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Sample records for degree-based graph construction

  1. Constructing Dense Graphs with Unique Hamiltonian Cycles

    ERIC Educational Resources Information Center

    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…

  2. A Ring Construction Using Finite Directed Graphs

    ERIC Educational Resources Information Center

    Bardzell, Michael

    2012-01-01

    In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

  3. Interpreting a Graph and Constructing Its Derivative Graph: Stability and Change in Students' Conceptions

    ERIC Educational Resources Information Center

    Ubuz, Behiye

    2007-01-01

    This present study investigated engineering students' conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the…

  4. Scale Construction for Graphing: An Investigation of Students' Resources

    ERIC Educational Resources Information Center

    Delgado, Cesar; Lucero, Margaret M.

    2015-01-01

    Graphing is a fundamental part of the scientific process. Scales are key but little-studied components of graphs. Adopting a resources-based framework of cognitive structure, we identify the potential intuitive resources that six undergraduates of diverse majors and years at a public US research university activated when constructing scales, and…

  5. Development of a Framework for Graph Choice and Construction

    ERIC Educational Resources Information Center

    Angra, Aakanksha; Gardner, Stephanie M.

    2016-01-01

    Research on graph interpretation and basic construction is extensive, and student difficulties, primarily in K-12 type settings, have been well documented [e.g., graph choice, labels for axes, variables, and scaling axes]. It is important to provide students with repeated opportunities to increase competency and practice critical reflection in…

  6. Measuring Graph Comprehension, Critique, and Construction in Science

    NASA Astrophysics Data System (ADS)

    Lai, Kevin; Cabrera, Julio; Vitale, Jonathan M.; Madhok, Jacquie; Tinker, Robert; Linn, Marcia C.

    2016-08-01

    Interpreting and creating graphs plays a critical role in scientific practice. The K-12 Next Generation Science Standards call for students to use graphs for scientific modeling, reasoning, and communication. To measure progress on this dimension, we need valid and reliable measures of graph understanding in science. In this research, we designed items to measure graph comprehension, critique, and construction and developed scoring rubrics based on the knowledge integration (KI) framework. We administered the items to over 460 middle school students. We found that the items formed a coherent scale and had good reliability using both item response theory and classical test theory. The KI scoring rubric showed that most students had difficulty linking graphs features to science concepts, especially when asked to critique or construct graphs. In addition, students with limited access to computers as well as those who speak a language other than English at home have less integrated understanding than others. These findings point to the need to increase the integration of graphing into science instruction. The results suggest directions for further research leading to comprehensive assessments of graph understanding.

  7. Fast construction of voxel-level functional connectivity graphs

    PubMed Central

    2014-01-01

    Background Graph-based analysis of fMRI data has recently emerged as a promising approach to study brain networks. Based on the assessment of synchronous fMRI activity at separate brain sites, functional connectivity graphs are constructed and analyzed using graph-theoretical concepts. Most previous studies investigated region-level graphs, which are computationally inexpensive, but bring along the problem of choosing sensible regions and involve blurring of more detailed information. In contrast, voxel-level graphs provide the finest granularity attainable from the data, enabling analyses at superior spatial resolution. They are, however, associated with considerable computational demands, which can render high-resolution analyses infeasible. In response, many existing studies investigating functional connectivity at the voxel-level reduced the computational burden by sacrificing spatial resolution. Methods Here, a novel, time-efficient method for graph construction is presented that retains the original spatial resolution. Performance gains are instead achieved through data reduction in the temporal domain based on dichotomization of voxel time series combined with tetrachoric correlation estimation and efficient implementation. Results By comparison with graph construction based on Pearson’s r, the technique used by the majority of previous studies, we find that the novel approach produces highly similar results an order of magnitude faster. Conclusions Its demonstrated performance makes the proposed approach a sensible and efficient alternative to customary practice. An open source software package containing the created programs is freely available for download. PMID:24947161

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

    PubMed

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

    2010-03-01

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

  9. Undergraduate student construction and interpretation of graphs in physics lab activities

    NASA Astrophysics Data System (ADS)

    Nixon, Ryan S.; Godfrey, T. J.; Mayhew, Nicholas T.; Wiegert, Craig C.

    2016-06-01

    Lab activities are an important element of an undergraduate physics course. In these lab activities, students construct and interpret graphs in order to connect the procedures of the lab with an understanding of the related physics concepts. This study investigated undergraduate students' construction and interpretation of graphs with best-fit lines in the context of two physics lab activities. Students' graphs were evaluated for overall graph quality and for the quality of the best-fit line. The strategies students used and their understanding of the meaning of the graph were accessed through interviews. The results suggest that undergraduate introductory physics students can successfully construct graphs with best-fit lines while not connecting the meaning of the graph to the underlying physics concepts. Furthermore, results indicated that the most challenging aspect of constructing a graph is setting up the scale, and that graphing is situated in specific contexts.

  10. Constructing and sampling graphs with a given joint degree distribution.

    SciTech Connect

    Pinar, Ali; Stanton, Isabelle

    2010-09-01

    One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, i.e. the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest understanding the relationship between network structure and the joint degree distribution of graphs is an interesting avenue of further research. An important tool for such studies are algorithms that can generate random instances of graphs with the same joint degree distribution. This is the main topic of this paper and we study the problem from both a theoretical and practical perspective. We provide an algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov Chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via end point switches. We empirically evaluate the mixing time of this Markov Chain by using experiments based on the autocorrelation of each edge. These experiments show that our Markov Chain mixes quickly on real graphs, allowing for utilization of our techniques in practice.

  11. The Interplay of Graph and Text in the Acquisition of Historical Constructs

    ERIC Educational Resources Information Center

    Shand, Kristen

    2009-01-01

    Graphs are often conjoined with text passages in history textbooks to help students comprehend complex constructs. Four linkages connect text and graphs: appropriate elements, fitting patterns, suitable labels and causal markers. Graphs in current textbooks contain few such linkages and seldom mirror the construct under study. An experiment…

  12. Self-description for construction and computation on graph-rewriting automata.

    PubMed

    Tomita, Kohji; Murata, Satoshi; Kurokawa, Haruhisa

    2007-01-01

    This article shows how self-description can be realized for construction and computation in a single framework of a variant of graph-rewriting systems called graph-rewriting automata. Graph-rewriting automata define symbol dynamics on graphs, in contrast to cellular automata on lattice space. Structural change is possible along with state transition. Self-replication based on a self-description is shown as an example of self-description for construction. This process is performed using a construction arm, which is realized as a subgraph, that executes a program described in the graph structure. In addition, a metanode structure is introduced to embed rule sets in the graph structure as self-description for computation. These are regarded as universal graph-rewriting automata that can serve as a model of systems that maintain themselves through replication and modification.

  13. Constructing Graphs over with Small Prescribed Mean-Curvature

    NASA Astrophysics Data System (ADS)

    Carley, Holly; Kiessling, Michael K.-H.

    2015-12-01

    In this paper nonlinear Hodge theory and Banach algebra estimates are employed to construct a convergent series expansion which solves the prescribed mean curvature equation for n-dimensional hypersurfaces in (+ sign) and (- sign) which are graphs of a smooth function , and whose mean curvature function H is α-Hölder continuous and integrable, with small norm. The radius of convergence is estimated explicitly from below. Our approach is inspired by, and applied to, the Maxwell-Born-Infeld theory of electromagnetism in , for which our method yields the first systematic way of explicitly computing the electrostatic potential for regular charge densities and small Born parameter, with explicit error estimates at any order of truncation of the series. In particular, our results level the ground for a controlled computation of Born-Infeld effects on the Hydrogen spectrum.

  14. Measuring Graph Comprehension, Critique, and Construction in Science

    ERIC Educational Resources Information Center

    Lai, Kevin; Cabrera, Julio; Vitale, Jonathan M.; Madhok, Jacquie; Tinker, Robert; Linn, Marcia C.

    2016-01-01

    Interpreting and creating graphs plays a critical role in scientific practice. The K-12 Next Generation Science Standards call for students to use graphs for scientific modeling, reasoning, and communication. To measure progress on this dimension, we need valid and reliable measures of graph understanding in science. In this research, we designed…

  15. Undergraduate Student Construction and Interpretation of Graphs in Physics Lab Activities

    ERIC Educational Resources Information Center

    Nixon, Ryan S.; Godfrey, T. J.; Mayhew, Nicholas T.; Wiegert, Craig C.

    2016-01-01

    Lab activities are an important element of an undergraduate physics course. In these lab activities, students construct and interpret graphs in order to connect the procedures of the lab with an understanding of the related physics concepts. This study investigated undergraduate students' construction and interpretation of graphs with best-fit…

  16. Constructing compact and effective graphs for recommender systems via node and edge aggregations

    SciTech Connect

    Lee, Sangkeun; Kahng, Minsuk; Lee, Sang-goo

    2014-12-10

    Exploiting graphs for recommender systems has great potential to flexibly incorporate heterogeneous information for producing better recommendation results. As our baseline approach, we first introduce a naive graph-based recommendation method, which operates with a heterogeneous log-metadata graph constructed from user log and content metadata databases. Although the na ve graph-based recommendation method is simple, it allows us to take advantages of heterogeneous information and shows promising flexibility and recommendation accuracy. However, it often leads to extensive processing time due to the sheer size of the graphs constructed from entire user log and content metadata databases. In this paper, we propose node and edge aggregation approaches to constructing compact and e ective graphs called Factor-Item bipartite graphs by aggregating nodes and edges of a log-metadata graph. Furthermore, experimental results using real world datasets indicate that our approach can significantly reduce the size of graphs exploited for recommender systems without sacrificing the recommendation quality.

  17. Constructing compact and effective graphs for recommender systems via node and edge aggregations

    DOE PAGES

    Lee, Sangkeun; Kahng, Minsuk; Lee, Sang-goo

    2014-12-10

    Exploiting graphs for recommender systems has great potential to flexibly incorporate heterogeneous information for producing better recommendation results. As our baseline approach, we first introduce a naive graph-based recommendation method, which operates with a heterogeneous log-metadata graph constructed from user log and content metadata databases. Although the na ve graph-based recommendation method is simple, it allows us to take advantages of heterogeneous information and shows promising flexibility and recommendation accuracy. However, it often leads to extensive processing time due to the sheer size of the graphs constructed from entire user log and content metadata databases. In this paper, we proposemore » node and edge aggregation approaches to constructing compact and e ective graphs called Factor-Item bipartite graphs by aggregating nodes and edges of a log-metadata graph. Furthermore, experimental results using real world datasets indicate that our approach can significantly reduce the size of graphs exploited for recommender systems without sacrificing the recommendation quality.« less

  18. Taking Advantage of Automated Assessment of Student-Constructed Graphs in Science

    ERIC Educational Resources Information Center

    Vitale, Jonathan M.; Lai, Kevin; Linn, Marcia C.

    2015-01-01

    We present a new system for automated scoring of graph construction items that address complex science concepts, feature qualitative prompts, and support a range of possible solutions. This system utilizes analysis of spatial features (e.g., slope of a line) to evaluate potential student ideas represented within graphs. Student ideas are then…

  19. How Do Secondary School Science Students Interpret and Construct Scientific Graphs?

    ERIC Educational Resources Information Center

    Tairab, Hassan H.; Khalaf Al-Naqbi, Ali K.

    2004-01-01

    The study explored how Grade 10 science students learned from scientific graphs. This paper explores (a) students' abilities to interpret graphical information; (b) students' abilities to represent information graphically; (c) factors that could impede the process of interpretation and construction of graphs among secondary school science…

  20. LEAF: A Microcomputer Program for Constructing the Tukey Stem and Leaf Graph.

    ERIC Educational Resources Information Center

    Pascale, Pietro J.; Smith, Joseph

    1986-01-01

    This paper presents a BASIC microcomputer program that constructs the Tukey (1977) stem and leaf graph. Options within the LEAF program include a modified stem and leaf where the stem is split and a parallel stem and leaf graph where two separate sets of data are displayed from a common stem. (Author)

  1. Fast construction of k-nearest neighbor graphs for point clouds.

    PubMed

    Connor, Michael; Kumar, Piyush

    2010-01-01

    We present a parallel algorithm for k-nearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: 1) faster construction of k-nearest neighbor graphs in practice on multicore machines, 2) less space usage, 3) better cache efficiency, 4) ability to handle large data sets, and 5) ease of parallelization and implementation. If the point set has a bounded expansion constant, our algorithm requires one-comparison-based parallel sort of points, according to Morton order plus near-linear additional steps to output the k-nearest neighbor graph.

  2. Constructing a Nonnegative Low-Rank and Sparse Graph With Data-Adaptive Features.

    PubMed

    Zhuang, Liansheng; Gao, Shenghua; Tang, Jinhui; Wang, Jingjing; Lin, Zhouchen; Ma, Yi; Yu, Nenghai

    2015-11-01

    This paper aims at constructing a good graph to discover the intrinsic data structures under a semisupervised learning setting. First, we propose to build a nonnegative low-rank and sparse (referred to as NNLRS) graph for the given data representation. In particular, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse reconstruction coefficients matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph captures both the global mixture of subspaces structure (by the low-rankness) and the locally linear structure (by the sparseness) of the data, hence it is both generative and discriminative. Second, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph simultaneously within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive NNLRS experiments on three publicly available data sets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semisupervised classification and discriminative analysis, which verifies the effectiveness of our proposed method.

  3. Constructing a Graph Database for Semantic Literature-Based Discovery.

    PubMed

    Hristovski, Dimitar; Kastrin, Andrej; Dinevski, Dejan; Rindflesch, Thomas C

    2015-01-01

    Literature-based discovery (LBD) generates discoveries, or hypotheses, by combining what is already known in the literature. Potential discoveries have the form of relations between biomedical concepts; for example, a drug may be determined to treat a disease other than the one for which it was intended. LBD views the knowledge in a domain as a network; a set of concepts along with the relations between them. As a starting point, we used SemMedDB, a database of semantic relations between biomedical concepts extracted with SemRep from Medline. SemMedDB is distributed as a MySQL relational database, which has some problems when dealing with network data. We transformed and uploaded SemMedDB into the Neo4j graph database, and implemented the basic LBD discovery algorithms with the Cypher query language. We conclude that storing the data needed for semantic LBD is more natural in a graph database. Also, implementing LBD discovery algorithms is conceptually simpler with a graph query language when compared with standard SQL. PMID:26262393

  4. An Optimal Parallel Algorithm for Constructing a Spanning Forest on Trapezoid Graphs

    NASA Astrophysics Data System (ADS)

    Honma, Hirotoshi; Masuyama, Shigeru

    Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. An optimal parallel algorithm for finding a spanning tree on the trapezoid graph is given by Bera et al., it takes O(logn) time with O(n/logn) processors on the EREW (Exclusive-Read Exclusive-Write) PRAM. Bera et al.'s algorithm is very simple and elegant. Moreover, it can correctly construct a spanning tree when the graph is connected. However, their algorithm can not accept a disconnected graph as an input. Applying their algorithm to a disconnected graph, Concurrent-Write occurs once for each connected component, thus this can not be achieved on EREW PRAM. In this paper we present an O(logn) time parallel algorithm with O(n/logn) processors for constructing a spanning forest on trapezoid graph G on EREW PRAM even if G is a disconnected graph.

  5. Par@Graph - a parallel toolbox for the construction and analysis of large complex climate networks

    NASA Astrophysics Data System (ADS)

    Ihshaish, H.; Tantet, A.; Dijkzeul, J. C. M.; Dijkstra, H. A.

    2015-10-01

    In this paper, we present Par@Graph, a software toolbox to reconstruct and analyze complex climate networks having a large number of nodes (up to at least 106) and edges (up to at least 1012). The key innovation is an efficient set of parallel software tools designed to leverage the inherited hybrid parallelism in distributed-memory clusters of multi-core machines. The performance of the toolbox is illustrated through networks derived from sea surface height (SSH) data of a global high-resolution ocean model. Less than 8 min are needed on 90 Intel Xeon E5-4650 processors to reconstruct a climate network including the preprocessing and the correlation of 3 × 105 SSH time series, resulting in a weighted graph with the same number of vertices and about 3.2 × 108 edges. In less than 14 min on 30 processors, the resulted graph's degree centrality, strength, connected components, eigenvector centrality, entropy and clustering coefficient metrics were obtained. These results indicate that a complete cycle to construct and analyze a large-scale climate network is available under 22 min Par@Graph therefore facilitates the application of climate network analysis on high-resolution observations and model results, by enabling fast network reconstruct from the calculation of statistical similarities between climate time series. It also enables network analysis at unprecedented scales on a variety of different sizes of input data sets.

  6. Estimates of general Mayer graphs. I: Construction of upper bounds for a given graph by means of sets of subgraphs

    NASA Astrophysics Data System (ADS)

    Lavaud, Michel

    1982-03-01

    A large number of physical quantities (thermodynamic and correlation functions, scattering amplitudes, intermolecular potentials, etc. ...) can be expressed as sums of an infinite number of multiple integrals of the following type: Γ ( {x_1 ,. . . , x_n } ) = int {prod {f_L ( {x_{i,} x_j } )dx_{n + 1} . . . dx_{n + k} } } These are called Mayer graphs in statistical mechanics, Feynman graphs in quantum field theory, and multicenter integrals in quantum chemistry. We call them n-graphs here. In a preceding note [ Physics Letters 62A:295 (1977)], we have proposed a new estimation method which provides upper bounds for arbitrary n-graphs. This article is devoted to developing in detail the foundations of this method. As a first application, we prove that all virial coefficients of polar systems are finite. More generally, we show on some examples that our estimation method can give finite upper bounds for n-graphs occurring in the perturbative developments of thermodynamic functions of neutral, polar, and ionized gases and of Green's functions of Euclidean quantum field theories (thus improving Weinberg's theorem), as also in variational approximations of intermolecular potentials. Our estimation method is based on the Hölder inequality which is an improvement over the mean value estimation method, employed by Riddell, Uhlenbeck, and Groeneveld, except for the hard-sphere gas, where both methods coincide. The method is applied so far only to individual graphs and not to thermodynamic functions.

  7. Assessing students' abilities to construct and interpret line graphs: Disparities between multiple-choice and free-response instruments

    NASA Astrophysics Data System (ADS)

    Berg, Craig A.; Smith, Philip

    The author is concerned about the methodology and instrumentation used to assess both graphing abilities and the impact of microcomputer-based laboratories (MBL) on students' graphing abilities for four reasons: (1) the ability to construct and interpret graphs is critical for developing key ideas in science; (2) science educators need to have valid information for making teaching decisions; (3) educators and researchers are heralding the arrival of MBL as a tool for developing graphing abilities; and (4) some of the research which supports using MBL appears to have significant validity problems. In this article, the author will describe the research which challenges the validity of using multiple-choice instruments to assess graphing abilities. The evidence from this research will identify numerous disparities between the results of multiple-choice and free-response instruments. In the first study, 72 subjects in the seventh, ninth, and eleventh grades were administered individual clinical interviews to assess their ability to construct and interpret graphs. A wide variety of graphs and situations were assessed. In three instances during the interview, students drew a graph that would best represent a situation and then explained their drawings. The results of these clinical graphing interviews were very different from similar questions assessed through multiple-choice formats in other research studies. In addition, insights into students' thinking about graphing reveal that some multiple-choice graphing questions from prior research studies and standardized tests do not discriminate between right answers/right reasons, right answers/wrong reasons, and answers scored wrong but correct for valid reasons. These results indicate that in some instances multiple-choice questions are not a valid measure of graphing abilities. In a second study, the researcher continued to pursue the questions raised about the validity of multiple-choice tests to assess graphing

  8. Campaign graphs

    SciTech Connect

    Simmons, G.J.

    1988-01-01

    We define a class of geometrical constructions in the plane in which each (unextended) line lies on (precisely) k points, and every point is an endpoint of (precisely) one line. We will refer to any construction satisfying these conditions as a campaign graph, or as a k-campaign graph if the value of k isn't clear from the context. A k-campaign graph, G, is said to be critical if no subgraph of G is also a k-campaign graph. 11 figs.

  9. Weights and topology: a study of the effects of graph construction on 3D image segmentation.

    PubMed

    Grady, Leo; Jolly, Marie-Pierre

    2008-01-01

    Graph-based algorithms have become increasingly popular for medical image segmentation. The fundamental process for each of these algorithms is to use the image content to generate a set of weights for the graph and then set conditions for an optimal partition of the graph with respect to these weights. To date, the heuristics used for generating the weighted graphs from image intensities have largely been ignored, while the primary focus of attention has been on the details of providing the partitioning conditions. In this paper we empirically study the effects of graph connectivity and weighting function on the quality of the segmentation results. To control for algorithm-specific effects, we employ both the Graph Cuts and Random Walker algorithms in our experiments.

  10. Universal spectral statistics in Wigner-Dyson, chiral, and Andreev star graphs. I. Construction and numerical results

    NASA Astrophysics Data System (ADS)

    Gnutzmann, Sven; Seif, Burkhard

    2004-05-01

    In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star graphs in the ten symmetry classes. A generalization of the Bohigas-Giannoni-Schmit conjecture is given that covers all these symmetry classes. The conjecture is supported by numerical results that demonstrate the fidelity of the spectral statistics of star graphs to the corresponding Gaussian random-matrix theories.

  11. Graphing for Any Grade.

    ERIC Educational Resources Information Center

    Nibbelink, William

    1982-01-01

    An instructional sequence for teaching graphing that has been extensively field tested in kindergarten through grade six is detailed. The material begins with point graphs, employs a movable y-axis to begin with minimal clutter, and has graphs constructed before reading graphs is required. (MP)

  12. Exploiting Semantic Annotations and Q-Learning for Constructing an Efficient Hierarchy/Graph Texts Organization

    PubMed Central

    El-Said, Asmaa M.; Eldesoky, Ali I.; Arafat, Hesham A.

    2015-01-01

    Tremendous growth in the number of textual documents has produced daily requirements for effective development to explore, analyze, and discover knowledge from these textual documents. Conventional text mining and managing systems mainly use the presence or absence of key words to discover and analyze useful information from textual documents. However, simple word counts and frequency distributions of term appearances do not capture the meaning behind the words, which results in limiting the ability to mine the texts. This paper proposes an efficient methodology for constructing hierarchy/graph-based texts organization and representation scheme based on semantic annotation and Q-learning. This methodology is based on semantic notions to represent the text in documents, to infer unknown dependencies and relationships among concepts in a text, to measure the relatedness between text documents, and to apply mining processes using the representation and the relatedness measure. The representation scheme reflects the existing relationships among concepts and facilitates accurate relatedness measurements that result in a better mining performance. An extensive experimental evaluation is conducted on real datasets from various domains, indicating the importance of the proposed approach. PMID:25685832

  13. Efficient and Accurate Construction of Genetic Linkage Maps from the Minimum Spanning Tree of a Graph

    PubMed Central

    Wu, Yonghui; Bhat, Prasanna R.; Close, Timothy J.; Lonardi, Stefano

    2008-01-01

    Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap. PMID:18846212

  14. Exploiting semantic annotations and Q-learning for constructing an efficient hierarchy/graph texts organization.

    PubMed

    El-Said, Asmaa M; Eldesoky, Ali I; Arafat, Hesham A

    2015-01-01

    Tremendous growth in the number of textual documents has produced daily requirements for effective development to explore, analyze, and discover knowledge from these textual documents. Conventional text mining and managing systems mainly use the presence or absence of key words to discover and analyze useful information from textual documents. However, simple word counts and frequency distributions of term appearances do not capture the meaning behind the words, which results in limiting the ability to mine the texts. This paper proposes an efficient methodology for constructing hierarchy/graph-based texts organization and representation scheme based on semantic annotation and Q-learning. This methodology is based on semantic notions to represent the text in documents, to infer unknown dependencies and relationships among concepts in a text, to measure the relatedness between text documents, and to apply mining processes using the representation and the relatedness measure. The representation scheme reflects the existing relationships among concepts and facilitates accurate relatedness measurements that result in a better mining performance. An extensive experimental evaluation is conducted on real datasets from various domains, indicating the importance of the proposed approach.

  15. Graph-based retrospective 4D image construction from free-breathing MRI slice acquisitions

    NASA Astrophysics Data System (ADS)

    Tong, Yubing; Udupa, Jayaram K.; Ciesielski, Krzysztof C.; McDonough, Joseph M.; Mong, Andrew; Campbell, Robert M.

    2014-03-01

    4D or dynamic imaging of the thorax has many potential applications [1, 2]. CT and MRI offer sufficient speed to acquire motion information via 4D imaging. However they have different constraints and requirements. For both modalities both prospective and retrospective respiratory gating and tracking techniques have been developed [3, 4]. For pediatric imaging, x-ray radiation becomes a primary concern and MRI remains as the de facto choice. The pediatric subjects we deal with often suffer from extreme malformations of their chest wall, diaphragm, and/or spine, as such patient cooperation needed by some of the gating and tracking techniques are difficult to realize without causing patient discomfort. Moreover, we are interested in the mechanical function of their thorax in its natural form in tidal breathing. Therefore free-breathing MRI acquisition is the ideal modality of imaging for these patients. In our set up, for each coronal (or sagittal) slice position, slice images are acquired at a rate of about 200-300 ms/slice over several natural breathing cycles. This produces typically several thousands of slices which contain both the anatomic and dynamic information. However, it is not trivial to form a consistent and well defined 4D volume from these data. In this paper, we present a novel graph-based combinatorial optimization solution for constructing the best possible 4D scene from such data entirely in the digital domain. Our proposed method is purely image-based and does not need breath holding or any external surrogates or instruments to record respiratory motion or tidal volume. Both adult and children patients' data are used to illustrate the performance of the proposed method. Experimental results show that the reconstructed 4D scenes are smooth and consistent spatially and temporally, agreeing with known shape and motion of the lungs.

  16. Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions

    NASA Astrophysics Data System (ADS)

    Yu, Zu-Guo; Zhang, Huan; Huang, Da-Wen; Lin, Yong; Anh, Vo

    2016-03-01

    Many studies have shown that additional information can be gained on time series by investigating their associated complex networks. In this work, we investigate the multifractal property and Laplace spectrum of the horizontal visibility graphs (HVGs) constructed from fractional Brownian motions. We aim to identify via simulation and curve fitting the form of these properties in terms of the Hurst index H. First, we use the sandbox algorithm to study the multifractality of these HVGs. It is found that multifractality exists in these HVGs. We find that the average fractal dimension < D(0)> of HVGs approximately satisfies the prominent linear formula < D(0)> =2-H ; while the average information dimension < D(1)> and average correlation dimension < D(2)> are all approximately bi-linear functions of H when H≥slant 0.15 . Then, we calculate the spectrum and energy for the general Laplacian operator and normalized Laplacian operator of these HVGs. We find that, for the general Laplacian operator, the average logarithm of second-smallest eigenvalue < \\ln ≤ft({{u}2}\\right)> , the average logarithm of third-smallest eigenvalue < \\ln ≤ft({{u}3}\\right)> , and the average logarithm of maximum eigenvalue < \\ln ≤ft({{u}n}\\right)> of these HVGs are approximately linear functions of H; while the average Laplacian energy < {{E}\\text{nL}}> is approximately a quadratic polynomial function of H. For the normalized Laplacian operator, < \\ln ≤ft({{u}2}\\right)> and < \\ln ≤ft({{u}3}\\right)> of these HVGs approximately satisfy linear functions of H; while < \\ln ≤ft({{u}n}\\right)> and < {{E}\\text{nL}}> are approximately a 4th and cubic polynomial function of H respectively.

  17. Embodied Semiotic Activities and Their Role in the Construction of Mathematical Meaning of Motion Graphs

    ERIC Educational Resources Information Center

    Botzer, Galit; Yerushalmy, Michal

    2008-01-01

    This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of…

  18. Use of a General Graph-Drawing Algorithm in the Construction of Association Maps.

    ERIC Educational Resources Information Center

    Craven, Timothy C.

    1992-01-01

    Describes research that investigated a method of automatically generating concept association maps that could be useful to abstractors. The use of word stems as concept surrogates, cooccurrence to define concept links, and a general-purpose graph-drawing algorithm is described; and results of evaluation of two link selection methods are reported.…

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

    PubMed

    Li, Zhigang; Shi, Zhongping; Li, Xin

    2014-05-01

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

  20. Methods of visualizing graphs

    SciTech Connect

    Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.

    2008-12-23

    Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.

  1. Clique graphs and overlapping communities

    NASA Astrophysics Data System (ADS)

    Evans, T. S.

    2010-12-01

    It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.

  2. Graph Library

    2007-06-12

    GraphLib is a support library used by other tools to create, manipulate, store, and export graphs. It provides a simple interface to specifS’ arbitrary directed and undirected graphs by adding nodes and edges. Each node and edge can be associated with a set of attributes describing size, color, and shape. Once created, graphs can be manipulated using a set of graph analysis algorithms, including merge, prune, and path coloring operations. GraphLib also has the abilitymore » to export graphs into various open formats such as DOT and GML.« less

  3. Quantum walks on quotient graphs

    SciTech Connect

    Krovi, Hari; Brun, Todd A.

    2007-06-15

    A discrete-time quantum walk on a graph {gamma} 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.

  4. Commuting projections on graphs

    SciTech Connect

    Vassilevski, Panayot S.; Zikatanov, Ludmil T.

    2013-02-19

    For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ2-projection QH onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π H from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π H and QH commute with the discrete divergence operator, i.e., we have div π H = QH div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.

  5. Graphs for Early Elementary Social Studies.

    ERIC Educational Resources Information Center

    Freeland, Kent; Brewer, Samrie

    1989-01-01

    Describes a lesson plan that instructs third graders to use graphs. Explains learning objectives, motivating students, conducting a class activity that includes graph construction, and concluding and evaluating the lesson. Lists materials needed. (GG)

  6. Graphing Predictions

    ERIC Educational Resources Information Center

    Connery, Keely Flynn

    2007-01-01

    Graphing predictions is especially important in classes where relationships between variables need to be explored and derived. In this article, the author describes how his students sketch the graphs of their predictions before they begin their investigations on two laboratory activities: Distance Versus Time Cart Race Lab and Resistance; and…

  7. Graph Theory

    SciTech Connect

    Sanfilippo, Antonio P.

    2005-12-27

    Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms.

  8. Constructing Phylogenies.

    ERIC Educational Resources Information Center

    Bilardello, Nicholas; Valdes, Linda

    1998-01-01

    Introduces a method for constructing phylogenies using molecular traits and elementary graph theory. Discusses analyzing molecular data and using weighted graphs, minimum-weight spanning trees, and rooted cube phylogenies to display the data. (DDR)

  9. Graphing Reality

    NASA Astrophysics Data System (ADS)

    Beeken, Paul

    2014-11-01

    Graphing is an essential skill that forms the foundation of any physical science.1 Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations.2 Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary school instruction, the job of graphing skills falls heavily on physics teachers. By virtue of the nature of the topics we cover, it is our mission to develop this skill to the fine art that it is.

  10. Graphing Reality

    ERIC Educational Resources Information Center

    Beeken, Paul

    2014-01-01

    Graphing is an essential skill that forms the foundation of any physical science. Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations. Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary…

  11. Aspects of Performance on Line Graph Description Tasks: Influenced by Graph Familiarity and Different Task Features

    ERIC Educational Resources Information Center

    Xi, Xiaoming

    2010-01-01

    Motivated by cognitive theories of graph comprehension, this study systematically manipulated characteristics of a line graph description task in a speaking test in ways to mitigate the influence of graph familiarity, a potential source of construct-irrelevant variance. It extends Xi (2005), which found that the differences in holistic scores on…

  12. The construction of graph models for calculations of the properties of substitution isomers of basis structures on the basis of additivity of energy contributions

    NASA Astrophysics Data System (ADS)

    Nilov, D. Yu.; Smolyakov, V. M.

    2012-05-01

    A method for the construction of additive models for calculations of the properties of substitution isomers of basis structures is described for the example of a series of X-substituted methylsilanes CH3 - k X k -SiH3 - l X l (where X = CH3, F, Cl, …, k, l = 0, 1, 2, 3). The method is based on similarity of subgraphs in graphs of several molecules and the arrangement of polygonal numbers (triangular, tetrahedral) of the Pascal triangle. Parameters taking into account multiple nonvalence interactions (-C-Si<, >C-Si<, …) through two atoms along the molecular chain of an X-substituted methylsilane (X = CH3) were for the first time explicitly included in the calculation scheme. Taking these interactions into account allows us to completely differentiate all the structural isomers of certain molecules and obtain numerical parameter values for predicting properties P under consideration in various approximations. Numerical calculations of Δf H {g,298/K o} were performed for 16 alkylsilanes (as X-substituted methylsilanes), including 7 compounds not studied experimentally.

  13. Computing Information Value from RDF Graph Properties

    SciTech Connect

    al-Saffar, Sinan; Heileman, Gregory

    2010-11-08

    Information value has been implicitly utilized and mostly non-subjectively computed in information retrieval (IR) systems. We explicitly define and compute the value of an information piece as a function of two parameters, the first is the potential semantic impact the target information can subjectively have on its recipient's world-knowledge, and the second parameter is trust in the information source. We model these two parameters as properties of RDF graphs. Two graphs are constructed, a target graph representing the semantics of the target body of information and a context graph representing the context of the consumer of that information. We compute information value subjectively as a function of both potential change to the context graph (impact) and the overlap between the two graphs (trust). Graph change is computed as a graph edit distance measuring the dissimilarity between the context graph before and after the learning of the target graph. A particular application of this subjective information valuation is in the construction of a personalized ranking component in Web search engines. Based on our method, we construct a Web re-ranking system that personalizes the information experience for the information-consumer.

  14. On Ramsey (P3, P6)-minimal graphs

    NASA Astrophysics Data System (ADS)

    Rahmadani, Desi; Baskoro, Edy Tri; Assiyatun, Hilda

    2016-02-01

    Finding all Ramsey (G, H)-minimal graphs for a certain pair of graphs G and H is an interesting and difficult problem. Even though, it is just for small graphs G and H. In this paper, we determine some Ramsey (P3, P6)-minimal graphs of small order. We also characterize all such Ramsey minimal graphs of order 6 by using their degree sequences. We prove that Ramsey (P3, P6)-minimal graphs have diameter at least two. We construct an infinite class of trees [6] which provides Ramsey (P3, P6)-minimal graphs.

  15. Understanding Graphs & Charts.

    ERIC Educational Resources Information Center

    Cleary, John J.; Gravely, Mary Liles

    Developed by educators from the Emily Griffith Opportunity School, this teacher's guide was developed for a 4-hour workshop to teach employees how to read the charts and graphs they need in the workplace. The unit covers four types of graphs: pictographs, bar graphs, line graphs, and circle graphs. The guide is divided into four sections: reading…

  16. Separability of Generalized Graph Product States

    NASA Astrophysics Data System (ADS)

    Zhao, Hui; Fan, Jiao

    2013-09-01

    We construct two classes of generalized graph product states and study the entanglement of these states. It is first presented that the density matrices of complex edge-weighted digraphs associated with the generalized graph product in mn systems are positive partial transformation and separable states. Then we prove that the density matrices of the vertex-weighted digraphs associated with another generalized graph product are entangled states.

  17. Generalized graph states based on Hadamard matrices

    SciTech Connect

    Cui, Shawn X.; Yu, Nengkun; Zeng, Bei

    2015-07-15

    Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.

  18. Degree-based attacks and defense strategies in complex networks

    NASA Astrophysics Data System (ADS)

    Yehezkel, Aviv; Cohen, Reuven

    2012-12-01

    We study the stability of random scale-free networks to degree-dependent attacks. We present analytical and numerical results to compute the critical fraction pc of nodes that need to be removed for destroying the network under this attack for different attack parameters. We study the effect of different defense strategies, based on the addition of a constant number of links on network robustness. We test defense strategies based on adding links to either low degree, middegree or high degree nodes. We find using analytical results and simulations that the middegree nodes defense strategy leads to the largest improvement to the network robustness against degree-based attacks. We also test these defense strategies on an internet autonomous systems map and obtain similar results.

  19. Ezekiel graphs

    SciTech Connect

    Simmons, G.J.

    1991-01-01

    In spite of the old adage that No finite sequence of symbols is random,'' there are many instances in which it is desirable to quantify how random'' a finite sequence is. Pseudorandom number generators and cryptographic key generators typically expand a short, randomly chosen, seed sequence into a much longer sequence which should appear random to anyone ignorant of the seed. Unique initiating signals chosen to minimize the likelihood of an accidental initiation of an important action should be random'' to lessen the chance of their natural occurrence, etc. Consequently, numerous tests for the randomness of finite sequences have been proposed. John Milnor argued that if a binary sequence is random then the fraction of 1's, r{sub 1}, should be very nearly 1/2 in it and in all of what he called its derivatives. Since every sequence has a unique derivative this defines a natural family of digraphs, G{sub n}, on 2{sup n} vertices in which vertices are labeled with n-bit binary sequences and an edge is directed from the vertex labeled with the sequence A to the vertex labeled with the sequence B if B is the derivative of A. Each component of G{sub n} is eventually cyclic. This paper is concerned with a special case in which the sequences in a cycle are all cyclic shifts of a single sequence -- hence the name of Ezekiel graphs. Surprising, there are Ezekiel graphs for which r{sub 1} is as close to 1/2 as is numerically possible, i.e., that satisfy Milnor's test for randomness as closely as it can be satisfied, even though the sequence of sequences are about as far from random as is conceivable. In this paper the existence and properties of Ezekiel sequences are investigated from an algebraic standpoint.

  20. Components in time-varying graphs

    NASA Astrophysics Data System (ADS)

    Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito

    2012-06-01

    Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.

  1. Components in time-varying graphs.

    PubMed

    Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito

    2012-06-01

    Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis. PMID:22757508

  2. Graph modeling systems and methods

    DOEpatents

    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.

  3. Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

    ERIC Educational Resources Information Center

    Hillman, Thomas

    2014-01-01

    This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

  4. Fifth through Eighth Grade Students' Difficulties in Constructing Bar Graphs: Data Organization, Data Aggregation, and Integration of a Second Variable

    ERIC Educational Resources Information Center

    Garcia-Mila, Merce; Marti, Eduard; Gilabert, Sandra; Castells, Marina

    2014-01-01

    Studies that consider the displays that students create to organize data are not common in the literature. This article compares fifth through eighth graders' difficulties with the creation of bar graphs using either raw data (Study 1, n = 155) or a provided table (Study 2, n = 152). Data in Study 1 showed statistical differences for the type…

  5. Graphing Polar Curves

    ERIC Educational Resources Information Center

    Lawes, Jonathan F.

    2013-01-01

    Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

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

    PubMed

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

    2016-05-01

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

  7. Tight Lower Bound for Percolation Threshold on an Infinite Graph

    NASA Astrophysics Data System (ADS)

    Hamilton, Kathleen E.; Pryadko, Leonid P.

    2014-11-01

    We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graph's adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.

  8. A notion of graph likelihood and an infinite monkey theorem

    NASA Astrophysics Data System (ADS)

    Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone

    2014-01-01

    We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.

  9. The fragment assembly string graph.

    PubMed

    Myers, Eugene W

    2005-09-01

    We present a concept and formalism, the string graph, which represents all that is inferable about a DNA sequence from a collection of shotgun sequencing reads collected from it. We give time and space efficient algorithms for constructing a string graph given the collection of overlaps between the reads and, in particular, present a novel linear expected time algorithm for transitive reduction in this context. The result demonstrates that the decomposition of reads into kmers employed in the de Bruijn graph approach described earlier is not essential, and exposes its close connection to the unitig approach we developed at Celera. This paper is a preliminary piece giving the basic algorithm and results that demonstrate the efficiency and scalability of the method. These ideas are being used to build a next-generation whole genome assembler called BOA (Berkeley Open Assembler) that will easily scale to mammalian genomes.

  10. Box graphs and resolutions I

    NASA Astrophysics Data System (ADS)

    Braun, Andreas P.; Schäfer-Nameki, Sakura

    2016-04-01

    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.

  11. Contact Graph Routing

    NASA Technical Reports Server (NTRS)

    Burleigh, Scott C.

    2011-01-01

    Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic

  12. On linear area embedding of planar graphs

    NASA Astrophysics Data System (ADS)

    Dolev, D.; Trickey, H.

    1981-09-01

    Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. An algorithm to embed outerplanar graphs in linear area is given. This algorithm is extended to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs.

  13. Hierarchical, 4-connected Small-World Graph

    NASA Astrophysics Data System (ADS)

    Goncalves, Bruno; Boettcher, Stefan

    2008-03-01

    A new sequences of graphs are introduced that mimic small-world properties. The graphs are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical sequence of long-distance links in a pattern reminiscent of the tower-of-hanoi sequence. These 4-regular graphs are non-planar, have a diameter growing as 2^√2N^2 (or as [2N]^α with α˜√2N^2/22N^2), and a nontrivial phase transition Tc>0, for the Ising ferromagnet. These results suggest that these graphs are similar to small-world graphs with mean-field-like properties.

  14. Graphing Inequalities, Connecting Meaning

    ERIC Educational Resources Information Center

    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…

  15. Graph-Plotting Routine

    NASA Technical Reports Server (NTRS)

    Kantak, Anil V.

    1987-01-01

    Plotter routine for IBM PC (AKPLOT) designed for engineers and scientists who use graphs as integral parts of their documentation. Allows user to generate graph and edit its appearance on cathode-ray tube. Graph may undergo many interactive alterations before finally dumped from screen to be plotted by printer. Written in BASIC.

  16. Graphing Important People

    ERIC Educational Resources Information Center

    Reading Teacher, 2012

    2012-01-01

    The "Toolbox" column features content adapted from ReadWriteThink.org lesson plans and provides practical tools for classroom teachers. This issue's column features a lesson plan adapted from "Graphing Plot and Character in a Novel" by Lisa Storm Fink and "Bio-graph: Graphing Life Events" by Susan Spangler. Students retell biographic events…

  17. Universal Quantum Graphs

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2014-04-01

    For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.

  18. Genome alignment with graph data structures: a comparison

    PubMed Central

    2014-01-01

    Background Recent advances in rapid, low-cost sequencing have opened up the opportunity to study complete genome sequences. The computational approach of multiple genome alignment allows investigation of evolutionarily related genomes in an integrated fashion, providing a basis for downstream analyses such as rearrangement studies and phylogenetic inference. Graphs have proven to be a powerful tool for coping with the complexity of genome-scale sequence alignments. The potential of graphs to intuitively represent all aspects of genome alignments led to the development of graph-based approaches for genome alignment. These approaches construct a graph from a set of local alignments, and derive a genome alignment through identification and removal of graph substructures that indicate errors in the alignment. Results We compare the structures of commonly used graphs in terms of their abilities to represent alignment information. We describe how the graphs can be transformed into each other, and identify and classify graph substructures common to one or more graphs. Based on previous approaches, we compile a list of modifications that remove these substructures. Conclusion We show that crucial pieces of alignment information, associated with inversions and duplications, are not visible in the structure of all graphs. If we neglect vertex or edge labels, the graphs differ in their information content. Still, many ideas are shared among all graph-based approaches. Based on these findings, we outline a conceptual framework for graph-based genome alignment that can assist in the development of future genome alignment tools. PMID:24712884

  19. Graphing with "LogoWriter."

    ERIC Educational Resources Information Center

    Yoder, Sharon K.

    This book discusses four kinds of graphs that are taught in mathematics at the middle school level: pictographs, bar graphs, line graphs, and circle graphs. The chapters on each of these types of graphs contain information such as starting, scaling, drawing, labeling, and finishing the graphs using "LogoWriter." The final chapter of the book…

  20. Loops in Reeb Graphs of 2-Manifolds

    SciTech Connect

    Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V

    2004-12-16

    Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

  1. Loops in Reeb Graphs of 2-Manifolds

    SciTech Connect

    Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V

    2003-02-11

    Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

  2. Zeta functions of the Dirac operator on quantum graphs

    NASA Astrophysics Data System (ADS)

    Harrison, J. M.; Weyand, T.; Kirsten, K.

    2016-10-01

    We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with general energy independent matching conditions at the vertices. The regularized spectral determinant of the Dirac operator is also obtained as the derivative of the zeta function at a special value. In each case the zeta function is formulated using a contour integral method, which extends results obtained for Laplace and Schrödinger operators on graphs.

  3. Argument Graph as a Tool for Promoting Collaborative Online Reading

    ERIC Educational Resources Information Center

    Kiili, Carita

    2013-01-01

    This study explored how the construction of an argument graph promotes students' collaborative online reading compared to note-taking. Upper secondary school students ("n"?=?76) worked in pairs. The pairs were asked to search for and read source material on the Web for a joint essay and either construct an argument graph or take notes during…

  4. Data relationship degree-based clustering data aggregation for VANET

    NASA Astrophysics Data System (ADS)

    Kumar, Rakesh; Dave, Mayank

    2016-03-01

    Data aggregation is one of the major needs of vehicular ad hoc networks (VANETs) due to the constraints of resources. Data aggregation in VANET can reduce the data redundancy in the process of data gathering and thus conserving the bandwidth. In realistic applications, it is always important to construct an effective route strategy that optimises not only communication cost but also the aggregation cost. Data aggregation at the cluster head by individual vehicle causes flooding of the data, which results in maximum latency and bandwidth consumption. Another approach of data aggregation in VANET is sending local representative data based on spatial correlation of sampled data. In this article, we emphasise on the problem that recent spatial correlation data models of vehicles in VANET are not appropriate for measuring the correlation in a complex and composite environment. Moreover, the data represented by these models is generally inaccurate when compared to the real data. To minimise this problem, we propose a group-based data aggregation method that uses data relationship degree (DRD). In the proposed approach, DRD is a spatial relationship measurement parameter that measures the correlation between a vehicle's data and its neighbouring vehicles' data. The DRD clustering method where grouping of vehicle's data is done based on the available data and its correlation is presented in detail. Results prove that the representative data using proposed approach have a low distortion and provides an improvement in packet delivery ratio and throughput (up to of 10.84% and 24.82% respectively) as compared to the other state-of-the-art solutions like Cluster-Based Accurate Syntactic Compression of Aggregated Data in VANETs.

  5. On atom bond connectivity index of some molecular graphs

    NASA Astrophysics Data System (ADS)

    Mohammed, Mohanad A.; Atan, K. A.; Khalaf, A. M.; Said, M. R. Md.; Hasni, R.

    2016-06-01

    The atom-bond connectivity (ABC) index is one of the newly most studied degree based molecular structure descriptors, which have chemical applications. For a graph G, the ABC index can be defined as A B C (G )=Σuv ∈E (G )√{dv+du-2 /dv.du } , where du, the degree of the vertex u is the number of edges with u as an end vertex denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkenes and cycloalkenes.

  6. Topologies on directed graphs

    NASA Technical Reports Server (NTRS)

    Lieberman, R. N.

    1972-01-01

    Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.

  7. Hydride, hydrogen, proton, and electron affinities of imines and their reaction intermediates in acetonitrile and construction of thermodynamic characteristic graphs (TCGs) of imines as a "molecule ID card".

    PubMed

    Zhu, Xiao-Qing; Liu, Qiao-Yun; Chen, Qiang; Mei, Lian-Rui

    2010-02-01

    A series of 61 imines with various typical structures were synthesized, and the thermodynamic affinities (defined as enthalpy changes or redox potentials in this work) of the imines to abstract hydride anions, hydrogen atoms, and electrons, the thermodynamic affinities of the radical anions of the imines to abstract hydrogen atoms and protons, and the thermodynamic affinities of the hydrogen adducts of the imines to abstract electrons in acetonitrile were determined by using titration calorimetry and electrochemical methods. The pure heterolytic and homolytic dissociation energies of the C=N pi-bond in the imines were estimated. The polarity of the C=N double bond in the imines was examined using a linear free-energy relationship. The idea of a thermodynamic characteristic graph (TCG) of imines as an efficient "Molecule ID Card" was introduced. The TCG can be used to quantitatively diagnose and predict the characteristic chemical properties of imines and their various reaction intermediates as well as the reduction mechanism of the imines. The information disclosed in this work could not only supply a gap of thermodynamics for the chemistry of imines but also strongly promote the fast development of the applications of imines.

  8. Graph Generator Survey

    SciTech Connect

    Lothian, Josh; Powers, Sarah S; Sullivan, Blair D; Baker, Matthew B; Schrock, Jonathan; Poole, Stephen W

    2013-12-01

    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 dierent 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.

  9. mpiGraph

    2007-05-22

    MpiGraph consists of an MPI application called mpiGraph written in C to measure message bandwidth and an associated crunch_mpiGraph script written in Perl to process the application output into an HTMO report. The mpiGraph application is designed to inspect the health and scalability of a high-performance interconnect while under heavy load. This is useful to detect hardware and software problems in a system, such as slow nodes, links, switches, or contention in switch routing. Itmore » is also useful to characterize how interconnect performance changes with different settings or how one interconnect type compares to another.« less

  10. Graph representation of protein free energy landscape

    SciTech Connect

    Li, Minghai; Duan, Mojie; Fan, Jue; Huo, Shuanghong; Han, Li

    2013-11-14

    The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.

  11. Graph representation of protein free energy landscape.

    PubMed

    Li, Minghai; Duan, Mojie; Fan, Jue; Han, Li; Huo, Shuanghong

    2013-11-14

    The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.

  12. How Fast Do Trees Grow? Using Tables and Graphs to Explore Slope

    ERIC Educational Resources Information Center

    Joram, Elana; Oleson, Vicki

    2007-01-01

    This article describes a lesson unit in which students constructed tables and graphs to represent the growth of different trees. Students then compared the graphs to develop an understanding of slope.

  13. Bipartite graph partitioning and data clustering

    SciTech Connect

    Zha, Hongyuan; He, Xiaofeng; Ding, Chris; Gu, Ming; Simon, Horst D.

    2001-05-07

    Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, the authors propose a new data clustering method based on partitioning the underlying biopartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. They show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. They point out the connection of their clustering algorithm to correspondence analysis used in multivariate analysis. They also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, they apply their clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.

  14. Graphs, matrices, and the GraphBLAS: Seven good reasons

    DOE PAGES

    Kepner, Jeremy; Bader, David; Buluç, Aydın; Gilbert, John; Mattson, Timothy; Meyerhenke, Henning

    2015-01-01

    The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implementmore » a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.« less

  15. Graphs, matrices, and the GraphBLAS: Seven good reasons

    SciTech Connect

    Kepner, Jeremy; Bader, David; Buluç, Aydın; Gilbert, John; Mattson, Timothy; Meyerhenke, Henning

    2015-01-01

    The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.

  16. Visibility graph analysis on heartbeat dynamics of meditation training

    NASA Astrophysics Data System (ADS)

    Jiang, Sen; Bian, Chunhua; Ning, Xinbao; Ma, Qianli D. Y.

    2013-06-01

    We apply the visibility graph analysis to human heartbeat dynamics by constructing the complex networks of heartbeat interval time series and investigating the statistical properties of the network before and during chi and yoga meditation. The experiment results show that visibility graph analysis can reveal the dynamical changes caused by meditation training manifested as regular heartbeat, which is closely related to the adjustment of autonomous neural system, and visibility graph analysis is effective to evaluate the effect of meditation.

  17. Reaction route graphs. III. Non-minimal kinetic mechanisms.

    PubMed

    Fishtik, Ilie; Callaghan, Caitlin A; Datta, Ravindra

    2005-02-24

    The concept of reaction route (RR) graphs introduced recently by us for kinetic mechanisms that produce minimal graphs is extended to the problem of non-minimal kinetic mechanisms for the case of a single overall reaction (OR). A RR graph is said to be minimal if all of the stoichiometric numbers in all direct RRs of the mechanism are equal to +/-1 and non-minimal if at least one stoichiometric number in a direct RR is non-unity, e.g., equal to +/-2. For a given mechanism, four unique topological characteristics of RR graphs are defined and enumerated, namely, direct full routes (FRs), empty routes (ERs), intermediate nodes (INs), and terminal nodes (TNs). These are further utilized to construct the RR graphs. One algorithm involves viewing each IN as a central node in a RR sub-graph. As a result, the construction and enumeration of RR graphs are reduced to the problem of balancing the peripheral nodes in the RR sub-graphs according to the list of FRs, ERs, INs, and TNs. An alternate method involves using an independent set of RRs to draw the RR graph while satisfying the INs and TNs. Three examples are presented to illustrate the application of non-minimal RR graph theory.

  18. Knowledge Representation Issues in Semantic Graphs for Relationship Detection

    SciTech Connect

    Barthelemy, M; Chow, E; Eliassi-Rad, T

    2005-02-02

    An important task for Homeland Security is the prediction of threat vulnerabilities, such as through the detection of relationships between seemingly disjoint entities. A structure used for this task is a ''semantic graph'', also known as a ''relational data graph'' or an ''attributed relational graph''. These graphs encode relationships as typed links between a pair of typed nodes. Indeed, semantic graphs are very similar to semantic networks used in AI. The node and link types are related through an ontology graph (also known as a schema). Furthermore, each node has a set of attributes associated with it (e.g., ''age'' may be an attribute of a node of type ''person''). Unfortunately, the selection of types and attributes for both nodes and links depends on human expertise and is somewhat subjective and even arbitrary. This subjectiveness introduces biases into any algorithm that operates on semantic graphs. Here, we raise some knowledge representation issues for semantic graphs and provide some possible solutions using recently developed ideas in the field of complex networks. In particular, we use the concept of transitivity to evaluate the relevance of individual links in the semantic graph for detecting relationships. We also propose new statistical measures for semantic graphs and illustrate these semantic measures on graphs constructed from movies and terrorism data.

  19. Real World Graph Connectivity

    ERIC Educational Resources Information Center

    Lind, Joy; Narayan, Darren

    2009-01-01

    We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give…

  20. Walking Out Graphs

    ERIC Educational Resources Information Center

    Shen, Ji

    2009-01-01

    In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of…

  1. Reflections on "The Graph"

    ERIC Educational Resources Information Center

    Petrosino, Anthony

    2012-01-01

    This article responds to arguments by Skidmore and Thompson (this issue of "Educational Researcher") that a graph published more than 10 years ago was erroneously reproduced and "gratuitously damaged" perceptions of the quality of education research. After describing the purpose of the original graph, the author counters assertions that the graph…

  2. Exploring Graphs: WYSIWYG.

    ERIC Educational Resources Information Center

    Johnson, Millie

    1997-01-01

    Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…

  3. Making "Photo" Graphs

    ERIC Educational Resources Information Center

    Doto, Julianne; Golbeck, Susan

    2007-01-01

    Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students…

  4. ACTIVITIES: Graphs and Games

    ERIC Educational Resources Information Center

    Hirsch, Christian R.

    1975-01-01

    Using a set of worksheets, students will discover and apply Euler's formula regarding connected planar graphs and play and analyze the game of Sprouts. One sheet leads to the discovery of Euler's formula; another concerns traversability of a graph; another gives an example and a game involving these ideas. (Author/KM)

  5. Using Specialized Graph Paper.

    ERIC Educational Resources Information Center

    James, C.

    1988-01-01

    Discusses the use of logarithm and reciprocal graphs in the college physics classroom. Provides examples, such as electrical conductivity, reliability function in the Weibull model, and the Clausius-Clapeyron equation for latent heat of vaporation. Shows graphs with weighting of points. (YP)

  6. Equitable random graphs

    NASA Astrophysics Data System (ADS)

    Newman, M. E. J.; Martin, Travis

    2014-11-01

    Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdős and Rényi, in particular, as well as the so-called configuration model, have served as the starting point for numerous calculations. In this paper we describe another large class of random graph models, which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure, including community structure, bipartite structure, degree correlations, stratification, and others, yet are exactly solvable for a wide range of properties in the limit of large graph size, including percolation properties, complete spectral density, and the behavior of homogeneous dynamical systems, such as coupled oscillators or epidemic models.

  7. Topological structure of dictionary graphs

    NASA Astrophysics Data System (ADS)

    Fukś, Henryk; Krzemiński, Mark

    2009-09-01

    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 103 and 104. 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.

  8. Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

    NASA Astrophysics Data System (ADS)

    Luque, B.; Ballesteros, F. J.; Núñez, A. M.; Robledo, A.

    2013-04-01

    A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. Finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy.

  9. From time series to complex networks: the visibility graph.

    PubMed

    Lacasa, Lucas; Luque, Bartolo; Ballesteros, Fernando; Luque, Jordi; Nuño, Juan Carlos

    2008-04-01

    In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.

  10. Learning a Nonnegative Sparse Graph for Linear Regression.

    PubMed

    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.

  11. Ringo: Interactive Graph Analytics on Big-Memory Machines

    PubMed Central

    Perez, Yonathan; Sosič, Rok; Banerjee, Arijit; Puttagunta, Rohan; Raison, Martin; Shah, Pararth; Leskovec, Jure

    2016-01-01

    We present Ringo, a system for analysis of large graphs. Graphs provide a way to represent and analyze systems of interacting objects (people, proteins, webpages) with edges between the objects denoting interactions (friendships, physical interactions, links). Mining graphs provides valuable insights about individual objects as well as the relationships among them. In building Ringo, we take advantage of the fact that machines with large memory and many cores are widely available and also relatively affordable. This allows us to build an easy-to-use interactive high-performance graph analytics system. Graphs also need to be built from input data, which often resides in the form of relational tables. Thus, Ringo provides rich functionality for manipulating raw input data tables into various kinds of graphs. Furthermore, Ringo also provides over 200 graph analytics functions that can then be applied to constructed graphs. We show that a single big-memory machine provides a very attractive platform for performing analytics on all but the largest graphs as it offers excellent performance and ease of use as compared to alternative approaches. With Ringo, we also demonstrate how to integrate graph analytics with an iterative process of trial-and-error data exploration and rapid experimentation, common in data mining workloads. PMID:27081215

  12. Genus Ranges of 4-Regular Rigid Vertex Graphs

    PubMed Central

    Buck, Dorothy; Dolzhenko, Egor; Jonoska, Nataša; Saito, Masahico; Valencia, Karin

    2016-01-01

    A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a graph is embedded cellularly, and the embeddings of rigid vertex graphs are required to preserve the prescribed cyclic order of incident edges at every vertex. The genus ranges of 4-regular rigid vertex graphs are sets of consecutive integers, and we address two questions: which intervals of integers appear as genus ranges of such graphs, and what types of graphs realize a given genus range. For graphs with 2n vertices (n > 1), we prove that all intervals [a, b] for all a < b ≤ n, and singletons [h, h] for some h ≤ n, are realized as genus ranges. For graphs with 2n − 1 vertices (n ≥ 1), we prove that all intervals [a, b] for all a < b ≤ n except [0, n], and [h, h] for some h ≤ n, are realized as genus ranges. We also provide constructions of graphs that realize these ranges.

  13. A Graphing Investigation of the Ellipse.

    ERIC Educational Resources Information Center

    Davis, Jennifer; Hofstetter, Elaine

    1998-01-01

    Discusses ways to present mathematics concepts dealing with the ellipse to high school students, particularly by using a graphing calculator. Real-world occurrences of ellipses are considered, and a one-page student worksheet on constructing an ellipse is included. (LRW)

  14. Evolving Polygons Revisited: Inequalities and Computer Graphing

    ERIC Educational Resources Information Center

    Abramovich, Sergei; Brouwer, Peter

    2009-01-01

    This paper was developed with the goal of enhancing the mathematical preparation of secondary school teachers in the technological paradigm. It shows how two-variable inequalities can be utilized as models for the construction of geometric objects using the software Graphing Calculator 3.5 (produced by Pacific Tech) as a relation grapher. An…

  15. Reaction spreading on graphs

    NASA Astrophysics Data System (ADS)

    Burioni, Raffaella; Chibbaro, Sergio; Vergni, Davide; Vulpiani, Angelo

    2012-11-01

    We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product M(t). At variance with pure diffusive processes, characterized by the spectral dimension ds, the important quantity for reaction spreading is found to be the connectivity dimension dl. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)˜tdl. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)˜eαt with α proportional to ln, where is the average degree of the graph.

  16. A study on vague graphs.

    PubMed

    Rashmanlou, Hossein; Samanta, Sovan; Pal, Madhumangal; Borzooei, R A

    2016-01-01

    The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined. PMID:27536517

  17. A Semantic Graph Query Language

    SciTech Connect

    Kaplan, I L

    2006-10-16

    Semantic graphs can be used to organize large amounts of information from a number of sources into one unified structure. A semantic query language provides a foundation for extracting information from the semantic graph. The graph query language described here provides a simple, powerful method for querying semantic graphs.

  18. Turning Spreadsheets into Graphs: An Information Technology Lesson in Whole Brain Thinking

    ERIC Educational Resources Information Center

    Patterson, Thomas F.; Leonard, Jonathan G.

    2005-01-01

    We have concluded that teaching undergraduate students to use spreadsheet software to analyze, interpret, and communicate spreadsheet data through a graph is an information technology exercise in whole brain thinking. In investigating why our students have difficulty constructing proper graphs, we have discovered that graphing requires two…

  19. Students' Images of Two-Variable Functions and Their Graphs

    ERIC Educational Resources Information Center

    Weber, Eric; Thompson, Patrick W.

    2014-01-01

    This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…

  20. Geometry of loop quantum gravity on a graph

    SciTech Connect

    Rovelli, Carlo; Speziale, Simone

    2010-08-15

    We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the 'twisted geometries' and derive a simple relation between these and Regge geometries.

  1. Percolation threshold on planar Euclidean Gabriel graphs

    NASA Astrophysics Data System (ADS)

    Norrenbrock, Christoph

    2016-04-01

    In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of "proximity graphs" and are discussed, e.g., in context of the construction of backbones for wireless ad-hoc networks. Finite-size scaling analyses have been performed to find the critical points and critical exponents ν, β and γ. The critical exponents obtained this way verify that the associated universality class is that of standard 2D percolation.

  2. Internet topology: connectivity of IP graphs

    NASA Astrophysics Data System (ADS)

    Broido, Andre; claffy, kc

    2001-07-01

    In this paper we introduce a framework for analyzing local properties of Internet connectivity. We compare BGP and probed topology data, finding that currently probed topology data yields much denser coverage of AS-level connectivity. We describe data acquisition and construction of several IP- level graphs derived from a collection of 220 M skitter traceroutes. We find that a graph consisting of IP nodes and links contains 90.5% of its 629 K nodes in the acyclic subgraph. In particular, 55% of the IP nodes are in trees. Full bidirectional connectivity is observed for a giant component containing 8.3% of IP nodes.

  3. Horizontal visibility graphs generated by type-I intermittency

    NASA Astrophysics Data System (ADS)

    Núñez, Ángel M.; Luque, Bartolo; Lacasa, Lucas; Gómez, Jose Patricio; Robledo, Alberto

    2013-05-01

    The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

  4. Horizontal visibility graphs generated by type-I intermittency.

    PubMed

    Núñez, Ángel M; Luque, Bartolo; Lacasa, Lucas; Gómez, Jose Patricio; Robledo, Alberto

    2013-05-01

    The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

  5. Optimized Graph Search Using Multi-Level Graph Clustering

    NASA Astrophysics Data System (ADS)

    Kala, Rahul; Shukla, Anupam; Tiwari, Ritu

    Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visualized in the search engines to carry search operations and provide results. Various searching algorithms have been developed for searching in graphs. In this paper we propose that the entire network graph be clustered. The larger graphs are clustered to make smaller graphs. These smaller graphs can again be clustered to further reduce the size of graph. The search is performed on the smallest graph to identify the general path, which may be further build up to actual nodes by working on the individual clusters involved. Since many searches are carried out on the same graph, clustering may be done once and the data may be used for multiple searches over the time. If the graph changes considerably, only then we may re-cluster the graph.

  6. Subdominant pseudoultrametric on graphs

    SciTech Connect

    Dovgoshei, A A; Petrov, E A

    2013-08-31

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

  7. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  8. Creating single-subject design graphs in Microsoft Excel 2007.

    PubMed

    Dixon, Mark R; Jackson, James W; Small, Stacey L; Horner-King, Mollie J; Lik, Nicholas Mui Ker; Garcia, Yors; Rosales, Rocio

    2009-01-01

    Over 10 years have passed since the publication of Carr and Burkholder's (1998) technical article on how to construct single-subject graphs using Microsoft Excel. Over the course of the past decade, the Excel program has undergone a series of revisions that make the Carr and Burkholder paper somewhat difficult to follow with newer versions. The present article provides task analyses for constructing various types of commonly used single-subject design graphs in Microsoft Excel 2007. The task analyses were evaluated using a between-subjects design that compared the graphing skills of 22 behavior-analytic graduate students using Excel 2007 and either the Carr and Burkholder or newly developed task analyses. Results indicate that the new task analyses yielded more accurate and faster graph construction than the Carr and Burkholder instructions.

  9. Graphing Calculator Mini Course

    NASA Technical Reports Server (NTRS)

    Karnawat, Sunil R.

    1996-01-01

    The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

  10. Feature Tracking Using Reeb Graphs

    SciTech Connect

    Weber, Gunther H.; Bremer, Peer-Timo; Day, Marcus S.; Bell, John B.; Pascucci, Valerio

    2010-08-02

    Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a temperature isosurface. Tracking such regions as they merge and split over time can provide important insights into the impact of turbulence on the combustion process. However, the convoluted nature of the temperature isosurface and its rapid movement make this analysis particularly challenging. Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field. It then obtains isosurfaces for the original simulation time steps and labels individual connected 'burning' regions based on the local fuel consumption value. Based on this information, a boundary surface between burning and non-burning regions is constructed. The Reeb graph of this boundary surface is the tracking graph for burning regions.

  11. Robustness of random graphs based on graph spectra

    NASA Astrophysics Data System (ADS)

    Wu, Jun; Barahona, Mauricio; Tan, Yue-jin; Deng, Hong-zhong

    2012-12-01

    It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.

  12. Graph ensemble boosting for imbalanced noisy graph stream classification.

    PubMed

    Pan, Shirui; Wu, Jia; Zhu, Xingquan; Zhang, Chengqi

    2015-05-01

    Many applications involve stream data with structural dependency, graph representations, and continuously increasing volumes. For these applications, it is very common that their class distributions are imbalanced with minority (or positive) samples being only a small portion of the population, which imposes significant challenges for learning models to accurately identify minority samples. This problem is further complicated with the presence of noise, because they are similar to minority samples and any treatment for the class imbalance may falsely focus on the noise and result in deterioration of accuracy. In this paper, we propose a classification model to tackle imbalanced graph streams with noise. Our method, graph ensemble boosting, employs an ensemble-based framework to partition graph stream into chunks each containing a number of noisy graphs with imbalanced class distributions. For each individual chunk, we propose a boosting algorithm to combine discriminative subgraph pattern selection and model learning as a unified framework for graph classification. To tackle concept drifting in graph streams, an instance level weighting mechanism is used to dynamically adjust the instance weight, through which the boosting framework can emphasize on difficult graph samples. The classifiers built from different graph chunks form an ensemble for graph stream classification. Experiments on real-life imbalanced graph streams demonstrate clear benefits of our boosting design for handling imbalanced noisy graph stream.

  13. Graph for locked rotor current

    NASA Technical Reports Server (NTRS)

    Peck, R. R.

    1972-01-01

    Graph determines effect of stalled motor on a distribution system and eliminates hand calculation of amperage in emergencies. Graph is useful to any manufacturer, contractor, or maintenance department involved in electrical technology.

  14. A Graph Summarization Algorithm Based on RFID Logistics

    NASA Astrophysics Data System (ADS)

    Sun, Yan; Hu, Kongfa; Lu, Zhipeng; Zhao, Li; Chen, Ling

    Radio Frequency Identification (RFID) applications are set to play an essential role in object tracking and supply chain management systems. The volume of data generated by a typical RFID application will be enormous as each item will generate a complete history of all the individual locations that it occupied at every point in time. The movement trails of such RFID data form gigantic commodity flowgraph representing the locations and durations of the path stages traversed by each item. In this paper, we use graph to construct a warehouse of RFID commodity flows, and introduce a database-style operation to summarize graphs, which produces a summary graph by grouping nodes based on user-selected node attributes, further allows users to control the hierarchy of summaries. It can cut down the size of graphs, and provide convenience for users to study just on the shrunk graph which they interested. Through extensive experiments, we demonstrate the effectiveness and efficiency of the proposed method.

  15. GraphLib

    2013-02-19

    This library is used in several LLNL projects, including STAT (the Stack Trace Analysis Tool for scalable debugging) and some modules in P^nMPI (a tool MPI tool infrastructure). It can also be used standalone for creating and manipulationg graphs, but its API is primarily tuned to support these other projects

  16. Line Graph Learning

    ERIC Educational Resources Information Center

    Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.

    2007-01-01

    In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…

  17. Straight Line Graphs

    ERIC Educational Resources Information Center

    Krueger, Tom

    2010-01-01

    In this article, the author shares one effective lesson idea on straight line graphs that he applied in his lower ability Y9 class. The author wanted something interesting for his class to do, something that was fun and engaging with direct feedback, and something that worked because someone else had tried it before. In a word, the author admits…

  18. Introduction to Graphing.

    ERIC Educational Resources Information Center

    Sokol, William

    In this autoinstructional packet, the student is given an experimental situation which introduces him to the process of graphing. The lesson is presented for secondary school students in chemistry. Algebra I and a Del Mod System program (indicated as SE 018 020) are suggested prerequisites for the use of this program. Behavioral objectives are…

  19. Cookies and Graphs

    ERIC Educational Resources Information Center

    Cooper, Carol

    1975-01-01

    Teachers of an integrated elementary classroom used cookie-sharing time as a learning experience for students. Responsible for dividing varying amounts of cookies daily, the students learned to translate their experiences to graphs of differing sophistication and analyses. Further interpretation and application were done by individual students…

  20. Physics on Graphs

    NASA Astrophysics Data System (ADS)

    Schrader, Robert

    This is an extended version of the talk given at the Nato Advanced Research Workshop: New Challenges in Complex System Physics, May 20-24, 2013 in Samarkand (Uzbekistan). We report on results on three topics in joint work with V. Kostrykin (Mainz, Germany) and J. Potthoff (Mannheim, Germany): Propagation of waves on graphs,

  1. Graph-theoretical exorcism

    SciTech Connect

    Simmons, G.J.

    1985-01-01

    Given a graph G and an ordering phi of the vertices, V(G), we define a parsimonious proper coloring (PPC) of V(G) under phi to be a proper coloring of V(G) in the order phi, where a new color is introduced only when a vertex cannot be properly colored in its order with any of the colors already used.

  2. Coloring geographical threshold graphs

    SciTech Connect

    Bradonjic, Milan; Percus, Allon; Muller, Tobias

    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.

  3. New Conic Graph Paper

    ERIC Educational Resources Information Center

    Rose, Kenneth

    1974-01-01

    Two new types of graph paper are described; focus-focus conic paper and focus-directrix paper. Both types make it easier to draw families of conics. Suggestions for further work are given as is a method for establishing a connection with other ways of looking at the conic sections. (LS)

  4. Temporal Representation in Semantic Graphs

    SciTech Connect

    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.

  5. Relativity on rotated graph paper

    NASA Astrophysics Data System (ADS)

    Salgado, Roberto B.

    2016-05-01

    We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45°. The diagonal grid lines represent light-flash worldlines in Minkowski spacetime, and the boxes in the grid (called "clock diamonds") represent units of measurement corresponding to the ticks of an inertial observer's light clock. We show that many quantitative results can be read off a spacetime diagram simply by counting boxes, with very little algebra. In particular, we show that the squared interval between two events is equal to the signed area of the parallelogram on the grid (called the "causal diamond") with opposite vertices corresponding to those events. We use the Doppler effect—without explicit use of the Doppler formula—to motivate the method.

  6. A Clustering Graph Generator

    SciTech Connect

    Winlaw, Manda; De Sterck, Hans; Sanders, Geoffrey

    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.

  7. Mining and Indexing Graph Databases

    ERIC Educational Resources Information Center

    Yuan, Dayu

    2013-01-01

    Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…

  8. Recursive Feature Extraction in Graphs

    SciTech Connect

    2014-08-14

    ReFeX extracts recursive topological features from graph data. The input is a graph as a csv file and the output is a csv file containing feature values for each node in the graph. The features are based on topological counts in the neighborhoods of each nodes, as well as recursive summaries of neighbors' features.

  9. Editing graphs for maximum effect

    SciTech Connect

    Murphy, P.W.; Rhiner, R.W.

    1991-01-08

    The paper contains over eighty rules for editing graphs, arranged under nine major headings in a logical sequence for editing all the graphs in a manuscript. It is excerpted from a monograph used at the Lawrence Livermore National Laboratory to train beginning technical editors in editing graphs; a corresponding Hypercard stack is also used in this training. 6 refs., 4 figs.

  10. A Note on Hamiltonian Graphs

    ERIC Educational Resources Information Center

    Skurnick, Ronald; Davi, Charles; Skurnick, Mia

    2005-01-01

    Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

  11. Topic Model for Graph Mining.

    PubMed

    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.

  12. Obstructions to the realization of distance graphs with large chromatic numbers on spheres of small radii

    SciTech Connect

    Kupavskii, A B; Raigorodskii, A M

    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.

  13. New methods for analyzing semantic graph based assessments in science education

    NASA Astrophysics Data System (ADS)

    Vikaros, Lance Steven

    This research investigated how the scoring of semantic graphs (known by many as concept maps) could be improved and automated in order to address issues of inter-rater reliability and scalability. As part of the NSF funded SENSE-IT project to introduce secondary school science students to sensor networks (NSF Grant No. 0833440), semantic graphs illustrating how temperature change affects water ecology were collected from 221 students across 16 schools. The graphing task did not constrain students' use of terms, as is often done with semantic graph based assessment due to coding and scoring concerns. The graphing software used provided real-time feedback to help students learn how to construct graphs, stay on topic and effectively communicate ideas. The collected graphs were scored by human raters using assessment methods expected to boost reliability, which included adaptations of traditional holistic and propositional scoring methods, use of expert raters, topical rubrics, and criterion graphs. High levels of inter-rater reliability were achieved, demonstrating that vocabulary constraints may not be necessary after all. To investigate a new approach to automating the scoring of graphs, thirty-two different graph features characterizing graphs' structure, semantics, configuration and process of construction were then used to predict human raters' scoring of graphs in order to identify feature patterns correlated to raters' evaluations of graphs' topical accuracy and complexity. Results led to the development of a regression model able to predict raters' scoring with 77% accuracy, with 46% accuracy expected when used to score new sets of graphs, as estimated via cross-validation tests. Although such performance is comparable to other graph and essay based scoring systems, cross-context testing of the model and methods used to develop it would be needed before it could be recommended for widespread use. Still, the findings suggest techniques for improving the

  14. K-theory of locally finite graph C∗-algebras

    NASA Astrophysics Data System (ADS)

    Iyudu, Natalia

    2013-09-01

    We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).

  15. What is a complex graph?

    NASA Astrophysics Data System (ADS)

    Kim, Jongkwang; Wilhelm, Thomas

    2008-04-01

    Many papers published in recent years show that real-world graphs G(n,m) ( n nodes, m edges) are more or less “complex” in the sense that different topological features deviate from random graphs. Here we narrow the definition of graph complexity and argue that a complex graph contains many different subgraphs. We present different measures that quantify this complexity, for instance C1e, the relative number of non-isomorphic one-edge-deleted subgraphs (i.e. DECK size). However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined “product measures”, the products of two quantities which are zero in the extreme cases of a path and clique, and “entropy measures” quantifying the diversity of different topological features. The previously defined network/graph complexity measures Medium Articulation and Offdiagonal complexity ( OdC) belong to these two classes. We study OdC measures in some detail and compare it with our new measures. For all measures, the most complex graph G has a medium number of edges, between the edge numbers of the minimum and the maximum connected graph n-1graph complexity measures are characterized with the help of different example graphs. For all measures the corresponding time complexity is given. Finally, we discuss the complexity of 33 real-world graphs of different biological, social and economic systems with the six computationally most simple measures (including OdC). The complexities of the real graphs are compared with average complexities of two different random graph versions: complete random graphs (just fixed n,m) and rewired graphs with fixed node degrees.

  16. Spectral fluctuations of quantum graphs

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2014-10-01

    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.

  17. Spectral fluctuations of quantum graphs

    SciTech Connect

    Pluhař, Z.; Weidenmüller, H. A.

    2014-10-15

    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.

  18. Generic quantum walks with memory on regular graphs

    NASA Astrophysics Data System (ADS)

    Li, Dan; Mc Gettrick, Michael; Gao, Fei; Xu, Jie; Wen, Qiao-Yan

    2016-04-01

    Quantum walks with memory (QWM) are a type of modified quantum walks that record the walker's latest path. As we know, only two kinds of QWM have been presented up to now. It is desired to design more QWM for research, so that we can explore the potential of QWM. In this work, by presenting the one-to-one correspondence between QWM on a regular graph and quantum walks without memory (QWoM) on a line digraph of the regular graph, we construct a generic model of QWM on regular graphs. This construction gives a general scheme for building all possible standard QWM on regular graphs and makes it possible to study properties of different kinds of QWM. Here, by taking the simplest example, which is QWM with one memory on the line, we analyze some properties of QWM, such as variance, occupancy rate, and localization.

  19. Random graph states, maximal flow and Fuss-Catalan distributions

    NASA Astrophysics Data System (ADS)

    Collins, Benoît; Nechita, Ion; Życzkowski, Karol

    2010-07-01

    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.

  20. Graph characterization via Ihara coefficients.

    PubMed

    Ren, Peng; Wilson, Richard C; Hancock, Edwin R

    2011-02-01

    The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.

  1. An Unusual Exponential Graph

    ERIC Educational Resources Information Center

    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…

  2. Mathematical formula recognition using graph grammar

    NASA Astrophysics Data System (ADS)

    Lavirotte, Stephane; Pottier, Loic

    1998-04-01

    This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.

  3. Horizontal visibility graphs from integer sequences

    NASA Astrophysics Data System (ADS)

    Lacasa, Lucas

    2016-09-01

    The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has been used to describe and theoretically compare different types of dynamics and has been applied to characterize empirical signals, by extracting topological features from the associated HVGs which have shown to be informative on the class of dynamics. Among some other measures, it has been shown that the degree distribution of these graphs is a very informative feature that encapsulates nontrivial information of the series's generative dynamics. In particular, the HVG associated to a bi-infinite real-valued series of independent and identically distributed random variables is a universal exponential law P(k)=(1/3){(2/3)}k-2, independent of the series marginal distribution. Most of the current applications have however only addressed real-valued time series, as no exact results are known for the topological properties of HVGs associated to integer-valued series. In this paper we explore this latter situation and address univariate time series where each variable can only take a finite number n of consecutive integer values. We are able to construct an explicit formula for the parametric degree distribution {P}n(k), which we prove to converge to the continuous case for large n and deviates otherwise. A few applications are then considered.

  4. A global/local affinity graph for image segmentation.

    PubMed

    Xiaofang Wang; Yuxing Tang; Masnou, Simon; Liming Chen

    2015-04-01

    Construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph-cut based image segmentation methods. In this paper, we propose a novel sparse global/local affinity graph over superpixels of an input image to capture both short- and long-range grouping cues, and thereby enabling perceptual grouping laws, including proximity, similarity, continuity, and to enter in action through a suitable graph-cut algorithm. Moreover, we also evaluate three major visual features, namely, color, texture, and shape, for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics, which suggest combining these visual features with different emphases for perceptual grouping. In particular, an input image is first oversegmented into superpixels at different scales. We postulate a gravitation law based on empirical observations and divide superpixels adaptively into small-, medium-, and large-sized sets. Global grouping is achieved using medium-sized superpixels through a sparse representation of superpixels' features by solving a ℓ0-minimization problem, and thereby enabling continuity or propagation of local smoothness over long-range connections. Small- and large-sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space, and thus implementing perceptual laws, for example, similarity and proximity. Finally, a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales. Extensive experiments are carried out on the Berkeley segmentation database in comparison with several state-of-the-art graph constructions. The results show the effectiveness of the proposed approach, which outperforms state-of-the-art graphs using four different objective criteria, namely, the probabilistic rand index, the variation of information, the global consistency error, and the

  5. A global/local affinity graph for image segmentation.

    PubMed

    Xiaofang Wang; Yuxing Tang; Masnou, Simon; Liming Chen

    2015-04-01

    Construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph-cut based image segmentation methods. In this paper, we propose a novel sparse global/local affinity graph over superpixels of an input image to capture both short- and long-range grouping cues, and thereby enabling perceptual grouping laws, including proximity, similarity, continuity, and to enter in action through a suitable graph-cut algorithm. Moreover, we also evaluate three major visual features, namely, color, texture, and shape, for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics, which suggest combining these visual features with different emphases for perceptual grouping. In particular, an input image is first oversegmented into superpixels at different scales. We postulate a gravitation law based on empirical observations and divide superpixels adaptively into small-, medium-, and large-sized sets. Global grouping is achieved using medium-sized superpixels through a sparse representation of superpixels' features by solving a ℓ0-minimization problem, and thereby enabling continuity or propagation of local smoothness over long-range connections. Small- and large-sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space, and thus implementing perceptual laws, for example, similarity and proximity. Finally, a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales. Extensive experiments are carried out on the Berkeley segmentation database in comparison with several state-of-the-art graph constructions. The results show the effectiveness of the proposed approach, which outperforms state-of-the-art graphs using four different objective criteria, namely, the probabilistic rand index, the variation of information, the global consistency error, and the

  6. Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems

    SciTech Connect

    Hong, Seokyong; Sukumar, Sreenivas Rangan; Vatsavai, Raju

    2016-01-01

    Graph analysis has emerged as a powerful method for data scientists to represent, integrate, query, and explore heterogeneous data sources. As a result, graph data management and mining became a popular area of research, and led to the development of plethora of systems in recent years. Unfortunately, the number of emerging graph analysis systems and the wide range of applications, coupled with a lack of apples-to-apples comparisons, make it difficult to understand the trade-offs between different systems and the graph operations for which they are designed. A fair comparison of these systems is a challenging task for the following reasons: multiple data models, non-standardized serialization formats, various query interfaces to users, and diverse environments they operate in. To address these key challenges, in this paper we present a new benchmark suite by extending the Lehigh University Benchmark (LUBM) to cover the most common capabilities of various graph analysis systems. We provide the design process of the benchmark, which generalizes the workflow for data scientists to conduct the desired graph analysis on different graph analysis systems. Equipped with this extended benchmark suite, we present performance comparison for nine subgraph pattern retrieval operations over six graph analysis systems, namely NetworkX, Neo4j, Jena, Titan, GraphX, and uRiKA. Through the proposed benchmark suite, this study reveals both quantitative and qualitative findings in (1) implications in loading data into each system; (2) challenges in describing graph patterns for each query interface; and (3) different sensitivity of each system to query selectivity. We envision that this study will pave the road for: (i) data scientists to select the suitable graph analysis systems, and (ii) data management system designers to advance graph analysis systems.

  7. Graph Coarsening for Path Finding in Cybersecurity Graphs

    SciTech Connect

    Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh

    2013-01-01

    n the pass-the-hash attack, hackers repeatedly steal password hashes and move through a computer network with the goal of reaching a computer with high level administrative privileges. In this paper we apply graph coarsening in network graphs for the purpose of detecting hackers using this attack or assessing the risk level of the network's current state. We repeatedly take graph minors, which preserve the existence of paths in the graph, and take powers of the adjacency matrix to count the paths. This allows us to detect the existence of paths as well as find paths that have high risk of being used by adversaries.

  8. A comparison of video modeling, text-based instruction, and no instruction for creating multiple baseline graphs in Microsoft Excel.

    PubMed

    Tyner, Bryan C; Fienup, Daniel M

    2015-09-01

    Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance. Participants who used VM constructed graphs significantly faster and with fewer errors than those who used text-based instruction or no instruction. Implications for instruction are discussed.

  9. Range charts and no-space graphs

    USGS Publications Warehouse

    Edwards, L.E.

    1978-01-01

    No-space graphs present one solution to the familiar problem: given data on the occurrence of fossil taxa in separate, well-sampled sections, determine a range chart; that is, a reasonable working hypothesis of the total range in the area in question of each taxon studied. The solution presented here treats only the relative sequence of biostratigraphic events (first and last occurrences of taxa) and does not attempt to determine an amount of spacing between events. Relative to a hypothesized sequence, observed events in any section may be in-place or out-of-place. Out-of-place events may indicate (1) the event in question reflects a taxon that did not fill its entire range (unfilled-range event), or (2) the event in question indicates a need for the revision of the hypothesized sequence. A graph of relative position only (no-space graph) can be used to facilitate the recognition of in-place and out-of-place events by presenting a visual comparison of the observations from each section with the hypothesized sequence. The geometry of the graph as constructed here is such that in-place events will lie along a line series and out-of-place events will lie above or below it. First-occurrence events below the line series and last-occurrence events above the line series indicate unfilled ranges. First-occurrence events above the line series and last-occurrence events below the line series indicate a need for the revision of the hypothesis. Knowing this, the stratigrapher considers alternative positionings of the line series as alternative range hypotheses and seeks the line series that best fits his geologic and paleontologic judgment. No-space graphs are used to revise an initial hypothesis until a final hypothesis is reached. In this final hypothesis every event is found in-place in at least one section, and all events in all sections may be interpreted to represent in-place events or unfilled-range events. No event may indicate a need for further range revision. The

  10. Applied and computational harmonic analysis on graphs and networks

    NASA Astrophysics Data System (ADS)

    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.

  11. Composing Data Parallel Code for a SPARQL Graph Engine

    SciTech Connect

    Castellana, Vito G.; Tumeo, Antonino; Villa, Oreste; Haglin, David J.; Feo, John

    2013-09-08

    Big data analytics process large amount of data to extract knowledge from them. Semantic databases are big data applications that adopt the Resource Description Framework (RDF) to structure metadata through a graph-based representation. The graph based representation provides several benefits, such as the possibility to perform in memory processing with large amounts of parallelism. SPARQL is a language used to perform queries on RDF-structured data through graph matching. In this paper we present a tool that automatically translates SPARQL queries to parallel graph crawling and graph matching operations. The tool also supports complex SPARQL constructs, which requires more than basic graph matching for their implementation. The tool generates parallel code annotated with OpenMP pragmas for x86 Shared-memory Multiprocessors (SMPs). With respect to commercial database systems such as Virtuoso, our approach reduces memory occupation due to join operations and provides higher performance. We show the scaling of the automatically generated graph-matching code on a 48-core SMP.

  12. A path following algorithm for the graph matching problem.

    PubMed

    Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

    2009-12-01

    We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

  13. Efficient enumeration of monocyclic chemical graphs with given path frequencies

    PubMed Central

    2014-01-01

    Background The enumeration of chemical graphs (molecular graphs) satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics because it leads to a variety of useful applications including structure determination and development of novel chemical compounds. Results We consider the problem of enumerating chemical graphs with monocyclic structure (a graph structure that contains exactly one cycle) from a given set of feature vectors, where a feature vector represents the frequency of the prescribed paths in a chemical compound to be constructed and the set is specified by a pair of upper and lower feature vectors. To enumerate all tree-like (acyclic) chemical graphs from a given set of feature vectors, Shimizu et al. and Suzuki et al. proposed efficient branch-and-bound algorithms based on a fast tree enumeration algorithm. In this study, we devise a novel method for extending these algorithms to enumeration of chemical graphs with monocyclic structure by designing a fast algorithm for testing uniqueness. The results of computational experiments reveal that the computational efficiency of the new algorithm is as good as those for enumeration of tree-like chemical compounds. Conclusions We succeed in expanding the class of chemical graphs that are able to be enumerated efficiently. PMID:24955135

  14. MTC: A Fast and Robust Graph-Based Transductive Learning Method.

    PubMed

    Zhang, Yan-Ming; Huang, Kaizhu; Geng, Guang-Gang; Liu, Cheng-Lin

    2015-09-01

    Despite the great success of graph-based transductive learning methods, most of them have serious problems in scalability and robustness. In this paper, we propose an efficient and robust graph-based transductive classification method, called minimum tree cut (MTC), which is suitable for large-scale data. Motivated from the sparse representation of graph, we approximate a graph by a spanning tree. Exploiting the simple structure, we develop a linear-time algorithm to label the tree such that the cut size of the tree is minimized. This significantly improves graph-based methods, which typically have a polynomial time complexity. Moreover, we theoretically and empirically show that the performance of MTC is robust to the graph construction, overcoming another big problem of traditional graph-based methods. Extensive experiments on public data sets and applications on web-spam detection and interactive image segmentation demonstrate our method's advantages in aspect of accuracy, speed, and robustness.

  15. Jargon and Graph Modularity on Twitter

    SciTech Connect

    Dowling, Chase P.; Corley, Courtney D.; Farber, Robert M.; Reynolds, William

    2013-09-01

    The language of conversation is just as dependent upon word choice as it is on who is taking part. Twitter provides an excellent test-bed in which to conduct experiments not only on language usage but on who is using what language with whom. To this end, we combine large scale graph analytical techniques with known socio-linguistic methods. In this article we leverage both expert curated vocabularies and naive mathematical graph analyses to determine if network behavior on Twitter corroborates with the current understanding of language usage. The results reported indicate that, based on networks constructed from user to user communication and communities identified using the Clauset- Newman greedy modularity algorithm we find that more prolific users of these curated vocabularies are concentrated in distinct network communities.

  16. Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge about Slope and Y-Intercept

    ERIC Educational Resources Information Center

    Hattikudur, Shanta; Prather, Richard W.; Asquith, Pamela; Alibali, Martha W.; Knuth, Eric J.; Nathan, Mitchell

    2012-01-01

    Middle-school students are expected to understand key components of graphs, such as slope and y-intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and…

  17. Detecting alternative graph clusterings.

    PubMed

    Mandala, Supreet; Kumara, Soundar; Yao, Tao

    2012-07-01

    The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.

  18. Quantum Graph Analysis

    SciTech Connect

    Maunz, Peter Lukas Wilhelm; Sterk, Jonathan David; Lobser, Daniel; Parekh, Ojas D.; Ryan-Anderson, Ciaran

    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%.

  19. Graph Visualization for RDF Graphs with SPARQL-EndPoints

    SciTech Connect

    Sukumar, Sreenivas R; Bond, Nathaniel

    2014-07-11

    RDF graphs are hard to visualize as triples. This software module is a web interface that connects to a SPARQL endpoint and retrieves graph data that the user can explore interactively and seamlessly. The software written in python and JavaScript has been tested to work on screens as little as the smart phones to large screens such as EVEREST.

  20. Quantization of gauge fields, graph polynomials and graph homology

    SciTech Connect

    Kreimer, Dirk; Sars, Matthias; Suijlekom, Walter D. van

    2013-09-15

    We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.

  1. Graph-based sampling for approximating global helical topologies of RNA.

    PubMed

    Kim, Namhee; Laing, Christian; Elmetwaly, Shereef; Jung, Segun; Curuksu, Jeremy; Schlick, Tamar

    2014-03-18

    A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.

  2. Graphs and Zero-Divisors

    ERIC Educational Resources Information Center

    Axtell, M.; Stickles, J.

    2010-01-01

    The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

  3. A PVS Graph Theory Library

    NASA Technical Reports Server (NTRS)

    Butler, Ricky W.; Sjogren, Jon A.

    1998-01-01

    This paper documents the NASA Langley PVS graph theory library. The library provides fundamental definitions for graphs, subgraphs, walks, paths, subgraphs generated by walks, trees, cycles, degree, separating sets, and four notions of connectedness. Theorems provided include Ramsey's and Menger's and the equivalence of all four notions of connectedness.

  4. Graphs as Statements of Belief.

    ERIC Educational Resources Information Center

    Lake, David

    2002-01-01

    Identifies points where beliefs are important when making decisions about how graphs are drawn. Describes a simple case of the reaction between 'bicarb soda' and orange or lemon juice and discusses how drawing a graph becomes a statement of belief. (KHR)

  5. A Collection of Features for Semantic Graphs

    SciTech Connect

    Eliassi-Rad, T; Fodor, I K; Gallagher, B

    2007-05-02

    Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.

  6. Graph Partitioning and Sequencing Software

    1995-09-19

    Graph partitioning is a fundemental problem in many scientific contexts. CHACO2.0 is a software package designed to partition and sequence graphs. CHACO2.0 allows for recursive application of several methods for finding small edge separators in weighted graphs. These methods include inertial, spectral, Kernighan Lin and multilevel methods in addition to several simpler strategies. Each of these approaches can be used to partition the graph into two, four, or eight pieces at each level of recursion.more » In addition, the Kernighan Lin method can be used to improve partitions generated by any of the other algorithms. CHACO2.0 can also be used to address various graph sequencing problems, with applications to scientific computing, database design, gene sequencing and other problems.« less

  7. Semi-Markov Graph Dynamics

    PubMed Central

    Raberto, Marco; Rapallo, Fabio; Scalas, Enrico

    2011-01-01

    In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245

  8. Path similarity skeleton graph matching.

    PubMed

    Bai, Xiang; Latecki, Longin Jan

    2008-07-01

    This paper presents a novel framework to for shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the shortest paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we completely ignore the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of shortest paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and occlusion.

  9. Comparison of Student Understanding of Line Graph Slope in Physics and Mathematics

    ERIC Educational Resources Information Center

    Planinic, Maja; Milin-Sipus, Zeljka; Katic, Helena; Susac, Ana; Ivanjek, Lana

    2012-01-01

    This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…

  10. Guidelines for Graphing Data with Microsoft[R] PowerPoint[TM

    ERIC Educational Resources Information Center

    Barton, Erin E.; Reichow, Brian; Wolery, Mark

    2007-01-01

    Graphs are vital components for analyzing data in the experimental analysis of behavior using single subject research methods. This paper extends the previous literature on the construction of single subject graphs by providing instructions for using Microsoft[R] Power Point[TM] and Microsoft[R] PowerPoint for Mac[R], and describes improved…

  11. Impact of a Spreadsheet Exploration on Secondary School Students' Understanding of Statistical Graphs

    ERIC Educational Resources Information Center

    Wu, Yingkang; Wong, Khoon Yoong

    2007-01-01

    This case study investigated the impact of a spreadsheet (EXCEL) exploration on the understanding of statistical graphs among twenty Singapore secondary school students of average ability. Four EXCEL templates were constructed to allow students to explore four aspects of statistical graphs: zero in scale, effect of different scales, size…

  12. Semantic graphs and associative memories.

    PubMed

    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.

  13. Semantic graphs and associative memories

    NASA Astrophysics Data System (ADS)

    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.

  14. Graphing the Past

    ERIC Educational Resources Information Center

    Clary, Renee; Wandersee, James

    2014-01-01

    Renee Clary and James Wandersee implemented the Stratigraphy and Data Interpretation Project described in this article when they recognized that some students were having difficulties constructing appropriate graphics and interpreting their constructed graphics for an earlier mathematics-science project in their classrooms. They also previously…

  15. Analyzing and Synthesizing Phylogenies Using Tree Alignment Graphs

    PubMed Central

    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. PMID:24086118

  16. Multigraph: Reusable Interactive Data Graphs

    NASA Astrophysics Data System (ADS)

    Phillips, M. B.

    2010-12-01

    There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web

  17. Constructing Brambles

    NASA Astrophysics Data System (ADS)

    Chapelle, Mathieu; Mazoit, Frédéric; Todinca, Ioan

    Given an arbitrary graph G and a number k, it is well-known by a result of Seymour and Thomas [22] that G has treewidth strictly larger than k if and only if it has a bramble of order k + 2. Brambles are used in combinatorics as certificates proving that the treewidth of a graph is large. From an algorithmic point of view there are several algorithms computing tree-decompositions of G of width at most k, if such decompositions exist and the running time is polynomial for constant k. Nevertheless, when the treewidth of the input graph is larger than k, to our knowledge there is no algorithm constructing a bramble of order k + 2. We give here such an algorithm, running in {mathcal O}(n^{k+4}) time. For classes of graphs with polynomial number of minimal separators, we define a notion of compact brambles and show how to compute compact brambles of order k + 2 in polynomial time, not depending on k.

  18. Development of Image Selection Method Using Graph Cuts

    NASA Astrophysics Data System (ADS)

    Fuse, T.; Harada, R.

    2016-06-01

    3D models have been widely used by spread of many available free-software. Additionally, enormous images can be easily acquired, and images are utilized for creating the 3D models recently. The creation of 3D models by using huge amount of images, however, takes a lot of time and effort, and then efficiency for 3D measurement are required. In the efficient strategy, the accuracy of the measurement is also required. This paper develops an image selection method based on network design that means surveying network construction. The proposed method uses image connectivity graph. The image connectivity graph consists of nodes and edges. The nodes correspond to images to be used. The edges connected between nodes represent image relationships with costs as accuracies of orientation elements. For the efficiency, the image connectivity graph should be constructed with smaller number of edges. Once the image connectivity graph is built, the image selection problem is regarded as combinatorial optimization problem and the graph cuts technique can be applied. In the process of 3D reconstruction, low quality images and similar images are also extracted and removed. Through the experiments, the significance of the proposed method is confirmed. It implies potential to efficient and accurate 3D measurement.

  19. R-Matrices and the Tensor Product Graph Method

    NASA Astrophysics Data System (ADS)

    Gould, Mark D.; Zhang, Yao-Zhong

    2002-11-01

    A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

  20. R-Matrices and the Tensor Product Graph Method

    NASA Astrophysics Data System (ADS)

    Gould, Mark D.; Zhang, Yao-Zhong

    A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

  1. Graph anomalies in cyber communications

    SciTech Connect

    Vander Wiel, Scott A; Storlie, Curtis B; Sandine, Gary; Hagberg, Aric A; Fisk, Michael

    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.

  2. Yamabe type equations on graphs

    NASA Astrophysics Data System (ADS)

    Grigor'yan, Alexander; Lin, Yong; Yang, Yunyan

    2016-11-01

    Let G = (V , E) be a locally finite graph, Ω ⊂ V be a bounded domain, Δ be the usual graph Laplacian, and λ1 (Ω) be the first eigenvalue of -Δ with respect to Dirichlet boundary condition. Using the mountain pass theorem due to Ambrosetti-Rabinowitz, we prove that if α <λ1 (Ω), then for any p > 2, there exists a positive solution to

  3. Graph signatures for visual analytics.

    PubMed

    Wong, Pak Chung; Foote, Harlan; Chin, George; Mackey, Patrick; Perrine, Ken

    2006-01-01

    We present a visual analytics technique to explore graphs using the concept of a data signature. A data signature, in our context, is a multidimensional vector that captures the local topology information surrounding each graph node. Signature vectors extracted from a graph are projected onto a low-dimensional scatterplot through the use of scaling. The resultant scatterplot, which reflects the similarities of the vectors, allows analysts to examine the graph structures and their corresponding real-life interpretations through repeated use of brushing and linking between the two visualizations. The interpretation of the graph structures is based on the outcomes of multiple participatory analysis sessions with intelligence analysts conducted by the authors at the Pacific Northwest National Laboratory. The paper first uses three public domain data sets with either well-known or obvious features to explain the rationale of our design and illustrate its results. More advanced examples are then used in a customized usability study to evaluate the effectiveness and efficiency of our approach. The study results reveal not only the limitations and weaknesses of the traditional approach based solely on graph visualization, but also the advantages and strengths of our signature-guided approach presented in the paper.

  4. Expanding our understanding of students' use of graphs for learning physics

    NASA Astrophysics Data System (ADS)

    Laverty, James T.

    It is generally agreed that the ability to visualize functional dependencies or physical relationships as graphs is an important step in modeling and learning. However, several studies in Physics Education Research (PER) have shown that many students in fact do not master this form of representation and even have misconceptions about the meaning of graphs that impede learning physics concepts. Working with graphs in classroom settings has been shown to improve student abilities with graphs, particularly when the students can interact with them. We introduce a novel problem type in an online homework system, which requires students to construct the graphs themselves in free form, and requires no hand-grading by instructors. A study of pre/post-test data using the Test of Understanding Graphs in Kinematics (TUG-K) over several semesters indicates that students learn significantly more from these graph construction problems than from the usual graph interpretation problems, and that graph interpretation alone may not have any significant effect. The interpretation of graphs, as well as the representation translation between textual, mathematical, and graphical representations of physics scenarios, are frequently listed among the higher order thinking skills we wish to convey in an undergraduate course. But to what degree do we succeed? Do students indeed employ higher order thinking skills when working through graphing exercises? We investigate students working through a variety of graph problems, and, using a think-aloud protocol, aim to reconstruct the cognitive processes that the students go through. We find that to a certain degree, these problems become commoditized and do not trigger the desired higher order thinking processes; simply translating ``textbook-like'' problems into the graphical realm will not achieve any additional educational goals. Whether the students have to interpret or construct a graph makes very little difference in the methods used by the

  5. Khovanov homology of graph-links

    SciTech Connect

    Nikonov, Igor M

    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.

  6. Private Graphs - Access Rights on Graphs for Seamless Navigation

    NASA Astrophysics Data System (ADS)

    Dorner, W.; Hau, F.; Pagany, R.

    2016-06-01

    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.

  7. Subvoxel accurate graph search using non-Euclidean graph space.

    PubMed

    Abràmoff, Michael D; Wu, Xiaodong; Lee, Kyungmoo; Tang, Li

    2014-01-01

    Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT) images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.

  8. Sharing Teaching Ideas: Graphing Families of Curves Using Transformations of Reference Graphs

    ERIC Educational Resources Information Center

    Kukla, David

    2007-01-01

    This article provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.

  9. Building Specialized Multilingual Lexical Graphs Using Community Resources

    NASA Astrophysics Data System (ADS)

    Daoud, Mohammad; Boitet, Christian; Kageura, Kyo; Kitamoto, Asanobu; Mangeot, Mathieu; Daoud, Daoud

    We are describing methods for compiling domain-dedicated multilingual terminological data from various resources. We focus on collecting data from online community users as a main source, therefore, our approach depends on acquiring contributions from volunteers (explicit approach), and it depends on analyzing users' behaviors to extract interesting patterns and facts (implicit approach). As a generic repository that can handle the collected multilingual terminological data, we are describing the concept of dedicated Multilingual Preterminological Graphs MPGs, and some automatic approaches for constructing them by analyzing the behavior of online community users. A Multilingual Preterminological Graph is a special lexical resource that contains massive amount of terms related to a special domain. We call it preterminological, because it is a raw material that can be used to build a standardized terminological repository. Building such a graph is difficult using traditional approaches, as it needs huge efforts by domain specialists and terminologists. In our approach, we build such a graph by analyzing the access log files of the website of the community, and by finding the important terms that have been used to search in that website, and their association with each other. We aim at making this graph as a seed repository so multilingual volunteers can contribute. We are experimenting this approach with the Digital Silk Road Project. We have used its access log files since its beginning in 2003, and obtained an initial graph of around 116000 terms. As an application, we used this graph to obtain a preterminological multilingual database that is serving a CLIR system for the DSR project.

  10. Visual graph query formulation and exploration: a new perspective on information retrieval at the edge

    NASA Astrophysics Data System (ADS)

    Kase, Sue E.; Vanni, Michelle; Knight, Joanne A.; Su, Yu; Yan, Xifeng

    2016-05-01

    Within operational environments decisions must be made quickly based on the information available. Identifying an appropriate knowledge base and accurately formulating a search query are critical tasks for decision-making effectiveness in dynamic situations. The spreading of graph data management tools to access large graph databases is a rapidly emerging research area of potential benefit to the intelligence community. A graph representation provides a natural way of modeling data in a wide variety of domains. Graph structures use nodes, edges, and properties to represent and store data. This research investigates the advantages of information search by graph query initiated by the analyst and interactively refined within the contextual dimensions of the answer space toward a solution. The paper introduces SLQ, a user-friendly graph querying system enabling the visual formulation of schemaless and structureless graph queries. SLQ is demonstrated with an intelligence analyst information search scenario focused on identifying individuals responsible for manufacturing a mosquito-hosted deadly virus. The scenario highlights the interactive construction of graph queries without prior training in complex query languages or graph databases, intuitive navigation through the problem space, and visualization of results in graphical format.

  11. Building dynamic population graph for accurate correspondence detection.

    PubMed

    Du, Shaoyi; Guo, Yanrong; Sanroma, Gerard; Ni, Dong; Wu, Guorong; Shen, Dinggang

    2015-12-01

    In medical imaging studies, there is an increasing trend for discovering the intrinsic anatomical difference across individual subjects in a dataset, such as hand images for skeletal bone age estimation. Pair-wise matching is often used to detect correspondences between each individual subject and a pre-selected model image with manually-placed landmarks. However, the large anatomical variability across individual subjects can easily compromise such pair-wise matching step. In this paper, we present a new framework to simultaneously detect correspondences among a population of individual subjects, by propagating all manually-placed landmarks from a small set of model images through a dynamically constructed image graph. Specifically, we first establish graph links between models and individual subjects according to pair-wise shape similarity (called as forward step). Next, we detect correspondences for the individual subjects with direct links to any of model images, which is achieved by a new multi-model correspondence detection approach based on our recently-published sparse point matching method. To correct those inaccurate correspondences, we further apply an error detection mechanism to automatically detect wrong correspondences and then update the image graph accordingly (called as backward step). After that, all subject images with detected correspondences are included into the set of model images, and the above two steps of graph expansion and error correction are repeated until accurate correspondences for all subject images are established. Evaluations on real hand X-ray images demonstrate that our proposed method using a dynamic graph construction approach can achieve much higher accuracy and robustness, when compared with the state-of-the-art pair-wise correspondence detection methods as well as a similar method but using static population graph.

  12. Exploring the computing literature using temporal graph visualization

    NASA Astrophysics Data System (ADS)

    Erten, Cesim; Harding, Philip J.; Kobourov, Stephen G.; Wampler, Kevin; Yee, Gary

    2004-06-01

    We present a system for the visualization of computing literature with an emphasis on collaboration patterns, interactions between related research specialties and the evolution of these characteristics through time. Our computing literature visualization system, has four major components: A mapping of bibliographical data to relational schema coupled with an RDBMS to store the relational data, an interactive GUI that allows queries and the dynamic construction of graphs, a temporal graph layout algorithm, and an interactive visualization tool. We use a novel technique for visualization of large graphs that evolve through time. Given a dynamic graph, the layout algorithm produces two-dimensional representations of each timeslice, while preserving the mental map of the graph from one slice to the next. A combined view, with all the timeslices can also be viewed and explored. For our analysis we use data from the Association of Computing Machinery's Digital Library of Scientific Literature which contains more than one hundred thousand research papers and authors. Our system can be found online at http://tgrip.cs.arizona.edu.

  13. Hierarchical sequencing of online social graphs

    NASA Astrophysics Data System (ADS)

    Andjelković, Miroslav; Tadić, Bosiljka; Maletić, Slobodan; Rajković, Milan

    2015-10-01

    In online communications, patterns of conduct of individual actors and use of emotions in the process can lead to a complex social graph exhibiting multilayered structure and mesoscopic communities. Using simplicial complexes representation of graphs, we investigate in-depth topology of the online social network constructed from MySpace dialogs which exhibits original community structure. A simulation of emotion spreading in this network leads to the identification of two emotion-propagating layers. Three topological measures are introduced, referred to as the structure vectors, which quantify graph's architecture at different dimension levels. Notably, structures emerging through shared links, triangles and tetrahedral faces, frequently occur and range from tree-like to maximal 5-cliques and their respective complexes. On the other hand, the structures which spread only negative or only positive emotion messages appear to have much simpler topology consisting of links and triangles. The node's structure vector represents the number of simplices at each topology level in which the node resides and the total number of such simplices determines what we define as the node's topological dimension. The presented results suggest that the node's topological dimension provides a suitable measure of the social capital which measures the actor's ability to act as a broker in compact communities, the so called Simmelian brokerage. We also generalize the results to a wider class of computer-generated networks. Investigating components of the node's vector over network layers reveals that same nodes develop different socio-emotional relations and that the influential nodes build social capital by combining their connections in different layers.

  14. Sequential visibility-graph motifs

    NASA Astrophysics Data System (ADS)

    Iacovacci, Jacopo; Lacasa, Lucas

    2016-04-01

    Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility-graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated with general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable of distinguishing among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.

  15. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  16. Graph Analytics for Signature Discovery

    SciTech Connect

    Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh; Lo, Chaomei

    2013-06-01

    Within large amounts of seemingly unstructured data it can be diffcult to find signatures of events. In our work we transform unstructured data into a graph representation. By doing this we expose underlying structure in the data and can take advantage of existing graph analytics capabilities, as well as develop new capabilities. Currently we focus on applications in cybersecurity and communication domains. Within cybersecurity we aim to find signatures for perpetrators using the pass-the-hash attack, and in communications we look for emails or phone calls going up or down a chain of command. In both of these areas, and in many others, the signature we look for is a path with certain temporal properties. In this paper we discuss our methodology for finding these temporal paths within large graphs.

  17. Quantum snake walk on graphs

    SciTech Connect

    Rosmanis, Ansis

    2011-02-15

    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.

  18. Synchronizability of random rectangular graphs

    SciTech Connect

    Estrada, Ernesto Chen, Guanrong

    2015-08-15

    Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.

  19. Midlet Navigation Graphs in JML

    NASA Astrophysics Data System (ADS)

    Mostowski, Wojciech; Poll, Erik

    In the context of the EU project Mobius on Proof Carrying Code for Java programs (midlets) on mobile devices, we present a way to express midlet navigation graphs in JML. Such navigation graphs express certain security policies for a midlet. The resulting JML specifications can be automatically checked with the static checker ESC/Java2. Our work was guided by a realistically sized case study developed as demonstrator in the project. We discuss practical difficulties with creating efficient and meaningful JML specifications for automatic verification with a lightweight verification tool such as ESC/Java2, and the potential use of these specifications for PCC.

  20. Aligning Biomolecular Networks Using Modular Graph Kernels

    NASA Astrophysics Data System (ADS)

    Towfic, Fadi; Greenlee, M. Heather West; Honavar, Vasant

    Comparative analysis of biomolecular networks constructed using measurements from different conditions, tissues, and organisms offer a powerful approach to understanding the structure, function, dynamics, and evolution of complex biological systems. We explore a class of algorithms for aligning large biomolecular networks by breaking down such networks into subgraphs and computing the alignment of the networks based on the alignment of their subgraphs. The resulting subnetworks are compared using graph kernels as scoring functions. We provide implementations of the resulting algorithms as part of BiNA, an open source biomolecular network alignment toolkit. Our experiments using Drosophila melanogaster, Saccharomyces cerevisiae, Mus musculus and Homo sapiens protein-protein interaction networks extracted from the DIP repository of protein-protein interaction data demonstrate that the performance of the proposed algorithms (as measured by % GO term enrichment of subnetworks identified by the alignment) is competitive with some of the state-of-the-art algorithms for pair-wise alignment of large protein-protein interaction networks. Our results also show that the inter-species similarity scores computed based on graph kernels can be used to cluster the species into a species tree that is consistent with the known phylogenetic relationships among the species.

  1. Visibility Graph Based Time Series Analysis.

    PubMed

    Stephen, Mutua; Gu, Changgui; Yang, Huijie

    2015-01-01

    Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.

  2. Visibility Graph Based Time Series Analysis

    PubMed Central

    Stephen, Mutua; Gu, Changgui; Yang, Huijie

    2015-01-01

    Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it’s microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks. PMID:26571115

  3. Thermodynamic characterization of networks using graph polynomials

    NASA Astrophysics Data System (ADS)

    Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.

    2015-09-01

    In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.

  4. Boosting for multi-graph classification.

    PubMed

    Wu, Jia; Pan, Shirui; Zhu, Xingquan; Cai, Zhihua

    2015-03-01

    In this paper, we formulate a novel graph-based learning problem, multi-graph classification (MGC), which aims to learn a classifier from a set of labeled bags each containing a number of graphs inside the bag. A bag is labeled positive, if at least one graph in the bag is positive, and negative otherwise. Such a multi-graph representation can be used for many real-world applications, such as webpage classification, where a webpage can be regarded as a bag with texts and images inside the webpage being represented as graphs. This problem is a generalization of multi-instance learning (MIL) but with vital differences, mainly because instances in MIL share a common feature space whereas no feature is available to represent graphs in a multi-graph bag. To solve the problem, we propose a boosting based multi-graph classification framework (bMGC). Given a set of labeled multi-graph bags, bMGC employs dynamic weight adjustment at both bag- and graph-levels to select one subgraph in each iteration as a weak classifier. In each iteration, bag and graph weights are adjusted such that an incorrectly classified bag will receive a higher weight because its predicted bag label conflicts to the genuine label, whereas an incorrectly classified graph will receive a lower weight value if the graph is in a positive bag (or a higher weight if the graph is in a negative bag). Accordingly, bMGC is able to differentiate graphs in positive and negative bags to derive effective classifiers to form a boosting model for MGC. Experiments and comparisons on real-world multi-graph learning tasks demonstrate the algorithm performance.

  5. Standard Distributions: One Graph Fits All

    ERIC Educational Resources Information Center

    Wagner, Clifford H.

    2007-01-01

    Standard distributions are ubiquitous but not unique. With suitable scaling, the graph of a standard distribution serves as the graph for every distribution in the family. The standard exponential can easily be taught in elementary statistics courses.

  6. Understanding Conic Sections Using Alternate Graph Paper

    ERIC Educational Resources Information Center

    Brown, Elizabeth M.; Jones, Elizabeth

    2006-01-01

    This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.

  7. Graphing and Social Studies: An Interdisciplinary Activity.

    ERIC Educational Resources Information Center

    Brehm, Julia L.

    1996-01-01

    Describes a graphing activity that promotes mathematical connections with social studies lessons. Students should be familiar with graphing on the Cartesian coordinate system to play this variation of the game Battleship on maps of various regions of the world. (AIM)

  8. Comparison Graph of Sea Ice Minimum - 2010

    NASA Video Gallery

    This animated graph tracks the retreat of sea ice, measured in millions of square kilometers, averaged from the start of the satellite record in 1979 through 2000 (white). Next, the graph follows t...

  9. Mathematical Minute: Rotating a Function Graph

    ERIC Educational Resources Information Center

    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.

  10. Dr.L: Distributed Recursive (Graph) Layout

    2007-11-19

    Dr. L provides two-dimensional visualizations of very large abstract graph structures. it can be used for data mining applications including biology, scientific literature, and social network analysis. Dr. L is a graph layout program that uses a multilevel force-directed algorithm. A graph is input and drawn using a force-directed algorithm based on simulated annealing. The resulting layout is clustered using a single link algorithm. This clustering is used to produce a coarsened graph (fewer nodes)more » which is then re-drawn. this process is repeated until a sufficiently small graph is produced. The smallest graph is drawn and then used as a basis for drawing the original graph by refining the series of coarsened graphs that were produced. The layout engine can be run in serial or in parallel.« less

  11. Box graphs and resolutions II: From Coulomb phases to fiber faces

    NASA Astrophysics Data System (ADS)

    Braun, Andreas P.; Schäfer-Nameki, Sakura

    2016-04-01

    Box graphs, or equivalently Coulomb phases of three-dimensional N = 2 supersymmetric gauge theories with matter, give a succinct, comprehensive and elegant characterization of crepant resolutions of singular elliptically fibered varieties. Furthermore, the box graphs predict that the phases are organized in terms of a network of flop transitions. The geometric construction of the resolutions associated to the phases is, however, a difficult problem. Here, we identify a correspondence between box graphs for the gauge algebras su (2 k + 1) with resolutions obtained using toric tops and generalizations thereof. Moreover, flop transitions between different such resolutions agree with those predicted by the box graphs. Our results thereby provide explicit realizations of the box graph resolutions.

  12. Microcomputer Unit: Graphing Straight Lines.

    ERIC Educational Resources Information Center

    Hastings, Ellen H.; Yates, Daniel S.

    1983-01-01

    The material is designed to help pupils investigate how the value for slope in the equation of a line affects the inclination for the graph of an equation. A program written in BASIC designed to run on an Apple microcomputer is included. Worksheet masters for duplication are provided. (MP)

  13. Situating Graphs as Workplace Knowledge

    ERIC Educational Resources Information Center

    Noss, Richard; Bakker, Arthur; Hoyles, Celia; Kent, Phillip

    2007-01-01

    We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the…

  14. Fibonacci Identities, Matrices, and Graphs

    ERIC Educational Resources Information Center

    Huang, Danrun

    2005-01-01

    General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…

  15. Box graphs and singular fibers

    NASA Astrophysics Data System (ADS)

    Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schafer-Nameki, Sakura

    2014-05-01

    We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as "flopping" of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6, E7 and E 8.

  16. Affect and Graphing Calculator Use

    ERIC Educational Resources Information Center

    McCulloch, Allison W.

    2011-01-01

    This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…

  17. Ancestral Genres of Mathematical Graphs

    ERIC Educational Resources Information Center

    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…

  18. Humidity Graphs for All Seasons.

    ERIC Educational Resources Information Center

    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)

  19. Graphs and Enhancing Maple Multiplication.

    ERIC Educational Resources Information Center

    Cecil, David R.; Wang, Rongdong

    2002-01-01

    Description of a technique in Maple programming language that automatically prints all paths of any desired length along with the name of each vertex, proceeding in order from the beginning vertex to the ending vertex for a given graph. (Author/MM)

  20. Control by quantum dynamics on graphs

    SciTech Connect

    Godsil, Chris; Severini, Simone

    2010-05-15

    We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies of sparse graphs, the results translate into continuous-time quantum walks for universal computation.

  1. Sexually Transmitted Diseases on Bipartite Graph

    NASA Astrophysics Data System (ADS)

    Wen, Luo-Sheng; Zhong, Jiang; Yang, Xiao-Fan

    2009-01-01

    We study the susceptible-infected-susceptible (SIS) epidemic model on bipartite graph. According to the difference of sex conception in western and oriental nations, we construct the Barabási Albert-Barabási Albert (BA-BA) model and Barabási-Albert Homogeneity (BA-HO) model for sexually transmitted diseases (STDs). Applying the rate equation approach, the positive equilibria of both models are given analytically. We find that the ratio between infected females and infected males is distinctly different in both models and the infected density in the BA-HO model is much less than that in the BA-BA model. These results explain that the countries with small ratio have less infected density than those with large ratio. Our numerical simulations verify these theoretical results.

  2. Efficient broadcast on random geometric graphs

    SciTech Connect

    Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias; Sauerwald, Thomas

    2009-01-01

    A Randon Geometric Graph (RGG) is constructed by distributing n nodes uniformly at random in the unit square and connecting two nodes if their Euclidean distance is at most r, for some prescribed r. They analyze the following randomized broadcast algorithm on RGGs. At the beginning, there is only one informed node. Then in each round, each informed node chooses a neighbor uniformly at random and informs it. They prove that this algorithm informs every node in the largest component of a RGG in {Omicron}({radical}n/r) rounds with high probability. This holds for any value of r larger than the critical value for the emergence of a giant component. In particular, the result implies that the diameter of the giant component is {Theta}({radical}n/r).

  3. Chemical Applications of Graph Theory: Part II. Isomer Enumeration.

    ERIC Educational Resources Information Center

    Hansen, Peter J.; Jurs, Peter C.

    1988-01-01

    Discusses the use of graph theory to aid in the depiction of organic molecular structures. Gives a historical perspective of graph theory and explains graph theory terminology with organic examples. Lists applications of graph theory to current research projects. (ML)

  4. My Bar Graph Tells a Story

    ERIC Educational Resources Information Center

    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…

  5. So Many Graphs, So Little Time

    ERIC Educational Resources Information Center

    Wall, Jennifer J.; Benson, Christine C.

    2009-01-01

    Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…

  6. Collaborative Robotic Instruction: A Graph Teaching Experience

    ERIC Educational Resources Information Center

    Mitnik, Ruben; Recabarren, Matias; Nussbaum, Miguel; Soto, Alvaro

    2009-01-01

    Graphing is a key skill in the study of Physics. Drawing and interpreting graphs play a key role in the understanding of science, while the lack of these has proved to be a handicap and a limiting factor in the learning of scientific concepts. It has been observed that despite the amount of previous graph-working experience, students of all ages…

  7. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  8. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 47 Telecommunication 5 2011-10-01 2011-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  9. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 47 Telecommunication 5 2013-10-01 2013-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  10. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 47 Telecommunication 5 2012-10-01 2012-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  11. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 47 Telecommunication 5 2014-10-01 2014-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  12. NextSearch: A Search Engine for Mass Spectrometry Data against a Compact Nucleotide Exon Graph.

    PubMed

    Kim, Hyunwoo; Park, Heejin; Paek, Eunok

    2015-07-01

    Proteogenomics research has been using six-frame translation of the whole genome or amino acid exon graphs to overcome the limitations of reference protein sequence database; however, six-frame translation is not suitable for annotating genes that span over multiple exons, and amino acid exon graphs are not convenient to represent novel splice variants and exon skipping events between exons of incompatible reading frames. We propose a proteogenomic pipeline NextSearch (Nucleotide EXon-graph Transcriptome Search) that is based on a nucleotide exon graph. This pipeline consists of constructing a compact nucleotide exon graph that systematically incorporates novel splice variations and a search tool that identifies peptides by directly searching the nucleotide exon graph against tandem mass spectra. Because our exon graph stores nucleotide sequences, it can easily represent novel splice variations and exon skipping events between incompatible reading frame exons. Searching for peptide identification is performed against this nucleotide exon graph, without converting it into a protein sequence in FASTA format, achieving an order of magnitude reduction in the size of the sequence database storage. NextSearch outputs the proteome-genome/transcriptome mapping results in a general feature format (GFF) file, which can be visualized by public tools such as the UCSC Genome Browser.

  13. Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

    SciTech Connect

    Rudinger, Kenneth; Gamble, John King; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.

    2013-07-01

    Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erences in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.

  14. Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

    DOE PAGES

    Rudinger, Kenneth; Gamble, John King; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.

    2013-07-01

    Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

  15. Fast graph operations in quantum computation

    NASA Astrophysics Data System (ADS)

    Zhao, Liming; Pérez-Delgado, Carlos A.; Fitzsimons, Joseph F.

    2016-03-01

    The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure, which allows for more efficient manipulation and comparison of graphs than any possible classical structure. We introduce efficient algorithms for many transformation and comparison operations on graphs represented as graph states, and prove that no classical data structure can have similar performance for the full set of operations studied.

  16. Methodologies and Metrics for Assessing the Strength of Relationships between Entities within Semantic Graphs

    SciTech Connect

    Hickling, T L; Hanley, W G

    2005-09-29

    Semantic graphs are becoming a valuable tool for organizing and discovering information in an increasingly complex analysis environment. This paper investigates the use of graph topology to measure the strength of relationships in a semantic graph. These relationships are comprised of some number of distinct paths, whose length and configuration jointly characterize the strength of association. We explore these characteristics through the use of three distinct algorithms respectively based upon an electrical conductance model, Newman and Girvan's measure of betweenness [5], and cutsets. Algorithmic performance is assessed based upon a collection of partially ordered subgraphs which were constructed according to our subjective beliefs regarding strength of association.

  17. Constrained Graph Optimization: Interdiction and Preservation Problems

    SciTech Connect

    Schild, Aaron V

    2012-07-30

    The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.

  18. Hierarchical structure of the logical Internet graph

    NASA Astrophysics Data System (ADS)

    Ge, Zihui; Figueiredo, Daniel R.; Jaiswal, Sharad; Gao, Lixin

    2001-07-01

    The study of the Internet topology has recently received much attention from the research community. In particular, the observation that the network graph has interesting properties, such as power laws, that might be explored in a myriad of ways. Most of the work in characterizing the Internet graph is based on the physical network graph, i.e., the connectivity graph. In this paper we investigate how logical relationships between nodes of the AS graph can be used to gain insight to its structure. We characterize the logical graph using various metrics and identify the presence of power laws in the number of customers that a provider has. Using these logical relationships we define a structural model of the AS graph. The model highlights the hierarchical nature of logical relationships and the preferential connection to larger providers. We also investigate the consistency of this model over time and observe interesting properties of the hierarchical structure.

  19. Molecular graph convolutions: moving beyond fingerprints.

    PubMed

    Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick

    2016-08-01

    Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement. PMID:27558503

  20. The Feynman Identity for Planar Graphs

    NASA Astrophysics Data System (ADS)

    da Costa, G. A. T. F.

    2016-08-01

    The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.

  1. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  2. Molecular graph convolutions: moving beyond fingerprints.

    PubMed

    Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick

    2016-08-01

    Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.

  3. On a programming language for graph algorithms

    NASA Technical Reports Server (NTRS)

    Rheinboldt, W. C.; Basili, V. R.; Mesztenyi, C. K.

    1971-01-01

    An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.

  4. Molecular graph convolutions: moving beyond fingerprints

    NASA Astrophysics Data System (ADS)

    Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick

    2016-08-01

    Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular "graph convolutions", a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph---atoms, bonds, distances, etc.---which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.

  5. Subgraph-Based Filterbanks for Graph Signals

    NASA Astrophysics Data System (ADS)

    Tremblay, Nicolas; Borgnat, Pierre

    2016-08-01

    We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the design is based on a partition of the graph in connected subgraphs. Coarsening is achieved by defining one "supernode" for each subgraph and the edges for this coarsened graph derives from the connectivity between the subgraphs. Unlike the "one every two nodes" downsampling on bipartite graphs, this coarsening operation does not have an exact formulation in the graph Fourier domain. Instead, we rely on the local Fourier bases of each subgraph to define filtering operations. We apply successfully this method to decompose graph signals, and show promising performance on compression and denoising.

  6. Line graphs as social networks

    NASA Astrophysics Data System (ADS)

    Krawczyk, M. J.; Muchnik, L.; Mańka-Krasoń, A.; Kułakowski, K.

    2011-07-01

    It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10 6 people.

  7. Graph distance for complex networks

    NASA Astrophysics Data System (ADS)

    Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki

    2016-10-01

    Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.

  8. Graph distance for complex networks

    PubMed Central

    Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki

    2016-01-01

    Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions. PMID:27725690

  9. Graph theoretic analysis of structural connectivity across the spectrum of Alzheimer's disease: The importance of graph creation methods.

    PubMed

    Phillips, David J; McGlaughlin, Alec; Ruth, David; Jager, Leah R; Soldan, Anja

    2015-01-01

    Graph theory is increasingly being used to study brain connectivity across the spectrum of Alzheimer's disease (AD), but prior findings have been inconsistent, likely reflecting methodological differences. We systematically investigated how methods of graph creation (i.e., type of correlation matrix and edge weighting) affect structural network properties and group differences. We estimated the structural connectivity of brain networks based on correlation maps of cortical thickness obtained from MRI. Four groups were compared: 126 cognitively normal older adults, 103 individuals with Mild Cognitive Impairment (MCI) who retained MCI status for at least 3 years (stable MCI), 108 individuals with MCI who progressed to AD-dementia within 3 years (progressive MCI), and 105 individuals with AD-dementia. Small-world measures of connectivity (characteristic path length and clustering coefficient) differed across groups, consistent with prior studies. Groups were best discriminated by the Randić index, which measures the degree to which highly connected nodes connect to other highly connected nodes. The Randić index differentiated the stable and progressive MCI groups, suggesting that it might be useful for tracking and predicting the progression of AD. Notably, however, the magnitude and direction of group differences in all three measures were dependent on the method of graph creation, indicating that it is crucial to take into account how graphs are constructed when interpreting differences across diagnostic groups and studies. The algebraic connectivity measures showed few group differences, independent of the method of graph construction, suggesting that global connectivity as it relates to node degree is not altered in early AD.

  10. Fast dual graph-based hotspot detection

    NASA Astrophysics Data System (ADS)

    Kahng, Andrew B.; Park, Chul-Hong; Xu, Xu

    2006-10-01

    features or "L-shaped" features; (2) face-level detection finds the pattern-related hotspots which span several close features; and (3) merged-face-level detection finds hotspots with more complex patterns. To find the merged faces which capture the pattern-related hotspots, we propose to convert the layout into a planar graph G. We then construct its dual graph G D and sort the dual nodes according to their weights. We merge the sorted dual nodes (i.e., the faces in G) that share a given feature, in sequence. We have tested our flow on several industry testcases. The experimental results show that our method is promising: for a 90nm metal layer with 17 hotspots detected by commercial optical rule check (ORC) tools, our method can detect all of them while the overall runtime improvement is more than 287X.

  11. Relativity on Rotated Graph Paper

    NASA Astrophysics Data System (ADS)

    Salgado, Roberto

    2011-11-01

    We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid (called light-clock diamonds) represent ticks of an inertial observer's lightclock. We show that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra.

  12. STRUCTURAL ANNOTATION OF EM IMAGES BY GRAPH CUT

    SciTech Connect

    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).

  13. Graph-based layout analysis for PDF documents

    NASA Astrophysics Data System (ADS)

    Xu, Canhui; Tang, Zhi; Tao, Xin; Li, Yun; Shi, Cao

    2013-03-01

    To increase the flexibility and enrich the reading experience of e-book on small portable screens, a graph based method is proposed to perform layout analysis on Portable Document Format (PDF) documents. Digital born document has its inherent advantages like representing texts and fractional images in explicit form, which can be straightforwardly exploited. To integrate traditional image-based document analysis and the inherent meta-data provided by PDF parser, the page primitives including text, image and path elements are processed to produce text and non text layer for respective analysis. Graph-based method is developed in superpixel representation level, and page text elements corresponding to vertices are used to construct an undirected graph. Euclidean distance between adjacent vertices is applied in a top-down manner to cut the graph tree formed by Kruskal's algorithm. And edge orientation is then used in a bottom-up manner to extract text lines from each sub tree. On the other hand, non-textual objects are segmented by connected component analysis. For each segmented text and non-text composite, a 13-dimensional feature vector is extracted for labelling purpose. The experimental results on selected pages from PDF books are presented.

  14. Scale-free Graphs for General Aviation Flight Schedules

    NASA Technical Reports Server (NTRS)

    Alexandov, Natalia M. (Technical Monitor); Kincaid, Rex K.

    2003-01-01

    In the late 1990s a number of researchers noticed that networks in biology, sociology, and telecommunications exhibited similar characteristics unlike standard random networks. In particular, they found that the cummulative degree distributions of these graphs followed a power law rather than a binomial distribution and that their clustering coefficients tended to a nonzero constant as the number of nodes, n, became large rather than O(1/n). Moreover, these networks shared an important property with traditional random graphs as n becomes large the average shortest path length scales with log n. This latter property has been coined the small-world property. When taken together these three properties small-world, power law, and constant clustering coefficient describe what are now most commonly referred to as scale-free networks. Since 1997 at least six books and over 400 articles have been written about scale-free networks. In this manuscript an overview of the salient characteristics of scale-free networks. Computational experience will be provided for two mechanisms that grow (dynamic) scale-free graphs. Additional computational experience will be given for constructing (static) scale-free graphs via a tabu search optimization approach. Finally, a discussion of potential applications to general aviation networks is given.

  15. A VLSI decomposition of the deBruijn graph

    NASA Technical Reports Server (NTRS)

    Collins, Oliver; Dolinar, Sam; Mceliece, Robert; Pollara, Fabrizio

    1992-01-01

    The nth order deBruijn graph Bn is the state diagram for an n-stage binary shift register. It is a directed graph with 2 to the n vertices, each labeled with an n-bit binary string, and 2 to the n+1 edges, each labeled with an (n+1)-bit binary string. It is shown that Bn can be built by appropriately connecting together with extra edges many isomorphic copies of a fixed graph, which is called a building block for Bn. The efficiency of such a building block is refined as the fraction of the edges of Bn which are present in the copies of the building block. It is then shown that for any alpha less than 1, there exists a graph which is a building block for Bn of efficiency greater than alpha for all sufficiently large n. The results are illustrated by showing how a special hierarchical family of building blocks has been used to construct a very large Viterbi decoder which will be used on the Galileo mission.

  16. Graph run-length matrices for histopathological image segmentation.

    PubMed

    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.

  17. Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software

    NASA Astrophysics Data System (ADS)

    Zucker, Andrew; Kay, Rachel; Staudt, Carolyn

    2014-06-01

    Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding graphs. SmartGraphs allows students to interact with graphs and provides hints and scaffolding to help students, if they need help. SmartGraphs activities can be authored to be useful in teaching and learning a variety of topics that use graphs (such as slope, velocity, half-life, and global warming). A 2-year experimental study in physical science classrooms was conducted with dozens of teachers and thousands of students. In the first year, teachers were randomly assigned to experimental or control conditions. Data show that students of teachers who use SmartGraphs as a supplement to normal instruction make greater gains understanding graphs than control students studying the same content using the same textbooks, but without SmartGraphs. Additionally, teachers believe that the SmartGraphs activities help students meet learning goals in the physical science course, and a great majority reported they would use the activities with students again. In the second year of the study, several specific variations of SmartGraphs were researched to help determine what makes SmartGraphs effective.

  18. Computational Genomics Using Graph Theory

    NASA Astrophysics Data System (ADS)

    Schlick, Tamar

    2005-03-01

    With exciting new discoveries concerning RNA's regulatory cellular roles in gene expression, structural and functional problems associated with DNA's venerable cousin have come to the forefront. RNA folding, for example, is analogous to the well-known protein folding problem, and seeks to link RNA's primary sequence with secondary and tertiary structures. As a single-stranded polynucleotide, RNA's secondary structures are defined by a network of hydrogen bonds, which lead to a variety of stems, loops, junctions, bulges, and other motifs. Supersecondary pseudoknot structures can also occur and, together, lead to RNA's complex tertiary interactions stabilized by salt and solvent ions in the natural cellular milieu. Besides folding, challenges in RNA research include identifying locations and functions of RNA genes, discovering RNA's structural repertoire (folding motifs), designing novel RNAs, and developing new antiviral and antibiotic compounds composed of, or targeting, RNAs. In this talk, I will describe some of these new biological findings concerning RNA and present an approach using graph theory (network theory) to represent RNA secondary structures. Because the RNA motif space using graphs is vastly smaller than RNA's sequence space, many problems related to analyzing and discovering new RNAs can be simplified and studied systematically. Some preliminary applications to designing novel RNAs will also be described.Related ReadingH. H. Gan, S. Pasquali, and T. Schlick, ``A Survey of Existing RNAs using Graph Theory with Implications to RNA Analysis and Design,'' Nuc. Acids Res. 31: 2926--2943 (2003). J. Zorn, H. H. Gan, N. Shiffeldrim, and T. Schlick, ``Structural Motifs in Ribosomal RNAs: Implications for RNA Design and Genomics,'' Biopolymers 73: 340--347 (2004). H. H. Gan, D. Fera, J. Zorn, M. Tang, N. Shiffeldrim, U. Laserson, N. Kim, and T. Schlick,``RAG: RNA-As-Graphs Database -- Concepts, Analysis, and Features,'' Bioinformatics 20: 1285--1291 (2004). U

  19. Local dependence in random graph models: characterization, properties and statistical inference

    PubMed Central

    Schweinberger, Michael; Handcock, Mark S.

    2015-01-01

    Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

  20. JavaGenes: Evolving Graphs with Crossover

    NASA Technical Reports Server (NTRS)

    Globus, Al; Atsatt, Sean; Lawton, John; Wipke, Todd

    2000-01-01

    Genetic algorithms usually use string or tree representations. We have developed a novel crossover operator for a directed and undirected graph representation, and used this operator to evolve molecules and circuits. Unlike strings or trees, a single point in the representation cannot divide every possible graph into two parts, because graphs may contain cycles. Thus, the crossover operator is non-trivial. A steady-state, tournament selection genetic algorithm code (JavaGenes) was written to implement and test the graph crossover operator. All runs were executed by cycle-scavagging on networked workstations using the Condor batch processing system. The JavaGenes code has evolved pharmaceutical drug molecules and simple digital circuits. Results to date suggest that JavaGenes can evolve moderate sized drug molecules and very small circuits in reasonable time. The algorithm has greater difficulty with somewhat larger circuits, suggesting that directed graphs (circuits) are more difficult to evolve than undirected graphs (molecules), although necessary differences in the crossover operator may also explain the results. In principle, JavaGenes should be able to evolve other graph-representable systems, such as transportation networks, metabolic pathways, and computer networks. However, large graphs evolve significantly slower than smaller graphs, presumably because the space-of-all-graphs explodes combinatorially with graph size. Since the representation strongly affects genetic algorithm performance, adding graphs to the evolutionary programmer's bag-of-tricks should be beneficial. Also, since graph evolution operates directly on the phenotype, the genotype-phenotype translation step, common in genetic algorithm work, is eliminated.

  1. On the spectral distribution of distance-k graph of free product graphs

    NASA Astrophysics Data System (ADS)

    Arizmendi, Octavio; Gaxiola, Tulio

    2016-08-01

    We calculate the distribution with respect to the vacuum state of the distance-k graph of a d-regular tree. From this result we show that the distance-k graph of a d-regular graphs converges to the distribution of the distance-k graph of a regular tree. Finally, we prove that, properly normalized, the asymptotic distributions of distance-k graphs of the d-fold free product graph, as d tends to infinity, is given by the distribution of Pk(s), where s is a semicirlce random variable and Pk is the kth Chebychev polynomial.

  2. Area law for random graph states

    NASA Astrophysics Data System (ADS)

    Collins, Benoît; Nechita, Ion; Życzkowski, Karol

    2013-08-01

    Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed according to the Haar measure, while each edge of the graph represents a bipartite, maximally entangled state. For any splitting of the graph into two parts we consider the corresponding partition of the quantum system and compute the average entropy of entanglement. First, in the special case where the partition does not cross any vertex of the graph, we show that the area law is satisfied exactly. In the general case, we show that the entropy of entanglement obeys an area law on average, this time with a correction term that depends on the topologies of the graph and of the partition. The results obtained are applied to the problem of distribution of quantum entanglement in a quantum network with prescribed topology.

  3. Replica methods for loopy sparse random graphs

    NASA Astrophysics Data System (ADS)

    Coolen, ACC

    2016-03-01

    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. This paper is dedicated to the memory of our colleague and friend Jun-Ichi Inoue, with whom the author has had the great pleasure and privilege of collaborating.

  4. Graph Frequency Analysis of Brain Signals

    NASA Astrophysics Data System (ADS)

    Huang, Weiyu; Goldsberry, Leah; Wymbs, Nicholas F.; Grafton, Scott T.; Bassett, Danielle S.; Ribeiro, Alejandro

    2016-10-01

    This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed, and recognize the most contributing and important frequency signatures at different task familiarity.

  5. Fast generation of sparse random kernel graphs

    SciTech Connect

    Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

    2015-09-10

    The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.

  6. Fast generation of sparse random kernel graphs

    DOE PAGES

    Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

    2015-09-10

    The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less

  7. Image clustering using fuzzy graph theory

    NASA Astrophysics Data System (ADS)

    Jafarkhani, Hamid; Tarokh, Vahid

    1999-12-01

    We propose an image clustering algorithm which uses fuzzy graph theory. First, we define a fuzzy graph and the concept of connectivity for a fuzzy graph. Then, based on our definition of connectivity we propose an algorithm which finds connected subgraphs of the original fuzzy graph. Each connected subgraph can be considered as a cluster. As an application of our algorithm, we consider a database of images. We calculate a similarity measure between any paris of images in the database and generate the corresponding fuzzy graph. The, we find the subgraphs of the resulting fuzzy graph using our algorithm. Each subgraph corresponds to a cluster. We apply our image clustering algorithm to the key frames of news programs to find the anchorperson clusters. Simulation results show that our algorithm is successful to find most of anchorperson frames from the database.

  8. Spectral correlations of individual quantum graphs.

    PubMed

    Gnutzmann, Sven; Altland, Alexander

    2005-11-01

    We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear -model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

  9. Spectral correlations of individual quantum graphs

    SciTech Connect

    Gnutzmann, Sven; Altland, Alexander

    2005-11-01

    We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear {sigma}-model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

  10. Breddin's graph for tectonic regimes

    NASA Astrophysics Data System (ADS)

    Célérier, Bernard; Séranne, Michel

    2001-05-01

    A simple graphical method is proposed to infer the tectonic regime from a fault and slip data set. An abacus is overlaid on a plot of the rake versus strike of the data. This yields the horizontal principal stress directions and a constraint on the stress tensor aspect ratio, in a manner similar to Breddin's graph for two-dimensional strain analysis. The main requirement is that one of the principal stress directions is close to the vertical. This method is illustrated on monophase synthetic and natural data, but is also expected to help sort out multiphase data sets.

  11. Naming on a Directed Graph

    NASA Astrophysics Data System (ADS)

    Gosti, Giorgio; Batchelder, William H.

    We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: the first proves that under certain topologies the system always converges to a name-object agreement; the second proves that if these conditions are not met the system may end up in a state in which sub-networks with different competing object-name associations coexist.

  12. The alignment-distribution graph

    NASA Technical Reports Server (NTRS)

    Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert

    1993-01-01

    Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment-distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.

  13. The alignment-distribution graph

    NASA Technical Reports Server (NTRS)

    Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert

    1993-01-01

    Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.

  14. Givental Graphs and Inversion Symmetry

    NASA Astrophysics Data System (ADS)

    Dunin-Barkowski, Petr; Shadrin, Sergey; Spitz, Loek

    2013-05-01

    Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.

  15. Graph algorithms in the titan toolkit.

    SciTech Connect

    McLendon, William Clarence, III; Wylie, Brian Neil

    2009-10-01

    Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.

  16. Evolutionary Games of Multiplayer Cooperation on Graphs.

    PubMed

    Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne

    2016-08-01

    There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

  17. Simple scale interpolator facilitates reading of graphs

    NASA Technical Reports Server (NTRS)

    Fetterman, D. E., Jr.

    1965-01-01

    Simple transparent overlay with interpolation scale facilitates accurate, rapid reading of graph coordinate points. This device can be used for enlarging drawings and locating points on perspective drawings.

  18. Evolutionary Games of Multiplayer Cooperation on Graphs.

    PubMed

    Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne

    2016-08-01

    There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.

  19. Generation of graph-state streams

    SciTech Connect

    Ballester, Daniel; Cho, Jaeyoon; Kim, M. S.

    2011-01-15

    We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atomlike qubit and the generation of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.

  20. Evolutionary Games of Multiplayer Cooperation on Graphs

    PubMed Central

    Arranz, Jordi; Traulsen, Arne

    2016-01-01

    There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

  1. Information Retrieval and Graph Analysis Approaches for Book Recommendation.

    PubMed

    Benkoussas, Chahinez; Bellot, Patrice

    2015-01-01

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

  2. GPD: a graph pattern diffusion kernel for accurate graph classification with applications in cheminformatics.

    PubMed

    Smalter, Aaron; Huan, Jun Luke; Jia, Yi; Lushington, Gerald

    2010-01-01

    Graph data mining is an active research area. Graphs are general modeling tools to organize information from heterogeneous sources and have been applied in many scientific, engineering, and business fields. With the fast accumulation of graph data, building highly accurate predictive models for graph data emerges as a new challenge that has not been fully explored in the data mining community. In this paper, we demonstrate a novel technique called graph pattern diffusion (GPD) kernel. Our idea is to leverage existing frequent pattern discovery methods and to explore the application of kernel classifier (e.g., support vector machine) in building highly accurate graph classification. In our method, we first identify all frequent patterns from a graph database. We then map subgraphs to graphs in the graph database and use a process we call "pattern diffusion" to label nodes in the graphs. Finally, we designed a graph alignment algorithm to compute the inner product of two graphs. We have tested our algorithm using a number of chemical structure data. The experimental results demonstrate that our method is significantly better than competing methods such as those kernel functions based on paths, cycles, and subgraphs.

  3. Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software

    ERIC Educational Resources Information Center

    Zucker, Andrew; Kay, Rachel; Staudt, Carolyn

    2014-01-01

    Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding…

  4. Clique percolation in random graphs

    NASA Astrophysics Data System (ADS)

    Li, Ming; Deng, Youjin; Wang, Bing-Hong

    2015-10-01

    As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l graphs, which gives not only the exact solutions of the critical point, but also the corresponding order parameter. Based on this, we prove theoretically that the fraction ψ of cliques in the giant clique cluster always makes a continuous phase transition as the classical percolation. However, the fraction ϕ of vertices in the giant clique cluster for l >1 makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l =1 . More interesting, our analysis shows that at the critical point, the order parameter ϕc for l >1 is neither 0 nor 1, but a constant depending on k and l . All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.

  5. Graph states of prime-power dimension from generalized CNOT quantum circuit.

    PubMed

    Chen, Lin; Zhou, D L

    2016-01-01

    We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401

  6. Graph states of prime-power dimension from generalized CNOT quantum circuit

    PubMed Central

    Chen, Lin; Zhou, D. L.

    2016-01-01

    We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401

  7. Graph states of prime-power dimension from generalized CNOT quantum circuit.

    PubMed

    Chen, Lin; Zhou, D L

    2016-06-07

    We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four.

  8. Enabling Graph Appliance for Genome Assembly

    SciTech Connect

    Singh, Rina; Graves, Jeffrey A; Lee, Sangkeun; Sukumar, Sreenivas R; Shankar, Mallikarjun

    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.

  9. Teaching Discrete Mathematics with Graphing Calculators.

    ERIC Educational Resources Information Center

    Masat, Francis E.

    Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…

  10. Student Reasoning about Graphs in Different Contexts

    ERIC Educational Resources Information Center

    Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

    2016-01-01

    This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…

  11. Universal spectral statistics in quantum graphs.

    PubMed

    Gnutzmann, Sven; Altland, Alexander

    2004-11-01

    We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.

  12. Graphs and Statistics: A Resource Handbook.

    ERIC Educational Resources Information Center

    New York State Education Dept., Albany. Bureau of General Education Curriculum Development.

    Graphical representation of statistical data is the focus of this resource handbook. Only graphs which present numerical information are discussed. Activities involving the making, interpreting, and use of various types of graphs and tables are included. Sections are also included which discuss statistical terms, normal distribution and…

  13. Using a Microcomputer for Graphing Practice.

    ERIC Educational Resources Information Center

    Beichner, Robert J.

    1986-01-01

    Describes a laboratory exercise that introduces physics students to graphing. Presents the program format and sample output of a computer simulation of an experiment which tests the effects of sound intensity on the crawling speed of a snail. Provides students with practice in making exponential or logarithmic graphs. (ML)

  14. Graphing Calculators: The Newest Revolution in Mathematics.

    ERIC Educational Resources Information Center

    Clutter, Martha

    1999-01-01

    Asserts that there are numerous advantages to using graphing calculators, including the teaching of higher-level thinking skills and allowing students to draw conclusions about what they are learning. However, mathematics educators face such challenges as teaching students when it is appropriate to use graphing calculators, course-content…

  15. Multi-A Graph Patrolling and Partitioning

    NASA Astrophysics Data System (ADS)

    Elor, Y.; Bruckstein, A. M.

    2012-12-01

    We introduce a novel multi agent patrolling algorithm inspired by the behavior of gas filled balloons. Very low capability ant-like agents are considered with the task of patrolling an unknown area modeled as a graph. While executing the proposed algorithm, the agents dynamically partition the graph between them using simple local interactions, every agent assuming the responsibility for patrolling his subgraph. Balanced graph partition is an emergent behavior due to the local interactions between the agents in the swarm. Extensive simulations on various graphs (environments) showed that the average time to reach a balanced partition is linear with the graph size. The simulations yielded a convincing argument for conjecturing that if the graph being patrolled contains a balanced partition, the agents will find it. However, we could not prove this. Nevertheless, we have proved that if a balanced partition is reached, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most twice the optimal so the patrol quality is at least half the optimal. In case of weighted graphs the patrol quality is at least (1)/(2){lmin}/{lmax} of the optimal where lmax (lmin) is the longest (shortest) edge in the graph.

  16. Cognitive Aids for Guiding Graph Comprehension

    ERIC Educational Resources Information Center

    Mautone, Patricia D.; Mayer, Richard E.

    2007-01-01

    This study sought to improve students' comprehension of scientific graphs by adapting scaffolding techniques used to aid text comprehension. In 3 experiments involving 121 female and 88 male college students, some students were shown cognitive aids prior to viewing 4 geography graphs whereas others were not; all students were then asked to write a…

  17. Pattern Perception and the Comprehension of Graphs.

    ERIC Educational Resources Information Center

    Pinker, Steven

    Three experiments tested the hypothesis that graphs convey information effectively because they can display global trends as geometric patterns that visual systems encode easily. A novel type of graph was invented in which angles/lengths of line segments joined end-to-end represented variables of rainfall and temperature of a set of months. It was…

  18. Developing Data Graph Comprehension. Third Edition

    ERIC Educational Resources Information Center

    Curcio, Frances

    2010-01-01

    Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…

  19. TI-83 Graphing Calculator Keystroke Guide.

    ERIC Educational Resources Information Center

    Panik, Cathy

    This document presents keystrokes for the Texas Instrument (TI-83) graphing calculator. After presenting some basic TI-83 keystrokes, activities for student practice are listed. This is followed by keystrokes for TI-83 advanced functions such as evaluating function values, finding the zero of a function, finding the intersection of two graphs,…

  20. Supplantation of Mental Operations on Graphs

    ERIC Educational Resources Information Center

    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…

  1. Graph Mining Meets the Semantic Web

    SciTech Connect

    Lee, Sangkeun; Sukumar, Sreenivas R; Lim, Seung-Hwan

    2015-01-01

    The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.

  2. Vortices and superfields on a graph

    SciTech Connect

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-15

    We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the 'theory space'. We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]{sup p} (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.

  3. Vortices and superfields on a graph

    NASA Astrophysics Data System (ADS)

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-01

    We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the “theory space.” We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]p (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.

  4. Structure and strategy in encoding simplified graphs

    NASA Technical Reports Server (NTRS)

    Schiano, Diane J.; Tversky, Barbara

    1992-01-01

    Tversky and Schiano (1989) found a systematic bias toward the 45-deg line in memory for the slopes of identical lines when embedded in graphs, but not in maps, suggesting the use of a cognitive reference frame specifically for encoding meaningful graphs. The present experiments explore this issue further using the linear configurations alone as stimuli. Experiments 1 and 2 demonstrate that perception and immediate memory for the slope of a test line within orthogonal 'axes' are predictable from purely structural considerations. In Experiments 3 and 4, subjects were instructed to use a diagonal-reference strategy in viewing the stimuli, which were described as 'graphs' only in Experiment 3. Results for both studies showed the diagonal bias previously found only for graphs. This pattern provides converging evidence for the diagonal as a cognitive reference frame in encoding linear graphs, and demonstrates that even in highly simplified displays, strategic factors can produce encoding biases not predictable solely from stimulus structure alone.

  5. Quantum graphs and random-matrix theory

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2015-07-01

    For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.

  6. GraphReduce: Large-Scale Graph Analytics on Accelerator-Based HPC Systems

    SciTech Connect

    Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen; Schwan, Karsten

    2015-09-30

    Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of both edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host and the device.

  7. GraphReduce: Processing Large-Scale Graphs on Accelerator-Based Systems

    SciTech Connect

    Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil; Schwan, Karsten

    2015-11-15

    Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host and device.

  8. Balanced Paths in Colored Graphs

    NASA Astrophysics Data System (ADS)

    Bianco, Alessandro; Faella, Marco; Mogavero, Fabio; Murano, Aniello

    We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two notions can be viewed as refinements of the classical notion of fair path, whose simplest form checks whether all colors occur infinitely often. Our notions provide stronger criteria, particularly suitable for scheduling applications based on a coarse-grained model of the jobs involved. We show that both problems are solvable in polynomial time, by reducing them to the feasibility of a linear program.

  9. Development of antibiotic regimens using graph based evolutionary algorithms.

    PubMed

    Corns, Steven M; Ashlock, Daniel A; Bryden, Kenneth M

    2013-12-01

    This paper examines the use of evolutionary algorithms in the development of antibiotic regimens given to production animals. A model is constructed that combines the lifespan of the animal and the bacteria living in the animal's gastro-intestinal tract from the early finishing stage until the animal reaches market weight. This model is used as the fitness evaluation for a set of graph based evolutionary algorithms to assess the impact of diversity control on the evolving antibiotic regimens. The graph based evolutionary algorithms have two objectives: to find an antibiotic treatment regimen that maintains the weight gain and health benefits of antibiotic use and to reduce the risk of spreading antibiotic resistant bacteria. This study examines different regimens of tylosin phosphate use on bacteria populations divided into Gram positive and Gram negative types, with a focus on Campylobacter spp. Treatment regimens were found that provided decreased antibiotic resistance relative to conventional methods while providing nearly the same benefits as conventional antibiotic regimes. By using a graph to control the information flow in the evolutionary algorithm, a variety of solutions along the Pareto front can be found automatically for this and other multi-objective problems.

  10. Contact Graph Routing Enhancements Developed in ION for DTN

    NASA Technical Reports Server (NTRS)

    Segui, John S.; Burleigh, Scott

    2013-01-01

    The Interplanetary Overlay Network (ION) software suite is an open-source, flight-ready implementation of networking protocols including the Delay/Disruption Tolerant Networking (DTN) Bundle Protocol (BP), the CCSDS (Consultative Committee for Space Data Systems) File Delivery Protocol (CFDP), and many others including the Contact Graph Routing (CGR) DTN routing system. While DTN offers the capability to tolerate disruption and long signal propagation delays in transmission, without an appropriate routing protocol, no data can be delivered. CGR was built for space exploration networks with scheduled communication opportunities (typically based on trajectories and orbits), represented as a contact graph. Since CGR uses knowledge of future connectivity, the contact graph can grow rather large, and so efficient processing is desired. These enhancements allow CGR to scale to predicted NASA space network complexities and beyond. This software improves upon CGR by adopting an earliest-arrival-time cost metric and using the Dijkstra path selection algorithm. Moving to Dijkstra path selection also enables construction of an earliest- arrival-time tree for multicast routing. The enhancements have been rolled into ION 3.0 available on sourceforge.net.

  11. Proximity graphs based multi-scale image segmentation

    SciTech Connect

    Skurikhin, Alexei N

    2008-01-01

    We present a novel multi-scale image segmentation approach based on irregular triangular and polygonal tessellations produced by proximity graphs. Our approach consists of two separate stages: polygonal seeds generation followed by an iterative bottom-up polygon agglomeration into larger chunks. We employ constrained Delaunay triangulation combined with the principles known from the visual perception to extract an initial ,irregular polygonal tessellation of the image. These initial polygons are built upon a triangular mesh composed of irregular sized triangles and their shapes are ad'apted to the image content. We then represent the image as a graph with vertices corresponding to the polygons and edges reflecting polygon relations. The segmentation problem is then formulated as Minimum Spanning Tree extraction. We build a successive fine-to-coarse hierarchy of irregular polygonal grids by an iterative graph contraction constructing Minimum Spanning Tree. The contraction uses local information and merges the polygons bottom-up based on local region-and edge-based characteristics.

  12. Dynamic Uncertain Causality Graph for Knowledge Representation and Probabilistic Reasoning: Directed Cyclic Graph and Joint Probability Distribution.

    PubMed

    Zhang, Qin

    2015-07-01

    Probabilistic graphical models (PGMs) such as Bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning. Dynamic uncertain causality graph (DUCG) is a newly presented model of PGMs, which can be applied to fault diagnosis of large and complex industrial systems, disease diagnosis, and so on. The basic methodology of DUCG has been previously presented, in which only the directed acyclic graph (DAG) was addressed. However, the mathematical meaning of DUCG was not discussed. In this paper, the DUCG with directed cyclic graphs (DCGs) is addressed. In contrast, BN does not allow DCGs, as otherwise the conditional independence will not be satisfied. The inference algorithm for the DUCG with DCGs is presented, which not only extends the capabilities of DUCG from DAGs to DCGs but also enables users to decompose a large and complex DUCG into a set of small, simple sub-DUCGs, so that a large and complex knowledge base can be easily constructed, understood, and maintained. The basic mathematical definition of a complete DUCG with or without DCGs is proved to be a joint probability distribution (JPD) over a set of random variables. The incomplete DUCG as a part of a complete DUCG may represent a part of JPD. Examples are provided to illustrate the methodology.

  13. Dynamic Uncertain Causality Graph for Knowledge Representation and Probabilistic Reasoning: Directed Cyclic Graph and Joint Probability Distribution.

    PubMed

    Zhang, Qin

    2015-07-01

    Probabilistic graphical models (PGMs) such as Bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning. Dynamic uncertain causality graph (DUCG) is a newly presented model of PGMs, which can be applied to fault diagnosis of large and complex industrial systems, disease diagnosis, and so on. The basic methodology of DUCG has been previously presented, in which only the directed acyclic graph (DAG) was addressed. However, the mathematical meaning of DUCG was not discussed. In this paper, the DUCG with directed cyclic graphs (DCGs) is addressed. In contrast, BN does not allow DCGs, as otherwise the conditional independence will not be satisfied. The inference algorithm for the DUCG with DCGs is presented, which not only extends the capabilities of DUCG from DAGs to DCGs but also enables users to decompose a large and complex DUCG into a set of small, simple sub-DUCGs, so that a large and complex knowledge base can be easily constructed, understood, and maintained. The basic mathematical definition of a complete DUCG with or without DCGs is proved to be a joint probability distribution (JPD) over a set of random variables. The incomplete DUCG as a part of a complete DUCG may represent a part of JPD. Examples are provided to illustrate the methodology. PMID:25781960

  14. Massive graph visualization : LDRD final report.

    SciTech Connect

    Wylie, Brian Neil; Moreland, Kenneth D.

    2007-10-01

    Graphs are a vital way of organizing data with complex correlations. A good visualization of a graph can fundamentally change human understanding of the data. Consequently, there is a rich body of work on graph visualization. Although there are many techniques that are effective on small to medium sized graphs (tens of thousands of nodes), there is a void in the research for visualizing massive graphs containing millions of nodes. Sandia is one of the few entities in the world that has the means and motivation to handle data on such a massive scale. For example, homeland security generates graphs from prolific media sources such as television, telephone, and the Internet. The purpose of this project is to provide the groundwork for visualizing such massive graphs. The research provides for two major feature gaps: a parallel, interactive visualization framework and scalable algorithms to make the framework usable to a practical application. Both the frameworks and algorithms are designed to run on distributed parallel computers, which are already available at Sandia. Some features are integrated into the ThreatView{trademark} application and future work will integrate further parallel algorithms.

  15. Object Discovery: Soft Attributed Graph Mining.

    PubMed

    Zhang, Quanshi; Song, Xuan; Shao, Xiaowei; Zhao, Huijing; Shibasaki, Ryosuke

    2016-03-01

    We categorize this research in terms of its contribution to both graph theory and computer vision. From the theoretical perspective, this study can be considered as the first attempt to formulate the idea of mining maximal frequent subgraphs in the challenging domain of messy visual data, and as a conceptual extension to the unsupervised learning of graph matching. We define a soft attributed pattern (SAP) to represent the common subgraph pattern among a set of attributed relational graphs (ARGs), considering both their structure and attributes. Regarding the differences between ARGs with fuzzy attributes and conventional labeled graphs, we propose a new mining strategy that directly extracts the SAP with the maximal graph size without applying node enumeration. Given an initial graph template and a number of ARGs, we develop an unsupervised method to modify the graph template into the maximal-size SAP. From a practical perspective, this research develops a general platform for learning the category model (i.e., the SAP) from cluttered visual data (i.e., the ARGs) without labeling "what is where," thereby opening the possibility for a series of applications in the era of big visual data. Experiments demonstrate the superior performance of the proposed method on RGB/RGB-D images and videos.

  16. Graph isomorphism and adiabatic quantum computing

    NASA Astrophysics Data System (ADS)

    Gaitan, Frank; Clark, Lane

    2014-03-01

    In the Graph Isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and maps G --> G'. If yes (no), then G and G' are said to be isomorphic (non-isomorphic). The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. We present a quantum algorithm that solves arbitrary instances of GI, and which provides a novel approach to determining all automorphisms of a graph. The algorithm converts a GI instance to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. Numerical simulation of the algorithm's quantum dynamics shows that it correctly distinguishes non-isomorphic graphs; recognizes isomorphic graphs; and finds the automorphism group of a graph. We also discuss the algorithm's experimental implementation and show how it can be leveraged to solve arbitrary instances of the NP-Complete Sub-Graph Isomorphism problem.

  17. Object Discovery: Soft Attributed Graph Mining.

    PubMed

    Zhang, Quanshi; Song, Xuan; Shao, Xiaowei; Zhao, Huijing; Shibasaki, Ryosuke

    2016-03-01

    We categorize this research in terms of its contribution to both graph theory and computer vision. From the theoretical perspective, this study can be considered as the first attempt to formulate the idea of mining maximal frequent subgraphs in the challenging domain of messy visual data, and as a conceptual extension to the unsupervised learning of graph matching. We define a soft attributed pattern (SAP) to represent the common subgraph pattern among a set of attributed relational graphs (ARGs), considering both their structure and attributes. Regarding the differences between ARGs with fuzzy attributes and conventional labeled graphs, we propose a new mining strategy that directly extracts the SAP with the maximal graph size without applying node enumeration. Given an initial graph template and a number of ARGs, we develop an unsupervised method to modify the graph template into the maximal-size SAP. From a practical perspective, this research develops a general platform for learning the category model (i.e., the SAP) from cluttered visual data (i.e., the ARGs) without labeling "what is where," thereby opening the possibility for a series of applications in the era of big visual data. Experiments demonstrate the superior performance of the proposed method on RGB/RGB-D images and videos. PMID:27046496

  18. Sketch Matching on Topology Product Graph.

    PubMed

    Liang, Shuang; Luo, Jun; Liu, Wenyin; Wei, Yichen

    2015-08-01

    Sketch matching is the fundamental problem in sketch based interfaces. After years of study, it remains challenging when there exists large irregularity and variations in the hand drawn sketch shapes. While most existing works exploit topology relations and graph representations for this problem, they are usually limited by the coarse topology exploration and heuristic (thus suboptimal) similarity metrics between graphs. We present a new sketch matching method with two novel contributions. We introduce a comprehensive definition of topology relations, which results in a rich and informative graph representation of sketches. For graph matching, we propose topology product graph that retains the full correspondence for matching two graphs. Based on it, we derive an intuitive sketch similarity metric whose exact solution is easy to compute. In addition, the graph representation and new metric naturally support partial matching, an important practical problem that received less attention in the literature. Extensive experimental results on a real challenging dataset and the superior performance of our method show that it outperforms the state-of-the-art.

  19. Partitioning sparse matrices with eigenvectors of graphs

    NASA Technical Reports Server (NTRS)

    Pothen, Alex; Simon, Horst D.; Liou, Kang-Pu

    1990-01-01

    The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.

  20. Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results

    NASA Astrophysics Data System (ADS)

    Zhou, Haijun; Wang, Chuang

    2012-08-01

    Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph method, are theoretical approaches for treating the complicated short-loop-induced local correlations. For graphical models represented by non-redundant or redundant region graphs, approximate free energy landscapes are constructed in this paper through the mathematical framework of region graph partition function expansion. Several free energy functionals are obtained, each of which use a set of probability distribution functions or functionals as order parameters. These probability distribution function/functionals are required to satisfy the region graph belief-propagation equation or the region graph survey-propagation equation to ensure vanishing correction contributions of region subgraphs with dangling edges. As a simple application of the general theory, we perform region graph belief-propagation simulations on the square-lattice ferromagnetic Ising model and the Edwards-Anderson model. Considerable improvements over the conventional Bethe-Peierls approximation are achieved. Collective domains of different sizes in the disordered and frustrated square lattice are identified by the message-passing procedure. Such collective domains and the frustrations among them are responsible for the low-temperature glass-like dynamical behaviors of the system.

  1. An adaptive grid for graph-based segmentation in retinal OCT

    PubMed Central

    Lang, Andrew; Carass, Aaron; Calabresi, Peter A.; Ying, Howard S.; Prince, Jerry L.

    2016-01-01

    Graph-based methods for retinal layer segmentation have proven to be popular due to their efficiency and accuracy. These methods build a graph with nodes at each voxel location and use edges connecting nodes to encode the hard constraints of each layer’s thickness and smoothness. In this work, we explore deforming the regular voxel grid to allow adjacent vertices in the graph to more closely follow the natural curvature of the retina. This deformed grid is constructed by fixing node locations based on a regression model of each layer’s thickness relative to the overall retina thickness, thus we generate a subject specific grid. Graph vertices are not at voxel locations, which allows for control over the resolution that the graph represents. By incorporating soft constraints between adjacent nodes, segmentation on this grid will favor smoothly varying surfaces consistent with the shape of the retina. Our final segmentation method then follows our previous work. Boundary probabilities are estimated using a random forest classifier followed by an optimal graph search algorithm on the new adaptive grid to produce a final segmentation. Our method is shown to produce a more consistent segmentation with an overall accuracy of 3.38 μm across all boundaries.

  2. A graph lattice approach to maintaining and learning dense collections of subgraphs as image features.

    PubMed

    Saund, Eric

    2013-10-01

    Effective object and scene classification and indexing depend on extraction of informative image features. This paper shows how large families of complex image features in the form of subgraphs can be built out of simpler ones through construction of a graph lattice—a hierarchy of related subgraphs linked in a lattice. Robustness is achieved by matching many overlapping and redundant subgraphs, which allows the use of inexpensive exact graph matching, instead of relying on expensive error-tolerant graph matching to a minimal set of ideal model graphs. Efficiency in exact matching is gained by exploitation of the graph lattice data structure. Additionally, the graph lattice enables methods for adaptively growing a feature space of subgraphs tailored to observed data. We develop the approach in the domain of rectilinear line art, specifically for the practical problem of document forms recognition. We are especially interested in methods that require only one or very few labeled training examples per category. We demonstrate two approaches to using the subgraph features for this purpose. Using a bag-of-words feature vector we achieve essentially single-instance learning on a benchmark forms database, following an unsupervised clustering stage. Further performance gains are achieved on a more difficult dataset using a feature voting method and feature selection procedure.

  3. Computational prediction of riboswitch tertiary structures including pseudoknots by RAGTOP: a hierarchical graph sampling approach.

    PubMed

    Kim, Namhee; Zahran, Mai; Schlick, Tamar

    2015-01-01

    The modular organization of RNA structure has been exploited in various computational and theoretical approaches to identify RNA tertiary (3D) motifs and assemble RNA structures. Riboswitches exemplify this modularity in terms of both structural and functional adaptability of RNA components. Here, we extend our computational approach based on tree graph sampling to the prediction of riboswitch topologies by defining additional edges to mimick pseudoknots. Starting from a secondary (2D) structure, we construct an initial graph deduced from predicted junction topologies by our data-mining algorithm RNAJAG trained on known RNAs; we sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. We present graph sampling results for 10 representative riboswitches, 6 of them with pseudoknots, and compare our predictions to solved structures based on global and local RMSD measures. Our results indicate that the helical arrangements in riboswitches can be approximated using our combination of modified 3D tree graph representations for pseudoknots, junction prediction, graph moves, and scoring functions. Future challenges in the field of riboswitch prediction and design are also discussed. PMID:25726463

  4. Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra

    NASA Astrophysics Data System (ADS)

    Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.

    2016-05-01

    We study the infinite family of spider-web graphs \\{{{ S }}k,N,M\\}, k≥slant 2, N≥slant 0 and M≥slant 1, initiated in the 50s in the context of network theory. It was later shown in physical literature that these graphs have remarkable percolation and spectral properties. We provide a mathematical explanation of these properties by putting the spider-web graphs in the context of group theory and algebraic graph theory. Namely, we realize them as tensor products of the well-known de Bruijn graphs \\{{{ B }}k,N\\} with cyclic graphs \\{{C}M\\} and show that these graphs are described by the action of the lamplighter group {{ L }}k={Z}/k{Z}\\wr {Z} on the infinite binary tree. Our main result is the identification of the infinite limit of \\{{{ S }}k,N,M\\}, as N,M\\to ∞ , with the Cayley graph of the lamplighter group {{ L }}k which, in turn, is one of the famous Diestel–Leader graphs {{DL}}k,k. As an application we compute the spectra of all spider-web graphs and show their convergence to the discrete spectral distribution associated with the Laplacian on the lamplighter group.

  5. Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra

    NASA Astrophysics Data System (ADS)

    Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.

    2016-05-01

    We study the infinite family of spider-web graphs \\{{{ S }}k,N,M\\}, k≥slant 2, N≥slant 0 and M≥slant 1, initiated in the 50s in the context of network theory. It was later shown in physical literature that these graphs have remarkable percolation and spectral properties. We provide a mathematical explanation of these properties by putting the spider-web graphs in the context of group theory and algebraic graph theory. Namely, we realize them as tensor products of the well-known de Bruijn graphs \\{{{ B }}k,N\\} with cyclic graphs \\{{C}M\\} and show that these graphs are described by the action of the lamplighter group {{ L }}k={Z}/k{Z}\\wr {Z} on the infinite binary tree. Our main result is the identification of the infinite limit of \\{{{ S }}k,N,M\\}, as N,M\\to ∞ , with the Cayley graph of the lamplighter group {{ L }}k which, in turn, is one of the famous Diestel-Leader graphs {{DL}}k,k. As an application we compute the spectra of all spider-web graphs and show their convergence to the discrete spectral distribution associated with the Laplacian on the lamplighter group.

  6. BioGraphE: high-performance bionetwork analysis using the Biological Graph Environment

    PubMed Central

    Chin, George; Chavarria, Daniel G; Nakamura, Grant C; Sofia, Heidi J

    2008-01-01

    Background Graphs and networks are common analysis representations for biological systems. Many traditional graph algorithms such as k-clique, k-coloring, and subgraph matching have great potential as analysis techniques for newly available data in biology. Yet, as the amount of genomic and bionetwork information rapidly grows, scientists need advanced new computational strategies and tools for dealing with the complexities of the bionetwork analysis and the volume of the data. Results We introduce a computational framework for graph analysis called the Biological Graph Environment (BioGraphE), which provides a general, scalable integration platform for connecting graph problems in biology to optimized computational solvers and high-performance systems. This framework enables biology researchers and computational scientists to identify and deploy network analysis applications and to easily connect them to efficient and powerful computational software and hardware that are specifically designed and tuned to solve complex graph problems. In our particular application of BioGraphE to support network analysis in genome biology, we investigate the use of a Boolean satisfiability solver known as Survey Propagation as a core computational solver executing on standard high-performance parallel systems, as well as multi-threaded architectures. Conclusion In our application of BioGraphE to conduct bionetwork analysis of homology networks, we found that BioGraphE and a custom, parallel implementation of the Survey Propagation SAT solver were capable of solving very large bionetwork problems at high rates of execution on different high-performance computing platforms. PMID:18541059

  7. Enabling Graph Mining in RDF Triplestores using SPARQL for Holistic In-situ Graph Analysis

    SciTech Connect

    Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong; Lim, Seung-Hwan

    2016-01-01

    The graph analysis is now considered as a promising technique to discover useful knowledge in data with a new perspective. We envi- sion that there are two dimensions of graph analysis: OnLine Graph Analytic Processing (OLGAP) and Graph Mining (GM) where each respectively focuses on subgraph pattern matching and automatic knowledge discovery in graph. Moreover, as these two dimensions aim to complementarily solve complex problems, holistic in-situ graph analysis which covers both OLGAP and GM in a single system is critical for minimizing the burdens of operating multiple graph systems and transferring intermediate result-sets between those systems. Nevertheless, most existing graph analysis systems are only capable of one dimension of graph analysis. In this work, we take an approach to enabling GM capabilities (e.g., PageRank, connected-component analysis, node eccentricity, etc.) in RDF triplestores, which are originally developed to store RDF datasets and provide OLGAP capability. More specifically, to achieve our goal, we implemented six representative graph mining algorithms using SPARQL. The approach allows a wide range of available RDF data sets directly applicable for holistic graph analysis within a system. For validation of our approach, we evaluate performance of our implementations with nine real-world datasets and three different computing environments - a laptop computer, an Amazon EC2 instance, and a shared-memory Cray XMT2 URIKA-GD graph-processing appliance. The experimen- tal results show that our implementation can provide promising and scalable performance for real world graph analysis in all tested environments. The developed software is publicly available in an open-source project that we initiated.

  8. Enabling Graph Mining in RDF Triplestores using SPARQL for Holistic In-situ Graph Analysis

    DOE PAGES

    Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong; Lim, Seung-Hwan

    2016-01-01

    The graph analysis is now considered as a promising technique to discover useful knowledge in data with a new perspective. We envi- sion that there are two dimensions of graph analysis: OnLine Graph Analytic Processing (OLGAP) and Graph Mining (GM) where each respectively focuses on subgraph pattern matching and automatic knowledge discovery in graph. Moreover, as these two dimensions aim to complementarily solve complex problems, holistic in-situ graph analysis which covers both OLGAP and GM in a single system is critical for minimizing the burdens of operating multiple graph systems and transferring intermediate result-sets between those systems. Nevertheless, most existingmore » graph analysis systems are only capable of one dimension of graph analysis. In this work, we take an approach to enabling GM capabilities (e.g., PageRank, connected-component analysis, node eccentricity, etc.) in RDF triplestores, which are originally developed to store RDF datasets and provide OLGAP capability. More specifically, to achieve our goal, we implemented six representative graph mining algorithms using SPARQL. The approach allows a wide range of available RDF data sets directly applicable for holistic graph analysis within a system. For validation of our approach, we evaluate performance of our implementations with nine real-world datasets and three different computing environments - a laptop computer, an Amazon EC2 instance, and a shared-memory Cray XMT2 URIKA-GD graph-processing appliance. The experimen- tal results show that our implementation can provide promising and scalable performance for real world graph analysis in all tested environments. The developed software is publicly available in an open-source project that we initiated.« less

  9. Computing the isoperimetric number of a graph

    SciTech Connect

    Golovach, P.A.

    1995-01-01

    Let G be a finite graph. Denote by {partial_derivative}X, where X {contained_in} VG, the set of edges of the graph G with one end in X and the other end in the set VG{backslash}X. The ratio i(G) = min {vert_bar}{vert_bar}X{vert_bar}/{vert_bar}X{vert_bar}, where the minimum is over all nonempty subsets X of the set VG such that {vert_bar}X{vert_bar} {le} {vert_bar} VG {vert_bar}/2, is called the isoperimetric number of the graph G. It is easy to see that the isoperimetric number may be used as a {open_quotes}measure of connectivity{close_quotes} of the graph. The problem of determining the isoperimetric number is clearly linked with graph partition problems, which often arise in various applications. The isoperimetric number is also important for studying Riemann surfaces. These and other applications of the isoperimetric number justify the analysis of graphs of this kind. The properties of the isoperimetric number are presented in more detail elsewhere. It is shown elsewhere that the computation of the isoperimetric number is an NP-hard problem for graphs with multiple edges. We will show that the decision problem {open_quotes}given the graph G and two integers s and t decide if i(G) {le} s/t{close_quotes} is NP-complete even for simple graphs with vertex degrees not exceeding 3. Note that the isoperimetric number of a tree can be computed by a known polynomial-time algorithm.

  10. Intelligent Graph Layout Using Many Users' Input.

    PubMed

    Yuan, Xiaoru; Che, Limei; Hu, Yifan; Zhang, Xin

    2012-12-01

    In this paper, we propose a new strategy for graph drawing utilizing layouts of many sub-graphs supplied by a large group of people in a crowd sourcing manner. We developed an algorithm based on Laplacian constrained distance embedding to merge subgraphs submitted by different users, while attempting to maintain the topological information of the individual input layouts. To facilitate collection of layouts from many people, a light-weight interactive system has been designed to enable convenient dynamic viewing, modification and traversing between layouts. Compared with other existing graph layout algorithms, our approach can achieve more aesthetic and meaningful layouts with high user preference.

  11. Line graphs for a multiplex network.

    PubMed

    Criado, Regino; Flores, Julio; García Del Amo, Alejandro; Romance, Miguel; Barrena, Eva; Mesa, Juan A

    2016-06-01

    It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multi-plexed and multi-layered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated.

  12. Searching for nodes in random graphs.

    PubMed

    Lancaster, David

    2011-11-01

    We consider the problem of searching for a node on a labeled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of random graph are proposed with properties particularly amenable to this kind of algorithm. We derive equations for the probability that the search is successful and also study the number of hops required, finding both numerical and analytic evidence of a transition as the number of links is varied.

  13. Line graphs for a multiplex network.

    PubMed

    Criado, Regino; Flores, Julio; García Del Amo, Alejandro; Romance, Miguel; Barrena, Eva; Mesa, Juan A

    2016-06-01

    It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multi-plexed and multi-layered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated. PMID:27368798

  14. Graph states for quantum secret sharing

    NASA Astrophysics Data System (ADS)

    Markham, Damian; Sanders, Barry C.

    2008-10-01

    We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by graph states, our approach provides a generalization of threshold classical secret sharing via insecure quantum channels beyond the current requirement of 100% collaboration by players to just a simple majority in the case of five players. Another innovation here is the introduction of embedded protocols within a larger graph state that serves as a one-way quantum-information processing system.

  15. The MultiThreaded Graph Library (MTGL)

    SciTech Connect

    Berry, Jonathan; Leung, Vitus; McLendon, III, William; & Madduri, Kamesh

    2008-07-17

    The MultiThreaded Graph Library (MTGL) is a set of header files that implement graph algorithm in such a way that they can run on massively multithreaded architectures. It is based upon the Boost Graph Library, but doesn’t use Boost since the latter doesn’t run well on these architectures.

  16. A heterogeneous graph-based recommendation simulator

    SciTech Connect

    Yeonchan, Ahn; Sungchan, Park; Lee, Matt Sangkeun; Sang-goo, Lee

    2013-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  18. Graph states as ground states of two-body frustration-free Hamiltonians

    NASA Astrophysics Data System (ADS)

    Darmawan, Andrew S.; Bartlett, Stephen D.

    2014-07-01

    The framework of measurement-based quantum computation (MBQC) allows us to view the ground states of local Hamiltonians as potential resources for universal quantum computation. A central goal in this field is to find models with ground states that are universal for MBQC and that are also natural in the sense that they involve only two-body interactions and have a small local Hilbert space dimension. Graph states are the original resource states for MBQC, and while it is not possible to obtain graph states as exact ground states of two-body Hamiltonians, here we construct two-body frustration-free Hamiltonians that have arbitrarily good approximations of graph states as unique ground states. The construction involves taking a two-body frustration-free model that has a ground state convertible to a graph state with stochastic local operations, then deforming the model such that its ground state is close to a graph state. Each graph state qubit resides in a subspace of a higher dimensional particle. This deformation can be applied to two-body frustration-free Affleck-Kennedy-Lieb-Tasaki (AKLT) models, yielding Hamiltonians that are exactly solvable with exact tensor network expressions for ground states. For the star-lattice AKLT model, the ground state of which is not expected to be a universal resource for MBQC, applying such a deformation appears to enhance the computational power of the ground state, promoting it to a universal resource for MBQC. Transitions in computational power, similar to percolation phase transitions, can be observed when Hamiltonians are deformed in this way. Improving the fidelity of the ground state comes at the cost of a shrinking gap. While analytically proving gap properties for these types of models is difficult in general, we provide a detailed analysis of the deformation of a spin-1 AKLT state to a linear graph state.

  19. Creating Single-Subject Design Graphs in Microsoft Excel[TM] 2007

    ERIC Educational Resources Information Center

    Dixon, Mark R.; Jackson, James W.; Small, Stacey L.; Horner-King, Mollie J.; Mui Ker Lik, Nicholas; Garcia, Yors; Rosales, Rocio

    2009-01-01

    Over 10 years have passed since the publication of Carr and Burkholder's (1998) technical article on how to construct single-subject graphs using Microsoft Excel. Over the course of the past decade, the Excel program has undergone a series of revisions that make the Carr and Burkholder paper somewhat difficult to follow with newer versions. The…

  20. Math: Data Relationships. Graphs, Ratios and Proportions, Statistics and Probability. Grades K-9. Revised Edition.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    To help classroom teachers in grades K-9 construct mathematics tests, fifteen general objectives, corresponding sub-objectives, sample test items, and answers are presented. In general, sub-objectives are arranged in increasing order of difficulty. The objectives were written to comprehensively cover three categories. The first, graphs, covers the…

  1. Experiments on parallel graph coloring and applications

    SciTech Connect

    Lewandowski, G.; Condon, A.

    1994-12-31

    The graph coloring problem is an NP-Complete problem with a wide array of applications, such as course scheduling, exam scheduling, register allocation, and parallelizing solutions for sparse systems of linear equations. Much theoretical effort has been put into designing heuristics that perform well on randomly generated graphs. The best sequential heuristics require large amounts of time and tuning of various parameters in the heuristics. We have used parallelism to combine exhaustive search with successful heuristic strategies to create a new heuristic, Hybrid, which does well on a wide variety of graphs, without any tuning of parameters. We have also gathered real application data and tested several heuristics on this data. Our study of real data points out some flaws in studying only random graphs and also suggests interesting new problems for study.

  2. Graph500 in OpenSHMEM

    SciTech Connect

    D'Azevedo, Ed F; Imam, Neena

    2015-01-01

    This document describes the effort to implement the Graph 500 benchmark using OpenSHMEM based on the MPI-2 one-side version. The Graph 500 benchmark performs a breadth-first search in parallel on a large randomly generated undirected graph and can be implemented using basic MPI-1 and MPI-2 one-sided communication. Graph 500 requires atomic bit-wise operations on unsigned long integers but neither atomic bit-wise operations nor OpenSHMEM for unsigned long are available in OpenSHEM. Such needed bit-wise atomic operations and support for unsigned long are implemented using atomic condition swap (CSWAP) on signed long integers. Preliminary results on comparing the OpenSHMEM and MPI-2 one-sided implementations on a Silicon Graphics Incorporated (SGI) cluster and the Cray XK7 are presented.

  3. An Investigation of the Coauthor Graph.

    ERIC Educational Resources Information Center

    Logan, Elisabeth L.; Shaw, W. M., Jr.

    1987-01-01

    The role of the coauthor relationship in the structure of informal communications networks within disciplines is explored, and the validity of coauthor graphs used to map these relationships is tested for both small and large databases. (CLB)

  4. The signed permutation group on Feynman graphs

    NASA Astrophysics Data System (ADS)

    Purkart, Julian

    2016-08-01

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

  5. Fault-tolerant dynamic task graph scheduling

    SciTech Connect

    Kurt, Mehmet C.; Krishnamoorthy, Sriram; Agrawal, Kunal; Agrawal, Gagan

    2014-11-16

    In this paper, we present an approach to fault tolerant execution of dynamic task graphs scheduled using work stealing. In particular, we focus on selective and localized recovery of tasks in the presence of soft faults. We elicit from the user the basic task graph structure in terms of successor and predecessor relationships. The work stealing-based algorithm to schedule such a task graph is augmented to enable recovery when the data and meta-data associated with a task get corrupted. We use this redundancy, and the knowledge of the task graph structure, to selectively recover from faults with low space and time overheads. We show that the fault tolerant design retains the essential properties of the underlying work stealing-based task scheduling algorithm, and that the fault tolerant execution is asymptotically optimal when task re-execution is taken into account. Experimental evaluation demonstrates the low cost of recovery under various fault scenarios.

  6. Teaching Waves with a Graphing Calculator.

    ERIC Educational Resources Information Center

    Raggett, Matthew

    2000-01-01

    Stresses the value of graphing and computer algebra systems calculators when teaching about waves. Discusses how to input data into these calculators. Highlights the Texas Instruments' (TI) Web site at http://www.ti.com. (YDS)

  7. Continuous Time Group Discovery in Dynamic Graphs

    SciTech Connect

    Miller, K; Eliassi-Rad, T

    2010-11-04

    With the rise in availability and importance of graphs and networks, it has become increasingly important to have good models to describe their behavior. While much work has focused on modeling static graphs, we focus on group discovery in dynamic graphs. We adapt a dynamic extension of Latent Dirichlet Allocation to this task and demonstrate good performance on two datasets. Modeling relational data has become increasingly important in recent years. Much work has focused on static graphs - that is fixed graphs at a single point in time. Here we focus on the problem of modeling dynamic (i.e. time-evolving) graphs. We propose a scalable Bayesian approach for community discovery in dynamic graphs. Our approach is based on extensions of Latent Dirichlet Allocation (LDA). LDA is a latent variable model for topic modeling in text corpora. It was extended to deal with topic changes in discrete time and later in continuous time. These models were referred to as the discrete Dynamic Topic Model (dDTM) and the continuous Dynamic Topic Model (cDTM), respectively. When adapting these models to graphs, we take our inspiration from LDA-G and SSN-LDA, applications of LDA to static graphs that have been shown to effectively factor out community structure to explain link patterns in graphs. In this paper, we demonstrate how to adapt and apply the cDTM to the task of finding communities in dynamic networks. We use link prediction to measure the quality of the discovered community structure and apply it to two different relational datasets - DBLP author-keyword and CAIDA autonomous systems relationships. We also discuss a parallel implementation of this approach using Hadoop. In Section 2, we review LDA and LDA-G. In Section 3, we review the cDTM and introduce cDTMG, its adaptation to modeling dynamic graphs. We discuss inference for the cDTM-G and details of our parallel implementation in Section 4 and present its performance on two datasets in Section 5 before concluding in

  8. Pre-Service Elementary Teachers' Understandings of Graphs

    ERIC Educational Resources Information Center

    Alacaci, Cengiz; Lewis, Scott; O'Brien, George E.; Jiang, Zhonghong

    2011-01-01

    Choosing graphs to display quantitative information is a component of "graph sense". An important aspect of pre-service elementary teachers' content knowledge; ability to choose appropriate graphs in applied contexts is investigated in this study. They were given three scenarios followed by four graphs representing the same quantitative data. They…

  9. Accelerating semantic graph databases on commodity clusters

    SciTech Connect

    Morari, Alessandro; Castellana, Vito G.; Haglin, David J.; Feo, John T.; Weaver, Jesse R.; Tumeo, Antonino; Villa, Oreste

    2013-10-06

    We are developing a full software system for accelerating semantic graph databases on commodity cluster that scales to hundreds of nodes while maintaining constant query throughput. Our framework comprises a SPARQL to C++ compiler, a library of parallel graph methods and a custom multithreaded runtime layer, which provides a Partitioned Global Address Space (PGAS) programming model with fork/join parallelism and automatic load balancing over a commodity clusters. We present preliminary results for the compiler and for the runtime.

  10. On the Kirchhoff Index of Graphs

    NASA Astrophysics Data System (ADS)

    Das, Kinkar C.

    2013-09-01

    Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ ... ≥ μn-1 > mn = 0. The Kirchhoff index of G is defined as [xxx] In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus-Gaddum-type result for the Kirchhoff index.

  11. A software tool for dataflow graph scheduling

    NASA Technical Reports Server (NTRS)

    Jones, Robert L., III

    1994-01-01

    A graph-theoretic design process and software tool is presented for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described using a dataflow graph and are intended to be executed repetitively on multiple processors. The dataflow paradigm is very useful in exposing the parallelism inherent in algorithms. It provides a graphical and mathematical model which describes a partial ordering of algorithm tasks based on data precedence.

  12. Program for Generating Graphs and Charts

    NASA Technical Reports Server (NTRS)

    Ackerson, C. T.

    1986-01-01

    Office Automation Pilot (OAP) Graphics Database system offers IBM personal computer user assistance in producing wide variety of graphs and charts and convenient data-base system, called chart base, for creating and maintaining data associated with graphs and charts. Thirteen different graphics packages available. Access graphics capabilities obtained in similar manner. User chooses creation, revision, or chartbase-maintenance options from initial menu; Enters or modifies data displayed on graphic chart. OAP graphics data-base system written in Microsoft PASCAL.

  13. A Fermi golden rule for quantum graphs

    NASA Astrophysics Data System (ADS)

    Lee, Minjae; Zworski, Maciej

    2016-09-01

    We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a notationally simpler setting, we first describe a Fermi golden rule for boundary value problems on surfaces with constant curvature cusps. We also provide a resonance existence result which is uniform on compact sets of energies and metric graphs. The results are illustrated by numerical experiments.

  14. Student reasoning about graphs in different contexts

    NASA Astrophysics Data System (ADS)

    Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

    2016-06-01

    This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students' main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students' answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.

  15. Bipartite separability and nonlocal quantum operations on graphs

    NASA Astrophysics Data System (ADS)

    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.

  16. Time-varying Reeb Graphs: A Topological Framework Supporting the Analysis of Continuous Time-varying Data

    SciTech Connect

    Mascarenhas, Ajith Arthur

    2006-01-01

    difficult to resolve, making construction of time-varying Reeb graphs impractical. I investigate piecewise-linear, piecewise-trilinear, and piecewise-prismatic interpolants, and conclude that piecewise-prismatic is the best choice for computing time-varying Reeb graphs. Large Reeb graphs must be simplified for an effective presentation in a visualization system. I extend an algorithm for simplifying static Reeb graphs to compute simplifications of time-varying Reeb graphs as a first step towards building a visualization system to support the analysis of time-varying data.

  17. Quantum Graphs Whose Spectra Mimic the Zeros of the Riemann Zeta Function

    NASA Astrophysics Data System (ADS)

    Kuipers, Jack; Hummel, Quirin; Richter, Klaus

    2014-02-01

    One of the most famous problems in mathematics is the Riemann hypothesis: that the nontrivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that have the same oscillating part of the density of states as the Riemann zeros, offering an explanation of the overall minus sign. The smooth part is completely different, and hence also the spectrum, but the graphs pick out the low-lying zeros.

  18. Preserving Differential Privacy in Degree-Correlation based Graph Generation

    PubMed Central

    Wang, Yue; Wu, Xintao

    2014-01-01

    Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model. PMID:24723987

  19. Preserving Differential Privacy in Degree-Correlation based Graph Generation.

    PubMed

    Wang, Yue; Wu, Xintao

    2013-08-01

    Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model.

  20. GRETNA: a graph theoretical network analysis toolbox for imaging connectomics.

    PubMed

    Wang, Jinhui; Wang, Xindi; Xia, Mingrui; Liao, Xuhong; Evans, Alan; He, Yong

    2015-01-01

    Recent studies have suggested that the brain's structural and functional networks (i.e., connectomics) can be constructed by various imaging technologies (e.g., EEG/MEG; structural, diffusion and functional MRI) and further characterized by graph theory. Given the huge complexity of network construction, analysis and statistics, toolboxes incorporating these functions are largely lacking. Here, we developed the GRaph thEoreTical Network Analysis (GRETNA) toolbox for imaging connectomics. The GRETNA contains several key features as follows: (i) an open-source, Matlab-based, cross-platform (Windows and UNIX OS) package with a graphical user interface (GUI); (ii) allowing topological analyses of global and local network properties with parallel computing ability, independent of imaging modality and species; (iii) providing flexible manipulations in several key steps during network construction and analysis, which include network node definition, network connectivity processing, network type selection and choice of thresholding procedure; (iv) allowing statistical comparisons of global, nodal and connectional network metrics and assessments of relationship between these network metrics and clinical or behavioral variables of interest; and (v) including functionality in image preprocessing and network construction based on resting-state functional MRI (R-fMRI) data. After applying the GRETNA to a publicly released R-fMRI dataset of 54 healthy young adults, we demonstrated that human brain functional networks exhibit efficient small-world, assortative, hierarchical and modular organizations and possess highly connected hubs and that these findings are robust against different analytical strategies. With these efforts, we anticipate that GRETNA will accelerate imaging connectomics in an easy, quick and flexible manner. GRETNA is freely available on the NITRC website.

  1. A graph theoretic approach to scene matching

    NASA Technical Reports Server (NTRS)

    Ranganath, Heggere S.; Chipman, Laure J.

    1991-01-01

    The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors.

  2. Unraveling Protein Networks with Power Graph Analysis

    PubMed Central

    Royer, Loïc; Reimann, Matthias; Andreopoulos, Bill; Schroeder, Michael

    2008-01-01

    Networks play a crucial role in computational biology, yet their analysis and representation is still an open problem. Power Graph Analysis is a lossless transformation of biological networks into a compact, less redundant representation, exploiting the abundance of cliques and bicliques as elementary topological motifs. We demonstrate with five examples the advantages of Power Graph Analysis. Investigating protein-protein interaction networks, we show how the catalytic subunits of the casein kinase II complex are distinguishable from the regulatory subunits, how interaction profiles and sequence phylogeny of SH3 domains correlate, and how false positive interactions among high-throughput interactions are spotted. Additionally, we demonstrate the generality of Power Graph Analysis by applying it to two other types of networks. We show how power graphs induce a clustering of both transcription factors and target genes in bipartite transcription networks, and how the erosion of a phosphatase domain in type 22 non-receptor tyrosine phosphatases is detected. We apply Power Graph Analysis to high-throughput protein interaction networks and show that up to 85% (56% on average) of the information is redundant. Experimental networks are more compressible than rewired ones of same degree distribution, indicating that experimental networks are rich in cliques and bicliques. Power Graphs are a novel representation of networks, which reduces network complexity by explicitly representing re-occurring network motifs. Power Graphs compress up to 85% of the edges in protein interaction networks and are applicable to all types of networks such as protein interactions, regulatory networks, or homology networks. PMID:18617988

  3. Labeled Graph Kernel for Behavior Analysis.

    PubMed

    Zhao, Ruiqi; Martinez, Aleix M

    2016-08-01

    Automatic behavior analysis from video is a major topic in many areas of research, including computer vision, multimedia, robotics, biology, cognitive science, social psychology, psychiatry, and linguistics. Two major problems are of interest when analyzing behavior. First, we wish to automatically categorize observed behaviors into a discrete set of classes (i.e., classification). For example, to determine word production from video sequences in sign language. Second, we wish to understand the relevance of each behavioral feature in achieving this classification (i.e., decoding). For instance, to know which behavior variables are used to discriminate between the words apple and onion in American Sign Language (ASL). The present paper proposes to model behavior using a labeled graph, where the nodes define behavioral features and the edges are labels specifying their order (e.g., before, overlaps, start). In this approach, classification reduces to a simple labeled graph matching. Unfortunately, the complexity of labeled graph matching grows exponentially with the number of categories we wish to represent. Here, we derive a graph kernel to quickly and accurately compute this graph similarity. This approach is very general and can be plugged into any kernel-based classifier. Specifically, we derive a Labeled Graph Support Vector Machine (LGSVM) and a Labeled Graph Logistic Regressor (LGLR) that can be readily employed to discriminate between many actions (e.g., sign language concepts). The derived approach can be readily used for decoding too, yielding invaluable information for the understanding of a problem (e.g., to know how to teach a sign language). The derived algorithms allow us to achieve higher accuracy results than those of state-of-the-art algorithms in a fraction of the time. We show experimental results on a variety of problems and datasets, including multimodal data.

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

    ERIC Educational Resources Information Center

    Deniz, Hasan; Dulger, Mehmet F.

    2012-01-01

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

  5. Reflections on High School Students' Graphing Skills and Their Conceptual Understanding of Drawing Chemistry Graphs

    ERIC Educational Resources Information Center

    Gültepe, Nejla

    2016-01-01

    Graphing subjects in chemistry has been used to provide alternatives to verbal and algorithmic descriptions of a subject by handing students another way of improving their manipulation of concepts. Teachers should therefore know the level of students' graphing skills. Studies have identified that students have difficulty making connections with…

  6. New invariants of weighted graphs for calculating the critical properties of freons

    NASA Astrophysics Data System (ADS)

    Kruglyak, Yu. A.; Peredunova, I. V.

    2015-12-01

    A new approach to structure-property problems using new invariants of fully weighted graphs to provide a quantitative description of the critical properties of freons is proposed. A general principle for constructing topological invariants of fully weighted graphs for structure-property correlations is formulated. Two new invariants are proposed and used to calculate critical properties of freons of the methane, ethane, and propane series. It is shown that unlike all other known incremental methods, the proposed approach does not require the use of experimental data or calibrations to calculate critical properties. It ensures a statistically reliable linear dependence of all critical properties of freons on the value of the matching index for our corresponding molecular graph. Over 2.5 thousand previously unknown values of the critical properties of lower freons are calculated.

  7. Hybrid coexpression link similarity graph clustering for mining biological modules from multiple gene expression datasets

    PubMed Central

    2014-01-01

    Background Advances in genomic technologies have enabled the accumulation of vast amount of genomic data, including gene expression data for multiple species under various biological and environmental conditions. Integration of these gene expression datasets is a promising strategy to alleviate the challenges of protein functional annotation and biological module discovery based on a single gene expression data, which suffers from spurious coexpression. Results We propose a joint mining algorithm that constructs a weighted hybrid similarity graph whose nodes are the coexpression links. The weight of an edge between two coexpression links in this hybrid graph is a linear combination of the topological similarities and co-appearance similarities of the corresponding two coexpression links. Clustering the weighted hybrid similarity graph yields recurrent coexpression link clusters (modules). Experimental results on Human gene expression datasets show that the reported modules are functionally homogeneous as evident by their enrichment with biological process GO terms and KEGG pathways. PMID:25221624

  8. Linear Time Vertex Partitioning on Massive Graphs

    PubMed Central

    Mell, Peter; Harang, Richard; Gueye, Assane

    2016-01-01

    The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity. PMID:27336059

  9. DT-MRI segmentation using graph cuts

    NASA Astrophysics Data System (ADS)

    Weldeselassie, Yonas T.; Hamarneh, Ghassan

    2007-03-01

    An important problem in medical image analysis is the segmentation of anatomical regions of interest. Once regions of interest are segmented, one can extract shape, appearance, and structural features that can be analyzed for disease diagnosis or treatment evaluation. Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new medical imaging modality that captures unique water diffusion properties and fiber orientation information of the imaged tissues. In this paper, we extend the interactive multidimensional graph cuts segmentation technique to operate on DT-MRI data by utilizing latest advances in tensor calculus and diffusion tensor dissimilarity metrics. The user interactively selects certain tensors as object ("obj") or background ("bkg") to provide hard constraints for the segmentation. Additional soft constraints incorporate information about both regional tissue diffusion as well as boundaries between tissues of different diffusion properties. Graph cuts are used to find globally optimal segmentation of the underlying 3D DT-MR image among all segmentations satisfying the constraints. We develop a graph structure from the underlying DT-MR image with the tensor voxels corresponding to the graph vertices and with graph edge weights computed using either Log-Euclidean or the J-divergence tensor dissimilarity metric. The topology of our segmentation is unrestricted and both obj and bkg segments may consist of several isolated parts. We test our method on synthetic DT data and apply it to real 2D and 3D MRI, providing segmentations of the corpus callosum in the brain and the ventricles of the heart.

  10. Towards Scalable Graph Computation on Mobile Devices

    PubMed Central

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

    2015-01-01

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

  11. Deformed graph laplacian for semisupervised learning.

    PubMed

    Gong, Chen; Liu, Tongliang; Tao, Dacheng; Fu, Keren; Tu, Enmei; Yang, Jie

    2015-10-01

    Graph Laplacian has been widely exploited in traditional graph-based semisupervised learning (SSL) algorithms to regulate the labels of examples that vary smoothly on the graph. Although it achieves a promising performance in both transductive and inductive learning, it is not effective for handling ambiguous examples (shown in Fig. 1). This paper introduces deformed graph Laplacian (DGL) and presents label prediction via DGL (LPDGL) for SSL. The local smoothness term used in LPDGL, which regularizes examples and their neighbors locally, is able to improve classification accuracy by properly dealing with ambiguous examples. Theoretical studies reveal that LPDGL obtains the globally optimal decision function, and the free parameters are easy to tune. The generalization bound is derived based on the robustness analysis. Experiments on a variety of real-world data sets demonstrate that LPDGL achieves top-level performance on both transductive and inductive settings by comparing it with popular SSL algorithms, such as harmonic functions, AnchorGraph regularization, linear neighborhood propagation, Laplacian regularized least square, and Laplacian support vector machine.

  12. Visualizing intelligence information using correlation graphs

    NASA Astrophysics Data System (ADS)

    Verma, Vivek; Gagvani, Nikhil

    2005-03-01

    This paper presents a new information model to help intelligence analysts in organizing, querying, and visualizing the information present in large volumes of unstructured data sources such as text reports, multi-media, and human discourse. Our primary goal is to create a system that would combine the human pattern recognition abilities of intelligence analysis with the storage and processing capabilities of computers. Our system models the collective mental map of intelligence analysts in the form of the Correlation Graph, a modified graph data structure with objects and events as nodes and subjective probabilistic correlations between them as edges. Objects are entities such as people, places, and things. Events are actions that involve the objects. A taxonomy is also associated with the model to enable intelligence domain specific querying of the data. Graph drawing techniques are used to visualize the information represented by the correlation graph. Through real world examples, we demonstrate that the resulting information model can be used for efficient representation, presentation, and querying to discover novel patterns in the intelligence data via graph visualization techniques.

  13. Exploiting graph properties of game trees

    SciTech Connect

    Plaat, A.; Pijls, W.; Bruin, A. de; Schaeffer, J.

    1996-12-31

    The state space of most adversary games is a directed graph. However, due to the success of simple recursive algorithms based on alpha-beta, theoreticians and practitioners have concentrated on the traversal of trees, giving the field the name {open_quotes}game-tree search,{close_quotes} This paper shows that the focus on trees has obscured some important properties of the underlying graphs. One of the hallmarks of the field of game-tree search has been the notion of the minimal tree, the smallest tree that has to be searched by any algorithm to find the minimax value. In fact, for most games it is a directed graph. As demonstrated in chess and checkers, we show that the minimal graph is significantly smaller than previously thought, proving that there is more room for improvement of current algorithms. We exploit the graph properties of the search space to reduce the size of trees built in practice by at least 25%. For over a decade, fixed-depth alpha-beta searching has been considered a closed subject, with research moving on to more application-dependent techniques. This work opens up new avenues of research for further application-independent improvements.

  14. Fault Diagnosis of Steam Generator Using Signed Directed Graph and Artificial Neural Networks

    SciTech Connect

    Aly, Mohamed N.; Hegazy, Hesham N.

    2006-07-01

    Diagnosis is a very complex and important task for finding the root cause of faults in nuclear power plants. The objective of this paper is to investigate the feasibility of using the combination of signed directed graph (SDG) and artificial neural networks for fault diagnosis in nuclear power plants especially in U-Tube steam generator. Signed directed graph has been the most widely used form of qualitative based model methods for process fault diagnosis. It is constructed to represent the cause-effect relations among the dynamic process variables. Signed directed graph consists of nodes represent the process variables and branches. The branch represents the qualitative influence of a process variable on the related variable. The main problem in fault diagnosis using the signed directed graph is the unmeasured variables. Therefore, neural networks are used to estimate the values of unmeasured nodes. In this work, different four cases of faults in the steam generator ( SG) have been diagnosed, three of them are single fault and the fourth is multiple fault. The first three faults are by pass valve leakage (Vbp(+)), main feed water valve opening increase (Vfw(+)), main feed water valve opening decrease (Vfw (-)). The fourth fault is a multiple fault where by-pass valve leakage and main feed water valve opening decrease (Vbp(+) and Vfw (-)) in the same time. The used data are collected from a basic principle simulator of pressurized water reactor 925 Mwe. The signed directed graph of the steam generator is constructed to represent the cause-effect relations among SG variables. It consists of 26 nodes represent the SG variables, and 48 branches represent the cause effect relations among this variables. For each fault the values of measured nodes are coming from sensors and the values of unmeasured nodes are coming from the trained neural networks. These values of the nodes are compared by normal values to get the sign of the nodes. The cause-effect graph for each

  15. Compacting de Bruijn graphs from sequencing data quickly and in low memory

    PubMed Central

    Chikhi, Rayan; Limasset, Antoine; Medvedev, Paul

    2016-01-01

    Motivation: As the quantity of data per sequencing experiment increases, the challenges of fragment assembly are becoming increasingly computational. The de Bruijn graph is a widely used data structure in fragment assembly algorithms, used to represent the information from a set of reads. Compaction is an important data reduction step in most de Bruijn graph based algorithms where long simple paths are compacted into single vertices. Compaction has recently become the bottleneck in assembly pipelines, and improving its running time and memory usage is an important problem. Results: We present an algorithm and a tool bcalm 2 for the compaction of de Bruijn graphs. bcalm 2 is a parallel algorithm that distributes the input based on a minimizer hashing technique, allowing for good balance of memory usage throughout its execution. For human sequencing data, bcalm 2 reduces the computational burden of compacting the de Bruijn graph to roughly an hour and 3 GB of memory. We also applied bcalm 2 to the 22 Gbp loblolly pine and 20 Gbp white spruce sequencing datasets. Compacted graphs were constructed from raw reads in less than 2 days and 40 GB of memory on a single machine. Hence, bcalm 2 is at least an order of magnitude more efficient than other available methods. Availability and Implementation: Source code of bcalm 2 is freely available at: https://github.com/GATB/bcalm Contact: rayan.chikhi@univ-lille1.fr PMID:27307618

  16. Structure and Growth of the Leeward Kohala Field System: An Analysis with Directed Graphs

    PubMed Central

    Dye, Thomas S.

    2014-01-01

    This study illustrates how the theory of directed graphs can be used to investigate the structure and growth of the leeward Kohala field system, a traditional Hawaiian archaeological site that presents an unparalleled opportunity to investigate relative chronology. The relative chronological relationships of agricultural walls and trails in two detailed study areas are represented as directed graphs and then investigated using graph theoretic concepts including cycle, level, and connectedness. The structural properties of the directed graphs reveal structure in the field system at several spatial scales. A process of deduction yields a history of construction in each detailed study area that is different than the history produced by an earlier investigation. These results indicate that it is now possible to study the structure and growth of the entire field system remnant using computer software implementations of graph theoretic concepts applied to observations of agricultural wall and trail intersections made on aerial imagery and/or during fieldwork. A relative chronology of field system development with a resolution of one generation is a possible result. PMID:25058167

  17. A graph algebra for scalable visual analytics.

    PubMed

    Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V

    2012-01-01

    Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data. PMID:24806630

  18. Directed transport in quantum star graphs

    NASA Astrophysics Data System (ADS)

    Yusupov, Jambul; Dolgushev, Maxim; Blumen, Alexander; Mülken, Oliver

    2016-04-01

    We study the quantum dynamics of Gaussian wave packets on star graphs whose arms feature each a periodic potential and an external time-dependent field. Assuming that the potentials and the field can be manipulated separately for each arm of the star, we show that it is possible to manipulate the direction of the motion of a Gaussian wave packet through the bifurcation point by a suitable choice of the parameters of the external fields. In doing so, one can achieve a transmission of the wave packet into the desired arm with nearly 70 % while also keeping the shape of the wave packet approximately intact. Since a star graph is the simplest element of many other complex graphs, the obtained results can be considered as the first step to wave packet manipulations on complex networks.

  19. Dynamic graph system for a semantic database

    SciTech Connect

    Mizell, David

    2015-01-27

    A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.

  20. Interactive Web Graphs with Fewer Restrictions

    NASA Technical Reports Server (NTRS)

    Fiedler, James

    2012-01-01

    There is growing popularity for interactive, statistical web graphs and programs to generate them. However, it seems that these programs tend to be somewhat restricted in which web browsers and statistical software are supported. For example, the software might use SVG (e.g., Protovis, gridSVG) or HTML canvas, both of which exclude most versions of Internet Explorer, or the software might be made specifically for R (gridSVG, CRanvas), thus excluding users of other stats software. There are more general tools (d3, Rapha lJS) which are compatible with most browsers, but using one of these to make statistical graphs requires more coding than is probably desired, and requires learning a new tool. This talk will present a method for making interactive web graphs, which, by design, attempts to support as many browsers and as many statistical programs as possible, while also aiming to be relatively easy to use and relatively easy to extend.

  1. Scale-invariant geometric random graphs.

    PubMed

    Xie, Zheng; Rogers, Tim

    2016-03-01

    We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs. PMID:27078369

  2. A graph algebra for scalable visual analytics.

    PubMed

    Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V

    2012-01-01

    Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data.

  3. Dynamic graph system for a semantic database

    DOEpatents

    Mizell, David

    2016-04-12

    A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.

  4. Recession curbs gas pipeline construction costs

    SciTech Connect

    Morgan, J.M.

    1983-01-24

    This paper shows how after 5 yrs. of inflation, gas pipeline construction costs have finally felt the effects of a severe building recession. First quarter (1982) construction activity, compressor equipment and drive units, and high-pressure gas-station piping are discussed. Graphs of OGJ-Morgan composite gas pipeline cost, and gas pipeline cost component indexes are presented.

  5. Cognitive and attitudinal predictors related to graphing achievement among pre-service elementary teachers

    NASA Astrophysics Data System (ADS)

    Szyjka, Sebastian P.

    procedure allowed the researcher to explore the relationships among the affective and cognitive variables that were included in the regression analysis. The results for CFA indicated that the revised QALGS measure was sound in its psychometric properties when tested against the QASG. Reliability statistics indicated that the overall reliability for the 32 items in the QALGS was .90. The learning preferences construct had the lowest reliability (.67), while enjoyment (.89), confidence (.86) and usefulness (.77) constructs had moderate to high reliabilities. The first four measurement models fit the data well as indicated by the appropriate descriptive and statistical indices. However, the fifth measurement model did not fit the data well statistically, and only fit well with two descriptive indices. The results addressing the research question indicated that mathematical and logical thinking ability were significant predictors of line graph performance among the remaining group of variables. These predictors accounted for 41% of the total variability on the line graph performance variable. Partial correlation coefficients indicated that mathematics ability accounted for 20.5% of the variance on the line graphing performance variable when removing the effect of logical thinking. The logical thinking variable accounted for 4.7% of the variance on the line graphing performance variable when removing the effect of mathematics ability.

  6. The uniqueness of DMAX-matrix graph invariants.

    PubMed

    Dehmer, Matthias; Shi, Yongtang

    2014-01-01

    In this paper, we examine the uniqueness (discrimination power) of a newly proposed graph invariant based on the matrix DMAX defined by Randić et al. In order to do so, we use exhaustively generated graphs instead of special graph classes such as trees only. Using these graph classes allow us to generalize the findings towards complex networks as they usually do not possess any structural constraints. We obtain that the uniqueness of this newly proposed graph invariant is approximately as low as the uniqueness of the Balaban J index on exhaustively generated (general) graphs. PMID:24392099

  7. Graph isomorphism and adiabatic quantum computing

    NASA Astrophysics Data System (ADS)

    Gaitan, Frank; Clark, Lane

    2014-02-01

    In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G →G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap Δ (N) separating the ground and first-excited states in the limit of large problem size N ≫1. Calculating Δ (N) in this limit is a fundamental open problem in adiabatic quantum computing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantum computing has been shown to be equivalent to the circuit model of quantum computing, and so development of adiabatic quantum algorithms continues to be of great interest.

  8. Building an EEG-fMRI Multi-Modal Brain Graph: A Concurrent EEG-fMRI Study

    PubMed Central

    Yu, Qingbao; Wu, Lei; Bridwell, David A.; Erhardt, Erik B.; Du, Yuhui; He, Hao; Chen, Jiayu; Liu, Peng; Sui, Jing; Pearlson, Godfrey; Calhoun, Vince D.

    2016-01-01

    The topological architecture of brain connectivity has been well-characterized by graph theory based analysis. However, previous studies have primarily built brain graphs based on a single modality of brain imaging data. Here we develop a framework to construct multi-modal brain graphs using concurrent EEG-fMRI data which are simultaneously collected during eyes open (EO) and eyes closed (EC) resting states. FMRI data are decomposed into independent components with associated time courses by group independent component analysis (ICA). EEG time series are segmented, and then spectral power time courses are computed and averaged within 5 frequency bands (delta; theta; alpha; beta; low gamma). EEG-fMRI brain graphs, with EEG electrodes and fMRI brain components serving as nodes, are built by computing correlations within and between fMRI ICA time courses and EEG spectral power time courses. Dynamic EEG-fMRI graphs are built using a sliding window method, versus static ones treating the entire time course as stationary. In global level, static graph measures and properties of dynamic graph measures are different across frequency bands and are mainly showing higher values in eyes closed than eyes open. Nodal level graph measures of a few brain components are also showing higher values during eyes closed in specific frequency bands. Overall, these findings incorporate fMRI spatial localization and EEG frequency information which could not be obtained by examining only one modality. This work provides a new approach to examine EEG-fMRI associations within a graph theoretic framework with potential application to many topics. PMID:27733821

  9. Key-Node-Separated Graph Clustering and Layouts for Human Relationship Graph Visualization.

    PubMed

    Itoh, Takayuki; Klein, Karsten

    2015-01-01

    Many graph-drawing methods apply node-clustering techniques based on the density of edges to find tightly connected subgraphs and then hierarchically visualize the clustered graphs. However, users may want to focus on important nodes and their connections to groups of other nodes for some applications. For this purpose, it is effective to separately visualize the key nodes detected based on adjacency and attributes of the nodes. This article presents a graph visualization technique for attribute-embedded graphs that applies a graph-clustering algorithm that accounts for the combination of connections and attributes. The graph clustering step divides the nodes according to the commonality of connected nodes and similarity of feature value vectors. It then calculates the distances between arbitrary pairs of clusters according to the number of connecting edges and the similarity of feature value vectors and finally places the clusters based on the distances. Consequently, the technique separates important nodes that have connections to multiple large clusters and improves the visibility of such nodes' connections. To test this technique, this article presents examples with human relationship graph datasets, including a coauthorship and Twitter communication network dataset.

  10. From cognitive maps to cognitive graphs.

    PubMed

    Chrastil, Elizabeth R; Warren, William H

    2014-01-01

    We investigate the structure of spatial knowledge that spontaneously develops during free exploration of a novel environment. We present evidence that this structure is similar to a labeled graph: a network of topological connections between places, labeled with local metric information. In contrast to route knowledge, we find that the most frequent routes and detours to target locations had not been traveled during learning. Contrary to purely topological knowledge, participants typically traveled the shortest metric distance to a target, rather than topologically equivalent but longer paths. The results are consistent with the proposal that people learn a labeled graph of their environment.

  11. PolyGraph: a Polymer Visualization system

    NASA Astrophysics Data System (ADS)

    Cutkosky, Ashok; Tarazi, Najeeb; Lieberman Aiden, Erez

    2012-02-01

    Rapid advances in computational hardware and parallelization have made complex simulations of large polymers increasingly ubiquitous. However, visualizing such simulations remains a challenge. Here we present PolyGraph, a Blender-powered visualization system for complex polymer simulations. As a specific example, we study molecular dynamics simulations of condensing polymers. We illustrate our initial simulation results, suggesting that formation of local beads is an initial step in the condensation process. (This finding is consistent with earlier conjectures about polymer condensation.) PolyGraph makes it possible to create precise and visually appealing clips of polymer simulations. *contributed equally

  12. From Cognitive Maps to Cognitive Graphs

    PubMed Central

    Chrastil, Elizabeth R.; Warren, William H.

    2014-01-01

    We investigate the structure of spatial knowledge that spontaneously develops during free exploration of a novel environment. We present evidence that this structure is similar to a labeled graph: a network of topological connections between places, labeled with local metric information. In contrast to route knowledge, we find that the most frequent routes and detours to target locations had not been traveled during learning. Contrary to purely topological knowledge, participants typically traveled the shortest metric distance to a target, rather than topologically equivalent but longer paths. The results are consistent with the proposal that people learn a labeled graph of their environment. PMID:25389769

  13. Quasiperiodic graphs at the onset of chaos.

    PubMed

    Luque, B; Cordero-Gracia, M; Gómez, M; Robledo, A

    2013-12-01

    We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.

  14. Graphing techniques for materials laboratory using Excel

    NASA Technical Reports Server (NTRS)

    Kundu, Nikhil K.

    1994-01-01

    Engineering technology curricula stress hands on training and laboratory practices in most of the technical courses. Laboratory reports should include analytical as well as graphical evaluation of experimental data. Experience shows that many students neither have the mathematical background nor the expertise for graphing. This paper briefly describes the procedure and data obtained from a number of experiments such as spring rate, stress concentration, endurance limit, and column buckling for a variety of materials. Then with a brief introduction to Microsoft Excel the author explains the techniques used for linear regression and logarithmic graphing.

  15. Isomorphisms between Petri nets and dataflow graphs

    NASA Technical Reports Server (NTRS)

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

    1987-01-01

    Dataflow graphs are a generalized model of computation. Uninterpreted dataflow graphs with nondeterminism resolved via probabilities are shown to be isomorphic to a class of Petri nets known as free choice nets. Petri net analysis methods are readily available in the literature and this result makes those methods accessible to dataflow research. Nevertheless, combinatorial explosion can render Petri net analysis inoperative. Using a previously known technique for decomposing free choice nets into smaller components, it is demonstrated that, in principle, it is possible to determine aspects of the overall behavior from the particular behavior of components.

  16. Lattices of processes in graphs with inputs

    SciTech Connect

    Shakhbazyan, K.V.

    1995-09-01

    This article is a continuation of others work, presenting a detailed analysis of finite lattices of processes in graphs with input nodes. Lattices of processes in such graphs are studied by representing the lattices in the form of an algebra of pairs. We define the algebra of pairs somewhat generalizing the definition. Let K and D be bounded distributive lattices. A sublattice {delta} {contained_in} K x D is called an algebra of pairs if for all K {element_of} K we have (K, 1{sub D}) {element_of} {delta} and for all d {element_of} D we have (O{sub K}).

  17. A Similarity Search Using Molecular Topological Graphs

    PubMed Central

    Fukunishi, Yoshifumi; Nakamura, Haruki

    2009-01-01

    A molecular similarity measure has been developed using molecular topological graphs and atomic partial charges. Two kinds of topological graphs were used. One is the ordinary adjacency matrix and the other is a matrix which represents the minimum path length between two atoms of the molecule. The ordinary adjacency matrix is suitable to compare the local structures of molecules such as functional groups, and the other matrix is suitable to compare the global structures of molecules. The combination of these two matrices gave a similarity measure. This method was applied to in silico drug screening, and the results showed that it was effective as a similarity measure. PMID:20037730

  18. Single-qubit gates by graph scattering

    NASA Astrophysics Data System (ADS)

    Underwood, Michael S.; Blumer, Benjamin A.; Feder, David L.

    2012-02-01

    Continuous-time quantum walkers with tightly peaked momenta can simulate quantum computations by scattering off finite graphs. We enumerate all single-qubit gates that can be enacted by scattering off a single graph on up to n=9 vertices at certain momentum values, and provide numerical evidence that the number of such gates grows exponentially with n. The single-qubit rotations are about axes distributed roughly uniformly on the Bloch sphere, and rotations by both rational and irrational multiples of π are found.

  19. Quantifying Riverscape Connectivity with Graph Theory

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

  20. Information Retrieval and Graph Analysis Approaches for Book Recommendation

    PubMed Central

    Benkoussas, Chahinez; Bellot, Patrice

    2015-01-01

    A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments. PMID:26504899

  1. Percolation thresholds on planar Euclidean relative-neighborhood graphs

    NASA Astrophysics Data System (ADS)

    Melchert, O.

    2013-04-01

    In the present article, statistical properties regarding the topology and standard percolation on relative neighborhood graphs (RNGs) for planar sets of points, considering the Euclidean metric, are put under scrutiny. RNGs belong to the family of “proximity graphs”; i.e., their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge. Therefore they are, e.g., discussed in the context of the construction of backbones for wireless ad hoc networks that guarantee connectedness of all underlying nodes. Here, by means of numerical simulations, we determine the asymptotic degree and diameter of RNGs and we estimate their bond and site percolation thresholds, which were previously conjectured to be nontrivial. We compare the results to regular 2D graphs for which the degree is close to that of the RNG. Finally, we deduce the common percolation critical exponents from the RNG data to verify that the associated universality class is that of standard 2D percolation.

  2. Using graph theory to describe and model chromosome aberrations.

    PubMed

    Sachs, Rainer K; Arsuaga, Javier; Vázquez, Mariel; Hlatky, Lynn; Hahnfeldt, Philip

    2002-11-01

    A comprehensive description of chromosome aberrations is introduced that is suitable for all cytogenetic protocols (e.g. solid staining, banding, FISH, mFISH, SKY, bar coding) and for mathematical analyses. "Aberration multigraphs" systematically characterize and interrelate three basic aberration elements: (1) the initial configuration of chromosome breaks; (2) the exchange process, whose cycle structure helps to describe aberration complexity; and (3) the final configuration of rearranged chromosomes, which determines the observed pattern but may contain cryptic misrejoinings in addition. New aberration classification methods and a far-reaching generalization of mPAINT descriptors, applicable to any protocol, emerge. The difficult problem of trying to infer actual exchange processes from cytogenetically observed final patterns is analyzed using computer algorithms, adaptations of known theorems on cubic graphs, and some new graph-theoretical constructs. Results include the following: (1) For a painting protocol, unambiguously inferring the occurrence of a high-order cycle requires a corresponding number of different colors; (2) cycle structure can be computed by a simple trick directly from mPAINT descriptors if the initial configuration has no more than one break per homologue pair; and (3) higher-order cycles are more frequent than the obligate cycle structure specifies. Aberration multigraphs are a powerful new way to describe, classify and quantitatively analyze radiation-induced chromosome aberrations. They pinpoint (but do not eliminate) the problem that, with present cytogenetic techniques, one observed pattern corresponds to many possible initial configurations and exchange processes. PMID:12385633

  3. Interactive visual analysis of families of function graphs.

    PubMed

    Konyha, Zoltán; Matković, Kresimir; Gracanin, Denis; Jelović, Mario; Hauser, Helwig

    2006-01-01

    The analysis and exploration of multidimensional and multivariate data is still one of the most challenging areas in the field of visualization. In this paper, we describe an approach to visual analysis of an especially challenging set of problems that exhibit a complex internal data structure. We describe the interactive visual exploration and analysis of data that includes several (usually large) families of function graphs fi (x, t). We describe analysis procedures and practical aspects of the interactive visual analysis specific to this type of data (with emphasis on the function graph characteristic of the data). We adopted the well-proven approach of multiple, linked views with advanced interactive brushing to assess the data. Standard views such as histograms, scatterplots, and parallel coordinates are used to jointly visualize data. We support iterative visual analysis by providing means to create complex, composite brushes that span multiple views and that are constructed using different combination schemes. We demonstrate that engineering applications represent a challenging but very applicable area for visual analytics. As a case study, we describe the optimization of a fuel injection system in diesel engines of passenger cars.

  4. INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization

    SciTech Connect

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

    2012-10-01

    It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some \\emph{NP}-hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms we have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.

  5. Graph theoretical analysis of EEG functional connectivity during music perception.

    PubMed

    Wu, Junjie; Zhang, Junsong; Liu, Chu; Liu, Dongwei; Ding, Xiaojun; Zhou, Changle

    2012-11-01

    The present study evaluated the effect of music on large-scale structure of functional brain networks using graph theoretical concepts. While most studies on music perception used Western music as an acoustic stimulus, Guqin music, representative of Eastern music, was selected for this experiment to increase our knowledge of music perception. Electroencephalography (EEG) was recorded from non-musician volunteers in three conditions: Guqin music, noise and silence backgrounds. Phase coherence was calculated in the alpha band and between all pairs of EEG channels to construct correlation matrices. Each resulting matrix was converted into a weighted graph using a threshold, and two network measures: the clustering coefficient and characteristic path length were calculated. Music perception was found to display a higher level mean phase coherence. Over the whole range of thresholds, the clustering coefficient was larger while listening to music, whereas the path length was smaller. Networks in music background still had a shorter characteristic path length even after the correction for differences in mean synchronization level among background conditions. This topological change indicated a more optimal structure under music perception. Thus, prominent small-world properties are confirmed in functional brain networks. Furthermore, music perception shows an increase of functional connectivity and an enhancement of small-world network organizations.

  6. A graph-theoretic approach to comparing and integrating genetic, physical and sequence-based maps.

    PubMed Central

    Yap, Immanuel V; Schneider, David; Kleinberg, Jon; Matthews, David; Cartinhour, Samuel; McCouch, Susan R

    2003-01-01

    For many species, multiple maps are available, often constructed independently by different research groups using different sets of markers and different source material. Integration of these maps provides a higher density of markers and greater genome coverage than is possible using a single study. In this article, we describe a novel approach to comparing and integrating maps by using abstract graphs. A map is modeled as a directed graph in which nodes represent mapped markers and edges define the order of adjacent markers. Independently constructed graphs representing corresponding maps from different studies are merged on the basis of their common loci. Absence of a path between two nodes indicates that their order is undetermined. A cycle indicates inconsistency among the mapping studies with regard to the order of the loci involved. The integrated graph thus produced represents a complete picture of all of the mapping studies that comprise it, including all of the ambiguities and inconsistencies among them. The objective of this representation is to guide additional research aimed at interpreting these ambiguities and inconsistencies in locus order rather than presenting a "consensus order" that ignores these problems. PMID:14704199

  7. Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping.

    PubMed

    Behjat, Hamid; Leonardi, Nora; Sörnmo, Leif; Van De Ville, Dimitri

    2015-12-01

    A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.

  8. Decision graphs: a tool for developing real-time software

    SciTech Connect

    Kozubal, A.J.

    1981-01-01

    The use of decision graphs in the preparation of, in particular, real-time software is briefly described. The usefulness of decision graphs in software design, testing, and maintenance is pointed out. 2 figures. (RWR)

  9. On Ramsey (3K2, K3) - minimal graphs

    NASA Astrophysics Data System (ADS)

    Wijaya, Kristiana; Baskoro, Edy Tri; Assiyatun, Hilda; Suprijanto, Djoko

    2016-02-01

    The Ramsey graph theory has many interesting applications, such as in the fields of communications, information retrieval, and decision making. One of growing topics in Ramsey theory is Ramsey minimal graph. For any given graphs G and H, find graphs F such that any red-blue coloring of all edges of F contains either a red copy of G or a blue copy of H. If this condition is not satisfied by the graph F - e, then we call the graph F as a Ramsey (G, H) - minimal. In this paper, we derive the properties of (3K2, K3) - minimal graphs. We, then, characterize all Ramsey (3K2, K3) - minimal graphs.

  10. Using Dynamic Graphs to Reveal Student Reasoning

    ERIC Educational Resources Information Center

    Lassak, Marshall

    2009-01-01

    Using dynamic graphs, future secondary mathematics teachers were able to represent and communicate their understanding of a brief mathematical investigation in a way that a symbolic proof of the problem could not. Four different student work samples are discussed. (Contains 6 figures.)

  11. Communication Graph Generator for Parallel Programs

    SciTech Connect

    2014-04-08

    Graphator is a collection of relatively simple sequential programs that generate communication graphs/matrices for commonly occurring patterns in parallel programs. Currently, there is support for five communication patterns: two-dimensional 4-point stencil, four-dimensional 8-point stencil, all-to-alls over sub-communicators, random near-neighbor communication, and near-neighbor communication.

  12. Colour Mathematics: With Graphs and Numbers

    ERIC Educational Resources Information Center

    LoPresto, Michael C.

    2009-01-01

    The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…

  13. Colour mathematics: with graphs and numbers

    NASA Astrophysics Data System (ADS)

    Lo Presto, Michael C.

    2009-07-01

    The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just attempting to memorize them.

  14. Isoperimetric graph partitioning for image segmentation.

    PubMed

    Grady, Leo; Schwartz, Eric L

    2006-03-01

    Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.

  15. Examining Students' Reluctance to Use Graphs

    ERIC Educational Resources Information Center

    Dyke, Frances Van; White, Alexander

    2004-01-01

    An evaluation designed to test basic graphical-thinking skills to students entering calculus or applied calculus at American University was given to use the assessment to discover the underlying causes for student's inability to use graphs effectively. The study indicates that graphical representation is not emphasized properly in the curriculum…

  16. Marking Student Programs Using Graph Similarity

    ERIC Educational Resources Information Center

    Naude, Kevin A.; Greyling, Jean H.; Vogts, Dieter

    2010-01-01

    We present a novel approach to the automated marking of student programming assignments. Our technique quantifies the structural similarity between unmarked student submissions and marked solutions, and is the basis by which we assign marks. This is accomplished through an efficient novel graph similarity measure ("AssignSim"). Our experiments…

  17. An Ellipse Morphs to a Cosine Graph!

    ERIC Educational Resources Information Center

    King, L .R.

    2013-01-01

    We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the…

  18. Product disassembly scheduling using graph models

    NASA Astrophysics Data System (ADS)

    Puente Mendez, Santiago; Torres Medina, Fernando; Pomares Baeza, Jorge

    2002-02-01

    Disassembly problem is a current issue for industrial companies. Governments of different countries promote research in this field. This paper presents the following points. First a brief state of the art in disassembly planning. Next it exposes a solution for the disassembly problem of industrial products. It uses a combination between direct and indirect graph representation for the product, all components that have physical entity are considered as vertices of the graph. Edges of the graph represent the relationships between vertices. There are three different types of edges. First corresponds with accessibility and fastener restrictions. Second corresponds with direct relations between components without fasteners. Last one corresponds with contact relationships, which represent an indifferent choice of the vertices. Based on that representation the paper exposed a method to find the best sequence to disassemble a component. Costs of disassembling each component and of changing tool between each pair of vertices and different sequences of the disassembly are taken into consideration. This method consists in a function minimization defined in the graph domain. In the last point of the paper this method is tested with a remote control disassembly. This method gives a solution to the problem, if several solutions, with the same cost, exist then it gives all of them, and any one of these disassemble sequences could be used to achieve to the target component.

  19. Using Tables and Graphs for Reporting Data.

    PubMed

    Bavdekar, Sandeep B

    2015-10-01

    For presenting the study results, authors need to choose from one of the three formats: text, tables and graphs. The underlying consideration of any author while making the choice is to ensure that readers find it easy to understand, to assist the author present data in a way that would catch the reader's eye, hold his interest and enhance his understanding. The choice should, therefore, be based on the advantages and limitations of each of these formats. Most of the observations are reported in textual format. Tables are useful when comparisons are to be shown. Graphs attract readers' attention better and the data they depict remains in the reader's memory. The type of graph used is dependent upon the nature of data that is to be shown. Every research paper has a lot to say through the data that has been collected and analyzed. However, this data needs to be presented in a logical, coherent and easy-to-understand manner. The way data is presented can influence the reviewers' and editors' decision. It can also make the difference between a paper being appreciated by the readers or being neglected or even trashed by them. Tables and Graphs are the two important tools that authors use to make the data more presentable and easy to read and understand. PMID:27608693

  20. Simple scale interpolator facilitates reading of graphs

    NASA Technical Reports Server (NTRS)

    Fazio, A.; Henry, B.; Hood, D.

    1966-01-01

    Set of cards with scale divisions and a scale finder permits accurate reading of the coordinates of points on linear or logarithmic graphs plotted on rectangular grids. The set contains 34 different scales for linear plotting and 28 single cycle scales for log plots.

  1. Signals on Graphs: Uncertainty Principle and Sampling

    NASA Astrophysics Data System (ADS)

    Tsitsvero, Mikhail; Barbarossa, Sergio; Di Lorenzo, Paolo

    2016-09-01

    In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual. Then, building on this framework, we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band-limited signals from a subset of samples. We show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms, including a generalization to frame-based reconstruction methods. After showing that the performance of signal recovery algorithms is significantly affected by the location of samples, we suggest and compare a few alternative sampling strategies. Finally, we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise, showing that this problem is also intrinsically related to vertex-frequency localization properties.

  2. GraphPrints: Towards a Graph Analytic Method for Network Anomaly Detection

    SciTech Connect

    Harshaw, Chris R; Bridges, Robert A; Iannacone, Michael D; Reed, Joel W; Goodall, John R

    2016-01-01

    This paper introduces a novel graph-analytic approach for detecting anomalies in network flow data called \\textit{GraphPrints}. Building on foundational network-mining techniques, our method represents time slices of traffic as a graph, then counts graphlets\\textemdash small induced subgraphs that describe local topology. By performing outlier detection on the sequence of graphlet counts, anomalous intervals of traffic are identified, and furthermore, individual IPs experiencing abnormal behavior are singled-out. Initial testing of GraphPrints is performed on real network data with an implanted anomaly. Evaluation shows false positive rates bounded by 2.84\\% at the time-interval level, and 0.05\\% at the IP-level with 100\\% true positive rates at both.

  3. Multigraph: Interactive Data Graphs on the Web

    NASA Astrophysics Data System (ADS)

    Phillips, M. B.

    2010-12-01

    Many aspects of geophysical science involve time dependent data that is often presented in the form of a graph. Considering that the web has become a primary means of communication, there are surprisingly few good tools and techniques available for presenting time-series data on the web. The most common solution is to use a desktop tool such as Excel or Matlab to create a graph which is saved as an image and then included in a web page like any other image. This technique is straightforward, but it limits the user to one particular view of the data, and disconnects the graph from the data in a way that makes updating a graph with new data an often cumbersome manual process. This situation is somewhat analogous to the state of mapping before the advent of GIS. Maps existed only in printed form, and creating a map was a laborious process. In the last several years, however, the world of mapping has experienced a revolution in the form of web-based and other interactive computer technologies, so that it is now commonplace for anyone to easily browse through gigabytes of geographic data. Multigraph seeks to bring a similar ease of access to time series data. Multigraph is a program for displaying interactive time-series data graphs in web pages that includes a simple way of configuring the appearance of the graph and the data to be included. It allows multiple data sources to be combined into a single graph, and allows the user to explore the data interactively. Multigraph lets users explore and visualize "data space" in the same way that interactive mapping applications such as Google Maps facilitate exploring and visualizing geography. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file and requires no programming. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf

  4. Consensus dynamics on random rectangular graphs

    NASA Astrophysics Data System (ADS)

    Estrada, Ernesto; Sheerin, Matthew

    2016-06-01

    A random rectangular graph (RRG) is a generalization of the random geometric graph (RGG) in which the nodes are embedded into a rectangle with side lengths a and b = 1 / a, instead of on a unit square [ 0 , 1 ] 2. Two nodes are then connected if and only if they are separated at a Euclidean distance smaller than or equal to a certain threshold radius r. When a = 1 the RRG is identical to the RGG. Here we apply the consensus dynamics model to the RRG. Our main result is a lower bound for the time of consensus, i.e., the time at which the network reaches a global consensus state. To prove this result we need first to find an upper bound for the algebraic connectivity of the RRG, i.e., the second smallest eigenvalue of the combinatorial Laplacian of the graph. This bound is based on a tight lower bound found for the graph diameter. Our results prove that as the rectangle in which the nodes are embedded becomes more elongated, the RRG becomes a 'large-world', i.e., the diameter grows to infinity, and a poorly-connected graph, i.e., the algebraic connectivity decays to zero. The main consequence of these findings is the proof that the time of consensus in RRGs grows to infinity as the rectangle becomes more elongated. In closing, consensus dynamics in RRGs strongly depend on the geometric characteristics of the embedding space, and reaching the consensus state becomes more difficult as the rectangle is more elongated.

  5. Concepts and Misconceptions in Comprehension of Hierarchical Graphs

    ERIC Educational Resources Information Center

    Korner, Christof

    2005-01-01

    Hierarchical graphs represent relationships between objects (like computer file systems, family trees etc.). Graph nodes represent the objects and interconnecting lines represent the relationships. In two experiments we investigated what concepts are necessary for understanding hierarchical graphs, what misconceptions evolve when some of the…

  6. Hands-on Science: Getting-to-Know-You Graphing.

    ERIC Educational Resources Information Center

    Kepler, Lynne

    1992-01-01

    Elementary teachers can use graphing to introduce students to one another. An eye color graphing activity helps students learn more about each other while experimenting with different ways of organizing and displaying information. For follow up, students can apply their graphing knowledge by collecting and displaying data from their families. (SM)

  7. Can Comparison of Contrastive Examples Facilitate Graph Understanding?

    ERIC Educational Resources Information Center

    Smith, Linsey A.; Gentner, Dedre

    2011-01-01

    The authors explore the role of comparison in improving graph fluency. The ability to use graphs fluently is crucial for STEM achievement, but graphs are challenging to interpret and produce because they often involve integration of multiple variables, continuous change in variables over time, and omission of certain details in order to highlight…

  8. Sharing the Spotlight: Humane Education and Bar Graphs.

    ERIC Educational Resources Information Center

    Dewey, Paul

    1987-01-01

    Promotes the use of humane education as a vehicle for teaching students how to make bar graphs. Provides ideas for bar graph activities for both primary- and intermediate-grade children that focus on different kinds of domestic and wild animals. Suggests expanded types of graphing activities involving survey techniques. (TW)

  9. An Interactive Graphing Tool for Web-Based Courses.

    ERIC Educational Resources Information Center

    Kennedy, David M.; Fritze, Paul

    This paper reports on a project involving the development and formative evaluation of an interactive World Wide Web-based learning tool. The interactive graphing tool (IGT) permits students to sketch a graph on screen using a mouse and responds to a wide range of common graph types. The IGT facilitates an iterative approach to understanding…

  10. Graphing Online Searches with Lotus 1-2-3.

    ERIC Educational Resources Information Center

    Persson, Olle

    1986-01-01

    This article illustrates how Lotus 1-2-3 software can be used to create graphs using downloaded online searches as raw material, notes most commands applied, and outlines three required steps: downloading, importing the downloading file into the worksheet, and making graphs. An example in bibliometrics and sample graphs are included. (EJS)

  11. Deterministic dense coding and faithful teleportation with multipartite graph states

    SciTech Connect

    Huang, C.-Y.; Yu, I-C.; Lin, F.-L.; Hsu, L.-Y.

    2009-05-15

    We propose schemes to perform the deterministic dense coding and faithful teleportation with multipartite graph states. We also find the sufficient and necessary condition of a viable graph state for the proposed schemes. That is, for the associated graph, the reduced adjacency matrix of the Tanner-type subgraph between senders and receivers should be invertible.

  12. Students' Cognitive Reasoning of Graphs: Characteristics and Progression

    ERIC Educational Resources Information Center

    Wang, Zu Hao; Wei, Silin; Ding, Wei; Chen, Xiuyun; Wang, Xiaonan; Hu, Kaiyan

    2012-01-01

    Graphs are widely used to present scientific information. Information presented in graphs can be classified into three kinds: explicit information, tacit information, and conclusive information. Reading information from graphs requires not only science content knowledge and understanding but also general logical reasoning. This study examined the…

  13. Learning Financial Reports From Mixed Symbolic-Spatial Graphs

    ERIC Educational Resources Information Center

    Tanlamai, Uthai; Soongswang, Oranuj

    2011-01-01

    Mixed visuals of numbers and graphs are available in various financial reports that demonstrate the financial status and risks of a firm. GWN (graphs with numbers) and TWG (table of numbers with graphs) were used as two alternative visuals derived from the actual data of two large public companies, one from food manufacturing industry (food) and…

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

    PubMed Central

    Peebles, David; Ali, Nadia

    2015-01-01

    The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987) has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 × 2 “interaction” bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices—and contrary to the assumptions of several graph comprehension models—experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension. PMID:26579052

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

    PubMed

    Peebles, David; Ali, Nadia

    2015-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Wang, Na; Li, Dong; Wang, Qiwen

    2012-12-01

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

  17. Combination of graph heuristics in producing initial solution of curriculum based course timetabling problem

    NASA Astrophysics Data System (ADS)

    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.

  18. Graph Databases for Large-Scale Healthcare Systems: A Framework for Efficient Data Management and Data Services

    SciTech Connect

    Park, Yubin; Shankar, Mallikarjun; Park, Byung H.; Ghosh, Dr. Joydeep

    2014-01-01

    Designing a database system for both efficient data management and data services has been one of the enduring challenges in the healthcare domain. In many healthcare systems, data services and data management are often viewed as two orthogonal tasks; data services refer to retrieval and analytic queries such as search, joins, statistical data extraction, and simple data mining algorithms, while data management refers to building error-tolerant and non-redundant database systems. The gap between service and management has resulted in rigid database systems and schemas that do not support effective analytics. We compose a rich graph structure from an abstracted healthcare RDBMS to illustrate how we can fill this gap in practice. We show how a healthcare graph can be automatically constructed from a normalized relational database using the proposed 3NF Equivalent Graph (3EG) transformation.We discuss a set of real world graph queries such as finding self-referrals, shared providers, and collaborative filtering, and evaluate their performance over a relational database and its 3EG-transformed graph. Experimental results show that the graph representation serves as multiple de-normalized tables, thus reducing complexity in a database and enhancing data accessibility of users. Based on this finding, we propose an ensemble framework of databases for healthcare applications.

  19. Advantages of Micro-Based Labs: Electronic Data Acquisition, Computerized Graphing, or Both?

    ERIC Educational Resources Information Center

    Stuessy, Carol L.; Rowland, Paul M.

    1989-01-01

    Discusses a microcomputer-based laboratory (MBL) study (n=75) which uses multiple temperature gathering devices (mercury thermometer, digital thermometer, and computer probe) and graphing methods (hand graphs, delayed computer graphs, and real-time graphs). Reports that MBL real-time graphing provides significant increases in graphing skills. (MVL)

  20. Hyperspectral Data Classification Using Factor Graphs

    NASA Astrophysics Data System (ADS)

    Makarau, A.; Müller, R.; Palubinskas, G.; Reinartz, P.

    2012-07-01

    Accurate classification of hyperspectral data is still a competitive task and new classification methods are developed to achieve desired tasks of hyperspectral data use. The objective of this paper is to develop a new method for hyperspectral data classification ensuring the classification model properties like transferability, generalization, probabilistic interpretation, etc. While factor graphs (undirected graphical models) are unfortunately not widely employed in remote sensing tasks, these models possess important properties such as representation of complex systems to model estimation/decision making tasks. In this paper we present a new method for hyperspectral data classification using factor graphs. Factor graph (a bipartite graph consisting of variables and factor vertices) allows factorization of a more complex function leading to definition of variables (employed to store input data), latent variables (allow to bridge abstract class to data), and factors (defining prior probabilities for spectral features and abstract classes; input data mapping to spectral features mixture and further bridging of the mixture to an abstract class). Latent variables play an important role by defining two-level mapping of the input spectral features to a class. Configuration (learning) on training data of the model allows calculating a parameter set for the model to bridge the input data to a class. The classification algorithm is as follows. Spectral bands are separately pre-processed (unsupervised clustering is used) to be defined on a finite domain (alphabet) leading to a representation of the data on multinomial distribution. The represented hyperspectral data is used as input evidence (evidence vector is selected pixelwise) in a configured factor graph and an inference is run resulting in the posterior probability. Variational inference (Mean field) allows to obtain plausible results with a low calculation time. Calculating the posterior probability for each class

  1. Coverability graphs for a class of synchronously executed unbounded Petri net

    NASA Technical Reports Server (NTRS)

    Stotts, P. David; Pratt, Terrence W.

    1990-01-01

    After detailing a variant of the concurrent-execution rule for firing of maximal subsets, in which the simultaneous firing of conflicting transitions is prohibited, an algorithm is constructed for generating the coverability graph of a net executed under this synchronous firing rule. The omega insertion criteria in the algorithm are shown to be valid for any net on which the algorithm terminates. It is accordingly shown that the set of nets on which the algorithm terminates includes the 'conflict-free' class.

  2. Distance-based topological polynomials and indices of friendship graphs.

    PubMed

    Gao, Wei; Farahani, Mohammad Reza; Imran, Muhammad; Rajesh Kanna, M R

    2016-01-01

    Drugs and chemical compounds are often modeled as graphs in which the each vertex of the graph expresses an atom of molecule and covalent bounds between atoms are represented by the edges between their corresponding vertices. The topological indicators defined over this molecular graph have been shown to be strongly correlated to various chemical properties of the compounds. In this article, by means of graph structure analysis, we determine several distance based topological indices of friendship graph [Formula: see text] which is widely appeared in various classes of new nanomaterials, drugs and chemical compounds. PMID:27652136

  3. On the effective size of a non-Weyl graph

    NASA Astrophysics Data System (ADS)

    Lipovský, Jiřˇí

    2016-09-01

    We show how to find the coefficient of the leading term of the resonance asymptotics using the method of pseudo-orbit expansion for quantum graphs which do not obey Weyl asymptotics. For a non-Weyl graph we develop a method to reduce the number of edges of a corresponding directed graph. Through this method we prove bounds on the above coefficient depending on the structure of the graph, for graphs with the same lengths of internal edges. We explicitly find the positions of the resolvent resonances.

  4. StreamWorks - A system for Dynamic Graph Search

    SciTech Connect

    Choudhury, Sutanay; Holder, Larry; Chin, George; Ray, Abhik; Beus, Sherman J.; Feo, John T.

    2013-06-11

    Acting on time-critical events by processing ever growing social media, news or cyber data streams is a major technical challenge. Many of these data sources can be modeled as multi-relational graphs. Mining and searching for subgraph patterns in a continuous setting requires an efficient approach to incremental graph search. The goal of our work is to enable real-time search capabilities for graph databases. This demonstration will present a dynamic graph query system that leverages the structural and semantic characteristics of the underlying multi-relational graph.

  5. Modular Environment for Graph Research and Analysis with a Persistent

    2009-11-18

    The MEGRAPHS software package provides a front-end to graphs and vectors residing on special-purpose computing resources. It allows these data objects to be instantiated, destroyed, and manipulated. A variety of primitives needed for typical graph analyses are provided. An example program illustrating how MEGRAPHS can be used to implement a PageRank computation is included in the distribution.The MEGRAPHS software package is targeted towards developers of graph algorithms. Programmers using MEGRAPHS would write graph analysis programsmore » in terms of high-level graph and vector operations. These computations are transparently executed on the Cray XMT compute nodes.« less

  6. The F-coindex of some graph operations.

    PubMed

    De, Nilanjan; Nayeem, Sk Md Abu; Pal, Anita

    2016-01-01

    The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.

  7. A Graph Based Interface for Representing Volume Visualization Results

    NASA Technical Reports Server (NTRS)

    Patten, James M.; Ma, Kwan-Liu

    1998-01-01

    This paper discusses a graph based user interface for representing the results of the volume visualization process. As images are rendered, they are connected to other images in a graph based on their rendering parameters. The user can take advantage of the information in this graph to understand how certain rendering parameter changes affect a dataset, making the visualization process more efficient. Because the graph contains more information than is contained in an unstructured history of images, the image graph is also helpful for collaborative visualization and animation.

  8. Modular Environment for Graph Research and Analysis with a Persistent

    SciTech Connect

    JANSSEN, CURTIS; EVENSKY, DAVID

    2009-11-18

    The MEGRAPHS software package provides a front-end to graphs and vectors residing on special-purpose computing resources. It allows these data objects to be instantiated, destroyed, and manipulated. A variety of primitives needed for typical graph analyses are provided. An example program illustrating how MEGRAPHS can be used to implement a PageRank computation is included in the distribution.The MEGRAPHS software package is targeted towards developers of graph algorithms. Programmers using MEGRAPHS would write graph analysis programs in terms of high-level graph and vector operations. These computations are transparently executed on the Cray XMT compute nodes.

  9. Constructing Phylogenetic Networks Based on the Isomorphism of Datasets.

    PubMed

    Wang, Juan; Zhang, Zhibin; Li, Yanjuan

    2016-01-01

    Constructing rooted phylogenetic networks from rooted phylogenetic trees has become an important problem in molecular evolution. So far, many methods have been presented in this area, in which most efficient methods are based on the incompatible graph, such as the CASS, the LNETWORK, and the BIMLR. This paper will research the commonness of the methods based on the incompatible graph, the relationship between incompatible graph and the phylogenetic network, and the topologies of incompatible graphs. We can find out all the simplest datasets for a topology G and construct a network for every dataset. For any one dataset , we can compute a network from the network representing the simplest dataset which is isomorphic to . This process will save more time for the algorithms when constructing networks. PMID:27547759

  10. Constructing Phylogenetic Networks Based on the Isomorphism of Datasets

    PubMed Central

    Zhang, Zhibin; Li, Yanjuan

    2016-01-01

    Constructing rooted phylogenetic networks from rooted phylogenetic trees has become an important problem in molecular evolution. So far, many methods have been presented in this area, in which most efficient methods are based on the incompatible graph, such as the CASS, the LNETWORK, and the BIMLR. This paper will research the commonness of the methods based on the incompatible graph, the relationship between incompatible graph and the phylogenetic network, and the topologies of incompatible graphs. We can find out all the simplest datasets for a topology G and construct a network for every dataset. For any one dataset 𝒞, we can compute a network from the network representing the simplest dataset which is isomorphic to 𝒞. This process will save more time for the algorithms when constructing networks. PMID:27547759

  11. Frequent Subgraph Discovery in Large Attributed Streaming Graphs

    SciTech Connect

    Ray, Abhik; Holder, Larry; Choudhury, Sutanay

    2014-08-13

    The problem of finding frequent subgraphs in large dynamic graphs has so far only consid- ered a dynamic graph as being represented by a series of static snapshots taken at various points in time. This representation of a dynamic graph does not lend itself well to real time processing of real world graphs like social networks or internet traffic which consist of a stream of nodes and edges. In this paper we propose an algorithm that discovers the frequent subgraphs present in a graph represented by a stream of labeled nodes and edges. Our algorithm is efficient and consists of tunable parameters that can be tuned by the user to get interesting patterns from various kinds of graph data. In our model updates to the graph arrive in the form of batches which contain new nodes and edges. Our algorithm con- tinuously reports the frequent subgraphs that are estimated to be found in the entire graph as each batch arrives. We evaluate our system using 5 large dynamic graph datasets: the Hetrec 2011 challenge data, Twitter, DBLP and two synthetic. We evaluate our approach against two popular large graph miners, i.e., SUBDUE and GERM. Our experimental re- sults show that we can find the same frequent subgraphs as a non-incremental approach applied to snapshot graphs, and in less time.

  12. Graph processing platforms at scale: practices and experiences

    SciTech Connect

    Lim, Seung-Hwan; Lee, Sangkeun; Brown, Tyler C; Sukumar, Sreenivas R; Ganesh, Gautam

    2015-01-01

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

  13. Implementing Graph Pattern Queries on a Relational Database

    SciTech Connect

    Kaplan, I L; Abdulla, G M; Brugger, S T; Kohn, S R

    2007-12-26

    When a graph database is implemented on top of a relational database, queries in the graph query language are translated into relational SQL queries. Graph pattern queries are an important feature of a graph query language. Translating graph pattern queries into single SQL statements results in very poor query performance. By taking into account the pattern query structure and generating multiple SQL statements, pattern query performance can be dramatically improved. The performance problems encountered with the single SQL statements generated for pattern queries reflects a problem in the SQL query planner and optimizer. Addressing this problem would allow relational databases to better support semantic graph databases. Relational database systems that provide good support for graph databases may also be more flexible platforms for data warehouses.

  14. Dimer-monomer model on the Towers of Hanoi graphs

    NASA Astrophysics Data System (ADS)

    Chen, Hanlin; Wu, Renfang; Huang, Guihua; Deng, Hanyuan

    2015-07-01

    The number of dimer-monomers (matchings) of a graph G is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer-monomers m(G) on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer-monomers. Upper and lower bounds for the entropy per site, defined as μG = limv(G)→∞(lnm(G)/v(G)), where v(G) is the number of vertices in a graph G, on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.

  15. Students' Meaning Making in Science: Solving Energy Resource Problems in Virtual Worlds Combined with Spreadsheets to Develop Graphs

    ERIC Educational Resources Information Center

    Krange, Ingeborg; Arnseth, Hans Christian

    2012-01-01

    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…

  16. Modeling the Relationships between Test-Taking Strategies and Test Performance on a Graph-Writing Task: Implications for EAP

    ERIC Educational Resources Information Center

    Yang, Hui-Chun

    2012-01-01

    With the increasing use of integrated tasks in assessing writing, more and more research studies have been conducted to examine the construct validity of such tasks. Previous studies have largely focused on reading-writing tasks, while relatively little is known about graph-writing tasks. This study examines second language (L2) writers'…

  17. How mutation affects evolutionary games on graphs.

    PubMed

    Allen, Benjamin; Traulsen, Arne; Tarnita, Corina E; Nowak, Martin A

    2012-04-21

    Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration.

  18. Random geometric graphs with general connection functions.

    PubMed

    Dettmann, Carl P; Georgiou, Orestis

    2016-03-01

    In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations. PMID:27078372

  19. Random geometric graphs with general connection functions

    NASA Astrophysics Data System (ADS)

    Dettmann, Carl P.; Georgiou, Orestis

    2016-03-01

    In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.

  20. Component Evolution in General Random Intersection Graphs

    NASA Astrophysics Data System (ADS)

    Bradonjić, Milan; Hagberg, Aric; Hengartner, Nicolas W.; Percus, Allon G.

    Random intersection graphs (RIGs) are an important random structure with algorithmic applications in social networks, epidemic networks, blog readership, and wireless sensor networks. RIGs can be interpreted as a model for large randomly formed non-metric data sets. We analyze the component evolution in general RIGs, giving conditions on the existence and uniqueness of the giant component. Our techniques generalize existing methods for analysis of component evolution: we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts of the study of component evolution in Erdős-Rényi graphs. The major challenge comes from the underlying structure of RIGs, which involves both a set of nodes and a set of attributes, with different probabilities associated with each attribute.

  1. Intergroup networks as random threshold graphs

    NASA Astrophysics Data System (ADS)

    Saha, Sudipta; Ganguly, Niloy; Mukherjee, Animesh; Krueger, Tyll

    2014-04-01

    Similar-minded people tend to form social groups. Due to pluralistic homophily as well as a sort of heterophily, people also participate in a wide variety of groups. Thus, these groups generally overlap with each other; an overlap between two groups can be characterized by the number of common members. These common members can play a crucial role in the transmission of information between the groups. As a step towards understanding the information dissemination, we perceive the system as a pruned intergroup network and show that it maps to a very basic graph theoretic concept known as a threshold graph. We analyze several structural properties of this network such as degree distribution, largest component size, edge density, and local clustering coefficient. We compare the theoretical predictions with the results obtained from several online social networks (LiveJournal, Flickr, YouTube) and find a good match.

  2. Random graphs containing arbitrary distributions of subgraphs

    NASA Astrophysics Data System (ADS)

    Karrer, Brian; Newman, M. E. J.

    2010-12-01

    Traditional random graph models of networks generate networks that are locally treelike, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly nontreelike neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a class of random graph models that incorporates general subgraphs, allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.

  3. Random broadcast on random geometric graphs

    SciTech Connect

    Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias

    2009-01-01

    In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.

  4. Extracting Critical Path Graphs from MPI Applications

    SciTech Connect

    Schulz, M

    2005-07-27

    The critical path is one of the fundamental runtime characteristics of a parallel program. It identifies the longest execution sequence without wait delays. In other words, the critical path is the global execution path that inflicts wait operations on other nodes without itself being stalled. Hence, it dictates the overall runtime and knowing it is important to understand an application's runtime and message behavior and to target optimizations. We have developed a toolset that identifies the critical path of MPI applications, extracts it, and then produces a graphical representation of the corresponding program execution graph to visualize it. To implement this, we intercept all MPI library calls, use the information to build the relevant subset of the execution graph, and then extract the critical path from there. We have applied our technique to several scientific benchmarks and successfully produced critical path diagrams for applications running on up to 128 processors.

  5. On m-polar fuzzy graph structures.

    PubMed

    Akram, Muhammad; Akmal, Rabia; Alshehri, Noura

    2016-01-01

    Sometimes information in a network model is based on multi-agent, multi-attribute, multi-object, multi-polar information or uncertainty rather than a single bit. An m-polar fuzzy model is useful for such network models which gives more and more precision, flexibility, and comparability to the system as compared to the classical, fuzzy and bipolar fuzzy models. In this research article, we introduce the notion of m-polar fuzzy graph structure and present various operations, including Cartesian product, strong product, cross product, lexicographic product, composition, union and join of m-polar fuzzy graph structures. We illustrate these operations by several examples. We also investigate some of their related properties. PMID:27652024

  6. Quantum graph as a quantum spectral filter

    SciTech Connect

    Turek, Ondrej; Cheon, Taksu

    2013-03-15

    We study the transmission of a quantum particle along a straight input-output line to which a graph {Gamma} is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter {alpha}. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of {Gamma} as {alpha}{yields}{infinity}. This effect can be used for a spectral analysis of the given graph {Gamma}. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where {Gamma} is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

  7. A note on the stability and discriminability of graph-based features for classification problems in digital pathology

    NASA Astrophysics Data System (ADS)

    Cruz-Roa, Angel; Xu, Jun; Madabhushi, Anant

    2015-01-01

    Nuclear architecture or the spatial arrangement of individual cancer nuclei on histopathology images has been shown to be associated with different grades and differential risk for a number of solid tumors such as breast, prostate, and oropharyngeal. Graph-based representations of individual nuclei (nuclei representing the graph nodes) allows for mining of quantitative metrics to describe tumor morphology. These graph features can be broadly categorized into global and local depending on the type of graph construction method. While a number of local graph (e.g. Cell Cluster Graphs) and global graph (e.g. Voronoi, Delaunay Triangulation, Minimum Spanning Tree) features have been shown to associated with cancer grade, risk, and outcome for different cancer types, the sensitivity of the preceding segmentation algorithms in identifying individual nuclei can have a significant bearing on the discriminability of the resultant features. This therefore begs the question as to which features while being discriminative of cancer grade and aggressiveness are also the most resilient to the segmentation errors. These properties are particularly desirable in the context of digital pathology images, where the method of slide preparation, staining, and type of nuclear segmentation algorithm employed can all dramatically affect the quality of the nuclear graphs and corresponding features. In this paper we evaluated the trade off between discriminability and stability of both global and local graph-based features in conjunction with a few different segmentation algorithms and in the context of two different histopathology image datasets of breast cancer from whole-slide images (WSI) and tissue microarrays (TMA). Specifically in this paper we investigate a few different performance measures including stability, discriminability and stability vs discriminability trade off, all of which are based on p-values from the Kruskal-Wallis one-way analysis of variance for local and global

  8. Software For Generating Graphs And Charts

    NASA Technical Reports Server (NTRS)

    Hammond, Dana P.; Hofler, Alicia S.; Miner, David L.; Theophilos, Pauline M.; Taylor, Nancy L.

    1992-01-01

    Common Graphics Library (CGL) computer program designed to enable users to generate graphs and charts of quality sufficient for publication or optical projection. Quickly and easily generates linear, logarithmic, bar, pie, and composite charts. Features of linear charts include automatic scaling, increasing or decreasing numerical axes, and character axes. Features of pie charts include segment labels, exploded segments, and chart keys. One of general features, horizontal or vertical orientation of figures. Written in ANSI FORTRAN 77.

  9. Extracting Between-Pathway Models from E-MAP Interactions Using Expected Graph Compression

    NASA Astrophysics Data System (ADS)

    Kelley, David R.; Kingsford, Carl

    Genetic interactions (such as synthetic lethal interactions) have become quantifiable on a large-scale using the epistatic miniarray profile (E-MAP) method. An E-MAP allows the construction of a large, weighted network of both aggravating and alleviating genetic interactions between genes. By clustering genes into modules and establishing relationships between those modules, we can discover compensatory pathways. We introduce a general framework for applying greedy clustering heuristics to probabilistic graphs. We use this framework to apply a graph clustering method called graph summarization to an E-MAP that targets yeast chromosome biology. This results in a new method for clustering E-MAP data that we call Expected Graph Compression (EGC). We validate modules and compensatory pathways using enriched Gene Ontology annotations and a novel method based on correlated gene expression. EGC finds a number of modules that are not found by any previous methods to cluster E-MAP data. EGC also uncovers core submodules contained within several previously found modules, suggesting that EGC can reveal the finer structure of E-MAP networks.

  10. A small-world network derived from the deterministic uniform recursive tree by line graph operation

    NASA Astrophysics Data System (ADS)

    Hou, Pengfeng; Zhao, Haixing; Mao, Yaping; Wang, Zhao

    2016-03-01

    The deterministic uniform recursive tree ({DURT}) is one of the deterministic versions of the uniform recursive tree ({URT}). Zhang et al (2008 Eur. Phys. J. B 63 507-13) studied the properties of DURT, including its topological characteristics and spectral properties. Although DURT shows a logarithmic scaling with the size of the network, DURT is not a small-world network since its clustering coefficient is zero. Lu et al (2012 Physica A 391 87-92) proposed a deterministic small-world network by adding some edges with a simple rule in each DURT iteration. In this paper, we intoduce a method for constructing a new deterministic small-world network by the line graph operation in each DURT iteration. The line graph operation brings about cliques at each node of the previous given graph, and the resulting line graph possesses larger clustering coefficients. On the other hand, this operation can decrease the diameter at almost one, then giving the analytic solutions to several topological characteristics of the model proposed. Supported by The Ministry of Science and Technology 973 project (No. 2010C B334708); National Science Foundation of China (Nos. 61164005, 11161037, 11101232, 11461054, 11551001); The Ministry of education scholars and innovation team support plan of Yangtze River (No. IRT1068); Qinghai Province Nature Science Foundation Project (Nos. 2012-Z-943, 2014-ZJ-907).

  11. Graph Matching: Relax at Your Own Risk.

    PubMed

    Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo

    2016-01-01

    Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.

  12. Quantitative Literacy: Working with Log Graphs

    NASA Astrophysics Data System (ADS)

    Shawl, S.

    2013-04-01

    The need for working with and understanding different types of graphs is a common occurrence in everyday life. Examples include anything having to do investments, being an educated juror in a case that involves evidence presented graphically, and understanding many aspect of our current political discourse. Within a science class graphs play a crucial role in presenting and interpreting data. In astronomy, where the range of graphed values is many orders of magnitude, log-axes must be used and understood. Experience shows that students do not understand how to read and interpret log-axes or how they differ from linear. Alters (1996), in a study of college students in an algebra-based physics class, found little understanding of log plotting. The purpose of this poster is to show the method and progression I have developed for use in my “ASTRO 101” class, with the goal being to help students better understand the H-R diagram, mass-luminosity relationship, and digital spectra.

  13. Graph Curvature for Differentiating Cancer Networks

    PubMed Central

    Sandhu, Romeil; Georgiou, Tryphon; Reznik, Ed; Zhu, Liangjia; Kolesov, Ivan; Senbabaoglu, Yasin; Tannenbaum, Allen

    2015-01-01

    Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks. PMID:26169480

  14. Graph Matching: Relax at Your Own Risk.

    PubMed

    Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo

    2016-01-01

    Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches. PMID:26656578

  15. Index statistical properties of sparse random graphs

    NASA Astrophysics Data System (ADS)

    Metz, F. L.; Stariolo, Daniel A.

    2015-10-01

    Using the replica method, we develop an analytical approach to compute the characteristic function for the probability PN(K ,λ ) that a large N ×N adjacency matrix of sparse random graphs has K eigenvalues below a threshold λ . The method allows to determine, in principle, all moments of PN(K ,λ ) , from which the typical sample-to-sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with N ≫1 for |λ |>0 , with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdös-Rényi and regular random graphs, both exhibiting a prefactor with a nonmonotonic behavior as a function of λ . These results contrast with rotationally invariant random matrices, where the index variance scales only as lnN , with an universal prefactor that is independent of λ . Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.

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

    PubMed

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

    2013-02-01

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

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

    PubMed

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Ng, Liang S.; Champion, Corbin

    2016-02-01

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

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

    PubMed

    Kim, Namhee; Zheng, Zhe; Elmetwaly, Shereef; Schlick, Tamar

    2014-01-01

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

  20. A program generating homogeneous random graphs with given weights

    NASA Astrophysics Data System (ADS)

    Bogacz, L.; Burda, Z.; Janke, W.; Waclaw, B.

    2005-12-01

    We present a program package to generate homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph α is given in the form W(α)=∏i=1Np(q), where p(q) is an arbitrary user function and q are the degrees of the graph nodes. The program can be used to generate two types of graphs (simple graphs and pseudo-graphs) from three types of ensembles (micro-canonical, canonical and grand-canonical). Program summaryTitle of the program:GraphGen Catalogue identifier:ADWL Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWL Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: PC, Alpha workstation Operating systems or monitors under which the program has been tested:Linux, Unix, MS Windows XP Programing language used:C Memory required to execute with typical data:300 k words for a graph with 1000 nodes and up to 50 000 links No. of bits in a word:32 No. of processor used:1 Has the code been vectorized or parallelized:No No. of lines in distributed program, including test data, etc.:2253 No. of bytes in distributed program, including test data, etc.:14 330 Distribution format:tar.gz Keywords:Random graphs, complex networks, Markov process, Monte Carlo method Nature of the problem:The program generates random graphs. The probabilities of graph occurrence are proportional to their statistical weight, dependent on node degrees defined by arbitrary distributions Method of solution:The starting graph is taken arbitrary and then a sequence of graphs is generated. Each graph is obtained from the previous one by means of a simple modification. The probability of accepting or rejecting the new graph results from a detailed balance condition realized as Metropolis algorithm. When the length of the generated Markov chain increases, the probabilities of graph occurrence approach the stationary distribution given by