#### Sample records for degree-based graph construction

1. Constructing splits graphs.

PubMed

Dress, Andreas W M; Huson, Daniel H

2004-01-01

Phylogenetic trees correspond one-to-one to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetic algorithms are available that compute split systems that are not necessarily compatible and, thus, cannot always be represented by a tree. Such methods include the split decomposition, Neighbor-Net, consensus networks, and the Z-closure method. A more general split system of this kind can be represented graphically by a so-called splits graph, which generalizes the concept of a phylogenetic tree. This paper addresses the problem of computing a splits graph for a given set of splits. We have implemented all presented algorithms in a new program called SplitsTree4.

2. 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…

3. 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…

4. 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…

5. Qualitative Graphing: A Construction in Mathematics.

ERIC Educational Resources Information Center

Narode, Ronald

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

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

PubMed

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

2017-10-01

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

7. Adaptive graph construction for Isomap manifold learning

Tran, Loc; Zheng, Zezhong; Zhou, Guoqing; Li, Jiang

2015-03-01

Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the l1 norm. The l1 enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than the classical approach. Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.

8. FSG: Fast String Graph Construction for De Novo Assembly.

PubMed

Bonizzoni, Paola; Della Vedova, Gianluca; Pirola, Yuri; Previtali, Marco; Rizzi, Raffaella

2017-07-17

The string graph for a collection of next-generation reads is a lossless data representation that is fundamental for de novo assemblers based on the overlap-layout-consensus paradigm. In this article, we explore a novel approach to compute the string graph, based on the FM-index and Burrows and Wheeler Transform. We describe a simple algorithm that uses only the FM-index representation of the collection of reads to construct the string graph, without accessing the input reads. Our algorithm has been integrated into the string graph assembler (SGA) as a standalone module to construct the string graph. The new integrated assembler has been assessed on a standard benchmark, showing that fast string graph (FSG) is significantly faster than SGA while maintaining a moderate use of main memory, and showing practical advantages in running FSG on multiple threads. Moreover, we have studied the effect of coverage rates on the running times.

9. Reflecting on Graphs: Attributes of Graph Choice and Construction Practices in Biology

PubMed Central

Angra, Aakanksha; Gardner, Stephanie M.

2017-01-01

Undergraduate biology education reform aims to engage students in scientific practices such as experimental design, experimentation, and data analysis and communication. Graphs are ubiquitous in the biological sciences, and creating effective graphical representations involves quantitative and disciplinary concepts and skills. Past studies document student difficulties with graphing within the contexts of classroom or national assessments without evaluating student reasoning. Operating under the metarepresentational competence framework, we conducted think-aloud interviews to reveal differences in reasoning and graph quality between undergraduate biology students, graduate students, and professors in a pen-and-paper graphing task. All professors planned and thought about data before graph construction. When reflecting on their graphs, professors and graduate students focused on the function of graphs and experimental design, while most undergraduate students relied on intuition and data provided in the task. Most undergraduate students meticulously plotted all data with scaled axes, while professors and some graduate students transformed the data, aligned the graph with the research question, and reflected on statistics and sample size. Differences in reasoning and approaches taken in graph choice and construction corroborate and extend previous findings and provide rich targets for undergraduate and graduate instruction. PMID:28821538

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

ERIC Educational Resources Information Center

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…

11. 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…

12. 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…

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

ERIC Educational Resources Information Center

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…

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

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.

15. 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

16. Neural network for graphs: a contextual constructive approach.

PubMed

Micheli, Alessio

2009-03-01

This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic/cyclic, directed/undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results.

17. Knowledge graph for TCM health preservation: Design, construction, and applications.

PubMed

Yu, Tong; Li, Jinghua; Yu, Qi; Tian, Ye; Shun, Xiaofeng; Xu, Lili; Zhu, Ling; Gao, Hongjie

2017-03-01

Traditional Chinese Medicine (TCM) is one of the important non-material cultural heritages of the Chinese nation. It is an important development strategy of Chinese medicine to collect, analyzes, and manages the knowledge assets of TCM health care. As a novel and massive knowledge management technology, knowledge graph provides an ideal technical means to solve the problem of "Knowledge Island" in the field of traditional Chinese medicine. In this study, we construct a large-scale knowledge graph, which integrates terms, documents, databases and other knowledge resources. This knowledge graph can facilitate various knowledge services such as knowledge visualization, knowledge retrieval, and knowledge recommendation, and helps the sharing, interpretation, and utilization of TCM health care knowledge. Copyright © 2017 Elsevier B.V. All rights reserved.

18. Topological Polymer Chemistry Designing Complex Macromolecular Graph Constructions.

PubMed

Tezuka, Yasuyuki

2017-08-22

The precision design of topologically intriguing macromolecular architectures has continuously been an attractive challenge in polymer science and polymer materials engineering. A class of multicyclic polymer topologies, including three subclasses of spiro, bridged, and fused forms, are particularly unique not only from a topological geometry viewpoint but also from their biochemical relevance to programmed folding structures. In this Account, we describe recent progress in constructing this class of macromolecules, in particular by means of an electrostatic self-assembly and covalent fixation (ESA-CF) protocol, in which ion-paired polymer self-assemblies are employed as key intermediates. All three dicyclic constructions having either 8 (spiro), manacle (bridged), or θ (fused) forms, as well as a tricyclic trefoil (spiro) graph, have been constructed by the ESA-CF process. Moreover, a triply fused-tetracyclic macromolecular K3,3 graph has been constructed using a uniform-size dendritic polymer precursor having six cyclic ammonium salt end groups carrying two units of a trifunctional carboxylate counteranion. Remarkably, the K3,3 graph is known in topological geometry as a prototypical nonplanar graph and has been identified as topologically equivalent to some multicyclic polypeptides (cyclotides) produced through the intramolecular S-S bridging with cysteine residues. A series of single cyclic (ring) polymers having one, two, and even three designated functional groups at the prescribed positions along their cyclic backbone segment (kyklo-telechelics) have also been obtained by the ESA-CF protocol. And in conjunction with a tandem alkyne-azide addition (i.e., click) and an olefin metathesis (i.e., clip) reaction, the precision design of complex multicyclic macromolecular architectures has been achieved. Thus, a series of tri-, tetra-, and even hexacyclic polymer topologies of spiro- and bridged-forms and three doubly fused-tricycle (β-, γ-, and δ-graph) forms

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

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.

20. 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.

1. 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…

2. 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…

3. Constructing Coordinate Graphs: Representing Corresponding Ordered Values with Variation in Two-Dimensional Space

ERIC Educational Resources Information Center

Moritz, Jonathan

2003-01-01

Coordinate graphs of time-series data have been significant in the history of statistical graphing and in recent school mathematics curricula. A survey task to construct a graph to represent data about temperature change over time was administered to 133 students in Grades 3, 5, 7, and 9. Four response levels described the degree to which students…

4. Explicit and probabilistic constructions of distance graphs with small clique numbers and large chromatic numbers

Kupavskii, A. B.

2014-02-01

We study distance graphs with exponentially large chromatic numbers and without k-cliques, that is, complete subgraphs of size k. Explicit constructions of such graphs use vectors in the integer lattice. For a large class of graphs we find a sharp threshold for containing a k-clique. This enables us to improve the lower bounds for the maximum of the chromatic numbers of such graphs. We give a new probabilistic approach to the construction of distance graphs without k-cliques, and this yields better lower bounds for the maximum of the chromatic numbers for large k.

5. Constructing Graphs over with Small Prescribed Mean-Curvature

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.

6. 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…

7. 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…

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

Hao, Ruizhe; Huang, Jian

2017-08-01

Knowledge graph construction in military intelligence domain is sprouting but technically immature. This paper presents a method to construct the heterogeneous knowledge graph in the field of shipborne and airborne radar and equipment. Based on the expert knowledge and the up-to-date Internet open source information, we construct the knowledge graph of radar characteristic information and the equipment respectively, and establish relationships between two graphs, providing the pipeline and method for the intelligence organization and management in the context of the crowding battlefields big data.

9. 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…

10. 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…

11. 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

12. 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.

13. Label Information Guided Graph Construction for Semi-Supervised Learning.

PubMed

Zhuang, Liansheng; Zhou, Zihan; Gao, Shenghua; Yin, Jingwen; Lin, Zhouchen; Ma, Yi

2017-09-01

In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks.

14. 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)

15. 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…

16. 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…

17. 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.

18. 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.

19. An Optimal Parallel Algorithm for Constructing a Spanning Tree on Circular Permutation Graphs

Honma, Hirotoshi; Honma, Saki; Masuyama, Shigeru

The spanning tree problem is to find a tree that connects all the vertices of G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. Klein and Stein demonstrated that a spanning tree can be found in O(log n) time with O(n + m) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. Circular permutation graphs properly contain the set of permutation graphs as a subclass and are first introduced by Rotem and Urrutia. They provided O(n2.376) time recognition algorithm. Circular permutation graphs and their models find several applications in VLSI layout. In this paper, we propose an optimal parallel algorithm for constructing a spanning tree on circular permutation graphs. It runs in O(log n) time with O(n/ log n) processors on the EREW PRAM.

20. pGraph: Efficient Parallel Construction of Large-Scale Protein Sequence Homology Graphs

SciTech Connect

Wu, Changjun; Kalyanaraman, Anantharaman; Cannon, William R.

2012-09-15

Detecting sequence homology between protein sequences is a fundamental problem in computational molecular biology, with a pervasive application in nearly all analyses that aim to structurally and functionally characterize protein molecules. While detecting the homology between two protein sequences is relatively inexpensive, detecting pairwise homology for a large number of protein sequences can become computationally prohibitive for modern inputs, often requiring millions of CPU hours. Yet, there is currently no robust support to parallelize this kernel. In this paper, we identify the key characteristics that make this problemparticularly hard to parallelize, and then propose a new parallel algorithm that is suited for detecting homology on large data sets using distributed memory parallel computers. Our method, called pGraph, is a novel hybrid between the hierarchical multiple-master/worker model and producer-consumer model, and is designed to break the irregularities imposed by alignment computation and work generation. Experimental results show that pGraph achieves linear scaling on a 2,048 processor distributed memory cluster for a wide range of inputs ranging from as small as 20,000 sequences to 2,560,000 sequences. In addition to demonstrating strong scaling, we present an extensive report on the performance of the various system components and related parametric studies.

1. Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering.

PubMed

Peng, Xi; Yu, Zhiding; Yi, Zhang; Tang, Huajin

2017-04-01

Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intrasubspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that l1 -, l2 -, l∞ -, and nuclear-norm-based linear projection spaces share the property of intrasubspace projection dominance, i.e., the coefficients over intrasubspace data points are larger than those over intersubspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-graph. The subspace clustering and subspace learning algorithms are developed upon L2-graph. We conduct comprehensive experiment on subspace learning, image clustering, and motion segmentation and consider several quantitative benchmarks classification/clustering accuracy, normalized mutual information, and running time. Results show that L2-graph outperforms many state-of-the-art methods in our experiments, including L1-graph, low rank representation (LRR), and latent LRR, least square regression, sparse subspace clustering, and locally linear representation.

2. Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs.

PubMed

Kundeti, Vamsi K; Rajasekaran, Sanguthevar; Dinh, Hieu; Vaughn, Matthew; Thapar, Vishal

2010-11-15

any sequence assembly program based on Eulerian approach. Our algorithms for constructing Bi-directed de Bruijn graphs are efficient in parallel and out of core settings. These algorithms can be used in building large scale bi-directed de Bruijn graphs. Furthermore, our algorithms do not employ any all-to-all communications in a parallel setting and perform better than the prior algorithms. Finally our out-of-core algorithm is extremely memory efficient and can replace the existing graph construction algorithm in VELVET.

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

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

2015-01-01

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 O (106)) and of edges (up to at least O (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 construct 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 × 106 edges. In less than 5 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 13 min. Par@Graph therefore facilitates the application of climate network analysis on high-resolution observations and model results, by enabling fast network construction 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.

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

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.

5. Test of Graphing and Graph Interpretation Skills.

ERIC Educational Resources Information Center

Hermann, J.

This monograph is a test of graphing and graph interpretation skills which assesses performance on all the skills of graphing which are contained in the AAAS program, Science - A Process Approach. The testing includes construction of bar graphs, interpreting information on graphs, the use of the Cartesian coordinate system, making predictions from…

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

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

7. 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.

8. 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

9. Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions

Yamasaki, Hayata; Soeda, Akihito; Murao, Mio

2017-09-01

We introduce and analyze graph-associated entanglement cost, a generalization of the entanglement cost of quantum states to multipartite settings. We identify a necessary and sufficient condition for any multipartite entangled state to be constructible when quantum communication between the multiple parties is restricted to a quantum network represented by a tree. The condition for exact state construction is expressed in terms of the Schmidt ranks of the state defined with respect to edges of the tree. We also study approximate state construction and provide a second-order asymptotic analysis.

10. A graph-based approach to construct target-focused libraries for virtual screening.

PubMed

2016-01-01

. Furthermore, in a procedure mimicking the real application, where one expects to discover novel compounds based on a small set of already developed bioactives, eSynth is capable of generating diverse collections of molecules with the desired activity profiles. Thus, we are very optimistic that our effort will contribute to targeted drug discovery. eSynth is freely available to the academic community at www.brylinski.org/content/molecular-synthesis.Graphical abstractAssuming that organic compounds are composed of sets of rigid fragments connected by flexible linkers, a molecule can be decomposed into its building blocks tracking their atomic connectivity. Here, we developed eSynth, an automated method to synthesize new compounds by reconnecting these building blocks following the connectivity patterns via an exhaustive graph-based search algorithm. eSynth opens up a possibility to rapidly construct virtual screening libraries for targeted drug discovery.

11. Linear Error Correcting Code Constructed From Compete Graph with Five Vertices and Its Properties

Hossain, Sheikh Ahmed; Kar, Samarjit

2010-10-01

A graph can generate a 2- ary code. A binary code is a set of code words with the property that the modulo 2 sum any two code words in the set is also a codeword in the set. These code are also called linear codes. Using a Fundamental cut set matrix or a Fundamental circuit matrix of a graph, one can generate a code with parameters [n,k,d]2, where n is the number of edges in the graph, k is the dimension of the associated subspace, and d is the minimum distance between the code words. In our discussion we take some complete graphs and using a fundamental cut set matrix with respect to a spanning tree we generate a binary linear code and discuss the code theoretic properties of this code word.

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

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.

13. Differentials on graph complexes II: hairy graphs

Khoroshkin, Anton; Willwacher, Thomas; Živković, Marko

2017-10-01

We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain the hairy graph cohomology. Our results yield a way to construct many nonzero hairy graph cohomology classes out of (known) non-hairy classes by studying the cancellations in those sequences. This provide a first glimpse at the tentative global structure of the hairy graph cohomology.

14. Constructing knowledge. The role of graphs and tables in hard and soft psychology.

PubMed

Smith, Laurence D; Best, Lisa A; Stubbs, D Alan; Archibald, Andrea Bastiani; Roberson-Nay, Roxann

2002-10-01

Because graphs provide a compact, rhetorically powerful way of representing research findings, recent theories of science have postulated their use as a distinguishing feature of science. Studies have shown that the use of graphs in journal articles correlates highly with the hardness of scientific fields, both across disciplines and across sub-fields of psychology. In contrast, the use of tables and inferential statistics in psychology is inversely related to subfield hardness, suggesting that the relationship between hardness and graph use is not attributable to differences in the use of quantitative data in subfields or their commitment to empiricism. Enhanced "graphicacy" among psychologists could contribute to the progress of psychological science by providing alternatives to significance testing and by facilitating communication across subfields.

15. 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…

16. Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions

Szlam, Arthur D.; Maggioni, Mauro; Coifman, Ronald R.; Bremer, James C., Jr.

2005-08-01

Classically, analysis on manifolds and graphs has been based on the study of the eigenfunctions of the Laplacian and its generalizations. These objects from differential geometry and analysis on manifolds have proven useful in applications to partial differential equations, and their discrete counterparts have been applied to optimization problems, learning, clustering, routing and many other algorithms.1-7 The eigenfunctions of the Laplacian are in general global: their support often coincides with the whole manifold, and they are affected by global properties of the manifold (for example certain global topological invariants). Recently a framework for building natural multiresolution structures on manifolds and graphs was introduced, that greatly generalizes, among other things, the construction of wavelets and wavelet packets in Euclidean spaces.8,9 This allows the study of the manifold and of functions on it at different scales, which are naturally induced by the geometry of the manifold. This construction proceeds bottom-up, from the finest scale to the coarsest scale, using powers of a diffusion operator as dilations and a numerical rank constraint to critically sample the multiresolution subspaces. In this paper we introduce a novel multiscale construction, based on a top-down recursive partitioning induced by the eigenfunctions of the Laplacian. This yields associated local cosine packets on manifolds, generalizing local cosines in Euclidean spaces.10 We discuss some of the connections with the construction of diffusion wavelets. These constructions have direct applications to the approximation, denoising, compression and learning of functions on a manifold and are promising in view of applications to problems in manifold approximation, learning, dimensionality reduction.

17. 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. Copyright © 2014 Elsevier Ltd. All rights reserved.

18. The Oriented Graph Complexes

Willwacher, Thomas

2015-03-01

The oriented graph complexes are complexes of directed graphs without directed cycles. They govern, for example, the quantization of Lie bialgebras and infinite dimensional deformation quantization. Similar to the ordinary graph complexes GC n introduced by Kontsevich they come in two essentially different versions, depending on the parity of n. It is shown that, surprisingly, the oriented graph complex is quasi-isomorphic to the ordinary commutative graph complex of opposite parity GC n-1, up to some known classes. This yields in particular a combinatorial description of the action of on Lie bialgebras, and shows that a cycle-free formality morphism in the sense of Shoikhet can be constructed rationally without reference to configuration space integrals. Curiously, the obstruction class in the oriented graph complex found by Shoikhet corresponds to the well known theta graph in the ordinary graph complex.

19. Methods of visualizing graphs

DOEpatents

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.

20. Retrospective 4D MR image construction from free-breathing slice Acquisitions: A novel graph-based approach.

PubMed

Tong, Yubing; Udupa, Jayaram K; Ciesielski, Krzysztof C; Wu, Caiyun; McDonough, Joseph M; Mong, David A; Campbell, Robert M

2017-01-01

Dynamic or 4D imaging of the thorax has many applications. Both prospective and retrospective respiratory gating and tracking techniques have been developed for 4D imaging via CT and MRI. For pediatric imaging, due to radiation concerns, MRI becomes the de facto modality of choice. In thoracic insufficiency syndrome (TIS), patients often suffer from extreme malformations of the chest wall, diaphragm, and/or spine with inability of the thorax to support normal respiration or lung growth (Campbell et al., 2003, Campbell and Smith, 2007), as such patient cooperation needed by some of the gating and tracking techniques are difficult to realize without causing patient discomfort and interference with the breathing mechanism itself. Therefore (ventilator-supported) free-breathing MRI acquisition is currently the best choice for imaging these patients. This, however, raises a question of how to create a consistent 4D image from such acquisitions. This paper presents a novel graph-based technique for compiling the best 4D image volume representing the thorax over one respiratory cycle from slice images acquired during unencumbered natural tidal-breathing of pediatric TIS patients. In our approach, for each coronal (or sagittal) slice position, images are acquired at a rate of about 200-300ms/slice over several natural breathing cycles which yields over 2000 slices. A weighted graph is formed where each acquired slice constitutes a node and the weight of the arc between two nodes defines the degree of contiguity in space and time of the two slices. For each respiratory phase, an optimal 3D spatial image is constructed by finding the best path in the graph in the spatial direction. The set of all such 3D images for a given respiratory cycle constitutes a 4D image. Subsequently, the best 4D image among all such constructed images is found over all imaged respiratory cycles. Two types of evaluation studies are carried out to understand the behavior of this algorithm and in

1. Clique graphs and overlapping communities

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. KnowLife: a versatile approach for constructing a large knowledge graph for biomedical sciences.

PubMed

Ernst, Patrick; Siu, Amy; Weikum, Gerhard

2015-05-14

Biomedical knowledge bases (KB's) have become important assets in life sciences. Prior work on KB construction has three major limitations. First, most biomedical KBs are manually built and curated, and cannot keep up with the rate at which new findings are published. Second, for automatic information extraction (IE), the text genre of choice has been scientific publications, neglecting sources like health portals and online communities. Third, most prior work on IE has focused on the molecular level or chemogenomics only, like protein-protein interactions or gene-drug relationships, or solely address highly specific topics such as drug effects. We address these three limitations by a versatile and scalable approach to automatic KB construction. Using a small number of seed facts for distant supervision of pattern-based extraction, we harvest a huge number of facts in an automated manner without requiring any explicit training. We extend previous techniques for pattern-based IE with confidence statistics, and we combine this recall-oriented stage with logical reasoning for consistency constraint checking to achieve high precision. To our knowledge, this is the first method that uses consistency checking for biomedical relations. Our approach can be easily extended to incorporate additional relations and constraints. We ran extensive experiments not only for scientific publications, but also for encyclopedic health portals and online communities, creating different KB's based on different configurations. We assess the size and quality of each KB, in terms of number of facts and precision. The best configured KB, KnowLife, contains more than 500,000 facts at a precision of 93% for 13 relations covering genes, organs, diseases, symptoms, treatments, as well as environmental and lifestyle risk factors. KnowLife is a large knowledge base for health and life sciences, automatically constructed from different Web sources. As a unique feature, KnowLife is harvested from

3. Graphing Matters.

ERIC Educational Resources Information Center

Paine, Carolyn

1983-01-01

An explanation is given of the uses of graphs for conveying information pictorially. Picture, bar, line, and area graphs are illustrated. Graphing projects for science, social studies, mathematics, economics, and language arts are listed, and teaching tips are suggested. (FG)

4. Graph Library

SciTech Connect

Schulz, Martin; Arnold, Dorian

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 ability to export graphs into various open formats such as DOT and GML.

5. Higher-order graph wavelets and sparsity on circulant graphs

Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi

2015-08-01

The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.

6. 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.

7. 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 of…

8. 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 of…

9. 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.

10. Orthocomplemented complete lattices and graphs

Ollech, Astrid

1995-08-01

The problem I consider originates from Dörfler, who found a construction to assign an Orthocomplemented lattice H(G) to a graph G. By Dörfler it is known that for every finite Orthocomplemented lattice L there exists a graph G such that H(G)=L. Unfortunately, we can find more than one graph G with this property, i.e., orthocomplemented lattices which belong to different graphs can be isomorphic. I show some conditions under which two graphs have the same orthocomplemented lattice.

11. Tailored Random Graph Ensembles

Roberts, E. S.; Annibale, A.; Coolen, A. C. C.

2013-02-01

Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.

12. 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…

13. 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…

14. Scenario Graphs and Attack Graphs

DTIC Science & Technology

2004-04-14

46 6.1 Vulnerability Analysis of a Network . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2 Sandia Red Team Attack Graph...asymptotic bound. The test machine was a 1Ghz Pentium III with 1GB of RAM, running Red Hat Linux 7.3. Figure 4.1(a) plots running time of the implemen...host scanning tools network information vulnerability Attack Graph network Red

15. 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)

16. 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)

17. Hidden Behavior in Graphs.

ERIC Educational Resources Information Center

Donley, H. Edward; George, Elizabeth Ann

1993-01-01

Demonstrates how to construct rational, exponential, and sinusoidal functions that appear normal on one scale but exhibit interesting hidden behavior when viewed on another scale. By exploring these examples, students learn the importance of scale, window size, and resolution effects in computer and calculator graphing. (MAZ)

18. 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.

19. Noncommutative Riemannian geometry on graphs

Majid, Shahn

2013-07-01

We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a 'finite manifold structure' on the set of vertices. We equip any graph with a canonical 'Euclidean metric' and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations.

20. Adjusting protein graphs based on graph entropy.

PubMed

Peng, Sheng-Lung; Tsay, Yu-Wei

2014-01-01

Measuring protein structural similarity attempts to establish a relationship of equivalence between polymer structures based on their conformations. In several recent studies, researchers have explored protein-graph remodeling, instead of looking a minimum superimposition for pairwise proteins. When graphs are used to represent structured objects, the problem of measuring object similarity become one of computing the similarity between graphs. Graph theory provides an alternative perspective as well as efficiency. Once a protein graph has been created, its structural stability must be verified. Therefore, a criterion is needed to determine if a protein graph can be used for structural comparison. In this paper, we propose a measurement for protein graph remodeling based on graph entropy. We extend the concept of graph entropy to determine whether a graph is suitable for representing a protein. The experimental results suggest that when applied, graph entropy helps a conformational on protein graph modeling. Furthermore, it indirectly contributes to protein structural comparison if a protein graph is solid.

1. Graphing Reality

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.

2. Threshold Graph Limits and Random Threshold Graphs

PubMed Central

Diaconis, Persi; Holmes, Susan; Janson, Svante

2010-01-01

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits. PMID:20811581

3. 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…

4. 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…

5. 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…

6. 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…

7. GraphBench

SciTech Connect

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

2016-06-01

GraphBench is a benchmark suite for graph pattern mining and graph analysis systems. The benchmark suite is a significant addition to conducting apples-apples comparison of graph analysis software (databases, in-memory tools, triple stores, etc.)

8. Line graphs for fractals

Warchalowski, Wiktor; Krawczyk, Malgorzata J.

2017-03-01

We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.

9. Bipartite Graphs of Large Clique-Width

Recently, several constructions of bipartite graphs of large clique-width have been discovered in the literature. In the present paper, we propose a general framework for developing such constructions and use it to obtain new results on this topic.

10. VISAGE: Interactive Visual Graph Querying.

PubMed

Pienta, Robert; Navathe, Shamkant; Tamersoy, Acar; Tong, Hanghang; Endert, Alex; Chau, Duen Horng

2016-06-01

Extracting useful patterns from large network datasets has become a fundamental challenge in many domains. We present VISAGE, an interactive visual graph querying approach that empowers users to construct expressive queries, without writing complex code (e.g., finding money laundering rings of bankers and business owners). Our contributions are as follows: (1) we introduce graph autocomplete, an interactive approach that guides users to construct and refine queries, preventing over-specification; (2) VISAGE guides the construction of graph queries using a data-driven approach, enabling users to specify queries with varying levels of specificity, from concrete and detailed (e.g., query by example), to abstract (e.g., with "wildcard" nodes of any types), to purely structural matching; (3) a twelve-participant, within-subject user study demonstrates VISAGE's ease of use and the ability to construct graph queries significantly faster than using a conventional query language; (4) VISAGE works on real graphs with over 468K edges, achieving sub-second response times for common queries.

11. VISAGE: Interactive Visual Graph Querying

PubMed Central

Pienta, Robert; Navathe, Shamkant; Tamersoy, Acar; Tong, Hanghang; Endert, Alex; Chau, Duen Horng

2017-01-01

Extracting useful patterns from large network datasets has become a fundamental challenge in many domains. We present VISAGE, an interactive visual graph querying approach that empowers users to construct expressive queries, without writing complex code (e.g., finding money laundering rings of bankers and business owners). Our contributions are as follows: (1) we introduce graph autocomplete, an interactive approach that guides users to construct and refine queries, preventing over-specification; (2) VISAGE guides the construction of graph queries using a data-driven approach, enabling users to specify queries with varying levels of specificity, from concrete and detailed (e.g., query by example), to abstract (e.g., with “wildcard” nodes of any types), to purely structural matching; (3) a twelve-participant, within-subject user study demonstrates VISAGE’s ease of use and the ability to construct graph queries significantly faster than using a conventional query language; (4) VISAGE works on real graphs with over 468K edges, achieving sub-second response times for common queries. PMID:28553670

12. 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.

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

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.

14. Adjusting protein graphs based on graph entropy

PubMed Central

2014-01-01

Measuring protein structural similarity attempts to establish a relationship of equivalence between polymer structures based on their conformations. In several recent studies, researchers have explored protein-graph remodeling, instead of looking a minimum superimposition for pairwise proteins. When graphs are used to represent structured objects, the problem of measuring object similarity become one of computing the similarity between graphs. Graph theory provides an alternative perspective as well as efficiency. Once a protein graph has been created, its structural stability must be verified. Therefore, a criterion is needed to determine if a protein graph can be used for structural comparison. In this paper, we propose a measurement for protein graph remodeling based on graph entropy. We extend the concept of graph entropy to determine whether a graph is suitable for representing a protein. The experimental results suggest that when applied, graph entropy helps a conformational on protein graph modeling. Furthermore, it indirectly contributes to protein structural comparison if a protein graph is solid. PMID:25474347

15. Cayley Bipolar Fuzzy Graphs

PubMed Central

Alshehri, Noura O.

2013-01-01

We introduce the concept of Cayley bipolar fuzzy graphs and investigate some of their properties. We present some interesting properties of bipolar fuzzy graphs in terms of algebraic structures. We also discuss connectedness in Cayley bipolar fuzzy graphs. PMID:24453797

16. 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.

17. Graph modeling systems and methods

SciTech Connect

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.

18. 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…

19. 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…

20. Unsupervised spectral mesh segmentation driven by heterogeneous graphs.

PubMed

Theologou, Panagiotis; Pratikakis, Ioannis; Theoharis, Theoharis

2016-03-21

A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.

1. Unsupervised Spectral Mesh Segmentation Driven by Heterogeneous Graphs.

PubMed

Theologou, Panagiotis; Pratikakis, Ioannis; Theoharis, Theoharis

2017-02-01

A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.

2. 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…

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

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.

4. 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.

5. Integer sequence discovery from small graphs

PubMed Central

Hoppe, Travis; Petrone, Anna

2015-01-01

We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work. PMID:27034526

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

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.

7. Generative Graph Prototypes from Information Theory.

PubMed

Han, Lin; Wilson, Richard C; Hancock, Edwin R

2015-10-01

In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs.

8. Intrinsic graph structure estimation using graph Laplacian.

PubMed

Noda, Atsushi; Hino, Hideitsu; Tatsuno, Masami; Akaho, Shotaro; Murata, Noboru

2014-07-01

A graph is a mathematical representation of a set of variables where some pairs of the variables are connected by edges. Common examples of graphs are railroads, the Internet, and neural networks. It is both theoretically and practically important to estimate the intensity of direct connections between variables. In this study, a problem of estimating the intrinsic graph structure from observed data is considered. The observed data in this study are a matrix with elements representing dependency between nodes in the graph. The dependency represents more than direct connections because it includes influences of various paths. For example, each element of the observed matrix represents a co-occurrence of events at two nodes or a correlation of variables corresponding to two nodes. In this setting, spurious correlations make the estimation of direct connection difficult. To alleviate this difficulty, a digraph Laplacian is used for characterizing a graph. A generative model of this observed matrix is proposed, and a parameter estimation algorithm for the model is also introduced. The notable advantage of the proposed method is its ability to deal with directed graphs, while conventional graph structure estimation methods such as covariance selections are applicable only to undirected graphs. The algorithm is experimentally shown to be able to identify the intrinsic graph structure.

9. Interval Graph Limits

PubMed Central

Diaconis, Persi; Holmes, Susan; Janson, Svante

2015-01-01

We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits. PMID:26405368

10. Degree-based statistic and center persistency for brain connectivity analysis.

PubMed

Yoo, Kwangsun; Lee, Peter; Chung, Moo K; Sohn, William S; Chung, Sun Ju; Na, Duk L; Ju, Daheen; Jeong, Yong

2017-01-01

Brain connectivity analyses have been widely performed to investigate the organization and functioning of the brain, or to observe changes in neurological or psychiatric conditions. However, connectivity analysis inevitably introduces the problem of mass-univariate hypothesis testing. Although, several cluster-wise correction methods have been suggested to address this problem and shown to provide high sensitivity, these approaches fundamentally have two drawbacks: the lack of spatial specificity (localization power) and the arbitrariness of an initial cluster-forming threshold. In this study, we propose a novel method, degree-based statistic (DBS), performing cluster-wise inference. DBS is designed to overcome the above-mentioned two shortcomings. From a network perspective, a few brain regions are of critical importance and considered to play pivotal roles in network integration. Regarding this notion, DBS defines a cluster as a set of edges of which one ending node is shared. This definition enables the efficient detection of clusters and their center nodes. Furthermore, a new measure of a cluster, center persistency (CP) was introduced. The efficiency of DBS with a known "ground truth" simulation was demonstrated. Then they applied DBS to two experimental datasets and showed that DBS successfully detects the persistent clusters. In conclusion, by adopting a graph theoretical concept of degrees and borrowing the concept of persistence from algebraic topology, DBS could sensitively identify clusters with centric nodes that would play pivotal roles in an effect of interest. DBS is potentially widely applicable to variable cognitive or clinical situations and allows us to obtain statistically reliable and easily interpretable results. Hum Brain Mapp 38:165-181, 2017. © 2016 Wiley Periodicals, Inc.

11. Comparing pedigree graphs.

PubMed

Kirkpatrick, Bonnie; Reshef, Yakir; Finucane, Hilary; Jiang, Haitao; Zhu, Binhai; Karp, Richard M

2012-09-01

Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this article, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a linear-time algorithm for leaf-labeled pedigrees. The second is the pedigree edit distance problem, for which we present (1) several algorithms that are fast and exact in various special cases, and (2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the sub-pedigree isomorphism problem is NP-hard. We then show that the pedigree edit distance problem is APX-hard in general and NP-hard on leaf-labeled pedigrees. We use simulated pedigrees to compare our edit-distance algorithms to each other as well as to a branch-and-bound algorithm that always finds an optimal solution.

12. 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

13. A model of language inflection graphs

Fukś, Henryk; Farzad, Babak; Cao, Yi

2014-01-01

Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

14. Function plot response: A scalable system for teaching kinematics graphs

Laverty, James; Kortemeyer, Gerd

2012-08-01

Understanding and interpreting graphs are essential skills in all sciences. While students are mostly proficient in plotting given functions and reading values off graphs, they frequently lack the ability to construct and interpret graphs in a meaningful way. Students can use graphs as representations of value pairs, but often fail to interpret them as the representation of functions, and mostly fail to use them as representations of physical reality. 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. Initial experiences using the new problem type in an introductory physics course are reported.

15. On molecular graph comparison.

PubMed

Melo, Jenny A; Daza, Edgar

2011-06-01

Since the last half of the nineteenth century, molecular graphs have been present in several branches of chemistry. When used for molecular structure representation, they have been compared after mapping the corresponding graphs into mathematical objects. However, direct molecular comparison of molecular graphs is a research field less explored. The goal of this mini-review is to show some distance and similarity coefficients which were proposed to directly compare molecular graphs or which could be useful to do so.

16. GraphVar: a user-friendly toolbox for comprehensive graph analyses of functional brain connectivity.

PubMed

Kruschwitz, J D; List, D; Waller, L; Rubinov, M; Walter, H

2015-04-30

Graph theory provides a powerful and comprehensive formalism of global and local topological network properties of complex structural or functional brain connectivity. Software packages such as the Brain-Connectivity-Toolbox have contributed to graph theory's increasing popularity for characterization of brain networks. However, comparably comprehensive packages are command-line based and require programming experience; this precludes their use by users without a computational background, whose research would otherwise benefit from graph-theoretical methods. "GraphVar" is a user-friendly GUI-based toolbox for comprehensive graph-theoretical analyses of brain connectivity, including network construction and characterization, statistical analysis on network topological measures, network based statistics, and interactive exploration of results. GraphVar provides a comprehensive collection of graph analysis routines for analyses of functional brain connectivity in one single toolbox by combining features across multiple currently available toolboxes, such as the Brain Connectivity Toolbox, the Graph Analysis Toolbox, and the Network Based Statistic Toolbox (BCT, Rubinov and Sporns, 2010; GAT, Hosseini et al., 2012; NBS, Zalesky et al., 2010). GraphVar was developed under the GNU General Public License v3.0 and can be downloaded at www.rfmri.org/graphvar or www.nitrc.org/projects/graphvar. By combining together features across multiple toolboxes, GraphVar will allow comprehensive graph-theoretical analyses in one single toolbox without resorting to code. GraphVar will make graph theoretical methods more accessible for a broader audience of neuroimaging researchers. Copyright © 2015 Elsevier B.V. All rights reserved.

17. 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.

18. Graphs in Scientific Publications.

ERIC Educational Resources Information Center

Cleveland, William S.

Two surveys were carried out to help increase knowledge of current graph usage in science. A detailed analysis of all graphs in one volume of the journal "Science" revealed that 30 percent had errors. Graphs are used more in some disciplines than in others; a survey of 57 journals revealed natural science journals use far more graphs…

19. 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…

20. Are Graphs Finally Surfacing?

ERIC Educational Resources Information Center

Beineke, Lowell W.

1989-01-01

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

1. 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…

2. Graphing Important People

ERIC Educational Resources Information Center

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…

3. Graphing Important People

ERIC Educational Resources Information Center

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…

4. Flux networks in metabolic graphs

Warren, P. B.; Duarte Queiros, S. M.; Jones, J. L.

2009-12-01

A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms.

5. Pattern vectors from algebraic graph theory.

PubMed

Wilson, Richard C; Hancock, Edwin R; Luo, Bin

2005-07-01

Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs.

6. 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…

7. Zeta functions of the Dirac operator on quantum graphs

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.

8. 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.

9. 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.

10. Inverse scattering problem for quantum graph vertices

SciTech Connect

Cheon, Taksu; Turek, Ondrej; Exner, Pavel

2011-06-15

We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fueloep-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.

11. Hyperbolic graph generator

Aldecoa, Rodrigo; Orsini, Chiara; Krioukov, Dmitri

2015-11-01

Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks can be adequately modeled as random geometric graphs in hyperbolic spaces. In this paper, we present a computer program to generate such graphs. Besides real-world-like networks, the program can generate random graphs from other well-known graph ensembles, such as the soft configuration model, random geometric graphs on a circle, or Erdős-Rényi random graphs. The simulations show a good match between the expected values of different network structural properties and the corresponding empirical values measured in generated graphs, confirming the accurate behavior of the program.

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

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.

13. A general method for computing Tutte polynomials of self-similar graphs

Gong, Helin; Jin, Xian'an

2017-10-01

Self-similar graphs were widely studied in both combinatorics and statistical physics. Motivated by the construction of the well-known 3-dimensional Sierpiński gasket graphs, in this paper we introduce a family of recursively constructed self-similar graphs whose inner duals are of the self-similar property. By combining the dual property of the Tutte polynomial and the subgraph-decomposition trick, we show that the Tutte polynomial of this family of graphs can be computed in an iterative way and in particular the exact expression of the formula of the number of their spanning trees is derived. Furthermore, we show our method is a general one that is easily extended to compute Tutte polynomials for other families of self-similar graphs such as Farey graphs, 2-dimensional Sierpiński gasket graphs, Hanoi graphs, modified Koch graphs, Apollonian graphs, pseudofractal scale-free web, fractal scale-free network, etc.

14. Graphing trillions of triangles

PubMed Central

Burkhardt, Paul

2016-01-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed. PMID:28690426

15. Resistance Distances and Kirchhoff Index in Generalised Join Graphs

Chen, Haiyan

2017-03-01

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G=H[G1, G2, …, Gk ] be the generalised join graph of G1, G2, …, Gk determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of {G'_i}s and H. Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when {G'_i}s and H take some special graphs, such as the complete graph, the path, and the cycle.

16. Ridge network detection in crumpled paper via graph density maximization.

PubMed

Hsu, Chiou-Ting; Huang, Marvin

2012-10-01

Crumpled sheets of paper tend to exhibit a specific and complex structure, which is described by physicists as ridge networks. Existing literature shows that the automation of ridge network detection in crumpled paper is very challenging because of its complex structure and measuring distortion. In this paper, we propose to model the ridge network as a weighted graph and formulate the ridge network detection as an optimization problem in terms of the graph density. First, we detect a set of graph nodes and then determine the edge weight between each pair of nodes to construct a complete graph. Next, we define a graph density criterion and formulate the detection problem to determine a subgraph with maximal graph density. Further, we also propose to refine the graph density by including a pairwise connectivity into the criterion to improve the connectivity of the detected ridge network. Our experimental results show that, with the density criterion, our proposed method effectively automates the ridge network detection.

17. Nested Tracking Graphs

DOE PAGES

Lukasczyk, Jonas; Weber, Gunther; Maciejewski, Ross; ...

2017-06-01

Tracking graphs are a well established tool in topological analysis to visualize the evolution of components and their properties over time, i.e., when components appear, disappear, merge, and split. However, tracking graphs are limited to a single level threshold and the graphs may vary substantially even under small changes to the threshold. To examine the evolution of features for varying levels, users have to compare multiple tracking graphs without a direct visual link between them. We propose a novel, interactive, nested graph visualization based on the fact that the tracked superlevel set components for different levels are related to eachmore » other through their nesting hierarchy. This approach allows us to set multiple tracking graphs in context to each other and enables users to effectively follow the evolution of components for different levels simultaneously. We show the effectiveness of our approach on datasets from finite pointset methods, computational fluid dynamics, and cosmology simulations.« less

18. 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.

19. 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.

20. 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.

1. 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.

2. 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.

3. Online dynamic graph drawing.

PubMed

Frishman, Yaniv; Tal, Ayellet

2008-01-01

This paper presents an algorithm for drawing a sequence of graphs online. The algorithm strives to maintain the global structure of the graph and thus the user's mental map, while allowing arbitrary modifications between consecutive layouts. The algorithm works online and uses various execution culling methods in order to reduce the layout time and handle large dynamic graphs. Techniques for representing graphs on the GPU allow a speedup by a factor of up to 17 compared to the CPU implementation. The scalability of the algorithm across GPU generations is demonstrated. Applications of the algorithm to the visualization of discussion threads in Internet sites and to the visualization of social networks are provided.

4. 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.

5. Recognition of Probe Ptolemaic Graphs

Chang, Maw-Shang; Hung, Ling-Ju

Let G denote a graph class. An undirected graph G is called a probe G graph if one can make G a graph in G by adding edges between vertices in some independent set of G. By definition graph class G is a subclass of probe G graphs. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distance-hereditary graphs. Many problems NP-hard on chordal graphs can be solved in polynomial time on ptolemaic graphs. We proposed an O(nm)-time algorithm to recognize probe ptolemaic graphs where n and m are the numbers of vertices and edges of the input graph respectively.

6. 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.

7. Logical reasoning necessary to make line graphs

Wavering, Michael J.

A study was conducted to determine the logical reasoning necessary to construct line graphs. Three types of line graphs were used: a straight line with a positive slope, a straight line with a negative slope, and an exponentially increasing curve. The subjects were students in grades six through twelve enrolled in a laboratory school. The responses were classified into one of nine categories. The categories ranged from no attempt to make a graph to a complete graph with a statement of a relationship between the variables. Subjects in grades six through eight exhibited behaviors mainly in the first four categories, ninth- and tenth-grade subjects scored in the middle categories, and eleventh and twelfth graders scored mainly in the upper categories. These response categories also showed a close fit with Piagetian concrete operational structures for single and double seriation and formal operational structures for proportional reasoning and correlational reasoning.

8. Visibility graph analysis on heartbeat dynamics of meditation training

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.

9. 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.

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

DOE PAGES

Kepner, Jeremy; Bader, David; Buluç, Aydın; ...

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

11. 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.

12. 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.

13. 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…

14. Graphing from Everyday Experience.

ERIC Educational Resources Information Center

Carraher, David; Schliemann, Analucia; Nemirousky, Ricardo

1995-01-01

Discusses the importance of teaching grounded in the everyday experiences and concerns of the learners. Studies how people with limited school experience can understand graphs and concludes that individuals with limited academic education can clarify the role of everyday experiences in learning about graphs. (ASK)

15. 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…

16. Learning graph matching.

PubMed

Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J

2009-06-01

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

17. 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…

18. 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)

19. 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)

20. 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…

1. 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…

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. 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)

4. 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…

5. 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…

6. Evolutionary stability on graphs.

PubMed

Ohtsuki, Hisashi; Nowak, Martin A

2008-04-21

Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs.

7. Quantum causal graph dynamics

Arrighi, Pablo; Martiel, Simon

2017-07-01

Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs—in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on quantum cellular automata with another on reversible causal graph dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. We discuss some of the implications for quantum gravity.

8. Evolutionary stability on graphs

PubMed Central

Ohtsuki, Hisashi; Nowak, Martin A.

2008-01-01

Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. PMID:18295801

9. Topological structure of dictionary graphs

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.

10. A graph-based reflexive artificial chemistry.

PubMed

Salzberg, Chris

2007-01-01

The conceptual divide between formal systems of computation and abstract models of chemistry is considered. As an attempt to concretely bridge this divide, a formalism is proposed that describes a constructive artificial chemistry on a space of directed graph structures. The idea for the formalism originates in computer science theory, with the traditional abstraction of a physical machine, the finite-state machine (FSM). In the FSM, the machine (state-transition graph) and input string (series of binary digits) are fundamentally distinct objects, separated by nature of the underlying formalism. This distinction is dissolved in the proposed system, resulting in a construction process that is reflexive: graphs interact with their own topological structure to generate a product. It is argued that this property of reflexivity is a key element missing from earlier model chemistries. Examples demonstrate the continuous emergence complex self-similar topologies, novel reaction pathways, and seemingly open-ended diversity. Implications of these findings are discussed.

11. 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.

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

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.

13. 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.

14. Graph optimized Laplacian eigenmaps for face recognition

Dornaika, F.; Assoum, A.; Ruichek, Y.

2015-01-01

In recent years, a variety of nonlinear dimensionality reduction techniques (NLDR) have been proposed in the literature. They aim to address the limitations of traditional techniques such as PCA and classical scaling. Most of these techniques assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. They provide a mapping from the high-dimensional space to the low-dimensional embedding and may be viewed, in the context of machine learning, as a preliminary feature extraction step, after which pattern recognition algorithms are applied. Laplacian Eigenmaps (LE) is a nonlinear graph-based dimensionality reduction method. It has been successfully applied in many practical problems such as face recognition. However the construction of LE graph suffers, similarly to other graph-based DR techniques from the following issues: (1) the neighborhood graph is artificially defined in advance, and thus does not necessary benefit the desired DR task; (2) the graph is built using the nearest neighbor criterion which tends to work poorly due to the high-dimensionality of original space; and (3) its computation depends on two parameters whose values are generally uneasy to assign, the neighborhood size and the heat kernel parameter. To address the above-mentioned problems, for the particular case of the LPP method (a linear version of LE), L. Zhang et al.1 have developed a novel DR algorithm whose idea is to integrate graph construction with specific DR process into a unified framework. This algorithm results in an optimized graph rather than a predefined one.

15. Robust Spectral Clustering Using Statistical Sub-Graph Affinity Model

PubMed Central

Eichel, Justin A.; Wong, Alexander; Fieguth, Paul; Clausi, David A.

2013-01-01

Spectral clustering methods have been shown to be effective for image segmentation. Unfortunately, the presence of image noise as well as textural characteristics can have a significant negative effect on the segmentation performance. To accommodate for image noise and textural characteristics, this study introduces the concept of sub-graph affinity, where each node in the primary graph is modeled as a sub-graph characterizing the neighborhood surrounding the node. The statistical sub-graph affinity matrix is then constructed based on the statistical relationships between sub-graphs of connected nodes in the primary graph, thus counteracting the uncertainty associated with the image noise and textural characteristics by utilizing more information than traditional spectral clustering methods. Experiments using both synthetic and natural images under various levels of noise contamination demonstrate that the proposed approach can achieve improved segmentation performance when compared to existing spectral clustering methods. PMID:24386111

16. In search for graph invariants of chemical interes

1993-12-01

This article encourages readers to search for novel graph invariants that may be of potential interest in chemical applications of graph theory. It is also hoped that theoreticians, with their different backgrounds and different viewpoints, may identify or design novel graph invariants that have not yet been tested in chemistry and in this way enrich the pool of descriptors for use in studies of structure—property relationships. An outline of desirable attributes for graph invariants that have found use in chemistry is followed by a brief review of a selection of known ad hoc invariants. This continues with a description of families of structurally related invariants. We discuss some promising routes to construction of novel descriptors such as those based on consideration of graph fragments. A warning against useless and misleading descriptors is given. We end with a call for design of or verification of basis graphs.

17. Teaching Kinematics as a Way to understand Calculus and Graphs

Zavala, Genaro; Alarcon, H.

2006-12-01

In our institution we have implemented a remedial course in which one of its sections is dedicated to kinematics in one dimension. In that section we spend some time working with graphs understanding concepts from mean velocity to instantaneous velocity as a way to understand broader concepts such as mean rate-of-change and instantaneous rate-of-change. Students calculate instantaneous velocity by three methods: using the graph, using the ratio of change of position to time interval when the time interval is sufficiently small, and using derivatives. Students are able to compare the three methods realizing that the first method gives them an approximation; the second one, by using significant figures, is able give them the correct answer; and the last method give them the correct answer. At the end of the section, students are able to construct velocity graphs from position graphs and vice versa, position graphs from velocity graphs.

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

PubMed

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

2015-01-01

A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a graph is embedded cellularly, and the embeddings of rigid vertex graphs are required to preserve the prescribed cyclic order of incident edges at every vertex. The genus ranges of 4-regular rigid vertex graphs are sets of consecutive integers, and we address two questions: which intervals of integers appear as genus ranges of such graphs, and what types of graphs realize a given genus range. For graphs with 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.

19. 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. PMID:27807395

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

PubMed

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

2015-01-01

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.

1. 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

2. Quantum secret sharing with qudit graph states

SciTech Connect

Keet, Adrian; Fortescue, Ben; Sanders, Barry C.; Markham, Damian

2010-12-15

We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.

3. Interactive Web Graphs for Economic Principles.

ERIC Educational Resources Information Center

Kaufman, Dennis A.; Kaufman, Rebecca S.

2002-01-01

Describes a Web site with animation and interactive activities containing graphs and basic economics concepts. Features changes in supply and market equilibrium, the construction of the long-run average cost curve, short-run profit maximization, long-run market equilibrium, and changes in aggregate demand and aggregate supply. States the…

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

ERIC Educational Resources Information Center

Öçal, Mehmet Fatih

2017-01-01

Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…

5. The Effect of Using Graphing Calculators in Complex Function Graphs

ERIC Educational Resources Information Center

Ocak, Mehmet Akif

2008-01-01

This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…

6. Construction

DTIC Science & Technology

2002-01-01

Harbor Deepening Project, Jacksonville, FL Palm Valley Bridge Project, Jacksonville, FL Rotary Club of San Juan, San Juan, PR Tren Urbano Subway...David. What is nanotechnology? What are its implications for construction?, Foresight/CRISP Workshop on Nanotechnology, Royal Society of Arts

7. Construction

DTIC Science & Technology

2002-01-01

San Juan, PR Tren Urbano Subway Project, San Juan, PR U.S. Army South, San Juan, PR U.S. Coast Guard Housing Project, San Juan, PR U.S. Coast Guard...construction?, Foresight/CRISP Workshop on Nanotechnology, Royal Society of Arts . Cheltenham, England: 2001, p.5. 56 Concrete Proposals, Economist, July 24

8. Understanding graphs with two independent variables

Cooper, Jennifer L.

Adults are not necessarily competent users of graphs with two independent variables, despite the frequency of this representational format. The three tasks in this thesis address the impact of interpretation statements and graph patterns. Interpretation statements were based on the statistical effects -- simple effects, main effects, and interactions. Graph patterns were systematically varied based on a novel classification scheme of graphs with two IVs. I suggest that the complexity of a graph's data pattern depends on the consistency of the simple effects' directions and magnitudes. In the first study, undergraduates constructed graphs based on statements about data patterns. Errors reflected a misunderstanding of how two IVs could be combined and represented graphically. When the experimental group had graph-relevant information added (variable labels spatially located on axes), the ability to represent the relationships among the IVs significantly increased. The ability to satisfy the constraints imposed by the statements was not affected. Adding labels specifically targeted skills relevant to graphical literacy. Transfer to a third trial was stronger for those of higher math abilities. The second study focused on the effect of an introductory statistics course. Overall, undergraduates performed well on statements describing the simple effects of the IVs. However, even though they improved from Time 1 to Time 2 for interaction statements, performance on statements about main effects and interactions still showed considerable room for improvement. In the third study, repeated trials of the 20 patterns proposed by the simple effects consistency model established that the proposed classification scheme addresses additional sources of variability in reasoning with graphs (i.e., sources not captured by traditional classification schemes). As the complexity level of the data pattern increased, performance (based on accuracy and RT) decreased, with parallel impacts on

9. 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…

10. 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…

11. 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…

PubMed

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 d{s}, the important quantity for reaction spreading is found to be the connectivity dimension d{l}. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)∼t{d{l}}. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)e{αt} with α proportional to ln(k), where (k) is the average degree of the graph.

13. 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.

14. Entanglement witnesses for graph states: General theory and examples

SciTech Connect

Jungnitsch, Bastian; Moroder, Tobias; Guehne, Otfried

2011-09-15

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to 1 when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.

15. Horizontal Visibility graphs generated by type-II intermittency

Núñez, Ángel M.; Lacasa, Lucas; Patricio Gómez, Jose

2014-01-01

In this contribution we study the onset of chaos via type-II intermittency within the framework of Horizontal Visibility graph theory. We construct graphs associated to time series generated by an iterated map close to a Neimark-Sacker bifurcation and study, both numerically and analytically, their main topological properties. We find well defined equivalences between the main statistical properties of intermittent series (scaling of laminar trends and Lyapunov exponent) and those of the resulting graphs, and accordingly construct a graph-theoretical description of type-II intermittency. We finally recast this theory into a graph-theoretical renormalization group (RG) framework, and show that the fixed point structure of RG flow diagram separates regular, critical and chaotic dynamics.

16. 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.

17. Visual exploration of complex time-varying graphs.

PubMed

Kumar, Gautam; Garland, Michael

2006-01-01

Many graph drawing and visualization algorithms, such as force-directed layout and line-dot rendering, work very well on relatively small and sparse graphs. However, they often produce extremely tangled results and exhibit impractical running times for highly non-planar graphs with large edge density. And very few graph layout algorithms support dynamic time-varying graphs; applying them independently to each frame produces distracting temporally incoherent visualizations. We have developed a new visualization technique based on a novel approach to hierarchically structuring dense graphs via stratification. Using this structure, we formulate a hierarchical force-directed layout algorithm that is both efficient and produces quality graph layouts. The stratification of the graph also allows us to present views of the data that abstract away many small details of its structure. Rather than displaying all edges and nodes at once, resulting in a convoluted rendering, we present an interactive tool that filters edges and nodes using the graph hierarchy and allows users to drill down into the graph for details. Our layout algorithm also accommodates time-varying graphs in a natural way, producing a temporally coherent animation that can be used to analyze and extract trends from dynamic graph data. For example, we demonstrate the use of our method to explore financial correlation data for the U.S. stock market in the period from 1990 to 2005. The user can easily analyze the time-varying correlation graph of the market, uncovering information such as market sector trends, representative stocks for portfolio construction, and the interrelationship of stocks over time.

18. Construction

DTIC Science & Technology

2003-01-01

hot water, appliances, lightening and misc.66 Average and efficient energy costs were determined for each base. The collection of average and...data and the appropriate regional median condominium87 and apartment O&M costs . For new housing projects the energy efficient utility costs were used...supply of domestic skilled laborers and the increasing cost of insurance. The construction industry has always contracted and expanded based

19. Assortativity of complementary graphs

Wang, H.; Winterbach, W.; van Mieghem, P.

2011-09-01

Newman's measure for (dis)assortativity, the linear degree correlationρD, is widely studied although analytic insight into the assortativity of an arbitrary network remains far from well understood. In this paper, we derive the general relation (2), (3) and Theorem 1 between the assortativity ρD(G) of a graph G and the assortativityρD(Gc) of its complement Gc. Both ρD(G) and ρD(Gc) are linearly related by the degree distribution in G. When the graph G(N,p) possesses a binomial degree distribution as in the Erdős-Rényi random graphs Gp(N), its complementary graph Gpc(N) = G1-p(N) follows a binomial degree distribution as in the Erdős-Rényi random graphs G1-p(N). We prove that the maximum and minimum assortativity of a class of graphs with a binomial distribution are asymptotically antisymmetric: ρmax(N,p) = -ρmin(N,p) for N → ∞. The general relation (3) nicely leads to (a) the relation (10) and (16) between the assortativity range ρmax(G)-ρmin(G) of a graph with a given degree distribution and the range ρmax(Gc)-ρmin(Gc) of its complementary graph and (b) new bounds (6) and (15) of the assortativity. These results together with our numerical experiments in over 30 real-world complex networks illustrate that the assortativity range ρmax-ρmin is generally large in sparse networks, which underlines the importance of assortativity as a network characterizer.

20. Percolation threshold on planar Euclidean Gabriel graphs

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.

1. Internet topology: connectivity of IP graphs

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.

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

PubMed

Nguyen, Quan-Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra

2017-02-24

Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

3. Visualizing Evaluation Structures using Layered Graph Drawings.

PubMed

2016-03-18

We propose a method for visualizing evaluation structures that is based on layered graph drawing techniques. An evaluation structure is a hierarchical structure of human cognition extracted from interviews based on the evaluation grid method. An evaluation structure can be defined as a directed acyclic graph (DAG). The Sugiyama framework is a popular method for constructing DAGs. A new layer assignment method that is a part of the Sugiyama framework is proposed to satisfy the requirements for drawing evaluation structures. We formulate a layer assignment problem by considering the sum of squares of arc lengths to be an integer quadratic programming (IQP) problem. Moreover, we transform the IQP problem into an equivalent integer linear programming (ILP) problem for computational efficiency. Evaluations demonstrate that the layered graph drawing with the proposed layer assignment method is preferred by users and aids in the understanding of evaluation structures.

4. Deitmar schemes, graphs and zeta functions

Mérida-Angulo, Manuel; Thas, Koen

2017-07-01

In Thas (2014) it was explained how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F1) to a so-called ;loose graph; (which is a generalization of a graph). Several properties of the Deitmar scheme can be proven easily from the combinatorics of the (loose) graph, and known realizations of objects over F1 such as combinatorial F1-projective and F1-affine spaces exactly depict the loose graph which corresponds to the associated Deitmar scheme. In this paper, we first modify the construction of loc. cit., and show that Deitmar schemes which are defined by finite trees (with possible end points) are ;defined over F1; in Kurokawa's sense; we then derive a precise formula for the Kurokawa zeta function for such schemes (and so also for the counting polynomial of all associated Fq-schemes). As a corollary, we find a zeta function for all such trees which contains information such as the number of inner points and the spectrum of degrees, and which is thus very different than Ihara's zeta function (which is trivial in this case). Using a process called ;surgery,; we show that one can determine the zeta function of a general loose graph and its associated {Deitmar, Grothendieck}-schemes in a number of steps, eventually reducing the calculation essentially to trees. We study a number of classes of examples of loose graphs, and introduce the Grothendieck ring ofF1-schemes along the way in order to perform the calculations. Finally, we include a computer program for performing more tedious calculations, and compare the new zeta function to Ihara's zeta function for graphs in a number of examples.

5. 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.

6. Horizontal visibility graphs generated by type-I intermittency

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.

7. On support relations and semantic scene graphs

Yang, Michael Ying; Liao, Wentong; Ackermann, Hanno; Rosenhahn, Bodo

2017-09-01

Scene understanding is one of the essential and challenging topics in computer vision and photogrammetry. Scene graph provides valuable information for such scene understanding. This paper proposes a novel framework for automatic generation of semantic scene graphs which interpret indoor environments. First, a Convolutional Neural Network is used to detect objects of interest in the given image. Then, the precise support relations between objects are inferred by taking two important auxiliary information in the indoor environments: the physical stability and the prior support knowledge between object categories. Finally, a semantic scene graph describing the contextual relations within a cluttered indoor scene is constructed. In contrast to the previous methods for extracting support relations, our approach provides more accurate results. Furthermore, we do not use pixel-wise segmentation to obtain objects, which is computation costly. We also propose different methods to evaluate the generated scene graphs, which lacks in this community. Our experiments are carried out on the NYUv2 dataset. The experimental results demonstrated that our approach outperforms the state-of-the-art methods in inferring support relations. The estimated scene graphs are accurately compared with ground truth.

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. Optimized Graph Search Using Multi-Level Graph Clustering

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.

10. Filtering Random Graph Processes Over Random Time-Varying Graphs

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

2017-08-01

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochastic- ity in both the graph topology as well as the signal itself. To bridge this gap, we examine the statistical behavior of the two key filter types, finite impulse response (FIR) and autoregressive moving average (ARMA) graph filters, when operating on random time- varying graph signals (or random graph processes) over random time-varying graphs. Our analysis shows that (i) in expectation, the filters behave as the same deterministic filters operating on a deterministic graph, being the expected graph, having as input signal a deterministic signal, being the expected signal, and (ii) there are meaningful upper bounds for the variance of the filter output. We conclude the paper by proposing two novel ways of exploiting randomness to improve (joint graph-time) noise cancellation, as well as to reduce the computational complexity of graph filtering. As demonstrated by numerical results, these methods outperform the disjoint average and denoise algorithm, and yield a (up to) four times complexity redution, with very little difference from the optimal solution.

11. 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.

12. 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.

13. Quantum ergodicity on graphs.

PubMed

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

2008-12-31

We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear sigma model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

14. Quantum Ergodicity on Graphs

SciTech Connect

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

2008-12-31

We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear {sigma} model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

15. 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.

16. Ancestral recombinations graph: a reconstructability perspective using random-graphs framework.

PubMed

Parida, Laxmi

2010-10-01

We present a random graphs framework to study pedigree history in an ideal (Wright Fisher) population. This framework correlates the underlying mathematical objects in, for example, pedigree graph, mtDNA or NRY Chr tree, ARG (Ancestral Recombinations Graph), and HUD used in literature, into a single unified random graph framework. It also gives a natural definition, based solely on the topology, of an ARG, one of the most interesting as well as useful mathematical objects in this area. The random graphs framework gives an alternative parametrization of the ARG that does not use the recombination rate q and instead uses a parameter M based on the (estimate of ) the number of non-mixing segments in the extant units. This seems more natural in a setting that attempts to tease apart the population dynamics from the biology of the units. This framework also gives a purely topological definition of GMRCA, analogous to MRCA on trees (which has a purely topological description i.e., it is a root, graph-theoretically speaking, of a tree). Secondly, with a natural extension of the ideas from random-graphs we present a sampling (simulation) algorithm to construct random instances of ARG/unilinear transmission graph. This is the first (to the best of the author's knowledge) algorithm that guarantees uniform sampling of the space of ARG instances, reflecting the ideal population model. Finally, using a measure of reconstructability of the past historical events given a collection of extant sequences, we conclude for a given set of extant sequences, the joint history of local segments along a chromosome is reconstructible.

17. 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.

18. A semantic graph-based approach to biomedical summarisation.

PubMed

Plaza, Laura; Díaz, Alberto; Gervás, Pablo

2011-09-01

Access to the vast body of research literature that is available in biomedicine and related fields may be improved by automatic summarisation. This paper presents a method for summarising biomedical scientific literature that takes into consideration the characteristics of the domain and the type of documents. To address the problem of identifying salient sentences in biomedical texts, concepts and relations derived from the Unified Medical Language System (UMLS) are arranged to construct a semantic graph that represents the document. A degree-based clustering algorithm is then used to identify different themes or topics within the text. Different heuristics for sentence selection, intended to generate different types of summaries, are tested. A real document case is drawn up to illustrate how the method works. A large-scale evaluation is performed using the recall-oriented understudy for gisting-evaluation (ROUGE) metrics. The results are compared with those achieved by three well-known summarisers (two research prototypes and a commercial application) and two baselines. Our method significantly outperforms all summarisers and baselines. The best of our heuristics achieves an improvement in performance of almost 7.7 percentage units in the ROUGE-1 score over the LexRank summariser (0.7862 versus 0.7302). A qualitative analysis of the summaries also shows that our method succeeds in identifying sentences that cover the main topic of the document and also considers other secondary or "satellite" information that might be relevant to the user. The method proposed is proved to be an efficient approach to biomedical literature summarisation, which confirms that the use of concepts rather than terms can be very useful in automatic summarisation, especially when dealing with highly specialised domains. Copyright © 2011 Elsevier B.V. All rights reserved.

19. A Graph Summarization Algorithm Based on RFID Logistics

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.

20. Experimental Study of Quantum Graphs with Microwave Networks

Fu, Ziyuan; Koch, Trystan; Antonsen, Thomas; Ott, Edward; Anlage, Steven; Wave Chaos Team

An experimental setup consisting of microwave networks is used to simulate quantum graphs. The networks are constructed from coaxial cables connected by T junctions. The networks are built for operation both at room temperature and superconducting versions that operate at cryogenic temperatures. In the experiments, a phase shifter is connected to one of the network bonds to generate an ensemble of quantum graphs by varying the phase delay. The eigenvalue spectrum is found from S-parameter measurements on one-port graphs. With the experimental data, the nearest-neighbor spacing statistics and the impedance statistics of the graphs are examined. It is also demonstrated that time-reversal invariance for microwave propagation in the graphs can be broken without increasing dissipation significantly by making nodes with circulators. Random matrix theory (RMT) successfully describes universal statistical properties of the system. We acknowledge support under contract AFOSR COE Grant FA9550-15-1-0171.

1. 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.

2. 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.

3. Relativity on rotated graph paper

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.

4. 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…

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…

6. Body Motion and Graphing.

ERIC Educational Resources Information Center

Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy

1998-01-01

Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…

7. 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…

8. 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…

9. GraphLib

SciTech Connect

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

10. 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.

11. 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.

12. 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…

13. 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…

14. 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.

15. On the assumption of cubic graphs of vascular networks

Cha, Sung-Hyuk; Chang, Sukmoon; Gargano, Michael L.

2006-03-01

A vascular network is often represented by a Reeb graph, which is a topological skeleton, and graph theory has been widely applied to analyze properties of a vascular network. A Reeb graph model for a vascular network is obtained by assigning the branch points of the network to be the vertices of the graph and the vessels between branch points to be the edges of the graph. Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Vascular networks develop by way of two biological mechanisms of vessel sprouting (budding) and splitting (intussusception). According to a graph theory modeling of two vascular network growth mechanisms, all nodes in the Reeb graph must be cubic in degree except for two special nodes: the afferent (A) and efferent (E) nodes. We define that a vascular network is cubic if all internal nodes are cubic in degree. We consider six normal adult rat renal glomerular networks and use their reeb graphs already constructed and published in the literature. We observe that five of them contain internal vertices of degree higher than three. Branch points in vascular networks may appear to be of a higher degree if the imaging resolution cannot differentiate between blood vessels that are very close in proximity. Here, we propose a random graph theory model that edits a non-cubic vascular network into a cubic graph. We observe that the edited cubic graph from a non-cubic vascular network has the similar size and order as the one cubic vascular network.

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

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

17. 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.

18. 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.…

19. 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.

20. 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.…

1. 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.

2. Kevin Bacon and Graph Theory

ERIC Educational Resources Information Center

Hopkins, Brian

2004-01-01

The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…

3. 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…

4. 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…

5. Kevin Bacon and Graph Theory

ERIC Educational Resources Information Center

Hopkins, Brian

2004-01-01

The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…

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

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).

7. Jamming graphs: A local approach to global mechanical rigidity

Lopez, Jorge H.; Cao, L.; Schwarz, J. M.

2013-12-01

We revisit the concept of minimal rigidity as applied to frictionless, repulsive soft sphere packings in two dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's theorem in two dimensions. It constrains the global, average coordination number of the graph, for example. However, minimal rigidity does not address the geometry of local mechanical stability. The jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability. We demonstrate how jamming graphs can be constructed using local moves via the Henneberg construction such that these graphs fall under the jurisdiction of correlated percolation. We then probe how jamming graphs destabilize, or become unjammed, by deleting a bond and computing the resulting rigid cluster distribution. We also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra (redundant) contacts destabilizes. The latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut-out (or frozen-in) subsystems.

8. Plane representations of graphs and visibility between parallel segments

Tamassia, R.; Tollis, I. G.

1985-04-01

Several layout compaction strategies for VLSI are based on the concept of visibility between parallel segments, where we say that two parallel segments of a given set are visible if they can be joined by a segment orthogonal to them, which does not intersect any other segment. This paper studies visibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments drawn between visible vertex-segments. Clearly, every graph that admits such a representation must be a planar. The authors consider three types of visibility representations, and give complete characterizations of the classes of graphs that admit them. Furthermore, they present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs.

9. Free energy disconnectivity graphs: Application to peptide models

Krivov, Sergei V.; Karplus, Martin

2002-12-01

Disconnectivity graphs are widely used for understanding the multidimensional potential energy surfaces (PES) of complex systems. Since entropic contributions to the free energy can be important, particularly for polypeptide chains and other polymers, conclusions concerning the equilibrium properties and kinetics of the system based on potential energy disconnectivity graphs (PE DG) can be misleading. We present an approach for constructing free energy surfaces (FES) and free energy disconnectivity graphs (FE DG) and give examples of their applications to peptides. They show that the FES and FE DG can differ significantly from the PES and PE DG.

10. What is a complex graph?

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.

11. A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and k-Nearest Neighbor Graph

PubMed Central

Pan, Yongke; Niu, Wenjia

2017-01-01

Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines. PMID:28316616

12. A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and k-Nearest Neighbor Graph.

PubMed

Zu, Baokai; Xia, Kewen; Pan, Yongke; Niu, Wenjia

2017-01-01

Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines.

13. 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.

14. Graph pyramids for protein function prediction

PubMed Central

2015-01-01

Background Uncovering the hidden organizational characteristics and regularities among biological sequences is the key issue for detailed understanding of an underlying biological phenomenon. Thus pattern recognition from nucleic acid sequences is an important affair for protein function prediction. As proteins from the same family exhibit similar characteristics, homology based approaches predict protein functions via protein classification. But conventional classification approaches mostly rely on the global features by considering only strong protein similarity matches. This leads to significant loss of prediction accuracy. Methods Here we construct the Protein-Protein Similarity (PPS) network, which captures the subtle properties of protein families. The proposed method considers the local as well as the global features, by examining the interactions among 'weakly interacting proteins' in the PPS network and by using hierarchical graph analysis via the graph pyramid. Different underlying properties of the protein families are uncovered by operating the proposed graph based features at various pyramid levels. Results Experimental results on benchmark data sets show that the proposed hierarchical voting algorithm using graph pyramid helps to improve computational efficiency as well the protein classification accuracy. Quantitatively, among 14,086 test sequences, on an average the proposed method misclassified only 21.1 sequences whereas baseline BLAST score based global feature matching method misclassified 362.9 sequences. With each correctly classified test sequence, the fast incremental learning ability of the proposed method further enhances the training model. Thus it has achieved more than 96% protein classification accuracy using only 20% per class training data. PMID:26044522

15. Mathematical formula recognition using graph grammar

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.

16. Graph pyramids for protein function prediction.

PubMed

Sandhan, Tushar; Yoo, Youngjun; Choi, Jin; Kim, Sun

2015-01-01

Uncovering the hidden organizational characteristics and regularities among biological sequences is the key issue for detailed understanding of an underlying biological phenomenon. Thus pattern recognition from nucleic acid sequences is an important affair for protein function prediction. As proteins from the same family exhibit similar characteristics, homology based approaches predict protein functions via protein classification. But conventional classification approaches mostly rely on the global features by considering only strong protein similarity matches. This leads to significant loss of prediction accuracy. Here we construct the Protein-Protein Similarity (PPS) network, which captures the subtle properties of protein families. The proposed method considers the local as well as the global features, by examining the interactions among 'weakly interacting proteins' in the PPS network and by using hierarchical graph analysis via the graph pyramid. Different underlying properties of the protein families are uncovered by operating the proposed graph based features at various pyramid levels. Experimental results on benchmark data sets show that the proposed hierarchical voting algorithm using graph pyramid helps to improve computational efficiency as well the protein classification accuracy. Quantitatively, among 14,086 test sequences, on an average the proposed method misclassified only 21.1 sequences whereas baseline BLAST score based global feature matching method misclassified 362.9 sequences. With each correctly classified test sequence, the fast incremental learning ability of the proposed method further enhances the training model. Thus it has achieved more than 96% protein classification accuracy using only 20% per class training data.

17. The Relationship Between the Sequence of Graph Interpretation Skills and the Sequence of Mathematics Skills for Kindergarten Through Ninth Grade.

ERIC Educational Resources Information Center

Appel, Ida J.

The purpose of the study was to determine in what sequence skills in graph interpretation should be presented in grades K-9. A sequential list of mathematics skills for grades K-9 was constructed, graph skills were identified and arranged in a sequential and spiral manner, then graph skills were matched with appropriate mathematics skills and…

18. 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…

19. Optical tomography on graphs

Chung, Francis J.; Gilbert, Anna C.; Hoskins, Jeremy G.; Schotland, John C.

2017-05-01

We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving estimates characterizing the domain of convergence, approximation errors, and stability of our approach. We also present a modification which allows additional information on the structure of the potential to be incorporated, facilitating recovery for a broader class of problems.

20. 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…

1. Convex Graph Invariants

DTIC Science & Technology

2010-12-02

evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in

2. Factorized Graph Matching.

PubMed

Zhou, Feng; de la Torre, Fernando

2015-11-19

Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.

3. 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

4. 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…

5. 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…

6. Lung segmentation with graph cuts: Graph size versus performance

Pazokifard, Banafsheh; Sowmya, Arcot

2013-10-01

The effect of graph size on segmentation performance and speed is investigated, where segmentation is based on the graph cuts algorithm. The study is performed on lung extraction in 50 complete multi detector computed tomography (MDCT) datasets, and a fully automatic procedure. The experiments were performed on different graph sizes for both 2-D (4 and 8 neighbours) and 3-D (6 and 26 neighbours) graphs. Five slices from each segmented dataset were compared to the reference delineation provided by a radiologist. Our evaluations highlight the fact that when medical image segmentation is performed using graph cuts, increasing graph and neighbourhood connection size does not necessarily improve the segmentation performance, but also increase the running time dramatically.

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

SciTech Connect

Hong, Seokyong; Lee, Sangkeun; Lim, Seung-Hwan; 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.

8. Automated Program Recognition by Graph Parsing

DTIC Science & Technology

1992-07-01

programs are represented as attributed dataflow graphs and a library of clichis is encoded as an attributed graph grammar . Graph parsing is used to...recognition. Second, we investigate the expressiveness of our graph grammar formalism for capturing pro- gramming cliches. Third, we empirically and...library of cliches is encoded as an attributed graph grammar . Graph parsing is used to recognize clich6s in the code. We demonstrate that this graph

9. 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.

10. 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.

11. Applied and computational harmonic analysis on graphs and networks

Irion, Jeff; Saito, Naoki

2015-09-01

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

12. 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

13. 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.

14. Low-algorithmic-complexity entropy-deceiving graphs

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

2017-07-01

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

15. 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

16. On Edge Exchangeable Random Graphs

Janson, Svante

2017-06-01

We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show that the model can produce dense, sparse and extremely sparse random graphs. One example yields a power-law degree distribution. We give some examples where the random graph is dense and converges a.s. in the sense of graph limit theory, but also an example where a.s. every graph limit is the limit of some subsequence. Another example is sparse and yields convergence to a non-integrable generalized graphon defined on (0,∞).

17. Dimension theory of graphs and networks

Nowotny, Thomas; Requardt, Manfred

1998-03-01

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of continuum physics and mathematics. A core concept is the notion of dimension. In the following we develop such a notion for irregular structures such as (large) graphs and networks and derive a number of its properties. Among other things we show its stability under a wide class of perturbations which is important if one has  dimensional phase transitions' in mind. Furthermore we systematically construct graphs with almost arbitrary  fractal dimension' which may be of some use in the context of  dimensional renormalization' or statistical mechanics on irregular sets.

18. 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.

19. Potts model and graph theory

Wu, F. Y.

1988-07-01

Elementary exposition is given of some recent developments in studies of graphtheoretic aspects of the Potts model. Topics discussed include graphical expansions of the Potts partition function and correlation functions and their relationships with the chromatic, dichromatic, and flow polynomials occurring in graph theory. It is also shown that the Potts model realization of these classic graph-theoretic problems provides alternate and direct proofs of properties established heretofore only in the context of formal graph theory.

20. Eigensolutions of dodecahedron graphs

Ghosh, Piyali; Karmakar, Somnath; Mandal, Bholanath

2014-02-01

Eigensolutions of 20-vertex cage (i.e. dodecahedron) have been determined with the use of fivefold rotational symmetry. For homo-dodecahedron the eigensolutions become analytical but for the hetero-dodecahedron having two different types of atoms ((C,N),(C,B),(B,N)) the eigensolutions are found to be factored out into five 4-degree polynomials with one corresponding to nondegenerate and other four corresponding to two degenerate eigensolutions. Eigenspectra and total π-electron energies of homo- and hetero-dodecahedron graphs have been calculated.

1. Strongly Regular Graphs,

DTIC Science & Technology

1973-10-01

The theory of strongly regular graphs was introduced by Bose r7 1 in 1963, in connection with partial geometries and 2 class association schemes. One...non adjacent vertices is constant and equal to ~. We shall denote by ~(p) (reap.r(p)) the set of vertices adjacent (resp.non adjacent) to a vertex p...is the complement of .2’ if the set of vertices of ~ is the set of vertices of .2’ and if two vertices in .2’ are adjacent if and only if they were

2. Graph Theory of Tower Tasks

PubMed Central

Hinz, Andreas M.

2012-01-01

The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks. PMID:22207419

3. Spectral partitioning in equitable graphs

Barucca, Paolo

2017-06-01

Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.

4. From time series to complex networks: The visibility graph

PubMed Central

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

2008-01-01

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. PMID:18362361

5. Graph states and local unitary transformations beyond local Clifford operations

Tsimakuridze, Nikoloz; Gühne, Otfried

2017-05-01

Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus on non-Clifford operations and find for certain transformations a graphical description in terms of weighted hypergraphs. This leads to the indentification of hypergraph states that are locally equivalent to graph states. Moreover, we present a systematic way to construct pairs of graph states which are equivalent under local unitary operations, but not equivalent under local Clifford operations. This generates counterexamples to a conjecture known as LU-LC conjecture. So far, the only counterexamples to this conjecture were found by random search. Our method reproduces the smallest known counterexample as a special case and provides a physical interpretation.

6. Graphical rule of transforming continuous-variable graph states by local homodyne detection

SciTech Connect

Zhang Jing

2010-09-15

Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules--local complement operation and vertex deletion (single quadrature-amplitude x measurement)--the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.

7. Sparse graph-based inductive learning with its application to image classification

Huang, Qianying; Zhang, Xiaohong; Huang, Sheng; Yang, Dan

2016-09-01

We present a graph-based classification approach called sparse graph-based inductive learning (SGIL). Different to the conventional graph-based classifiers, which perform the classification in a semisupervised way, SGIL is a purely supervised method whose classifier is totally learned in an inductive fashion instead of transductive fashion. Similar to the idea of sparse graph-based classifier, SGIL constructs a sparse graph to encode the correlations of training samples, and considers the classification issue as a regularized sparse graph partition issue where the optimal graph cut should not only minimize the correlation loss of the training samples but also minimize the classification errors. Essentially, the learned graph cut plays a role as the predicted labels here. Thus, a linear classifier can be inductively derived by learning a mapping between the training samples and the graph cuts. Since SGIL is purely supervised, it enjoys several desirable properties over the semisupervised ones in graph construction and model training. We evaluate our work on several popular image datasets. The experimental results demonstrate its superiority.

8. Cross over of recurrence networks to random graphs and random geometric graphs

Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.

2017-02-01

Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.

9. 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.

10. 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%.

11. Manual Refinement System for Graph-Based Segmentation Results in the Medical Domain

PubMed Central

Colen, Rivka R.; Freisleben, Bernd; Nimsky, Christopher

2013-01-01

The basic principle of graph-based approaches for image segmentation is to interpret an image as a graph, where the nodes of the graph represent 2D pixels or 3D voxels of the image. The weighted edges of the graph are obtained by intensity differences in the image. Once the graph is constructed, the minimal cost closed set on the graph can be computed via a polynomial time s-t cut, dividing the graph into two parts: the object and the background. However, no segmentation method provides perfect results, so additional manual editing is required, especially in the sensitive field of medical image processing. In this study, we present a manual refinement method that takes advantage of the basic design of graph-based image segmentation algorithms. Our approach restricts a graph-cut by using additional user-defined seed points to set up fixed nodes in the graph. The advantage is that manual edits can be integrated intuitively and quickly into the segmentation result of a graph-based approach. The method can be applied to both 2D and 3D objects that have to be segmented. Experimental results for synthetic and real images are presented to demonstrate the feasibility of our approach. PMID:21826501

12. 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.

13. 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.

14. Constructing Brambles

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.

15. Network reconstruction via graph blending

2016-05-01

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

16. 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)

17. 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…

18. Blind Identification of Graph Filters

Segarra, Santiago; Mateos, Gonzalo; Marques, Antonio G.; Ribeiro, Alejandro

2017-03-01

Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper deals with the problem of joint identification of a graph filter and its input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to the less-structured graph domain. Given a graph signal $\\mathbf{y}$ modeled as the output of a graph filter, the goal is to recover the vector of filter coefficients $\\mathbf{h}$, and the input signal $\\mathbf{x}$ which is assumed to be sparse. While $\\mathbf{y}$ is a bilinear function of $\\mathbf{x}$ and $\\mathbf{h}$, the filtered graph signal is also a linear combination of the entries of the lifted rank-one, row-sparse matrix $\\mathbf{x} \\mathbf{h}^T$. The blind graph-filter identification problem can thus be tackled via rank and sparsity minimization subject to linear constraints, an inverse problem amenable to convex relaxations offering provable recovery guarantees under simplifying assumptions. Numerical tests using both synthetic and real-world networks illustrate the merits of the proposed algorithms, as well as the benefits of leveraging multiple signals to aid the blind identification task.

19. 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…

20. 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)

1. 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.

2. 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.

3. 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

4. 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.

5. Quantum Ergodicity on Regular Graphs

Anantharaman, Nalini

2017-07-01

We give three different proofs of the main result of Anantharaman and Le Masson (Duke Math J 164(4):723-765, 2015), establishing quantum ergodicity—a form of delocalization—for eigenfunctions of the laplacian on large regular graphs of fixed degree. These three proofs are much shorter than the original one, quite different from one another, and we feel that each of the four proofs sheds a different light on the problem. The goal of this exploration is to find a proof that could be adapted for other models of interest in mathematical physics, such as the Anderson model on large regular graphs, regular graphs with weighted edges, or possibly certain models of non-regular graphs. A source of optimism in this direction is that we are able to extend the last proof to the case of anisotropic random walks on large regular graphs.

6. Flow graphs: interweaving dynamics and structure.

PubMed

Lambiotte, R; Sinatra, R; Delvenne, J-C; Evans, T S; Barahona, M; Latora, V

2011-07-01

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes.

7. 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…

8. 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…

9. 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…

10. 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…

11. 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…

12. Completeness and regularity of generalized fuzzy graphs.

PubMed

Samanta, Sovan; Sarkar, Biswajit; Shin, Dongmin; Pal, Madhumangal

2016-01-01

Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.

13. Comparison and enumeration of chemical graphs.

PubMed

Akutsu, Tatsuya; Nagamochi, Hiroshi

2013-01-01

Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds.

14. Comparison and Enumeration of Chemical Graphs

PubMed Central

Akutsu, Tatsuya; Nagamochi, Hiroshi

2013-01-01

Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds. PMID:24688697

15. GRAPH III: a digitizing and graph plotting program

SciTech Connect

Selleck, C.B.

1986-03-01

GRAPH is an interactive program that allows the user to perform two functions. The first is to plot two dimensional graphs and the second is to digitize graphs or plots to create data files of points. The program is designed to allow the user to get results quickly and easily. It is written in RATIV (a FORTRAN preprocessor) and is currently in use at Sandia under VMS on a VAX computer and CTSS on a Cray supercomputer. The program provides graphical output through all of the Sandia Virtual Device Interface (VDI) graphics devices. 2 refs., 3 figs., 3 tabs.

16. PieceStack: Toward Better Understanding of Stacked Graphs.

PubMed

Wu, Tongshuang; Wu, Yingcai; Shi, Conglei; Qu, Huamin; Cui, Weiwei

2016-02-24

Stacked graphs have been widely adopted in various fields, because they are capable of hierarchically visualizing a set of temporal sequences as well as their aggregation. However, because of visual illusion issues, connections between overly-detailed individual layers and overly-generalized aggregation are intercepted. Consequently, information in this area has yet to be fully excavated. Thus, we present PieceStack in this paper, to reveal the relevance of stacked graphs in understanding intrinsic details of their displayed shapes. This new visual analytic design interprets the ways through which aggregations are generated with individual layers by interactively splitting and re-constructing the stacked graphs. A clustering algorithm is designed to partition stacked graphs into sub-aggregated pieces based on trend similarities of layers. We then visualize the pieces with augmented encoding to help analysts decompose and explore the graphs with respect to their interests. Case studies and a user study are conducted to demonstrate the usefulness of our technique in understanding the formation of stacked graphs.

17. Graph Representation for Configurational Properties of Crystalline Solids

Yuge, Koretaka

2017-02-01

We propose representation of configurational physical quantities and microscopic structures for multicomponent system on lattice, by extending a concept of generalized Ising model (GIM) to graph theory. We construct graph Laplacian (and adjacency matrix) composed of symmetry-equivalent neighboring edges, whose landscape of spectrum explicitly represents GIM description of structures as well as low-dimensional topological information in terms of graph. The proposed representation indicates the importance of linear combination of graph to further investigate the role of spatial constraint on equilibrium properties in classical systems. We demonstrate that spectrum for such linear combination of graph can find out additional characteristic microscopic structures compared with GIM-based descriptions for given set of figures on the same low-dimensional configuration space, coming from the proposed representation explicitly having more structural information for, e.g., higher-order closed links of selected element. Statistical interdependence for density of microscopic states including graph representation for structures is also examined, which exhibits similar behavior that has been seen for GIM description of the microscopic structures.

18. 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

19. 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…

20. 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…

1. Interval-valued fuzzy [Formula: see text]-tolerance competition graphs.

PubMed

Pramanik, Tarasankar; Samanta, Sovan; Pal, Madhumangal; Mondal, Sukumar; Sarkar, Biswajit

2016-01-01

This paper develops an interval-valued fuzzy [Formula: see text]-tolerance competition graphs which is the extension of basic fuzzy graphs and [Formula: see text] is any real valued function. Interval-valued fuzzy [Formula: see text]-tolerance competition graph is constructed by taking all the fuzzy sets of a fuzzy [Formula: see text]-tolerance competition graph as interval-valued fuzzy sets. Product of two IVFPTCGs and relations between them are defined. Here, some hereditary properties of products of interval-valued fuzzy [Formula: see text]-tolerance competition graphs are represented. Application of interval-valued fuzzy competition graph in image matching is given to illustrate the model.

2. Flying through Graphs: An Introduction to Graph Theory.

ERIC Educational Resources Information Center

McDuffie, Amy Roth

2001-01-01

Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)

3. Flying through Graphs: An Introduction to Graph Theory.

ERIC Educational Resources Information Center

McDuffie, Amy Roth

2001-01-01

Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)

4. Locating-coloring on Halin graphs with a certain number of inner faces

Purwasih, I. A.; Baskoro, E. T.; Assiyatun, H.; Suprijanto, D.

2016-02-01

For any tree T with at least four vertices and no vertices of degree two, define a Halin graph H(T) as a planar graph constructed from an embedding of T in a plane by connecting all the leaves (the vertices of degree 1) of T to form a cycle C that passes around T in the natural cyclic order defined by the embedding of T . The study of the properties of a Halin graph has received much attention. For instances, it has been shown that every Halin graph is 3-connected and Hamiltonian. A Halin graph has also treewidth at most three, so that many graph optimization problems that are NP-complete for arbitrary planar graphs may be solved in linear time on Halin graphs using dynamic programming. In this paper, we characterize all Halin graphs with 3,4,5,6, and 7 inner faces and give their locating-chromatic number. Furthermore, we show that there exist a Halin graph having locating-chromatic number k ≥ 4 with r ≥max {3 ,(k/-2) 3-(k-2 ) 2 2 +1 } inner faces.

5. Alzheimer's disease: connecting findings from graph theoretical studies of brain networks.

PubMed

Tijms, Betty M; Wink, Alle Meije; de Haan, Willem; van der Flier, Wiesje M; Stam, Cornelis J; Scheltens, Philip; Barkhof, Frederik

2013-08-01

The interrelationships between pathological processes and emerging clinical phenotypes in Alzheimer's disease (AD) are important yet complicated to study, because the brain is a complex network where local disruptions can have widespread effects. Recently, properties in brain networks obtained with neuroimaging techniques have been studied in AD with tools from graph theory. However, the interpretation of graph alterations remains unclear, because the definition of connectivity depends on the imaging modality used. Here we examined which graph properties have been consistently reported to be disturbed in AD studies, using a heuristically defined "graph space" to investigate which theoretical models can best explain graph alterations in AD. Findings from structural and functional graphs point to a loss of highly connected areas in AD. However, studies showed considerable variability in reported group differences of most graph properties. This suggests that brain graphs might not be isometric, which complicates the interpretation of graph measurements. We highlight confounding factors such as differences in graph construction methods and provide recommendations for future research.

6. Graph - Based High Resolution Satellite Image Segmentation for Object Recognition

Ravali, K.; Kumar, M. V. Ravi; Venugopala Rao, K.

2014-11-01

Object based image processing and analysis is challenging research in very high resolution satellite utilisation. Commonly ei ther pixel based classification or visual interpretation is used to recognize and delineate land cover categories. The pixel based classification techniques use rich spectral content of satellite images and fail to utilise spatial relations. To overcome th is drawback, traditional time consuming visual interpretation methods are being used operational ly for preparation of thematic maps. This paper addresses computational vision principles to object level image segmentation. In this study, computer vision algorithms are developed to define the boundary between two object regions and segmentation by representing image as graph. Image is represented as a graph G (V, E), where nodes belong to pixels and, edges (E) connect nodes belonging to neighbouring pixels. The transformed Mahalanobis distance has been used to define a weight function for partition of graph into components such that each component represents the region of land category. This implies that edges between two vertices in the same component have relatively low weights and edges between vertices in different components should have higher weights. The derived segments are categorised to different land cover using supervised classification. The paper presents the experimental results on real world multi-spectral remote sensing images of different landscapes such as Urban, agriculture and mixed land cover. Graph construction done in C program and list the run time for both graph construction and segmentation calculation on dual core Intel i7 system with 16 GB RAM, running 64bit window 7.

7. DNA Rearrangements through Spatial Graphs

Jonoska, Nataša; Saito, Masahico

The paper is a short overview of a recent model of homologous DNA recombination events guided by RNA templates that have been observed in certain species of ciliates. This model uses spatial graphs to describe DNA rearrangements and show how gene recombination can be modeled as topological braiding of the DNA. We show that a graph structure, which we refer to as an assembly graph, containing only 1- and 4-valent rigid vertices can provide a physical representation of the DNA at the time of recombination. With this representation, 4-valent vertices correspond to the alignment of the recombination sites, and we model the actual recombination event as smoothing of these vertices.

8. Multigraph: Reusable Interactive Data Graphs

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

9. 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.

10. Multibody graph transformations and analysis

PubMed Central

2013-01-01

This two-part paper uses graph transformation methods to develop methods for partitioning, aggregating, and constraint embedding for multibody systems. This first part focuses on tree-topology systems and reviews the key notion of spatial kernel operator (SKO) models for such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of the component subsystems based on the path-induced property of the component subgraphs. It shows that the sparsity structure of key matrix operators and the mass matrix for the multibody system can be described using partitioning transformations. Subsequently, the notions of node contractions and subgraph aggregation and their role in coarsening graphs are discussed. It is shown that the tree property of a graph is preserved after subgraph aggregation if and only if the subgraph satisfies an aggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems. PMID:24288438

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

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

12. CUDA Enabled Graph Subset Examiner

SciTech Connect

Johnston, Jeremy T.

2016-12-22

Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.

13. Graph theory data for topological quantum chemistry

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

2017-08-01

Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.

14. Graph theory data for topological quantum chemistry.

PubMed

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

2017-08-01

Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.

15. Robust (semi) nonnegative graph embedding.

PubMed

Zhang, Hanwang; Zha, Zheng-Jun; Yang, Yang; Yan, Shuicheng; Chua, Tat-Seng

2014-07-01

Nonnegative matrix factorization (NMF) has received considerable attention in image processing, computer vision, and patter recognition. An important variant of NMF is nonnegative graph embedding (NGE), which encodes the statistical or geometric information of data in the process of matrix factorization. The NGE offers a general framework for unsupervised/supervised settings. However, NGE-like algorithms often suffer from noisy data, unreliable graphs, and noisy labels, which are commonly encountered in real-world applications. To address these issues, in this paper, we first propose a robust nonnegative graph embedding (RNGE) framework, where the joint sparsity in both graph embedding and data reconstruction endues robustness to undesirable noises. Next, we present a robust seminonnegative graph embedding (RsNGE) framework, which only constrains the coefficient matrix to be nonnegative while places no constraint on the base matrix. This extends the applicable range of RNGE to data which are not nonnegative and endows more discriminative power of the learnt base matrix. The RNGE/RsNGE provides a general formulation such that all the algorithms unified within the graph embedding framework can be easily extended to obtain their robust nonnegative/seminonnegative solutions. Further, we develop elegant multiplicative updating solutions that can solve RNGE/RsNGE efficiently and offer a rigorous convergence analysis. We conduct extensive experiments on four real-world data sets and compare the proposed RNGE/RsNGE to other representative NMF variants and data factorization methods. The experimental results demonstrate the robustness and effectiveness of the proposed approaches.

16. Chromatic polynomials of random graphs

Van Bussel, Frank; Ehrlich, Christoph; Fliegner, Denny; Stolzenberg, Sebastian; Timme, Marc

2010-04-01

Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

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.

18. Image Registration Through The Exploitation Of Perspective Invariant Graphs

Gilmore, John F.

1983-10-01

This paper describes two new techniques of image registration as applied to scenes consisting of natural terrain. The first technique is a syntactic pattern recognition approach which combines the spatial relationships of a point pattern with point classifications to accurately perform image registration. In this approach, a preprocessor analyzes each image in order to identify points of interest and to classify these points based on statistical features. A classified graph possessing perspective invariant properties is created and is converted into a classification-based grammar string. A local match analysis is performed and the best global match is con-structed. A probability-of-match metric is computed in order to evaluate match confidence. The second technique described is an isomorphic graph matching approach called Mean Neighbors (MN). A MN graph is constructed from a given point pattern taking into account the elliptical projections of real world scenes onto a two dimensional surface. This approach exploits the spatial relationships of the given points of interest but neglects the point classifications used in syntactic processing. A projective, perspective invariant graph is constructed for both the reference and sensed images and a mapping of the coincidence edges occurs. A probability of match metric is used to evaluate the confidence of the best mapping.

19. Principal Graph and Structure Learning Based on Reversed Graph Embedding.

PubMed

Mao, Qi; Wang, Li; Tsang, Ivor; Sun, Yijun

2016-12-05

Many scientific datasets are of high dimension, and the analysis usually requires retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are mathematically formulated by curves, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected 1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.

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

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.

1. GraphMeta: Managing HPC Rich Metadata in Graphs

SciTech Connect

Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert

2016-01-01

High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.

2. Graph Regularized Nonnegative Matrix Factorization for Data Representation.

PubMed

Cai, Deng; He, Xiaofei; Han, Jiawei; Huang, Thomas S

2011-08-01

Matrix factorization techniques have been frequently applied in information retrieval, computer vision, and pattern recognition. Among them, Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain. On the other hand, from the geometric perspective, the data is usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space. One then hopes to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called Graph Regularized Nonnegative Matrix Factorization (GNMF), for this purpose. In GNMF, an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization, which respects the graph structure. Our empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.

3. Graph Structured Program Evolution: Evolution of Loop Structures

Shirakawa, Shinichi; Nagao, Tomoharu

Recently, numerous automatic programming techniques have been developed and applied in various fields. A typical example is genetic programming (GP), and various extensions and representations of GP have been proposed thus far. Complex programs and hand-written programs, however, may contain several loops and handle multiple data types. In this chapter, we propose a new method called Graph Structured Program Evolution (GRAPE). The representation of GRAPE is a graph structure; therefore, it can represent branches and loops using this structure. Each programis constructed as an arbitrary directed graph of nodes and a data set. The GRAPE program handles multiple data types using the data set for each type, and the genotype of GRAPE takes the form of a linear string of integers. We apply GRAPE to three test problems, factorial, exponentiation, and list sorting, and demonstrate that the optimum solution in each problem is obtained by the GRAPE system.

4. DRUG TARGET PREDICTIONS BASED ON HETEROGENEOUS GRAPH INFERENCE

PubMed Central

Wang, Wenhui; Yang, Sen; Li, JING

2013-01-01

A key issue in drug development is to understand the hidden relationships among drugs and targets. Computational methods for novel drug target predictions can greatly reduce time and costs compared with experimental methods. In this paper, we propose a network based computational approach for novel drug and target association predictions. More specifically, a heterogeneous drug-target graph, which incorporates known drug-target interactions as well as drug-drug and target-target similarities, is first constructed. Based on this graph, a novel graph-based inference method is introduced. Compared with two state-of-the-art methods, large-scale cross-validation results indicate that the proposed method can greatly improve novel target predictions. PMID:23424111

5. Nodal domains on isospectral quantum graphs: the resolution of isospectrality?

Band, Ram; Shapira, Talia; Smilansky, Uzy

2006-11-01

We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in {\\bb R}^{2} which were introduced recently in Gordon et al (1992 Bull. Am. Math. Soc. 27 134-8), Chapman (1995 Am. Math. Mon. 102 124), Buser et al (1994 Int. Math. Res. Not. 9 391-400), Okada and Shudo (2001 J. Phys. A: Math. Gen. 34 5911-22), Jakobson et al (2006 J. Comput. Appl. Math. 194 141-55) and Levitin et al (2006 J. Phys. A: Math. Gen. 39 2073-82)) all based on Sunada's construction of isospectral domains (Sunada T 1985 Ann. Math. 121 196-86). After presenting some of the properties of these graphs, we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity.

6. Building Specialized Multilingual Lexical Graphs Using Community Resources

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.

7. 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.

8. Bipartite graphs as models of population structures in evolutionary multiplayer games.

PubMed

Peña, Jorge; Rochat, Yannick

2012-01-01

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

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

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.

10. Quantification of Graph Complexity Based on the Edge Weight Distribution Balance: Application to Brain Networks.

PubMed

Gomez-Pilar, Javier; Poza, Jesús; Bachiller, Alejandro; Gómez, Carlos; Núñez, Pablo; Lubeiro, Alba; Molina, Vicente; Hornero, Roberto

2017-05-23

The aim of this study was to introduce a novel global measure of graph complexity: Shannon graph complexity (SGC). This measure was specifically developed for weighted graphs, but it can also be applied to binary graphs. The proposed complexity measure was designed to capture the interplay between two properties of a system: the 'information' (calculated by means of Shannon entropy) and the 'order' of the system (estimated by means of a disequilibrium measure). SGC is based on the concept that complex graphs should maintain an equilibrium between the aforementioned two properties, which can be measured by means of the edge weight distribution. In this study, SGC was assessed using four synthetic graph datasets and a real dataset, formed by electroencephalographic (EEG) recordings from controls and schizophrenia patients. SGC was compared with graph density (GD), a classical measure used to evaluate graph complexity. Our results showed that SGC is invariant with respect to GD and independent of node degree distribution. Furthermore, its variation with graph size [Formula: see text] is close to zero for [Formula: see text]. Results from the real dataset showed an increment in the weight distribution balance during the cognitive processing for both controls and schizophrenia patients, although these changes are more relevant for controls. Our findings revealed that SGC does not need a comparison with null-hypothesis networks constructed by a surrogate process. In addition, SGC results on the real dataset suggest that schizophrenia is associated with a deficit in the brain dynamic reorganization related to secondary pathways of the brain network.

11. A comparative study of theoretical graph models for characterizing structural networks of human brain.

PubMed

Li, Xiaojin; Hu, Xintao; Jin, Changfeng; Han, Junwei; Liu, Tianming; Guo, Lei; Hao, Wei; Li, Lingjiang

2013-01-01

Previous studies have investigated both structural and functional brain networks via graph-theoretical methods. However, there is an important issue that has not been adequately discussed before: what is the optimal theoretical graph model for describing the structural networks of human brain? In this paper, we perform a comparative study to address this problem. Firstly, large-scale cortical regions of interest (ROIs) are localized by recently developed and validated brain reference system named Dense Individualized Common Connectivity-based Cortical Landmarks (DICCCOL) to address the limitations in the identification of the brain network ROIs in previous studies. Then, we construct structural brain networks based on diffusion tensor imaging (DTI) data. Afterwards, the global and local graph properties of the constructed structural brain networks are measured using the state-of-the-art graph analysis algorithms and tools and are further compared with seven popular theoretical graph models. In addition, we compare the topological properties between two graph models, namely, stickiness-index-based model (STICKY) and scale-free gene duplication model (SF-GD), that have higher similarity with the real structural brain networks in terms of global and local graph properties. Our experimental results suggest that among the seven theoretical graph models compared in this study, STICKY and SF-GD models have better performances in characterizing the structural human brain network.

12. 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.

13. Graph isomorphism algorithm for verification of VLSI circuits

Kresh, Kobi

1987-08-01

VLSI circuit verification requires comparison between the physical layout and the corresponding circuit description. This is done by generating graphs from the layout and the schematic, and an algorithm is required to compare the graphs and accurately locate differences. A randomized algorithm for this purpose is presented. The principles and basic concepts of the algorithm are presented and the construction of the isomorphism function is described. Automatic error correction techniques are described and the problems involved in deciding which elements in a graph are considered incorrect are discussed. Human engineering and system engineering aspects of reporting comparison results to the user of a Computer Aided Design (CAD) system are considered. The algorithm is presented in detail, and an overview is presented of its general structure and stages. Experimental results are presented of the use of the algorithm in handling various kinds of graphs. Two aspects of computer science are described, in describing how an algorithm that solves a well known problem in graph theory is devised, implemented and used as a CAD tool for designing VLSI circuits.

14. Exploring the computing literature using temporal graph visualization

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.

15. Graph classification by means of Lipschitz embedding.

PubMed

Riesen, Kaspar; Bunke, Horst

2009-12-01

In pattern recognition and related fields, graph-based representations offer a versatile alternative to the widely used feature vectors. Therefore, an emerging trend of representing objects by graphs can be observed. This trend is intensified by the development of novel approaches in graph-based machine learning, such as graph kernels or graph-embedding techniques. These procedures overcome a major drawback of graphs, which consists of a serious lack of algorithms for classification. This paper is inspired by the idea of representing graphs through dissimilarities and extends our previous work to the more general setting of Lipschitz embeddings. In an experimental evaluation, we empirically confirm that classifiers that rely on the original graph distances can be outperformed by a classification system using the Lipschitz embedded graphs.

16. Hierarchical sequencing of online social graphs

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.

17. Optimal preparation of graph states

SciTech Connect

Cabello, Adan; Lopez-Tarrida, Antonio J.; Danielsen, Lars Eirik; Portillo, Jose R.

2011-04-15

We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.

18. 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.

19. The star arboricity of graphs

Algor, Ilan

1988-03-01

The problem concerns the minimum time in which a number of messages can be transmitted through a communication network in which each node can transmit to many other nodes simultaneously but can receive only one message at a time. In the undirected version of the problem, the graphs, G, representing the messages are finite, undirected and simple; the messages transmitted in unit time form a subgraph which is a star. The star aboricity, st(G) of a graph G is the minimum number of star forests whose union covers all edges of G. A maximum value is derived for the star aboricity of any d-regular graph G, and is proved through probabilistic arguments.

20. 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.

1. 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.

2. Sequential visibility-graph motifs

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.

3. 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

4. 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.

5. Stability of graph communities across time scales

PubMed Central

Delvenne, J.-C.; Yaliraki, S. N.; Barahona, M.

2010-01-01

The complexity of biological, social, and engineering networks makes it desirable to find natural partitions into clusters (or communities) that can provide insight into the structure of the overall system and even act as simplified functional descriptions. Although methods for community detection abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We introduce here the stability of a partition, a measure of its quality as a community structure based on the clustered autocovariance of a dynamic Markov process taking place on the network. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser communities. Our dynamical definition provides a unifying framework for several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler’s spectral clustering emerges at long times. We apply our method to characterize the relevance of partitions over time for constructive and real networks, including hierarchical graphs and social networks, and use it to obtain reduced descriptions for atomic-level protein structures over different time scales. PMID:20615936

6. Hyperspectral Anomaly Detection by Graph Pixel Selection.

PubMed

Yuan, Yuan; Ma, Dandan; Wang, Qi

2016-12-01

Hyperspectral anomaly detection (AD) is an important problem in remote sensing field. It can make full use of the spectral differences to discover certain potential interesting regions without any target priors. Traditional Mahalanobis-distance-based anomaly detectors assume the background spectrum distribution conforms to a Gaussian distribution. However, this and other similar distributions may not be satisfied for the real hyperspectral images. Moreover, the background statistics are susceptible to contamination of anomaly targets which will lead to a high false-positive rate. To address these intrinsic problems, this paper proposes a novel AD method based on the graph theory. We first construct a vertex- and edge-weighted graph and then utilize a pixel selection process to locate the anomaly targets. Two contributions are claimed in this paper: 1) no background distributions are required which makes the method more adaptive and 2) both the vertex and edge weights are considered which enables a more accurate detection performance and better robustness to noise. Intensive experiments on the simulated and real hyperspectral images demonstrate that the proposed method outperforms other benchmark competitors. In addition, the robustness of the proposed method has been validated by using various window sizes. This experimental result also demonstrates the valuable characteristic of less computational complexity and less parameter tuning for real applications.

7. Thermodynamic characterization of networks using graph polynomials

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.

8. Potential-controlled filtering in quantum star graphs

SciTech Connect

Turek, Ondrej Cheon, Taksu

2013-03-15

We study the scattering in a quantum star graph with a Fueloep-Tsutsui coupling in its vertex and with external potentials on the lines. We find certain special couplings for which the probability of the transmission between two given lines of the graph is strongly influenced by the potential applied on another line. On the basis of this phenomenon we design a tunable quantum band-pass spectral filter. The transmission from the input to the output line is governed by a potential added on the controlling line. The strength of the potential directly determines the passband position, which allows to control the filter in a macroscopic manner. Generalization of this concept to quantum devices with multiple controlling lines proves possible. It enables the construction of spectral filters with more controllable parameters or with more operation modes. In particular, we design a band-pass filter with independently adjustable multiple passbands. We also address the problem of the physical realization of Fueloep-Tsutsui couplings and demonstrate that the couplings needed for the construction of the proposed quantum devices can be approximated by simple graphs carrying only {delta} potentials. - Highlights: Black-Right-Pointing-Pointer Spectral filtering devices based on quantum graphs are designed theoretically. Black-Right-Pointing-Pointer The passband is controlled by the application of macroscopic potentials on lines. Black-Right-Pointing-Pointer The filters are built upon special Fulop-Tsutsui type couplings at graph vertices. Black-Right-Pointing-Pointer A method of construction of Fulop-Tsutsui vertices from delta potentials is devised.

9. Synchronizability of random rectangular graphs

SciTech Connect

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.

10. Interacting particle systems on graphs

Sood, Vishal

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

11. COMPLEX DIFFUSION ON IMAGE GRAPHS

PubMed Central

Seo, Dohyung; Vemuri, Baba C

2009-01-01

Complex diffusion was introduced in image processing literature as a means to achieve simultaneous denoising and enhancement of scalar valued images. In this paper, we present a novel geometric framework for achieving complex diffusion on color images expressed as image graphs. In this framework, we develop a new variational formulation for achieving complex diffusion. This formulation involves a modified harmonic map functional and is quite distinct from the Polyakov action described in earlier work by Sochen et al. Our formulation provides a framework for simultaneous (feature preserving) denoising and enhancement. We present results of comparison between the complex diffusion, and Beltrami flow all in the image graph framework. PMID:20490365

12. 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.

13. Mathematical foundations of the GraphBLAS

DOE PAGES

Kepner, Jeremy; Aaltonen, Peter; Bader, David; ...

2016-12-01

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS 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 study provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, themore » two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Finally, performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.« less

14. Multiple graph regularized protein domain ranking

PubMed Central

2012-01-01

Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. PMID:23157331

15. Approximate Graph Edit Distance in Quadratic Time.

PubMed

Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

2015-09-14

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

16. Mathematical foundations of the GraphBLAS

SciTech Connect

Kepner, Jeremy; Aaltonen, Peter; Bader, David; Buluc, Aydin; Franchetti, Franz; Gilbert, John; Hutchison, Dylan; Kumar, Manoj; Lumsdaine, Andrew; Meyerhenke, Henning; McMillan, Scott; Yang, Carl; Owens, John D.; Zalewski, Marcin; Mattson, Timothy; Moreira, Jose

2016-12-01

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS 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 study provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Finally, performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

17. The tetrakisoctahedral group of the Dyck graph and its molecular realization†

Ceulemans, A.; Lijnen, E.; Ceulemans, L. J.; Fowler, P. W.

2004-01-01

The group of automorphisms of the 32-vertex Dyck graph is identified as the tetrakisoctahedral group, 4O. This group has 96 elements and conserves orientation on the standard embedding of the Dyck graph on a surface of genus 3, consisting of 12 octagons. An alternative regular map of the Dyck graph on a torus is found, which is made up of 16 hexagons. Orientation on this surface is conserved by another group of 96 elements, 4Th, which is non-isomorphic to 4O. The subgroup structures of 4O and 4Th are derived, and character tables of 4O and some of its subgroups are constructed. The symmetry representations of the Dyck graph and its topological dual are determined. Finally a molecular realization of the Dyck graph on the genus-3 'Plumber's nightmare' is proposed, which can be considered as a new type of octagonal carbon network.

18. Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

Ni, Xiao-Hui; Jiang, Zhi-Qiang; Zhou, Wei-Xing

2009-10-01

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.

19. 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)

20. 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.

1. 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.

2. 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.

3. 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.

4. Torsional rigidity, isospectrality and quantum graphs

Colladay, Don; Kaganovskiy, Leon; McDonald, Patrick

2017-01-01

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

5. Comparison Graph of Sea Ice Minimum - 2010

NASA Image and Video Library

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...

6. Sexually Transmitted Diseases on Bipartite Graph

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.

7. 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).

8. 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…

9. 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…

10. Two-Player Graph Pebbling

Prudente, Matthew James

Given a graph G with pebbles on the vertices, we define a pebbling move as removing two pebbles from a vertex u, placing one pebble on a neighbor v, and discarding the other pebble, like a toll. The pebbling number pi( G) is the least number of pebbles needed so that every arrangement of pi(G) pebbles can place a pebble on any vertex through a sequence of pebbling moves. We introduce a new variation on graph pebbling called two-player pebbling. In this, players called the mover and the defender alternate moves, with the stipulation that the defender cannot reverse the previous move. The mover wins only if they can place a pebble on a specified vertex and the defender wins if the mover cannot. We define η(G), analogously, as the minimum number of pebbles such that given every configuration of the η( G) pebbles and every specified vertex r, the mover has a winning strategy. First, we will investigate upper bounds for η( G) on various classes of graphs and find a certain structure for which the defender has a winning strategy, no matter how many pebbles are in a configuration. Then, we characterize winning configurations for both players on a special class of diameter 2 graphs. Finally, we show winning configurations for the mover on paths using a recursive argument.

11. 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…

12. 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)

13. 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…

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. 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)

16. 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)

17. 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…

18. 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…

19. Readjoiner: a fast and memory efficient string graph-based sequence assembler

PubMed Central

2012-01-01

Background Ongoing improvements in throughput of the next-generation sequencing technologies challenge the current generation of de novo sequence assemblers. Most recent sequence assemblers are based on the construction of a de Bruijn graph. An alternative framework of growing interest is the assembly string graph, not necessitating a division of the reads into k-mers, but requiring fast algorithms for the computation of suffix-prefix matches among all pairs of reads. Results Here we present efficient methods for the construction of a string graph from a set of sequencing reads. Our approach employs suffix sorting and scanning methods to compute suffix-prefix matches. Transitive edges are recognized and eliminated early in the process and the graph is efficiently constructed including irreducible edges only. Conclusions Our suffix-prefix match determination and string graph construction algorithms have been implemented in the software package Readjoiner. Comparison with existing string graph-based assemblers shows that Readjoiner is faster and more space efficient. Readjoiner is available at http://www.zbh.uni-hamburg.de/readjoiner. PMID:22559072

20. Diversity of Graphs with Highly Variable Connectivity

DTIC Science & Technology

2016-06-07

of acyclic graphs i.e., trees and then later comment on how our results apply to general graphs. Our experiment uses in- cremental growth via...generate a tree having n=100 nodes using pref- erential attachment rule given by 7. That is, each trial re- sults in a tree having its own degree...studied graph properties. First, high-degree nodes in the smax graph have high centrality, and for trees this relationship was shown to be monotonic

1. Claw-Free Maximal Planar Graphs

DTIC Science & Technology

1989-01-01

0, 1,2 and 3 points of degree 6 respectively.) Now suppose G,. has no claws for 3 < r < i and consider graph G ,+,. Graph G,+ 1 is obtained from Gr by...adjacent to a point v by N(v) and call the induced subgraph GiN(v)] the neighborhood graph of v in G . Graph G is said to be locally n-connected if for all

2. Conceptual graphs for semantics and knowledge processing

SciTech Connect

Fargues, J.; Landau, M.C.; Dugourd, A.; Catach, L.

1986-01-01

This paper discusses the representational and algorithmic power of the conceptual graph model for natural language semantics and knowledge processing. Also described is a Prolog-like resolution method for conceptual graphs, which allows to perform deduction on very large semantic domains. The interpreter developed is similar to a Prolog interpreter in which the terms are any conceptual graphs and in which the unification algorithm is replaced by a specialized algorithm for conceptual graphs.

3. Identifying Codes on Directed De Bruijn Graphs

DTIC Science & Technology

2015-08-27

2. 15. SUBJECT TERMS Identifying Code; De Bruijn Network; Graph Theory 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER...in graphs . IEEE Trans. Inform. Theory , 44(2):599–611, 1998. 1 [10] Samir Khuller, Balaji Raghavachari, and Azriel Rosenfeld. Landmarks in graphs ...JOURNAL ARTICLE (POST PRINT) 3. DATES COVERED (From - To) JUN 2013 – AUG 2015 4. TITLE AND SUBTITLE IDENTIFYING CODES ON DIRECTED DE BRUIJN GRAPHS 5a

4. 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)

5. 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)

6. Teaching and Assessing Graphing Using Active Learning

ERIC Educational Resources Information Center

McFarland, Jenny

2010-01-01

As a college biology instructor, I often see graphs in lab reports that do not meet my expectations. I also observe that many college students do not always adequately differentiate between good and poor (or misleading) graphs. The activity described in this paper is the result of my work with students to improve their graphing literacy. The…

7. 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…

8. Around the Sun in a Graphing Calculator.

ERIC Educational Resources Information Center

Demana, Franklin; Waits, Bert K.

1989-01-01

Discusses the use of graphing calculators for polar and parametric equations. Presents eight lines of the program for the graph of a parametric equation and 11 lines of the program for a graph of a polar equation. Illustrates the application of the programs for planetary motion and free-fall motion. (YP)

9. 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...

10. Positive and Unlabeled Multi-Graph Learning.

PubMed

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

2016-03-23

In this paper, we advance graph classification to handle multi-graph learning for complicated objects, where each object is represented as a bag of graphs and the label is only available to each bag but not individual graphs. In addition, when training classifiers, users are only given a handful of positive bags and many unlabeled bags, and the learning objective is to train models to classify previously unseen graph bags with maximum accuracy. To achieve the goal, we propose a positive and unlabeled multi-graph learning (puMGL) framework to first select informative subgraphs to convert graphs into a feature space. To utilize unlabeled bags for learning, puMGL assigns a confidence weight to each bag and dynamically adjusts its weight value to select "reliable negative bags." A number of representative graphs, selected from positive bags and identified reliable negative graph bags, form a "margin graph pool" which serves as the base for deriving subgraph patterns, training graph classifiers, and further updating the bag weight values. A closed-loop iterative process helps discover optimal subgraphs from positive and unlabeled graph bags for learning. Experimental comparisons demonstrate the performance of puMGL for classifying real-world complicated objects.

11. 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...

12. 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...

13. 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…

14. 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…

15. 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...

16. 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...

17. Some Applications of Graph Theory to Clustering

ERIC Educational Resources Information Center

Hubert, Lawrence J.

1974-01-01

The connection between graph theory and clustering is reviewed and extended. Major emphasis is on restating, in a graph-theoretic context, selected past work in clustering, and conversely, developing alternative strategies from several standard concepts used in graph theory per se. (Author/RC)

18. Teaching and Assessing Graphing Using Active Learning

ERIC Educational Resources Information Center

McFarland, Jenny

2010-01-01

As a college biology instructor, I often see graphs in lab reports that do not meet my expectations. I also observe that many college students do not always adequately differentiate between good and poor (or misleading) graphs. The activity described in this paper is the result of my work with students to improve their graphing literacy. The…

19. 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…

20. Graph Partitioning Models for Parallel Computing

SciTech Connect

Hendrickson, B.; Kolda, T.G.

1999-03-02

Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.

1. Some Applications of Graph Theory to Clustering

ERIC Educational Resources Information Center

Hubert, Lawrence J.

1974-01-01

The connection between graph theory and clustering is reviewed and extended. Major emphasis is on restating, in a graph-theoretic context, selected past work in clustering, and conversely, developing alternative strategies from several standard concepts used in graph theory per se. (Author/RC)

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

PubMed

Kim, Hyunwoo; Park, Heejin; Paek, Eunok

2015-07-02

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.

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

DOE PAGES

Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

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

4. 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.

5. Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

PubMed Central

Peña, Jorge; Rochat, Yannick

2012-01-01

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

6. 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. © Society for the Experimental Analysis of Behavior.

7. Optimal weighting scheme and the role of coupling strength against load failures in degree-based weighted interdependent networks

Qiu, Yuzhuo

2013-04-01

The optimal weighting scheme and the role of coupling strength against load failures on symmetrically and asymmetrically coupled interdependent networks were investigated. The degree-based weighting scheme was extended to interdependent networks, with the flow dynamics dominated by global redistribution based on weighted betweenness centrality. Through contingency analysis of one-node removal, we demonstrated that there still exists an optimal weighting parameter on interdependent networks, but it might shift as compared to the case in isolated networks because of the break of symmetry. And it will be easier for the symmetrically and asymmetrically coupled interdependent networks to achieve robustness and better cost configuration against the one-node-removal-induced cascade of load failures when coupling strength was weaker. Our findings might have great generality for characterizing load-failure-induced cascading dynamics in real-world degree-based weighted interdependent networks.

8. Identification of domains and domain interface residues in multidomain proteins from graph spectral method.

PubMed

Sistla, Ramesh K; K V, Brinda; Vishveshwara, Saraswathi

2005-05-15

We present a novel method for the identification of structural domains and domain interface residues in proteins by graph spectral method. This method converts the three-dimensional structure of the protein into a graph by using atomic coordinates from the PDB file. Domain definitions are obtained by constructing either a protein backbone graph or a protein side-chain graph. The graph is constructed based on the interactions between amino acid residues in the three-dimensional structure of the proteins. The spectral parameters of such a graph contain information regarding the domains and subdomains in the protein structure. This is based on the fact that the interactions among amino acids are higher within a domain than across domains. This is evident in the spectra of the protein backbone and the side-chain graphs, thus differentiating the structural domains from one another. Further, residues that occur at the interface of two domains can also be easily identified from the spectra. This method is simple, elegant, and robust. Moreover, a single numeric computation yields both the domain definitions and the interface residues. Copyright 2005 Wiley-Liss, Inc.

9. Canonical horizontal visibility graphs are uniquely determined by their degree sequence

Luque, Bartolo; Lacasa, Lucas

2017-02-01

Horizontal visibility graphs (HVGs) are graphs constructed in correspondence with number sequences that have been introduced and explored recently in the context of graph-theoretical time series analysis. In most of the cases simple measures based on the degree sequence (or functionals of these such as entropies over degree and joint degree distributions) appear to be highly informative features for automatic classification and provide nontrivial information on the associated dynamical process, working even better than more sophisticated topological metrics. It is thus an open question why these seemingly simple measures capture so much information. Here we prove that, under suitable conditions, there exist a bijection between the adjacency matrix of an HVG and its degree sequence, and we give an explicit construction of such bijection. As a consequence, under these conditions HVGs are unigraphs and the degree sequence fully encapsulates all the information of these graphs, thereby giving a plausible reason for its apparently unreasonable effectiveness.

10. Exactly solvable interacting two-particle quantum graphs

Bolte, Jens; Garforth, George

2017-03-01

We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing compatibility with the Bethe ansatz method, we calculate quantisation conditions in the form of secular equations from which the spectra can be deduced. We compare spectral statistics of some examples to well known results in random matrix theory, analysing the chaotic properties of their classical counterparts.

11. On the Primitive Ideal spaces of the C(*) -algebras of graphs

Bates, Teresa

2005-11-01

We characterise the topological spaces which arise as the primitive ideal spaces of the Cuntz-Krieger algebras of graphs satisfying condition (K): directed graphs in which every vertex lying on a loop lies on at least two loops. We deduce that the spaces which arise as Prim;C(*(E)) are precisely the spaces which arise as the primitive ideal spaces of AF-algebras. Finally, we construct a graph wt{E} from E such that C(*(wt{E})) is an AF-algebra and Prim;C(*(E)) and Prim;C(*(wt{E})) are homeomorphic.

12. 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.

13. Analysis of the contact graph routing algorithm: Bounding interplanetary paths

Birrane, Edward; Burleigh, Scott; Kasch, Niels

2012-06-01

Interplanetary communication networks comprise orbiters, deep-space relays, and stations on planetary surfaces. These networks must overcome node mobility, constrained resources, and significant propagation delays. Opportunities for wireless contact rely on calculating transmit and receive opportunities, but the Euclidean-distance diameter of these networks (measured in light-seconds and light-minutes) precludes node discovery and contact negotiation. Propagation delay may be larger than the line-of-sight contact between nodes. For example, Mars and Earth orbiters may be separated by up to 20.8 min of signal propagation time. Such spacecraft may never share line-of-sight, but may uni-directionally communicate if one orbiter knows the other's future position. The Contact Graph Routing (CGR) approach is a family of algorithms presented to solve the messaging problem of interplanetary communications. These algorithms exploit networks where nodes exhibit deterministic mobility. For CGR, mobility and bandwidth information is pre-configured throughout the network allowing nodes to construct transmit opportunities. Once constructed, routing algorithms operate on this contact graph to build an efficient path through the network. The interpretation of the contact graph, and the construction of a bounded approximate path, is critically important for adoption in operational systems. Brute force approaches, while effective in small networks, are computationally expensive and will not scale. Methods of inferring cycles or other librations within the graph are difficult to detect and will guide the practical implementation of any routing algorithm. This paper presents a mathematical analysis of a multi-destination contact graph algorithm (MD-CGR), demonstrates that it is NP-complete, and proposes realistic constraints that make the problem solvable in polynomial time, as is the case with the originally proposed CGR algorithm. An analysis of path construction to complement hop

14. Life-Span Development of Brain Network Integration Assessed with Phase Lag Index Connectivity and Minimum Spanning Tree Graphs.

PubMed

Smit, Dirk J A; de Geus, Eco J C; Boersma, Maria; Boomsma, Dorret I; Stam, Cornelis J

2016-05-01

Graph analysis of electroencephalography (EEG) has previously revealed developmental increases in connectivity between distant brain areas and a decrease in randomness and increased integration in the brain network with concurrent increased modularity. Comparisons of graph parameters across age groups, however, may be confounded with network degree distributions. In this study, we analyzed graph parameters from minimum spanning tree (MST) graphs and compared their developmental trajectories to those of graph parameters based on full graphs published previously. MST graphs are constructed by selecting only the strongest available connections avoiding loops, resulting in a backbone graph that is thought to reflect the major qualitative properties of the network, while allowing a better comparison across age groups by avoiding the degree of distribution confound. EEG was recorded in a large (n = 1500) population-based sample aged 5-71 years. Connectivity was assessed using phase lag index to reduce effects of volume conduction. Connectivity in the MST graph increased significantly from childhood to adolescence, continuing to grow nonsignificantly into adulthood, and decreasing significantly about 57 years of age. Leaf number, degree, degree correlation, and maximum centrality from the MST graph indicated a pattern of increased integration and decreased randomness from childhood into early adulthood. The observed development in network topology suggested that maturation at the neuronal level is aimed to increase connectivity as well as increase integration of the brain network. We confirm that brain network connectivity shows quantitative changes across the life span and additionally demonstrate parallel qualitative changes in the connectivity pattern.

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

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

2014-07-01

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

16. Stability Properties of Inclusive Connectivity for Graphs

DTIC Science & Technology

1993-12-01

of G . Graphs illustrating the two possible relationships between the three inclusive connectivity parameters for edges are shown in Figures 2.12 and...For simplicity in this section, we will call this graph G the "internal G graph " due to its location in the figures, and the "K4 with one edge doubly...to one copy of the subdivided K4 producing the graph in Figure 5.25. 117 1(4 with one edge Internal G graph K4 with one edge Figure 5.24 The

17. Proving relations between modular graph functions

Basu, Anirban

2016-12-01

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

18. Graph theoretical analysis of climate data

Zerenner, T.; Hense, A.

2012-04-01

Applying methods from graph and network theory to climatological data is a quite new approach and contains numerous difficulties. The atmosphere is a high dimensional and complex dynamical system which per se does not show a network-like structure. It does not consist of well-defined nodes and edges. Thus considering such a system as a network or graph inevitably involves radical simplifications and ambiguities. Nevertheless network analysis has provided useful results for different kinds of complex systems for example in biology or medical science (neural and gene interaction networks). The application of these methods on climate data provides interesting results as well. If the network construction is based on the correlation matrix of the underlying data, the resulting network structures show many well known patterns and characteristics of the atmospheric circulation (Tsonis et al. 2006, Donges et al. 2009). The interpretation of these network structures is yet questionable. Using Pearson Correlation for network construction does not allow to differ between direct and indirect dependencies. An edge does not necessarily represent a causal connection. An interpretation of these structures for instance concerning the stability of the climate system is therefore doubtful. Gene interaction networks for example are often constructed using partial correlations (Wu et al. 2003), which makes it possible to distinguish between direct and indirect dependencies. Although a high value of partial correlation does not guarantee causality it is a step in the direction of measuring causal dependencies. This approach is known as Gaussian Graphical Models, GGMs. For high dimensional datasets such as climate data partial correlations can be obtained by calculating the precision matrix, the inverse covariance matrix. Since the maximum likelihood estimates of covariance matrices of climate datasets are singular the precision matrices can only be estimated for example by using the

19. 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.

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

PubMed Central

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. PMID:25984446

1. 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.

2. Generating GraphML XML Files for Graph Visualization of Architectures and Event Traces for the Monterey Phoenix Program

DTIC Science & Technology

2012-09-01

files that conform to the Graph Markup Language (GraphML). MPGrapher compiles well-formed XML files that conform to the yEd GraphML schema. These...PLANARIZATION ........................................................................22 E. THE GRAPH MARKUP LANGUAGE ...26 F. ALTERNATIVES TO THE GRAPH MARKUP LANGUAGE ...............27 1. Graph Modelling Language (GML

3. Efficient Graph Sequence Mining Using Reverse Search

Inokuchi, Akihiro; Ikuta, Hiroaki; Washio, Takashi

The mining of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences. A method, called GTRACE, has been proposed to mine frequent patterns from graph sequences under the assumption that changes in graphs are gradual. Although GTRACE mines the frequent patterns efficiently, it still needs substantial computation time to mine the patterns from graph sequences containing large graphs and long sequences. In this paper, we propose a new version of GTRACE that permits efficient mining of frequent patterns based on the principle of a reverse search. The underlying concept of the reverse search is a general scheme for designing efficient algorithms for hard enumeration problems. Our performance study shows that the proposed method is efficient and scalable for mining both long and large graph sequence patterns and is several orders of magnitude faster than the original GTRACE.

4. Evaluation of Graph Sampling: A Visualization Perspective.

PubMed

Wu, Yanhong; Cao, Nan; Archambault, Daniel; Shen, Qiaomu; Qu, Huamin; Cui, Weiwei

2017-01-01

Graph sampling is frequently used to address scalability issues when analyzing large graphs. Many algorithms have been proposed to sample graphs, and the performance of these algorithms has been quantified through metrics based on graph structural properties preserved by the sampling: degree distribution, clustering coefficient, and others. However, a perspective that is missing is the impact of these sampling strategies on the resultant visualizations. In this paper, we present the results of three user studies that investigate how sampling strategies influence node-link visualizations of graphs. In particular, five sampling strategies widely used in the graph mining literature are tested to determine how well they preserve visual features in node-link diagrams. Our results show that depending on the sampling strategy used different visual features are preserved. These results provide a complimentary view to metric evaluations conducted in the graph mining literature and provide an impetus to conduct future visualization studies.

5. 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.

6. The Feynman Identity for Planar Graphs

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.

7. 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

8. Hierarchical structure of the logical Internet graph

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.

9. Fast approximate quadratic programming for graph matching.

PubMed

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.

10. 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.

11. Fast dual graph-based hotspot detection

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.

12. 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.

13. Graph-based layout analysis for PDF documents

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. 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.

15. Machine learning in a graph framework for subcortical segmentation

Guo, Zhihui; Kashyap, Satyananda; Sonka, Milan; Oguz, Ipek

2017-02-01

Automated and reliable segmentation of subcortical structures from human brain magnetic resonance images is of great importance for volumetric and shape analyses in quantitative neuroimaging studies. However, poor boundary contrast and variable shape of these structures make the automated segmentation a tough task. We propose a 3D graph-based machine learning method, called LOGISMOS-RF, to segment the caudate and the putamen from brain MRI scans in a robust and accurate way. An atlas-based tissue classification and bias-field correction method is applied to the images to generate an initial segmentation for each structure. Then a 3D graph framework is utilized to construct a geometric graph for each initial segmentation. A locally trained random forest classifier is used to assign a cost to each graph node. The max-flow algorithm is applied to solve the segmentation problem. Evaluation was performed on a dataset of T1-weighted MRI's of 62 subjects, with 42 images used for training and 20 images for testing. For comparison, FreeSurfer, FSL and BRAINSCut approaches were also evaluated using the same dataset. Dice overlap coefficients and surface-to-surfaces distances between the automated segmentation and expert manual segmentations indicate the results of our method are statistically significantly more accurate than the three other methods, for both the caudate (Dice: 0.89 +/- 0.03) and the putamen (0.89 +/- 0.03).

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. Machine learning in a graph framework for subcortical segmentation

PubMed Central

Guo, Zhihui; Kashyap, Satyananda; Sonka, Milan; Oguz, Ipek

2017-01-01

Automated and reliable segmentation of subcortical structures from human brain magnetic resonance images is of great importance for volumetric and shape analyses in quantitative neuroimaging studies. However, poor boundary contrast and variable shape of these structures make the automated segmentation a tough task. We propose a 3D graph-based machine learning method, called LOGISMOS-RF, to segment the caudate and the putamen from brain MRI scans in a robust and accurate way. An atlas-based tissue classification and bias-field correction method is applied to the images to generate an initial segmentation for each structure. Then a 3D graph framework is utilized to construct a geometric graph for each initial segmentation. A locally trained random forest classifier is used to assign a cost to each graph node. The max-flow algorithm is applied to solve the segmentation problem. Evaluation was performed on a dataset of T1-weighted MRI’s of 62 subjects, with 42 images used for training and 20 images for testing. For comparison, FreeSurfer and FSL approaches were also evaluated using the same dataset. Dice overlap coefficients and surface-to-surfaces distances between the automated segmentation and expert manual segmentations indicate the results of our method are statistically significantly more accurate than the other two methods, for both the caudate (Dice: 0.89 ± 0.03) and the putamen (0.89 ± 0.03). PMID:28626291

18. 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).

19. Graph Embedded Extreme Learning Machine.

PubMed

Iosifidis, Alexandros; Tefas, Anastasios; Pitas, Ioannis

2016-01-01

In this paper, we propose a novel extension of the extreme learning machine (ELM) algorithm for single-hidden layer feedforward neural network training that is able to incorporate subspace learning (SL) criteria on the optimization process followed for the calculation of the network's output weights. The proposed graph embedded ELM (GEELM) algorithm is able to naturally exploit both intrinsic and penalty SL criteria that have been (or will be) designed under the graph embedding framework. In addition, we extend the proposed GEELM algorithm in order to be able to exploit SL criteria in arbitrary (even infinite) dimensional ELM spaces. We evaluate the proposed approach on eight standard classification problems and nine publicly available datasets designed for three problems related to human behavior analysis, i.e., the recognition of human face, facial expression, and activity. Experimental results denote the effectiveness of the proposed approach, since it outperforms other ELM-based classification schemes in all the cases.

20. Graph distance for complex networks

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.

1. 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

2. Line graphs as social networks

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.

3. Dynamic molecular graphs: "hopping" structures.

PubMed

Cortés-Guzmán, Fernando; Rocha-Rinza, Tomas; Guevara-Vela, José Manuel; Cuevas, Gabriel; Gómez, Rosa María

2014-05-05

This work aims to contribute to the discussion about the suitability of bond paths and bond-critical points as indicators of chemical bonding defined within the theoretical framework of the quantum theory of atoms in molecules. For this purpose, we consider the temporal evolution of the molecular structure of [Fe{C(CH2 )3 }(CO)3 ] throughout Born-Oppenheimer molecular dynamics (BOMD), which illustrates the changing behaviour of the molecular graph (MG) of an electronic system. Several MGs with significant lifespans are observed across the BOMD simulations. The bond paths between the trimethylenemethane and the metallic core are uninterruptedly formed and broken. This situation is reminiscent of a "hopping" ligand over the iron atom. The molecular graph wherein the bonding between trimethylenemethane and the iron atom takes place only by means of the tertiary carbon atom has the longest lifespan of all the considered structures, which is consistent with the MG found by X-ray diffraction experiments and quantum chemical calculations. In contrast, the η(4) complex predicted by molecular-orbital theory has an extremely brief lifetime. The lifespan of different molecular structures is related to bond descriptors on the basis of the topology of the electron density such as the ellipticities at the FeCH2 bond-critical points and electron delocalisation indices. This work also proposes the concept of a dynamic molecular graph composed of the different structures found throughout the BOMD trajectories in analogy to a resonance hybrid of Lewis structures. It is our hope that the notion of dynamic molecular graphs will prove useful in the discussion of electronic systems, in particular for those in which analysis on the basis of static structures leads to controversial conclusions.

4. Relativity on Rotated Graph Paper

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.

5. Metabolic networks: beyond the graph.

PubMed

Bernal, Andrés; Daza, Edgar

2011-06-01

Drugs are devised to enter into the metabolism of an organism in order to produce a desired effect. From the chemical point of view, cellular metabolism is constituted by a complex network of reactions transforming metabolites one in each other. Knowledge on the structure of this network could help to develop novel methods for drug design, and to comprehend the root of known unexpected side effects. Many large-scale studies on the structure of metabolic networks have been developed following models based on different kinds of graphs as the fundamental image of the reaction network. Graphs models, however, comport wrong assumptions regarding the structure of reaction networks that may lead into wrong conclusions if they are not taken into account. In this article we critically review some graph-theoretical approaches to the analysis of centrality, vulnerability and modularity of metabolic networks, analyzing their limitations in estimating these key network properties, consider some proposals explicit or implicitly based on directed hypergraphs regarding their ability to overcome these issues, and review some recent implementation improvements that make the application of these models in increasingly large networks a viable option.

6. A class of finite symmetric graphs with 2-arc transitive quotients

Li, Cai Heng; Praeger, Cheryl E.; Zhou, Sanming

2000-07-01

Let [Gamma] be a finite G-symmetric graph whose vertex set admits a non-trivial G-invariant partition [script B] with block size v. A framework for studying such graphs [Gamma] was developed by Gardiner and Praeger which involved an analysis of the quotient graph [Gamma][script B] relative to [script B], the bipartite subgraph [Gamma][B, C] of [Gamma] induced by adjacent blocks B, C of [Gamma][script B] and a certain 1-design [script D](B) induced by a block B [set membership] [script B]. The present paper studies the case where the size k of the blocks of [script D](B) satisfies k = v [minus sign] 1. In the general case, where k = v [minus sign] 1 [gt-or-equal, slanted] 2, the setwise stabilizer GB is doubly transitive on B and G is faithful on [script B]. We prove that [script D](B) contains no repeated blocks if and only if [Gamma][script B] is (G, 2)-arc transitive and give a method for constructing such a graph from a 2-arc transitive graph with a self-paired orbit on 3-arcs. We show further that each such graph may be constructed by this method. In particular every 3-arc transitive graph, and every 2-arc transitive graph of even valency, may occur as [Gamma][script B] for some graph [Gamma] with these properties. We prove further that [Gamma][B, C] [congruent with] Kv[minus sign]1,v[minus sign]1 if and only if [Gamma][script B] is (G, 3)-arc transitive.

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

PubMed

Schweinberger, Michael; Handcock, Mark S

2015-06-01

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'.

8. 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

9. What is the difference between the breakpoint graph and the de Bruijn graph?

PubMed

Lin, Yu; Nurk, Sergey; Pevzner, Pavel A

2014-01-01

The breakpoint graph and the de Bruijn graph are two key data structures in the studies of genome rearrangements and genome assembly. However, the classical breakpoint graphs are defined on two genomes (represented as sequences of synteny blocks), while the classical de Bruijn graphs are defined on a single genome (represented as DNA strings). Thus, the connection between these two graph models is not explicit. We generalize the notions of both the breakpoint graph and the de Bruijn graph, and make it transparent that the breakpoint graph and the de Bruijn graph are mathematically equivalent. The explicit description of the connection between these important data structures provides a bridge between two previously separated bioinformatics communities studying genome rearrangements and genome assembly.

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

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.

11. Computational Genomics Using Graph Theory

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

12. Inferring Pedigree Graphs from Genetic Distances

Tamura, Takeyuki; Ito, Hiro

In this paper, we study a problem of inferring blood relationships which satisfy a given matrix of genetic distances between all pairs of n nodes. Blood relationships are represented by our proposed graph class, which is called a pedigree graph. A pedigree graph is a directed acyclic graph in which the maximum indegree is at most two. We show that the number of pedigree graphs which satisfy the condition of given genetic distances may be exponential, but they can be represented by one directed acyclic graph with n nodes. Moreover, an O(n3) time algorithm which solves the problem is also given. Although phylogenetic trees and phylogenetic networks are similar data structures to pedigree graphs, it seems that inferring methods for phylogenetic trees and networks cannot be applied to infer pedigree graphs since nodes of phylogenetic trees and networks represent species whereas nodes of pedigree graphs represent individuals. We also show an O(n2) time algorithm which detects a contradiction between a given pedigreee graph and distance matrix of genetic distances.

13. 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.

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

DTIC Science & Technology

2017-09-01

software technologies. SNAP a system designed for interactive analytics on large graphs that fit into the memory of a single server and Delite a DSL...Specific Languages,” TECS󈧒: ACM Transactions on Embedded Computing Systems , July 2014. 19. T. Rompf, A. K. Sujeeth, K. J. Brown, H. Lee, H. Chafi and K...Kozyrakis and K. Olukotun, “A Case of System -level Hardware/Software Co- design and Co-verification of a Commodity Multi-Processor System with Custom

15. Utilizing knowledge-base semantics in graph-based algorithms

SciTech Connect

Darwiche, A.

1996-12-31

Graph-based algorithms convert a knowledge base with a graph structure into one with a tree structure (a join-tree) and then apply tree-inference on the result. Nodes in the join-tree are cliques of variables and tree-inference is exponential in w*, the size of the maximal clique in the join-tree. A central property of join-trees that validates tree-inference is the running-intersection property: the intersection of any two cliques must belong to every clique on the path between them. We present two key results in connection to graph-based algorithms. First, we show that the running-intersection property, although sufficient, is not necessary for validating tree-inference. We present a weaker property for this purpose, called running-interaction, that depends on non-structural (semantical) properties of a knowledge base. We also present a linear algorithm that may reduce w* of a join-tree, possibly destroying its running-intersection property, while maintaining its running-interaction property and, hence, its validity for tree-inference. Second, we develop a simple algorithm for generating trees satisfying the running-interaction property. The algorithm bypasses triangulation (the standard technique for constructing join-trees) and does not construct a join-tree first. We show that the proposed algorithm may in some cases generate trees that are more efficient than those generated by modifying a join-tree.

16. Graph-based segmentation of abnormal nuclei in cervical cytology.

PubMed

Zhang, Ling; Kong, Hui; Liu, Shaoxiong; Wang, Tianfu; Chen, Siping; Sonka, Milan

2017-03-01

A general method is reported for improving the segmentation of abnormal cell nuclei in cervical cytology images. In automation-assisted reading of cervical cytology, one of the essential steps is the segmentation of nuclei. Despite some progress, there is a need to improve the sensitivity, particularly the segmentation of abnormal nuclei. Our method starts with pre-segmenting the nucleus to define the coarse center and size of nucleus, which is used to construct a graph by image unfolding that maps ellipse-like border in the Cartesian coordinate system to lines in the polar coordinate system. The cost function jointly reflects properties of nucleus border and nucleus region. The prior constraints regarding the context of nucleus-cytoplasm position are utilized to modify the local cost functions. The globally optimal path in the constructed graph is then identified by dynamic programming with an iterative approach ensuring an optimal closed contour. Validation of our method was performed on abnormal nuclei from two cervical cell image datasets, Herlev and H&E stained manual liquid-based cytology (HEMLBC). Compared with five state-of-the-art approaches, our graph-search based method shows superior performance.

17. F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly.

PubMed

Jain, Swati; Schlick, Tamar

2017-10-05

Coarse-grained models represent attractive approaches to analyze and simulate RNA molecules, for example for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs, and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate 3D tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a dataset of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures, and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications. Copyright © 2017. Published by Elsevier Ltd.

18. Comparison of Different Generalizations of Clustering Coefficient and Local Efficiency for Weighted Undirected Graphs.

PubMed

Wang, Yu; Ghumare, Eshwar; Vandenberghe, Rik; Dupont, Patrick

2017-02-01

Binary undirected graphs are well established, but when these graphs are constructed, often a threshold is applied to a parameter describing the connection between two nodes. Therefore, the use of weighted graphs is more appropriate. In this work, we focus on weighted undirected graphs. This implies that we have to incorporate edge weights in the graph measures, which require generalizations of common graph metrics. After reviewing existing generalizations of the clustering coefficient and the local efficiency, we proposed new generalizations for these graph measures. To be able to compare different generalizations, a number of essential and useful properties were defined that ideally should be satisfied. We applied the generalizations to two real-world networks of different sizes. As a result, we found that not all existing generalizations satisfy all essential properties. Furthermore, we determined the best generalization for the clustering coefficient and local efficiency based on their properties and the performance when applied to two networks. We found that the best generalization of the clustering coefficient is [Formula: see text], defined in Miyajima and Sakuragawa ( 2014 ), while the best generalization of the local efficiency is [Formula: see text], proposed in this letter. Depending on the application and the relative importance of sensitivity and robustness to noise, other generalizations may be selected on the basis of the properties investigated in this letter.

19. Complex graph matrix representations and characterizations of proteomic maps and chemically induced changes to proteomes.

PubMed

Balasubramanian, Krishnan; Khokhani, Kanan; Basak, Subhash C

2006-05-01

We have presented a complex graph matrix representation to characterize proteomics maps obtained from 2D-gel electrophoresis. In this method, each bubble in a 2D-gel proteomics map is represented by a complex number with components which are charge and mass. Then, a graph with complex weights is constructed by connecting the vertices in the relative order of abundance. This yields adjacency matrices and distance matrices of the proteomics graph with complex weights. We have computed the spectra, eigenvectors, and other properties of complex graphs and the Euclidian/graph distance obtained from the complex graphs. The leading eigenvalues and eigenvectors and, likewise, the smallest eigenvalues and eigenvectors, and the entire graph spectral patterns of the complex matrices derived from them yield novel weighted biodescriptors that characterize proteomics maps with information of charge and masses of proteins. We have also applied these eigenvector and eigenvalue maps to contrast the normal cells and cells exposed to four peroxisome proliferators, namely, clofibrate, diethylhexyl phthalate (DEHP), perfluorodecanoic acid (PFDA), and perfluoroctanoic acid (PFOA). Our complex eigenspectra show that the proteomic response induced by DEHP differs from the corresponding responses of other three chemicals consistent with their chemical structures and properties.

20. Generalized Graphs, Methods for Obtaining Graph Spectra. Application of Graph Spectra in Chemistry

Shen, Mingzuo

Various graphical methods in the literature for getting at some features of the MO energy level spectra of especially pi systems and some related three-dimensional molecules are studied in detail. These include the graphical methods of Sinanoglu (although its mathematical, quantum-physical foundations, e.g. Sinanoglu's structural-covariance theory, are not discussed in this thesis), the edge-deletion method of Jiang, the specialized method of Sheng for benzenoid graphs, pairing theorems, graph splitting methods of e.g. McClelland, and more general one of R. A. Davidson. Of these the Sinanoglu method is found to be the only one generally applicable to diverse types of molecules without the need to introduce additional and complicated rules for each new graph type. The Sinanoglu method however is intended to be only a qualitative tool (giving the number of bonding, nonbonding, and antibonding levels and their changes upon reaction or geometrical distortions, large or small, of the molecule). Thus the other methods, although highly specialized, could be of help in getting some further information on the spectra. In particular, the "negative graph" concept in Chapter 3 of this thesis would be found useful in ascertaining the energy gap between the lowest and highest MO levels. In case where the Sinanoglu method cannot distinguish between differing stabilities of two molecules with the same signature and number of elections, this energy gap will be particularly useful. In the thesis, many alternative and simpler derivations of the graph-theoretic methods of Jiang, Davidson and others mentioned above are given. Some methods are generalized further. In the last chapter of the thesis starting with S 5.3, the graphical method is applied extensively to various types of molecules thought to have through-space interactions. Especially the Sinanoglu method is used to obtain the signature (instead of using a computer) and qualitative stabilities of these molecules are discussed

1. Molecular graph convolutions: moving beyond fingerprints

PubMed Central

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

2016-01-01

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

2. 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.

3. 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

4. Molecular graph convolutions: moving beyond fingerprints

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. On a class of coedge regular graphs

Makhnev, A. A.; Paduchikh, D. V.

2005-12-01

We study graphs in which \\lambda(a,b)=\\lambda_1,\\lambda_2 for every edge \\{a,b\\} and all \\mu-subgraphs are 2-cocliques. We give a description of connected edge-regular graphs for k\\ge (b_1^2+3b_1-4)/2. In particular, the following examples confirm that the inequality k>b_1(b_1+3)/2 is a sharp bound for strong regularity: the n-gon, the icosahedron graph, the graph in \\mathrm{MP}(6) and the distance-regular graph of diameter 4 with intersection massive \\{x,x-1,4,1;1,2,x-1,x\\}, which is an antipodal 3-covering of the strongly regular graph with parameters ((x+2)(x+3)/6,x,0,6).

6. API Requirements for Dynamic Graph Prediction

SciTech Connect

2006-10-13

Given a large-scale time-evolving multi-modal and multi-relational complex network (a.k.a., a large-scale dynamic semantic graph), we want to implement algorithms that discover patterns of activities on the graph and learn predictive models of those discovered patterns. This document outlines the application programming interface (API) requirements for fast prototyping of feature extraction, learning, and prediction algorithms on large dynamic semantic graphs. Since our algorithms must operate on large-scale dynamic semantic graphs, we have chosen to use the graph API developed in the CASC Complex Networks Project. This API is supported on the back end by a semantic graph database (developed by Scott Kohn and his team). The advantages of using this API are (i) we have full-control of its development and (ii) the current API meets almost all of the requirements outlined in this document.

7. Replica methods for loopy sparse random graphs

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.

8. Time series characterization via horizontal visibility graph and Information Theory

Gonçalves, Bruna Amin; Carpi, Laura; Rosso, Osvaldo A.; Ravetti, Martín G.

2016-12-01

Complex networks theory have gained wider applicability since methods for transformation of time series to networks were proposed and successfully tested. In the last few years, horizontal visibility graph has become a popular method due to its simplicity and good results when applied to natural and artificially generated data. In this work, we explore different ways of extracting information from the network constructed from the horizontal visibility graph and evaluated by Information Theory quantifiers. Most works use the degree distribution of the network, however, we found alternative probability distributions, more efficient than the degree distribution in characterizing dynamical systems. In particular, we find that, when using distributions based on distances and amplitude values, significant shorter time series are required. We analyze fractional Brownian motion time series, and a paleoclimatic proxy record of ENSO from the Pallcacocha Lake to study dynamical changes during the Holocene.

9. 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.

10. Graph Zeta function and gauge theories

He, Yang-Hui

2011-03-01

Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis.

11. 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.

12. Employing the therapeutic operating characteristic (TOC) graph for individualised dose prescription.

PubMed

Hoffmann, Aswin L; Huizenga, Henk; Kaanders, Johannes H A M

2013-03-07

In current practice, patients scheduled for radiotherapy are treated according to 'rigid' protocols with predefined dose prescriptions that do not consider risk-taking preferences of individuals. The therapeutic operating characteristic (TOC) graph is applied as a decision-aid to assess the trade-off between treatment benefit and morbidity to facilitate dose prescription customisation. Historical dose-response data from prostate cancer patient cohorts treated with 3D-conformal radiotherapy is used to construct TOC graphs. Next, intensity-modulated (IMRT) plans are generated by optimisation based on dosimetric criteria and dose-response relationships. TOC graphs are constructed for dose-scaling of the optimised IMRT plan and individualised dose prescription. The area under the TOC curve (AUC) is estimated to measure the therapeutic power of these plans. On a continuous scale, the TOC graph directly visualises treatment benefit and morbidity risk of physicians' or patients' choices for dose (de-)escalation. The trade-off between these probabilities facilitates the selection of an individualised dose prescription. TOC graphs show broader therapeutic window and higher AUCs with increasing target dose heterogeneity. The TOC graph gives patients and physicians access to a decision-aid and read-out of the trade-off between treatment benefit and morbidity risks for individualised dose prescription customisation over a continuous range of dose levels.

13. Employing the therapeutic operating characteristic (TOC) graph for individualised dose prescription

PubMed Central

2013-01-01

Background In current practice, patients scheduled for radiotherapy are treated according to ‘rigid’ protocols with predefined dose prescriptions that do not consider risk-taking preferences of individuals. The therapeutic operating characteristic (TOC) graph is applied as a decision-aid to assess the trade-off between treatment benefit and morbidity to facilitate dose prescription customisation. Methods Historical dose-response data from prostate cancer patient cohorts treated with 3D-conformal radiotherapy is used to construct TOC graphs. Next, intensity-modulated (IMRT) plans are generated by optimisation based on dosimetric criteria and dose-response relationships. TOC graphs are constructed for dose-scaling of the optimised IMRT plan and individualised dose prescription. The area under the TOC curve (AUC) is estimated to measure the therapeutic power of these plans. Results On a continuous scale, the TOC graph directly visualises treatment benefit and morbidity risk of physicians’ or patients’ choices for dose (de-)escalation. The trade-off between these probabilities facilitates the selection of an individualised dose prescription. TOC graphs show broader therapeutic window and higher AUCs with increasing target dose heterogeneity. Conclusions The TOC graph gives patients and physicians access to a decision-aid and read-out of the trade-off between treatment benefit and morbidity risks for individualised dose prescription customisation over a continuous range of dose levels. PMID:23497640

14. Speed of evolution on graphs.

PubMed

Sui, Xiukai; Wu, Bin; Wang, Long

2015-12-01

The likelihood that a mutant fixates in the wild population, i.e., fixation probability, has been intensively studied in evolutionary game theory, where individuals' fitness is frequency dependent. However, it is of limited interest when it takes long to take over. Thus the speed of evolution becomes an important issue. In general, it is still unclear how fixation times are affected by the population structure, although the fixation times have already been addressed in the well-mixed populations. Here we theoretically address this issue by pair approximation and diffusion approximation on regular graphs. It is shown (i) that under neutral selection, both unconditional and conditional fixation time are shortened by increasing the number of neighbors; (ii) that under weak selection, for the simplified prisoner's dilemma game, if benefit-to-cost ratio exceeds the degree of the graph, then the unconditional fixation time of a single cooperator is slower than that in the neutral case; and (iii) that under weak selection, for the conditional fixation time, limited neighbor size dilutes the counterintuitive stochastic slowdown which was found in well-mixed populations. Interestingly, we find that all of our results can be interpreted as that in the well-mixed population with a transformed payoff matrix. This interpretation is also valid for both death-birth and birth-death processes on graphs. This interpretation bridges the fixation time in the structured population and that in the well-mixed population. Thus it opens the avenue to investigate the challenging fixation time in structured populations by the known results in well-mixed populations.

15. Speed of evolution on graphs

Sui, Xiukai; Wu, Bin; Wang, Long

2015-12-01

The likelihood that a mutant fixates in the wild population, i.e., fixation probability, has been intensively studied in evolutionary game theory, where individuals' fitness is frequency dependent. However, it is of limited interest when it takes long to take over. Thus the speed of evolution becomes an important issue. In general, it is still unclear how fixation times are affected by the population structure, although the fixation times have already been addressed in the well-mixed populations. Here we theoretically address this issue by pair approximation and diffusion approximation on regular graphs. It is shown (i) that under neutral selection, both unconditional and conditional fixation time are shortened by increasing the number of neighbors; (ii) that under weak selection, for the simplified prisoner's dilemma game, if benefit-to-cost ratio exceeds the degree of the graph, then the unconditional fixation time of a single cooperator is slower than that in the neutral case; and (iii) that under weak selection, for the conditional fixation time, limited neighbor size dilutes the counterintuitive stochastic slowdown which was found in well-mixed populations. Interestingly, we find that all of our results can be interpreted as that in the well-mixed population with a transformed payoff matrix. This interpretation is also valid for both death-birth and birth-death processes on graphs. This interpretation bridges the fixation time in the structured population and that in the well-mixed population. Thus it opens the avenue to investigate the challenging fixation time in structured populations by the known results in well-mixed populations.

16. Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures

Gnutzmann, Sven; Waltner, Daniel

2016-12-01

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016), 10.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.

17. Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures.

PubMed

Gnutzmann, Sven; Waltner, Daniel

2016-12-01

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016)2470-004510.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.

18. Naming on a Directed Graph

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.

19. 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.

20. 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.