in showing that when a male face was presented at the right and a female face at the left endpoint of the line, a clear rightward bias emerged compared to the other experimental conditions, indicating that male faces captured attention more than female faces. Importantly, male faces used across Experiments 1 and 2 were rated as more threatening than female faces, suggesting that perceived level of threat may have been responsible for the observed bias toward the male face. Experiment 3 corroborated this hypothesis by finding an attentional bias toward the male face with high threat (angry) faces but not with low threat (smiling) faces.
Spectral bisection algorithm for solving Schrodinger equation using upper and lower solutions
Qutaibeh Deeb Katatbeh
2007-10-01
Full Text Available This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schr"odinger equation $ -Deltapsi(r+V(rpsi(r=Epsi(r$ in $N$ spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for the ground state eigenfunctions of Schrodinger equation. We determine also lower and upper solutions for the exact wave function of the ground state eigenfunctions using the computed upper and lower bounds for the eigenvalues obtained by variational methods. In other words, by using this criteria, we prove that the substitution of the lower(upper bound of the eigenvalue in Schrodinger equation leads to an upper(lower solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses Raielgh-Ritz theorem. Meanwhile, the second approach uses a new numerical spectral bisection technique. We apply our results for a wide class of potentials in quantum mechanics such as sum of power-law potentials in quantum mechanics.
Contextual Weisfeiler-Lehman Graph Kernel For Malware Detection
Narayanan, Annamalai; Meng, Guozhu; Yang, Liu; Liu, Jinliang; Chen, Lihui
2016-01-01
In this paper, we propose a novel graph kernel specifically to address a challenging problem in the field of cyber-security, namely, malware detection. Previous research has revealed the following: (1) Graph representations of programs are ideally suited for malware detection as they are robust against several attacks, (2) Besides capturing topological neighbourhoods (i.e., structural information) from these graphs it is important to capture the context under which the neighbourhoods are reac...
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.
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.
Hannukainen, A.; Korotov, S.; Křížek, Michal
2014-01-01
Roč. 90, Part A (2014), s. 34-41 ISSN 0167-6423 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : bisection algorithm * conforming finite element method * regular family of partitions Subject RIV: BA - General Mathematics Impact factor: 0.715, year: 2014 http://www.sciencedirect.com/science/article/pii/S0167642313001226
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.
Antoine, Sophie; Ranzini, Mariagrazia; Gebuis, Titia; van Dijck, Jean-Philippe; Gevers, Wim
2017-10-01
A largely substantiated view in the domain of working memory is that the maintenance of serial order is achieved by generating associations of each item with an independent representation of its position, so-called position markers. Recent studies reported that the ordinal position of an item in verbal working memory interacts with spatial processing. This suggests that position markers might be spatial in nature. However, these interactions were so far observed in tasks implying a clear binary categorization of space (i.e., with left and right responses or targets). Such binary categorizations leave room for alternative interpretations, such as congruency between non-spatial categorical codes for ordinal position (e.g., begin and end) and spatial categorical codes for response (e.g., left and right). Here we discard this interpretation by providing evidence that this interaction can also be observed in a task that draws upon a continuous processing of space, the line bisection task. Specifically, bisections are modulated by ordinal position in verbal working memory, with lines bisected more towards the right after retrieving items from the end compared to the beginning of the memorized sequence. This supports the idea that position markers are intrinsically spatial in nature.
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 ...
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.
2012-01-01
at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar
PERANCANGAN SISTEM PENJADWALAN PEMBELAJARAN MENGGUNAKAN GRAPH COLORING
Taufik Hidayatulloh
2016-03-01
Full Text Available Abstract - In learning scheduling problem often faced by schools in the new academic year. Sometimes collisions on the schedule was not found when the learning process has begun, so it is necessary to re-schedule on the schedule. And this resulted in the teaching and learning first weeks less to run well. Researchers previously have used various methods to solve the scheduling as Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (coloring of a graph is the simplest method and the experimental results indicate that the development of methods of scheduling Graph Coloring deliver results that meet an average of 93% across the specified constraints. At the time of split schedules that require extra energy at the start of learning did not experience a collision. With this system is expected to facilitate the allocation of space, teachers, lessons to avoid a collision. Keywords: Information Systems, Scheduling, graph coloring Abstraksi - Dalam masalah penjadwalan pembelajaran sering dihadapi sekolah pada tahun ajaran baru. Terkadang tabrakan pada jadwal itu baru ditemukan ketika proses belajar mengajar telah dimulai, sehingga perlu dilakukan penjadwalan ulang pada jadwal tersebut. Dan hal ini mengakibatkan kegiatan belajar mengajar pada minggu-minggu pertama kurang dapat berjalan dengan baik. Para peneliti sebelumnya telah menggunakan berbagai metode untuk memecahkan penjadwalan seperti Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (pewarnaan graf merupakan metode yang paling sederhana dan hasil percobaan menunjukkan bahwa pengembangan metode Graph Coloring memberikan hasil penjadwalan yang memenuhi rata-rata 93% seluruh constraints yang ditentukan. Pada saat membagi jadwal memerlukan energi ekstra agar pada saat di mulai pembelajaran tidak mengalami tabrakan. Dengan sistem ini diharapkan dapat mempermudah dalam mengalokasikan ruangan, guru, pelajaran agar tidak mengalami tabrakan. Kata
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.
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.
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.
Generalized belief propagation on tree robust structured region graphs
Gelfand, A.E.; Welling, M.; Murphy, K.; de Freitas, N.
2012-01-01
This paper provides some new guidance in the construction of region graphs for Generalized Belief Propagation (GBP). We connect the problem of choosing the outer regions of a LoopStructured Region Graph (SRG) to that of finding a fundamental cycle basis of the corresponding Markov network. We also
Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs
I.Z. Emiris; E.P. Tsigaridas; A. Varvitsiotis (Antonios); E.R. Gasner
2009-01-01
textabstract The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture embeddability by polynomial systems
Bisimulation reduction of big graphs on MapReduce
Luo, Y.; Lange, de Y.; Fletcher, G.H.L.; De Bra, P.M.E.; Hidders, A.J.H.; Gottlob, G.; Grasso, G.; Olteanu, D.; Schallhart, C.
2013-01-01
Computing the bisimulation partition of a graph is a fundamental problem which plays a key role in a wide range of basic applications. Intuitively, two nodes in a graph are bisimilar if they share basic structural properties such as labeling and neighborhood topology. In data management, reducing a
First-passage percolation on the random graph
Hofstad, van der R.W.; Hooghiemstra, G.; Van Mieghem, P.
2001-01-01
We study first-passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph, this problem can be described in terms of a continuous-time Markov chain and recursive trees. The Markov chain X(t) describes the number of
Optimizing graph algorithms on pregel-like systems
Salihoglu, Semih
2014-03-01
We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel\\'s vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.
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\
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...
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.
Transduction on Directed Graphs via Absorbing Random Walks.
De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li
2017-08-11
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.
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...
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.
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
On semidefinite programming bounds for graph bandwidth
de Klerk, E.; Nagy, M.; Sotirov, R.
2013-01-01
In this paper, we propose two new lower bounds on graph bandwidth and cyclic bandwidth based on semidefinite programming (SDP) relaxations of the quadratic assignment problem. We compare the new bounds with two other SDP bounds reported in [A. Blum, G. Konjevod, R. Ravi, and S. Vempala,
Dynamic Matchings in Convex Bipartite Graphs
Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt
2007-01-01
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...
Connected feedback vertex set in planar graphs
Grigoriev, Alexander; Sitters, René
2010-01-01
We study the problem of finding a minimum tree spanning the faces of a given planar graph. We show that a constant factor approximation follows from the unconnected version if the minimum degree is 3. Moreover, we present a polynomial time approximation scheme for both the connected and unconnected
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
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
Dynamic airspace configuration method based on a weighted graph model
Chen Yangzhou
2014-08-01
Full Text Available This paper proposes a new method for dynamic airspace configuration based on a weighted graph model. The method begins with the construction of an undirected graph for the given airspace, where the vertices represent those key points such as airports, waypoints, and the edges represent those air routes. Those vertices are used as the sites of Voronoi diagram, which divides the airspace into units called as cells. Then, aircraft counts of both each cell and of each air-route are computed. Thus, by assigning both the vertices and the edges with those aircraft counts, a weighted graph model comes into being. Accordingly the airspace configuration problem is described as a weighted graph partitioning problem. Then, the problem is solved by a graph partitioning algorithm, which is a mixture of general weighted graph cuts algorithm, an optimal dynamic load balancing algorithm and a heuristic algorithm. After the cuts algorithm partitions the model into sub-graphs, the load balancing algorithm together with the heuristic algorithm transfers aircraft counts to balance workload among sub-graphs. Lastly, airspace configuration is completed by determining the sector boundaries. The simulation result shows that the designed sectors satisfy not only workload balancing condition, but also the constraints such as convexity, connectivity, as well as minimum distance constraint.
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
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.
Network evolution driven by dynamics applied to graph coloring
Wu Jian-She; Li Li-Guang; Yu Xin; Jiao Li-Cheng; Wang Xiao-Hua
2013-01-01
An evolutionary network driven by dynamics is studied and applied to the graph coloring problem. From an initial structure, both the topology and the coupling weights evolve according to the dynamics. On the other hand, the dynamics of the network are determined by the topology and the coupling weights, so an interesting structure-dynamics co-evolutionary scheme appears. By providing two evolutionary strategies, a network described by the complement of a graph will evolve into several clusters of nodes according to their dynamics. The nodes in each cluster can be assigned the same color and nodes in different clusters assigned different colors. In this way, a co-evolution phenomenon is applied to the graph coloring problem. The proposed scheme is tested on several benchmark graphs for graph coloring
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.
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...
Analysis and enumeration algorithms for biological graphs
Marino, Andrea
2015-01-01
In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions...
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
Incremental Frequent Subgraph Mining on Large Evolving Graphs
Abdelhamid, Ehab
2017-08-22
Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.
graphkernels: R and Python packages for graph comparison.
Sugiyama, Mahito; Ghisu, M Elisabetta; Llinares-López, Felipe; Borgwardt, Karsten
2018-02-01
Measuring the similarity of graphs is a fundamental step in the analysis of graph-structured data, which is omnipresent in computational biology. Graph kernels have been proposed as a powerful and efficient approach to this problem of graph comparison. Here we provide graphkernels, the first R and Python graph kernel libraries including baseline kernels such as label histogram based kernels, classic graph kernels such as random walk based kernels, and the state-of-the-art Weisfeiler-Lehman graph kernel. The core of all graph kernels is implemented in C ++ for efficiency. Using the kernel matrices computed by the package, we can easily perform tasks such as classification, regression and clustering on graph-structured samples. The R and Python packages including source code are available at https://CRAN.R-project.org/package=graphkernels and https://pypi.python.org/pypi/graphkernels. mahito@nii.ac.jp or elisabetta.ghisu@bsse.ethz.ch. Supplementary data are available online at Bioinformatics. © The Author(s) 2017. Published by Oxford University Press.
Learning a Nonnegative Sparse Graph for Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung
2015-09-01
Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.
GRAMI: Generalized Frequent Subgraph Mining in Large Graphs
El Saeedy, Mohammed El Sayed
2011-07-24
Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper we propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. We developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. We also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. Our experiments on real data demonstrate that our framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.
Yamanoi, Takashi; Oda, Yoshiki; Katsuraya, Kaname; Inazu, Toshiyuki; Yamamoto, Kenji
2016-06-02
This study describes the complete nuclear magnetic resonance (NMR) spectral assignment of a bisecting hybrid-type oligosaccharide 1, transferred by Mucor hiemalis endo-β-N-acetylglucosaminidase (Endo-M). Through (1)H- and (13)C-NMR, DQF-COSY, HSQC, HMBC, TOCSY, and NOESY experiments, we determine the structure of the glycoside linkage formed by the Endo-M transglycosylation, i.e., the connection between GlcNAc and GlcNAc in oligosaccharide 1. Copyright © 2016 Elsevier Ltd. All rights reserved.
A linear time algorithm for minimum fill-in and treewidth for distance heredity graphs
Broersma, Haitze J.; Dahlhaus, E.; Kloks, A.J.J.; Kloks, T.
2000-01-01
A graph is distance hereditary if it preserves distances in all its connected induced subgraphs. The MINIMUM FILL-IN problem is the problem of finding a chordal supergraph with the smallest possible number of edges. The TREEWIDTH problem is the problem of finding a chordal embedding of the graph
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
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...
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
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
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
Minimum nonuniform graph partitioning with unrelated weights
Makarychev, K. S.; Makarychev, Yu S.
2017-12-01
We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G=(V,E) and k numbers ρ_1,\\dots, ρ_k. The goal is to partition V into k disjoint sets (bins) P_1,\\dots, P_k satisfying \\vert P_i\\vert≤ ρi \\vert V\\vert for all i, so as to minimize the number of edges cut by the partition. Our bi-criteria algorithm gives an O(\\sqrt{log \\vert V\\vert log k}) approximation for the objective function in general graphs and an O(1) approximation in graphs excluding a fixed minor. The approximate solution satisfies the relaxed capacity constraints \\vert P_i\\vert ≤ (5+ \\varepsilon)ρi \\vert V\\vert. This algorithm is an improvement upon the O(log \\vert V\\vert)-approximation algorithm by Krauthgamer, Naor, Schwartz and Talwar. We extend our results to the case of 'unrelated weights' and to the case of 'unrelated d-dimensional weights'. A preliminary version of this work was presented at the 41st International Colloquium on Automata, Languages and Programming (ICALP 2014). Bibliography: 7 titles.
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.
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
Application of Bipolar Fuzzy Sets in Graph Structures
Muhammad Akram
2016-01-01
Full Text Available A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS, strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study ϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.
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...
Parallel Algorithms for Graph Optimization using Tree Decompositions
Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL; Groer, Christopher S [ORNL
2012-06-01
Although many $\\cal{NP}$-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the necessary dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree decomposition-based approach to solve the maximum weighted independent set problem. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.
Inverse scattering problem for quantum graph vertices
Cheon, T.; Exner, Pavel; Turek, O.
2011-01-01
Roč. 83, č. 6 (2011), 062715/1-062715/4 ISSN 1050-2947 R&D Projects: GA MŠk LC06002; GA ČR GAP203/11/0701 Institutional research plan: CEZ:AV0Z10480505 Keywords : WIRES Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.878, year: 2011
Sergio Marrero-Osorio
2011-05-01
Full Text Available El autor realiza una concisa revisión sobre la aplicación de grafos en la resolución de problemas decómputo en ingeniería, enfatizando en un método propuesto por Martínez Escanaverino que utilizagrafos dicromáticos y ha sido usado en el ámbito científico técnico de Cuba. Analiza, basado en seisejemplos, el escaso empleo que se ha dado hasta el momento al software disponible para trazar yeditar los sucesivos grafos durante el proceso de resolución; estudiando y evaluando un grupo de 18editores de grafos por sus aptitudes para aplicar el mencionado método. Finalmente se recomiendauno de ellos para su uso futuro y se confirma la conveniencia de su empleo a través de unacomparación.Palabras claves: análisis estructural, resolución de problemas, algoritmos, modelo matemático, grafosdicromáticos, editores de grafos.___________________________________________________________________AbstractAuthor makes a concise review about employment of graphs in solving engineering computationalproblems, emphasizing in one method proposed by Martinez Escanaverino which uses dichromaticgraphs and has been applied in Cuban technical sciences. Analyzes, based in six examples, lack inuse (until this moment of software for graph drawing and edition through problem solving process,studying and evaluating 18 available graph editors and suggesting one of them for future applicationsof mentioned method. Finally, making a comparison, are confirmed advantages of its usage.Key words: structural analysis, problem solving, algorithms, mathematical models, dichromatic graphs,graph editors.
Pathfinding in graph-theoretic sabotage models. I. Simultaneous attack by several teams
Hulme, B.L.
1976-07-01
Graph models are developed for fixed-site safeguards systems. The problem of finding optimal routes for several sabotage teams is cast as a problem of finding shortest paths in a graph. The motivation, rationale, and interpretation of the mathematical models are discussed in detail, and an algorithm for efficiently solving the associated path problem is described
Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
2008-01-01
We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log...
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 $Hcong overline{F_n}$.
GraphStore: A Distributed Graph Storage System for Big Data Networks
Martha, VenkataSwamy
2013-01-01
Networks, such as social networks, are a universal solution for modeling complex problems in real time, especially in the Big Data community. While previous studies have attempted to enhance network processing algorithms, none have paved a path for the development of a persistent storage system. The proposed solution, GraphStore, provides an…
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
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, R.; Maskey, M.; Gatlin, P. N.; Zhang, J.; Duan, X.; Bugbee, K.; Christopher, S. A.; Miller, J. J.
2017-12-01
Estimates indicate that the world's information will grow by 800% in the next five years. In any given field, a single researcher or a team of researchers cannot keep up with this rate of knowledge expansion without the help of cognitive systems. Cognitive computing, defined as the use of information technology to augment human cognition, can help tackle large systemic problems. Knowledge graphs, one of the foundational components of cognitive systems, link key entities in a specific domain with other entities via relationships. Researchers could mine these graphs to make probabilistic recommendations and to infer new knowledge. At this point, however, there is a dearth of tools to generate scalable Knowledge graphs using existing corpus of scientific literature for Earth science research. Our project is currently developing an end-to-end automated methodology for incrementally constructing Knowledge graphs for Earth Science. Semantic Entity Recognition (SER) is one of the key steps in this methodology. SER for Earth Science uses external resources (including metadata catalogs and controlled vocabulary) as references to guide entity extraction and recognition (i.e., labeling) from unstructured text, in order to build a large training set to seed the subsequent auto-learning component in our algorithm. Results from several SER experiments will be presented as well as lessons learned.
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.
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...
On domination multisubdivision number of unicyclic graphs
Joanna Raczek
2018-01-01
Full Text Available The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009, 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.
Gromov hyperbolicity in lexicographic product graphs
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on the group [17]. The concept of hyperbolicity appears also in discrete mathematics, algorithms and networking. For .... graph (of a presentation with solvable word problem) there is an algorithm which allows to decide if it is ...... of Theorem 3.14, i.e., dG1◦{w}(Vp, [π(x)π(z)] ∪ [π(z)π(y)]) = δ(G1) with π the canonical projection.
Parallel algorithms for finding cliques in a graph
Szabo, S
2011-01-01
A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.
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...
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.
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.
Graph Design via Convex Optimization: Online and Distributed Perspectives
Meng, De
Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation
Zago, Laure; Petit, Laurent; Jobard, Gael; Hay, Julien; Mazoyer, Bernard; Tzourio-Mazoyer, Nathalie; Karnath, Hans-Otto; Mellet, Emmanuel
2017-01-08
The objective of this study was to validate a line bisection judgement (LBJ) task for use in investigating the lateralized cerebral bases of spatial attention in a sample of 51 right-handed healthy participants. Using functional magnetic resonance imaging (fMRI), the participants performed a LBJ task that was compared to a visuomotor control task during which the participants made similar saccadic and motoric responses. Cerebral lateralization was determined using a voxel-based functional asymmetry analysis and a hemispheric functional lateralization index (HFLI) computed from fMRI contrast images. Behavioural attentional deviation biases were assessed during the LBJ task and a "paper and pencil" symbol cancellation task (SCT). Individual visuospatial skills were also evaluated. The results showed that both the LBJ and SCT tasks elicited leftward spatial biases in healthy subjects, although the biases were not correlated, which indicated their independence. Neuroimaging results showed that the LBJ task elicited a right hemispheric lateralization, with rightward asymmetries found in a large posterior occipito-parietal area, the posterior calcarine sulcus (V1p) and the temporo-occipital junction (TOJ) and in the inferior frontal gyrus, the anterior insula and the superior medial frontal gyrus. The comparison of the LBJ asymmetry map to the lesion map of neglect patients who suffer line bisection deviation demonstrated maximum overlap in a network that included the middle occipital gyrus (MOG), the TOJ, the anterior insula and the inferior frontal region, likely subtending spatial LBJ bias. Finally, the LBJ task-related cerebral lateralization was specifically correlated with the LBJ spatial bias but not with the SCT bias or with the visuospatial skills of the participants. Taken together, these results demonstrated that the LBJ task is adequate for investigating spatial lateralization in healthy subjects and is suitable for determining the factors underlying the
Himmelberger, Jeffery J.; And Others
1995-01-01
Summarizes key research implications of Three Mile Island and other major hazard events as related to tourism. Examines how the proposed Yucca Mountain nuclear waste repository system will impact tourism in southern Nevada and other visitor-oriented rural counties bisected by planned waste transportation corridors. (AIM)
Fink, G.R.; Marshall, J.C.; Weiss, P.H.; Toni, I.; Zilles, K.
2002-01-01
Manual line bisection and a perceptual variant thereof (the Landmark test) are widely used to assess visuospatial neglect in neurological patients, but little is known about the cognitive strategies involved. In the Landmark test, one could explicitly compare the lengths of the left and right line
Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms
Furmańczyk Hanna
2016-09-01
Full Text Available In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
Distributed-Memory Breadth-First Search on Massive Graphs
Buluc, Aydin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Beamer, Scott [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Madduri, Kamesh [Pennsylvania State Univ., University Park, PA (United States). Computer Science & Engineering Dept.; Asanovic, Krste [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Patterson, David [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences
2017-09-26
This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.
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.
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.
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.
How Symmetric Are Real-World Graphs? A Large-Scale Study
Fabian Ball
2018-01-01
Full Text Available The analysis of symmetry is a main principle in natural sciences, especially physics. For network sciences, for example, in social sciences, computer science and data science, only a few small-scale studies of the symmetry of complex real-world graphs exist. Graph symmetry is a topic rooted in mathematics and is not yet well-received and applied in practice. This article underlines the importance of analyzing symmetry by showing the existence of symmetry in real-world graphs. An analysis of over 1500 graph datasets from the meta-repository networkrepository.com is carried out and a normalized version of the “network redundancy” measure is presented. It quantifies graph symmetry in terms of the number of orbits of the symmetry group from zero (no symmetries to one (completely symmetric, and improves the recognition of asymmetric graphs. Over 70% of the analyzed graphs contain symmetries (i.e., graph automorphisms, independent of size and modularity. Therefore, we conclude that real-world graphs are likely to contain symmetries. This contribution is the first larger-scale study of symmetry in graphs and it shows the necessity of handling symmetry in data analysis: The existence of symmetries in graphs is the cause of two problems in graph clustering we are aware of, namely, the existence of multiple equivalent solutions with the same value of the clustering criterion and, secondly, the inability of all standard partition-comparison measures of cluster analysis to identify automorphic partitions as equivalent.
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.
Graphs and matroids weighted in a bounded incline algebra.
Lu, Ling-Xia; Zhang, Bei
2014-01-01
Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.
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...
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)
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
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)
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.
Label Information Guided Graph Construction for Semi-Supervised Learning.
Zhuang, Liansheng; Zhou, Zihan; Gao, Shenghua; Yin, Jingwen; Lin, Zhouchen; Ma, Yi
2017-09-01
In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks.
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.
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.
Optimal graph based segmentation using flow lines with application to airway wall segmentation
Petersen, Jens; Nielsen, Mads; Lo, Pechin
2011-01-01
This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited for ...
Optimal graph based segmentation using flow lines with application to airway wall segmentation
Petersen, Jens; Nielsen, Mads; Lo, Pechin Chien Pau
2011-01-01
This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited...
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.
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 ...
Dynamic graphs, community detection, and Riemannian geometry
Bakker, Craig; Halappanavar, Mahantesh; Visweswara Sathanur, Arun
2018-03-29
A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.
Mutual Contextualization in Tripartite Graphs of Folksonomies
Yeung, Ching-Man Au; Gibbins, Nicholas; Shadbolt, Nigel
The use of tags to describe Web resources in a collaborative manner has experienced rising popularity among Web users in recent years. The product of such activity is given the name folksonomy, which can be considered as a scheme of organizing information in the users' own way. This research work attempts to analyze tripartite graphs - graphs involving users, tags and resources - of folksonomies and discuss how these elements acquire their semantics through their associations with other elements, a process we call mutual contextualization. By studying such process, we try to identify solutions to problems such as tag disambiguation, retrieving documents of similar topics and discovering communities of users. This paper describes the basis of the research work, mentions work done so far and outlines future plans.
Graph-related optimization and decision support systems
Krichen, Saoussen
2014-01-01
Constrained optimization is a challenging branch of operations research that aims to create a model which has a wide range of applications in the supply chain, telecommunications and medical fields. As the problem structure is split into two main components, the objective is to accomplish the feasible set framed by the system constraints. The aim of this book is expose optimization problems that can be expressed as graphs, by detailing, for each studied problem, the set of nodes and the set of edges. This graph modeling is an incentive for designing a platform that integrates all optimizatio
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.
Kupavskii, A B; Raigorodskii, A M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2013-10-31
We investigate in detail some properties of distance graphs constructed on the integer lattice. Such graphs find wide applications in problems of combinatorial geometry, in particular, such graphs were employed to answer Borsuk's question in the negative and to obtain exponential estimates for the chromatic number of the space. This work is devoted to the study of the number of cliques and the chromatic number of such graphs under certain conditions. Constructions of sequences of distance graphs are given, in which the graphs have unit length edges and contain a large number of triangles that lie on a sphere of radius 1/√3 (which is the minimum possible). At the same time, the chromatic numbers of the graphs depend exponentially on their dimension. The results of this work strengthen and generalize some of the results obtained in a series of papers devoted to related issues. Bibliography: 29 titles.
Laplacian eigenvectors of graphs Perron-Frobenius and Faber-Krahn type theorems
Biyikoğu, Türker; Stadler, Peter F
2007-01-01
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.
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...
Dim target detection method based on salient graph fusion
Hu, Ruo-lan; Shen, Yi-yan; Jiang, Jun
2018-02-01
Dim target detection is one key problem in digital image processing field. With development of multi-spectrum imaging sensor, it becomes a trend to improve the performance of dim target detection by fusing the information from different spectral images. In this paper, one dim target detection method based on salient graph fusion was proposed. In the method, Gabor filter with multi-direction and contrast filter with multi-scale were combined to construct salient graph from digital image. And then, the maximum salience fusion strategy was designed to fuse the salient graph from different spectral images. Top-hat filter was used to detect dim target from the fusion salient graph. Experimental results show that proposal method improved the probability of target detection and reduced the probability of false alarm on clutter background images.
Random graph states, maximal flow and Fuss-Catalan distributions
Collins, BenoIt; Nechita, Ion; Zyczkowski, Karol
2010-01-01
For any graph consisting of k vertices and m edges we construct an ensemble of random pure quantum states which describe a system composed of 2m subsystems. Each edge of the graph represents a bipartite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated with a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze the statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.
Multiple Illuminant Colour Estimation via Statistical Inference on Factor Graphs.
Mutimbu, Lawrence; Robles-Kelly, Antonio
2016-08-31
This paper presents a method to recover a spatially varying illuminant colour estimate from scenes lit by multiple light sources. Starting with the image formation process, we formulate the illuminant recovery problem in a statistically datadriven setting. To do this, we use a factor graph defined across the scale space of the input image. In the graph, we utilise a set of illuminant prototypes computed using a data driven approach. As a result, our method delivers a pixelwise illuminant colour estimate being devoid of libraries or user input. The use of a factor graph also allows for the illuminant estimates to be recovered making use of a maximum a posteriori (MAP) inference process. Moreover, we compute the probability marginals by performing a Delaunay triangulation on our factor graph. We illustrate the utility of our method for pixelwise illuminant colour recovery on widely available datasets and compare against a number of alternatives. We also show sample colour correction results on real-world images.
Calculating Graph Algorithms for Dominance and Shortest Path
Sergey, Ilya; Midtgaard, Jan; Clarke, Dave
2012-01-01
We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point...... expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length. The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school...... of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation...
Bond graph to digraph conversion: A sensor placement optimization ...
In this paper, we consider the optimal sensors placement problem for ... is due to the fact that the construction is generally done from the state equations, ... The Bond Graph (BG) tool defined in Paynter (1961) formal- ... Sensor placement and structural problem formulation .... Thus the obtained four matrices are as follows:.
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.
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.
Nichols, Jeri Ann
This study examined the relationship between mathematics background and performance on graph-related problems in physics before and after instruction on the graphical analysis of motion and several microcomputer-based laboratory experiences. Students identified as either having or not having a graphing technology enhanced precalculus mathematics background were further categorized into one of four groups according to mathematics placement at the university. The performances of these groups were compared to identity differences. Pre- and Post-test data were collected from 589 students and 312 students during Autumn Quarter 1990 and Winter Quarter 1991 respectively. Background information was collected from each student. Significant differences were found between students with the technology enhanced mathematics background and those without when considering the entire populations both quarters. The students with the technology background were favored Autumn quarter and students without the technology background were favored Winter quarter. However, the entire population included an underrepresentation of students at the highest and lowest placements; hence, these were eliminated from the analyses. No significant differences were found between the technology/no technology groups after the elimination of the underrepresented groups. All categories of students increased their mean scores from pretest to post-test; the average increase was 8.23 points Autumn Quarter and 11.41 points Winter Quarter. Males consistently outperformed females on both the pretest and the post-test Autumn 1990. All students found questions involving the concept of acceleration more difficult than questions involving velocity or distance. Questions requiring students to create graphs were more difficult than questions requiring students to interpret graphs. Further research involving a qualitative component is recommended to identify the specific skills students use when solving graph
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...
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...
Wiener index and Diameter of a Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
2009-01-01
Consider the problem of computing the sum of distances between each pair of vertices of an unweighted graph. This sum is also known as the Wiener index of the graph, a generalization of a definition given by H. Wiener in 1947. A molecular topological index is a value obtained from the graph...... structure of a molecule such that this value (hopefully) correlates with physical and/or chemical properties of the molecule. The Wiener index is perhaps the most studied molecular topological index with more than a thousand publications. It is open whether the Wiener index of a planar graph can be obtained...... in subquadratic time. In my talk, I will solve this open problem by exhibiting an O(n2 log log n / log n) time algorithm, where n is the size of the graph. A simple modification yields an algorithm with the same time bound that computes the diameter (maximum distance between any vertex pair) of a planar graph. I...
A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.
Wei, Wei; Gao, Bin; Liu, Tie-Yan; Wang, Taifeng; Li, Guohui; Li, Hang
2016-04-01
Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.
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.
Approximating centrality in evolving graphs: toward sublinearity
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
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.
Multidimensional Brain MRI segmentation using graph cuts
Lecoeur, Jeremy
2010-01-01
This thesis deals with the segmentation of multimodal brain MRIs by graph cuts method. First, we propose a method that utilizes three MRI modalities by merging them. The border information given by the spectral gradient is then challenged by a region information, given by the seeds selected by the user, using a graph cut algorithm. Then, we propose three enhancements of this method. The first consists in finding an optimal spectral space because the spectral gradient is based on natural images and then inadequate for multimodal medical images. This results in a learning based segmentation method. We then explore the automation of the graph cut method. Here, the various pieces of information usually given by the user are inferred from a robust expectation-maximization algorithm. We show the performance of these two enhanced versions on multiple sclerosis lesions. Finally, we integrate atlases for the automatic segmentation of deep brain structures. These three new techniques show the adaptability of our method to various problems. Our different segmentation methods are better than most of nowadays techniques, speaking of computation time or segmentation accuracy. (authors)
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.
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...
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.
Weighted Maximum-Clique Transversal Sets of Graphs
Chuan-Min Lee
2011-01-01
A maximum-clique transversal set of a graph G is a subset of vertices intersecting all maximum cliques of G. The maximum-clique transversal set problem is to find a maximum-clique transversal set of G of minimum cardinality. Motivated by the placement of transmitters for cellular telephones, Chang, Kloks, and Lee introduced the concept of maximum-clique transversal sets on graphs in 2001. In this paper, we study the weighted version of the maximum-clique transversal set problem for split grap...
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
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
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.
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-cut based discrete-valued image reconstruction.
Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim
2015-05-01
Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.
Neuro-symbolic representation learning on biological knowledge graphs.
Alshahrani, Mona; Khan, Mohammad Asif; Maddouri, Omar; Kinjo, Akira R; Queralt-Rosinach, Núria; Hoehndorf, Robert
2017-09-01
Biological data and knowledge bases increasingly rely on Semantic Web technologies and the use of knowledge graphs for data integration, retrieval and federated queries. In the past years, feature learning methods that are applicable to graph-structured data are becoming available, but have not yet widely been applied and evaluated on structured biological knowledge. Results: We develop a novel method for feature learning on biological knowledge graphs. Our method combines symbolic methods, in particular knowledge representation using symbolic logic and automated reasoning, with neural networks to generate embeddings of nodes that encode for related information within knowledge graphs. Through the use of symbolic logic, these embeddings contain both explicit and implicit information. We apply these embeddings to the prediction of edges in the knowledge graph representing problems of function prediction, finding candidate genes of diseases, protein-protein interactions, or drug target relations, and demonstrate performance that matches and sometimes outperforms traditional approaches based on manually crafted features. Our method can be applied to any biological knowledge graph, and will thereby open up the increasing amount of Semantic Web based knowledge bases in biology to use in machine learning and data analytics. https://github.com/bio-ontology-research-group/walking-rdf-and-owl. robert.hoehndorf@kaust.edu.sa. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.
Neuro-symbolic representation learning on biological knowledge graphs
Alshahrani, Mona
2017-04-21
Biological data and knowledge bases increasingly rely on Semantic Web technologies and the use of knowledge graphs for data integration, retrieval and federated queries. In the past years, feature learning methods that are applicable to graph-structured data are becoming available, but have not yet widely been applied and evaluated on structured biological knowledge.We develop a novel method for feature learning on biological knowledge graphs. Our method combines symbolic methods, in particular knowledge representation using symbolic logic and automated reasoning, with neural networks to generate embeddings of nodes that encode for related information within knowledge graphs. Through the use of symbolic logic, these embeddings contain both explicit and implicit information. We apply these embeddings to the prediction of edges in the knowledge graph representing problems of function prediction, finding candidate genes of diseases, protein-protein interactions, or drug target relations, and demonstrate performance that matches and sometimes outperforms traditional approaches based on manually crafted features. Our method can be applied to any biological knowledge graph, and will thereby open up the increasing amount of SemanticWeb based knowledge bases in biology to use in machine learning and data analytics.https://github.com/bio-ontology-research-group/walking-rdf-and-owl.robert.hoehndorf@kaust.edu.sa.Supplementary data are available at Bioinformatics online.
Regular graph construction for semi-supervised learning
Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang
2014-01-01
Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN
Scalable force directed graph layout algorithms using fast multipole methods
Yunis, Enas Abdulrahman
2012-06-01
We present an extension to ExaFMM, a Fast Multipole Method library, as a generalized approach for fast and scalable execution of the Force-Directed Graph Layout algorithm. The Force-Directed Graph Layout algorithm is a physics-based approach to graph layout that treats the vertices V as repelling charged particles with the edges E connecting them acting as springs. Traditionally, the amount of work required in applying the Force-Directed Graph Layout algorithm is O(|V|2 + |E|) using direct calculations and O(|V| log |V| + |E|) using truncation, filtering, and/or multi-level techniques. Correct application of the Fast Multipole Method allows us to maintain a lower complexity of O(|V| + |E|) while regaining most of the precision lost in other techniques. Solving layout problems for truly large graphs with millions of vertices still requires a scalable algorithm and implementation. We have been able to leverage the scalability and architectural adaptability of the ExaFMM library to create a Force-Directed Graph Layout implementation that runs efficiently on distributed multicore and multi-GPU architectures. © 2012 IEEE.
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.
Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics
Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal
2017-12-01
Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.
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.
Discrete geometric analysis of message passing algorithm on graphs
Watanabe, Yusuke
2010-04-01
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.
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)
Dynamic Programming and Graph Algorithms in Computer Vision*
Felzenszwalb, Pedro F.; Zabih, Ramin
2013-01-01
Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition. PMID:20660950
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
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.
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
Memoryless cooperative graph search based on the simulated annealing algorithm
Hou Jian; Yan Gang-Feng; Fan Zhen
2011-01-01
We have studied the problem of reaching a globally optimal segment for a graph-like environment with a single or a group of autonomous mobile agents. Firstly, two efficient simulated-annealing-like algorithms are given for a single agent to solve the problem in a partially known environment and an unknown environment, respectively. It shows that under both proposed control strategies, the agent will eventually converge to a globally optimal segment with probability 1. Secondly, we use multi-agent searching to simultaneously reduce the computation complexity and accelerate convergence based on the algorithms we have given for a single agent. By exploiting graph partition, a gossip-consensus method based scheme is presented to update the key parameter—radius of the graph, ensuring that the agents spend much less time finding a globally optimal segment. (interdisciplinary physics and related areas of science and technology)
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.
Zero Forcing Sets and Controllability of Dynamical Systems Defined on Graphs
Monshizadeh Naini, Nima; Zhang, Shuo; Camlibel, M. Kanat
In this technical note, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network
Approximating maximum weight cycle covers in directed graphs with weights zero and one
Bläser, Markus; Manthey, Bodo
2005-01-01
A cycle cover of a graph is a spanning subgraph each node of which is part of exactly one simple cycle. A $k$-cycle cover is a cycle cover where each cycle has length at least $k$. Given a complete directed graph with edge weights zero and one, Max-$k$-DCC(0, 1) is the problem of finding a k-cycle
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…
The Use of Graphs in Specific Situations of the Initial Conditions of Linear Differential Equations
Buendía, Gabriela; Cordero, Francisco
2013-01-01
In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the…
Strong oriented chromatic number of planar graphs without short cycles
Mickaël Montassier
2008-01-01
Full Text Available Let M be an additive abelian group. A strong oriented coloringof an oriented graph G is a mapping φ from V(G to M such that (1 φ(u ≠ φ(v whenever uv is an arc in G and (2 φ(v - φ(u ≠ -(φ(t - φ(z whenever uv and zt are two arcs in G. We say that G has a M-strong-oriented coloring. The strong oriented chromatic number of an oriented graph, denoted by χ s (G, is the minimal order of a group M, such that G has M-strong-oriented coloring. This notion was introduced by Nešetřil and Raspaud. In this paper, we pose the following problem: Let i ≥ 4 be an integer. Let G be an oriented planar graph without cycles of lengths 4 to i. Which is the strong oriented chromatic number of G ? Our aim is to determine the impact of triangles on the strong oriented coloring. We give some hints of answers to this problem by proving that: (1 the strong oriented chromatic number of any oriented planar graph without cycles of lengths 4 to 12 is at most 7, and (2 the strong oriented chromatic number of any oriented planar graph without cycles of length 4 or 6 is at most 19.
Xu, Zhiqiang
2017-02-16
Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.
Xu, Zhiqiang; Cheng, James; Xiao, Xiaokui; Fujimaki, Ryohei; Muraoka, Yusuke
2017-01-01
Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.
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.
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Hierarchical organisation of causal graphs
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
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:
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 ...
Méthodes de graphe pour la segmentation d'images et le suivi d'objets dynamiques
Wang , Xiaofang
2015-01-01
Image segmentation is a fundamental problem in computer vision. In particular, unsupervised image segmentation is an important component in many high-level algorithms and practical vision systems. In this dissertation, we propose three methods that approach image segmentation from different angles of graph based methods and are proved powerful to address these problems. Our first method develops an original graph construction method. We also analyze different types of graph construction metho...
Shortest path problems. Road network on cities and we want to navigate between cities. . – p.8/30 ..... The rest of the talk... Computing connectivities between all pairs of vertices good algorithm wrt both space and time to compute the exact solution. . – p.15/30 ...
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.
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.
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
Recovery scheduling for industrial pocesses using graph constraints
Saltik, M.B.; van Gameren, S.; Özkan, L.; Weiland, S.
2017-01-01
This paper considers a class of scheduling problems cast for processes that consist of several interconnected subprocesses. We model the temporal constraints (On-Off status) on each subprocess using labeled directed graphs to form the admissible set of schedules. Furthermore, we consider physical
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...
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. .
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.
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
Kostenko, A. S.; Malamud, M. M.; Neidhardt, H.; Exner, Pavel
2017-01-01
Roč. 95, č. 1 (2017), s. 31-36 ISSN 1064-5624 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : boundary value problems * Schrodinger operators Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 0.472, year: 2016
A novel line segment detection algorithm based on graph search
Zhao, Hong-dan; Liu, Guo-ying; Song, Xu
2018-02-01
To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).
Voice-Centric LTE Femtocells and Improper Graph Colorings
Garcia, Luis Guilherme Uzeda; Pedersen, Klaus; Mogensen, Preben
2012-01-01
. The investigation revolves around the sensible definition of the underlying graph, i.e. the network model, rather than focusing on the coloring algorithms and their properties. Ultimately, we posit that improper online graph-coloring suffices and is actually preferable. In short, settling for less......This paper addresses carrier-based inter-cell interference coordination (CB-ICIC) among LTE femtocells operating on a single carrier. CB-ICIC is in many ways linked to the widely investigated dynamic channel assignment problem, which is often studied in the context of graph coloring......-than-optimal configurations avoids uncontrolled service interruptions. Such disruptions tend to raise understandable concerns when it comes to fully autonomous selection of operational CCs. Our results dispel such concerns by showing that conservative methods can achieve most of the benefits of unrestricted off-line coloring...
The hard-core model on random graphs revisited
Barbier, Jean; Krzakala, Florent; Zhang, Pan; Zdeborová, Lenka
2013-01-01
We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random graph. Although the case of random graphs with small and very large average degrees respectively are quite well understood, they yield qualitatively different results and our aim here is to reconciliate these two cases. We revisit results that can be obtained using the (heuristic) cavity method and show that it provides a closed-form conjecture for the exact density of the densest packing on random regular graphs with degree K ≥ 20, and that for K > 16 the nature of the phase transition is the same as for large K. This also shows that the hard-code model is the simplest mean-field lattice model for structural glasses and jamming
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.
Fingerprint recognition system by use of graph matching
Shen, Wei; Shen, Jun; Zheng, Huicheng
2001-09-01
Fingerprint recognition is an important subject in biometrics to identify or verify persons by physiological characteristics, and has found wide applications in different domains. In the present paper, we present a finger recognition system that combines singular points and structures. The principal steps of processing in our system are: preprocessing and ridge segmentation, singular point extraction and selection, graph representation, and finger recognition by graphs matching. Our fingerprint recognition system is implemented and tested for many fingerprint images and the experimental result are satisfactory. Different techniques are used in our system, such as fast calculation of orientation field, local fuzzy dynamical thresholding, algebraic analysis of connections and fingerprints representation and matching by graphs. Wed find that for fingerprint database that is not very large, the recognition rate is very high even without using a prior coarse category classification. This system works well for both one-to-few and one-to-many problems.
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
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)
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)
Interactive exploration of large-scale time-varying data using dynamic tracking graphs
Widanagamaachchi, W.
2012-10-01
Exploring and analyzing the temporal evolution of features in large-scale time-varying datasets is a common problem in many areas of science and engineering. One natural representation of such data is tracking graphs, i.e., constrained graph layouts that use one spatial dimension to indicate time and show the "tracks" of each feature as it evolves, merges or disappears. However, for practical data sets creating the corresponding optimal graph layouts that minimize the number of intersections can take hours to compute with existing techniques. Furthermore, the resulting graphs are often unmanageably large and complex even with an ideal layout. Finally, due to the cost of the layout, changing the feature definition, e.g. by changing an iso-value, or analyzing properly adjusted sub-graphs is infeasible. To address these challenges, this paper presents a new framework that couples hierarchical feature definitions with progressive graph layout algorithms to provide an interactive exploration of dynamically constructed tracking graphs. Our system enables users to change feature definitions on-the-fly and filter features using arbitrary attributes while providing an interactive view of the resulting tracking graphs. Furthermore, the graph display is integrated into a linked view system that provides a traditional 3D view of the current set of features and allows a cross-linked selection to enable a fully flexible spatio-temporal exploration of data. We demonstrate the utility of our approach with several large-scale scientific simulations from combustion science. © 2012 IEEE.
GraMi: Generalized Frequent Pattern Mining in a Single Large Graph
Saeedy, Mohammed El
2011-11-01
Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper the authors propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. The authors developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. The authors also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. The experiments on real data demonstrate that the authors framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.
Bisectional fault detection system
Archer, Charles Jens [Rochester, MN; Pinnow, Kurt Walter [Rochester, MN; Ratterman, Joseph D [Rochester, MN; Smith, Brian Edward [Rochester, MN
2009-08-04
An apparatus and program product logically divide a group of nodes and causes node pairs comprising a node from each section to communicate. Results from the communications may be analyzed to determine performance characteristics, such as bandwidth and proper connectivity.
Bisectional fault detection system
Archer, Charles Jens [Rochester, MN; Pinnow, Kurt Walter [Rochester, MN; Ratterman, Joseph D [Rochester, MN; Smith, Brian Edward [Rochester, MN
2008-11-11
An apparatus, program product and method logically divides a group of nodes and causes node pairs comprising a node from each section to communicate. Results from the communications may be analyzed to determine performance characteristics, such as bandwidth and proper connectivity.
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
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...
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....
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
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
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...
GraMi: Generalized Frequent Pattern Mining in a Single Large Graph
Saeedy, Mohammed El; Kalnis, Panos
2011-01-01
resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. The authors also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI
Himmelberger, J.J.; Baughman, M.; Ogneva-Himmelberger, Y.A.
1995-01-01
Whether the proposed Yucca Mountain nuclear waste repository system will adversely impact tourism in southern Nevada is an open question of particular importance to visitor-oriented rural counties bisected by planned waste transportation corridors (highway or rail). As part of one such county's repository impact assessment program, tourism implications of Three Mile Island (TMI) and other major hazard events have been revisited to inform ongoing county-wide socioeconomic assessments and contingency planning efforts. This paper summarizes key research implications of such research as applied to Lincoln County, Nevada. Implications for other rural counties are discussed in light of the research findings
Himmelberger, J.J.; Ogneva-Himmelberger, Y.A. [Clark Univ., Worcester, MA (United States); Baughman, M. [Interech Services Corporation, Carson City, NV (United States)
1995-11-01
Whether the proposed Yucca Mountain nuclear waste repository system will adversely impact tourism in southern Nevada is an open question of particular importance to visitor-oriented rural counties bisected by planned waste transportation corridors (highway or rail). As part of one such county`s repository impact assessment program, tourism implications of Three Mile Island (TMI) and other major hazard events have been revisited to inform ongoing county-wide socioeconomic assessments and contingency planning efforts. This paper summarizes key research implications of such research as applied to Lincoln County, Nevada. Implications for other rural counties are discussed in light of the research findings. 29 refs., 3 figs., 1 tab.
Sarunya Kanjanawattana
2017-01-01
Full Text Available literature. Extracting graph information clearly contributes to readers, who are interested in graph information interpretation, because we can obtain significant information presenting in the graph. A typical tool used to transform image-based characters to computer editable characters is optical character recognition (OCR. Unfortunately, OCR cannot guarantee perfect results, because it is sensitive to noise and input quality. This becomes a serious problem because misrecognition provides misunderstanding information to readers and causes misleading communication. In this study, we present a novel method for OCR-error correction based on bar graphs using semantics, such as ontologies and dependency parsing. Moreover, we used a graph component extraction proposed in our previous study to omit irrelevant parts from graph components. It was applied to clean and prepare input data for this OCR-error correction. The main objectives of this paper are to extract significant information from the graph using OCR and to correct OCR errors using semantics. As a result, our method provided remarkable performance with the highest accuracies and F-measures. Moreover, we examined that our input data contained less of noise because of an efficiency of our graph component extraction. Based on the evidence, we conclude that our solution to the OCR problem achieves the objectives.
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.
Chinese Postman Problem on edge-colored multigraphs
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
It is well-known that the Chinese Postman Problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese Postman Problem on mixed graphs, i.e., graphs with directed and undirected edges, for ...
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.
Computing paths and cycles in biological interaction graphs
von Kamp Axel
2009-06-01
Full Text Available Abstract Background Interaction graphs (signed directed graphs provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments. Results We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops. Conclusion The calculation of shortest positive
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.
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)
Kuhlemann, Verena [Emory Univ., Atlanta, GA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2013-10-28
Matrix-vector multiplication is the key operation in any Krylov-subspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scale-free graphs. Furthermore, computations with graphs of this type on parallel distributed-memory computers are challenging. This is due to the fact that scale-free graphs have a degree distribution that follows a power law, and currently available graph partitioners are not efficient for such an irregular degree distribution. The lack of a good partitioning leads to excessive interprocessor communication requirements during every matrix-vector product. Here, we present an approach to alleviate this problem based on embedding the original irregular graph into a more regular one by disaggregating (splitting up) vertices in the original graph. The matrix-vector operations for the original graph are performed via a factored triple matrix-vector product involving the embedding graph. And even though the latter graph is larger, we are able to decrease the communication requirements considerably and improve the performance of the matrix-vector product.
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...
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.
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 ...
Analyzing and synthesizing phylogenies using tree alignment graphs.
Stephen A Smith
Full Text Available Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG. The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees, we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to
Analyzing and synthesizing phylogenies using tree alignment graphs.
Smith, Stephen A; Brown, Joseph W; Hinchliff, Cody E
2013-01-01
Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG). The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees), we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to observe.
Topological structure of dictionary graphs
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Machado, Armando; Arantes, Joana
2006-06-01
To contrast two models of timing, Scalar Expectancy Theory (SET) and Learning to Time (LeT), pigeons were exposed to a double temporal bisection procedure. On half of the trials, they learned to choose a red key after a 1s signal and a green key after a 4s signal; on the other half of the trials, they learned to choose a blue key after a 4-s signal and a yellow key after a 16-s signal. This was Phase A of an ABA design. On Phase B, the pigeons were divided into two groups and exposed to a new bisection task in which the signals ranged from 1 to 16s and the choice keys were blue and green. One group was reinforced for choosing blue after 1-s signals and green after 16-s signals and the other group was reinforced for the opposite mapping (green after 1-s signals and blue after 16-s signals). Whereas SET predicted no differences between the groups, LeT predicted that the former group would learn the new discrimination faster than the latter group. The results were consistent with LeT. Finally, the pigeons returned to Phase A. Only LeT made specific predictions regarding the reacquisition of the four temporal discriminations. These predictions were only partly consistent with the results.
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.)
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.)
Maximum-entropy networks pattern detection, network reconstruction and graph combinatorics
Squartini, Tiziano
2017-01-01
This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem o...
Many-core graph analytics using accelerated sparse linear algebra routines
Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric
2016-05-01
Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.
Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph
P. Anusha Devi
2015-10-01
Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$ The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.
Xiaojin Li
2013-01-01
Full Text Available Previous studies have investigated both structural and functional brain networks via graph-theoretical methods. However, there is an important issue that has not been adequately discussed before: what is the optimal theoretical graph model for describing the structural networks of human brain? In this paper, we perform a comparative study to address this problem. Firstly, large-scale cortical regions of interest (ROIs are localized by recently developed and validated brain reference system named Dense Individualized Common Connectivity-based Cortical Landmarks (DICCCOL to address the limitations in the identification of the brain network ROIs in previous studies. Then, we construct structural brain networks based on diffusion tensor imaging (DTI data. Afterwards, the global and local graph properties of the constructed structural brain networks are measured using the state-of-the-art graph analysis algorithms and tools and are further compared with seven popular theoretical graph models. In addition, we compare the topological properties between two graph models, namely, stickiness-index-based model (STICKY and scale-free gene duplication model (SF-GD, that have higher similarity with the real structural brain networks in terms of global and local graph properties. Our experimental results suggest that among the seven theoretical graph models compared in this study, STICKY and SF-GD models have better performances in characterizing the structural human brain network.
Wang, Jim Jing-Yan
2014-09-20
Nonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMFFS and AGNMFMK, by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.
Navigability of Random Geometric Graphs in the Universe and Other Spacetimes.
Cunningham, William; Zuev, Konstantin; Krioukov, Dmitri
2017-08-18
Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.
Entity-Linking via Graph-Distance Minimization
Roi Blanco
2014-07-01
Full Text Available Entity-linking is a natural-language–processing task that consists in identifying the entities mentioned in a piece of text, linking each to an appropriate item in some knowledge base; when the knowledge base is Wikipedia, the problem comes to be known as wikification (in this case, items are wikipedia articles. One instance of entity-linking can be formalized as an optimization problem on the underlying concept graph, where the quantity to be optimized is the average distance between chosen items. Inspired by this application, we define a new graph problem which is a natural variant of the Maximum Capacity Representative Set. We prove that our problem is NP-hard for general graphs; nonetheless, under some restrictive assumptions, it turns out to be solvable in linear time. For the general case, we propose two heuristics: one tries to enforce the above assumptions and another one is based on the notion of hitting distance; we show experimentally how these approaches perform with respect to some baselines on a real-world dataset.
Artistic image analysis using graph-based learning approaches.
Carneiro, Gustavo
2013-08-01
We introduce a new methodology for the problem of artistic image analysis, which among other tasks, involves the automatic identification of visual classes present in an art work. In this paper, we advocate the idea that artistic image analysis must explore a graph that captures the network of artistic influences by computing the similarities in terms of appearance and manual annotation. One of the novelties of our methodology is the proposed formulation that is a principled way of combining these two similarities in a single graph. Using this graph, we show that an efficient random walk algorithm based on an inverted label propagation formulation produces more accurate annotation and retrieval results compared with the following baseline algorithms: bag of visual words, label propagation, matrix completion, and structural learning. We also show that the proposed approach leads to a more efficient inference and training procedures. This experiment is run on a database containing 988 artistic images (with 49 visual classification problems divided into a multiclass problem with 27 classes and 48 binary problems), where we show the inference and training running times, and quantitative comparisons with respect to several retrieval and annotation performance measures.
Greedy Local Search and Vertex Cover in Sparse Random Graphs
Witt, Carsten
2009-01-01
. This work starts with a rigorous explanation for this claim based on the refined analysis of the Karp-Sipser algorithm by Aronson et al. Subsequently, theoretical supplements are given to experimental studies of search heuristics on random graphs. For c 1, a greedy and randomized local-search heuristic...... finds an optimal cover in polynomial time with a probability arbitrarily close to 1. This behavior relies on the absence of a giant component. As an additional insight into the randomized search, it is shown that the heuristic fails badly also on graphs consisting of a single tree component of maximum......Recently, various randomized search heuristics have been studied for the solution of the minimum vertex cover problem, in particular for sparse random instances according to the G(n, c/n) model, where c > 0 is a constant. Methods from statistical physics suggest that the problem is easy if c
Parasol: An Architecture for Cross-Cloud Federated Graph Querying
Lieberman, Michael; Choudhury, Sutanay; Hughes, Marisa; Patrone, Dennis; Hider, Sandy; Piatko, Christine; Chapman, Matthew; Marple, JP; Silberberg, David
2014-06-22
Large scale data fusion of multiple datasets can often provide in- sights that examining datasets individually cannot. However, when these datasets reside in different data centers and cannot be collocated due to technical, administrative, or policy barriers, a unique set of problems arise that hamper querying and data fusion. To ad- dress these problems, a system and architecture named Parasol is presented that enables federated queries over graph databases residing in multiple clouds. Parasol’s design is flexible and requires only minimal assumptions for participant clouds. Query optimization techniques are also described that are compatible with Parasol’s lightweight architecture. Experiments on a prototype implementation of Parasol indicate its suitability for cross-cloud federated graph queries.
A lossy graph model for delay reduction in generalized instantly decodable network coding
Douik, Ahmed S.
2014-06-01
The problem of minimizing the decoding delay in Generalized instantly decodable network coding (G-IDNC) for both perfect and lossy feedback scenarios is formulated as a maximum weight clique problem over the G-IDNC graph in. In this letter, we introduce a new lossy G-IDNC graph (LG-IDNC) model to further minimize the decoding delay in lossy feedback scenarios. Whereas the G-IDNC graph represents only doubtless combinable packets, the LG-IDNC graph represents also uncertain packet combinations, arising from lossy feedback events, when the expected decoding delay of XORing them among themselves or with other certain packets is lower than that expected when sending these packets separately. We compare the decoding delay performance of LG-IDNC and G-IDNC graphs through extensive simulations. Numerical results show that our new LG-IDNC graph formulation outperforms the G-IDNC graph formulation in all lossy feedback situations and achieves significant improvement in the decoding delay especially when the feedback erasure probability is higher than the packet erasure probability. © 2012 IEEE.
The heat kernel as the pagerank of a graph
Chung, Fan
2007-01-01
The concept of pagerank was first started as a way for determining the ranking of Web pages by Web search engines. Based on relations in interconnected networks, pagerank has become a major tool for addressing fundamental problems arising in general graphs, especially for large information networks with hundreds of thousands of nodes. A notable notion of pagerank, introduced by Brin and Page and denoted by PageRank, is based on random walks as a geometric sum. In this paper, we consider a notion of pagerank that is based on the (discrete) heat kernel and can be expressed as an exponential sum of random walks. The heat kernel satisfies the heat equation and can be used to analyze many useful properties of random walks in a graph. A local Cheeger inequality is established, which implies that, by focusing on cuts determined by linear orderings of vertices using the heat kernel pageranks, the resulting partition is within a quadratic factor of the optimum. This is true, even if we restrict the volume of the small part separated by the cut to be close to some specified target value. This leads to a graph partitioning algorithm for which the running time is proportional to the size of the targeted volume (instead of the size of the whole graph).
Results on Laplacian spectra of graphs with pockets
Sasmita Barik
2018-04-01
Full Text Available Let F , H v be simple connected graphs on n and m + 1 vertices, respectively. Let v be a specified vertex of H v and u 1 , … , u k ∈ F . Then the graph G = G [ F , u 1 , … , u k , H v ] obtained by taking one copy of F and k copies of H v , and then attaching the i th copy of H v to the vertex u i , i = 1 , … , k , at the vertex v of H v (identify u i with the vertex v of the i th copy is called a graph with k pockets. In 2008, Barik raised the question that ‘how far can the Laplacian spectrum of G be described by using the Laplacian spectra of F and H v ?’ and discussed the case when deg ( v = m in H v . In this article, we study the problem for more general cases and describe the Laplacian spectrum. As an application, we construct new nonisomorphic Laplacian cospectral graphs from the known ones. Keywords: Laplacian matrix, Laplacian spectrum, Join, Pockets
STRUCTURAL ANNOTATION OF EM IMAGES BY GRAPH CUT
Chang, Hang; Auer, Manfred; Parvin, Bahram
2009-05-08
Biological images have the potential to reveal complex signatures that may not be amenable to morphological modeling in terms of shape, location, texture, and color. An effective analytical method is to characterize the composition of a specimen based on user-defined patterns of texture and contrast formation. However, such a simple requirement demands an improved model for stability and robustness. Here, an interactive computational model is introduced for learning patterns of interest by example. The learned patterns bound an active contour model in which the traditional gradient descent optimization is replaced by the more efficient optimization of the graph cut methods. First, the energy function is defined according to the curve evolution. Next, a graph is constructed with weighted edges on the energy function and is optimized with the graph cut algorithm. As a result, the method combines the advantages of the level set method and graph cut algorithm, i.e.,"topological" invariance and computational efficiency. The technique is extended to the multi-phase segmentation problem; the method is validated on synthetic images and then applied to specimens imaged by transmission electron microscopy(TEM).
VIGOR: Interactive Visual Exploration of Graph Query Results.
Pienta, Robert; Hohman, Fred; Endert, Alex; Tamersoy, Acar; Roundy, Kevin; Gates, Chris; Navathe, Shamkant; Chau, Duen Horng
2018-01-01
Finding patterns in graphs has become a vital challenge in many domains from biological systems, network security, to finance (e.g., finding money laundering rings of bankers and business owners). While there is significant interest in graph databases and querying techniques, less research has focused on helping analysts make sense of underlying patterns within a group of subgraph results. Visualizing graph query results is challenging, requiring effective summarization of a large number of subgraphs, each having potentially shared node-values, rich node features, and flexible structure across queries. We present VIGOR, a novel interactive visual analytics system, for exploring and making sense of query results. VIGOR uses multiple coordinated views, leveraging different data representations and organizations to streamline analysts sensemaking process. VIGOR contributes: (1) an exemplar-based interaction technique, where an analyst starts with a specific result and relaxes constraints to find other similar results or starts with only the structure (i.e., without node value constraints), and adds constraints to narrow in on specific results; and (2) a novel feature-aware subgraph result summarization. Through a collaboration with Symantec, we demonstrate how VIGOR helps tackle real-world problems through the discovery of security blindspots in a cybersecurity dataset with over 11,000 incidents. We also evaluate VIGOR with a within-subjects study, demonstrating VIGOR's ease of use over a leading graph database management system, and its ability to help analysts understand their results at higher speed and make fewer errors.
Graph run-length matrices for histopathological image segmentation.
Tosun, Akif Burak; Gunduz-Demir, Cigdem
2011-03-01
The histopathological examination of tissue specimens is essential for cancer diagnosis and grading. However, this examination is subject to a considerable amount of observer variability as it mainly relies on visual interpretation of pathologists. To alleviate this problem, it is very important to develop computational quantitative tools, for which image segmentation constitutes the core step. In this paper, we introduce an effective and robust algorithm for the segmentation of histopathological tissue images. This algorithm incorporates the background knowledge of the tissue organization into segmentation. For this purpose, it quantifies spatial relations of cytological tissue components by constructing a graph and uses this graph to define new texture features for image segmentation. This new texture definition makes use of the idea of gray-level run-length matrices. However, it considers the runs of cytological components on a graph to form a matrix, instead of considering the runs of pixel intensities. Working with colon tissue images, our experiments demonstrate that the texture features extracted from "graph run-length matrices" lead to high segmentation accuracies, also providing a reasonable number of segmented regions. Compared with four other segmentation algorithms, the results show that the proposed algorithm is more effective in histopathological image segmentation.
EIT Imaging Regularization Based on Spectral Graph Wavelets.
Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut
2017-09-01
The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.
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.
Improving Estimation of Betweenness Centrality for Scale-Free Graphs
Bromberger, Seth A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Klymko, Christine F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Henderson, Keith A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Pearce, Roger [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoff [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-11-07
Betweenness centrality is a graph statistic used to nd vertices that are participants in a large number of shortest paths in a graph. This centrality measure is commonly used in path and network interdiction problems and its complete form requires the calculation of all-pairs shortest paths for each vertex. This leads to a time complexity of O(jV jjEj), which is impractical for large graphs. Estimation of betweenness centrality has focused on performing shortest-path calculations on a subset of randomly- selected vertices. This reduces the complexity of the centrality estimation to O(jSjjEj); jSj < jV j, which can be scaled appropriately based on the computing resources available. An estimation strategy that uses random selection of vertices for seed selection is fast and simple to implement, but may not provide optimal estimation of betweenness centrality when the number of samples is constrained. Our experimentation has identi ed a number of alternate seed-selection strategies that provide lower error than random selection in common scale-free graphs. These strategies are discussed and experimental results are presented.
A Faster Algorithm to Recognize Even-Hole-Free Graphs
Chang, Hsien-Chih; Lu, Hsueh-I
2013-01-01
We study the problem of determining whether an $n$-node graph $G$ has an even hole, i.e., an induced simple cycle consisting of an even number of nodes. Conforti, Cornu\\'ejols, Kapoor, and Vu\\v{s}kovi\\'c gave the first polynomial-time algorithm for the problem, which runs in $O(n^{40})$ time. Later, Chudnovsky, Kawarabayashi, and Seymour reduced the running time to $O(n^{31})$. The best previously known algorithm for the problem, due to da Silva and Vu\\v{s}kovi\\'c, runs in $O(n^{19})$ time. I...
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)
Chemical Graph Transformation with Stereo-Information
Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel
2017-01-01
Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...
Reconstructing Topological Graphs and Continua
Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf
2015-01-01
The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...
Decomposing a graph into bistars
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...... is isomorphic to T. The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1)....
Wiener Index, Diameter, and Stretch Factor of a Weighted Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
over all pairs of distinct vertices of the ratio between the graph distance and the Euclidean distance between the two vertices). More specifically, we show that the Wiener index and diameter can be found in O(n^2*(log log n)^4/log n) worst-case time and that the stretch factor can be found in O(n^2......We solve three open problems: the existence of subquadratic time algorithms for computing the Wiener index (sum of APSP distances) and the diameter (maximum distance between any vertex pair) of a planar graph with non-negative edge weights and the stretch factor of a plane geometric graph (maximum...
Edges and vertices in a unique signed circle in a signed graph
Richard Behr
2017-12-01
Full Text Available We examine the conditions under which a signed graph contains an edge or a vertex that is contained in a unique negative circle or a unique positive circle. For an edge in a unique signed circle, the positive and negative case require the same structure on the underlying graph, but the requirements on the signature are different. We characterize the structure of the underlying graph necessary to support such an edge in terms of bridges of a circle. We then use the results from the edge version of the problem to help solve the vertex version.
MSGD: Scalable back-end for indoor magnetic field-based GraphSLAM
Gao, C; Harle, Robert Keith
2017-01-01
Simultaneous Localisation and Mapping (SLAM) systems that recover the trajectory of a robot or mobile device are characterised by a front-end and back-end. The front-end uses sensor observations to identify loop closures; the back-end optimises the estimated trajectory to be consistent with these closures. The GraphSLAM framework formulates the back-end problem as a graph-based optimisation on a pose graph. This paper describes a back-end system optimised for very dense sequence-based lo...